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http://tex.stackexchange.com/questions/123749/error-compilation-tikz-intersection-foreach/123756
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# Error compilation tikz, intersection & foreach
I want to compile this code (using PDFLaTeX)
\documentclass[12pt]{article}
\usepackage[ansinew]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{color}
\usetikzlibrary{arrows,shapes,scopes,calc,intersections}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\begin{document}
\newcommand{\coorpente}[4]{\coordinate(#1) at ($(#2)+({#4/(sqrt((#3*#3)+1))},{#3*#4/(sqrt((#3*#3)+1))})$);}
\newcommand{\inter}[3]{\path [name intersections={of=#2 and #3,by=#1}];}
\newcommand{\linenp}[4]{\path[name path=#1,#4](#2)--(#3);}
\begin{tikzpicture}[]
\draw[help lines,step=1,line width=1.5pt,black!50] (0,-1) grid (10,6);
\draw[help lines,step=.2] (0,-1) grid (10,6);
\coordinate(ptg1) at (0.5,-1) ;
\coordinate(ptg2) at (10,5) ;
%espace
\draw[cyan,line width=4pt,name path=gamma] (ptg1)to [out=90,in=195] (ptg2);
\draw[line width=1.5pt,name path=gammab] (ptg1)to [out=90,in=195] (ptg2);
\def\pente {3.5}
%iterations
%1d
\coordinate(iterdb1) at (10,3);
\coorpente{iterd1}{iterdb1}{\pente}{-4}
\linenp{itd1}{iterdb1}{iterd1}{}
\draw(iterdb1)--(intd1);
\foreach \nuuu/\nddd in{1/2,2/3,3/4,4/5,5/6}
{
%u
\coorpente{iteru\nuuu}{intd\nuuu}{-\pente}{-5}
\linenp{itu\nuuu}{iteru\nuuu}{intd\nuuu}{}
\inter{intu\nuuu}{itu\nuuu}{gamma}
\draw(intd\nuuu)--(intu\nuuu);
%d
\coorpente{iterd\nddd}{intu\nuuu}{\pente}{-5}
\linenp{itd\nddd}{intu\nuuu}{iterd\nddd}{}
\draw(intu\nuuu)--(intd\nddd);
}
\end{tikzpicture}
\end{document}
I obtain the weird error message:
! Undefined control sequence.
\tikz@intersect@namedpaths ...@path@name@itd\nddd
\endcsname {\pgfsyssoftpat...
When I remove or comment the line containing \draw (ptad1)--(ptg1);, I don't obtain any error. I think that the error is due to the "foreach" command: when I suppress the \foreach command and I write the command manually (for each step of the foreach command), I don't have any error.
Do you have an idea about the origin of this error?
-
Please reduce your code to something more readable, i.e. a MWE. Typically this lets you discover your own mistakes. But the error stems from \foreach not expanding the arguments of the macros, thus it searches for a point named iteru\nuuu and not iteru0, iteru1 etc. There are several similar questions on this site. And welcome! – zeroth Jul 12 '13 at 12:29
possible duplicate of Draw a path between many nodes using foreach – zeroth Jul 12 '13 at 12:31
I get several errors before the Undefined control sequence one; please, fix the code. – egreg Jul 12 '13 at 12:36
@zeroth both points (ptad1) and (ptg1) don't depend of the content of the \foreach command and without the \draw (ptad1) -- (ptg1). So I don't understand why tikz crashes in this case. I will try to simplify my code but currently the easiest solution is to suppress the \foreachcommand. – Guuk Jul 12 '13 at 12:40
@egreg I have fixed one mistake. The code is also available at the following url: writelatex.com/268046xmrpwj – Guuk Jul 12 '13 at 12:48
\newcommand{\coorpente}[4]{%
\begingroup\edef\x{\endgroup
\noexpand\coordinate(#1) at
($(#2)+({#4/(sqrt((#3*#3)+1))},{#3*#4/(sqrt((#3*#3)+1))})$);}\x}
\newcommand{\inter}[3]{%
\begingroup\edef\x{\endgroup
\noexpand\path [name intersections={of=#2 and #3,by=#1}];}\x}
\newcommand{\linenp}[4]{%
\begingroup\edef\x{\endgroup
\noexpand\path[name path=#1,#4](#2)--(#3);}\x}
In this way \nuuu and \nddd will be expanded before the \coordinate and \path commands start their work.
-
Your solution works perfectly. Thank you!! – Guuk Jul 12 '13 at 13:16
|
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|
http://www.markedbyteachers.com/as-and-a-level/science/torsional-pendulum-preliminary-experiment.html
|
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Torsional Pendulum Preliminary experiment
Extracts from this document...
Introduction
A2 Physics Coursework
Aim: To investigate a Torsional Pendulum.
Research and equations:
As we are working in circular motion, rather than linear motion, the equations that will help me investigate the Torsional pendulum will have to be derived. Here is how it is derived.
Using Force= Mass x Acceleration which is what you use for linear motion, this becomes Torque=Moment of Inertia x Angular acceleration. Using Force= -kx from a simple pendulum, this becomes Force=- Torsional Constant x Angular displacement
Therefore This can definitely be compared to a=-ω2x and becomes However therefore I then found out the exact expression which allowed me to directly work out I and K. The moment of inertia was simply mL2 However for the Torsional constant I first found the formula for the polar moment of inertia which was Ip=πd4/32 and the angle of twist φ=TL/GIp this was rearranged to T= GIp/L where T is the Torsional constant, then substituting in Ip I got Torsional constant= Using the equation I can now substitute in expressions for I and K to get an overall equation which came out to be: T=2π T=Time Period I=Moment of Inertia of the bar L=Length of wire G= Shear Modulus of material d= diameter of wire
The following web pages were used to help me derive these equations:
http://www.engin.umich.
Middle
Using 0.1 meters as the starting point, make the length 0.1m using a meter rule, measuring from the base of the bung to the top of the bar at the knot.Turn the bar 90 degrees anticlockwise and release it, start the stopwatch at the same time of release.The time period for one complete oscillation is; for the end of the bar to go around clockwise once and changes direction then anticlockwise until it changes again, the moment it stops just before changing direction for a second time is one oscillation. Allow 5 complete oscillations for once length and divide the end time by five. Record the time period on a suitable table.Loosen the clamp and increase the length by 0.1m and repeat above steps until approximately 8 results are complete.Now measure the length of the bar using a meter ruler, and the diameter of the bar using a micrometer. Also measure the length of the wire using a meter ruler and its diameter using a micrometer. Record all these results.
To ensure that the experiment is carried out in safe environment I will make sure that I have plenty of space around me, with any obstacles removed to ensure the experiment can run smoothly.
Theory:
If simple harmonic motion applies, which I am
Conclusion
±0.05seconds, therefore maximum reading error was (0.005/6.162)x100=0.081%, this is however a lot less significant than experimental error.The scale is accurate to ±0.05 grams. Therefore maximum error is (0.05/201.1) x 100 = 0.0249%, therefore this error was not so significant.The micrometer is accurate to ±0.005mm, as smallest division is 0.01mm, therefore error for my reading was (0.005/0.41) x 100 = 1.219%, this error was quite significant and a lot larger than I expected.
The value for the gradient I obtained was 0.4375, however I was expecting 0.5, therefore there is clearly errors in the time period and length, which is what determined the gradient, with reasons for these errors stated above. The error for the gradient will be the total error of the time and length, therefore approximately 6% error, when adding average most significant error of the time period and length.
Using the Equation T=2π I can work out the overall error of my experiment. As 2π x =T and as I found out that T=16.788 x l0.4375
Therefore 2π should be equal to 16.788 if my experiment had no errors. I will now work out how close to this value I actually got.
=2π = 14.12
Therefore the total error from what the true value should be is [(16.788-14.12)/16.788] x 100= 15.89%
From all the percentage errors above I can see that there are clearly issues with this preliminary experiment and that changes will have to be made for the final experiment to increase accuracy and reduce errors.
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|
https://tex.stackexchange.com/questions/240552/multiple-equations-in-square-bracket-matrix
|
# Multiple equations in square bracket matrix [duplicate]
When solving many equations you usually stuff them in matrices and solve them using Gauss-Jordan elimination. Where I come from, we write it like this and this is what should appear in my document:
The gray parts of image are there for clarity and are not part of what I need. I just need (n+1) x n matrix with separation line. I will also need to display multiple of the matrices next to each other to show the GEM process:
How can I do it?
## marked as duplicate by barbara beeton, Werner math-mode StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Apr 25 '15 at 17:04
• That's really interesting, thanks. I'll try to figure out how to make the brackers square. – Tomáš Zato Apr 25 '15 at 16:39
• If you want to use gauss, there's a way for using square brackets. Just do \begin{gmatrix}[b] instead of \begin{gmatrix}[p] – egreg Apr 25 '15 at 16:45
• The documentation for the gauss package on page 8 explains how to change the delimiters texdoc.net/texmf-dist/doc/latex/gauss/gauss-doc.pdf – R. Schumacher Apr 25 '15 at 16:46
Taken from Stefan's answer in https://tex.stackexchange.com/a/2244/46716
\documentclass{article}
\usepackage{amsmath}
\makeatletter
\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{%
\hskip -\arraycolsep
\let\@ifnextchar\new@ifnextchar
\array{#1}}
\makeatother
\begin{document}
$\begin{bmatrix}[*3c|c] 2 & 5 & 0 & 7 \\ 3 & 0 & 4 & 2 \\ 4 & 2 & 6 & 3 \\ \end{bmatrix} \Rightarrow \begin{bmatrix}[*3c|c] 2 & 2 & 2 & 6 \\ 3 & 0 & 4 & 6 \\ 5 & 2 & 6 & 6 \\ \end{bmatrix}$
\end{document}
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http://physics.stackexchange.com/questions/88703/vertical-uniform-circular-motion-can-it-really-be-uniform
|
# Vertical uniform circular motion.. can it really be uniform? [closed]
This is the picture in my mind:
For centripetal force, I learned that: $T-mg\cos\theta= \frac{mv^2}{r}$
In vertical circular motion, the velocity is naturally going to decrease as kinetic energy is converted to potential energy as the particle moves up the circle- and thus resulting into a non-uniform circular motion.
However, I was told that if tension changes accordingly, the velocity will remain constant(as from the equation). What I do not get about this part of the explanation is that which force will balance mgsinθ (tangential force in the diagram )?
-
The equation you are giving is a condition on T so that the movement be circular. The equation does not give an explanation about the time evolution of v. You are absolutely right. There is no way that the speed can be a constant. The tension does no work on the system. Therefore, the only force entering the energy conservation is gravity -> the mass will be slower at the top. Another way to see it is as you mention in your post : nothing in this system can cancel mg sin$\theta$. – Mathusalem Dec 2 '13 at 13:46
@Mathusalem: could you please elaborate "time evolution of v" – Eliza Dec 2 '13 at 13:55
why close vote? – Eliza Dec 2 '13 at 16:18
## closed as off-topic by Waffle's Crazy Peanut, tpg2114, Brandon Enright, Qmechanic♦Dec 3 '13 at 1:02
This question appears to be off-topic. The users who voted to close gave this specific reason:
• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Waffle's Crazy Peanut, tpg2114, Brandon Enright, Qmechanic
If this question can be reworded to fit the rules in the help center, please edit the question.
In the situation at hand, you'll never be able to achieve uniform circular motion.
$\frac{d\vec{v}}{dt} = \frac{1}{m}\sum \vec{F}_{\text{ext}}$
This is a vectorial equation. If you look at the picture you've drawn, you have forces on the radial as well as the tangential direction.
On the radial direction, there is the tension force, and $mg\cos\theta$. The equation you have given is the outcome of a calculation which tells you that in order to have the object moving at velocity $v = |\vec{v}|$ on a circle of radius $R$, you have to apply to it a net perpendicular force of equal to $\frac{mv^2}{R}$. That's all it says.
However, there is the tangential part still.
$\frac{d}{dt}v_{tan} = mg\sin{\theta} \neq 0 \text{ in general}$
This means that the speed along the circle is always subject to a gravitational force. Thus, the speed along the circle varies. Since the tension force is orthogonal to it, it can not act on the magnitude of this speed, it can only act on its direction, so it can do nothing to keep it constant. The examples given in the reply of User58220 are misleading because they have added mechanisms which contribute to give forces such, that the tangential part of the gravitational force is cancelled.
In short : no, tension won't make it go at a constant speed.
-
:so unless there is a force in the direction of mgsinθ (which tension or thrust cannot provide), the particle will just move with non-uniform circular motion? – Eliza Dec 2 '13 at 16:25
Yes. You need a force to annihilate mgsin$\theta$. – Mathusalem Dec 2 '13 at 16:49
In case of the London eye (example from user 58220), what is the "mechanism" that annihilates mgsinθ? – Eliza Dec 2 '13 at 16:58
Well there is a motor making the whole structure spin. If the motor doesn't spin, neither does the London eye. – Mathusalem Dec 2 '13 at 17:34
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http://www.maa.org/programs/faculty-and-departments/course-communities/browse?term_node_tid_depth=All&page=63
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# Browse Course Communities
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https://handleshaus.wordpress.com/2013/10/05/go-ask-janet/
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## Go Ask Janet
‘Go ask Janet Yellen (about to get this job) what?’ – you ask?
Whether you should go to college, that’s what. At least, whether you should do so as a financial matter. Who knows if she’s qualified to provide advice with regards to any other basis of evaluation, but I’m confident she’s very competent at finance, and more to the point, she’s going to be setting nominal interest rates pretty soon, and that’s what really matters.
Now, we neoreactionaries are keen on trying to understand human nature which we assert is highly heritable, variable between diverse human population groups, and robust to efforts to neutralize and replace it through social engineering.
Here’s human nature – I write a giant post demonstrating mathematically how unskilled immigration can increase inequality and depress wages for your existing working class citizens (absent some semi-preposterous assumptions) – a subject of imminent political import – and I get zero feedback on the merits of the argument. That’s to be expected. Nobody likes math modelling. Not Vladimir, and I’m not quite sure about zhai2nan2 over at vulture of critique.
On the other hand, since I’m a social, friendly guy who believes in building community, I would like all the bloggers and commenters towards which I feel affinities to also try to get along better and be friendlier with each other and to see me as an ally instead of an adversary. Also I thought it might get his attention and nudge Nick B. Steves to come out of hibernation (mission accomplished!). So I tried to smooth things over with Charlton by inviting him and other to talk about religion a little and Bam, I start getting bombarded, including multiple hits from freakin’ Kyrgyzstan. How’s Manas doing boys?
The point is, that’s what people want to talk about, arguing about religion and such, the universal past-time, and that’s human nature. They certainly don’t want to engage with equations. As Derb points out, it’s a bizarre minority taste.
I get it. But, you know what? My blog, my rules, my math.
Vladimir is skeptical of mathematical presentations claiming to model reality but without solid epistemological foundations. That’s fine with me. But you know what everyone agrees we should use math to do? Accounting. So let’s do some college accounting.
Why? Well, there’s a constant stream of chaotic and unorganized higher-education chatter in the econoblogosphere these days. Is it just signalling or acquisition of useful, valuable skills? For example, Arnold Kling supports ‘The Null Hypothesis‘ while Caplan makes the case for signalling.
The answer to these questions depends a lot, I think, on what kind of person we’re talking about. College is just an enjoyably social, but time-and-money wasting hoop to jump through for a lot of people on their way to adult working life. They wouldn’t do it if it wasn’t essential to getting a good job and having higher social status. They never cared about what was being taught, and they rarely retain more than scant amounts of the content.
Only the other hand, the above benefits are merely perks and icing-on-the-knowledge-cake for others, who have talent and motivation and derive a lot of personal and professional value from their college experience.
The backdrop for all these concerns is the explosion in tuition costs over the past generation. WaPo just did a 10-part series on it. Glenn Reynolds wrote a whole book about it. It’s starting to bite, and so people are noodling on the whole subject. It’s interesting to me how little good practical advice is available for teenagers and parents. But I’m from the government and I’m here to help, so let’s get started.
The Model:
Our finance-obsessed teenager is a hard-core Friedman fan and loves him some Consumption Smoothing. In fact, at 18, all he cares about regarding the decision of whether to attend university or begin working is which path will give him the highest smoothed consumption level over his lifetime. He starts out with zero savings.
If he starts work, he sets out on a non-college income path, finances some of his consumption with debt early in life, but gradually breaks even and accumulates equity until retirement, which he then spends into nothing at the moment of his death.
If, instead, he goes to college, he has to borrow a lot of money to pay the hefty tuition and also forgo the opportunity to work for four years. But then he has the opportunity to work on a higher income path. It’s kind of like the decision to go into the military as an enlistedman or an officer, but without the education and pension benefits. But will he be able to come out ahead?
He goes to his gypsy psychic and government statistics parser high school guidance counselor and she looks in her crystal ball and tells him the two income paths for High School graduate ($I_H$) and College Graduate ($I_C$), as well as Tuition (T):
$I_H(\tau)=I_H+a\tau$
$I_C(\tau)=I_C+b\tau$
Which combined with college tuition should look something like this:
With equity over time looking something like this if you retire at 65 and die at 80 (the numbers aren’t important at this point, just the relative shapes of the curves):
Now, the first thing we’re going to need is a way to transform the start points and income paths into equity and an unknown smoothed consumption level given continuous interest operating on a arithmetic annuity. Thankfully, we can do this with a basic first order linear differential equation solution technique. (Who knows if education is useless or not for people in general, but I learned techniques like this in high school, have never used it in my work in my whole life and it’s never been part of my compensation, and yet really value knowing how to do it. I don’t know if I would have ever learned it on my own if left to my own devices.)
Well, after a little manipulation, we get an equity equation over time, where C is the smoothed consumption level, i is the interest rate, and F is the annual raise our youngster can expect to receive:
$E(\tau)=E_o i^{\tau}+\frac{i^{\tau}-1}{\ln i}\Big(I_o-C+\frac{F}{\ln i}\Big)-\frac{F}{\ln i}\tau$
For the High School case, you start at equity 0, sove for E(R), where R is retirement age, and then solve for the level of consumption that brings equity down to zero at death age, D.
Now, wait a minute. It’s one thing to estimate one’s retirement age. It’s another to know how long you’re going to live. The huge uncertainty involved is why we have things like Social Security. What is this, some Greek Mythology Existential Crisis?
Well, fortunately, and logically if you assume you’ll retire at the same age and live just as long in both paths, all that really matters to is the amount of savings you have at retirement. We only have to solve for zero at death as an intermediate step, but it must somehow cancel away later. $I_H$ is his starting salary and $a$ is his annual raise.
What we get is a mouthful:
$C_H=\frac{i^{D-18}-i^{D-R}}{i^{D-18}-1}\Big(I_H+a(\frac{1}{\ln i}-\frac{R-18}{i^{R-18}-1})\Big)$
We do the same thing for the College Graduate path ($I_C$, starting salary, $b$, annual raise, $T$, tuition) but in three steps. Down for four years, up for working career, then down again from Retirement (R) until Death (D). An slightly bigger morsel to chew on.
$C_C=\frac{i^{D-22}-i^{D-R}}{i^{D-18}-1}\Big\{I_C+b\Big(\frac{1}{\ln i}-\frac{R-22}{i^{R-22}-1}\Big)-T\Big(\frac{i^{R-18}-i^{R-22}}{i^{R-22}-1}\Big)\Big\}$
And now we’re going to combine them into a real mouth stuffer: Let $Q=\frac{C_C}{C_H}$
$Q=\frac{i^{R-22}-1}{i^{R-18}-1}\frac{I_C+b\Big(\frac{1}{\ln i}-\frac{R-22}{i^{R-22}-1}\Big)-T\Big(\frac{i^{R-18}-i^{R-22}}{i^{R-22}-1}\Big)}{I_H+a(\frac{1}{\ln i}-\frac{R-18}{i^{R-18}-1}}$
Whew! We’re going to set $Q=1$ because that will help us determine the conditions of our decision-change point. Since the prices are nominally arbitrary, we’ll scale them all to $I_H$ using $\hat{a}, \hat{b}$ and $\hat{T}$
Now we can define $Z=(\frac{I_C}{I_H})_{Q=1}$ which is the minimum ratio between the High School Graduate starting wage and the College Graduate starting wage needed to financially justify picking the college path. Stretch your esophagus and throat muscles for this one:
$Z=\frac{i^{R-18}-1}{i^{R-22}-1}\Big\{1+\hat{a}\Big(\frac{1}{\ln i}-\frac{R-18}{i^{R-18}-1}\Big)\Big\}-\hat{b}\Big(\frac{1}{\ln i}-\frac{R-22}{i^{R-22}-1}\Big)+\hat{T}\frac{i^{R-18}-i^{R-22}}{i^{R-22}-1}$
Now for a few slights-of-hand, er, I mean, ‘reasonable assumptions for simplification’.
Let’s assume the scaled annual raises are both small compared to total wages (on the order of the interest rate) and close to each other. That should make the $\hat{a}$ and $\hat{b}$ terms above nearly cancel out. Exemplary justification: If $R=65$ and $i=1.03$ then if the raises are close the remainder is only $0.254\hat{a}$. Remember that $\hat{a}$ is scaled in terms of $I_H$, so it’s probably less than 0.1 and the remainder error in Z is probably less than 0.02. Even if bigger, it’s still small enough to ignore, and there’s always the wage compression phenomenon to help us out.
The next reasonable slight of hand is to assume that college tuition is in the same ballpark as a starting High School Graduate salary, so $\hat{T}\approx{1}$. What’s left now?
$Z \approx{\frac{2i^{R-18}-i^{R-22}-1}{i^{R-22}-1}}$
Much more manageable! Now, let’s set Retirement at 65 years old. And lets express the interest rate in terms of x% instead of $i=1+x/100$. A good approximation is:
$Z\approx{51/43+0.55x}$
Voila! Goodness, only the interest rate is left.
Assuming all the reasonable things we assumed, even if the interest rate is zero, a college graduate starting salary must be at least 20% greater than a high school graduate starting salary. As the interest rate rises, so does Z, but not too fast. At about 6% it means a minimum 50% premium for financial justification.
Even if you can’t do all this symbolic manipulation nonsense, it’s ridiculously easy to simulate all of this in any spreadsheet. I imagine one could write a Java app that did it, and maybe even pulled in the latest interest rate and some government statistics on tuition, employment, and income vs. SAT scores. An advice machine. Why doesn’t this exist already? Why isn’t junior being advised in this very practical manner?
Anyway, you may make the mild objection that it is Congress that now sets the interest rates on student loans, and that, under present law, these have nothing to do with either market rates or the Federal Reserve’s discount rate. Furthermore, while there may be some impact in the short run, over the long run Monetary Policy is not thought to influence the real interest rate.
Yes, but. The model assumed the same average interest rate, both for debt and savings, throughout the whole period. That’s a reasonable-enough assumption for the high-school graduate, who accumulates his debts and savings slowly and over a long period of time.
It’s not reasonable for the college graduate, who accumulates a lot of debt over at the very beginning and in a short time frame. The interest rate on those loans are fixed (assuming Congress doesn’t allow ‘refinancing’) and the nominal price of servicing them is thus sticky. His early attempts at savings are mostly trying to fight the compound interest on that nominal debt.
Enter the Federal Reserve. If average nominal interest rates over your life are higher than when you took out your fixed-rate loans, then it acts like inflation-induced debt-forgiveness and you sign praises to the keepers of the secrets of the temple. It also means, if you anticipate this will happen, you can financially justify going to college at a lower wage premium.
On the other hand, if interest rates were high when you took out your loans (which you can’t refinance without a penalty that would nullify the effort anyway), and lower for the rest of your life, then you needed a much bigger premium to justify college. In fact, if soon after college, you were surprised with pegged-to-zero risk-free rates and rampant under/malemployment for college graduates, then … oh snap. Does any of this sound familiar?
That’s bound to make a lot of the younger victims of that process angry and frustrated. But if they can’t understand what happened, they’re bound to make a lot of random, incoherent complains at whatever their ideological preferences tell them should be thought of as ‘the bad guys’. OWS, anyone?
Where were their guidance counselors? Down at the group-think lounge, eating up that pretty-lie cake: ‘everyone should go to college, even below-average kids‘.
Next time, go ask Janet.
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### 8 Responses to Go Ask Janet
1. A gem of a post! You sir, are a natural blogger.
So, just to say it out loud, I could show this to my younger brother or nephew or what have you contemplating going to college, I should ask him what the max salary is that he can command right out of HS and depending on his major and planned career path (and demand in the economy for the profession etc) what his expected starting salary is. If it’s anything < 20% the decision is no.
Amazing.
• Handle says:
Thank you sir. You should resume blogging, it’s been two years now, time to get back in the saddle.
The 20% figure assumes no risk premium, which we know is sizable and inversely correlated with SAT scores.
But more to the point, life is full of uncertainty. When one tries to tailor population statistics to one’s particular profiles, what you get is an actuarial approach to major gambles.
It’s hard for most people to think statistically, and it’s even harder for them to assess themselves honestly.
So a real guidance counselor would be able to provide a young individuals the insurance company’s actuary’s view of the risks and benefits of attending a particular college to which you’ve been admitted. Then you can check with accounting to get a justification letter, and then you can head to finance to try and hedge your interest-rate risks and exposures. Of course, you’d want a few job offers on hand to be able to compare options.
And the ultimate point is that, to the best of my knowledge, no one, anywhere, is doing any of this.
Which means that no one really thinks about college in terms of cold equations and financial trade offs. It’s a much more sacred thing than that.
If people had been thinking that way, there would have been some equilibrium-restoration demand shedding before tuition could get to where it is today. But, to be honest, we use the heuristic ‘every smart person should go to college, whatever the cost, it’s always worth it’, and then we think it’s strange if a smart person doesn’t go to college.
A similar thing applies to medical care. Who can think clearly in terms of finances when the health, even lives, of loved-ones is at stake?
If the only answer is ‘a bureaucrat’, then death panels it is.
We need college death panels too. We need guidance counselors to tell kids the truth, ‘no, you shouldn’t go to college’.
But then we’d need other places for those kids to go. But those are the things we death-paneled. Whoops.
• Anthony says:
Glenn Reynolds has suggested that colleges co-sign for a percentage of student loans, even a small one, to give them an incentive to do these evaluations.
• Handle says:
Marketability of one’s college experience is a different issue altogether – my analysis assumed ideal conditions, but obviously the situation is worse. Part of the problem is that college education is a combination of consumption (“edu-tainment”) and investment in marketability. People’s demand profile for certain careers also shows that income / consumption-level is from from a solitary obsession with most college graduates – who express strong trade-offs of income for status, intellectual fulfillment, and quality of peer colleagues. Not to mention job security.
The surety argument is much older than Reynolds. Eliminating non-dischargeability in bankruptcy had had a lot of advocates over the years. Private issuers of credit might have the incentive to scrutinize applicants more rationally. Milton Friedman argues that a government subsidy could be justified, but that it should be a rate subsidy on top of this kind of intelligent evaluation.
The bottom line is that we’ve in the opposite direction of all this. It’s hard to tell people the hard, ugly truth through the credit channel and the mechanism of denial of a loan. The government makes all loans, they are nondischargeable, and there is no connection between issuance of credit and a distinction between majors or rational evaluation of students’ market prospects.
Bottom Line: There is a critical shortage of truth and reality in the market for education advice and policy. Perhaps we can contribute a remedy.
• And the ultimate point is that, to the best of my knowledge, no one, anywhere, is doing any of this.
Which means that no one really thinks about college in terms of cold equations and financial trade offs. It’s a much more sacred thing than that.
Paraphrasing Robin Hanson, college is not about skill acquisition.
I think it’s a clear example of a failure of the readjustment of norms to a new socio-economic reality. The heuristic of going to college for most kids may have been a defensible path to a middle class lifestyle for a couple generations but isn’t anymore, but the readjustment to reality is prevented by sacred fencing and ideological markings of the norm.
• Handle says:
Well said, but then, most of the people who ought to know this are discussing the topic in ‘education premium’ financial terms.
Like Sailer’s quote of animal house, “Knowledge is Good”, a decent neoreactionary motto is “Reality is Good. More Reality!”
Let’s help people adjust.
2. Jefferson says:
I have to admit that I started skimming after a certain point; many of these mathy things I haven’t seen in over a decade and clearly haven’t retained as well as other folks have. That said, isn’t there a qualitative difference between college grads and HS grads? The job I worked out of college (in the military) did not require my BA, but was soul-crushing in ways that comparably paying college-requiring professions are (beyond-terrible hours, beyond-incompetent bosses, etc.). On the other hand, when I got out of school there were jobs available to grads. My younger brother dropped out and joined the Navy, lucked into a great shop and is getting paid considerably more than most of his friends who followed all the advice, finished school, and are SOL now as far as jobs go.
• Handle says:
‘isn’t there a qualitative difference between college grads and HS grads?’
Naturally, that’s the whole E vs M split in Gedankenexperiment.
The question is what choice should an E make given labor market conditions and interest rates.
Also note the arbitrage opportunity if Caplan’s pure signalling model or Kling’s Null Hypothesis were true.
If employers really believed that college didn’t impact a worker’s marginal productivity, then they could offer the smart kids a job out of high school. Because the student doesn’t have to repay costly loans, the company can win by offering a lower salary while still ensuring the employee gets more net lifetime compensation with a higher smoothed consumption level.
That this isn’t happening should be telling us something.
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https://cdcvs.fnal.gov/redmine/projects/des-sci-verification/wiki/IQ-R4/2/annotate
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## IQ-R4 » History » Version 2
Jiangang Hao, 07/03/2012 01:36 PM
1 2 3 1 Jiangang Hao h1. IQ-R4 1 Jiangang Hao 1 Jiangang Hao Requirements: 1 Jiangang Hao 1 Jiangang Hao * TO.2: The delivered PSF from the telescope, instrument, and other factors exclusive of the site seeing will be no greater than 0.55 arcsec FWHM (DES-doc-806-v25). 1 Jiangang Hao 1 Jiangang Hao * R-18: The PSF FWHM in each of the r, i, and z bands should, over all exposures and over the survey area, have a median of less than 0.9”. Moreover, for 95% of the survey area, there should be at least one exposure in each of these bands for which the mean PSF FWHM is 0.9” or smaller (DES-doc-20-v32). 1 Jiangang Hao 1 Jiangang Hao 1 Jiangang Hao 1 Jiangang Hao Procedures: 1 Jiangang Hao 1 Jiangang Hao * When pointing to the Zenith, the PSF FWHM from DECam are compared to the CTIO DIMM seeing measurements according to the model FWHM^2 = DIMM^2 + \sigma^2. The best fit value is \sigma <= 0.55" across the full array. Therefore, we can measure the contribution of the PSF from the DECam by subtracting the DIMM seeing from the measured PSF by quadrature. 1 Jiangang Hao 2 Jiangang Hao * Step 1: Point the telescope to zenith, take 10 exposures of 100 sec each in r, i and z band. 2 Jiangang Hao * Step 2: Measure the FWHM around bright stars after Flat-fielding and bias-subtraction 2 Jiangang Hao * Step 3: Get the DIMM FWHM from http://www.ctio.noao.edu/environ/environ.html and calculate the FWHM due to the DECam. The maximum of the sqrt(WFHM^2 - DIMM^2) should be less than 0.55". This is a check of TO.2. 2 Jiangang Hao * Step 4: Get the median of the FWHM and check whether it is less than 0.9" in r, i and z band.
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https://doc.freefem.org/documentation/mesh-generation.html
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FreeFEM Documentation on GitHub
stars - forks
# Mesh Generation
In this section, operators and tools on meshes are presented.
FreeFEM type for mesh variable:
• 1D mesh: meshL
• 2D mesh: mesh
• 3D volume mesh: mesh3
• 3D border meshes
• 3D surface meshS
• 3D curve meshL
Through this presentation, the principal commands for the mesh generation and links between mesh - mesh3 - meshS - meshL are described.
## The type mesh in 2 dimension
### Commands for 2d mesh Generation
The FreeFEM type to define a 2d mesh object is mesh.
#### The command square
The command square triangulates the unit square.
The following generates a $$4 \times 5$$ grid in the unit square $$[0,1]^2$$. The labels of the boundaries are shown in Fig. 57.
1 mesh Th = square(4, 5);
To construct a $$n\times m$$ grid in the rectangle $$[x_0,x_1]\times [y_0,y_1]$$, proceed as follows:
1 real x0 = 1.2;
2 real x1 = 1.8;
3 real y0 = 0;
4 real y1 = 1;
5 int n = 5;
6 real m = 20;
7 mesh Th = square(n, m, [x0+(x1-x0)*x, y0+(y1-y0)*y]);
Note
Adding the named parameter flags=icase with icase:
1. will produce a mesh where all quads are split with diagonal $$x-y=constant$$
2. will produce a Union Jack flag type of mesh
3. will produce a mesh where all quads are split with diagonal $$x+y=constant$$
4. same as in case 0, except two corners where the triangles are the same as case 2, to avoid having 3 vertices on the boundary
5. same as in case 2, except two corners where the triangles are the same as case 0, to avoid having 3 vertices on the boundary
1 mesh Th = square(n, m, [x0+(x1-x0)*x, y0+(y1-y0)*y], flags=icase);
Note
Adding the named parameter label=labs will change the 4 default label numbers to labs[i-1], for example int[int] labs=[11, 12, 13, 14], and adding the named parameter region=10 will change the region number to $$10$$, for instance (v 3.8).
To see all of these flags at work, check Square mesh example:
1 for (int i = 0; i < 5; ++i){
2 int[int] labs = [11, 12, 13, 14];
3 mesh Th = square(3, 3, flags=i, label=labs, region=10);
4 plot(Th, wait=1, cmm="square flags = "+i );
5 }
#### The command buildmesh
mesh building with border
Boundaries are defined piecewise by parametrized curves. The pieces can only intersect at their endpoints, but it is possible to join more than two endpoints. This can be used to structure the mesh if an area touches a border and create new regions by dividing larger ones:
1 int upper = 1;
2 int others = 2;
3 int inner = 3;
4
5 border C01(t=0, 1){x=0; y=-1+t; label=upper;}
6 border C02(t=0, 1){x=1.5-1.5*t; y=-1; label=upper;}
7 border C03(t=0, 1){x=1.5; y=-t; label=upper;}
8 border C04(t=0, 1){x=1+0.5*t; y=0; label=others;}
9 border C05(t=0, 1){x=0.5+0.5*t; y=0; label=others;}
10 border C06(t=0, 1){x=0.5*t; y=0; label=others;}
11 border C11(t=0, 1){x=0.5; y=-0.5*t; label=inner;}
12 border C12(t=0, 1){x=0.5+0.5*t; y=-0.5; label=inner;}
13 border C13(t=0, 1){x=1; y=-0.5+0.5*t; label=inner;}
14
15 int n = 10;
16 plot(C01(-n) + C02(-n) + C03(-n) + C04(-n) + C05(-n)
17 + C06(-n) + C11(n) + C12(n) + C13(n), wait=true);
18
19 mesh Th = buildmesh(C01(-n) + C02(-n) + C03(-n) + C04(-n) + C05(-n)
20 + C06(-n) + C11(n) + C12(n) + C13(n));
21
22 plot(Th, wait=true);
23
24 cout << "Part 1 has region number " << Th(0.75, -0.25).region << endl;
25 cout << "Part 2 has redion number " << Th(0.25, -0.25).region << endl;
Borders and mesh are respectively shown in Fig. 58 and Fig. 59.
Border
Triangulation keywords assume that the domain is defined as being on the left (resp right) of its oriented parameterized boundary
$\Gamma_j = \{(x,y)\left|\; x=\varphi_x(t),\, y=\varphi_y(t),\, a_j\le t\le b_j\right.\}$
To check the orientation plot $$t\mapsto (\varphi_x(t),\varphi_y(t)),\, t_0\le t\le t_1$$. If it is as in Fig. 60, then the domain lies on the shaded area, otherwise it lies on the opposite side.
The general expression to define a triangulation with buildmesh is
1 mesh Mesh_Name = buildmesh(Gamma1(m1)+...+GammaJ(mj), OptionalParameter);
where $$m_j$$ are positive or negative numbers to indicate how many vertices should be on $$\Gamma_j,\, \Gamma=\cup_{j=1}^J \Gamma_J$$, and the optional parameter (see also References), separated with a comma, can be:
• nbvx= int, to set the maximum number of vertices in the mesh.
• fixedborder= bool, to say if the mesh generator can change the boundary mesh or not (by default the boundary mesh can change; beware that with periodic boundary conditions (see. Finite Element), it can be dangerous.
The orientation of boundaries can be changed by changing the sign of $$m_j$$.
The following example shows how to change the orientation. The example generates the unit disk with a small circular hole, and assigns “1” to the unit disk (“2” to the circle inside). The boundary label must be non-zero, but it can also be omitted.
1 border a(t=0, 2*pi){x=cos(t); y=sin(t); label=1;}
2 border b(t=0, 2*pi){x=0.3+0.3*cos(t); y=0.3*sin(t); label=2;}
3 plot(a(50) + b(30)); //to see a plot of the border mesh
4 mesh Thwithouthole = buildmesh(a(50) + b(30));
5 mesh Thwithhole = buildmesh(a(50) + b(-30));
6 plot(Thwithouthole, ps="Thwithouthole.eps");
7 plot(Thwithhole, ps="Thwithhole.eps");
Note
Notice that the orientation is changed by b(-30) in the 5th line. In the 7th line, ps="fileName" is used to generate a postscript file with identification shown on the figure.
Mesh with a hole
Note
Borders are evaluated only at the time plot or buildmesh is called so the global variables are defined at this time. In this case, since $$r$$ is changed between the two border calls, the following code will not work because the first border will be computed with r=0.3:
1 real r=1;
2 border a(t=0, 2*pi){x=r*cos(t); y=r*sin(t); label=1;}
3 r=0.3;
4 border b(t=0, 2*pi){x=r*cos(t); y=r*sin(t); label=1;}
5 mesh Thwithhole = buildmesh(a(50) + b(-30)); // bug (a trap) because
6 // the two circles have the same radius = :math:0.3
mesh building with array of border
Sometimes it can be useful to make an array of the border, but unfortunately it is incompatible with the FreeFEM syntax. To bypass this problem, if the number of segments of the discretization $$n$$ is an array, we make an implicit loop on all of the values of the array, and the index variable $$i$$ of the loop is defined after the parameter definition, like in border a(t=0, 2*pi; i)
A first very small example:
1 border a(t=0, 2*pi; i){x=(i+1)*cos(t); y=(i+1)*sin(t); label=1;}
2 int[int] nn = [10, 20, 30];
3 plot(a(nn)); //plot 3 circles with 10, 20, 30 points
And a more complex example to define a square with small circles:
1 real[int] xx = [0, 1, 1, 0],
2 yy = [0, 0, 1, 1];
3 //radius, center of the 4 circles
4 real[int] RC = [0.1, 0.05, 0.05, 0.1],
5 XC = [0.2, 0.8, 0.2, 0.8],
6 YC = [0.2, 0.8, 0.8, 0.2];
7 int[int] NC = [-10,-11,-12,13]; //list number of :math:\pm segments of the 4 circles borders
8
9 border bb(t=0, 1; i)
10 {
11 // i is the index variable of the multi border loop
12 int ii = (i+1)%4;
13 real t1 = 1-t;
14 x = xx[i]*t1 + xx[ii]*t;
15 y = yy[i]*t1 + yy[ii]*t;
16 label = 0;
17 }
18
19 border cc(t=0, 2*pi; i)
20 {
21 x = RC[i]*cos(t) + XC[i];
22 y = RC[i]*sin(t) + YC[i];
23 label = i + 1;
24 }
25 int[int] nn = [4, 4, 5, 7]; //4 border, with 4, 4, 5, 7 segment respectively
26 plot(bb(nn), cc(NC), wait=1);
27 mesh th = buildmesh(bb(nn) + cc(NC));
28 plot(th, wait=1);
### Mesh Connectivity and data
The following example explains methods to obtain mesh information.
1 // Mesh
2 mesh Th = square(2, 2);
3
4 cout << "// Get data of the mesh" << endl;
5 {
6 int NbTriangles = Th.nt;
7 real MeshArea = Th.measure;
8 real BorderLength = Th.bordermeasure;
9
10 cout << "Number of triangle(s) = " << NbTriangles << endl;
11 cout << "Mesh area = " << MeshArea << endl;
12 cout << "Border length = " << BorderLength << endl;
13
14 // Th(i) return the vextex i of Th
15 // Th[k] return the triangle k of Th
16 // Th[k][i] return the vertex i of the triangle k of Th
17 for (int i = 0; i < NbTriangles; i++)
18 for (int j = 0; j < 3; j++)
19 cout << i << " " << j << " - Th[i][j] = " << Th[i][j]
20 << ", x = " << Th[i][j].x
21 << ", y= " << Th[i][j].y
22 << ", label=" << Th[i][j].label << endl;
23 }
24
25 cout << "// Hack to get vertex coordinates" << endl;
26 {
27 fespace femp1(Th, P1);
28 femp1 Thx=x,Thy=y;
29
30 int NbVertices = Th.nv;
31 cout << "Number of vertices = " << NbVertices << endl;
32
33 for (int i = 0; i < NbVertices; i++)
34 cout << "Th(" << i << ") : " << Th(i).x << " " << Th(i).y << " " << Th(i).label
35 << endl << "\told method: " << Thx[][i] << " " << Thy[][i] << endl;
36 }
37
38 cout << "// Method to find information of point (0.55,0.6)" << endl;
39 {
40 int TNumber = Th(0.55, 0.6).nuTriangle; //the triangle number
41 int RLabel = Th(0.55, 0.6).region; //the region label
42
43 cout << "Triangle number in point (0.55, 0.6): " << TNumber << endl;
44 cout << "Region label in point (0.55, 0.6): " << RLabel << endl;
45 }
46
47 cout << "// Information of triangle" << endl;
48 {
49 int TNumber = Th(0.55, 0.6).nuTriangle;
50 real TArea = Th[TNumber].area; //triangle area
51 real TRegion = Th[TNumber].region; //triangle region
52 real TLabel = Th[TNumber].label; //triangle label, same as region for triangles
53
54 cout << "Area of triangle " << TNumber << ": " << TArea << endl;
55 cout << "Region of triangle " << TNumber << ": " << TRegion << endl;
56 cout << "Label of triangle " << TNumber << ": " << TLabel << endl;
57 }
58
59 cout << "// Hack to get a triangle containing point x, y or region number (old method)" << endl;
60 {
61 fespace femp0(Th, P0);
62 femp0 TNumbers; //a P0 function to get triangle numbering
63 for (int i = 0; i < Th.nt; i++)
64 TNumbers[][i] = i;
65 femp0 RNumbers = region; //a P0 function to get the region number
66
67 int TNumber = TNumbers(0.55, 0.6); // Number of the triangle containing (0.55, 0,6)
68 int RNumber = RNumbers(0.55, 0.6); // Number of the region containing (0.55, 0,6)
69
70 cout << "Point (0.55,0,6) :" << endl;
71 cout << "\tTriangle number = " << TNumber << endl;
72 cout << "\tRegion number = " << RNumber << endl;
73 }
74
75 cout << "// New method to get boundary information and mesh adjacent" << endl;
76 {
77 int k = 0;
78 int l=1;
79 int e=1;
80
81 // Number of boundary elements
82 int NbBoundaryElements = Th.nbe;
83 cout << "Number of boundary element = " << NbBoundaryElements << endl;
84 // Boundary element k in {0, ..., Th.nbe}
85 int BoundaryElement = Th.be(k);
86 cout << "Boundary element " << k << " = " << BoundaryElement << endl;
87 // Vertice l in {0, 1} of boundary element k
88 int Vertex = Th.be(k)[l];
89 cout << "Vertex " << l << " of boundary element " << k << " = " << Vertex << endl;
90 // Triangle containg the boundary element k
91 int Triangle = Th.be(k).Element;
92 cout << "Triangle containing the boundary element " << k << " = " << Triangle << endl;
93 // Triangle egde nubmer containing the boundary element k
94 int Edge = Th.be(k).whoinElement;
95 cout << "Triangle edge number containing the boundary element " << k << " = " << Edge << endl;
96 // Adjacent triangle of the triangle k by edge e
97 int Adjacent = Th[k].adj(e); //The value of e is changed to the corresponding edge in the adjacent triangle
98 cout << "Adjacent triangle of the triangle " << k << " by edge " << e << " = " << Adjacent << endl;
99 cout << "\tCorresponding edge = " << e << endl;
100 // If there is no adjacent triangle by edge e, the same triangle is returned
101 //Th[k] == Th[k].adj(e)
102 // Else a different triangle is returned
103 //Th[k] != Th[k].adj(e)
104 }
105
106 cout << "// Print mesh connectivity " << endl;
107 {
108 int NbTriangles = Th.nt;
109 for (int k = 0; k < NbTriangles; k++)
110 cout << k << " : " << int(Th[k][0]) << " " << int(Th[k][1])
111 << " " << int(Th[k][2])
112 << ", label " << Th[k].label << endl;
113
114 for (int k = 0; k < NbTriangles; k++)
115 for (int e = 0, ee; e < 3; e++)
116 //set ee to e, and ee is change by method adj,
117 cout << k << " " << e << " <=> " << int(Th[k].adj((ee=e))) << " " << ee
118 << ", adj: " << (Th[k].adj((ee=e)) != Th[k]) << endl;
119
120 int NbBoundaryElements = Th.nbe;
121 for (int k = 0; k < NbBoundaryElements; k++)
122 cout << k << " : " << Th.be(k)[0] << " " << Th.be(k)[1]
123 << " , label " << Th.be(k).label
124 << ", triangle " << int(Th.be(k).Element)
125 << " " << Th.be(k).whoinElement << endl;
126
127 real[int] bb(4);
128 boundingbox(Th, bb);
129 // bb[0] = xmin, bb[1] = xmax, bb[2] = ymin, bb[3] =ymax
130 cout << "boundingbox:" << endl;
131 cout << "xmin = " << bb[0]
132 << ", xmax = " << bb[1]
133 << ", ymin = " << bb[2]
134 << ", ymax = " << bb[3] << endl;
135 }
The output is:
1 // Get data of the mesh
2 Number of triangle = 8
3 Mesh area = 1
4 Border length = 4
5 0 0 - Th[i][j] = 0, x = 0, y= 0, label=4
6 0 1 - Th[i][j] = 1, x = 0.5, y= 0, label=1
7 0 2 - Th[i][j] = 4, x = 0.5, y= 0.5, label=0
8 1 0 - Th[i][j] = 0, x = 0, y= 0, label=4
9 1 1 - Th[i][j] = 4, x = 0.5, y= 0.5, label=0
10 1 2 - Th[i][j] = 3, x = 0, y= 0.5, label=4
11 2 0 - Th[i][j] = 1, x = 0.5, y= 0, label=1
12 2 1 - Th[i][j] = 2, x = 1, y= 0, label=2
13 2 2 - Th[i][j] = 5, x = 1, y= 0.5, label=2
14 3 0 - Th[i][j] = 1, x = 0.5, y= 0, label=1
15 3 1 - Th[i][j] = 5, x = 1, y= 0.5, label=2
16 3 2 - Th[i][j] = 4, x = 0.5, y= 0.5, label=0
17 4 0 - Th[i][j] = 3, x = 0, y= 0.5, label=4
18 4 1 - Th[i][j] = 4, x = 0.5, y= 0.5, label=0
19 4 2 - Th[i][j] = 7, x = 0.5, y= 1, label=3
20 5 0 - Th[i][j] = 3, x = 0, y= 0.5, label=4
21 5 1 - Th[i][j] = 7, x = 0.5, y= 1, label=3
22 5 2 - Th[i][j] = 6, x = 0, y= 1, label=4
23 6 0 - Th[i][j] = 4, x = 0.5, y= 0.5, label=0
24 6 1 - Th[i][j] = 5, x = 1, y= 0.5, label=2
25 6 2 - Th[i][j] = 8, x = 1, y= 1, label=3
26 7 0 - Th[i][j] = 4, x = 0.5, y= 0.5, label=0
27 7 1 - Th[i][j] = 8, x = 1, y= 1, label=3
28 7 2 - Th[i][j] = 7, x = 0.5, y= 1, label=3
29 // Hack to get vertex coordinates
30 Number of vertices = 9
31 Th(0) : 0 0 4
32 old method: 0 0
33 Th(1) : 0.5 0 1
34 old method: 0.5 0
35 Th(2) : 1 0 2
36 old method: 1 0
37 Th(3) : 0 0.5 4
38 old method: 0 0.5
39 Th(4) : 0.5 0.5 0
40 old method: 0.5 0.5
41 Th(5) : 1 0.5 2
42 old method: 1 0.5
43 Th(6) : 0 1 4
44 old method: 0 1
45 Th(7) : 0.5 1 3
46 old method: 0.5 1
47 Th(8) : 1 1 3
48 old method: 1 1
49 // Method to find the information of point (0.55,0.6)
50 Triangle number in point (0.55, 0.6): 7
51 Region label in point (0.55, 0.6): 0
52 // Information of a triangle
53 Area of triangle 7: 0.125
54 Region of triangle 7: 0
55 Label of triangle 7: 0
56 // Hack to get a triangle containing point x, y or region number (old method)
57 Point (0.55,0,6) :
58 Triangle number = 7
59 Region number = 0
60 // New method to get boundary information and mesh adjacent
61 Number of boundary element = 8
62 Boundary element 0 = 0
63 Vertex 1 of boundary element 0 = 1
64 Triangle containing the boundary element 0 = 0
65 Triangle edge number containing the boundary element 0 = 2
66 Adjacent triangle of the triangle 0 by edge 1 = 1
67 Corresponding edge = 2
68 // Print mesh connectivity
69 0 : 0 1 4, label 0
70 1 : 0 4 3, label 0
71 2 : 1 2 5, label 0
72 3 : 1 5 4, label 0
73 4 : 3 4 7, label 0
74 5 : 3 7 6, label 0
75 6 : 4 5 8, label 0
76 7 : 4 8 7, label 0
77 0 0 <=> 3 1, adj: 1
78 0 1 <=> 1 2, adj: 1
79 0 2 <=> 0 2, adj: 0
80 1 0 <=> 4 2, adj: 1
81 1 1 <=> 1 1, adj: 0
82 1 2 <=> 0 1, adj: 1
83 2 0 <=> 2 0, adj: 0
84 2 1 <=> 3 2, adj: 1
85 2 2 <=> 2 2, adj: 0
86 3 0 <=> 6 2, adj: 1
87 3 1 <=> 0 0, adj: 1
88 3 2 <=> 2 1, adj: 1
89 4 0 <=> 7 1, adj: 1
90 4 1 <=> 5 2, adj: 1
91 4 2 <=> 1 0, adj: 1
92 5 0 <=> 5 0, adj: 0
93 5 1 <=> 5 1, adj: 0
94 5 2 <=> 4 1, adj: 1
95 6 0 <=> 6 0, adj: 0
96 6 1 <=> 7 2, adj: 1
97 6 2 <=> 3 0, adj: 1
98 7 0 <=> 7 0, adj: 0
99 7 1 <=> 4 0, adj: 1
100 7 2 <=> 6 1, adj: 1
101 0 : 0 1 , label 1, triangle 0 2
102 1 : 1 2 , label 1, triangle 2 2
103 2 : 2 5 , label 2, triangle 2 0
104 3 : 5 8 , label 2, triangle 6 0
105 4 : 6 7 , label 3, triangle 5 0
106 5 : 7 8 , label 3, triangle 7 0
107 6 : 0 3 , label 4, triangle 1 1
108 7 : 3 6 , label 4, triangle 5 1
109 boundingbox:
110 xmin = 0, xmax = 1, ymin = 0, ymax = 1
The real characteristic function of a mesh Th is chi(Th) in 2D and 3D where:
chi(Th)(P)=1 if $$P\in Th$$
chi(Th)(P)=0 if $$P\not\in Th$$
### The keyword “triangulate”
FreeFEM is able to build a triangulation from a set of points. This triangulation is a Delaunay mesh of the convex hull of the set of points. It can be useful to build a mesh from a table function.
The coordinates of the points and the value of the table function are defined separately with rows of the form: x y f(x,y) in a file such as:
1 0.51387 0.175741 0.636237
2 0.308652 0.534534 0.746765
3 0.947628 0.171736 0.899823
4 0.702231 0.226431 0.800819
5 0.494773 0.12472 0.580623
6 0.0838988 0.389647 0.456045
7 ...............
Triangulate
The third column of each line is left untouched by the triangulate command. But you can use this third value to define a table function with rows of the form: x y f(x,y).
The following example shows how to make a mesh from the file xyf with the format stated just above. The command triangulate only uses the 1st and 2nd columns.
1 // Build the Delaunay mesh of the convex hull
2 mesh Thxy=triangulate("xyf"); //points are defined by the first 2 columns of file xyf
3
4 // Plot the created mesh
5 plot(Thxy);
6
7 // Fespace
8 fespace Vhxy(Thxy, P1);
9 Vhxy fxy;
10
11 // Reading the 3rd column to define the function fxy
12 {
13 ifstream file("xyf");
14 real xx, yy;
15 for(int i = 0; i < fxy.n; i++)
16 file >> xx >> yy >> fxy[][i]; //to read third row only.
17 //xx and yy are just skipped
18 }
19
20 // Plot
21 plot(fxy);
One new way to build a mesh is to have two arrays: one for the $$x$$ values and the other for the $$y$$ values.
1 //set two arrays for the x's and y's
2 Vhxy xx=x, yy=y;
3 //build the mesh
4 mesh Th = triangulate(xx[], yy[]);
### 2d Finite Element space on a boundary
To define a Finite Element space on a boundary, we came up with the idea of a mesh with no internal points (called empty mesh). It can be useful to handle Lagrange multipliers in mixed and mortar methods.
So the function emptymesh removes all the internal points of a mesh except points on internal boundaries.
1 {
2 border a(t=0, 2*pi){x=cos(t); y=sin(t); label=1;}
3 mesh Th = buildmesh(a(20));
4 Th = emptymesh(Th);
5 plot(Th);
6 }
It is also possible to build an empty mesh of a pseudo subregion with emptymesh(Th, ssd) using the set of edges from the mesh Th; an edge $$e$$ is in this set when, with the two adjacent triangles $$e =t1\cap t2$$ and $$ssd[T1] \neq ssd[T2]$$ where $$ssd$$ refers to the pseudo region numbering of triangles, they are stored in the int[int] array of size “the number of triangles”.
1 {
2 mesh Th = square(10, 10);
3 int[int] ssd(Th.nt);
4 //build the pseudo region numbering
5 for(int i = 0; i < ssd.n; i++){
6 int iq = i/2; //because 2 triangles per quad
7 int ix = iq%10;
8 int iy = iq/10;
9 ssd[i] = 1 + (ix>=5) + (iy>=5)*2;
10 }
11 //build emtpy with all edges $e=T1 \cap T2$ and $ssd[T1] \neq ssd[T2]$
12 Th = emptymesh(Th, ssd);
13 //plot
14 plot(Th);
15 savemesh(Th, "emptymesh.msh");
16 }
Empty mesh
### Remeshing
#### The command movemesh
Meshes can be translated, rotated, and deformed by movemesh; this is useful for elasticity to watch the deformation due to the displacement $$\mathbf{\Phi}(x,y)=(\Phi_1(x,y),\Phi_2(x,y))$$ of shape.
It is also useful to handle free boundary problems or optimal shape problems.
If $$\Omega$$ is triangulated as $$T_h(\Omega)$$, and $$\mathbf{\Phi}$$ is a displacement vector then $$\mathbf{\Phi}(T_h)$$ is obtained by:
1 mesh Th = movemesh(Th,[Phi1, Phi2]);
Sometimes the transformed mesh is invalid because some triangles have flipped over (meaning it now has a negative area). To spot such problems, one may check the minimum triangle area in the transformed mesh with checkmovemesh before any real transformation.
For example:
$\begin{split}\begin{array}{rcl} \Phi_1(x,y) &=& x+k*\sin(y*\pi)/10)\\ \Phi_2(x,y) &=& y+k*\cos(y\pi)/10) \end{array}\end{split}$
for a big number $$k>1$$.
1 verbosity = 4;
2
3 // Parameters
4 real coef = 1;
5
6 // Mesh
7 border a(t=0, 1){x=t; y=0; label=1;};
8 border b(t=0, 0.5){x=1; y=t; label=1;};
9 border c(t=0, 0.5){x=1-t; y=0.5; label=1;};
10 border d(t=0.5, 1){x=0.5; y=t; label=1;};
11 border e(t=0.5, 1){x=1-t; y=1; label=1;};
12 border f(t=0, 1){x=0; y=1-t; label=1;};
13 mesh Th = buildmesh(a(6) + b(4) + c(4) + d(4) + e(4) + f(6));
14 plot(Th, wait=true, fill=true, ps="Lshape.eps");
15
16 // Function
17 func uu = sin(y*pi)/10;
18 func vv = cos(x*pi)/10;
19
20 // Checkmovemesh
21 real minT0 = checkmovemesh(Th, [x, y]); //return the min triangle area
22 while(1){ // find a correct move mesh
23 real minT = checkmovemesh(Th, [x+coef*uu, y+coef*vv]);
24 if (minT > minT0/5) break; //if big enough
25 coef /= 1.5;
26 }
27
28 // Movemesh
29 Th = movemesh(Th, [x+coef*uu, y+coef*vv]);
30 plot(Th, wait=true, fill=true, ps="MovedMesh.eps");
Move mesh
Note
Consider a function $$u$$ defined on a mesh Th. A statement like Th=movemesh(Th...) does not change $$u$$ and so the old mesh still exists. It will be destroyed when no function uses it. A statement like $$u=u$$ redefines $$u$$ on the new mesh Th with interpolation and therefore destroys the old Th, if $$u$$ was the only function using it.
Now, we give an example of moving a mesh with a Lagrangian function $$u$$ defined on the moving mesh.
1 // Parameters
2 int nn = 10;
3 real dt = 0.1;
4
5 // Mesh
6 mesh Th = square(nn, nn);
7
8 // Fespace
9 fespace Vh(Th, P1);
10 Vh u=y;
11
12 // Loop
13 real t=0;
14 for (int i = 0; i < 4; i++){
15 t = i*dt;
16 Vh f=x*t;
17 real minarea = checkmovemesh(Th, [x, y+f]);
18 if (minarea > 0) //movemesh will be ok
19 Th = movemesh(Th, [x, y+f]);
20
21 cout << " Min area = " << minarea << endl;
22
23 real[int] tmp(u[].n);
24 tmp = u[]; //save the value
25 u = 0;//to change the FEspace and mesh associated with u
26 u[] = tmp;//set the value of u without any mesh update
27 plot(Th, u, wait=true);
28 }
29 // In this program, since u is only defined on the last mesh, all the
30 // previous meshes are deleted from memory.
#### The command hTriangle
This section presents the way to obtain a regular triangulation with FreeFEM.
For a set $$S$$, we define the diameter of $$S$$ by
$\textrm{diam}(S)=\sup\{|\mathbf{x}-\mathbf{y}|; \; \mathbf{x},\, \mathbf{y}\in S\}$
The sequence $$\{\mathcal{T}_h\}_{h\rightarrow 0}$$ of $$\Omega$$ is called regular if they satisfy the following:
1. $$\lim_{h\rightarrow 0}\max\{\textrm{diam}(T_k)|\; T_k\in \mathcal{T}_h\}=0$$
2. There is a number $$\sigma>0$$ independent of $$h$$ such that $$\frac{\rho(T_k)}{\textrm{diam}(T_k)}\ge \sigma\quad \textrm{for all }T_k\in \mathcal{T}_h$$ where $$\rho(T_k)$$ are the diameter of the inscribed circle of $$T_k$$.
We put $$h(\mathcal{T}_h)=\max\{\textrm{diam}(T_k)|\; T_k\in \mathcal{T}_h\}$$, which is obtained by
1 mesh Th = ......;
2 fespace Ph(Th, P0);
3 Ph h = hTriangle;
4 cout << "size of mesh = " << h[].max << endl;
#### The command adaptmesh
The function:
$f(x,y) = 10.0x^3+y^3+\tan^{-1}[\varepsilon/(\sin(5.0y)-2.0x)],\ \varepsilon = 0.0001$
sharply varies in value and the initial mesh given by one of the commands in the Mesh Generation part cannot reflect its sharp variations.
1 // Parameters
2 real eps = 0.0001;
3 real h = 1;
4 real hmin = 0.05;
5 func f = 10.0*x^3 + y^3 + h*atan2(eps, sin(5.0*y)-2.0*x);
6
7 // Mesh
8 mesh Th = square(5, 5, [-1+2*x, -1+2*y]);
9
10 // Fespace
11 fespace Vh(Th,P1);
12 Vh fh = f;
13 plot(fh);
14
16 for (int i = 0; i < 2; i++){
17 Th = adaptmesh(Th, fh);
18 fh = f; //old mesh is deleted
19 plot(Th, fh, wait=true);
20 }
FreeFEM uses a variable metric/Delaunay automatic meshing algorithm.
The command:
1 mesh ATh = adaptmesh(Th, f);
create the new mesh ATh adapted to the Hessian
$D^2f=(\partial^2 f/\partial x^2,\, \partial^2 f/\partial x\partial y, \partial^2 f/\partial y^2)$
of a function (formula or FE-function).
Mesh adaptation is a very powerful tool when the solution of a problem varies locally and sharply.
Here we solve the Poisson’s problem, when $$f=1$$ and $$\Omega$$ is an L-shape domain.
Tip
The solution has the singularity $$r^{3/2},\, r=|x-\gamma|$$ at the point $$\gamma$$ of the intersection of two lines $$bc$$ and $$bd$$ (see Fig. 70).
1 // Parameters
2 real error = 0.1;
3
4 // Mesh
5 border ba(t=0, 1){x=t; y=0; label=1;}
6 border bb(t=0, 0.5){x=1; y=t; label=1;}
7 border bc(t=0, 0.5){x=1-t; y=0.5; label=1;}
8 border bd(t=0.5, 1){x=0.5; y=t; label=1;}
9 border be(t=0.5, 1){x=1-t; y=1; label=1;}
10 border bf(t=0, 1){x=0; y=1-t; label=1;}
11 mesh Th = buildmesh(ba(6) + bb(4) + bc(4) + bd(4) + be(4) + bf(6));
12
13 // Fespace
14 fespace Vh(Th, P1);
15 Vh u, v;
16
17 // Function
18 func f = 1;
19
20 // Problem
21 problem Poisson(u, v, solver=CG, eps=1.e-6)
22 = int2d(Th)(
23 dx(u)*dx(v)
24 + dy(u)*dy(v)
25 )
26 - int2d(Th)(
27 f*v
28 )
29 + on(1, u=0);
30
31 // Adaptmesh loop
32 for (int i = 0; i < 4; i++){
33 Poisson;
34 Th = adaptmesh(Th, u, err=error);
35 error = error/2;
36 }
37
38 // Plot
39 plot(u);
To speed up the adaptation, the default parameter err of adaptmesh is changed by hand; it specifies the required precision, so as to make the new mesh finer or coarser.
The problem is coercive and symmetric, so the linear system can be solved with the conjugate gradient method (parameter solver=CG) with the stopping criteria on the residual, here eps=1.e-6).
By adaptmesh, the slope of the final solution is correctly computed near the point of intersection of $$bc$$ and $$bd$$ as in Fig. 71.
This method is described in detail in [HECHT1998]. It has a number of default parameters which can be modified.
If f1,f2 are functions and thold, Thnew are meshes:
1 Thnew = adaptmesh(Thold, f1 ... );
2 Thnew = adaptmesh(Thold, f1,f2 ... ]);
3 Thnew = adaptmesh(Thold, [f1,f2] ... );
The additional parameters of adaptmesh are:
• hmin= Minimum edge size.
Its default is related to the size of the domain to be meshed and the precision of the mesh generator.
• hmax= Maximum edge size.
It defaults to the diameter of the domain to be meshed.
• err= $$P_1$$ interpolation error level (0.01 is the default).
• errg= Relative geometrical error.
By default this error is 0.01, and in any case it must be lower than $$1/\sqrt{2}$$. Meshes created with this option may have some edges smaller than the -hmin due to geometrical constraints.
• nbvx= Maximum number of vertices generated by the mesh generator (9000 is the default).
• nbsmooth= number of iterations of the smoothing procedure (5 is the default).
• nbjacoby= number of iterations in a smoothing procedure during the metric construction, 0 means no smoothing, 6 is the default.
• ratio= ratio for a prescribed smoothing on the metric.
If the value is 0 or less than 1.1 no smoothing is done on the metric. 1.8 is the default. If ratio > 1.1, the speed of mesh size variations is bounded by $$log(\mathtt{ratio})$$.
Note
As ratio gets closer to 1, the number of generated vertices increases. This may be useful to control the thickness of refined regions near shocks or boundary layers.
• omega= relaxation parameter for the smoothing procedure. 1.0 is the default.
• iso= If true, forces the metric to be isotropic. false is the default.
• abserror= If false, the metric is evaluated using the criteria of equi-repartion of relative error.
false is the default. In this case the metric is defined by:
$\mathcal{M} = \left({1\over\mathtt{err}\,\, \mathtt{coef}^2} \quad { |\mathcal{H}| \over max(\mathtt{CutOff},|\eta|)}\right)^p$
Otherwise, the metric is evaluated using the criteria of equi-distribution of errors. In this case the metric is defined by:
$\mathcal{M} = \left({1\over \mathtt{err}\,\,\mathtt{coef}^2} \quad {|{\mathcal{H}|} \over {\sup(\eta)-\inf(\eta)}}\right)^p.\label{eq err abs}$
• cutoff= lower limit for the relative error evaluation. 1.0e-6 is the default.
• verbosity= informational messages level (can be chosen between 0 and $$\infty$$).
Also changes the value of the global variable verbosity (obsolete).
• inquire= To inquire graphically about the mesh. false is the default.
• splitpbedge= If true, splits all internal edges in half with two boundary vertices.
true is the default.
• maxsubdiv= Changes the metric such that the maximum subdivision of a background edge is bound by val.
Always limited by 10, and 10 is also the default.
• rescaling= if true, the function, with respect to which the mesh is adapted, is rescaled to be between 0 and 1.
true is the default.
• keepbackvertices= if true, tries to keep as many vertices from the original mesh as possible.
true is the default.
• IsMetric= if true, the metric is defined explicitly.
false is the default. If the 3 functions $$m_{11}, m_{12}, m_{22}$$ are given, they directly define a symmetric matrix field whose Hessian is computed to define a metric. If only one function is given, then it represents the isotropic mesh size at every point.
For example, if the partial derivatives fxx ($$=\partial^2 f/\partial x^2$$), fxy ($$=\partial^2 f/\partial x\partial y$$), fyy ($$=\partial^2 f/\partial y^2$$) are given, we can set Th = adaptmesh(Th, fxx, fxy, fyy, IsMetric=1, nbvx=10000, hmin=hmin);
• power= exponent power of the Hessian used to compute the metric.
1 is the default.
• thetamax= minimum corner angle in degrees.
Default is $$10^\circ$$ where the corner is $$ABC$$ and the angle is the angle of the two vectors $${AB}, {BC}$$, ($$0$$ imply no corner, $$90$$ imply perpendicular corner, …).
• splitin2= boolean value.
If true, splits all triangles of the final mesh into 4 sub-triangles.
• metric= an array of 3 real arrays to set or get metric data information.
The size of these three arrays must be the number of vertices. So if m11,m12,m22 are three P1 finite elements related to the mesh to adapt, you can write: metric=[m11[],m12[],m22[]] (see file convect-apt.edp for a full example)
• nomeshgeneration= If true, no adapted mesh is generated (useful to compute only a metric).
• periodic= Writing periodic=[[4,y],[2,y],[1,x],[3,x]]; builds an adapted periodic mesh.
The sample builds a biperiodic mesh of a square. (see periodic finite element spaces, and see the Sphere example for a full example)
We can use the command adaptmesh to build a uniform mesh with a constant mesh size. To build a mesh with a constant mesh size equal to $$\frac{1}{30}$$ try:
1 mesh Th=square(2, 2); //the initial mesh
2 plot(Th, wait=true, ps="square-0.eps");
3
4 Th = adaptmesh(Th, 1./30., IsMetric=1, nbvx=10000);
5 plot(Th, wait=true, ps="square-1.eps");
6
7 Th = adaptmesh(Th, 1./30., IsMetric=1, nbvx=10000); //More the one time du to
8 Th = adaptmesh(Th, 1./30., IsMetric=1, nbvx=10000); //Adaptation bound maxsubdiv=
9 plot(Th, wait=true, ps="square-2.eps");
#### The command trunc
Two operators have been introduced to remove triangles from a mesh or to divide them. Operator trunc has the following parameters:
• boolean function to keep or remove elements
• label= sets the label number of new boundary item, one by default.
• split= sets the level $$n$$ of triangle splitting.
Each triangle is split in $$n\times n$$, one by default.
To create the mesh Th3 where all triangles of a mesh Th are split in $$3{\times}3$$, just write:
1 mesh Th3 = trunc(Th, 1, split=3);
The following example construct all “trunced” meshes to the support of the basic function of the space Vh (cf. abs(u)>0), split all the triangles in $$5{\times} 5$$, and put a label number to $$2$$ on a new boundary.
1 // Mesh
2 mesh Th = square(3, 3);
3
4 // Fespace
5 fespace Vh(Th, P1);
6 Vh u=0;
7
8 // Loop on all degrees of freedom
9 int n=u.n;
10 for (int i = 0; i < n; i++){
11 u[][i] = 1; // The basis function i
12 plot(u, wait=true);
13 mesh Sh1 = trunc(Th, abs(u)>1.e-10, split=5, label=2);
14 plot(Th, Sh1, wait=true, ps="trunc"+i+".eps");
15 u[][i] = 0; // reset
16 }
Trunc
#### The command change
This command changes the label of elements and border elements of a mesh.
Changing the label of elements and border elements will be done using the keyword change. The parameters for this command line are for two dimensional and three dimensional cases:
• refe= is an array of integers to change the references on edges
• reft= is an array of integers to change the references on triangles
• label= is an array of integers to change the 4 default label numbers
• region= is an array of integers to change the default region numbers
• renumv= is an array of integers, which explicitly gives the new numbering of vertices in the new mesh. By default, this numbering is that of the original mesh
• renumt= is an array of integers, which explicitly gives the new numbering of elements in the new mesh, according the new vertices numbering given by renumv=. By default, this numbering is that of the original mesh
• flabel= is an integer function given the new value of the label
• fregion= is an integer function given the new value of the region
• rmledges= is an integer to remove edges in the new mesh, following a label
• rmInternalEdges= is a boolean, if equal to true to remove the internal edges. By default, the internal edges are stored
These vectors are composed of $$n_{l}$$ successive pairs of numbers $$O,N$$ where $$n_{l}$$ is the number (label or region) that we want to change. For example, we have :
(8)$\begin{split}\mathtt{label} &= [ O_{1}, N_{1}, ..., O_{n_{l}},N_{n_{l}} ] \\ \mathtt{region} &= [ O_{1}, N_{1}, ..., O_{n_{l}},N_{n_{l}} ]\end{split}$
An application example is given here:
1 // Mesh
2 mesh Th1 = square(10, 10);
3 mesh Th2 = square(20, 10, [x+1, y]);
4
5 int[int] r1=[2,0];
6 plot(Th1, wait=true);
7
8 Th1 = change(Th1, label=r1); //change the label of Edges 2 in 0.
9 plot(Th1, wait=true);
10
11 // boundary label: 1 -> 1 bottom, 2 -> 1 right, 3->1 top, 4->1 left boundary label is 1
12 int[int] re=[1,1, 2,1, 3,1, 4,1]
13 Th2=change(Th2,refe=re);
14 plot(Th2,wait=1) ;
#### The command splitmesh
Another way to split mesh triangles is to use splitmesh, for example:
1 // Mesh
2 border a(t=0, 2*pi){x=cos(t); y=sin(t); label=1;}
3 mesh Th = buildmesh(a(20));
4 plot(Th, wait=true, ps="NotSplittedMesh.eps");
5
6 // Splitmesh
7 Th = splitmesh(Th, 1 + 5*(square(x-0.5) + y*y));
8 plot(Th, wait=true, ps="SplittedMesh.eps");
Split mesh
### Meshing Examples
Tip
Two rectangles touching by a side
1 border a(t=0, 1){x=t; y=0;};
2 border b(t=0, 1){x=1; y=t;};
3 border c(t=1, 0){x=t; y=1;};
4 border d(t=1, 0){x=0; y=t;};
5 border c1(t=0, 1){x=t; y=1;};
6 border e(t=0, 0.2){x=1; y=1+t;};
7 border f(t=1, 0){x=t; y=1.2;};
8 border g(t=0.2, 0){x=0; y=1+t;};
9 int n=1;
10 mesh th = buildmesh(a(10*n) + b(10*n) + c(10*n) + d(10*n));
11 mesh TH = buildmesh(c1(10*n) + e(5*n) + f(10*n) + g(5*n));
12 plot(th, TH, ps="TouchSide.esp");
Tip
NACA0012 Airfoil
1 border upper(t=0, 1){x=t; y=0.17735*sqrt(t) - 0.075597*t - 0.212836*(t^2) + 0.17363*(t^3) - 0.06254*(t^4);}
2 border lower(t=1, 0){x = t; y=-(0.17735*sqrt(t) -0.075597*t - 0.212836*(t^2) + 0.17363*(t^3) - 0.06254*(t^4));}
3 border c(t=0, 2*pi){x=0.8*cos(t) + 0.5; y=0.8*sin(t);}
4 mesh Th = buildmesh(c(30) + upper(35) + lower(35));
5 plot(Th, ps="NACA0012.eps", bw=true);
Tip
Cardioid
1 real b = 1, a = b;
2 border C(t=0, 2*pi){x=(a+b)*cos(t)-b*cos((a+b)*t/b); y=(a+b)*sin(t)-b*sin((a+b)*t/b);}
3 mesh Th = buildmesh(C(50));
4 plot(Th, ps="Cardioid.eps", bw=true);
Tip
Cassini Egg
1 border C(t=0, 2*pi) {x=(2*cos(2*t)+3)*cos(t); y=(2*cos(2*t)+3)*sin(t);}
2 mesh Th = buildmesh(C(50));
3 plot(Th, ps="Cassini.eps", bw=true);
Tip
By cubic Bezier curve
1 // A cubic Bezier curve connecting two points with two control points
2 func real bzi(real p0, real p1, real q1, real q2, real t){
3 return p0*(1-t)^3 + q1*3*(1-t)^2*t + q2*3*(1-t)*t^2 + p1*t^3;
4 }
5
6 real[int] p00 = [0, 1], p01 = [0, -1], q00 = [-2, 0.1], q01 = [-2, -0.5];
7 real[int] p11 = [1,-0.9], q10 = [0.1, -0.95], q11=[0.5, -1];
8 real[int] p21 = [2, 0.7], q20 = [3, -0.4], q21 = [4, 0.5];
9 real[int] q30 = [0.5, 1.1], q31 = [1.5, 1.2];
10 border G1(t=0, 1){
11 x=bzi(p00[0], p01[0], q00[0], q01[0], t);
12 y=bzi(p00[1], p01[1], q00[1], q01[1], t);
13 }
14 border G2(t=0, 1){
15 x=bzi(p01[0], p11[0], q10[0], q11[0], t);
16 y=bzi(p01[1], p11[1], q10[1], q11[1], t);
17 }
18 border G3(t=0, 1){
19 x=bzi(p11[0], p21[0], q20[0], q21[0], t);
20 y=bzi(p11[1], p21[1], q20[1], q21[1], t);
21 }
22 border G4(t=0, 1){
23 x=bzi(p21[0], p00[0], q30[0], q31[0], t);
24 y=bzi(p21[1], p00[1], q30[1], q31[1], t);
25 }
26 int m = 5;
27 mesh Th = buildmesh(G1(2*m) + G2(m) + G3(3*m) + G4(m));
28 plot(Th, ps="Bezier.eps", bw=true);
Tip
Section of Engine
1 real a = 6., b = 1., c = 0.5;
2
3 border L1(t=0, 1){x=-a; y=1+b-2*(1+b)*t;}
4 border L2(t=0, 1){x=-a+2*a*t; y=-1-b*(x/a)*(x/a)*(3-2*abs(x)/a );}
5 border L3(t=0, 1){x=a; y=-1-b+(1+b)*t; }
6 border L4(t=0, 1){x=a-a*t; y=0;}
7 border L5(t=0, pi){x=-c*sin(t)/2; y=c/2-c*cos(t)/2;}
8 border L6(t=0, 1){x=a*t; y=c;}
9 border L7(t=0, 1){x=a; y=c+(1+b-c)*t;}
10 border L8(t=0, 1){x=a-2*a*t; y=1+b*(x/a)*(x/a)*(3-2*abs(x)/a);}
11 mesh Th = buildmesh(L1(8) + L2(26) + L3(8) + L4(20) + L5(8) + L6(30) + L7(8) + L8(30));
12 plot(Th, ps="Engine.eps", bw=true);
Tip
Domain with U-shape channel
1 real d = 0.1; //width of U-shape
2 border L1(t=0, 1-d){x=-1; y=-d-t;}
3 border L2(t=0, 1-d){x=-1; y=1-t;}
4 border B(t=0, 2){x=-1+t; y=-1;}
5 border C1(t=0, 1){x=t-1; y=d;}
6 border C2(t=0, 2*d){x=0; y=d-t;}
7 border C3(t=0, 1){x=-t; y=-d;}
8 border R(t=0, 2){x=1; y=-1+t;}
9 border T(t=0, 2){x=1-t; y=1;}
10 int n = 5;
11 mesh Th = buildmesh(L1(n/2) + L2(n/2) + B(n) + C1(n) + C2(3) + C3(n) + R(n) + T(n));
12 plot(Th, ps="U-shape.eps", bw=true);
Tip
Domain with V-shape cut
1 real dAg = 0.02; //angle of V-shape
2 border C(t=dAg, 2*pi-dAg){x=cos(t); y=sin(t);};
3 real[int] pa(2), pb(2), pc(2);
4 pa[0] = cos(dAg);
5 pa[1] = sin(dAg);
6 pb[0] = cos(2*pi-dAg);
7 pb[1] = sin(2*pi-dAg);
8 pc[0] = 0;
9 pc[1] = 0;
10 border seg1(t=0, 1){x=(1-t)*pb[0]+t*pc[0]; y=(1-t)*pb[1]+t*pc[1];};
11 border seg2(t=0, 1){x=(1-t)*pc[0]+t*pa[0]; y=(1-t)*pc[1]+t*pa[1];};
12 mesh Th = buildmesh(seg1(20) + C(40) + seg2(20));
13 plot(Th, ps="V-shape.eps", bw=true);
Tip
Smiling face
1 real d=0.1; int m = 5; real a = 1.5, b = 2, c = 0.7, e = 0.01;
2
3 border F(t=0, 2*pi){x=a*cos(t); y=b*sin(t);}
4 border E1(t=0, 2*pi){x=0.2*cos(t)-0.5; y=0.2*sin(t)+0.5;}
5 border E2(t=0, 2*pi){x=0.2*cos(t)+0.5; y=0.2*sin(t)+0.5;}
6 func real st(real t){
7 return sin(pi*t) - pi/2;
8 }
9 border C1(t=-0.5, 0.5){x=(1-d)*c*cos(st(t)); y=(1-d)*c*sin(st(t));}
10 border C2(t=0, 1){x=((1-d)+d*t)*c*cos(st(0.5)); y=((1-d)+d*t)*c*sin(st(0.5));}
11 border C3(t=0.5, -0.5){x=c*cos(st(t)); y=c*sin(st(t));}
12 border C4(t=0, 1){x=(1-d*t)*c*cos(st(-0.5)); y=(1-d*t)*c*sin(st(-0.5));}
13 border C0(t=0, 2*pi){x=0.1*cos(t); y=0.1*sin(t);}
14
15 mesh Th=buildmesh(F(10*m) + C1(2*m) + C2(3) + C3(2*m) + C4(3)
16 + C0(m) + E1(-2*m) + E2(-2*m));
17 plot(Th, ps="SmileFace.eps", bw=true);
Tip
3 points bending
1 // Square for Three-Point Bend Specimens fixed on Fix1, Fix2
2 // It will be loaded on Load.
3 real a = 1, b = 5, c = 0.1;
4 int n = 5, m = b*n;
5 border Left(t=0, 2*a){x=-b; y=a-t;}
6 border Bot1(t=0, b/2-c){x=-b+t; y=-a;}
7 border Fix1(t=0, 2*c){x=-b/2-c+t; y=-a;}
8 border Bot2(t=0, b-2*c){x=-b/2+c+t; y=-a;}
9 border Fix2(t=0, 2*c){x=b/2-c+t; y=-a;}
10 border Bot3(t=0, b/2-c){x=b/2+c+t; y=-a;}
11 border Right(t=0, 2*a){x=b; y=-a+t;}
12 border Top1(t=0, b-c){x=b-t; y=a;}
13 border Load(t=0, 2*c){x=c-t; y=a;}
14 border Top2(t=0, b-c){x=-c-t; y=a;}
15 mesh Th = buildmesh(Left(n) + Bot1(m/4) + Fix1(5) + Bot2(m/2)
16 + Fix2(5) + Bot3(m/4) + Right(n) + Top1(m/2) + Load(10) + Top2(m/2));
17 plot(Th, ps="ThreePoint.eps", bw=true);
## The type mesh3 in 3 dimension
Note
Up to the version 3, FreeFEM allowed to consider a surface problem such as the PDE is treated like boundary conditions on the boundary domain (on triangles describing the boundary domain). With the version 4, in particular 4.2.1, a completed model for surface problem is possible, with the definition of a surface mesh and a surface problem with a variational form on domain ( with triangle elements) and application of boundary conditions on border domain (describing by edges). The keywords to define a surface mesh is meshS.
### 3d mesh generation
Note
For 3D mesh tools, put load "msh3" at the top of the .edp script.
#### The command cube
The function cube like its 2d function square is a simple way to build cubic objects, it is contained in plugin msh3 (import with load "msh3").
The following code generates a $$3\times 4 \times 5$$ grid in the unit cube $$[0, 1]^3$$.
1 mesh3 Th = cube(3, 4, 5);
By default the labels are :
1. face $$y=0$$,
2. face $$x=1$$,
3. face $$y=1$$,
4. face $$x=0$$,
5. face $$z=0$$,
6. face $$z=1$$
and the region number is $$0$$.
A full example of this function to build a mesh of cube $$]-1,1[^3$$ with face label given by $$(ix + 4*(iy+1) + 16*(iz+1))$$ where $$(ix, iy, iz)$$ are the coordinates of the barycenter of the current face, is given below.
1 load "msh3"
2
3 int[int] l6 = [37, 42, 45, 40, 25, 57];
4 int r11 = 11;
5 mesh3 Th = cube(4, 5, 6, [x*2-1, y*2-1, z*2-1], label=l6, flags =3, region=r11);
6
7 cout << "Volume = " << Th.measure << ", border area = " << Th.bordermeasure << endl;
8
9 int err = 0;
10 for(int i = 0; i < 100; ++i){
11 real s = int2d(Th,i)(1.);
12 real sx = int2d(Th,i)(x);
13 real sy = int2d(Th,i)(y);
14 real sz = int2d(Th,i)(z);
15
16 if(s){
17 int ix = (sx/s+1.5);
18 int iy = (sy/s+1.5);
19 int iz = (sz/s+1.5);
20 int ii = (ix + 4*(iy+1) + 16*(iz+1) );
21 //value of ix,iy,iz => face min 0, face max 2, no face 1
22 cout << "Label = " << i << ", s = " << s << " " << ix << iy << iz << " : " << ii << endl;
23 if( i != ii ) err++;
24 }
25 }
26 real volr11 = int3d(Th,r11)(1.);
27 cout << "Volume region = " << 11 << ": " << volr11 << endl;
28 if((volr11 - Th.measure )>1e-8) err++;
29 plot(Th, fill=false);
30 cout << "Nb err = " << err << endl;
31 assert(err==0);
The output of this script is:
1 Enter: BuildCube: 3
2 kind = 3 n tet Cube = 6 / n slip 6 19
3 Cube nv=210 nt=720 nbe=296
4 Out: BuildCube
5 Volume = 8, border area = 24
6 Label = 25, s = 4 110 : 25
7 Label = 37, s = 4 101 : 37
8 Label = 40, s = 4 011 : 40
9 Label = 42, s = 4 211 : 42
10 Label = 45, s = 4 121 : 45
11 Label = 57, s = 4 112 : 57
12 Volume region = 11: 8
13 Nb err = 0
#### The command buildlayers
This mesh is obtained by extending a two dimensional mesh in the $$z$$-axis.
The domain $$\Omega_{3d}$$ defined by the layer mesh is equal to $$\Omega_{3d} = \Omega_{2d} \times [zmin, zmax]$$ where $$\Omega_{2d}$$ is the domain defined by the two dimensional meshes. $$zmin$$ and $$zmax$$ are functions of $$\Omega_{2d}$$ in $$\R$$ that defines respectively the lower surface and upper surface of $$\Omega_{3d}$$.
For a vertex of a two dimensional mesh $$V_{i}^{2d} = (x_{i},y_{i})$$, we introduce the number of associated vertices in the $$z-$$axis $$M_{i}+1$$.
We denote by $$M$$ the maximum of $$M_{i}$$ over the vertices of the two dimensional mesh. This value is called the number of layers (if $$\forall i, \; M_{i}=M$$ then there are $$M$$ layers in the mesh of $$\Omega_{3d}$$). $$V_{i}^{2d}$$ generated $$M+1$$ vertices which are defined by:
$\forall j=0, \ldots, M, \quad V_{i,j}^{3d} = ( x_{i}, y_{i}, \theta_{i}(z_{i,j}) ),$
where $$(z_{i,j})_{j=0,\ldots,M}$$ are the $$M+1$$ equidistant points on the interval $$[zmin( V_{i}^{2d} ), zmax( V_{i}^{2d})]$$:
$z_{i,j} = j \: \delta \alpha + zmin(V_{i}^{2d}), \quad \delta \alpha= \frac{ zmax( V_{i}^{2d} ) - zmin( V_{i}^{2d}) }{M}.$
The function $$\theta_{i}$$, defined on $$[zmin( V_{i}^{2d} ), zmax( V_{i}^{2d} )]$$, is given by:
$\begin{split}\theta_{i}(z) = \left \{ \begin{array}{cl} \theta_{i,0} & \mbox{if} \: z=zmin(V_{i}^{2d}), \\ \theta_{i,j} & \mbox{if} \: z \in ] \theta_{i,j-1}, \theta_{i,j}],\\ \end{array} \right.\end{split}$
with $$(\theta_{i,j})_{j=0,\ldots,M_{i}}$$ are the $$M_{i}+1$$ equidistant points on the interval $$[zmin( V_{i}^{2d} ), zmax( V_{i}^{2d} )]$$.
Set a triangle $$K=(V_{i1}^{2d}$$, $$V_{i2}^{2d}$$, $$V_{i3}^{2d})$$ of the two dimensional mesh. $$K$$ is associated with a triangle on the upper surface (resp. on the lower surface) of layer mesh:
$$( V_{i1,M}^{3d}, V_{i2,M}^{3d}, V_{i3,M}^{3d} )$$ (resp. $$( V_{i1,0}^{3d}, V_{i2,0}^{3d}, V_{i3,0}^{3d})$$).
Also $$K$$ is associated with $$M$$ volume prismatic elements which are defined by:
$\forall j=0,\ldots,M, \quad H_{j} = ( V_{i1,j}^{3d}, V_{i2,j}^{3d}, V_{i3,j}^{3d}, V_{i1,j+1}^{3d}, V_{i2,j+1}^{3d}, V_{i3,j+1}^{3d} ).$
Theses volume elements can have some merged point:
• 0 merged point : prism
• 1 merged points : pyramid
• 2 merged points : tetrahedra
• 3 merged points : no elements
The elements with merged points are called degenerate elements. To obtain a mesh with tetrahedra, we decompose the pyramid into two tetrahedra and the prism into three tetrahedra. These tetrahedra are obtained by cutting the quadrilateral face of pyramid and prism with the diagonal which have the vertex with the maximum index (see [HECHT1992] for the reason of this choice).
The triangles on the middle surface obtained with the decomposition of the volume prismatic elements are the triangles generated by the edges on the border of the two dimensional mesh. The label of triangles on the border elements and tetrahedra are defined with the label of these associated elements.
The arguments of buildlayers is a two dimensional mesh and the number of layers $$M$$.
The parameters of this command are:
• zbound= $$[zmin,zmax]$$ where $$zmin$$ and $$zmax$$ are functions expression.
Theses functions define the lower surface mesh and upper mesh of surface mesh.
• coef= A function expression between [0,1].
This parameter is used to introduce degenerate element in mesh.
The number of associated points or vertex $$V_{i}^{2d}$$ is the integer part of $$coef(V_{i}^{2d}) M$$.
• region= This vector is used to initialize the region of tetrahedra.
This vector contains successive pairs of the 2d region number at index $$2i$$ and the corresponding 3d region number at index $$2i+1$$, like change.
• labelmid= This vector is used to initialize the 3d labels number of the vertical face or mid face from the 2d label number.
This vector contains successive pairs of the 2d label number at index $$2i$$ and the corresponding 3d label number at index $$2i+1$$, like change.
• labelup= This vector is used to initialize the 3d label numbers of the upper/top face from the 2d region number.
This vector contains successive pairs of the 2d region number at index $$2i$$ and the corresponding 3d label number at index $$2i+1$$, like change.
• labeldown= Same as the previous case but for the lower/down face label.
Moreover, we also add post processing parameters that allow to moving the mesh. These parameters correspond to parameters transfo, facemerge and ptmerge of the command line movemesh.
The vector region, labelmid, labelup and labeldown These vectors are composed of $$n_{l}$$ successive pairs of number $$O_i,N_l$$ where $$n_{l}$$ is the number (label or region) that we want to get.
An example of this command is given in the Build layer mesh example.
Tip
Cube
1 //Cube.idp
4
5 func mesh3 Cube (int[int] &NN, real[int, int] &BB, int[int, int] &L){
6 real x0 = BB(0,0), x1 = BB(0,1);
7 real y0 = BB(1,0), y1 = BB(1,1);
8 real z0 = BB(2,0), z1 = BB(2,1);
9
10 int nx = NN[0], ny = NN[1], nz = NN[2];
11
12 // 2D mesh
13 mesh Thx = square(nx, ny, [x0+(x1-x0)*x, y0+(y1-y0)*y]);
14
15 // 3D mesh
16 int[int] rup = [0, L(2,1)], rdown=[0, L(2,0)];
17 int[int] rmid=[1, L(1,0), 2, L(0,1), 3, L(1,1), 4, L(0,0)];
18 mesh3 Th = buildlayers(Thx, nz, zbound=[z0,z1],
19 labelmid=rmid, labelup = rup, labeldown = rdown);
20
21 return Th;
22 }
Tip
Unit cube
1 include "Cube.idp"
2
3 int[int] NN = [10,10,10]; //the number of step in each direction
4 real [int, int] BB = [[0,1],[0,1],[0,1]]; //the bounding box
5 int [int, int] L = [[1,2],[3,4],[5,6]]; //the label of the 6 face left,right, front, back, down, right
6 mesh3 Th = Cube(NN, BB, L);
7 medit("Th", Th);
Tip
Cone
An axisymtric mesh on a triangle with degenerateness
1 load "msh3"
3
4 // Parameters
5 real RR = 1;
6 real HH = 1;
7
8 int nn=10;
9
10 // 2D mesh
11 border Taxe(t=0, HH){x=t; y=0; label=0;}
12 border Hypo(t=1, 0){x=HH*t; y=RR*t; label=1;}
13 border Vert(t=0, RR){x=HH; y=t; label=2;}
14 mesh Th2 = buildmesh(Taxe(HH*nn) + Hypo(sqrt(HH*HH+RR*RR)*nn) + Vert(RR*nn));
15 plot(Th2, wait=true);
16
17 // 3D mesh
18 real h = 1./nn;
19 int MaxLayersT = (int(2*pi*RR/h)/4)*4;//number of layers
20 real zminT = 0;
21 real zmaxT = 2*pi; //height 2*pi
22 func fx = y*cos(z);
23 func fy = y*sin(z);
24 func fz = x;
25 int[int] r1T = [0,0], r2T = [0,0,2,2], r4T = [0,2];
26 //trick function:
27 //The function defined the proportion
28 //of number layer close to axis with reference MaxLayersT
29 func deg = max(.01, y/max(x/HH, 0.4)/RR);
30 mesh3 Th3T = buildlayers(Th2, coef=deg, MaxLayersT,
31 zbound=[zminT, zmaxT], transfo=[fx, fy, fz],
32 facemerge=0, region=r1T, labelmid=r2T);
33 medit("cone", Th3T);
Tip
Buildlayer mesh
1 load "msh3"
4
5 // Parameters
6 int C1 = 99;
7 int C2 = 98;
8
9 // 2D mesh
10 border C01(t=0, pi){x=t; y=0; label=1;}
11 border C02(t=0, 2*pi){ x=pi; y=t; label=1;}
12 border C03(t=0, pi){ x=pi-t; y=2*pi; label=1;}
13 border C04(t=0, 2*pi){ x=0; y=2*pi-t; label=1;}
14
15 border C11(t=0, 0.7){x=0.5+t; y=2.5; label=C1;}
16 border C12(t=0, 2){x=1.2; y=2.5+t; label=C1;}
17 border C13(t=0, 0.7){x=1.2-t; y=4.5; label=C1;}
18 border C14(t=0, 2){x=0.5; y=4.5-t; label=C1;}
19
20 border C21(t=0, 0.7){x=2.3+t; y=2.5; label=C2;}
21 border C22(t=0, 2){x=3; y=2.5+t; label=C2;}
22 border C23(t=0, 0.7){x=3-t; y=4.5; label=C2;}
23 border C24(t=0, 2){x=2.3; y=4.5-t; label=C2;}
24
25 mesh Th = buildmesh(C01(10) + C02(10) + C03(10) + C04(10)
26 + C11(5) + C12(5) + C13(5) + C14(5)
27 + C21(-5) + C22(-5) + C23(-5) + C24(-5));
28
29 mesh Ths = buildmesh(C01(10) + C02(10) + C03(10) + C04(10)
30 + C11(5) + C12(5) + C13(5) + C14(5));
31
32 // Construction of a box with one hole and two regions
33 func zmin = 0.;
34 func zmax = 1.;
35 int MaxLayer = 10;
36
37 func XX = x*cos(y);
38 func YY = x*sin(y);
39 func ZZ = z;
40
41 int[int] r1 = [0, 41], r2 = [98, 98, 99, 99, 1, 56];
42 int[int] r3 = [4, 12]; //the triangles of uppper surface mesh
43 //generated by the triangle in the 2D region
44 //of mesh Th of label 4 as label 12
45 int[int] r4 = [4, 45]; //the triangles of lower surface mesh
46 //generated by the triangle in the 2D region
47 //of mesh Th of label 4 as label 45.
48
49 mesh3 Th3 = buildlayers(Th, MaxLayer, zbound=[zmin, zmax], region=r1,
50 labelmid=r2, labelup=r3, labeldown=r4);
51 medit("box 2 regions 1 hole", Th3);
52
53 // Construction of a sphere with TetGen
54 func XX1 = cos(y)*sin(x);
55 func YY1 = sin(y)*sin(x);
56 func ZZ1 = cos(x);
57
58 real[int] domain = [0., 0., 0., 0, 0.001];
59 string test = "paACQ";
60 cout << "test = " << test << endl;
61 mesh3 Th3sph = tetgtransfo(Ths, transfo=[XX1, YY1, ZZ1],
62 switch=test, nbofregions=1, regionlist=domain);
63 medit("sphere 2 regions", Th3sph);
### Remeshing
Note
if an operation on a mesh3 is performed then the same operation is applyed on its surface part (its meshS associated)
#### The command change
This command changes the label of elements and border elements of a mesh. It’s the equivalent command in 2d mesh case.
Changing the label of elements and border elements will be done using the keyword change. The parameters for this command line are for two dimensional and three dimensional cases:
• reftet= is a vector of integer that contains successive pairs of the old label number to the new label number.
• refface= is a vector of integer that contains successive pairs of the old region number to new region number.
• flabel= is an integer function given the new value of the label.
• fregion= is an integer function given the new value of the region.
• rmInternalFaces= is a boolean, equal true to remove the internal faces.
• rmlfaces= is a vector of integer, where triangle’s label given are remove of the mesh
These vectors are composed of $$n_{l}$$ successive pairs of numbers $$O,N$$ where $$n_{l}$$ is the number (label or region) that we want to change. For example, we have:
$\begin{split}\mathtt{label} &= [ O_{1}, N_{1}, ..., O_{n_{l}},N_{n_{l}} ] \\ \mathtt{region} &= [ O_{1}, N_{1}, ..., O_{n_{l}},N_{n_{l}} ]\end{split}$
An example of use:
1 // Mesh
2 mesh3 Th1 = cube(10, 10);
3 mesh3 Th2 = cube(20, 10, [x+1, y,z]);
4
5 int[int] r1=[2,0];
6 plot(Th1, wait=true);
7
8 Th1 = change(Th1, label=r1); //change the label of Edges 2 in 0.
9 plot(Th1, wait=true);
10
11 // boundary label: 1 -> 1 bottom, 2 -> 1 right, 3->1 top, 4->1 left boundary label is 1
12 int[int] re=[1,1, 2,1, 3,1, 4,1]
13 Th2=change(Th2,refe=re);
14 plot(Th2,wait=1) ;
#### The command trunc
This operator have been introduce to remove a piece of mesh or/and split all element or for a particular label element The three named parameter - boolean function to keep or remove elements - split= sets the level n of triangle splitting. each triangle is splitted in n × n ( one by default) - freefem:label= sets the label number of new boundary item (1 by default)
An example of use
1 load "msh3"
3 int nn=8;
4 mesh3 Th=cube(nn,nn,nn);
5 // remove the small cube $]1/2,1[^2$
6 Th= trunc(Th,((x<0.5) |(y< 0.5)| (z<0.5)), split=3, label=3);
7 medit("cube",Th);
#### The command movemesh
3D meshes can be translated, rotated, and deformed using the command line movemesh as in the 2D case (see section movemesh). If $$\Omega$$ is tetrahedrized as $$T_{h}(\Omega)$$, and $$\Phi(x,y)=(\Phi1(x,y,z), \Phi2(x,y,z), \Phi3(x,y,z))$$ is the transformation vector then $$\Phi(T_{h})$$ is obtained by:
1 mesh3 Th = movemesh(Th, [Phi1, Phi2, Phi3], ...);
2 mesh3 Th = movemesh3(Th, transfo=[Phi1, Phi2, Phi3], ...); (syntax with transfo=)
The parameters of movemesh in three dimensions are:
• transfo= sets the geometric transformation $$\Phi(x,y)=(\Phi1(x,y,z), \Phi2(x,y,z), \Phi3(x,y,z))$$
• region= sets the integer labels of the tetrahedra.
0 by default.
• label= sets the labels of the border faces.
This parameter is initialized as the label for the keyword change.
• facemerge= An integer expression.
When you transform a mesh, some faces can be merged. This parameter equals to one if the merges’ faces is considered. Otherwise it equals to zero. By default, this parameter is equal to 1.
• ptmerge = A real expression.
When you transform a mesh, some points can be merged. This parameter is the criteria to define two merging points. By default, we use
$ptmerge \: = \: 1e-7 \: \:Vol( B ),$
where $$B$$ is the smallest axis parallel boxes containing the discretion domain of $$\Omega$$ and $$Vol(B)$$ is the volume of this box.
• orientation = An integer expression equal 1, give the oientation of the triangulation, elements must be in the reference orientation (counter clock wise) equal -1 reverse the orientation of the tetrahedra
Note
The orientation of tetrahedra are checked by the positivity of its area and automatically corrected during the building of the adjacency.
An example of this command can be found in the Poisson’s equation 3D example.
1 load "medit"
2 include "cube.idp"
3 int[int] Nxyz=[20,5,5];
4 real [int,int] Bxyz=[[0.,5.],[0.,1.],[0.,1.]];
5 int [int,int] Lxyz=[[1,2],[2,2],[2,2]];
6 real E = 21.5e4;
7 real sigma = 0.29;
8 real mu = E/(2*(1+sigma));
9 real lambda = E*sigma/((1+sigma)*(1-2*sigma));
10 real gravity = -0.05;
11 real sqrt2=sqrt(2.);
12
13 mesh3 Th=Cube(Nxyz,Bxyz,Lxyz);
14 fespace Vh(Th,[P1,P1,P1]);
15 Vh [u1,u2,u3], [v1,v2,v3];
16
17 macro epsilon(u1,u2,u3) [dx(u1),dy(u2),dz(u3),(dz(u2)+dy(u3))/sqrt2,(dz(u1)+dx(u3))/sqrt2,(dy(u1)+dx(u2))/sqrt2] // EOM
18 macro div(u1,u2,u3) ( dx(u1)+dy(u2)+dz(u3) ) // EOM
19
20 solve Lame([u1,u2,u3],[v1,v2,v3])=
21 int3d(Th)(
22 lambda*div(u1,u2,u3)*div(v1,v2,v3)
23 +2.*mu*( epsilon(u1,u2,u3)'*epsilon(v1,v2,v3) )
24 )
25 - int3d(Th) (gravity*v3)
26 + on(1,u1=0,u2=0,u3=0);
27
28 real dmax= u1[].max;
29 real coef= 0.1/dmax;
30
31 int[int] ref2=[1,0,2,0]; // array
32 mesh3 Thm=movemesh(Th,[x+u1*coef,y+u2*coef,z+u3*coef],label=ref2);
33 // mesh3 Thm=movemesh3(Th,transfo=[x+u1*coef,y+u2*coef,z+u3*coef],label=ref2); older syntax
34 Thm=change(Thm,label=ref2);
35 plot(Th,Thm, wait=1,cmm="coef amplification = "+coef );
movemesh doesn’t use the prefix tranfo= [.,.,.], the geometric transformation is directly given by [.,.,.] in the arguments list
#### The command extract
This command offers the possibility to extract a boundary part of a mesh3
• refface , is a vector of integer that contains a list of triangle face references, where the extract function must be apply.
• label , is a vector of integer that contains a list of tetrahedra label
1 load"msh3"
2 int nn = 30;
3 int[int] labs = [1, 2, 2, 1, 1, 2]; // Label numbering
4 mesh3 Th = cube(nn, nn, nn, label=labs);
5 // extract the surface (boundary) of the cube
6 int[int] llabs = [1, 2];
7 meshS ThS = extract(Th,label=llabs);
#### The command buildSurface
This new function allows to build the surface mesh of a volume mesh, under the condition the surface is the boundary of the volume. By definition, a mesh3 is defined by a list of vertices, tetrahedron elements and triangle border elements. buildSurface function create the meshS corresponding, given the list vertices which are on the border domain, the triangle elements and build the list of edges. Remark, for a closed surface mesh, the edges list is empty.
#### The command movemesh23
A simple method to tranform a 2D mesh in 3D Surface mesh. The principe is to project a two dimensional domain in a three dimensional space, 2d surface in the (x,y,z)-space to create a surface mesh 3D, meshS.
Warning
Since the release 4.2.1, the FreeFEM function movemesh23 returns a meshS type.
This corresponds to translate, rotate or deforme the domain by a displacement vector of this form $$\mathbf{\Phi(x,y)} = (\Phi1(x,y), \Phi2(x,y), \Phi3(x,y))$$.
The result of moving a two dimensional mesh Th2 by this three dimensional displacement is obtained using:
1 **meshS** Th3 = movemesh23(Th2, transfo=[Phi(1), Phi(2), Phi(3)]);
The parameters of this command line are:
• transfo= [$$\Phi 1$$, $$\Phi 2$$, $$\Phi 3$$] sets the displacement vector of transformation $$\mathbf{\Phi(x,y)} = [\Phi1(x,y), \Phi2(x,y), \Phi3(x,y)]$$.
• label= sets an integer label of triangles.
• orientation= sets an integer orientation to give the global orientation of the surface of mesh. Equal 1, give a triangulation in the reference orientation (counter clock wise) equal -1 reverse the orientation of the triangles
• ptmerge= A real expression.
When you transform a mesh, some points can be merged. This parameter is the criteria to define two merging points. By default, we use
$ptmerge \: = \: 1e-7 \: \:Vol( B ),$
where $$B$$ is the smallest axis, parallel boxes containing the discretized domain of $$\Omega$$ and $$Vol(B)$$ is the volume of this box.
We can do a “gluing” of surface meshes using the process given in Change section. An example to obtain a three dimensional mesh using the command line tetg and movemesh23 is given below.
1 load "msh3"
3
4 // Parameters
5 real x10 = 1.;
6 real x11 = 2.;
7 real y10 = 0.;
8 real y11 = 2.*pi;
9
10 func ZZ1min = 0;
11 func ZZ1max = 1.5;
12 func XX1 = x;
13 func YY1 = y;
14
15 real x20 = 1.;
16 real x21 = 2.;
17 real y20=0.;
18 real y21=1.5;
19
20 func ZZ2 = y;
21 func XX2 = x;
22 func YY2min = 0.;
23 func YY2max = 2*pi;
24
25 real x30=0.;
26 real x31=2*pi;
27 real y30=0.;
28 real y31=1.5;
29
30 func XX3min = 1.;
31 func XX3max = 2.;
32 func YY3 = x;
33 func ZZ3 = y;
34
35 // Mesh
36 mesh Thsq1 = square(5, 35, [x10+(x11-x10)*x, y10+(y11-y10)*y]);
37 mesh Thsq2 = square(5, 8, [x20+(x21-x20)*x, y20+(y21-y20)*y]);
38 mesh Thsq3 = square(35, 8, [x30+(x31-x30)*x, y30+(y31-y30)*y]);
39
40 // Mesh 2D to 3D surface
41 meshS Th31h = movemesh23(Thsq1, transfo=[XX1, YY1, ZZ1max], orientation=1);
42 meshS Th31b = movemesh23(Thsq1, transfo=[XX1, YY1, ZZ1min], orientation=-1);
43
44 meshS Th32h = movemesh23(Thsq2, transfo=[XX2, YY2max, ZZ2], orientation=-1);
45 meshS Th32b = movemesh23(Thsq2, transfo=[XX2, YY2min, ZZ2], orientation=1);
46
47 meshS Th33h = movemesh23(Thsq3, transfo=[XX3max, YY3, ZZ3], orientation=1);
48 meshS Th33b = movemesh23(Thsq3, transfo=[XX3min, YY3, ZZ3], orientation=-1);
49
50 // Gluing surfaces
51 meshS Th33 = Th31h + Th31b + Th32h + Th32b + Th33h + Th33b;
52 plot(Th33, cmm="Th33");
53
54 // Tetrahelize the interior of the cube with TetGen
55 real[int] domain =[1.5, pi, 0.75, 145, 0.0025];
56 meshS Thfinal = tetg(Th33, switch="paAAQY", regionlist=domain);
57 plot(Thfinal, cmm="Thfinal");
58
59 // Build a mesh of a half cylindrical shell of interior radius 1, and exterior radius 2 and a height of 1.5
60 func mv2x = x*cos(y);
61 func mv2y = x*sin(y);
62 func mv2z = z;
63 meshS Thmv2 = movemesh(Thfinal, transfo=[mv2x, mv2y, mv2z], facemerge=0);
64 plot(Thmv2, cmm="Thmv2");
### 3d Meshing examples
Tip
Lake
1 load "msh3"
3
4 // Parameters
5 int nn = 5;
6
7 // 2D mesh
8 border cc(t=0, 2*pi){x=cos(t); y=sin(t); label=1;}
9 mesh Th2 = buildmesh(cc(100));
10
11 // 3D mesh
12 int[int] rup = [0, 2], rlow = [0, 1];
13 int[int] rmid = [1, 1, 2, 1, 3, 1, 4, 1];
14 func zmin = 2-sqrt(4-(x*x+y*y));
15 func zmax = 2-sqrt(3.);
16
17 mesh3 Th = buildlayers(Th2, nn,
18 coef=max((zmax-zmin)/zmax, 1./nn),
19 zbound=[zmin,zmax],
20 labelmid=rmid,
21 labelup=rup,
22 labeldown=rlow);
23
24 medit("Th", Th);
Tip
Hole region
1 load "msh3"
4
5 // 2D mesh
6 mesh Th = square(10, 20, [x*pi-pi/2, 2*y*pi]); // ]-pi/2, pi/2[X]0,2pi[
7
8 // 3D mesh
9 //parametrization of a sphere
10 func f1 = cos(x)*cos(y);
11 func f2 = cos(x)*sin(y);
12 func f3 = sin(x);
13 //partial derivative of the parametrization
14 func f1x = sin(x)*cos(y);
15 func f1y = -cos(x)*sin(y);
16 func f2x = -sin(x)*sin(y);
17 func f2y = cos(x)*cos(y);
18 func f3x = cos(x);
19 func f3y = 0;
20 //M = DF^t DF
21 func m11 = f1x^2 + f2x^2 + f3x^2;
22 func m21 = f1x*f1y + f2x*f2y + f3x*f3y;
23 func m22 = f1y^2 + f2y^2 + f3y^2;
24
25 func perio = [[4, y], [2, y], [1, x], [3, x]];
26 real hh = 0.1;
27 real vv = 1/square(hh);
28 verbosity = 2;
29 Th = adaptmesh(Th, m11*vv, m21*vv, m22*vv, IsMetric=1, periodic=perio);
30 Th = adaptmesh(Th, m11*vv, m21*vv, m22*vv, IsMetric=1, periodic=perio);
31 plot(Th, wait=true);
32
33 //construction of the surface of spheres
34 real Rmin = 1.;
35 func f1min = Rmin*f1;
36 func f2min = Rmin*f2;
37 func f3min = Rmin*f3;
38
39 meshS ThSsph = movemesh23(Th, transfo=[f1min, f2min, f3min]);
40
41 real Rmax = 2.;
42 func f1max = Rmax*f1;
43 func f2max = Rmax*f2;
44 func f3max = Rmax*f3;
45
46 meshS ThSsph2 = movemesh23(Th, transfo=[f1max, f2max, f3max]);
47
48 //gluing meshes
49 meshS ThS = ThSsph + ThSsph2;
50
51 cout << " TetGen call without hole " << endl;
52 real[int] domain2 = [1.5, 0., 0., 145, 0.001, 0.5, 0., 0., 18, 0.001];
53 mesh3 Th3fin = tetg(ThS, switch="paAAQYY", nbofregions=2, regionlist=domain2);
54 medit("Sphere with two regions", Th3fin);
55
56 cout << " TetGen call with hole " << endl;
57 real[int] hole = [0.,0.,0.];
58 real[int] domain = [1.5, 0., 0., 53, 0.001];
59 mesh3 Th3finhole = tetg(ThS, switch="paAAQYY",
60 nbofholes=1, holelist=hole, nbofregions=1, regionlist=domain);
61 medit("Sphere with a hole", Th3finhole);
Tip
Build a 3d mesh of a cube with a balloon
1 load "msh3"
4 include "MeshSurface.idp"
5
6 // Parameters
7 real hs = 0.1; //mesh size on sphere
8 int[int] N = [20, 20, 20];
9 real [int,int] B = [[-1, 1], [-1, 1], [-1, 1]];
10 int [int,int] L = [[1, 2], [3, 4], [5, 6]];
11
12 // Meshes
13 meshS ThH = SurfaceHex(N, B, L, 1);
14 meshS ThS = Sphere(0.5, hs, 7, 1);
15
16 meshS ThHS = ThH + ThS;
17 medit("Hex-Sphere", ThHS);
18
19 real voltet = (hs^3)/6.;
20 cout << "voltet = " << voltet << endl;
21 real[int] domain = [0, 0, 0, 1, voltet, 0, 0, 0.7, 2, voltet];
22 mesh3 Th = tetg(ThHS, switch="pqaAAYYQ", nbofregions=2, regionlist=domain);
23 medit("Cube with ball", Th);
Cube sphere
## The type meshS in 3 dimension
Warning
Since the release 4.2.1, the surface mesh3 object (list of vertices and border elements, without tetahedra elements) is remplaced by meshS type.
### Commands for 3d surface mesh generation
#### The command square3
The function square3 like the function square in 2d is the simple way to a build the unit square plan in the space $$\mathbb{R^3}$$. To use this command, it is necessary to load the pluging msh3 (need load "msh3"). A square in 3d consists in building a 2d square which is projected from $$\mathbb{R^2}$$ to $$\mathbb{R^3}$$. The parameters of this command line are:
• n,m generates a n×m grid in the unit square
• [.,.,.] is [ $$\Phi 1$$, $$\Phi 2$$, $$\Phi 3$$ ] is the geometric transformation from $$\mathbb{R^2}$$ to $$\mathbb{R^3}$$. By default, [ $$\Phi 1$$, $$\Phi 2$$, $$\Phi 3$$ ] = [x,y,0]
• orientation= equal 1, gives the orientation of the triangulation, elements are in the reference orientation (counter clock wise) equal -1 reverse the orientation of the triangles it’s the global orientation of the surface 1 extern (-1 intern)
1 real R = 3, r=1;
2 real h = 0.2; //
3 int nx = R*2*pi/h;
4 int ny = r*2*pi/h;
5 func torex= (R+r*cos(y*pi*2))*cos(x*pi*2);
6 func torey= (R+r*cos(y*pi*2))*sin(x*pi*2);
7 func torez= r*sin(y*pi*2);
8
9
10 meshS ThS=square3(nx,ny,[torex,torey,torez],orientation=-1) ;
The following code generates a $$3\times 4 \times 5$$ grid in the unit cube $$[0, 1]^3$$ with a clock wise triangulation.
#### surface mesh builders
Adding at the top of a FreeFEM script include "MeshSurface.idp", constructors of sphere, ellipsoid, surface mesh of a 3d box are available.
• SurfaceHex(N, B, L, orient)
• this operator allows to build the surface mesh of a 3d box
• int[int] N=[nx,ny,nz]; // the number of seg in the 3 direction
• real [int,int] B=[[xmin,xmax],[ymin,ymax],[zmin,zmax]]; // bounding bax
• int [int,int] L=[[1,2],[3,4],[5,6]]; // the label of the 6 face left,right, front, back, down, right
• orient the global orientation of the surface 1 extern (-1 intern),
• returns a meshS type
• Ellipsoide (RX, RY, RZ, h, L, OX, OY, OZ, orient)
• h is the mesh size
• L is the label
• orient the global orientation of the surface 1 extern (-1 intern)
• OX, OY, OZ are real numbers to give the Ellipsoide center ( optinal, by default is (0,0,0) )
• where RX, RY, RZ are real numbers such as the parametric equations of the ellipsoid is:
• returns a meshS type
$\forall u \in [- \frac{\pi}{2},\frac{\pi}{2} [ \text{ and } v \in [0, 2 \pi], \vectthree{x=\text{Rx } cos(u)cos(v) + \text{Ox }}{y=\text{Ry } cos(u)sin(v) + \text{Oy }}{z = \text{Rz } sin(v) + \text{Oz } }$
• Sphere(R, h, L, OX, OY, OZ, orient)
• where R is the raduis of the sphere,
• OX, OY, OZ are real numbers to give the Ellipsoide center ( optinal, by default is (0,0,0) )
• h is the mesh size of the shpere
• L is the label the the sphere
• orient the global orientation of the surface 1 extern (-1 intern)
• returns a meshS type
1 func meshS SurfaceHex(int[int] & N,real[int,int] &B ,int[int,int] & L,int orientation){
2 real x0=B(0,0),x1=B(0,1);
3 real y0=B(1,0),y1=B(1,1);
4 real z0=B(2,0),z1=B(2,1);
5
6 int nx=N[0],ny=N[1],nz=N[2];
7
8 mesh Thx = square(ny,nz,[y0+(y1-y0)*x,z0+(z1-z0)*y]);
9 mesh Thy = square(nx,nz,[x0+(x1-x0)*x,z0+(z1-z0)*y]);
10 mesh Thz = square(nx,ny,[x0+(x1-x0)*x,y0+(y1-y0)*y]);
11
12 int[int] refx=[0,L(0,0)],refX=[0,L(0,1)]; // Xmin, Ymax faces labels renumbering
13 int[int] refy=[0,L(1,0)],refY=[0,L(1,1)]; // Ymin, Ymax faces labesl renumbering
14 int[int] refz=[0,L(2,0)],refZ=[0,L(2,1)]; // Zmin, Zmax faces labels renumbering
15
16 meshS Thx0 = movemesh23(Thx,transfo=[x0,x,y],orientation=-orientation,label=refx);
17 meshS Thx1 = movemesh23(Thx,transfo=[x1,x,y],orientation=+orientation,label=refX);
18 meshS Thy0 = movemesh23(Thy,transfo=[x,y0,y],orientation=+orientation,label=refy);
19 meshS Thy1 = movemesh23(Thy,transfo=[x,y1,y],orientation=-orientation,label=refY);
20 meshS Thz0 = movemesh23(Thz,transfo=[x,y,z0],orientation=-orientation,label=refz);
21 meshS Thz1 = movemesh23(Thz,transfo=[x,y,z1],orientation=+orientation,label=refZ);
22 meshS Th= Thx0+Thx1+Thy0+Thy1+Thz0+Thz1;
23
24 return Th;
25 }
26
27 func meshS Ellipsoide (real RX,real RY,real RZ,real h,int L,real Ox,real Oy,real Oz,int orientation) {
28 mesh Th=square(10,20,[x*pi-pi/2,2*y*pi]); // $]\frac{-pi}{2},frac{-pi}{2}[\times]0,2\pi[$
29 // a parametrization of a sphere
30 func f1 =RX*cos(x)*cos(y);
31 func f2 =RY*cos(x)*sin(y);
32 func f3 =RZ*sin(x);
33 // partiel derivative
34 func f1x= -RX*sin(x)*cos(y);
35 func f1y= -RX*cos(x)*sin(y);
36 func f2x= -RY*sin(x)*sin(y);
37 func f2y= +RY*cos(x)*cos(y);
38 func f3x=-RZ*cos(x);
39 func f3y=0;
40 // the metric on the sphere $M = DF^t DF$
41 func m11=f1x^2+f2x^2+f3x^2;
42 func m21=f1x*f1y+f2x*f2y+f3x*f3y;
43 func m22=f1y^2+f2y^2+f3y^2;
44 func perio=[[4,y],[2,y],[1,x],[3,x]]; // to store the periodic condition
45 real hh=h;// hh mesh size on unite sphere
46 real vv= 1/square(hh);
51 int[int] ref=[0,L];
52 meshS ThS=movemesh23(Th,transfo=[f1,f2,f3],orientation=orientation,refface=ref);
54 return ThS;
55 }
56
57 func meshS Ellipsoide (real RX,real RY,real RZ,real h,int L,int orientation) {
58 return Ellipsoide (RX,RY,RZ,h,L,0.,0.,0.,orientation);
59 }
60 func meshS Sphere(real R,real h,int L,int orientation) {
61 return Ellipsoide(R,R,R,h,L,orientation);
62 }
63 func meshS Sphere(real R,real h,int L,real Ox,real Oy,real Oz,int orientation) {
64 return Ellipsoide(R,R,R,h,L,Ox,Oy,Oz,orientation);
65 }
#### 2D mesh generators combined with movemesh23
FreeFEM ‘s meshes can be built by the composition of the movemesh23 command from a 2d mesh generation. The operation is a projection of a 2d plane in $$\mathbb{R^3}$$ following the geometric transformation [ $$\Phi 1$$, $$\Phi 2$$, $$\Phi 3$$ ].
1 load "msh3"
2 real l = 3;
3 border a(t=-l,l){x=t; y=-l;label=1;};
4 border b(t=-l,l){x=l; y=t;label=1;};
5 border c(t=l,-l){x=t; y=l;label=1;};
6 border d(t=l,-l){x=-l; y=t;label=1;};
7 int n = 100;
8 border i(t=0,2*pi){x=1.1*cos(t);y=1.1*sin(t);label=5;};
9 mesh th= buildmesh(a(n)+b(n)+c(n)+d(n)+i(-n));
10 meshS Th= movemesh23(th,transfo=[x,y,cos(x)^2+sin(y)^2]);
### Remeshing
#### The command trunc
This operator allows to define a meshS by truncating another one, i.e. by removing triangles, and/or by splitting each triangle by a given positive integer s. In a FreeFEM script, this function must be called as follows:
meshS TS2= trunc (TS1, boolean function to keep or remove elements, split = s, label = …)
The command has the following arguments:
• boolean function to keep or remove elements
• split= sets the level n of triangle splitting. each triangle is splitted in n × n ( one by default)
• label= sets the label number of new boundary item (1 by default)
An example of how to call the function
1 real R = 3, r=1;
2 real h = 0.2; //
3 int nx = R*2*pi/h;
4 int ny = r*2*pi/h;
5 func torex= (R+r*cos(y*pi*2))*cos(x*pi*2);
6 func torey= (R+r*cos(y*pi*2))*sin(x*pi*2);
7 func torez= r*sin(y*pi*2);
8 // build a tore
9 meshS ThS=square3(nx,ny,[torex,torey,torez]) ;
10 ThS=trunc(ThS, (x < 0.5) | (y < 0.5) | (z > 1.), split=4);
#### The command movemesh
Like 2d and 3d type meshes in FreeFEM, meshS can be translated, rotated or deformated by an application [$$\Phi 1$$, $$\Phi 2$$, $$\Phi 3$$]. The image $$T_{h}(\Omega)$$ is obtained by the command movemeshS.
The parameters of movemeshS are:
• transfo= sets the geometric transformation $$\Phi(x,y)=(\Phi1(x,y,z), \Phi2(x,y,z), \Phi3(x,y,z))$$
• region= sets the integer labels of the triangles.
0 by default.
• label= sets the labels of the border edges.
This parameter is initialized as the label for the keyword change.
• edgemerge= An integer expression.
When you transform a mesh, some triangles can be merged and fix the parameter to 1, else 0 By default, this parameter is equal to 1.
• ptmerge = A real expression.
When you transform a mesh, some points can be merged. This parameter is the criteria to define two merging points. By default, we use
$ptmerge \: = \: 1e-7 \: \:Vol( B ),$
where $$B$$ is the smallest axis parallel boxes containing the discretion domain of $$\Omega$$ and $$Vol(B)$$ is the volume of this box.
• orientation = An integer expression
equal 1, give the oientation of the triangulation, elements must be in the reference orientation (counter clock wise) equal -1 reverse the orientation of the triangles. It’s the global orientation of the normals at the surface 1 extern (-1 intern)
Example of using
1 meshS Th1 = square3(n,n,[2*x,y,1],orientation=-1);
2 meshS Th2=movemeshS(Th1, transfo=[x,y,z]);
3 meshS Th3=movemesh(Th1, [x,y,z]);
#### The command change
Equivalent for a 2d or 3d mesh, the command change changes the label of elements and border elements of a meshS.
The parameters for this command line are:
• reftri= is a vector of integer that contains successive pairs of the old label number to the new label number for elements.
• refedge= is a vector of integer that contains successive pairs of the old region number to new region number for boundary elements.
• flabel= is an integer function given the new value of the label.
• fregion= is an integer function given the new value of the region.
• rmledges= is a vector of integer, where edge’s label given are remove of the mesh
These vectors are composed of $$n_{l}$$ successive pairs of numbers $$O,N$$ where $$n_{l}$$ is the number (label or region) that we want to change. For example, we have:
$\begin{split}\mathtt{label} &= [ O_{1}, N_{1}, ..., O_{n_{l}},N_{n_{l}} ] \\ \mathtt{region} &= [ O_{1}, N_{1}, ..., O_{n_{l}},N_{n_{l}} ]\end{split}$
## The type meshL in 3 dimension
### Commands for 3d curve mesh generation
#### The command segment
The function segment is a basic command to define a curve in 3D space.
The parameters of this command line are:
• n generates a n subsegments from the unit line
• [.,.,.] is [ $$\Phi 1$$, $$\Phi 2$$, $$\Phi 3$$ ] is the geometric transformation from $$\mathbb{R^1}$$ to $$\mathbb{R^3}$$. By default, [ $$\Phi 1$$, $$\Phi 2$$, $$\Phi 3$$ ] = [x,0,0]
• orientation= equal 1, gives the orientation of the triangulation, elements are in the reference orientation (counter clock wise) equal -1 reverse the orientation of the triangles it’s the global orientation of the surface 1 extern (-1 intern)
• cleanmesh= is a boolean, allowing remove the duplicated nodes
• removeduplicate= is a boolean, allowing remove the duplicated elements and border elements
• precismesh this parameter is the criteria to define two merging points.
By default, it value is 1e-7 and define the smallest axis parallel boxes containing the discretion domain of $$\Omega$$
By defaut, the border points are marked by label 1 and 2.
1 real R = 3, r=1;
2 real h = 0.1; //
3 int nx = R*2*pi/h;
4 func torex= (R+r*cos(y*pi*2))*cos(x*pi*2);
5 func torey= (R+r*cos(y*pi*2))*sin(x*pi*2);
6 func torez= r*sin(y*pi*2);
7 meshL Th=segment(nx,[torex,torey,torez],removeduplicate=true) ;
The following code generates a 10 subsegments from the unit line with a clock wise triangulation, according to the geometric transformation [torex,torey,torez] and removing the duplicated points/elements
#### The command buildmesh
This operator allows to define a curve mesh from multi-borders. The domain can be defined by a parametrized curve (keyword border), such as Th1 in the following example or piecewise by parametrized curves, such as the construction of the mesh Th2.
The pieces can only intersect at their endpoints, but it is possible to join more than two endpoints.
1 load "msh3"
2
3 // conical helix
4 border E1(t=0, 10.*pi){x=(1.)*t*cos(t); y=-(1.)*t*sin(t); z=t;}
5 meshL Th1=buildmeshL(E1(1000));
6
7 int upper = 1, others = 2, inner = 3, n = 10;
8 border D01(t=0, 1) {x=0; y=-1+t; }
9 border D02(t=0, 1){x=1.5-1.5*t; y=-1; z=3;label=upper;}
10 border D03(t=0, 1){x=1.5; y=-t; z=3;label=upper;}
11 border D04(t=0, 1){x=1+0.5*t; y=0; z=3;label=others;}
12 border D05(t=0, 1){x=0.5+0.5*t; y=0; z=3;label=others;}
13 border D06(t=0, 1){x=0.5*t; y=0; z=3;label=others;}
14 border D11(t=0, 1){x=0.5; y=-0.5*t; z=3;label=inner;}
15 border D12(t=0, 1){x=0.5+0.5*t; y=-0.5; z=3;label=inner;}
16 border D13(t=0, 1){x=1; y=-0.5+0.5*t; z=3;label=inner;}
17
18 meshL Th2=buildmeshL(D01(-n) + D02(-n) + D03(-n) + D04(-n) + D05(-n)
19 + D06(-n) + D11(n) + D12(n) + D13(n));
### Remeshing
#### The command trunc
This operator allows to define a meshL by truncating another one, i.e. by removing segments, and/or by splitting each element by a given positive integer s. Here, an example to use this function:
meshL ThL2= trunc (ThL1, boolean function to keep or remove elements, split = s, label = …)
The command has the following arguments:
• boolean function to keep or remove elements
• split= sets the level n of edge splitting, each edge is splitted in n subpart( one by default)
• label= sets the label number of new boundary item (1 by default)
• new2old
• old2new
• renum
• orientation=
equal 1, gives the orientation of the triangulation, elements are in the reference orientation (counter clock wise) equal -1 reverse the orientation of the triangles it’s the global orientation of the surface 1 extern (-1 intern)
• cleanmesh= is a boolean, allowing remove the duplicated nodes
• removeduplicate= is a boolean, allowing remove the duplicated elements and border elements
• precismesh this parameter is the criteria to define two merging points.
By default, it value is 1e-7 and define the smallest axis parallel boxes containing the discretion domain of $$\Omega$$
An example of how to call this function
1 int nx=10;
2 meshL Th=segment(nx,[5.*x,cos(pi*x),sin(pi*x)]);
3 Th=trunc(Th, (x < 0.5) | (y < 0.5) | (z > 1.), split=4);
#### The command movemesh
This is the classical mesh transformation FreeFEM function, meshL can be deformed by an application [ $$\Phi 1$$, $$\Phi 2$$, $$\Phi 3$$ ]. The image $$T_{h}(\Omega)$$ is obtained by the command movemeshL.
The parameters of movemesh are:
• transfo= sets the geometric transformation $$\Phi(x,y)=(\Phi1(x,y,z), \Phi2(x,y,z), \Phi3(x,y,z))$$
• refedge= sets the integer labels of the triangles.
0 by default.
• refpoint= sets the labels of the border points.
This parameter is initialized as the label for the keyword change.
• precismesh this parameter is the criteria to define two merging points.
By default, it value is 1e-7 and define the smallest axis parallel boxes containing the discretion domain of $$\Omega$$
• orientation = An integer expression
equal 1, give the oientation of the triangulation, elements must be in the reference orientation (counter clock wise) equal -1 reverse the orientation of the triangles. It’s the global orientation of the normals at the surface 1 extern (-1 intern)
• cleanmesh= is a boolean, allowing remove the duplicated nodes
• removeduplicate= is a boolean, allowing remove the duplicated elements and border elements
Note
The definition of the geometric transformation depends on the space dimension of the studied problem. It means that, with curve FEM, it’s possible to treat a real 1D problem (space coordinate is x) then the transformation is given by x: ->F(x), that means [F_x] and F_y=F_z=0 in FreeFEM function.
Example of using
1 int nx=100;
2 meshL Th=Sline(nx);
3 meshL Th31=movemesh(Th, [x]);
4 meshL Th32=movemesh(Th, [x,-x*(x-1)]);
5 meshL Th3=Th31+Th32;
#### The command change
The command change changes the label of elements and border elements of a meshL.
The parameters for this command line are:
• refedge= is a vector of integer that contains successive pairs of the old label number to the new label number for elements.
• refpoint= is a vector of integer that contains successive pairs of the old region number to new region number for boundary elements.
• flabel= is an integer function given the new value of the label.
• fregion= is an integer function given the new value of the region.
• rmlpoint= is a vector of integer, where edge’s label given are remove of the mesh
These vectors are composed of $$n_{l}$$ successive pairs of numbers $$O,N$$ where $$n_{l}$$ is the number (label or region) that we want to change. For example, we have:
$\begin{split}\mathtt{label} &= [ O_{1}, N_{1}, ..., O_{n_{l}},N_{n_{l}} ] \\ \mathtt{region} &= [ O_{1}, N_{1}, ..., O_{n_{l}},N_{n_{l}} ]\end{split}$
#### The commands buildBdMesh and Gamma
The command Gamma allows to extract the border mesh independly of a surface mesh. With this function, the constructed border mesh contains the full geometric description of th eboundary surface. In case where the border mesh doesn’t exist, before calling Gamma, must build it by calling the buildBdMesh function (see the next function description).
1 load "msh3"
2 int n= 10;
3 meshS Th=square3(n,n);
4 Th = buildBdMesh(Th); // build the border mesh
5 // build Th1, the border of Th, defined by edges elements and point border elements
6 meshL Th1 = Th.Gamma;
#### Glue of meshL meshes
An assembling of meshL is possible thanks to the operator +. The result returns a meshL, with caution of the right orientation at the merged interfaces. Here, the function checkmesh can be called.
1 int n=10;
2 meshL Th1 = segment(n);
3 meshL Th2 = segment(n,[0,x,0],orientation=1);
4 meshL Th3 = segment(n,[x,0,1],orientation=1);
5 meshL Th4 = segment(n,[0,0,x],orientation=-1);
6
7 meshL Th = Th1+Th2+Th3+Th4;
8 Th=rebuildBorder(Th, ridgeangledetection=pi/2.+0.0001);
Warning
For the moment, the case of no manifold mesh are not considered in FreeFEM. To check if the meshL contains no manifold elements, the command nbnomanifold.
#### The command extract
This operator allows to extract a labeled piece or the entire border of a 2D mesh and project it in 3D. Optionally, a geometic transformation can be applied.
1 mesh Th=square(10,10);
2 int[int] ll=[4];
3 meshL ThL = extract(Th,[x+2,y*5],refedge=ll);
#### The commands rebuildBorder
This operator, used in the last example, allows to reconstruted the border elements following a special criteria ridgeangledetection. By default, it value is $$\frac{8}{9}*arctan(1)\approx40°$$, the diedral angle for a decahedron.
### The commands checkmesh
This function is avalaible for all 3D meshes. It checkes and validates the a given mesh, allows to remove duplicate vertices and/or elements and border elements. The possible arguments are
• precismesh= this parameter is the criteria to define two merging points.
By default, it value is 1e-7 and define the smallest axis parallel boxes containing the discretion domain of $$\Omega$$
• removeduplicate= is a boolean, allowing remove the duplicated elements and border elements
• rebuildboundary= is a boolean, allowing rebuild the border elements (in case of incomplete list given by the mesh)
Example:
1 mesh3 Th = checkmesh(Th);
### TetGen: A tetrahedral mesh generator
TetGen is a software developed by Dr. Hang Si of Weierstrass Institute for Applied Analysis and Stochastics in Berlin, Germany [HANG2006]. TetGen is free for research and non-commercial use. For any commercial license utilization, a commercial license is available upon request to Hang Si.
This software is a tetrahedral mesh generator of a three dimensional domain defined by its boundary (a surface). The input domain takes into account a polyhedral or a piecewise linear complex. This tetrahedralization is a constrained Delaunay tetrahedralization.
The method used in TetGen to control the quality of the mesh is a Delaunay refinement due to Shewchuk [SHEWCHUK1998]. The quality measure of this algorithm is the Radius-Edge Ratio (see Section 1.3.1 [HANG2006] for more details). A theoretical bound of this ratio of the Shewchuk algorithm is obtained for a given complex of vertices, constrained segments and facets of surface mesh, with no input angle less than 90 degrees. This theoretical bound is 2.0.
The launch of TetGen is done with the keyword tetg. The parameters of this command line is:
• reftet= sets the label of tetrahedra.
• label= is a vector of integers that contains the old labels number at index $$2i$$ and the new labels number at index $$2i+1$$ of Triangles.
This parameter is initialized as a label for the keyword change.
• switch= A string expression.
This string corresponds to the command line switch of TetGen see Section 3.2 of [HANG2006].
• nbofholes= Number of holes (default value: “size of holelist / 3”).
• holelist= This array corresponds to holelist of TetGenio data structure [HANG2006].
A real vector of size 3 * nbofholes. In TetGen, each hole is associated with a point inside this domain. This vector is $$x_{1}^{h}, y_{1}^{h}, z_{1}^{h}, x_{2}^{h}, y_{2}^{h}, z_{2}^{h}, \cdots,$$ where $$x_{i}^{h},y_{i}^{h},z_{i}^{h}$$ is the associated point with the $$i^{\mathrm{th}}$$ hole.
• nbofregions= Number of regions (default value: “size of regionlist / 5”).
• regionlist= This array corresponds to regionlist of TetGenio data structure [HANG2006].
The attribute and the volume constraint of region are given in this real vector of size 5 * nbofregions. The $$i^{\mathrm{th}}$$ region is described by five elements: $$x-$$coordinate, $$y-$$coordinate and $$z-$$coordinate of a point inside this domain ($$x_{i},y_{i},z_{i}$$); the attribute ($$at_{i}$$) and the maximum volume for tetrahedra ($$mvol_{i}$$) for this region.
The regionlist vector is: $$x_{1}, y_{1}, z_{1}, at_{1}, mvol_{1}, x_{2}, y_{2}, z_{2}, at_{2}, mvol_{2}, \cdots$$.
• nboffacetcl= Number of facets constraints “size of facetcl / 2”).
• facetcl= This array corresponds to facetconstraintlist of TetGenio data structure [HANG2006].
The $$i^{th}$$ facet constraint is defined by the facet marker $$Ref_{i}^{fc}$$ and the maximum area for faces $$marea_{i}^{fc}$$. The facetcl array is: $$Ref_{1}^{fc}, marea_{1}^{fc}, Ref_{2}^{fc}, marea_{2}^{fc}, \cdots$$.
This parameters has no effect if switch q is not selected.
Principal switch parameters in TetGen:
• p Tetrahedralization of boundary.
• q Quality mesh generation.
The bound of Radius-Edge Ratio will be given after the option q. By default, this value is 2.0.
• a Constructs with the volume constraints on tetrahedra.
These volumes constraints are defined with the bound of the previous switch q or in the parameter regionlist.
• A Attributes reference to region given in the regionlist.
The other regions have label 0.
The option AA gives a different label at each region. This switch works with the option p. If option r is used, this switch has no effect.
• r Reconstructs and Refines a previously generated mesh.
This character is only used with the command line tetgreconstruction.
• Y This switch preserves the mesh on the exterior boundary.
This switch must be used to ensure a conformal mesh between two adjacent meshes.
• YY This switch preserves the mesh on the exterior and interior boundary.
• C The consistency of the result’s mesh is testing by TetGen.
• CC The consistency of the result’s mesh is testing by TetGen and also constrained checks of Delaunay mesh (if p switch is selected) or the consistency of Conformal Delaunay (if q switch is selected).
• V Give information of the work of TetGen.
More information can be obtained in specified VV or VVV.
• Q Quiet: No terminal output except errors
• M The coplanar facets are not merging.
• T Sets a tolerance for coplanar test.
The default value is $$1e-8$$.
• d Intersections of facets are detected.
To obtain a tetrahedral mesh with TetGen, we need the surface mesh of a three dimensional domain. We now give the command line in FreeFEM to construct these meshes.
The keyword tetgtransfo
This keyword corresponds to a composition of command line tetg and movemesh23.
1 tetgtransfo(Th2, transfo=[Phi(1), Phi(2), Phi(3)]), ...) = tetg(Th3surf, ...),
where Th3surf = movemesh23(Th2, transfo=[Phi(1), Phi(2), Phi(3)]) and Th2 is the input two dimensional mesh of tetgtransfo.
The parameters of this command line are, on one hand, the parameters label, switch, regionlist, nboffacetcl, facetcl of keyword tetg and on the other hand, the parameter ptmerge of keyword movemesh23.
Note
To use tetgtransfo, the result’s mesh of movemesh23 must be a closed surface and define one region only. Therefore, the parameter regionlist is defined for one region.
An example of this keyword can be found in line 61 of the Build layer mesh example.
The keyword tetgconvexhull
FreeFEM, using TetGen, is able to build a tetrahedralization from a set of points. This tetrahedralization is a Delaunay mesh of the convex hull of the set of points.
The coordinates of the points can be initialized in two ways. The first is a file that contains the coordinate of points $$X_{i}=(x_{i}, y_{i}, z_{i})$$. This file is organized as follows:
$\begin{split}\begin{array}{ccc} n_{v} & & \\ x_{1} & y_{1} & z_{1} \\ x_{2} & y_{2} & z_{2} \\ \vdots &\vdots & \vdots \\ x_{n_v} & y_{n_v} & z_{n_v} \end{array}\end{split}$
The second way is to give three arrays that correspond respectively to the $$x-$$coordinates, $$y-$$coordinates and $$z-$$coordinates.
The parameters of this command line are :
• switch= A string expression.
This string corresponds to the command line switch of TetGen see Section 3.2 of [HANG2006].
• reftet= An integer expression.
Set the label of tetrahedra.
• label= An integer expression.
Set the label of triangles.
In the string switch, we can’t used the option p and q of TetGen.
### Reconstruct/Refine a 3d mesh with TetGen
Meshes in three dimension can be refined using TetGen with the command line tetgreconstruction.
The parameter of this keyword are
• region= an integer array that changes the region number of tetrahedra.
This array is defined as the parameter reftet in the keyword change.
• label= an integer array that changes the label of boundary triangles.
This array is defined as the parameter label in the keyword change.
• sizeofvolume= a reel function.
This function constraints the volume size of the tetrahedra in the domain (see Isotrope mesh adaption section to build a 3d adapted mesh).
The parameters switch, nbofregions, regionlist, nboffacetcl and facetcl of the command line which call TetGen (tetg) is used for tetgrefine.
In the parameter switch=, the character r should be used without the character p.
For instance, see the manual of TetGen [HANG2006] for effect of r to other character.
The parameter regionlist defines a new volume constraint in the region. The label in the regionlist will be the previous label of region.
This parameter and nbofregions can’t be used with the parameter sizeofvolume.
**Example refinesphere.edp**
1 load "msh3"
4
5 mesh Th=square(10,20,[x*pi-pi/2,2*y*pi]); // $]\frac{-pi}{2},frac{-pi}{2}[\times]0,2\pi[$
6 // a parametrization of a sphere
7 func f1 =cos(x)*cos(y);
8 func f2 =cos(x)*sin(y);
9 func f3 = sin(x);
10 // partiel derivative of the parametrization DF
11 func f1x=sin(x)*cos(y);
12 func f1y=-cos(x)*sin(y);
13 func f2x=-sin(x)*sin(y);
14 func f2y=cos(x)*cos(y);
15 func f3x=cos(x);
16 func f3y=0;
17 // $M = DF^t DF$
18 func m11=f1x^2+f2x^2+f3x^2;
19 func m21=f1x*f1y+f2x*f2y+f3x*f3y;
20 func m22=f1y^2+f2y^2+f3y^2;
21
22 func perio=[[4,y],[2,y],[1,x],[3,x]];
23 real hh=0.1;
24 real vv= 1/square(hh);
25 verbosity=2;
28 plot(Th,wait=1);
29
30 verbosity=2;
31
32 // construction of the surface of spheres
33 real Rmin = 1.;
34 func f1min = Rmin*f1;
35 func f2min = Rmin*f2;
36 func f3min = Rmin*f3;
37
38 meshS ThS=movemesh23(Th,transfo=[f1min,f2min,f3min]);
39
40 real[int] domain = [0.,0.,0.,145,0.01];
41 mesh3 Th3sph=tetg(ThS,switch="paAAQYY",nbofregions=1,regionlist=domain);
42
43 int[int] newlabel = [145,18];
44 real[int] domainrefine = [0.,0.,0.,145,0.0001];
45 mesh3 Th3sphrefine=tetgreconstruction(Th3sph,switch="raAQ",region=newlabel,nbofregions=1,regionlist=domainrefine,sizeofvolume=0.0001);
46
47 int[int] newlabel2 = [145,53];
48 func fsize = 0.01/(( 1 + 5*sqrt( (x-0.5)^2+(y-0.5)^2+(z-0.5)^2) )^3);
49 mesh3 Th3sphrefine2=tetgreconstruction(Th3sph,switch="raAQ",region=newlabel2,sizeofvolume=fsize);
50
51 medit("sphere",Th3sph,wait=1);
52 medit("sphererefinedomain",wait=1,Th3sphrefine);
53 medit("sphererefinelocal",wait=1,Th3sphrefine2);
54
55 // FFCS: testing 3d plots
56 plot(Th3sph);
57 plot(Th3sphrefine);
58 plot(Th3sphrefine2);
## Read/Write Statements for meshes
### 2d case
#### format of mesh data
Users who want to read a triangulation made elsewhere should see the structure of the file generated below:
1 border C(t=0, 2*pi){x=cos(t); y=sin(t);}
2 mesh Th1 = buildmesh(C(10));
3 savemesh(Th1, "mesh.msh");
The mesh is shown on Fig. 95.
The information about Th are saved in the file mesh.msh whose structure is shown on Table 1. An external file contains a mesh at format .mesh can be read by the ommand readmesh(file_name).
There, $$n_v$$ denotes the number of vertices, $$n_t$$ the number of triangles and $$n_s$$ the number of edges on boundary.
For each vertex $$q^i,\, i=1,\cdots,n_v$$, denoted by $$(q^i_x,q^i_y)$$ the $$x$$-coordinate and $$y$$-coordinate.
Each triangle $$T_k, k=1,\cdots,n_t$$ has three vertices $$q^{k_1},\, q^{k_2},\,q^{k_3}$$ that are oriented counter-clockwise.
The boundary consists of 10 lines $$L_i,\, i=1,\cdots,10$$ whose end points are $$q^{i_1},\, q^{i_2}$$.
In the Fig. 95, we have the following.
$$n_v=14, n_t=16, n_s=10$$
$$q^1=(-0.309016994375, 0.951056516295)$$
$$\dots$$
$$q^{14}=(-0.309016994375, -0.951056516295)$$
The vertices of $$T_1$$ are $$q^9, q^{12},\, q^{10}$$.
$$\dots$$
The vertices of $$T_{16}$$ are $$q^9, q^{10}, q^{6}$$.
The edge of the 1st side $$L_1$$ are $$q^6, q^5$$.
$$\dots$$
The edge of the 10th side $$L_{10}$$ are $$q^{10}, q^6$$.
Table 1 The structure of mesh_sample.msh
Content of the file
Explanation
14 16 10
$$n_v\quad n_t\quad n_e$$
-0.309016994375 0.951056516295 1
0.309016994375 0.951056516295 1
-0.309016994375 -0.951056516295 1
$$q^1_x\quad q^1_y\quad$$ boundary label $$=1$$
$$q^2_x\quad q^2_y\quad$$ boundary label $$=1$$
$$q^{14}_x\quad q^{14}_y\quad$$ boundary label $$=1$$
9 12 10 0
5 9 6 0
9 10 6 0
$$1_1\quad 1_2\quad 1_3\quad$$ region label $$=0$$
$$2_1\quad 2_2\quad 2_3\quad$$ region label $$=0$$
$$16_1\quad 16_2\quad 16_3\quad$$ region label $$=0$$
6 5 1
5 2 1
10 6 1
$$1_1\quad 1_2\quad$$ boundary label $$=1$$
$$2_1\quad 2_2\quad$$ boundary label $$=1$$
$$10_1\quad 10_2\quad$$ boundary label $$=1$$
In FreeFEM there are many mesh file formats available for communication with other tools such as emc2, modulef, … (see Mesh format chapter ).
The extension of a file implies its format. More details can be found on the file format .msh in the article by F. Hecht “bamg : a bidimensional anisotropic mesh generator” [HECHT1998_2].
A mesh file can be read into FreeFEM except that the names of the borders are lost and only their reference numbers are kept. So these borders have to be referenced by the number which corresponds to their order of appearance in the program, unless this number is overwritten by the keyword label. Here are some examples:
1 // Parameters
2 int n = 10;
3
4 // Mesh
5 border floor(t=0, 1){x=t; y=0; label=1;};
6 border right(t=0, 1){x=1; y=t; label=5;};
7 border ceiling(t=1, 0){x=t; y=1; label=5;};
8 border left(t=1, 0){x=0; y=t; label=5;};
9
10 mesh th = buildmesh(floor(n) + right(n) + ceiling(n) + left(n));
11
12 //save mesh in different formats
13 savemesh(th, "toto.am_fmt"); // format "formated Marrocco"
14 savemesh(th, "toto.Th"); // format database db mesh "bamg"
15 savemesh(th, "toto.msh"); // format freefem
16 savemesh(th, "toto.nopo"); // modulef format
17
18 // Fespace
19 fespace femp1(th, P1);
20 femp1 f = sin(x)*cos(y);
21 femp1 g;
22
23 //save the fespace function in a file
24 {
25 ofstream file("f.txt");
26 file << f[] << endl;
27 } //the file is automatically closed at the end of the block
28 //read a file and put it in a fespace function
29 {
30 ifstream file("f.txt");
31 file >> g[] ;
32 }//the file is equally automatically closed
33
34 // Plot
35 plot(g);
36
37 // Mesh 2
39 mesh th2 = readmesh("toto.msh");
40
41 // Fespace 2
42 fespace Vh2(th2, P1);
43 Vh2 u, v;
44
45 // Problem
46 //solve:
47 // $u + \Delta u = g$ in $\Omega$
48 // $u=0$ on $\Gamma_1$
49 // $\frac{\partial u }{\partial n} = g$ on $\Gamma_2$
50 solve Problem(u, v)
51 = int2d(th2)(
52 u*v
53 - dx(u)*dx(v)
54 - dy(u)*dy(v)
55 )
56 + int2d(th2)(
57 - g*v
58 )
59 + int1d(th2, 5)(
60 g*v
61 )
62 + on(1, u=0)
63 ;
64
65 // Plot
66 plot(th2, u);
#### Input/output for a mesh
• the command readmesh
The function readmesh allows to build a mesh from a data file
1 mesh Th=readmeshS("Th.mesh");
2 mesh Thff = readmesh("Thff.msh"); // FreeFEM format
• the command savemesh
The function savemesh allows to export a mesh
1 savemesh(Th,"Th.mesh")
2 savemesh(Thff,"Thff.msh") // FreeFEM format
3
4 savemesh(th, "toto.msh"); // format freefem savemesh(th, "toto.am_fmt"); // format "formated Marrocco"
5 savemesh(th, "toto.Th"); // format database db mesh "bamg"
6 savemesh(th, "toto.nopo"); // modulef format
7 // allows to save the 2d mesh with the 3rd space coordinate as a scalar solution for visualise
8 savemesh(Th,"mm",[x,y,u]); // save surface mesh for medit, see for example minimal-surf.edp
9 exec("medit mm;rm mm.bb mm.faces mm.points");
• the command vtkloadS
The function vtkload allows to build a mesh from a data mesh at vtk format mesh
1 load "iovtk"
• the command savevtk
The function savevtk allows to export a mesh to a data mesh at vtk format mesh
1 load "iovtk"
2 savevtk("Th.vtk",Th);
• the command gmshload
The function gmshloadS allows to build a mesh from a data mesh file at formatmsh (GMSH)
1 load "gmsh"
• the command savegmsh
The function savegmsh allows to export a mesh to a data mesh msh (GMSH)
1 load "gmsh"
2 savegmsh(Th, "Th");
### 3d case
#### format of mesh data
In three dimensions, the file mesh format supported for input and output files by FreeFEM are the extension .msh and .mesh. These formats are described in the Mesh Format section.
Extension file .msh The structure of the files with extension .msh in 3D is given by:
$\begin{split}\begin{array}{cccccc} n_v & n_{tet} & n_{tri} & & \\ q^1_x & q^1_y & q^1_z & Vertex label & \\ q^2_x & q^2_y & q^2_z & Vertex label & \\ \vdots & \vdots & \vdots & \vdots & \\ q^{n_v}_x & q^{n_v}_y & q^{n_v}_z & Vertex label & \\ 1_1 & 1_2 & 1_3 & 1_4 & region label \\ 2_1 & 2_2 & 2_3 & 2_4 & region label \\ \vdots & \vdots & \vdots & \vdots & \vdots \\ (n_{tet})_1 & (n_{tet})_2 & (n_{tet})_3 & (n_{tet})_4 & region label \\ 1_1 & 1_2 & 1_3 & boundary label & \\ 2_1 & 2_2 & 2_3 & boundary label & \\ \vdots & \vdots & \vdots & \vdots & \\ (n_tri)_{1} & (n_{tri})_2 & (n_{tri})_3 & boundary label & \\ \end{array}\end{split}$
In this structure, $$n_v$$ denotes the number of vertices, $$n_{tet}$$ the number of tetrahedra and $$n_{tri}$$ the number of triangles.
For each vertex $$q^i,\, i=1,\cdots,n_v$$, we denote by $$(q^i_x,q^i_y,q^i_z)$$ the $$x$$-coordinate, the $$y$$-coordinate and the $$z$$-coordinate.
Each tetrahedra $$T_k, k=1,\cdots,n_{tet}$$ has four vertices $$q^{k_1},\, q^{k_2},\,q^{k_3}, \,q^{k_4}$$.
The boundary consists of a union of triangles. Each triangle $$tri_j, j=1,\cdots,n_{tri}$$ has three vertices $$q^{j_1},\, q^{j_2},\,q^{j_3}$$.
extension file .mesh The data structure for a three dimensional mesh is composed of the data structure presented in Mesh Format section and a data structure for the tetrahedra. The tetrahedra of a three dimensional mesh are referred using the following field:
1 Tetrahedra
2 NbTetrahedra
3 Vertex1 Vertex2 Vertex3 Vertex4 Label
4 ...
5 Vertex1 Vertex2 Vertex3 Vertex4 Label
6 Triangles
7 NbTriangles
8 Vertex1 Vertex2 Vertex3 Label
9 ...
10 Vertex1 Vertex2 Vertex3 Label
This field is express with the notation of Mesh Format section.
#### Input/output for a mesh3
• the command readmesh3
The function readmesh3 allows to build a mesh3 from a data file
1 mesh3 Th3=readmesh3("Th3.mesh");
2 mesh3 Th3ff = readmesh3("Th3ff.msh"); // FreeFEM format
• the command savemesh
The function savemesh allows to export a mesh3
1 savemesh(Th3,"Th3.mesh")
2 savemesh(Th3ff,"Th3ff.msh") // FreeFEM format
• the command vtkload3
The function vtkload3 allows to build a mesh3 from a data mesh at vtk format mesh
1 load "iovtk"
• the command savevtk
The function savevtk allows to export a mesh3 to a data mesh at vtk format mesh
1 load "iovtk"
2 savevtk("Th3.vtk",Th3);
• the command gmshload3
The function gmshload3 allows to build a mesh3 from a data mesh file at formatmsh (GMSH)
1 load "gmsh"
• the command savegmsh
The function savegmsh allows to export a mesh3 to a data mesh msh (GMSH)
1 load "gmsh"
2 savegmsh(Th3, "Th3");
### Surface 3d case
#### format of mesh data
Like 2d and 3d, the input and output format files supported by FreeFEM are the extension .msh and .mesh. These formats are described in the Mesh Format section.
Extension file .msh The structure of the files with extension .msh in surface 3D is given by:
$\begin{split}\begin{array}{cccccc} n_v & n_{tri} & n_{edges} & & \\ q^1_x & q^1_y & q^1_z & Vertex label & \\ q^2_x & q^2_y & q^2_z & Vertex label & \\ \vdots & \vdots & \vdots & \vdots & \\ q^{n_v}_x & q^{n_v}_y & q^{n_v}_z & Vertex label & \\ 1_1 & 1_2 & 1_3 & region label \\ 2_1 & 2_2 & 2_3 & region label \\ \vdots & \vdots & \vdots & \vdots \\ (n_{tri})_1 & (n_{tri})_2 & (n_{tri})_3 & region label \\ 1_1 & 1_2 & boundary label & \\ 2_1 & 2_2 & boundary label & \\ \vdots & \vdots & \vdots & \\ (n_edge)_{1} & (n_{edge})_2 & boundary label & \\ \end{array}\end{split}$
In this structure, $$n_v$$ denotes the number of vertices, $$n_{tet}$$ the number of tetrahedra and $$n_{tri}$$ the number of triangles.
For each vertex $$q^i,\, i=1,\cdots,n_v$$, we denote by $$(q^i_x,q^i_y,q^i_z)$$ the $$x$$-coordinate, the $$y$$-coordinate and the $$z$$-coordinate.
Each tetrahedra $$T_k, k=1,\cdots,n_{tet}$$ has four vertices $$q^{k_1},\, q^{k_2},\,q^{k_3}, \,q^{k_4}$$.
The boundary consists of a union of triangles. Each triangle $$be_j, j=1,\cdots,n_{tri}$$ has three vertices $$q^{j_1},\, q^{j_2},\,q^{j_3}$$.
extension file .mesh The data structure for a three dimensional mesh is composed of the data structure presented in Mesh Format section and a data structure for the tetrahedra. The tetrahedra of a three dimensional mesh are referred using the following field:
1 MeshVersionFormatted 2
2 Dimension 3
3
4 Vertices
5 NbVertices
6 (v0)x (v0)y (v0)z
7 ...
8 (vn)x (vn)y (vn)z
9
10 Triangles
11 NbTriangles
12 Vertex1 Vertex2 Vertex3 Label
13 ...
14 Vertex1 Vertex2 Vertex3 Label
15
16 Edges
17 NbEdges
18 Vertex1 Vertex2 Label
19 ...
20 Vertex1 Vertex2 Label
21
22 End
This field is express with the notation of Mesh Format section.
#### Input/output for a meshS
• the command readmesh3
The function readmeshS allows to build a meshS from a data file
1 meshS ThS=readmeshS("ThS.mesh");
2 meshS Th3ff = readmeshS("ThSff.msh"); // FreeFEM format
• the command savemesh
The function savemesh allows to export a meshS
1 savemesh(ThS,"ThS.mesh")
2 savemesh(ThSff,"ThSff.msh") // FreeFEM format
• the command vtkloadS
The function vtkloadS allows to build a meshS from a data mesh at vtk format mesh
1 load "iovtk"
• the command savevtk
The function savevtk allows to export a meshS to a data mesh at vtk format mesh
1 load "iovtk"
2 savevtk("ThS.vtk",ThS);
• the command gmshloadS
The function gmshloadS allows to build a meshS from a data mesh file at formatmsh (GMSH)
1 load "gmsh"
• the command savegmsh
The function savegmsh allows to export a meshS to a data mesh msh (GMSH)
1 load "gmsh"
2 savegmsh(ThS, "ThS");
## Medit
The keyword medit allows to display a mesh alone or a mesh and one or several functions defined on the mesh using the Pascal Frey’s freeware medit. medit opens its own window and uses OpenGL extensively. Naturally to use this command medit must be installed.
A vizualisation with medit of scalar solutions $$f1$$ and $$f2$$ continuous, piecewise linear and known at the vertices of the mesh Th is obtained using:
1 medit("sol1 sol2", Th, f1, f2, order=1);
The first plot named sol1 display f1. The second plot names sol2 display f2.
The arguments of the function medit are the name of the differents scenes (separated by a space) of medit, a mesh and solutions.
Each solution is associated with one scene. The scalar, vector and symmetric tensor solutions are specified in the format described in the section dealing with the keyword savesol.
The parameters of this command line are :
• order= 0 if the solution is given at the center of gravity of elements.
1 is the solution is given at the vertices of elements.
• meditff= set the name of execute command of medit.
By default, this string is medit.
• save= set the name of a file .sol or .solb to save solutions.
This command line allows also to represent two differents meshes and solutions on them in the same windows. The nature of solutions must be the same. Hence, we can vizualize in the same window the different domains in a domain decomposition method for instance. A vizualisation with medit of scalar solutions $$h1$$ and $$h2$$ at vertices of the mesh Th1 and Th2 respectively are obtained using:
1 medit("sol2domain", Th1, h1, Th2, h2, order=1);
Tip
Medit
1 load "medit"
2
3 // Initial Problem:
4 // Resolution of the following EDP:
5 // -Delta u_s = f on \Omega = { (x,y) | 1 <= sqrt(x^2+y^2) <= 2 }
6 // -Delta u_1 = f1 on \Omega_1 = { (x,y) | 0.5 <= sqrt(x^2+y^2) <= 1. }
7 // u = 1 on Gamma
8 // Null Neumman condition on Gamma_1 and on Gamma_2
9 // We find the solution u by solving two EDP defined on domain Omega and Omega_1
10 // This solution is visualize with medit
11
12 verbosity=3;
13
14 // Mesh
15 border Gamma(t=0, 2*pi){x=cos(t); y=sin(t); label=1;};
16 border Gamma1(t=0, 2*pi){x=2*cos(t); y=2*sin(t); label=2;};
17 border Gamma2(t=0, 2*pi){x=0.5*cos(t); y=0.5*sin(t); label=3;};
18
19 mesh Th = buildmesh(Gamma1(40) + Gamma(-40)); //Omega
20 mesh Th1 = buildmesh(Gamma(40) + Gamma2(-40)); //Omega_1
21
22 // Fespace
23 fespace Vh(Th, P2);
24 func f = sqrt(x*x + y*y);
25 Vh us, v;
26
27 fespace Vh1(Th1, P2);
28 func f1 = 10*sqrt(x*x+y*y);
29 Vh1 u1, v1;
30
31 // Macro
32 macro Grad2(us) [dx(us), dy(us)] // EOM
33
34 // Problem
35 problem Lap2dOmega (us, v, init=false)
36 = int2d(Th)(
38 )
39 - int2d(Th)(
40 f*v
41 )
42 +on(1, us=1)
43 ;
44
45 problem Lap2dOmega1 (u1, v1, init=false)
46 = int2d(Th1)(
48 )
49 - int2d(Th1)(
50 f1*v1
51 )
52 + on(1, u1=1)
53 ;
54
55 // Solve
56 Lap2dOmega;
57 Lap2dOmega1;
58
59 // Plot with medit
60 medit("solution", Th, us, Th1, u1, order=1, save="testsavemedit.solb");
## Mshmet
Mshmet is a software developed by P. Frey that allows to compute an anisotropic metric based on solutions (i.e. Hessian-based). This software can return also an isotropic metric. Moreover, mshmet can also construct a metric suitable for levelset interface capturing. The solution can be defined on 2D or 3D structured/unstructured meshes. For example, the solution can be an error estimate of a FE solution.
Solutions for mshmet are given as an argument. The solution can be a func, a vector func, a symmetric tensor, a fespace function, a fespace vector function and a fespace symmetric tensor. The symmetric tensor argument is defined as this type of data for datasol argument. This software accepts more than one solution.
For example, the metric $$M$$ computed with mshmet for the solution $$u$$ defined on the mesh $$Th$$ is obtained by writing:
1 fespace Vh(Th, P1);
2 Vh u; //a scalar fespace function
3 real[int] M = mshmet(Th, u);
The parameters of the keyword mshmet are :
• normalization = (b) do a normalization of all solution in $$[0,1]$$.
• aniso = (b) build anisotropic metric if 1 (default 0: isotropic)
• levelset = (b) build metric for levelset method (default: false)
• verbosity = (l) level of verbosity
• nbregul = (l) number of regularization’s iteration of solutions given (default 0).
• hmin = (d)
• hmax = (d)
• err = (d) level of error.
• width = (d) the width
• metric = a vector of double.
This vector contains an initial metric given to mshmet. The structure of the metric vector is described in the next paragraph.
• loptions = a vector of integer of size 7.
This vector contains the integer parameters of mshmet (for expert only).
• loptions(0): normalization (default 1).
• loptions(1): isotropic parameters (default 0).
1 for isotropic metric results otherwise 0.
• loptions(2): level set parameters (default 0).
1 for building level set metric otherwise 0.
• loptions(3): debug parameters (default 0).
1 for turning on debug mode otherwise 0.
• loptions(4): level of verbosity (default 10).
• loptions(5): number of regularization’s iteration of solutions given (default 0).
• loptions(6): previously metric parameter (default 0).
1 for using previous metric otherwise 0.
• doptions= a vector of double of size 4.
This vector contains the real parameters of mshmet (for expert only).
• doptions(0): hmin : min size parameters (default 0.01).
• doptions(1): hmax : max size parameters (default 1.0).
• doptions(2): eps : tolerance parameters (default 0.01).
• doptions(2): width : relative width for Level Set ($$0<w<1$$) (default 0.05).
The result of the keyword mshmet is a real[int] which contains the metric computed by mshmet at the different vertices $$V_{i}$$ of the mesh.
With $$nv$$ is the number of vertices, the structure of this vector is:
$M_{iso}= (m(V_0), m(V_1), \ldots, m(V_{nv}))^t$
for a isotropic metric $$m$$. For a symmetric tensor metric $$h=\left(\begin{array}{ccc} m_{1 1} & m_{1 2} & m_{1 3}\\ m_{2 1} & m_{2 2} & m_{2 3} \\ m_{3 1} & m_{3 2} & m_{3 3} \end{array}\right)$$ , the parameters metric is:
$M_{aniso}= (H(V_{0}), \ldots, H(V_{nv}) )^t$
where $$H(V_{i})$$ is the vector of size 6 defined by $$[m11,m21,m22,m31,m32,m33]$$
Tip
mshmet
1 load "mshmet"
4
5 // Parameters
6 real error = 0.01;
7 func zmin = 0;
8 func zmax = 1;
9 int MaxLayer = 10;
10
11 // Mesh
12 border a(t=0, 1.0){x=t; y=0; label=1;};
13 border b(t=0, 0.5){x=1; y=t; label=2;};
14 border c(t=0, 0.5){x=1-t; y=0.5; label=3;};
15 border d(t=0.5, 1){x=0.5; y=t; label=4;};
16 border e(t=0.5, 1){x=1-t; y=1; label=5;};
17 border f(t=0.0, 1){x=0; y=1-t; label=6;};
18 mesh Th = buildmesh(a(6) + b(4) + c(4) + d(4) + e(4) + f(6));
19 mesh3 Th3 = buildlayers(Th, MaxLayer, zbound=[zmin, zmax]);
20
21 // Fespace
22 fespace Vh3(Th3, P2);
23 Vh3 u3, v3;
24
25 fespace Vh3P1(Th3, P1);
26 Vh3P1 usol;
27
28 // Problem
29 problem Problem2(u3, v3, solver=sparsesolver)
30 = int3d(Th3)(
31 u3*v3*1.0e-10
32 + dx(u3)*dx(v3)
33 + dy(u3)*dy(v3)
34 + dz(u3)*dz(v3)
35 )
36 - int3d(Th3)(
37 v3
38 )
39 +on(0, 1, 2, 3, 4, 5, 6, u3=0)
40 ;
41
42 // Solve
43 Problem2;
44 cout << u3[].min << " " << u3[].max << endl;
45
46 medit("Sol", Th3, u3);
47
48 real[int] bb = mshmet(Th3,u3);
49 cout << "Metric:" << bb << endl;
50 for (int ii = 0; ii < Th3.nv; ii++)
51 usol[][ii] = bb[ii];
52
53 medit("Metric", Th3, usol);
## FreeYams
FreeYams is a surface mesh adaptation software which is developed by P. Frey. This software is a new version of yams. The adapted surface mesh is constructed with a geometric metric tensor field. This field is based on the intrinsic properties of the discrete surface.
Also, this software allows to construct a simplification of a mesh. This decimation is based on the Hausdorff distance between the initial and the current triangulation. Compared to the software yams, FreeYams can be used also to produce anisotropic triangulations adapted to levelset simulations. A technical report on freeYams documentation is available here.
To call FreeYams in FreeFEM, we used the keyword freeyams. The arguments of this function are the initial mesh and/or metric. The metric with freeyams are a func, a fespace function, a symmetric tensor function, a symmetric tensor fespace function or a vector of double (real[int]). If the metric is a vector of double, this data must be given in metric parameter. Otherwise, the metric is given in the argument.
For example, the adapted mesh of Thinit defined by the metric $$u$$ defined as fespace function is obtained by writing:
1 fespace Vh(Thinit, P1);
2 Vh u;
3 mesh3 Th = freeyams(Thinit, u);
The symmetric tensor argument for freeyams keyword is defined as this type of data for datasol argument.
• aniso= (b) aniso or iso metric (default 0, iso)
• mem= (l) memory of for freeyams in Mb (default -1, freeyams choose)
• hmin= (d)
• hmax= (d)
• gradation= (d)
• option= (l)
• 0 : mesh optimization (smoothing+swapping)
• 1 : decimation+enrichment adaptated to a metric map. (default)
• -1 : decimation adaptated to a metric map.
• 2 : decimation+enrichment with a Hausdorff-like method
• -2 : decimation with a Hausdorff-like method
• 4 : split triangles recursively.
• 9 : No-Shrinkage Vertex Smoothing
• ridgeangle= (d)
• absolute= (b)
• verbosity= (i)
• metric= vector expression.
This parameters contains the metric at the different vertices on the initial mesh. With $$nv$$ is the number of vertices, this vector is:
$M_{iso}= ( m(V_0), m(V_1), \ldots, m(V_{nv}) )^t$
for a scalar metric $$m$$. For a symmetric tensor metric $$h=\left(\begin{array}{ccc} m_{1 1} & m_{1 2} & m_{1 3}\\ m_{2 1} & m_{2 2} & m_{2 3} \\ m_{3 1} & m_{3 2} & m_{3 3} \end{array}\right)$$, the parameters metric is:
$M_{aniso}= ( H(V_{0}), \ldots, H(V_{nv}) )^t$
where $$H(V_{i})$$ is the vector of size 6 defined by $$[m11,m21,m22,m31,m32,m33]$$
• loptions= a vector of integer of size 13.
This vectors contains the integer options of FreeYams. (just for the expert)
• loptions(0): anisotropic parameter (default 0).
If you give an anisotropic metric 1 otherwise 0.
• loptions(1): Finite Element correction parameter (default 0).
1 for no Finite Element correction otherwise 0.
• loptions(2): Split multiple connected points parameter (default 1).
1 for splitting multiple connected points otherwise 0.
• loptions(3): maximum value of memory size in Mbytes (default -1: the size is given by freeyams).
• loptions(4): set the value of the connected component which we want to obtain.
(Remark: freeyams give an automatic value at each connected component).
• loptions(5): level of verbosity
• loptions(6): Create point on straight edge (no mapping) parameter (default 0).
1 for creating point on straight edge otherwise 0.
• loptions(7): validity check during smoothing parameter.
This parameter is only used with No-Shrinkage Vertex Smoothing optimization (optimization option parameter 9). 1 for No validity checking during smoothing otherwise 0.
• loptions(8): number of desired’s vertices (default -1).
• loptions(9): number of iteration of optimizations (default 30).
• loptions(10): no detection parameter (default 0).
1 for detecting the ridge on the mesh otherwise 0. The ridge definition is given in the parameter doptions(12).
• loptions(11): no vertex smoothing parameter (default 0).
1 for smoothing the vertices otherwise 0.
• loptions(12): Optimization level parameter (default 0).
• 0 : mesh optimization (smoothing+swapping)
• 1 : decimation+enrichment adaptated to a metric map.
• -1: decimation adaptated to a metric map.
• 2 : decimation+enrichment with a Hausdorff-like method
• -2: decimation with a Hausdorff-like method
• 4 : split triangles recursively.
• 9 : No-Shrinkage Vertex Smoothing
• doptions= a vector of double of size 11.
This vectors contains the real options of freeyams.
• doptions(0): Set the geometric approximation (Tangent plane deviation) (default 0.01).
• doptions(1): Set the lamda parameter (default -1).
• doptions(2): Set the mu parmeter (default -1).
• doptions(3): Set the gradation value (Mesh density control) (default 1.3).
• doptions(4): Set the minimal size(hmin) (default -2.0: the size is automatically computed).
• doptions(5): Set the maximal size(hmax) (default -2.0: the size is automatically computed).
• doptions(6): Set the tolerance of the control of Chordal deviation (default -2.0).
• doptions(7): Set the quality of degradation (default 0.599).
• doptions(8): Set the declic parameter (default 2.0).
• doptions(9): Set the angular walton limitation parameter (default 45 degree).
• doptions(10): Set the angular ridge detection (default 45 degree).
Tip
freeyams
1 load "msh3"
4
5 // Parameters
6 int nn = 20;
7 real zmin = 0;
8 real zmax = 1;
9
10 // Mesh
11 mesh Th2 = square(nn, nn);
12 int[int] rup = [0, 2], rdown = [0, 1];
13 int[int] rmid = [1, 1, 2, 1, 3, 1, 4, 1];
14 mesh3 Th = buildlayers(Th2, nn, zbound=[zmin, zmax], reffacemid=rmid, reffaceup=rup, reffacelow=rdown);
15 mesh3 Th3 = freeyams(Th);
16
17 medit("SurfaceMesh", Th3);
## mmg3d
Todo
mmg3d-v4.0
Mmg3d is a 3D remeshing software developed by C. Dobrzynski and P. Frey.
This software allows to remesh an initial mesh made of tetrahedra. This initial mesh is adapted to a geometric metric tensor field or to a displacement vector (moving rigid body). The metric can be obtained with mshmet.
Note
• If no metric is given, an isotropic metric is computed by analyzing the size of the edges in the initial mesh.
• If a displacement is given, the vertices of the surface triangles are moved without verifying the geometrical structure of the new surface mesh.
The parameters of mmg3d are :
• options= vector expression.
This vector contains the option parameters of mmg3d. It is a vector of 6 values, with the following meaning:
• Optimization parameters : (default 1)
0 : mesh optimization.
1 : adaptation with metric (deletion and insertion vertices) and optimization.
-1 : adaptation with metric (deletion and insertion vertices) without optimization.
4 : split tetrahedra (be careful modify the surface).
9 : moving mesh with optimization.
-9 : moving mesh without optimization.
• Debug mode : (default 0)
1 : turn on debug mode.
0 : otherwise.
• Specify the size of bucket per dimension (default 64)
• Swapping mode : (default 0)
1 : no edge or face flipping.
0 : otherwise.
• Insert points mode : (default 0)
1 : no edge splitting or collapsing and no insert points.
0 : otherwise.
1. Verbosity level (default 3)
• memory= integer expression.
Set the maximum memory size of new mesh in Mbytes. By default the number of maximum vertices, tetrahedra and triangles are respectively 500 000, 3000 000, 100000 which represent approximately a memory of 100 Mo.
• metric= vector expression.
This vector contains the metric given at mmg3d. It is a vector of size $$nv$$ or 6 $$nv$$ respectively for an isotropic and anisotropic metric where $$nv$$ is the number of vertices in the initial mesh. The structure of metric vector is described in the mshmet.
• displacement= $$[\Phi1, \Phi2, \Phi3]$$ set the displacement vector of the initial mesh $$\mathbf{\Phi(x,y)} = [\Phi1(x,y), \Phi2(x,y), \Phi3(x,y)]$$.
• displVect= sets the vector displacement in a vector expression.
This vector contains the displacement at each point of the initial mesh. It is a vector of size 3 $$nv$$.
Tip
mmg3d
1 load "msh3"
4 include "Cube.idp"
5
6 // Parameters
7 int n = 6;
8 int[int] Nxyz = [12, 12, 12];
9 real [int, int] Bxyz = [[0., 1.], [0., 1.], [0., 1.]];
10 int [int, int] Lxyz = [[1, 1], [2, 2], [2, 2]];
11
12 // Mesh
13 mesh3 Th = Cube(Nxyz, Bxyz, Lxyz);
14
15 real[int] isometric(Th.nv);
16 for (int ii = 0; ii < Th.nv; ii++)
17 isometric[ii] = 0.17;
18
19 mesh3 Th3 = mmg3d(Th, memory=100, metric=isometric);
20
21 // Plot
22 medit("Initial", Th);
23 medit("Isometric", Th3);
Tip
Falling spheres
1 load "msh3"
5 include "MeshSurface.idp"
6
7 // Parameters
8 real hs = 0.8;
9 int[int] N = [4/hs, 8/hs, 11.5/hs];
10 real [int, int] B = [[-2, 2], [-2, 6], [-10, 1.5]];
11 int [int, int] L = [[311, 311], [311, 311], [311, 311]];
12
13 int[int] opt = [9, 0, 64, 0, 0, 3];
14 real[int] vit=[0, 0, -0.3];
15 func zero = 0.;
16 func dep = vit[2];
17
18 // Meshes
19 meshS ThH = SurfaceHex(N, B, L, 1);
20 meshS ThSg = Sphere(1, hs, 300, -1);
21 meshS ThSd = Sphere(1, hs, 310, -1);
22 ThSd = movemesh(ThSd, [x, 4+y, z]);
23 meshS ThHS = ThH + ThSg + ThSd;
24 medit("ThHS", ThHS);
25
26 real voltet = (hs^3)/6.;
27 real[int] domain = [0, 0, -4, 1, voltet];
28 real [int] holes = [0, 0, 0, 0, 4, 0];
29 mesh3 Th = tetg(ThHS, switch="pqaAAYYQ", nbofregions=1, regionlist=domaine, nbofholes=2, holelist=holes);
30 medit("Box-With-two-Ball", Th);
31
32 // Fespace
33 fespace Vh(Th, P1);
34 Vh uh,vh;
35
36 // Macro
37 macro Grad(u) [dx(u),dy(u),dz(u)]
38
39 // Problem
40 problem Lap (uh, vh, solver=CG)
41 = int3d(Th)(
43 )
44 + on(310, 300, uh=dep)
45 + on(311, uh=0.)
46 ;
47
48 // Falling loop
49 for(int it = 0; it < 29; it++){
50 cout << " ITERATION " << it << endl;
51
52 // Solve
53 Lap;
54
55 // Plot
56 plot(Th, uh);
57
58 // Sphere falling
59 Th = mmg3d(Th, options=opt, displacement=[zero, zero, uh], memory=1000);
60 }
## A first 3d isotrope mesh adaptation process
Tip
1 load "msh3"
5
6 // Parameters
7 int nn = 6;
8 int[int] l1111 = [1, 1, 1, 1]; //labels
9 int[int] l01 = [0, 1];
10 int[int] l11 = [1, 1];
11
12 real errm = 1e-2; //level of error
13
14 // Mesh
15 mesh3 Th3 = buildlayers(square(nn, nn, region=0, label=l1111),
16 nn, zbound=[0, 1], labelmid=l11, labelup=l01, labeldown=l01);
17
18 Th3 = trunc(Th3, (x<0.5) | (y < 0.5) | (z < 0.5), label=1); //remove the ]0.5,1[^3 cube
19
20 // Fespace
21 fespace Vh(Th3, P1);
22 Vh u, v, usol, h;
23
24 // Macro
25 macro Grad(u) [dx(u), dy(u), dz(u)] // EOM
26
27 // Problem
28 problem Poisson (u, v, solver=CG)
29 = int3d(Th3)(
31 )
32 - int3d(Th3)(
33 1*v
34 )
35 + on(1, u=0)
36 ;
37
38 // Loop
39 for (int ii = 0; ii < 5; ii++){
40 // Solve
41 Poisson;
42 cout << "u min, max = " << u[].min << " "<< u[].max << endl;
43
44 h=0.; //for resizing h[] because the mesh change
45 h[] = mshmet(Th3, u, normalization=1, aniso=0, nbregul=1, hmin=1e-3, hmax=0.3, err=errm);
46 cout << "h min, max = " << h[].min << " "<< h[].max << " " << h[].n << " " << Th3.nv << endl;
47 plot(u, wait=true);
48
49 errm *= 0.8; //change the level of error
50 cout << "Th3 " << Th3.nv < " " << Th3.nt << endl;
51 Th3 = tetgreconstruction(Th3, switch="raAQ", sizeofvolume=h*h*h/6.); //rebuild mesh
52 medit("U-adap-iso-"+ii, Th3, u, wait=true);
53 }
## Build a 2d mesh from an isoline
The idea is to get the discretization of an isoline of fluid meshes, this tool can be useful to construct meshes from image. First, we give an example of the isovalue meshes $$0.2$$ of analytical function $$\sqrt{(x-1/2)^2 +(y-1/2)^2}$$, on unit square.
1 load "isoline"
2
3 real[int,int] xy(3, 1); //to store the isoline points
4 int[int] be(1); //to store the begin, end couple of lines
5 {
6 mesh Th = square(10, 10);
7 fespace Vh(Th, P1);
8 Vh u = sqrt(square(x-0.5) + square(y-0.5));
9 real iso = 0.2 ;
10 real[int] viso = [iso];
11 plot(u, viso=viso,Th);//to see the iso line
12
13 int nbc = isoline(Th, u, xy, close=1, iso=iso, beginend=be, smoothing=0.1);
The isoline parameters are Th the mesh, the expression $$u$$, the bidimentionnal array xy to store the list coordinate of the points. The list of named parameter are :
• iso= value of the isoline to compute (0 is the default value)
• close= close the isoline with the border (default true), we add the part of the mesh border such the value is less than the isovalue
• smoothing= number of smoothing process is the $${l} ^{r} {s}$$ where $$l$$ is the length of the current line component, $$r$$ the ratio, $$s$$ is smoothing value. The smoothing default value is 0.
• ratio= the ratio (1 by default).
• eps= relative $$\varepsilon$$ (default 1e-10)
• beginend= array to get begin, end couple of each of sub line (resize automatically)
• file= to save the data curve in data file for gnuplot
In the array xy you get the list of vertices of the isoline, each connex line go from $$i= i_0^c ,\dots, i_1^c-1$$ with $$i_0^c =be(2*c)$$ $$i_1^c =be(2*c+1)$$, and where $$x_i= xy(0,i), y_i=yx( 1,i), l_i=xy(2,i)$$.
Here $$l_i$$ is the length of the line (the origin of the line is point $$i_0^c$$).
The sense of the isoline is such that the upper part is at the left size of the isoline. So here : the minimum is a point $$0.5,05$$ so the curve 1 turn in the clockwise sense, the order of each component are sort such that the number of point by component is decreasing.
1 cout << "Number of the line component = " << nbc << endl;
2 cout << "Number of points = " << xy.m << endl;
3 cout << "be = " << be << endl;
4
5 // shows the lines component
6 for (int c = 0; c < nbc; ++c){
7 int i0 = be[2*c], i1 = be[2*c+1]-1;
8 cout << "Curve " << c << endl;
9 for(int i = i0; i <= i1; ++i)
10 cout << "x= " << xy(0,i) << " y= " << xy(1,i) << " s= " << xy(2, i) << endl;
11 plot([xy(0, i0:i1), xy(1, i0:i1)], wait=true, viso=viso, cmm=" curve "+c);
12 }
13 }
14
15 cout << "length of last curve = " << xy(2, xy.m-1) << endl;
We also have a new function to easily parametrize a discrete curve defined by the couple $$be, xy$$.
1 border Curve0(t=0, 1){
2 int c=0; //component 0
3 int i0=be[2*c], i1=be[2*c+1]-1;
4 P=Curve(xy, i0, i1, t); //Curve 0
5 label=1;
6 }
7
8 border Curve1(t=0, 1){
9 int c=1; //component 1
10 int i0=be[2*c], i1=be[2*c+1]-1;
11 P=Curve(xy, i0, i1, t); //Curve 1
12 label=1;
13 }
14
15 plot(Curve1(100)); //show curve
16 mesh Th = buildmesh(Curve1(-100));
17 plot(Th, wait=true);
Secondly, we use this idea to build meshes from an image, we use the plugins ppm2rnm to read pgm a gray scale image and then we extract the gray contour at level 0.25.
Tip
Leman lake
1 load "ppm2rnm"
3
4 // Parameters
5 string leman = "LemanLake.pgm";
6 real AreaLac = 580.03; //in km^2
7 real hsize = 5;
8 real[int, int] Curves(3, 1);
9 int[int] be(1);
10 int nc; //nb of curve
11 {
12 real[int, int] ff1(leman); //read image
13 //and set it in a rect. array
14 int nx = ff1.n, ny = ff1.m;
15 //build a Cartesian mesh such that the origin is in the right place.
16 mesh Th = square(nx-1, ny-1, [(nx-1)*(x), (ny-1)*(1-y)]);
17 //warning the numbering of the vertices (x,y) is
18 //given by $i = x/nx + nx* y/ny$
19 fespace Vh(Th, P1);
20 Vh f1;
21 f1[] = ff1; //transform array in finite element functions.
22 nc = isoline(Th, f1, iso=0.25, close=1, Curves, beginend=be, smoothing=.1, ratio=0.5);
23 }
24
25 //The longest isoline: the lake
26 int ic0 = be(0), ic1 = be(1)-1;
27 plot([Curves(0, ic0:ic1), Curves(1, ic0:ic1)], wait=true);
28
29 int NC = Curves(2, ic1)/hsize;
30 real xl = Curves(0, ic0:ic1).max - 5;
31 real yl = Curves(1, ic0:ic1).min + 5;
32 border G(t=0, 1){P=Curve(Curves, ic0, ic1, t); label=1+(x>xl)*2+(y<yl);}
33 plot(G(-NC), wait=true);
34
35 mesh Th = buildmesh(G(-NC));
36 plot(Th, wait=true);
37
38 real scale = sqrt(AreaLac/Th.area);
39 Th = movemesh(Th, [x*scale, y*scale]);
40 cout << "Th.area = " << Th.area << " Km^2 " << " == " << AreaLac << " Km^2 " << endl;
41 plot(Th, wait=true, ps="leman.eps");
Isoline
|
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|
https://www.scipost.org/SciPostPhys.11.2.046
|
## Chiral anomaly trapped in Weyl metals: Nonequilibrium valley polarization at zero magnetic field
Pablo M. Perez-Piskunow, Nicandro Bovenzi, Anton R. Akhmerov, Maxim Breitkreiz
SciPost Phys. 11, 046 (2021) · published 31 August 2021
### Abstract
In Weyl semimetals the application of parallel electric and magnetic fields leads to valley polarization -- an occupation disbalance of valleys of opposite chirality -- a direct consequence of the chiral anomaly. In this work, we present numerical tools to explore such nonequilibrium effects in spatially confined three-dimensional systems with a variable disorder potential, giving exact solutions to leading order in the disorder potential and the applied electric field. Application to a Weyl-metal slab shows that valley polarization also occurs without an external magnetic field as an effect of chiral anomaly "trapping": Spatial confinement produces chiral bulk states, which enable the valley polarization in a similar way as the chiral states induced by a magnetic field. Despite its finite-size origin, the valley polarization can persist up to macroscopic length scales if the disorder potential is sufficiently long ranged, so that direct inter-valley scattering is suppressed and the relaxation then goes via the Fermi-arc surface states.
### Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.
Funders for the research work leading to this publication
|
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|
https://pretextbook.org/doc/guide/html/xsltproc-setup.html
|
## Section44.1Setup
There are two components to processing your document, the PreTeXt stylesheets and the xsltproc program. We work at the command-line inside of a terminal or console . If you do not know what this is, it will seem very primitive at first. Sometimes the old ways are the best ways. This will be called a “Command Prompt” in Windows or a “Terminal” on a Mac. In Linux it may be known as a “console” or a “shell”. A tutorial, which is Linux-specific, can be found at Ryan's Tutorials 1 and certainly others exist.
The operating system on a Mac is built on Unix, which is very similar to Linux, so most of the directions here will be little changed between the two. Procedures can be very different in Windows (Appendix J ,Appendix K ). One alternative is CoCalc 2 which provides a full Linux computer for free in your web browser, so that may be an excellent place for initial experiments (Section 5.15 ).
### Step 1: PreTeXt.
You need to obtain the PreTeXt stylesheets, which are the main part of PreTeXt . Since you are reading this, it may be possible that you have this already. You can use git to clone the PreTeXt from the GitHub repository, and then be sure to checkout the dev branch to have the latest version. This is the best way to go, and you should only download the repository as a zip file once for an initial experiment, and then switch to using a clone instead.
Once you have a clone of the repository, you can issue git pull, and git will update your local copy with any recent changes. You should do this regularly — meaning on the order of daily. See the FAQ entry for more about why we expect you to do this.
See the PreTeXt site 3 for details and commands for this step, right on the main page.
### Step 2: xsltproc.
This is the command-line program which takes your document and a PreTeXt stylesheet to together produce output. On Linux or a Mac you probably already have it installed as part of system software. On Windows it is not so simple.
In either case see the website for details abut verifying you have this, or how to install it.
ryanstutorials.net/linuxtutorial/
cocalc.com
pretextbook.org
|
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|
https://bitbucket.org/anthony_tuininga/cx_freeze/src/8913025af703/doc/script.rst?at=tip
|
Full commit
# cxfreeze script
The cxfreeze script is included with other Python scripts. On Windows and the Mac this is in the Scripts subdirectory of your Python installation whereas on Unix platforms this in the bin directory of the prefix where Python is installed.
Assuming you have a script called hello.py which you want to turn into an executable, this can be accomplished by this command:
cxfreeze hello.py --target-dir dist
Further customization can be done using the following options:
option name description
--version show version number and exit
-h, --help show this help message and exit
-O optimize generated bytecode as per PYTHONOPTIMIZE; use -OO in order to remove doc strings
-c, --compress compress byte code in zip files
-s, --silent suppress all output except warnings
--base-name file on which to base the executable; if the name of the file is not an absolute file name, the subdirectory bases inside the cx_Freeze package will be searched for a file matching the name, without regard to the extension
--init-script script which will be executed upon startup; if the name of the file is not an absolute file name, the subdirectory initscripts inside the cx_Freeze package will be searched for a file matching the name, without regard to the extension
--target-dir directory in which to place the executable and any dependent files
--target-name the name of the file to create; the default is the base name of the script and the extension of the base executable name
--shared-name the name of the file to create; the default is the base name of the script and the extension of the base executable name
--no-copy-deps do not copy any dependent files (extensions, shared libraries, etc.) to the target directory; this also modifies the default init script to ConsoleKeepPath and means that the target executable requires a Python installation to execute properly
--default-path list of paths separated by the standard path separator for the platform which will be used to initialize the search path instead of sys.path
--include-path list of paths separated by the standard path separator for the platform which will be used to add to the search path
--replace-paths replace all the paths in modules found in the given paths with the given replacement string; multiple values are separated by the standard path separator for the platform and each value is of the form <search>=<replace>; <search> can be * which means all paths not already specified
--include-modules comma separated list of names of modules to include
--exclude-modules comma separated list of names of modules to exclude
--ext-list-file name of file in which to place the list of dependent files which were copied to the target directory
-z, --zip-include name of file to add to the zip file or a specification of the form <name>=<arcname> which will specify the archive name to use; multiple --zip-include arguments can be used
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https://mpdf.github.io/what-else-can-i-do/overwriting-existing-files.html
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mPDF Manual – What Else Can I Do
# Overwriting existing files
(mPDF >= 2.3)
Using Overwrite() function, an existing PDF file can be overwritten, replacing specified text with alternatives. For example you may have created a long complex PDF file, and you wish to produce copies with an individual number on each copy without having to re-generate the whole document each time.
Use first SetImportUse() to enable pdf import functions.
## See
• OverWrite() - Replace specified text strings in an existing PDF file
• SetImportUse() - Enable functions to import PDF files into document
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https://www.physicsforums.com/threads/newtons-law-application.16911/
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# Newton's law application
1. Mar 23, 2004
### nutzweb
hey guys! i need some help, a big help. this is urgent... can somebodyhelp me solve this problem:
what force, applied parallel to the plane, is necessary to move a 16 kg object up africtionless palne with a uniform acceleration of 2.0 m/s2 if the plane makes an angle of 60 degrees with the horizontal?
pls somebody help me. i really need it badly. hope somebody would reply today. thanks...
2. Mar 23, 2004
### outandbeyond2004
Is the plane on the surface of earth, so that the body is subject to a gravitational force of (16 kg)*(9.8 m/s^2)?
Is the acceleration wrt the plane or the ground? Makes a big difference.
I assume the answers are yes and wrt the plane.
The NET force necessary to move the body 2 m/s^2 is simply mass * acceleration = (16 kg)*(2 m/s^2).
However, you need more than that to overcome the gravitational force. The body is kept from moving straight down by the plane, so it would only go down the plane with a force of (16 kg)*(9.8 m/s^2)cos 30 degrees. Reverse that force and add to the above ("NET").
Now, I may have made a mistake somewhere, so go over that solution carefully. Don't blame me, it was a rush job, right, boss?
3. Mar 26, 2004
### Staff: Mentor
The component of the object's weight parallel to the plane is $mg\sin\theta$ acting down the plane. The applied force F (acting up the plane) must be enough to overcome that and produce the needed acceleration:
$$F = mg\sin\theta + ma$$
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https://plainmath.net/16508/from-standard-card-deck-what-probability-that-drawn-card-anything-besides
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Question
# From a standard 52-card deck, what is the probability that a drawn card is a club or anything besides a face card?
Upper level probability
From a standard 52-card deck, what is the probability that a drawn card is a club or anything besides a face card?
## Expert Answers (1)
2021-05-04
Clubs account for 1/4 of the cards in the deck. Face cards (Jack, Queen King) account for $$\displaystyle\frac{{3}}{{13}}$$ cards in each suit, leaving $$\displaystyle\frac{{10}}{{13}}$$ per suit.
The probability of the drawn card is as follows: $$P(Clubs) \bigcup P(Facecard)' P(Clubs) =$$ $$\displaystyle\frac{{13}}{{52}}=\frac{{1}}{{4}}$$
$$P(Facecard)' =$$ $$\displaystyle\frac{{40}}{{52}}=\frac{{10}}{{13}}$$
The union of the two possibilities is the possibility of the first, or the the second happening. If the possibilities overlap (a 6 of clubs for example), then that possibility is deducted in the second probability that is added.
$$P(Clubs) \bigcup P(Facecard)'=13/52 + (40/52 - 10/52) = 13/52 + 30/52 = 43/52$$
Your answer is the sum of the clubs suit and the remaining non-face cards in the deck. $$\displaystyle\frac{{43}}{{52}}$$ cards
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https://forum.allaboutcircuits.com/threads/designing-dc-bias-circuit.13628/
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# Designing DC Bias Circuit
#### sparkey2000
Joined Mar 9, 2008
8
Please can someone help me answer the attached question; I can work through examples and calculate IC, IE, VCE, IB and VBE etc.
However I'm stuck with the following question and I will need to do this for an exam this week; and help will be much appreciated.
#### Attachments
• 38.8 KB Views: 44
#### beenthere
Joined Apr 20, 2004
15,808
What results have you got for the problem?
#### yubyub
Joined Aug 13, 2008
19
Rc + Re ~= 16k, since Vcq = Vcc/2, Rc ~= Re = 8k
Ib ~= 6.67µA R1 ~= 2.4M (i think?) R2 = R1?
Those are approximations, and i'm not sure about R1, R2. The lack of working would cause you to get no marks though.
Assuming you have a textbook with BJT's, you should have no problem doing the working out properly.
#### mik3
Joined Feb 4, 2008
4,846
Please can someone help me answer the attached question; I can work through examples and calculate IC, IE, VCE, IB and VBE etc.
However I'm stuck with the following question and I will need to do this for an exam this week; and help will be much appreciated.
Vcq equals 8 volts because it is half the Vcc, thus Rc=(Vcc-Vcq)/Ic
Rc=8V/1mA=8K
then we assume that Ie equals Ic and that Ve equals Vcc/10
thus Re=Ve/Ie=1.6V/1mA=1.6K
then we assume that R2 equals 0.1*150*Re
thus R2=24K
then Vb equals Ve+0.7=2.1V
then make the voltage divider equation to find R1
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http://bsodtutorials.blogspot.ca/2013/
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## Tuesday, 31 December 2013
### Happy New Year 2014 (Almost)
Well, as we all know, it's the first day of 2014 tomorrow; New Year's Day. I thought I would write a very quick blog post wishing all my readers a Happy New Year, just in case I don't have time tomorrow to write one up.
Happy New Year!
## Sunday, 29 December 2013
### Timeout Detection and Recovery (Stop 0x116) Internals
Stop 0x116's and Stop 0x117's are largely the same bugcheck. There is also the Stop 0x119, which is related to the video scheduler causing problems. However, this blog post is going to look at the internals of Timeout Detection and Recovery and explain what this recovery process is, and how it may lead to a Stop 0x116 or Stop 0x117 bugcheck.
Since Windows Vista, Microsoft has introduced a new feature called TDR (Timeout Detection and Recovery), which as the name suggests, enables drivers to recover from hardware time-outs instead of the system completely crashing.
The GPU Scheduler firstly detects a graphics task is taking longer than it should, and goes to preempt this task and it's associated thread. If the GPU Scheduler is unable to complete or premept the task with the TDR Timeout period, then the GPU is considered to be frozen, and the preparation for recovery process begins.
The GPU Scheduler then calls the DxgkDdiResetFromTimeout which informs the graphics driver that the operating system has detected a timeout, and the GPU will need to be reset. The routine also stops the graphics card driver from accessing any form of memory. The routine causes the graphics card driver threads to run synchronously, as a result no other threads are running at the same time as the DxgkDdiResetFromTimeout routine. Furthermore, access to the frame buffer is not permitted and the PLL is also set for the memory controller. The PLL or Phase Locked Loop is used for digital clock signal synchronization for data transfers. A Frame Buffer, on the other hand, is used to store bitmaps of pixels (forming a entire image), and then storing this image in a Video RAM (VRAM) to be sent to the monitor for output. The KeSynchronizeExecution routine may be called to register interrupts and ISRs with graphics related reset routines.
If the DxgkDdiResetFromTimeout routine fails, then the system will bugcheck with a Stop 0x116. Otherwise, the recovery stage will be started and the graphics stack will be reset.
After the DxgkDdiResetFromTimeout routine has returned with STATUS_SUCCESS, then the operating system will begin to clear up any resources which are not being used. Other driver routines may be called here, which I will begin to explain below.
For example, lets begin with the DxgkDdiBuildPagingBuffer routine. This routine is used if a allocation was paged into a memory segment. A short concise explanation of memory segments and video memory should be described here to help explain this routine.
Memory Segments are used by the Miniport driver to describe the GPU's address space to the Video Memory Manager. Each Memory Segments are generally used to organize video memory resources. The driver creates a list of support segment types with the DxgkDdiQueryAdapterInfo routine, and then describes each segment with the
DXGK_SEGMENTDESCRIPTOR data structure.
When the Video Memory Manager wishes to allocate a certain video resource to a memory segment, the driver checks which segment (by the segment identifier) is most suitable for the video resource at hand and request. A allocation is created with the
DxgkDdiCreateAllocation routine, these allocations are then described with the
DXGK_ALLOCATIONINFO data structure.
The information above should be enough to understand, the DxgkDdiBuildPagingBuffer routine and it's role with releasing allocations. When the above routine is called after a reset, a paging buffer is created which is DMA buffer for the use by the GPU.
In this current situation, a paging buffer will be created for a transfer operation, thus the Operation member of the DXGKARG_BUILDPAGINGBUFFER data structure is set to
DXGK_OPERATION_TRANSFER to move the content of one allocation to another.
The Transfer.Size member is set to 0, since the content would have been lost during the reset.
On the other hand, if the Memory Segment was a aperture (physical address space assigned to a external device) memory segment, then the DXGKARG_BUILDPAGINGBUFFER Operation member is assigned the value of DXGK_OPERATION_UNMAP_APERTURE_SEGMENT which then umaps the allocation was the aperture.
The DxgkDdiReleaseSwizzlingRange routine may be called to release a swizzling range for a CPU based aperture memory segment. The DXGKARG_RELEASESWIZZLINGRANGE data structure is used to store information about releasing a swizzling range. The
DxgkDdiAcquireSwizzlingRange routine is used to create a swizzling range.
Swizzling for computer graphics commonly means organising vectors, so they provide better performance and better textures for graphics.
References
## Friday, 27 December 2013
### Advanced Debugging Tools
OllyDbg (V2.1) - This tool is mostly for examining malware and programs. I find the tool really useful, the Assembly is very good too, especially with tracing JMPs.
Hook Analyser (2.6) - Able to view application crashes with more detail, and hook onto running processes for malware analysis and debugging.
WinCheck (8.50) - Able to view Kernel Data Structures not available in WinDbg.
Documentation - WinCheck Blog
### Tis' The Season To Be Sharing - Sharing and Mapping Memory
This blog post is going to look at sharing memory, control areas and section objects, and how to view information about these mechanisms. Let's begin by looking at the general concept of sharing physical memory between two processes.
Process A and Process B both wish to use the same resource, this could be a library or some other kind of object. The pages used to map the shared resource, do cause any conflicts between the two processes, since the processes retain their own private virtual address space, and furthermore the pages will be marked with protection flags such as copy on write and execute only.
The sharing mechanism is mostly driven by a special object used by the Memory Manager called a Section Object. This may also be referred to as a File Mapping Object.
Sections Objects are created by calling the CreateFileMapping function, and then using a file handle to back the Section Object to, or using the INVALID_HANDLE_VALUE flag to use a page file backed region. The reasoning for the choice with the handle, is because Section Objects can be either be committed and then written to a page file on the hard disk, or a open file.
You may also notice other API function calls such as MapViewOfFile and MapViewOfFilEx. These are used when the Section Objects mapped to files much larger than the address space of the process, and therefore only a small portion of the Section Object will be mapped into the address space of a process. This is called a View of the Section Object.
Like all objects, the Section Object is manged by the Object Manager, and as a result the same techniques as discussed in my Object Manager posts can be used to gather information about a Section Object. We need to also understand the idea and concept of Control Areas.
Looking for Control Areas
Control Areas are used to store information about Section Objects and Mapped files. We can find Control Areas through several different methods, the first method is by using the !filecache WinDbg extension, which in turn displays the usage of file cache. If your why Section Objects and Control Areas can be found this way, it is because the Cache Manager uses mapped files.
The Control column lists all the Control Areas used by the Cache Manager and their addresses. The No Name for File message indicates that the Virtual Address Control Block (VACB) is not present and being cached for metadata. The VACB can be seen with the _VACB data structure in WinDbg.
The BaseAddress field of the data structure points to the starting address of the view used by the system cache, and is used in conjuction with the MmMapViewInSystemCache. The SharedCacheMap field is a pointer to another data structure, which belongs to the VACB and uses the Section Object used to map the view of the file. The ArrayHead field is pointer to a data structure which is used to manage the array of VACBs.
You could also use the !memusage extension to view the PFN database, and then view the Control Areas for the Section Objects from using that extension.
The last method, is to use the !handle extension, which dump all the handles for the current section objects for the current process.
Using the address of the Section Object, and then applying the dt command with the _SECTION_OBJECT data structure, we can locate the _CONTROL_AREA data structure by checking the _SEGMENT_OBJECT data structure.
If your wondering about the VAD Tree related fields, then please read my VAD Tree blog post, and see this blog post too - Hidding Module from the Virtual Address Descriptor Tree
Examining Control Areas
We can then view information about a Control Area with the !ca extension or by using the _CONTROL_AREA data structure.
Personally, I prefer to use the !ca extension instead of formatting the data structure in WinDbg. Using the !ca extension with the address of the Control Area, we can see three distinct categories: Control Area, Segment and Subsection.
The File Object field contains the address of the File Object associated with the file mapping, we can see the !fileobj extension or the _FILE_OBJECT data structure here to gather further information. Generally, the Control Area section contains information about the state of any mapped files. The Flush Count field contains the number of times a mapped view was flushed with the FlushViewOfFile function.
The most important field is the Section Object Pointers, which contains the address of the _SECTION_OBJECT_POINTERS data structure. This data structure is used by the Memory Manager or the Cache Manager to provide information about file mapping and cache information for a file stream.
The DataSectionObject field contains the address of the Control Area. A NULL value indicates that the file stream is not present in memory. See the WDK documentation for more information.
The Segment section contains information about the prototype PTEs used to map the pages used by the section object. This structure is allocated with paged pool.
The Subsection contains information contains information about the page protection and mapping information for each section of the file used in the mapping.
## Monday, 23 December 2013
### Physical Address Extension (PAE)
This blog post is going to explain the fundamentals and the internals of Physical Address Extension (PAE) on Windows.
PAE Mode enables x86 operating systems to be to address up to 64GB of Physical Memory (x86 processors), and 1,024GB on x64 when the processor is running in Legacy Mode, which is the same as running in x86 Protected Mode. The PDEs and PTEs are extended to 64-bits wide, and a extra layer is added called the Page Directory Pointer Table. The CR3 then points to the address of the this table instead of the Page Directory.
We can check if a system has the PAE bit enabled by checking bit 5 within he CR4 Register. According to my dump file, my system has the PAE bit set. However, due to licensing restrictions set by Microsoft, my operating system will still not address any larger than 4GB of RAM due to compatibility issues with drivers.
Additionally, when PAE has been enabled for x64 processors, then other features are also automatically enabled such as Data Execution Protection (DEP), hot-swappable memory and the support of NUMA (Non Uniform Access Memory).
Furthermore, some processes can still support more than the 2GB addressing limit with the AWE (Address Windowing Extension) setting.
AWE works by allocating the physical memory wished to be used, and then map these views of physical memory into the allocated virtual address space for the process as shown in the above diagram. It's also important to understand, that physical pages and and virtual memory ranges allocated by AWE can not be shared and therefore inherited by other processes. AWE allocated address ranges are always read and write, and so protection bits will not apply to these pages.
All memory allocated with AWE is non-paged pool. Since, AWE allocated memory must be freed as one unit of memory, then the MEM_RELEASE flag must be specified by using the VirtualFree API function. These pages will then be in the Free page state.
Setting PAE and Checking PAE Support
I've developed a very simple tool using the Win32 API, to check if your processor supports PAE. Please be aware that by default, x64 processors will always return a non-zero (true). The code is available below:
If you have DEP set, then PAE can't be disabled. You must disable DEP but disabling PAE. This can be achieved by editing the Boot Configuration Data through the use of Command Prompt.
We can enable PAE with the AlwaysEnable flag instead, or the AlwaysOn flag with DEP.
BCDEdit /set
## Thursday, 19 December 2013
### Where Did My Kernel Memory Dump Go?
Okay, this going to be a very short blog post about the common problem with Kernel Memory Dumps not being saved, despite your efforts to following all the instructions listed in this Sysnative Tutorial, Windows still doesn't seem to be saving your Kernel Memory Dumps. So what's the problem? The answer lies within the registry.
According to customer service feedback, many users were complaining about Kernel Memory Dumps using their hard drive space. For the average user, unless receiving support on a forum, then these Kernel Memory Dumps are valueless, as a result you will need to create a registry key called AlwaysKeepMemoryDump was created to address this issue.
If this registry key is set to 1, then Kernel Memory Dumps will always be saved regardless.
The highlighted key shows the maximum number of Minidumps which will be created.
Reference:
### Translation Lookaside Buffer (TLB) and Look Aside Lists
TLB Cache
The TLB Cache is very much a key part for the necessary performance of Virtual to Physical Address Translation. It's main purpose is to improve the performance of Virtual Address Translation. All modern CPUs and their MMUs (Memory Management Units) support the use of the TLB.
A important aspect to understand, is the difference between TLB Hit and TLB Miss. When a Virtual Address is accessed, and then looked up, the TLB Cache is checked first to see if the Virtual-Physical Address mapping is present and if so then a TLB Hit occurs. On the other hand, if the address isn't present, then a TLB Miss occurs and the MMU is forced to execute a Page Walk which is the process of looking through the Page Tables like discussed in my previous blog posts. Once, the Page Walk has completed and the physical address is found, then this information is loaded into the TLB Cache.
If Page Walk is unsuccessful, then a Page Fault is raised, and the Virtual to Physical Address Mapping is created in the Page Table. Generally, any changes to the Page Table Structure and the Paging Structure will resulting the flushing of the TLB with a Inter Processor Interrupt (IPI). This one of the reasons why you will tend to notice TLB flushing and IPIs with Stop 0x101 bugchecks.
The flushing of the TLB Cache can be achieved by reloading the CR3 (Page Directory Base Register), there is a easier method which I will explain too.
Here is a small segment of Assembly code from OSDev Wiki:
However, if the G flag has been set for a PTE or PDE, then that entry will not be flushed from the TLB Cache.
The other method would be to use the invlpg (Invalidate TLB Entry) instruction. This instruction is a privileged instruction, and therefore the CPL (Current Privilege Level) must be Level 0. This instruction also flushes or invalidates an entry for a specific page, and therefore is much more suited if you wish to only flush a certain entry. Although, in some circumstances, it may flush the entire TLB or multiple entries, there is the guarantee though that it will flush the entries associated with the current PCID (Process Context Identifier). See Volume 3: Section 4.10 in Intel Developer's Manual.
You can check if PCIDs are enabled by checking the 17th bit of the CR4 register.
The above example is from a AMD CPU, and I don't think AMD yet supports PCIDs. We could also use the j command with the addition of the .echo command, as seen below:
Getting back on topic back the TLB Cache, each entry is associated with a tag. The tag contains important information such as the part of the virtual address, physical page number, protection bits, valid bit and dirty bit. A Virtual address being checked, and is then matched against a tag within the TLB Cache. The 8 bit ASID (Address Space Identifier) is used to from part of the tag. The ASID part is the is matched between the TLB Entry and the Virtual Address (PTE).
Context Switches and Task Switches can invalidate TLB Entries, since the mappings will be different.
Look Aside Lists
The second part of my blog post will concern Look Aside Lists. Look Aside Lists are a type of pool allocation algorithm, although, the difference is that Look Aside Lists have fixed sizes and do not use spinlocks. They are also based around Singly Linked Lists, using a LIFO order.
Device Drivers and parts of the operating system (I/O Manager, Cache Manager and Object Manager) can build their own Look Aside Lists. The Executive versions of the Look Aside List are managed per a processor (see _KPRCB). These look-asides lists are managed by the operating system. Each Look-Aside List can be allocated with Paged Pool or Non-Paged Pool respectively. The operating system will increase the number of allocations to a Look Aside List if the demand is great, and thus the number of entries. The opposite is true if demand is low.
Furthermore, Look Aside Lists are managed automatically by the Balance Set Manager every second with the call from ExAdjustLookAsideDepth (reserved for System Use). This only happens if no allocations have happened recently. The Look Aside List depth will never drop below 4.
The main purpose of Look Aside Lists is when a device driver is going to be using specific sized pool blocks frequently. Each allocation is known as a entry, depending if the pool allocation type, the data structure used will either be _PAGED_LOOKASIDE_LIST or _NPAGED_LOOKASIDE_LIST.
Firstly, a Look Aside List is created by calling ExInitializeLookasideListEx, just a side note, before I continue writing, all the said functions should be fully documented in the WDK. The function mentioned, creates data structure called _LOOKASIDE_LIST_EX.
The data structure contains a pointer to a larger data structure called _GENERAL_LOOKASIDE_LIST which retains the information about the current Look Aside List.
The type of pool being used for the Look Aside List will depend upon if the driver is going to need to access the entries at IRQL Level 2 or IRQL Level 1. Obviously, Non-Paged Pool will need to be used if the driver is going to need to use the entries at IRQL Level 2, and Paged Pool will need to be used if the driver is not going to access these entries at any level above IRQL Level 1.
The Allocate and Free fields are used as function pointers to the functions in which you wish to use to allocate and free the entries in the list. The TotalAllocates and TotalFrees fields shows the total number of allocations and frees.
The Depth field contains the number of entries in the list.
The SingleListHead.Next field is used to point to the next free pool chunk.
We can use the !lookaside extension to see the efficiency and information about system lookaside lists.
## Wednesday, 18 December 2013
### Virtual to Physical Address Translation (Part 3)
All the pages resident in physical memory are manged by the PFN Database or Page Frame Number Database. The PFN is used to describe the page state of each page, and the number of references to this page.
Page States
The page states can be found in a enumeration called _MMLISTS:
Zeroed - The page already is free and already contains 0's, or has been freed and being zeroed.
Free - The page is free, but may still contain data since the Dirty bit could have not been set, therefore these pages are zeroed before being marked as a user page for user-mode processes.
Standby - The page has been recently been removed from the working set of a process, and as a result is currently in Transition. The page hasn't been written to or modified since removal and transfer to the hard disk, but the PTE (Invalid) may still refer to the physical page.
Modified - The page has been recently removed from the working set of a process, but has been written to and modified before it was written to the hard disk, thereby the contents of this page must be written to the hard disk before the physical page the PTE points to can be used.
Modified No-Write - The no write version of the Modified page state. The page will not be written to the hard disk.
Bad - The page has a parity error, or has other associated hardware issues with it. It may be used by the Kernel for look-aside caches and changing page states.
Active/Valid - The page is part of a working set (process or system), or is a non-paged pool page, and will therefore have a valid PTE.
Transition - Temporary page state used for pages which aren't present on working set lists and other page state lists. I/O for these pages will be in progress, and collided page faults can be used here.
ROM - Read Only Memory Page
Since, we now understand the different page states, there is two methods for gathering system wide information about the page states used by the PFN database. The first method is to use the WinDbg extension called !memusage.
You will always notice a few bad pages, for the reasons explained earlier. The second method and the fastest method, would be to use the MemInfo Tool with the -s switch.
The appropriate program version is shown in the image below:
Structure of the PFN Database
The PFN Database is a array of data structures such as _MMPFN and _MMPFNENTRY. Each PFN Entry data structure is used to store information about a physical page in memory.
The flags are all represented by certain bits, and these flag meanings will be explained below:
WriteInProgress - Indicates that a write operation is in progress for this page. A event object will become signaled when this operation is complete.
Modified - Shows if the page was modified, and if so, then contents of the page must be written out to the disk before the page can be removed from memory.
ReadInProgress - Indicates that a read and in-page operation is in progress for this page. Again, a event object will be signaled when this operation is complete.
Rom - The page is currently read-only memory.
InPageError - I/O error occurred during a in-page operation with this page.
KernelStack - The page is being used to contain a Kernel Stack, the PFN Entry will contain the owner of the the stack and the next stack for the PFN for the same thread.
RemovalRequested - Indicates that page is eligible to removal.
ParityError - Physical page contains parity errors or ECC errors. There is a white paper somewhere on parity and ECC errors.
The !pfn extension can give us information about a PFN Entry. Using the !pfn with the known page frame, we can see the output seen below. Remember that we can obtain the Page Frame from the !pte extension. The !pfn gives similar information to the _MMPFN structure.
We can see the Reference Count field which refers to the number of references to this page. The reference count is incremented when added to the working set of a process, and when the page has been locked into memory for I/O. The reference count is decremented when the share count becomes 0, or when the page has been unlocked from memory.
We can also see the Share Count field which refers to the number of PTEs which refers to the page, this value can be greater than one for shared pages.
The Colour field is used to link physical pages together by colour, which refers to their location within the processor cache. This is generally used for performance purposes.
The Priority field shows us the page priority of the PFN, and thereby which standby list it will be placed upon. I'll explain these page priorities a little later in my post.
Page Priority Levels
The page priority levels run from 0 to 7, with 0 being the lowest priority. The default priority level is 5, but the priority level can be inherited from the process' thread which caused the allocation. The Memory Manager will always take pages from the standby list of the lowest priority first.
Using the MemInfo Tool with the -c extension, we can then view the Page Priority Standby lists, as shown here:
I'm going to explain the TLB Cache and Look Aside Lists in my next blog post instead, since this topic got a little big.
## Monday, 16 December 2013
### Virtual to Physical Address Translation (Part 2)
The second part is going to concern paging structure on x86 and x64, and how virtual memory addresses and physical memory addresses are mapped according to this structure. The third part will look at how physical memory is managed with the PFN database.
Hardware PTEs and Paging Structure
A virtual address on a x86 system, is divided into three different parts: Page Directory Index (10 bits); Page Table Index (10 Bits) and the Byte Index (12 bits). The above image shows their relationship in relation to the general page table structure.
The Page Directory Index shows the address of the page table in which the desired PTE is located. The Page Table Index indicates the address of the PTE within the Page Table, and the Byte Index is used to find the correct physical page for which the PTE is mapped to.
Before we go onto briefly explaining the x64 version, and going into greater depth about each part of the translation process, let's quickly discuss how to find the Page Directory address. Remember it is unique to each process, and each thread running under one process will inherit this address, meaning that a context switch will not need to be formed when changing the context to a different thread.
Using the !process extension, the DirBase field shows the physical address of the Page Directory. This same physical address is stored within the Control Register called CR3. Using the r command with the @ character, we can see that the two addresses are identical.
Alternatively, you could also check the _KPROCESS data structure, and investigate the address from that standpoint. The CR3 register (Page Directory Base Register) will updated with the address of a different Page Directory if a process context switch occurs.
The Page Directory is identically a large array of PDEs (Page Directory Entry), each PDE points to the address of a Page Table, and is 4 bytes long (or 32-bits). Page Tables are created on demand, and therefore the VAD Tree is checked to see wherever a new Page Table should be created upon access of a virtual address without a corresponding Page Table Index and Page Directory Index.
The PDE virtual address can be found with the !pte extension, as shown below:
Each PDE points to the address of a Page Table, in the Page Table is similar in respect that it is a array of PTEs (Page Table Entry). The Page Table Index is used to find the relevant PTE within the array. 1,024 Page Tables are required to map the entire 4GB of address space for x86.
Each PTE then is used to point the relevant physical page, and the Byte Index is used to find the appropriate address within this page. The PTE has a number of different PTE Protection and Status bits associated with it, which I will explain here.
• Accessed (A) - The page has been read.
• Cache Disable (Cd) - Caching is disable for the page.
• Copy-on-Write (Cw) - Page is using copy on write.
• Dirty (D) - Page has been written to.
• Global (Gl) - Translation applies to all processes.
• Large Page (L) - PDE maps a 4MB page.
• Owner (O) - Shows if the page is accessible in User-Mode or Kernel-Mode.
• Prototype (P) - Prototype PTE, will be explained later.
• Valid (V) - Virtual Page maps to a physical page.
• Write Through (Wt) - Disables caching of writes.
• Write (W) - Page is writable.
These flags can also be found with the _HARDWARE_PTE data structure:
PTE's can be subdivided into three other categories: Invalid, Prototype and System. The next few paragraphs will explain these types of PTE, and then conclude with the TLB.
System PTEs
System PTEs are used to map the system address space. For example, kernel stacks, MDLs and I/O is mapped with the use of System PTEs. We can see the amount of System PTEs free to use, by using the !sysptes extension in WinDbg.
You can also view the number of System PTE Allocation failures, which could indicate a PTE Leak by dumping the address of _MI_SYSTEM_PTE_TYPE data structure, by gathering the address of the MiSystemPteInfo global variable.
The above address is then used with the dt command, as seen below:
As we can see, there isn't any allocation failures which is a positive sign, and suggests everything is running normally. On the other hand, if you do notice any allocation failures, then you could create a certain registry key called HKLM\SYSTEM\CurrentControlSet\Control\Session Manager\Memory Management\TrackPtes. By creating this DWORD key and setting it to 1, then you will be enabling the tracking of System PTEs. The next step would be to use the !sysptes extension with the 0x4 bit flag set.
Invalid PTEs
Invalid PTEs indicate that the PTE isn't accessible to the process, usually for the invalid PTE to become valid, a Page Fault exception is raised and the Page Fault is then resolved by the Memory Manager's fault handler called MmAccessFault. There are four different kinds of Invalid PTEs, which will be explained below:
Page File - The page is located within a page file on the hard drive, accessing this page will result in a page fault, which will allocate a physical page, and enable the Valid bit for the PTE. The page will also be added to the Working Set of the accessing process.
Demand Zero - The page will be written with a page of 0's, if this page is accessed then a zero filled page is added to the working set of the process. At first, the zero page list is checked, and if this is empty, then a page from the free list is taken and paged with 0's. Otherwise, the page is taken from a Standby List and paged with 0's.
Transition - The page is currently on a standby, modified, modified-on-write or no list and therefore will removed from the corresponding list and added to the working set of the process.
Unknown - PTE is zero, or there isn't a page table yet. This leads to the VAD Tree being checked to see if the page is committed, and if so, a page table will be created.
Prototype PTEs
Pages will are shared between processes are mapped with Prototype PTEs. When a sharable and mapped page is referenced by a process, a hardware PTE is used to point to the referenced page, thus both the Prototype PTE and the hardware PTE point to the physical page.For each reference to a shareable page, a counter is incremented within the PFN Database. This allows the Memory Manager to invalidate any pages and move these pages to the hard-drive or a transition list.
The PTE used by the process' page table has it's Valid flag cleared and is used to point to the Prototype PTE which points to the page.
If the page is later accessed, then the Prototype PTE can improve the lookup process. The diagram below illustrates this point, and how a Prototype PTE and Valid PTE may look in concept.
A Prototype PTE can used to used to describe the page state of a sharable page, these states are as follows:
Valid - Page is in physical memory.
Transition - The page is currently present on a standby or modified list, or may not be present on any list.
Modified-No-Write - The page is present in physical memory, and present on the modified-no-write list.
Demand Zero - The page will written with a page of 0's.
Page File - The page is present on a paging file
Mapped File - The page is present in a mapped file.
x64 Translation Process:
On x64 systems, the paging structure has expanded from two levels to four levels. The additional level or layer is called the Page Map Level 4. The Virtual Address on a x64 system therefore has more sections. I've created a diagram for the current 48-bit implementation.
The Page Map Level 4 Selector points to the Page Map Level 4, the Page Directory Pointer Selector then points to the Parent Page Directory Pointers Table. The Page Table Selector shows the Page Directory, and the Page Table Entry Selector then points to the correct PTE which maps to the physical page. The Byte Within Page points to the specific PFN. Remember the x64 paging structure still applies to each process. Using the above information, you can imagine the overall x64 paging structure being like the diagram below:
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https://www.gamedev.net/forums/topic/500804-normal-maps---artists-or-code/
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# Normal maps - Artists or Code?
This topic is 3637 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
Hi people, When a normal map appear wrong on a model, who to blame? The artists or the code? Can anyone give me tricks to handle that? If you think it's art related, how should they be careful in 3ds max while modeling, and in which direction to setup their normal maps. If it is the code, can somebody tell me what I am doing wrong? Here is how I compute a tangent / bitangent : ( Assuming I am calculing verts[0] for the triangle verts[0..2] )
Edge1.Set(
verts[1].x - verts[0].x,
verts[1].y - verts[0].y,
verts[1].z - verts[0].z);
Edge2.Set(
verts[2].x - verts[0].x,
verts[2].y - verts[0].y,
verts[2].z - verts[0].z);
Edge1uv.Set(
verts[1].u - verts[0].u,
verts[1].v - verts[0].v);
Edge2uv.Set(
verts[2].u - verts[0].u,
verts[2].v - verts[0].v);
HGfloat cp = Edge1uv.Cross(Edge2uv);
if (cp != 0.0f)
{
HGfloat mul = 1.0f / cp;
tangent = (Edge1 * -Edge2uv.y + Edge2 * Edge1uv.y) * mul;
bitangent = (Edge1 * -Edge2uv.x + Edge2 * Edge1uv.x) * mul;
normal.Set(verts[0].nx, verts[0].ny, verts[0].nz);
bool inverted = false;
if (normal.Dot(tangent.Cross(bitangent)) < 0) inverted = true;
if (inverted)
{
tangent = normal.Cross(bitangent).Normalize();
bitangent = tangent.Cross(normal).Normalize();
}
else
{
tangent = bitangent.Cross(normal).Normalize();
bitangent = normal.Cross(tangent).Normalize();
}
}
verts[0].tx = tangent.x;
verts[0].ty = tangent.y;
verts[0].tz = tangent.z;
verts[0].bx = bitangent.x;
verts[0].by = bitangent.y;
verts[0].bz = bitangent.z;
We will eventually rework the Max exporter to get the values 3ds max gives us, but for now I need the artists to visualize at least a correct model. Thanks a lot guys.
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Quote:
Original post by DaivukWhen a normal map appear wrong on a model, who to blame? The artists or the code?
If one is wrong, it's art. If all are wrong, it's code. :)
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https://www.physicsforums.com/threads/cant-decide-on-a-career-path.853854/
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# Can't decide on a career path
1. Jan 24, 2016
### FlashExplorer
Hello, I'm FlashExplorer, and I'm a 22 year old guy. Ever since graduating from high school I haven't been able to pinpoint what I wanted to do as a career.
First, I thought I wanted to get into IT because I've always been naturally technically inclined when it came to computers. I did OK with the terminal (computer) side of the course, but found the network side of it rather dry and boring. I liked solving the problems, but the course work wasn't interesting enough for me. I quickly fell behind and had to drop out in January, about halfway through the course. I got a little bit of my tuition back, but not all of it.
Next, I decided to pursue a career in the automotive trades because of my love of cars so I thought it would be a good idea. Since I lost most of my education funds and wasn't willing to take out a loan, I opted for a vocational course at a local high school. The first two months were all in class paper work based learning, after that my teacher placed each of us at a workplace as work experience. I was initially dead set on doing something involving engines, so I pleaded with my teacher to place me at an engine machining shop. I got what I wanted, and everything was fine for a while, but when winter rolled around, the work slowed to a stop. I went from machining a couple engines a day to sweeping the shop and changing oil filters. Since I wasn't experienced, the mechanics wouldn't let me do much more, & I became bored and hungry for money.
I asked my teacher if I could switch locations, and he suggested I go work at a Honda dealership where I learned how to do auto painting and paint prepping (well, the basics). I started there February of last year, & I really enjoyed it. It was related to one of my interests, but most of all I liked working with the people there. I worked my hardest, hoping that it would lead to a job working there, but by the end of April I was very disheartened to find out that they could not hire me, as they couldn't find a position that made financial sense if I was to be hired as a full-time staff member. As upsetting as this was, I was still determined to find a job in the automotive sector. I spent all summer trying (and mostly failing) to find a job at several places. All the jobs I managed to land only lasted at most, two weeks. There are many reasons I lost my jobs, but the main obstacles were my lack of experience, specifically because I didn't have any sort of degree or apprenticeship training in the works, as well as my choice to specialize in only auto painting and not all of Auto Body. The only job I ended on good terms was a temp job as a detailer, and that only lasted 2 weeks as well. I could have gone back to my job as a general labourer for a lawn care company like I had done for the past two years, but I was stubborn, and wanted to find work in the auto industry. I still have yet to find a job that I have been able to hold for any significant amount of time.
Recently though, I've been taking night classes in pre calculus and chemistry, with plans for physics with a friend of mine that I met through the previously mentioned automotive course. The reason for taking these courses was to upgrade my marks so that I could apply for Engineering at my local university. Like I've already mentioned, I have a passion for cars, learning about them and their engines, as well as trying to make them better. I'm also mildly fascinated by roadwork and infrastructure (bridges are cool). I remember trying to conjure up ideas for an overpass and exit ramps for the freeway in my city. The thing is though, I'm not completely sold on whether or not engineering is the best fit for me. I've always been average to maybe above average in science and math, & I never took physics. Even right now in my night courses, I'm doing average; 56 in Chemistry and a 78 in Pre-calculus. I'd chalk that up to poor studying habits moreso than my inability to understand.
Though I've failed to pinpoint what I want to do as a career over these 5 years, I think I've at least being able to identify what I like and what I'm good at. I'll just list them as bullet points to save time on this already wordy post.
• I love to design/draw things. I could always find time to doodle. I preferred to play with Lego rather than hang out (or even make) fris. In high school I spent lots of time making models in Google Sketchup. Also drafting was the only course I ever got a 90 in.
• I like to solve problems. Not much to say other than I find it highly satisfying to find a viable solution.
• I like cars and engines.
I think that's it. Wow that turned into a diary entry!
So what I want from you (the community) is some advice for me (am I suited for this? If not, what?), some of your life experiences working as an engineer, and what you do on a day to day basis. I want to know what the profession is like, or just any other advice you can give me.
2. Jan 24, 2016
### axmls
Just coming from an engineering student--you don't have to be phenomenal at math or physics to get an engineering degree. All it takes is a good amount of hard work. Yes, you learn plenty of math and physics, but that's not something some people can naturally do and some can't. With enough interest, anyone can do it.
3. Jan 24, 2016
### FlashExplorer
I see, I was worried because of the entrance requirements:
"A minimum of 85% average over the following, with no less than 60% in each course:
Pre-calculus 40S
Physics 40S
Chemistry 40S"
For the record my university is the University of Manitoba, and my marks are for grade 11. I still have grade 12 to improve them. Could this just imply that getting better marks would move me up the waiting list?
4. Jan 24, 2016
### axmls
I can't comment on your chances for admission. You certainly do need to improve your scores, but don't be disheartened before you've gotten into the meat of an engineering program. Once you get used to the science and math, it becomes easier.
You'll have to practice a lot, though.
5. Jan 24, 2016
### FlashExplorer
Ok. I still want to be sure that what I'm working towards is interesting enough to me to want to pursue it. Otherwise, it'll be a lot more effort to push myself to study and finish assignments. I'm going to visit the Engineering department soon so I can get a feel for the course, and what I can expect.
6. Jan 25, 2016
### axmls
Good idea. Some people can only get an interest in the math when they see the real life applications of it. If you enjoy understanding how things like engines work, including all the heavy physics behind it, then I'm sure it'll inspire you to learn that math. Really, I'm only a student, but I can tell you as an (electrical) engineering student that it can be very enriching to have a deeper understanding of how these things work. Not only that, but design is just fun.
7. Jan 29, 2016
### micromass
Staff Emeritus
Yeah, you probably should be worried of these requirements. Theyre not easy to obtain. The good news though, is that it doesnt require a lot of raw talent. Rather, it requires good study habits and a good deal of hard work. This means motivating yourself to learn something even though it is not always clear what the practical applications are. If you can pull this off, then you can do engineering.
Your grades right now are not good. You need to fix your study habits. Work as much as necessary. You will get there eventually then. If you choose not to work hard, then you won`t get there.
You can always attend a community college before going to a "real" university too. But really, improve your studying!
Similar Discussions: Can't decide on a career path
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https://astrobites.org/2012/04/04/an-extension-of-the-m-sigma-relation-to-globular-clusters/
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# An extension of the M-Sigma relation to globular clusters
Title: MBH − $\sigma$ relation between SMBHs and the velocity dispersion of the globular cluster systems
Authors: Raphael Sadoun and Jacques Colin
First Author’s Institution: UPMC, CNRS, Institut d’Astrophysique de Paris
If you look at books written as recently as 1974, you can read lines like this: ‘At the time of writing there is no conclusive observational evidence to support the speculation that black holes are a common type of object in the universe.’ Thirty years later, we have pretty conclusive evidence that black holes are at the centers of most galaxies, and we know even more than that. In particular, we know that there is a tight correlation between the mass of the central black hole and the velocity dispersion of the “hot” (energetic) part of the host galaxy (see this paper for details). What is the velocity dispersion, you ask? It is just the standard deviation of the velocities about their mean. Observational studies have shown that the black hole mass scales approximately as the 4th power of the velocity dispersion. The paper I’m discussing today extends this relationship to parts of the host galaxy more distant from the central black hole: globular clusters. This is an interesting result because it may shed light on how the $M-\sigma$ relation comes about, something that is not well understood. I’ll get into that, but first, a bit of background. What is a black hole? What is a globular cluster? And what can the extended $M-\sigma$ relation tell us?
• A quick black hole refresher
When a star ceases nuclear burning, it no longer has a source of heat. Most stars are supported against their own gravity by radiation pressure (pressure from photons), which is proportional to temperature to the fourth power. As the temperature falls because there is no more fusion, the star collapses. Skipping some important intermediate steps, what happens then is this: the star’s outer layers plummet inwards until the density of the star is such as to be able to once more support it against its own gravity. But for some stars, this is just not possible: no matter how dense the star becomes, it cannot produce enough pressure to support itself. This is the case for stars with masses greater than $1.4$ solar masses because they can no longer support themselves by electron degeneracy pressure. Basically, two electrons can’t occupy the same quantum state, so you can only squeeze so many electrons into a given volume before they push back: that is what is meant by electron degeneracy pressure. Instead of stabilizing, these stars continue collapsing into black holes.
So this is the basic black hole formation mechanism for the black holes we do understand. But these are stellar mass black holes. In contrast, the black holes dealt at the center of galaxies are supermassive black holes (SMBHs), which are much larger than the stellar mass black holes I describe the formation process for above (recall, black hole radius is proportional to black hole mass). There are still unanswered questions about how these huge black holes form.
Three proposed mechanisms are:
1) They form by collapse of primordial, metal-free (so-called Population III) stars in the early Universe. In this case the details might parallel the formation of stellar mass BH’s as described above.
2) They form by “direct collapse of gas in isolated protogalaxies.”
3) They form by mergers of such protogalaxies.
Further, since an SMBH’s mass is correlated with its host galaxy’s velocity dispersion (which in turn correlates with the mass and other properties of that galaxy), it must grow in a way that is linked with its host galaxy’s growth. How that happens is the central “mystery” behind the standard $M-\sigma$ relation. Sadoun and Colin’s work is interesting because the fact that a correlation also holds for globular clusters may shed light mechanisms for the standard $M-\sigma$ relation as well.
• And globular clusters?
A globular cluster is just a sphere of tightly gravitationally bound stars that orbits the center of a galaxy. Globular clusters reside near the edges of galaxies and contain old stars as compared to stars found elsewhere in these galaxies. There are around 150 globular clusters in the Milky Way, but larger galaxies can have even more: some large galaxies have on the order of 10,000 globular clusters!
• What can the extended M-Sigma relation tell us?
Sadoun and Colin’s paper takes the mass of the central black hole in 12 galaxies and correlates it with the velocity dispersion of the globular clusters. They find a power law that is, like the standard $M-\sigma$ relation, around 4, but slightly on the lower side of that, with $M\propto \sigma ^{3.78\pm .53}$. For the galaxies in their sample, they find that the correlation with the globular cluster velocity dispersion is just as good as the “standard” one with the velocity dispersion in the bulge (the inner, “hotter” part of the galaxy).
This plot from the paper shows the “M-sigma relation” for the black hole mass (y-axis) and globular cluster velocity dispersion (x-axis).
They also break up each data set to compute separate correlations for two different types of globular clusters: metal-poor (by metal, we mean anything heavier than helium!), old globular clusters far from the galaxy centers, and younger, metal-rich ones closer in. They find a stronger correlation of the black hole mass with the velocity dispersion of the younger, closer in clusters than with the velocity dispersion of the older, farther-out ones. Using this stronger correlation, they actually predict the (currently unknown) masses of the central black holes in five different galaxies.
Using the correlation between black hole mass and young, close globular clusters' velocity dispersions to predict the black hole mass for five galaxies where that is not yet known. From paper.
Even more interestingly, they use the correlation to constrain models of how the $M-\sigma$ relation arises. The relation is thought to come about via feedback: globular clusters can undergo both tidal disruption (different gravitational forces on different parts of the cluster which can distort or disrupt it entirely) and gravitational shocks if they pass on eccentric (very non-circular) orbits near the central black hole. These two mechanisms are possible causes of the $M-\sigma$ relation. Sadoun and Colin’s work, by showing that this relation goes beyond the bulge, can constrain how effective these feedback processes are.
So, this paper is exciting for two reasons:
• it gives us a method to predict black hole masses that we don’t know, and
• it may shed light on how the mysterious M-sigma relation comes about.
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https://arxiv.org/abs/0809.2562
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astro-ph
(what is this?)
(what is this?)
# Title:SCP06F6: A carbon-rich extragalactic transient at redshift z~0.14?
Abstract: We show that the spectrum of the unusual transient SCP06F6 is consistent with emission from a cool, optically thick and carbon-rich atmosphere if the transient is located at a redshift of z~0.14. The implied extragalactic nature of the transient rules out novae, shell flashes, and V838 Mon-like events as cause of the observed brightening. The distance to SCP06F6 implies a peak magnitude of M_I ~- 18, in the regime of supernovae. While the morphology of the light curve of SCP06F6 around the peak in brightness resembles the slowly evolving Type IIn supernovae SN1994Y and SN2006gy its spectroscopic appearence differs from all previous observed supernovae. We further report the detection of an X-ray source co-incident with SCP06F6 in a target of opportunity XMM-Newton observation made during the declining phase of the transient. The X-ray luminosity of L_X ~- (5+-1)e42 erg/s is two orders of magnitude higher than observed to date from supernovae. If related to a supernova event, SCP06F6 may define a new class. An alternative, though less likely, scenario is the tidal disruption of a carbon-rich star.
Comments: accepted version Subjects: Astrophysics (astro-ph) Journal reference: Astrophys.J.697:L129-L132,2009 DOI: 10.1088/0004-637X/697/2/L129 Cite as: arXiv:0809.2562 [astro-ph] (or arXiv:0809.2562v2 [astro-ph] for this version)
## Submission history
From: Boris Gaensicke [view email]
[v1] Mon, 15 Sep 2008 16:22:25 UTC (44 KB)
[v2] Thu, 10 Sep 2009 14:41:53 UTC (118 KB)
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http://mathhelpforum.com/calculus/1930-tangent-equation.html
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# Math Help - Tangent equation
1. ## Tangent equation
My aim is to compose a tangent equation for the line y=(x-1)*(x+1)*(x+2) provided that tangent points are intersections with x-axis.
Attached Thumbnails
2. Originally Posted by totalnewbie
My aim is to compose a tangent equation for the line y=(x-1)*(x+1)*(x+2) provided that tangent points are intersections with x-axis.
Hello,
you know already the intersections between x-axis and curve:
(-2,0), (-1,0), (1,0).
Now you need the slope of the tangent lines:
Your function is $y=f(x)=(x-1)(x+1)(x+2)=x^3+2x^2-x-2$
The gradient of the function gives the slope of the tangents:
$f'(x)=3x^2+4x-1$
First slope: $m_1=f'(-2)=3 \cdot 4 +4 \cdot(-2) - 1=3$
2nd slope: $m_2=f'(-1)=3 \cdot 1 +4 \cdot(-1) - 1=-2$
3rd slope: $m_3=f'(1)=3 \cdot 1 +4 \cdot(1) - 1=6$
Now use the point-slope-formula and you'll get:
$t_1:y=3 \cdot (x+2)$
$t_2:y=-2 \cdot (x+1)$
$t_3:y=6 \cdot (x-1)$
Greetings
EB
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https://www.nature.com/articles/jp201211?error=cookies_not_supported&code=a8855a0a-0e97-4434-a25d-ef7f7a268fc9
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Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.
State-of-the-Art
# Thermal protection of the newborn in resource-limited environments
## Abstract
Appropriate thermal protection of the newborn prevents hypothermia and its associated burden of morbidity and mortality. Yet, current global birth practices tend to not adequately address this challenge. Here, we discuss the pathophysiology of hypothermia in the newborn, its prevention and therapeutic options with particular attention to resource-limited environments. Newborns are equipped with sophisticated mechanisms of body temperature regulation. Neonatal thermoregulation is a critical function for newborn survival, regulated in the hypothalamus and mediated by endocrine pathways. Hypothermia activates cellular metabolism through shivering and non-shivering thermogenesis. In newborns, optimal temperature ranges are narrow and thermoregulatory mechanisms easily overwhelmed, particularly in premature and low-birth weight infants. Hyperthermia most commonly is associated with dehydration and potentially sepsis. The lack of thermal protection promptly leads to hypothermia, which is associated with detrimental metabolic and other pathophysiological processes. Simple thermal protection strategies are feasible at community and institutional levels in resource-limited environments. Appropriate interventions include skin-to-skin care, breastfeeding and protective clothing or devices. Due to poor provider training and limited awareness of the problem, appropriate thermal care of the newborn is often neglected in many settings. Education and appropriate devices might foster improved hypothermia management through mothers, birth attendants and health care workers. Integration of relatively simple thermal protection interventions into existing mother and child health programs can effectively prevent newborn hypothermia even in resource-limited environments.
## Introduction
The need for thermal newborn protection has long been known, as alluded to by Soranus of Ephesus (98 to 138 AD) in his four-volume treatise ‘On Diseases on Women’, which demonstrates the importance of keeping newborns warm.1 The Bible provides probably the most well-known example of thermal protection of the newborn in Luke 2: 7, ‘And she brought forth her firstborn son, and wrapped him in swaddling clothes, and laid him in a manger.’
Yet, in current times, the majority of the almost 4 million newborns globally who do not survive their first month of life2 die of complications associated with hypothermia, such as prematurity and severe infections (mostly sepsis and pneumonia).3 As two recent reviews have acknowledged, neonatal deaths related to hypothermia are relatively neglected, but considered easily preventable with attention to warmth, feeding and infection management.4, 5 This article focuses on the diagnosis of hypothermia and management of thermal protection of newborns in low-resource environments. We review mechanisms of neonatal thermoregulation, discuss the pathophysiology of newborn hypothermia and present simple strategies of thermal protection for the newborn.
## Neonatal thermoregulation
The normal body temperature of a newborn infant is usually defined as ranging between 36.5 and 37.5 °C (97.7 to 99.5 °F).6 A series of observational randomized trials starting in the late fifties7, 8 showed that keeping babies warm reduces mortality and morbidity, and spurred further research on the pathophysiology of thermoregulation in newborns. Thermoregulation is a biological priority for all homeothermic species.9 Newborns, particularly preterm and low-birth weight (LBW) infants, have limited capacity for thermoregulation during the first weeks of life. The optimal environmental temperature is termed thermal neutral temperature, at which metabolic requirements of the organism are minimal.10 Both a decreased and an increased core temperature increase the metabolic rate of newborns,11 who have only very limited ability to maintain a normal temperature and easily become hypothermic or hyperthermic. Although hyperthermia also increases energy needs, hypothermia seems to carry a higher risk of complications.12
When the infant's body temperature decreases in response to sudden exposure to cold extrauterine environments, signals from peripheral and central thermoreceptors reach the hypothalamus through afferent pathways.13 The resulting norepinephrine release then triggers nonshivering thermogenesis, or lipolysis of brown adipose tissue, which is the main homeothermic heat production mechanism in newborns. Heat production occurs through uncoupling ATP synthesis via the oxidation of fatty acids in the mitochondria, utilizing uncoupled protein.14
Afferent temperature information is processed in the hypothalamus. Thermoregulation requires an intact central nervous system,15 and impaired thermoregulation, either hypo- or hyperthermia, can be indicators of central nervous system damage. The hypothalamus has a central role in regulating the autonomic, somatic and endocrine systems to maintain a normal body temperature. Decreasing body temperatures trigger a release of thyroid-stimulating hormone, which leads to an increase in thyroxine and consequently triiodothyronine. The resulting norepinephrine release causes vasoconstriction, glycolysis and uncoupling of mitochondrial oxidation in the brown adipose tissue, further generating heat production.14 The latter process is ineffective in preterm infants, because it depends on the amount of brown fat as well as levels of the enzymes 5′/3′-monodeiodinase and thermogenin, which build up only later in fetal development.13
Shivering is not regularly involved in a newborn's reaction to cold stress.16 Another mechanism of heat production is infant behavior:10 the irritable baby prompts the mother to hold the baby, drying, cuddling and swaddling him or her, thus preventing heat loss.
Newborns are unable to maintain their body temperature on their own without thermal protection. Although a newborn's thermoregulation is as complex as in adults if not more sophisticated, as discussed above, their range of optimal or even tolerable body temperature is narrower. A newborn placed naked in an environment of 23 °C at birth suffers the same cold as does a naked adult at 0 °C.17 Without thermal protection, human neonates are functionally poikilothermic, that is, they change their body temperature according to environmental temperatures. In newborns placed in a colder environment, core temperature decreases at a rate 0.2 to 1.0 °C per minute and finally may lead to death from cessation of metabolic activities.10
## Pathophysiology of newborn hypothermia
The World Health Organization (WHO) defines neonatal hypothermia as a temperature below 36.5 °C (97.7 °F) and proposes the following classification:17 Mild hypothermia, caused by cold stress, is classified as a body temperature range from 36 to 36.5 °C (96.8 to 97.7 °F) and is considered a cause for concern,17 because the exposed infant begins to lose more heat than he or she can produce.13 Moderate hypothermia is a body temperature from 32 to 36 °C (89.6 to 96.8 °F), indicating danger and requiring warming of the baby. According to the WHO classification, a body temperature of <32 °C (89.6 °F) is considered severe hypothermia, or cold injury, with a potentially grave outcome, and needs immediate skilled attention.
Heat loss occurs in several ways. The most common scenario is that of a wet baby who is not dried, and in whom evaporation of fluid from the skin leads to heat loss. Evaporation often occurs with amniotic fluids during the first minutes of life or with water after a baby is bathed. The energy loss is substantial: immediately at delivery, when the environmental temperature surrounding the baby drops from 37 °C in the maternal womb to the usually less warm air temperature, evaporative heat loss begins at a rate of 0.58 kcal ml−1 fluid evaporated.10
A baby placed naked on a cold surface loses heat through conduction. A newborn exposed to cool surrounding air or draughts will lose heat through convection. Radiation from cool objects next to the baby (for example, a cold wall) can also lower its body temperature. Unlike in adults, sweat secretion has little or no role in the thermoregulation of a newborn or preterm baby.18
As all data on hypothermia are from observational studies and prospective randomized trials without treating hypothermia are not permissive, the direction of causality for factors associated with hypothermia is not entirely clear.
Some argue that lowering body temperatures might increase metabolic processes to generate heat, which could lead to hypoglycemia and hypoxia in response to increasing energy demands.13 As hypothermia and hypoglycemia both exacerbate hypoxia, this would reinforce a vicious circle19 and could on one hand explain the mortality associated with hypothermia. However, studies have shown that hypothermia is not a risk factor for neonatal hypoglycemia in analyses adjusted for confounders such as LBW or anemia.20 On the other hand, hypoglycemia is common among newborns in resource-limited settings20 and, instead of being a consequence, could rather be a cause of hypothermia.
Similarly, with regard to the reported associations of hypothermia with infections and organ failure,21, 22 hypothermia might be either a consequence or a cause of severe infections. Clinically, hypothermia is an indicator for severe infections analogous to hyperthermia, or fever. In fact, neonatal hypothermia is associated in an unclear direction of causality with various pathologies such as surfactant inactivation, increased morbidity from infection, abnormal coagulation, delayed readjustment from the fetal to newborn circulation, hyaline membrane disease and intraventricular hemorrhage in LBW infants.23
In contrast, mild therapeutic hypothermia has emerged as a neuroprotective strategy in the treatment of hypoxic ischemic encephalopathy. Recent randomized controlled trials have shown that therapeutic hypothermia initiated within 6 h of birth reduces death and disability in these infants.24 Induced under controlled clinical conditions, therapeutic hypothermia has been discussed as being beneficial and outweighing the adverse effects in term newborns with hypoxic ischemic encephalopathy25 and during or after cardiac surgery.26
## Neonatal hyperthermia
Heat is transferred in utero via the placenta through umbilical arterial blood flow and via the uterus through amniotic fluid to the fetus.14 At birth, fetal temperature is usually 0.5 to 1.0 °C higher than the mother's27 and increases not only with elevated maternal temperatures due to prolonged labor, prolonged rupture of the membranes or other infectious etiologies (chorioamnionitis, urinary tract infection, and so on), but also with nulliparity and epidural analgesia.28
The most common cause of elevation of body temperature in the newborn is dehydration.29 Rehydration is both therapeutic and diagnostic if the newborn improves. Elevated temperatures in the neonate rarely reflect intrauterine or perinatal infections. Among the 1 to 2.5% of newborns presenting with hyperthermia, <10% have culture-proven sepsis.10 In septic newborns, temperature instability more frequently presents as hypothermia. The exact mechanisms that lead to fever in some septic neonates and normal body temperatures in others are ill understood. Infection is thought to produce fever mediated through cytokines such as interleukin1. Antipyretics are effective in reducing the temperature by modifying the central set-point of the hypothalamus. In hyperthermia due to environmental overheating, antipyretics are ineffective, and newborns are appropriately managed by reducing the environmental heat exposure.
Central malformations and intracranial hemorrhages, or congenital pathologies such as the Crisponi syndrome,30 are rare causes of newborn hyperthermia.
Where thermoprotective devices are used, inappropriate incubation and exposure to radiant warmers are common causes of neonatal hyperthermia,10 especially when makeshift apparatuses such as light bulbs, hot stones, and so on, are used. These are usually not designed and tested for safety and efficiency, and we discourage their use in favor of skin-to-skin care (SSC).
## Management of newborn hypothermia
### Qualitative inquiries into current thermal practices
Although lack of equipment is a problem for high-risk neonates in resource-poor settings, knowledge of hypothermia diagnosis and management is another concern. For example, only about half of 160 surveyed health care professionals in India could define neonatal hypothermia correctly or considered it a significant problem, and <20% knew how to correctly record a newborn's temperature.31 A multinational study showed that knowledge on thermal control, especially concerning the physiology of thermoregulation and criteria for defining hypothermia, was insufficient and thermal control practices were frequently inadequate.23
Qualitative research on newborn care can help shed light on the beliefs and attitudes underlying potentially detrimental or harmful practices. Most published studies indicate that high-risk home delivery and newborn care practices that lead to heat loss, such as insufficient heating of the birthplace, placing of the uncovered newborn on the ground or other cold surfaces, delayed wrapping—partly with unclean clothes—and early bathing, remain common in resource-limited settings both in rural and urban areas, in facilities and during home births.5, 32, 33
Heating the birthplace is a critical issue for home births. Studies from Nepal reported that the birthplace was heated in only slightly over half of the settings,34 often only after birth.35 Wrapping the child prevents heat loss from evaporation, whereas bathing promotes heat loss. Less than half (46%) of the babies were wrapped within the first 10 min after birth, and almost all of them were bathed within 10 min (89%) or half an hour (96%) after birth.34 In another study, only 64% of the babies were observed to be wrapped within half an hour after birth, and almost all were bathed within 6 h after birth.35
In a study from Tanzania, the practice of bathing newborns immediately after delivery was shown to be motivated by concerns about ‘ritual pollution’.36 In Ghana, early bathing was linked to reducing body odor in later life, shaping the baby's head, and helping the baby sleep and feel clean, and informants felt that changing bathing behaviors would be difficult, especially as babies are bathed early in facilities.37 A study from Dhaka, Bangladesh, explained that babies are typically bathed soon after birth to purify them from the birth process.38 Several studies, from Uganda,39 Ghana37 and India40 suggested that in the absence of health facilities prepared to deliver essential newborn care, community members would accept thermoprotective practices such as SSC.
## Clinical presentation
It has been estimated that prompt recognition of hypothermia and re-warming of hypothermic infants will avert up to 40% of neonatal deaths.41 Newborn hypothermia presents with a combination of low core temperature and cold skin, pallor (acrocyanosis), tachypnea (respiratory distress), hypotonia, lethargy or irritability, poor feeding or vomiting. The non-specific clinical presentation and the complex process of thermoregulation discussed above imply a number of differential diagnoses such as infectious etiologies, respiratory distress syndrome, intraventricular hemorrhage or other central nervous causes, hypoglycemia, endocrine causes, or (maternal) drug side effects. Other factors potentially underlying hypothermia include prematurity, cardiovascular diseases and other congenital anomalies.
## Diagnosis
Initial assessment should include a history of the baby's exposure to cold and whether the baby has been appropriately clothed and protected.18 Although a rectal digital thermometer is used in many studies as standard method to measure a newborn's core temperature, this measurement site is associated not only with discomfort and disturbance to the newborn, but also with risks such as rectal perforation and vagal stimulation with resulting arrhythmias, bradycardia and apnea.42
The axilla is a less invasive, alternative site that provides reasonably accurate measurements. Mercury-in-glass, gallium-in-glass, digital thermometer, analogous electric thermometer, chemical thermometer and infrared thermometer are all accurate instrument options, with the latter being less hazardous and quicker than the former.43 Most developed institutions use tympanic thermometers, which have recently shown to be a quick and accurate method to measure a newborn's body temperature,44 whereas simple rectal thermometers are used in most resource-limited settings. WHO recommends frequent measurements, from every hour in a seriously ill baby, two to four times per day in a small or very small baby, to once daily in an infant progressing well.18 However, due to their cost, thermometers are often not available in low-resource environments. Moreover, illiteracy and inability to read Arabic numbers have been a challenge to thermometer use.
In the absence of a measurement device, human touch of feet and abdomen has been used as a proxy for body temperature. Studies in India and Nepal have shown human touch to be reasonably reliable for the detection of hypothermia when health workers were trained for these investigations.45, 46, 47, 48, 49 Mothers, however, seem to have a far lower sensitivity than health workers. Only 24% of mothers in India were able to correctly identify hypothermia.50
A device based on color indicators developed to detect hypothermia without the use of thermometers was previously found to accurately indicate hypothermia when used by health workers or mothers.51, 52 Its usefulness for some parts of the developing world and the feasibility for illiterate health workers to read the device have been debated.53, 54
## Therapeutic goals of thermal care
The therapeutic goal of thermal care is to keep the newborn in the thermoneutral zone, or thermal neutrality, the environmental temperature range in which the organism has least oxygen consumption.9 No single environmental temperature is optimal for all babies. In general, the smaller and more premature a newborn is, the less its ability to regulate cold and heat. The optimal environmental temperature thus depends on the maturity (usually estimated by the gestational age) and age of the newborn. Weight, body temperature and skin perfusion as well as clothing of the infant and air humidity also factor in, so that the optimal environmental temperature can be hard to determine. It is narrow, especially in LBW or sick babies, and generally ranges from 32 to 36 °C.55 It follows that a temperature appropriate for a healthy term baby can be too cold for a preterm infant (and, conversely, what is appropriate for the preterm infant can be too warm for the term baby). In general, most newborns at birth, if left wet and naked, cannot tolerate an environmental temperature of <32 °C. However, if the baby is immediately dried, put skin-to-skin with the mother and covered, the delivery room temperature can be as low as 25 to 28 °C.17
## Prevention of newborn hypothermia
WHO recognizes maintaining a normal body temperature as a primary principle of newborn care and recommends thermal protection for all infants, with special attention for sick, premature, or small for gestational age infants, for example, <2.5 kg at birth or born before 37 weeks gestation.18 Several methods can be used for warming the baby and maintaining the baby's body temperature (Table 1). The WHO proposes a ‘warm chain’, a set of 10 interlinked procedures carried out at birth and during the following hours and days. To be implemented in institutions and (in an abridged form) at home, the warm chain aims to minimize the risk of hypothermia in newborns, and includes warming the delivery room, immediate drying, SSC, early and exclusive breast-feeding, postponing bathing, appropriate clothing and bedding, placing mother and baby together, and in institutions warm transportation, warm resuscitation, and training and awareness raising.17
WHO recommends warming the delivery place in preparation for a birth (to at least 25 °C) and to keep the birthplace free from draughts. After delivery, it is crucial to devote some attention to the baby. The first and most substantial heat loss occurs through evaporation of amniotic fluid. Therefore, at birth, recommended first steps to prevent hypothermia are to immediately dry and cover the newborn, even before the cord is cut. While being dried, the baby should be on a warm surface, preferably the mother's chest or abdomen in skin-to-skin contact. The infant should then be clothed or covered, especially the head,56 and kept in a warm environment, again usually best with the mother. Bathing should be delayed. Draughts, cold surfaces or nearby cold sources such as windows or walls should be avoided as they contribute to heat loss via convection and radiation.
Early breastfeeding, ideally within an hour after delivery, should be encouraged if possible and if not contraindicated. SSC with the mother, for LBW infants also known as kangaroo mother care, most of the time is appropriate to ensure thermal protection of the baby.57 It requires minimal instructions and, when culturally accepted, can relatively easily be applied even in a community or home setting.58
## Treatment of newborn hypothermia
According to current WHO guidelines for the treatment of cold babies, moderate hypothermia should be treated by SSC.18 In severe hypothermia, rewarming the baby with an appropriate and available method in a health care facility setting is warranted, as close monitoring of vital signs including temperature and respiratory rate are essential parts of the management. Blood glucose should be controlled and hypoglycemia under 45 mg dl−1 (2.6 mmol l−1) should be treated accordingly. When treating for sepsis, all IV fluids should be given warm. The infant can be discharged once a stable normal temperature is sustained and there are no other issues. Upon discharge, the mother should be counseled to prevent hypothermia at home as discussed above.
There is a relative scarcity of data documenting the effects of recommended thermal newborn care. A recent meta-analysis showed that SSC in conjunction with breastfeeding and recognition of danger signs substantially reduced neonatal mortality in hospital-born preterm babies (birth weight <2000 g) in hospital, and was highly effective in reducing severe morbidity, particularly from infection.59 A study from Western India, in which 36.9% of hospitalized newborns were hypothermic, reported a decrease in this rate to 3.9% with kangaroo mother care.60 However, in many countries there is resistance from health professionals, mothers and families related to local cultural practices.61 Although evidence on the effectiveness of SSC in community-based settings is scarce,40, 62 it is estimated that SSC can avert up to 20% of newborn deaths.63
In the large Gadchiroli trial in India on home-based neonatal care assessing the outcome of sepsis management, case management included thermal protection of the newborn, and health care workers were given a thermometer, baby clothes and head cover, a blanket and a sleeping bag. Although the study included other interventions and was not specifically designed to prove a particular effect for hypothermia management, it showed a reduction in neonatal and infant mortality by nearly 50% among a malnourished, illiterate and rural study population.64 A study from Nepal that found a high incidence of hypothermia suggests that simple interventions including immediate drying and another treatment (breast contact, radiant heater and mustard oil massage, or swaddling with an inner layer of plastic wrap) could lower the incidence of hypothermia 2 h after birth from 78 to 23% and 24 h after birth from 49 to 18%.65 In Zambia, we recently showed that training traditional birth attendants in newborn care with special emphasis on resuscitation and simple thermal protection (wiping the newborn dry and wrapping the dried infant in a separate piece of cloth) along with an intervention to provide early treatment of possible sepsis reduced mortality rates at day 28 after birth by 45%.66
## Low-cost, low-tech treatment of newborn hypothermia
The use of incubators for thermal protection of newborns has been reported for more than 150 years, since the Parisian obstetrician Jean Louis Paul Denucé in 1857 engineered his couveuse, a device for the care of a premature infant. In 1878, his local colleague Stéphane Tarnier, using a modified warming chamber for the rearing of poultry, found a decrease in neonatal death rate from 66 to 38% among infants with birth weights <2000 g.67
Today, postnatal care devices (isolettes or infant warmers) combine the features of incubators and radiant warmer beds and have evolved with many features, including automated temperature and humidity regulations,68 oxygen supplementation and light therapy.11, 69 Although beneficial in resource-replete settings,70 utilization of their complex features requires electricity, concentrated oxygen supply, centralized suction and ongoing skilled maintenance. Priced at about US$15 000 to$36 000,71 these devices are not affordable for most of the developing world. Simplified versions, such as water-filled mattresses or Indian made, low-cost radiant warmers are power-dependent and not appropriate for resource-limited settings. Polyethylene occlusive skin wrapping is a useful and effective method for delivery room management,72 but mostly limited to immediate post-delivery care and protection during transport.
A number of postnatal care devices for resource-limited settings are currently in development, some including more sophisticated temperature and humidity regulations. Examples are the ‘mkat,’ ‘Life Raft Incubator,’ and ‘Neo.nurture’, projected to be priced between US $200 and US$625 per unit.73 The ‘Embrace Global’, projected to be priced at a US \$25 price, is a life vest style incubator in a ‘sleeping bag’ design.74 The heat source is a pouch-containing phase change material, which keeps its temperature relatively constant over an extended period of time. The pouch is warmed electrically or by the user simply pouring hot water into a compartment, upon indication by a thermal strip. It can fully open to double as a heat mattress. With some models electricity independent, it can be used both at the institutional and community levels, and serve as visual reminders to mothers and other caretakers, birth attendants and health care workers. Devices such as these, although more costly than education alone, might thus foster improved hypothermia management by transporting a behavioral message to the end user, for example, promoting SSC. Distributed commercially or donated, they could help to raise awareness and enhance perception of the burden of newborn hypothermia.
## Conclusions
Thermal protection of the newborn can relatively easily be achieved by warming of the delivery room, immediate drying, wrapping the infant after birth and keeping him or her in close contact with the mother, that is, kangaroo mother care or SSC, immediate and frequent exclusive breastfeeding, delaying of bathing until the infant is physiologically stable, and appropriate warm clothing. These behavior steps represent simple, low-cost measures, which should be integrated into holistic mother and child health packages.
Birth practices even in high-risk environments remain poor, so that interventions must primarily focus on participatory education about hygiene, infection prevention and management, as well as practices to avoid hypothermia. Low-cost, low-technology devices might be helpful in supporting and implementing these practices. Clinical effectiveness and implementation trials will have to investigate which intervention packages and messages for the thermal protection for newborns work best in a given environment, and how to optimally integrate them into existing maternal and newborn health programs.
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## Author information
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Correspondence to K Lunze.
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Lunze, K., Hamer, D. Thermal protection of the newborn in resource-limited environments. J Perinatol 32, 317–324 (2012). https://doi.org/10.1038/jp.2012.11
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### Keywords
• newborn
• neonatal
• hypothermia
• thermal protection
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http://math.stackexchange.com/questions/209274/modular-arithmetic-congruence-class-simple-proof/209289
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# modular arithmetic congruence class simple proof
Hello I have the following question but I'm unsure of how it can be approached by a method of proof. I'm new to modular arithmetic and any information on how to solve this would be great for me.
http://imgur.com/3iHvQ
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Imagine trying everything. Clearly $5\cdot 5$ is no good. All the other choices give (ordinary) product $m$ between $0$ and $20$, so it is clear that $25$ cannot divide $24-m$.
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First note that $24\equiv -1\pmod{25}$ and hence we are trying to show that $ts\not\equiv-1\pmod{25}$. Suppose for contradiction that $ts\equiv -1\pmod{25}$, then multiplying through by $-1$ we get $-ts\equiv 1\pmod{25}$ so $t$ or $s$ is invertible, say $t$ with inverse $-s$. Therefore $\gcd(t,25) = 1$ (why?), and hence $t = 1,2,3,4$. There is a unique value of $s$ corresponding to each of these (why?), each of which should give you a contradiction.
$[t][s]$ refers to the product of the equivalence classes of $[t]$ and $[s]$ taken modulo $25$ – John Martin Oct 8 '12 at 15:32
Hint $\$ If $\rm\:a\:|\:b\:$ in $\Bbb Z$ then so too in every ring, and the quotient is unique if $\rm\:a\:$ is not a zero divisor. Also, divisors of units are units, so $\rm\: mod\ 25\:$ the divisors of $\:24\equiv -1\:$ are units, so coprime to $5$.
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https://hci.iwr.uni-heidelberg.de/biblio?page=8&%3Bamp%3Bf%5Bauthor%5D=3060&%3Bf%5Bauthor%5D=2357&s=type&o=asc
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# Publications
Export 1500 results:
Author Title [ Type] Year
Conference Paper
(1995). A high-performance system for 3-dimensional particle tracking velocimetry in turbulent flow research using image sequences. Proc. ISPRS Intercommission workshop From Pixels to Sequences, Zürich, March 22-24. Risc Books. 30 Part 5W1 202--207
(2014). High-resolution 2-D fluorescence imaging of gas transfer at a free water surface. Ocean Science Meeting, 23--28. 02. 2014, Honolulu Hawaii
(1995). Horizontal and vertical spatial structures of turbulence beneath short wind waves. IAPSO Proceedings, XXI General Assembly, Honolulu, Hawai, August 1995, PS-10 Spatial Structure of Short Ocean Waves. 384
(2014). ilastik for Multi-modal Brain Tumor Segmentation. MICCAI BraTS (Brain Tumor Segmentation) Challenge. Proceedings, 3rdplace. 12-17 (405.91 KB)
(2011). ilastik: Interactive Learning and Segmentation Toolkit. Eighth IEEE International Symposium on Biomedical Imaging (ISBI 2011).Proceedings. 230-233
(2001). Image labeling and grouping by minimizing linear functionals over cones. Proc.~Third Int. Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR'01). Springer. 2134 267--282
Jähne, (2003). Image sequence analysis in environmental and live sciences. Proceedings of the 25th DAGM Symposium on Pattern Recognition. Springer. 2781 608--617
Jähne, (1987). Image sequence analysis of complex physical objects: nonlinear small scale water surface waves. Proc. of 1st International Conference on Computer Vision. IEEE. 191--200
(1993). Image sequence analysis of ocean wind waves. Imaging in Transport Processes. Begell House Publishers. 257--268. http://www.dl.begellhouse.com/references/1bb331655c289a0a,36adf33e6f249361.html
(2001). Image sequence analysis of satellite NO$_2$ concnetration maps. Pattern Recognition, 23rd DAGM Symposium Munich. Springer. 2191 223--230
(2006). Imaging concentration profiles of water boundary layer by Double-Dye LIF and inverse modelling. Verhandlungen der Deutschen Physikalischen Gesellschaft, Spring Conference, Heidelberg, 15.-17.03.2006. Deutsche Physikalische Gesellschaft. http://www.dpg-verhandlungen.de/2006/heidelberg/up.html
Jähne, (1993). Imaging of gas transfer across gas/liquid interfaces. Imaging in Transport Processes. Begell House Publishers. 247--256. http://www.dl.begellhouse.com/references/1bb331655c289a0a,36adf33e6f249361.html
(1995). An imaging optical technique for bubble measurements. Proc. Sea Surface Sound '94. World Scientific. 290--296
(2006). Imaging System for combined slope/height measurements of short wind waves : ISHG. Verhandlungen der Deutschen Physikalischen Gesellschaft, Spring Conference, Heidelberg, 15.-17.03.2006. Deutsche Physikalische Gesellschaft. http://www.dpg-verhandlungen.de/2006/heidelberg/up.html
(1995). Impact of quantitative visualization and image processing on the study of small-scale air-sea interaction. Air-Water Gas Transfer, Selected Papers, 3rd Intern. Symp. on Air-Water Gas Transfer. AEON. 3--12
(2011). Improved optical instrument for the measurement of water wave statistics in the field. Gas Transfer at Water Surfaces 2010. 524--534. http://hdl.handle.net/2433/156156
(2007). Improved training algorithm for tree-like classifiers and its application to vehicle detection. Proc. IEEE Intelligent Transportation Systems Conference (ITSC). 642--647
(2015). Improving 3D EM Data Segmentation by Joint Optimization over Boundary Evidence and Biological Priors. 12th {IEEE} International Symposium on Biomedical Imaging, {ISBI} 2015, Brooklyn, NY, USA, April 16-19, 2015. 536-539 (2.25 MB)
(2018). Improving Spatiotemporal Self-Supervision by Deep Reinforcement Learning. Proceedings of the European Conference on Computer Vision (ECCV). (UB and BB contributed equally), Munich, Germany (5.34 MB) (1.65 MB)
(1995). In situ determination of cell concentration in bioreactors with a new depth from focus technique. Computer Analysis of Images and Patterns. Springer. 970 392--399
(1995). In situ measurements of the air-sea gas transfer rate during the MBL/CoOP west coast experiment. Air-Water Gas Transfer - Selected Papers from the Third International Symposium on Air-Water Gas Transfer. AEON. 775--784
(1996). In-situ determination of cell concentration in bioreactors with a new depth-from-focus technique. Proc.\ Optical 3-D Measurement Techniques IV, Zurich, Sept. 29 - Oct. 2, 1997. 392--399
(1994). In-situ measurements of the air-sea gas transfer using heat as a proxy tracer. Proc. 2nd Inter. Conf. on Air-Sea Interaction and on Meteorology and Oceanography of the Coastal Zone, Lisbon, 22.--27. September 1994
(2014). Instance Label Prediction by Dirichlet Process Multiple Instance Learning. UAI. Proceedings (4.26 MB)
(2009). Instrument development for combined height/slope/curvature statistics measurements of wind water waves in the field. Poster abstracts SOLAS Open Science Conference, Barcelona, 16--19 Sep. 2009
(1995). Interaction of short wind waves and turbulent shear flow as revealed by simultaneous wave slope and surface turbulence visualization. IAPSO Proceedings, XXI General Assembly, Honolulu, Hawai, August 1995, PS-10 Spatial Structure of Short Ocean Waves. 387
(2009). Intrinsic Second-Order Geometric Optimization for Robust Point Set Registration Without Correspondence. Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2009). Springer. 5681 274-287. http://www.springerlink.com/content/1470n7577713069q/ (752.29 KB)
Jähne, (2010). Investigating the mechanisms of air-water gas transfer by quantitative imaging techniques: history, current progress and remaining challenges. 6th Int. Symp. Gas Transfer at Water Surfaces, Kyoto, May 17--21, 2010
(1998). Investigation of Parallel and Globally Convergent Iterative Schemes for Nonlinear Variational Image Smoothing and Segmentation. Proc.~IEEE Int.~Conf.~Image Proc
(2012). Investigation of small-scale air-sea interaction processes by active thermography. Geoscience and Remote Sensing Symposium (IGARSS). 358--361
(2002). On the investigations of statistical properties of the micro turbulence at the ocean surface. Gas Transfer at Water Surfaces. American Geophysical Union. 127 51--57
(2016). Joint Recursive Monocular Filtering of Camera Motion and Disparity Map. 38th German Conference on Pattern Recognition. Springer, Hannover. https://arxiv.org/abs/1606.02092 (2.34 MB)
(2013). K-smallest Spanning Tree Segmentations. German Conference on Pattern Recognition (DAGM/GCPR). Proceedings. Springer. 375-384 (1.18 MB)
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https://mospace.umsystem.edu/xmlui/handle/10355/251/browse?value=Zhang%2C+Qi&type=advisor
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Now showing items 1-1 of 1
• #### On projective morphisms of varieties with nef anticanonical divisor
(University of Missouri--Columbia, 2012)
We shall study and discuss some important properties of the projective varieties with nef anticanonical bundles and nef tangent bundles. And we shall review some background and history about the subject. Then we shall use ...
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http://dealii.org/developer/doxygen/deal.II/group__grid.html
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Reference documentation for deal.II version Git 041ea9b 2017-01-20 08:06:34 -0700
Grid classes
Collaboration diagram for Grid classes:
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## Modules
Boundary and manifold description for triangulations
Iterators on mesh-like containers
Manifold description for triangulations
## Namespaces
parallel::distributed::GridRefinement
GridGenerator
GridRefinement
GridTools
## Classes
struct GeometryInfo< 0 >
struct GeometryInfo< dim >
class FilteredIterator< BaseIterator >
class FilteredIterator< BaseIterator >::PredicateTemplate< Predicate >
class FilteredIterator< BaseIterator >::PredicateBase
class GridIn< dim, spacedim >
class GridOut
class GridReordering< dim, spacedim >
struct GridTools::PeriodicFacePair< CellIterator >
class InterGridMap< MeshType >
class PersistentTriangulation< dim, spacedim >
struct CellData< structdim >
struct SubCellData
class Triangulation< dim, spacedim >
struct Triangulation< dim, spacedim >::Signals
struct Triangulation< dim, spacedim >::CellWeightSum< T >
struct Triangulation< dim, spacedim >::DistortedCellList
class TriaAccessorBase< structdim, dim, spacedim >
class CellAccessor< dim, spacedim >
class TriaRawIterator< Accessor >
class TriaIterator< Accessor >
class TriaActiveIterator< Accessor >
## Enumerations
enum Triangulation< dim, spacedim >::MeshSmoothing {
Triangulation< dim, spacedim >::none = 0x0, Triangulation< dim, spacedim >::limit_level_difference_at_vertices = 0x1, Triangulation< dim, spacedim >::eliminate_unrefined_islands = 0x2, Triangulation< dim, spacedim >::patch_level_1 = 0x4,
Triangulation< dim, spacedim >::coarsest_level_1 = 0x8, Triangulation< dim, spacedim >::allow_anisotropic_smoothing = 0x10, Triangulation< dim, spacedim >::eliminate_refined_inner_islands = 0x100, Triangulation< dim, spacedim >::eliminate_refined_boundary_islands = 0x200,
Triangulation< dim, spacedim >::do_not_produce_unrefined_islands = 0x400, Triangulation< dim, spacedim >::smoothing_on_refinement, Triangulation< dim, spacedim >::smoothing_on_coarsening, Triangulation< dim, spacedim >::maximum_smoothing = 0xffff ^ allow_anisotropic_smoothing
}
## Keeping up with what happens to a triangulation
enum Triangulation< dim, spacedim >::CellStatus { Triangulation< dim, spacedim >::CELL_PERSIST, Triangulation< dim, spacedim >::CELL_REFINE, Triangulation< dim, spacedim >::CELL_COARSEN, Triangulation< dim, spacedim >::CELL_INVALID }
Signals Triangulation< dim, spacedim >::signals
## Detailed Description
This module groups classes that have to do with the topology and geometry of meshes. A mesh can be thought of a collection of cells; if the mesh has been refined (possibly in an adaptive way), then this collection is grouped into a hierarchy of refinement levels. In addition to cells, the geometric objects that make up a triangulation are the faces of cells (and in 3d the edges of cells) as well as the vertices of the cells. Note that we abuse the word triangulation somewhat, since deal.II only implements triangulations made up of linear, quadrilateral, and hexahedral cells; triangles and tetrahedra are not supported.
This collection of cells is managed by the Triangulation class. It holds the relevant data in memory and offers interfaces to query it. Most things you want to do on cells are performed in loops over all cells. For this purpose, the Triangulation class offers the concept of iterators (see Iterators on mesh-like containers): although implemented differently, they behave like pointers to cells or faces and can be queried for the geometric properties of cells as well as information like neighboring cells or faces of a cell.
It is worth noting that the Triangulation class only stores geometry (i.e. the location of vertices and cells) and topology of a mesh (i.e. which cells are neighbors of which other cells, etc). It has nothing to do with finite elements or degrees of freedom that might be defined on a mesh. These functions are performed by the DoFHandler class (see the Degrees of Freedom module) that gets a description of the finite element space and the allocates and manages degrees of freedom on vertices, faces, or cells, as described by the finite element class. This separation makes it possible to have multiple DoFHandler classes work on the same mesh at the same time.
### Grid generation
There are three ways to create a mesh:
• Creation by the GridGenerator class;
• Creation by hand.
For the first case, the GridGenerator class provides functions that can generate the simplest and most common geometries automatically. For example, a rectangular (or brick) geometry as well as circles, spheres, or cylinders can be generate with the functions in this class. Most of the tutorial programs use this mechanism.
Secondly, it is possible to read in meshes from an input file in a number of different formats using the GridIn class. Using this class, it is possible to read meshes with several 10 or 100 thousand cells, although this is not really recommended: the power of adaptive finite element methods only comes to bear if the initial mesh is as coarse as possible and there is room for a number of adaptive refinement steps. If the initial mesh is too fine already, then one runs out of memory or compute time before adaptive mesh refinement is able to do much good. Nevertheless, the GridIn class can be used in cases of complicated geometries or for comparison or interaction with other programs that compute on meshes that are then exchanged through this class The step-5 tutorial program shows how to use the GridIn class.
The third way is to create a mesh by hand, by building a data structure that describes the vertices and cells of a triangulation. This is useful in cases of moderate complexity where a mesh can still be built by hand without resorting to a mesh generator, but where the domain is not one of those already supported by the GridIn class. In this method, the data structure so built is handed to the create_triangulation() function of the Triangulation class. The step-14 tutorial program shows how this can be done.
### Grid output
Meshes can be written to output files in a number of different formats. If this involves simulation results obtained on this mesh, then this is done using the DataOut class (described in more detail in the Graphical output module). On the other hand, if only the geometry and topology of the mesh is to be written to a file, the GridOut class can do this for you.
### Tool classes
The GridTool class offers an assortment of functions that act on grids. For example, this includes moving around nodes, stretching or rotating entire triangulations, computing the diameter of a domain, or subdividing it into chunks of roughly equal size for parallel computations.
The GridRefinement class implements a number of mesh refinement algorithms, based on refinement indicators given to its member functions.
### Internal classes
In addition to the above, there are a significant number of classes in this module that are only used in the internal data structures of mesh handling. They are generally in the internal namespace, and not meant for use in application code.
## Enumeration Type Documentation
template<int dim, int spacedim = dim>
Declare some symbolic names for mesh smoothing algorithms. The meaning of these flags is documented in the Triangulation class.
Enumerator
none
No mesh smoothing at all, except that meshes have to remain one- irregular.
limit_level_difference_at_vertices
It can be shown, that degradation of approximation occurs if the triangulation contains vertices which are member of cells with levels differing by more than one. One such example is the following:
It would seem that in two space dimensions, the maximum jump in levels between cells sharing a common vertex is two (as in the example above). However, this is not true if more than four cells meet at a vertex. It is not uncommon that a coarse (initial) mesh contains vertices at which six or even eight cells meet, when small features of the domain have to be resolved even on the coarsest mesh. In that case, the maximum difference in levels is three or four, respectively. The problem gets even worse in three space dimensions.
Looking at an interpolation of the second derivative of the finite element solution (assuming bilinear finite elements), one sees that the numerical solution is almost totally wrong, compared with the true second derivative. Indeed, on regular meshes, there exist sharp estimations that the H2-error is only of order one, so we should not be surprised; however, the numerical solution may show a value for the second derivative which may be a factor of ten away from the true value. These problems are located on the small cell adjacent to the center vertex, where cells of non-subsequent levels meet, as well as on the upper and right neighbor of this cell (but with a less degree of deviation from the true value).
If the smoothing indicator given to the constructor contains the bit for limit_level_difference_at_vertices, situations as the above one are eliminated by also marking the lower left cell for refinement.
In case of anisotropic refinement, the level of a cell is not linked to the refinement of a cell as directly as in case of isotropic refinement. Furthermore, a cell can be strongly refined in one direction and not or at least much less refined in another. Therefore, it is very difficult to decide, which cases should be excluded from the refinement process. As a consequence, when using anisotropic refinement, the limit_level_difference_at_vertices flag must not be set. On the other hand, the implementation of multigrid methods in deal.II requires that this bit be set.
eliminate_unrefined_islands
Single cells which are not refined and are surrounded by cells which are refined usually also lead to a sharp decline in approximation properties locally. The reason is that the nodes on the faces between unrefined and refined cells are not real degrees of freedom but carry constraints. The patch without additional degrees of freedom is thus significantly larger then the unrefined cell itself. If in the parameter passed to the constructor the bit for eliminate_unrefined_islands is set, all cells which are not flagged for refinement but which are surrounded by more refined cells than unrefined cells are flagged for refinement. Cells which are not yet refined but flagged for that are accounted for the number of refined neighbors. Cells on the boundary are not accounted for at all. An unrefined island is, by this definition also a cell which (in 2D) is surrounded by three refined cells and one unrefined one, or one surrounded by two refined cells, one unrefined one and is at the boundary on one side. It is thus not a true island, as the name of the flag may indicate. However, no better name came to mind to the author by now.
patch_level_1
A triangulation of patch level 1 consists of patches, i.e. of cells that are refined once. This flag ensures that a mesh of patch level 1 is still of patch level 1 after coarsening and refinement. It is, however, the user's responsibility to ensure that the mesh is of patch level 1 before calling Triangulation::execute_coarsening_and_refinement() the first time. The easiest way to achieve this is by calling global_refine(1) straight after creation of the triangulation. It follows that if at least one of the children of a cell is or will be refined than all children need to be refined. If the patch_level_1 flag is set, than the flags eliminate_unrefined_islands, eliminate_refined_inner_islands and eliminate_refined_boundary_islands will be ignored as they will be fulfilled automatically.
coarsest_level_1
Each coarse grid cell is refined at least once, i.e. the triangulation might have active cells on level 1 but not on level 0. This flag ensures that a mesh which has coarsest_level_1 has still coarsest_level_1 after coarsening and refinement. It is, however, the user's responsibility to ensure that the mesh has coarsest_level_1 before calling execute_coarsening_and_refinement the first time. The easiest way to achieve this is by calling global_refine(1) straight after creation of the triangulation. It follows that active cells on level 1 may not be coarsened.
The main use of this flag is to ensure that each cell has at least one neighbor in each coordinate direction (i.e. each cell has at least a left or right, and at least an upper or lower neighbor in 2d). This is a necessary precondition for some algorithms that compute finite differences between cells. The DerivativeApproximation class is one of these algorithms that require that a triangulation is coarsest_level_1 unless all cells already have at least one neighbor in each coordinate direction on the coarsest level.
allow_anisotropic_smoothing
This flag is not included in maximum_smoothing. The flag is concerned with the following case: consider the case that an unrefined and a refined cell share a common face and that one of the children of the refined cell along the common face is flagged for further refinement. In that case, the resulting mesh would have more than one hanging node along one or more of the edges of the triangulation, a situation that is not allowed. Consequently, in order to perform the refinement, the coarser of the two original cells is also going to be refined.
However, in many cases it is sufficient to refine the coarser of the two original cells in an anisotropic way to avoid the case of multiple hanging vertices on a single edge. Doing only the minimal anisotropic refinement can save cells and degrees of freedom. By specifying this flag, the library can produce these anisotropic refinements.
The flag is not included by default since it may lead to anisotropically refined meshes even though no cell has ever been refined anisotropically explicitly by a user command. This surprising fact may lead to programs that do the wrong thing since they are not written for the additional cases that can happen with anisotropic meshes, see the discussion in the introduction to step-30.
eliminate_refined_inner_islands
This algorithm seeks for isolated cells which are refined or flagged for refinement. This definition is unlike that for eliminate_unrefined_islands, which would mean that an island is defined as a cell which is refined but more of its neighbors are not refined than are refined. For example, in 2D, a cell's refinement would be reverted if at most one of its neighbors is also refined (or refined but flagged for coarsening).
The reason for the change in definition of an island is, that this option would be a bit dangerous, since if you consider a chain of refined cells (e.g. along a kink in the solution), the cells at the two ends would be coarsened, after which the next outermost cells would need to be coarsened. Therefore, only one loop of flagging cells like this could be done to avoid eating up the whole chain of refined cells (`chain reaction'...).
This algorithm also takes into account cells which are not actually refined but are flagged for refinement. If necessary, it takes away the refinement flag.
Actually there are two versions of this flag, eliminate_refined_inner_islands and eliminate_refined_boundary_islands. There first eliminates islands defined by the definition above which are in the interior of the domain, while the second eliminates only those islands if the cell is at the boundary. The reason for this split of flags is that one often wants to eliminate such islands in the interior while those at the boundary may well be wanted, for example if one refines the mesh according to a criterion associated with a boundary integral or if one has rough boundary data.
eliminate_refined_boundary_islands
The result of this flag is very similar to eliminate_refined_inner_islands. See the documentation there.
do_not_produce_unrefined_islands
This flag prevents the occurrence of unrefined islands. In more detail: It prohibits the coarsening of a cell if 'most of the neighbors' will be refined after the step.
smoothing_on_refinement
This flag sums up all smoothing algorithms which may be performed upon refinement by flagging some more cells for refinement.
smoothing_on_coarsening
This flag sums up all smoothing algorithms which may be performed upon coarsening by flagging some more cells for coarsening.
maximum_smoothing
This flag includes all the above ones and therefore combines all smoothing algorithms implemented with the exception of anisotropic smoothing.
Definition at line 1266 of file tria.h.
template<int dim, int spacedim = dim>
Used to inform functions in derived classes how the cell with the given cell_iterator is going to change. Note that this may me different than the refine_flag() and coarsen_flag() in the cell_iterator in parallel calculations because of refinement constraints that this machine does not see.
Enumerator
CELL_PERSIST
The cell will not be refined or coarsened and might or might not move to a different processor.
CELL_REFINE
The cell will be or was refined.
CELL_COARSEN
The children of this cell will be or were coarsened into this cell.
CELL_INVALID
Invalid status. Will not occur for the user.
Definition at line 2019 of file tria.h.
## Variable Documentation
template<int dim, int spacedim = dim>
Signals Triangulation< dim, spacedim >::signals
mutable
Signals for the various actions that a triangulation can do to itself.
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http://www.archive.org/stream/theworksofthomas01cramuoft/theworksofthomas01cramuoft_djvu.txt
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# Full text of "The works of Thomas Cranmer ... Edited for the Parker society"
## See other formats
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Presented to the
LIBRARY of the
UNIVERSITY OF TORONTO
by
The Estate of the late
PROFESSOR A. S. P. WOODHOUSE
Department of English
University College
1944-1964
HANDBOUND
AT THE
ARCHBISHOP CRANMER
ON
THE SACRAMENT OF THE LORD S SUPPER.
jfor tfte publiratton of tfte OTorfes; of tfie
anJj arlp JKBnterg of tfte Eeformrtr
WRITINGS AND DISPUTATIONS
THOMAS CRANMER,
ARCHBISHOP OF CANTERBURY,
MARTYR, 1556,
RELATIVE TO THE SACRAMENT OF THE
LORD S SUPPER.
EDITED FOR
BY THE
REV. JOHN EDMUND COX, M.A.,
OF ALT, SOULS COLLEGE, OXFORD, CURATE AND LECTURER OF STKPNF.Y,
PRINTED AT
THE UNIVERSITY PEESS
M.DCCC.XLIV.
1039175
CONTENTS.
LIFE, State, and Story of Thomas Cranmer vii
An Answer to a Crafty and Sophistical Cavillation devised by Stephen
Gardiner 1
BOOK I. Of the Sacrament 9
BOOK III. Of the Presence of Christ 51
BOOK IV. Of the Eating and Drinking 201
BOOK II. Against Transubstantiation 239
BOOK V. Of the Oblation and Sacrifice of Christ 344
Answer to Smith s Preface 368
Matters wherein the Bishop of Winchester varied from other Papists, &c. 380
Disputations at Oxford S 89
Index 4 31
Defensio Verse et Catholics? Doctrinoe de Sacramento 1*
THE present volume contains the writings of archbishop Cranmer on the Sacrament of
the Lord s Supper, together with\he disputations held with him at Oxford previously to
his condemnation and martyrdom. The writings on the sacrament have been reprinted
from the edition of A. D. 1580, and exhibit the latest and most matured corrections of the
archbishop, which he is supposed to have made whilst under imprisonment previously to his
death. With this later edition, that of 1551, the original edition of his first work on
the sacrament, afterwards embodied by him in his answer to Winchester, as well as
bishop Gardiner s reply to it, have been carefully collated, and care has been taken to note
the various readings. The Latin edition of the first work, printed at Emden, A. D. 3557,
not previously reprinted, has been added; and this has likewise undergone a careful exami
nation, with the previous edition of the Latin translation, said by Strype to have been made
by Sir John Cheke. Wherever the additional references to the works of the Fathers are
found in the Emden edition, 1557, they have been noted in the margin of the body of this
reprint.
The Disputations held at Oxford are reprinted from the 1583 edition of Foxe s Acts
and Monuments, and have been collated with an earlier edition. Thus it is hoped, that the
pieces now given will be found to exhibit the last and most accurate thoughts of the arch
bishop, so far as they exist, arranged in a more complete form than has yet been attempted.
With reference to the succeeding volume, which will contain the rest of the writings
of archbishop Cranmer, the Editor has been engaged both at home and on the continent
in further researches, especially relating to a correspondence on the sacraments, supposed
to exist in some foreign public libraries. But after the most careful personal examination,
he is enabled to state, that nothing has been found beyond the letters previously printed by
Dr Jenkyns in his valuable edition of the works of the archbishop, except one brief letter
written by the archbishop a short time before his martyrdom, and which was discovered
at Zurich during the researches made there for the Parker Society. The biographical
sketch of the archbishop, and a full account of his remains, will be given with the succeeding
volume : but the memoir abridged from Foxe s Acts and Monuments, printed in the edition
of A. D. 1580, is here given, to put the reader in possession of a complete copy of that
work, printed in the reign of queen Elizabeth, with the exception of a few epistles which
will be found in the complete series of letters.
In conclusion, the Editor desires to acknowledge the valuable assistance he has derived
from the previous edition of Dr Jenkyns, which has relieved him from many difficulties :
nevertheless he has taken nothing from it, but has invariably examined early editions and
references for himself, and has stated the result of his own researches. He has also to
acknowledge the kind loan of a copy of the first edition of the archbishop s work on the
sacrament from the library of Gloucester Cathedral.
May 10, 1841.
THE
LIFE, STATE, AND STORY,
OF THE
REVEREND PASTOR AND PRELATE,
THOMAS CRANMER,
ARCHBISHOP OF CANTERBURY, MARTYR,
BURNED AT OXFORD FOR THE CONFESSION OF CHRIST S TRUE DOCTRINE.
ANNO 1556. MARCH 21.
FORASMUCH as the life and estate of the most reverend father in God and worthy Thomas
prelate of godly memory, Thomas Cranmer, late archbishop of Canterbury, togeth
with the original cause and occasion of his preferment to the dignity archiepiscopal, bury.
whereunto he was advanced immediately upon the death of bishop Warham, arch- Doctor cran-
bishop of the same, beyond all expectation, without support of money or friends, by archbishop
the only well-liking of the most renowned king of famous memory, Henry the Jp king
eighth, who with a fatherly care maintained his countenance, and defended his Doctor Cran-
innoccnt life, undermined sundry times by the manifold attempts of the horrible defended^
arch-enemy of Christ and his gospel, Stephen Gardiner, and other his complices;
with divers other circumstances of his most commendable conversation, charitable
consideration of the poor, constant care in reformation of corrupt religion, his
undaunted courage in continual defence of the same, and the perseverance therein
to the loss of his life, be already described at large in the book of Acts and Look for the
Monuments of Martyrs; it may seem needless to make a thorough discourse thereof tame boot
again at this present. Nevertheless, partly to stop the mouths of slanderous syco- and n ^ m u ~ h
phants, and partly for the ease of such as would happily be desirous, upon the view Jf 5 ^ 1110 "
of the title of this book, to be acquainted with the life of the author, being other
wise not able to have recourse to the story at large, as also because his virtuous
life and glorious death was such, as can never be commended sufficiently, I have
thought it not altogether amiss to renew the remembrance thereof by certain
brief notes, referring them that be desirous to know the whole to the story
thereof at large.
It is first therefore to be noted and considered, that the same Thomas Cranmcr Thomas
coming of ancient parentage, from the conquest to be deducted, and continuing sithens pnUeman
in the name and family of a gentleman, was born in a village called Arselacton in
Nottinghamshire. Of whose said name and family there remaineth at these days
one manor and mansion-house in Lincolnshire, called Cranmer Hall, &c. sometimes
of heritage of the said stock and family. Who being from his infancy kept at school,
and brought up, not without much good civility, came in process of time unto the ThomasCran-
university of Cambridge, and there prospering in right good knowledge amongst coming to
_ Cambridge.
the better sort of students, was chosen fellow of Jesus college in Cambridge. And
so being master of art, and fellow of the same college, it chanced him to marry
gentleman s daughter, by means whereof he lost and gave over his fellowship there,
and became the reader in Buckingham college; and for that he would with more
diligence apply that his office of reading, placed his said wife in an inn, called the
Vlll
THE LIFE, STATE, AND STORY
Dolphin, in Cambridge, the wife of the house being of affinity unto her. By means 1
of whose abode in that inn, and his often repair unto her, arose a certain slanderous
report, after he was preferred to be archbishop of Canterbury, bruited abroad by the
malicious disdain of certain sycophantical papists, that he was but an hosteler, and
altogether devoid of learning; which how falsely was forged upon him, may easily
Thomascran- appear hereby, that the masters and fellows of Jesus college, noting the virtuous
SaSof Ks disposition of the man, and the great travail he took, notwithstanding his marriage,
agSn^fStow w hiles he continued reader in Buckingham college, immediately upon the death of
coiieg^ us jjjg w jf e ( wno no t long after their enter marriage was in childbed surprised by death)
received him into their fellowship again; where he so behaved himself, that in few
Thomascran- years after he became the reader of the divinity lecture in the same college, and in
reader aid such special estimation and reputation with the whole university, that being doctor
divinity in o f divinity ne was commonly appointed one of the heads (which are two or three
Jesus College. " . .,-,
of t k e cn i e f es t learned men) to examine such as yearly profess, in commencement, e
ndgJ of bachelors or doctors of divinity, by whose approbation the whole university licenseth
?e e reto h pro- them to proceed unto their degree; and again, by whose disallowance the univer
sity also rejecteth them for a time to proceed, until they be better furnished with
more knowledge.
Now doctor Cranmer, ever much favouring the knowledge of the scripture, would
never admit any to proceed in divinity, unless they were substantially seen in the
Friars in story of the bible : by means whereof certain friars and other religious persons, who
doctor Con- were principally brought up in the study of school-authors, without regard had to
the authority of scriptures, were commonly rejected by him; so that he was greatly
for that his severe examination of the religious sort much hated and had in great in
dignation: and yet it came to pass in the end, that divers of them, being thus com
pelled to study the scriptures, became afterwards very well learned and well affected;
insomuch that, when they proceeded doctors of divinity, they could not overmuch extol
and commend master doctor Cranmer s goodness towards them, who had for a time
put them back to aspire unto better knowledge and perfection. Amongst whom doc-
Doctor Bar- tor Barret, a white friar, who afterwards dwelt at Norwich, was after that sort hand
led, giving him no less commendation for his happy rejecting of him for a better
amendment. Thus much I repeat, that our apish and popish sort of ignorant priests
may well understand that this his exercise, kind of life, and vocation was not alto
gether hostelerlike.
Doctor cran- I omit here how Cardinal Wolsey, after the foundation of his college in Oxford,
to e be feiiow" hearing the fame of his learning, used all means possible to place him in the same;
nai s college w hich he refused with great danger of indignation, contenting himself with his former
refused it. fellowship in Cambridge : until, upon occasion of the plague being in Cambridge,
he resorted to Waltham Abbey, and sojourned with one M. Cressey there, whose wife
was doctor Cranmer s niece, and two of her children his pupils in Cambridge. During
Question of this time the great and weighty cause of king Henry the eighth his divorce with
YOTcewith " the lady Catharine, dowager of Spain, was in question. "Wherein two cardinals, Cam-
dowager. peius and AVolsey, were appointed in commission from the pope to hear and deter
mine the controversy between the king and the queen; who by many dilatories, dal
lying, and delaying, the whole summer, until the month of August, taking occasion
to finish their commission, so moved the patience of the king, that in all haste he
removed from London to AValtham for a night or twain, whiles the dukes of Norfolk
and Suffolk dispatched cardinal Campeius home again to Rome. By means whereof it
[ By reason, Foxe. Ed. 1583.
OF THOMAS CRANMER. ix
chanced that the king s harbingers lodged, doctor Stephens 9 , secretary, and doctor Doctor ste-
Foxe, almoner, (who were the chief furtherers, preferrers, and defenders of the fore- JJ2? fifr"
said cause in the king s behalf,) in the house of the said M. Cressey, where doctor king^Ju
Cranmer was also resident as before. When supper-time came, and all three doc- iSor ste-
tors met together, being of old acquaintance, they entertained each other familiarly : dx"j s &
. Cranmer eon-
and the said doctor Stephens and doctor Foxe, taking occasion of their happy meet- JjJJJ "y tn e
ing together, began to confer with doctor Cranmer concerning the king s cause, re- king 8 cause-
questing him to declare his opinion therein.
Whcreunto doctor Cranmer answered, that he could say little in the matter, for
that he had not studied nor looked for it. Notwithstanding he said to them, that,
in his opinion, they made more ado in prosecuting the laws ecclesiastical than needed. Doctor cran-
"It were better, as I suppose," quoth doctor Cranmer, "that the question, whether ft in them*
tion of the
man may marry his brother s wife or no, were decided .and discussed by the divines Jji" g j s
and by the authority of the word of God, whereby the conscience of the prince
might be better satisfied and quieted, than thus, from year to year, by frustatory
delays to prolong the time, leaving the very truth of the matter unboulted out by
the word of God. There is but one truth in it, which the scripture will soon de
clare, make open and manifest, being by learned men well handled; and that may
be as well done in England, in the universities here, as at Rome, or elsewhere in
any foreign nation, the authority whereof will compel any judge soon to come to a
definitive sentence; and therefore, as I take it, you might this way have made an
end of this matter long sithens." When doctor Cranmer had thus ended his tale, the Doctor cran-
other two well liked of his device, and wished that they had so proceeded afore- weii iiked of.
time ; and thereupon conceived some matter of that device to instruct the king withal,
who then was minded to send to Rome again for a new commission.
Now the next day, when the king removed to Greenwich, like as he took him
self not well handled by the cardinals in thus deferring his cause, so his mind The king
being unquieted and desirous of an end of his long and tedious suit, he called to*tthe
cause of his
him this his two principal doers of his said cause, namely, the said doctor Stephens divorce -
and doctor Foxe, saying unto them : " What now, my masters," quoth the king,
"shall we do in this infinite cause of mine? I see by it there must be a new
commission procured from Rome; and when we shall have an end, God knoweth,
and not I." When the king had said somewhat his mind herein, the almoner
doctor Foxe, said unto the king again: "We trust that there shall be better ways
devised for your majesty, than to make travel so far to Rome 3 any more in your
highness cause, which by chance was put into our heads this other night, being at
Waltham :" and so discovered to the king their meeting and conference with doctor
Cranmer at M. Cressey s house.
Whereupon doctor Cranmer was sent for in post, being as then removed from Doctor c ran .
Waltham towards his friends in Lincolnshire 4 , and so brought to the court to the S7h*k!i5 r
king. Whom the noble prince benignly accepting, demanded his name, and said unto "
him : " Were you not at Waltham such a time, in the company of my secretary Talk between
and my almoner ?" Doctor Cranmer affirming the same, the king said again : " Had
you not conference with them concerning our matter of divorce now in question after
this sort ?" repeating the manner and order thereof. " That is right true, if it please
your highness," quoth doctor Cranmer. "Well," said the king, "I well perceive
that you have the right scope of this matter. You must understand," quoth the king,
[- i.e. Doctor Stephen Gardiner, sometime bishop I [ 3 So far as to Rome, Foxe. Ed. 1583.J
of Winchester.] [< Foxe says <k in Nottinghamshire/ ]
x THE LIFE, STATE, AND STORY
The king " that I have been long troubled in conscience ; and now I perceive that by this means
troubled in
conscience, j m ight have been long ago relieved one way or other from the same, if we had this
way proceeded. And therefore, master doctor, I pray you, and nevertheless, because
you are a subject, I charge and command you, (all your other business and affairs
set apart,) to take some pains to see this my cause to be furthered according to your
device, as much as it may lie in you," with many other words in commendation of
the queen s majesty.
Doctor cran- Doctor Cranmer, much disabling himself to meddle in so weighty a matter, be-
mcr excusing
h?mSto ling sought the king s highness to commit the trial and examining of this matter, by the
kin e- word of God, unto the best learned men of both his universities, Cambridge and
Oxford. " You say well," said the king, " and I am content therewith. But yet,
nevertheless, I will have you specially to write your mind therein." And so, calling the
Doctor Cran- earl of AViltshire to him, said : " I pray you, my lord, let doctor Cranmer have enter-
mer assigned
to search tile * ammt>n * m vour house at Durham place for a time, to the intent he may be there
the cSof *l u i et to accomplish my request, and let him lack neither books nor anything requi-
rce site for his study." And thus, after the king s departure, doctor Cranmer went with
my lord of Wiltshire unto his house, where he, incontinent, wrote his mind concern-
The king first ing the king s question, adding to the same besides the authorities of scriptures 1 , of
given to un-
th^ n iehath enera ^ councils, and of ancient writers; also his opinion, which was this: that the
?<?d!snense ty bishop of Rome had no such authority, as whereby he might dispense with the word
ofGod? W( rd of God and the scriptures 2 . When doctor Cranmer had made this book, and com
mitted it to the king, the king said to him: "Will you abide by this, that you
have here written, before the bishop of Rome ?" " That will I do, by God s grace,"
quoth doctor Cranmer, "if your majesty do send me thither." "Marry," quoth the
king, " I will send you even to him in a sure embassage."
The king s And thus, by means of doctor Cranmer s handling of this matter with the king
matter re-
the V< ?e r m not only certain learned men were sent abroad to the most part of the universities
tlTthe trial of m Christendom to dispute the question, but also the same being, by commission,
tures! np disputed by the divines in both the universities of Cambridge and Oxford, it was
The king s there concluded that no such matrimony was by the word of God lawful. Where-
marriage
u P n a s l emn embassage was prepared and sent to the bishop of Rome, then being
o/c ran- at Bonony, wherein went the earl of Wiltshire, doctor Cranmer, doctor Stokesly,
doctor Came, doctor Benet, and divers other learned men and gentlemen. And when
bassadorto the time came that they should come before the bishop of Rome to declare the
cause of their embassage, the bishop, sitting on high in his cloth of estate, and in his
rich apparel, with his sandals on his feet, offering, as it were, his foot to be kissed
of the ambassadors; the earl of Wiltshire with the rest of the ambassadors, disdaining
thereat, stood still, and made no countenance thereunto, and kept themselves from
that idolatry. In fine, the pontifical bishop seeing their constancy, without any
farther ceremony, gave ear to the ambassadors.
Arguing to Who entering there before the bishop, offered, on the king s behalf, to be defended,
traTy to\he n ~ ^ iat no man J ure divino, could or ought to marry his brother s wife, and that the
hehad f no d bishop of Rome by no means ought to dispense to the contrary. Divers promises
dispense were made, and sundry days appointed, wherein the question should have been dis
puted: and when our part was ready to answer, no man there appeared to dispute
in that behalf. So in the end, the bishop making to our ambassadors good counte-
Doctor cran- nance, and gratifying doctor Cranmer with the office of the penitentiaryship dis-
the pope s missed them undisputed withal.
penitentiary.
[> Of the scriptures, Foxe. Eel. 1583.] [ 2 The scripture, ibid.]
OF THOMAS ORANMER. xi
Whereupon the earl of Wiltshire and other commissioners, saving doctor Cranmer, Doctor cran-
returned home again into England. And forthwith doctor Cranmer went to the sactor to the
. m emperor.
emperor, being in his journey towards Vienna, in expedition against the Turk, there
to answer such learned men of the emperor s council, as would or could say any
thing to the contrary part. Where amongst the rest, at the same time, was Cor- Conference
nelius Agrippa, an high officer in the emperor s court; who, having private confer- bis > ho ) Cran -
encc with doctor Cranmer in the question, was so fully resolved and satisfied in the
matter, that afterwards there was never disputation openly offered to doctor Cran
mer in that behalf. For through the persuasion of Agrippa all other learned men
there were much discouraged.
This matter thus prospering on doctor Cranmer s behalf, as well touching the
king s question, as concerning the invalidity of the bishop of Rome s authority, bishop
Warham, then archbishop of Canterbury, departed this transitory life ; whereby that Doctor Cnm-
dignity then being in the king s gift and disposition, was immediately given to doc- a I rchbish i ) of
tor Cranmer, as worthy for his travail of such a promotion. Thus much touching
the preferment of doctor Cranmer unto his dignity, and by what means he achieved
unto the same: not by flattery, nor by bribes, nor by none other unlawful means:
which thing I have more at large discoursed, to stop the railing mouths of such, who,
being themselves obscure and unlearned, shame not to detract a learned man most
ignominiously with the surname of an hosteler, whom, for his godly zeal unto sincere
religion, they ought with much humility to have had in regard and reputation.
Now as concerning his behaviour and trade of life towards God and the world,
being entered 3 into his said dignity. True it is, that he was so throughly furnished
with all properties, qualities, and conditions belonging to a true bishop, as that it
shall be very hard in these strange days to find many that so nearly resemble that
lively exemplar, described by St Paul the apostle in his several epistles to Titus and i,Tim. in.
Timothy: so far he swerved from the common course of common bishops in his
time. But because the same is very well deciphered in the story at large 4 , it shall
not be so needful to discourse all the parts thereof in this place. Yet may not this
be forgotten : that, notwithstanding the great charge now committed unto him, the The order of
worthy prelate gave himself evermore to continual study, not breaking the order that mer s stud y-
he used commonly in the university. To wit, by five of the clock in the morning
in his study, and so until nine, continuing in prayer and study. From thence, until
dinner time, to hear suitors (if the prince s affairs did not call him away), committing
his temporal affairs, as well of household as other foreign business, to his officers. For
the most part, he would occupy himself in reformation of corrupt religion, and set
ting forth true and sincere doctrine; wherein he would associate himself always with
learned men, for the sifting and boulting out one matter or other, for the commodity
and profit of the church of England. After dinner, if any suitors were, he would
diligently hear them and dispatch them, in such sort as every man commended his
lenity and gentleness. That done, to his ordinary study again until five of the clock,
which hour he bestowed in hearing common prayer. After supper he would con
sume an hour at the least in some godly conference, and then again, until nine of
the clock, at one kind of study or other. So that no hour of the day was spent in
vain, but was bestowed as tended to God s glory, the service of his prince, or the
commodity of the church.
As touching his affability and easiness to be entreated, it was such as that in The gentle
all honest causes, wherein his letter, counsel, or speech, might gratify either nobleman, doctor cran-
[ 3 Being now entered, Foxe. Ed. 153.J [ 4 See Foxe. Ed. 1583, p. 1862-186."). J
xii THE LIFE, STATE, AND STORY
gentleman, mean man, or poor man, no man could be more tractable, or sooner won
Doctor cran- to yield. Only in causes appertaining: to God and his prince, no man more stout,
mer stout and .
constant in m0 re constant, or more hard to be won : as in that part his earnest defence in the
God s cause.
parliament-house, above three days together, in disputing against the six articles of
Gardiner s device, can testify. And though the king would needs have them upon
some politic consideration to go forward, yet he so handled himself, as well in the
parliament-house, as afterwards by writing so obediently and with such humble be
haviour in words towards his prince, protesting the cause not to be his, but Almighty
Doctor cran- God s who w r as the author of all truth, that the king did not only well like his
mer a stout
auiinJtthe defence, willing him to depart out of the parliament-house into the council chamber,
six articles. w ]jii s t the act should pass and be granted, for safeguard of his conscience, which he
with humble protestation refused, hoping that his majesty in process of time would
revoke them again; but also, after the parliament was finished, the king perceiving
the zealous affection that the archbishop bare towards the defence of his cause, which
many ways by scriptures and manifold authorities and reasons he had substantially
or this confirmed and defended, sent the lord Cromwell, then vicegerent, with the two dukes
the lord O f Xorfolk and Suffolk, and all the lords of the parliament, to dine with him at
Cromwell,
duke? to 1 the Lambeth : where it was declared by the vicegerent and the two dukes, that it was
archbishop. ^ Ding s pi easure) that they all should, in his highness behalf, cherish, comfort,
and animate him, as one that for his travail in that parliament had shewed himself
both greatly learned, and also discreet and wise, and therefore they willed him not
to be discouraged for anything that was passed contrary to his allegations. He most
humbly thanked the king s majesty of his great goodness towards him, and them all
for their pains, saying : " I hope in God, that hereafter my allegations and authorities
shall take place to the glory of God and the commodity of the realm ; in the mean
time I will satisfy myself with the honourable consent of your honours and the
whole parliament."
Here is to be noted, that this man s stout and godly defence of the truth herein
so bound the prince s conscience, that he would not permit the truth in that man
to be clean overthrown with authority and power ; and therefore this way God work
ing in the prince s mind, a plain token was declared hereby, that all things were not
so sincerely handled in the confirmation of the said six articles as it ought to have
been, for else the prince might have had just cause to have borne his great indigna-
SsiSicai t * on towar( * s *^ e archbishop. Let us pray that both the like stoutness may be per-
pastors. ceived in all ecclesiastical and learned men, where the truth ought to be defended, and
also the like relenting and flexibility may take place in princes and noblemen, when
they shall have occasion offered them to maintain the same, so that they utterly
overwhelm not the truth by self-will, power, and authority. Now in the end this
archbishop s constancy was such towards God s cause, that he confirmed all his doings
by bitter death in the fire, without respect of any worldly treasure or pleasure.
And as touching his stoutness in his prince s cause, the contrary resistance of the
duke of Northumberland against him proved right well his good mind that way:
Archbishop which chanced by reason that he would not consent to the dissolving of chanteries
Cran mer in 6
until the kin S came of a S e to tlie intent that the 7 might then better serve to fur-
n i sn ms royal estate, than to have so great treasure consumed in his nonage: which
his stoutness, joined with such simplicity, surely was thought to divers of the coun
cil a thing incredible, specially in such sort to contend with him who was so ac
counted in this realm, as few or none would or durst gainstand him.
So dear was to him the cause of God and of his prince, that for the one he would
not keep his conscience clogged, nor for the other lurk or hide his head. Otherwise, as
OF THOMAS CRANMER. xiii
it is said, his very enemies might easily entreat him in any cause reasonable : and such
things as he granted, he did without any suspicion of rebraiding or meed therefore. So
that he was altogether void of the vice of the stubbornness, and rather culpable of over
much facility and gentleness. Surely if overmuch patience may be a vice, this man may
seem peradventure to offend rather on this part than on the contrary. Albeit for all his The singular
patience of
doings I cannot say : for the most part, such was his mortification that way, that few jj?jj rch -
we shall find in whom the saying of our Saviour Christ so much prevailed as with him, .
who would not only have a man to forgive his enemies, but also to pray for them : that
lesson never went out of his memory. For it was known that he had many cruel
enemies, not for his own deserts, but only for his religion s sake : and yet, whatsoever
he was that either sought his hindrance, either in goods, estimation, or life, and upon
conference would seem never so slenderly anything to relent or excuse himself, he would
both forget the offence committed, and also evermore afterwards friendly entertain him,
and shew such pleasure to him, as by any means possible he might perform or declare.
Insomuch that it came into a common proverb : " Do unto my lord of Canterbury
displeasure or a shrewd turn, and then you may be sure to have him your friend whiles
he liveth." Of which his gentle disposition in abstaining from revengement, amongst
many examples thereof, I will repeat here one.
It chanced an ignorant priest and parson in the north parts, the town is not now A story be-
in remembrance, but he was kinsman of one Chersey a grocer, dwelling within London, archbishop of
J Canterbury
(being one of those priests that use more to study at the alehouse than in his chamber JJ^ftg" 811
or in his study,) to sit on a time with his honest neighbours at the alehouse within his enemy<
own parish, where was communication ministered in commendation of my lord Cranmer,
archbishop of Canterbury. This said parson, envying his name only for religion s sake,
said to his neighbours : " What make you of him?" quoth he, " he was but an hosteler, The railing
and hath no more learning than the goslings that goeth yonder on the green," with such nfotapriii*
like slanderous and uncomely words. These honest neighbours of his, not well bear
ing those his unseemly words, articled against him, and sent their complaint unto the lord
Cromwell, then vicegerent in causes ecclesiastical; who sent for the priest and committed
him to the Fleet, minding to have had him recant those his slanderous words at Paul s
Cross. Howbeit the lord Cromwell, having great affairs of the prince then in hand,
forgat his prisoner in the Fleet. So that this Chersey the grocer, understanding that
his kinsman was in durance in the Fleet, only for speaking words against my lord of
Canterbury, consulted with the priest, and between them devised to make suit rather
unto the archbishop for his deliverance, than to the lord Cromwell, before whom he
was accused; understanding right well that there was great diversity of natures be
tween those two estates, the one gentle and full of clemency, and the other severe
and somewhat intractable, namely against a papist. So that Chersey took upon him
first to try my lord of Canterbury s benignity, namely for that his cousin s accusation
touched only the offence against him and none other. Whereupon the said Chersey
came to one of the archbishop s gentlemen, (whose father bought yearly all his spices and
fruit of the said Chersey, and so thereby of familiar acquaintance with the gentleman,)
who, opening to him the trouble wherein his kinsman was, requested that he would
be a means to my lord his master to hear his suit in the behalf of his kinsman.
The matter was moved. The archbishop, like as he was of nature gentle, and of
much clemency, so would he never shew himself strange unto suitors, but incontinently
sent for the said Chersey. When he came before him, Chersey declared, " that there
was a kinsman of his in the Fleet, a priest of the north country, and as I may tell your
grace the truth," quoth Chersey, "a man of small civility and of less learning. And chersey suing
yet he hath a parsonage there, which now (by reason that my lord Cromwell hath u
archbishop.
XIV
THE LIFE, STATE, AND STORY
The priest
sent for to
the arch
bishop.
The arch
bishop s
words unto
the parson.
The priest
confesseth his
fault to the
archbishop.
The rash
tongues of
men slan
derously
speaking evil
by men whom
they never
kne w nor
saw before.
laid him in prison, being in his cure) is unserved ; and he hath continued in durance
above two months, and is called to no answer, and knoweth not when he shall come
to any end, so that this his imprisonment consumeth his substance, will utterly undo
him, unless your grace be his good lord." " I know not the man," said the arch
bishop, " nor what he hath done why he should be thus in trouble."
Said Chersey again: "He only hath offended against your grace, and against no
. man else, as may well be perceived by the articles objected against him :" the copy
whereof the said Chersey then exhibited unto the said archbishop of Canterbury. Who,
well perusing the said articles, said : " This is the common talk of all the ignorant
papistical priests in England against me. Surely," said he, " I was never made privy
unto this accusation, nor of his indurance I never heard before this time. Notwith
standing, if there be nothing else to charge him withal, against the prince or any of
the council, I will at your request take order with him, and send him home again to
his cure to do his duty:" and so thereupon sent his ring to the warden of the Fleet,
willing him to send the prisoner unto him with his keeper at afternoon.
When the keeper had brought the prisoner at the hour appointed, and Chersey
had well instructed his cousin in any wise to submit himself unto the archbishop,
confessing his fault, whereby that way he should most easily have an end and win his
favour : thus the parson being brought into the garden at Lambeth, and there sitting
under the vine, the archbishop demanded of the parson what was the cause of his
indurance, and who committed him to the Fleet? The parson answered and said:
" That the lord Cromwell sent him thither, for that certain malicious parishioners of
his parish, had wrongfully accused him of words which he never spake nor meant."
Chersey, hearing his foolish cousin so far out of the way from his former instruction,
said : " Thou dastardly dolt and varlet, is this thy promise that thou madest to me ?
Is there not a great number of thy honest neighbours hands against thee to prove
thee a liar? Surely, my lord," quoth Chersey, "it is pity to do him good. I am
sorry that I have troubled your grace thus far with him."
" Well," said the archbishop unto the parson, " if you have not offended me, I
can do you no good ; for I am entreated to help one out of trouble that hath offended
against me. If my lord Cromwell hath committed you to prison wrongfully, that
lieth in himself to amend, and not in me. If your offence only touch me, I will be
bold to do somewhat for your friend s sake here. If you have not offended against
me, then have I nothing to do with you, but that you may go and remain from whence
you came." Lord, what ado his kinsman Chersey made with him, calling him all kind
of opprobrious names ! In the end, my lord of Canterbury seeming to rise and go his
ways, the fond priest fell down on his knees, and said : " I beseech your grace to
forgive me this offence ; assuring your grace that I spake those words, being drunk,
and not well advised." " Ah \" said my lord, " this is somewhat, and yet it is no
good excuse ; for drunkenness evermore uttereth that which lieth hid in the heart of
man when he is sober," alleging a text or twain out of the scriptures concerning the
vice of drunkenness, which cometh not now to remembrance.
" Now therefore," said the archbishop, " that you acknowledge somewhat your fault,
I am content to commune with you, hoping that you are at this present of an indifferent
sobriety. Tell me then," quoth he, " did you ever see me, or were you ever acquainted
with me before this day?" The priest answered and said, that never in his life he
saw his grace. "Why then," said the archbishop, "what occasion had you to call
me an hosteler ; and that I had not so much learning as the goslings which then went
on the green before your face ? If I have no learning, you may now try it, and be out
of doubt thereof : therefore I pray you appose me, either in grammar or in other liberal
OF THOMAS CRANMER. xv
sciences ; for I have at one time or other tasted partly of them. Or else, if you are a
divine, say somewhat that way."
The priest, being amazed at my lord s familiar talk, made answer and said : " I The priest s
beseech your grace to pardon me. I am altogether unlearned, and understand not the
Latin tongue but very simply. My only study hath been to say my service and mass
fair and deliberate, which I can do as well as any priest in the country where I dwell,
I thank God." " Well," said the other, " if you will not appose me, I will be so bold
to appose you, and yet as easily as I can devise, and that only in the story of the
bible now in English, in which I suppose that you are daily exercised. Tell me there- The mass-
fore, who was king David s father ?" said my lord. The priest stood still pausing a
while, and said : " In good faith, my lord, I have forgotten his name." Then said the
other again to him : " If you cannot tell that, I pray you tell me then who was
Salomon s father?" The fond foolish priest, without all consideration what was de
manded of him before, made answer : " Good my lord, bear with me, I am not fur
ther seen in the bible, than is daily read in our service in the church."
The archbishop then answering said : " This my question may be found well answered
in your service. But I now well perceive, howsoever you have judged heretofore of my The guise of
learning, sure I am that you have none at all. But this is the common practice of all 5K Sey 8 s
favour not
you, which are ignorant and superstitious priests, to slander, backbite, and hate all such
as are learned and well affected towards God s word and sincere religion. Common Sj
reason might have taught you, what an unlikely thing it was, and contrary to all
manner of reason, that a prince, having two universities within his realm of well learned
men, and desirous to be resolved of as doubtful a question as in these many years
was not moved the like within Christendom, should be driven to that necessity for the
defence of his cause, to send out of his realm an hosteler, being a man of no better
knowledge than is a gosling, in an embassage to answer all learned men, both in the
court of Rome and in the emperor s court, in so difficult a question as toucheth the
king s matrimony, and the divorce thereof. I say, if you were men of any reasonable con
sideration, you might think it both unseemly and uncomely for a prince so to [do.] But
look, where malice reigneth in men, there reason can take no place : and therefore I see Evii-wiii
by it, that you all are at a point with me, that no reason or authority can persuade wen.
you to favour my name, who never meant evil to you, but your both commodity and
profit. Howbeit, God amend you all, forgive you, and send you better minds !"
With these words the priest seemed to weep, and desired his grace to pardon his
fault and frailty, so that by his means he might return to his cure again, and he would
sure recant those his foolish words before his parishioners so soon as he came home,
and would become a new man. " Well," said the archbishop, " so you had need."
And giving him a godly admonition to refuse the haunting of the alehouse, and to The arch-
bestow his time better in the continual reading of the scriptures, he dismissed him givetftand
ciismisseth
from the Fleet. the priest.
How little this prelate we speak of was infected with filthy desire of lucre, and The liberal
how he was no niggard, all kind of people that knew him, as well learned beyond thi s arch -
* bishop.
the seas and on this side, to whom yearly he gave in exhibition no small sums of
money, as other, both gentlemen, mean men, and poor men, who had in their neces
sity that which he could conveniently spare, lend, or make, can well testify. And
albeit such was his liberality to all sorts of men, that no man did lack whom he
could do for, either in giving or lending; yet nevertheless such was again his circum
spection, that when he was apprehended and committed by queen Mary to the tower,
he ought no man living a penny that could or would demand any duty of him, but
satisfied every man to the uttermost ; where else no small sums of money were owing
xvi THE LIFE, STATE, AND STORY
The arch. to him of divers persons, which by breaking their bills and obligations he freely for-
JBfSfhjT** gave and suppressed before his attainder. Insomuch that when lie perceived the fatal
his attainder, end of king Edward should work to him no good success touching his body and
goods, he incontinently called his officers, his steward and other, commanding them in
any wise to pay, where any penny was owing, which was out of hand dispatched.
In which archbishop this, moreover, is to be noted, with a memorandum, touching
the relief of the poor, impotent, sick, and such as then came from the wars at Bullein ,
and other parts beyond the seas, lame, wounded, and destitute ; for whom he provided,
besides his mansion-house at Beckisborne in Kent, the parsonage barn well furnished
with certain lodgings for the sick and maimed soldiers: to whom were also appointed
the almosiner, a physician, and surgeon, to attend upon them, and to dress and cure
such as were not able to resort to their countries, having daily from the bishop s kitchen
hot broth and meat ; for otherwise the common alms of the household was bestowed
upon the poor neighbours of the shire. And when any of the impotent did recover,
and were able to travel, they had convenient money delivered to bear their charges,
according to the number of miles from that place distant. And this good example of
mercy and liberal benignity I thought here good not in silence to be suppressed, whereby
other may be moved, according to their vocation, to walk in the steps of no less libe
rality than in him in this behalf appeared.
Amongst all other his virtues, his constancy in Christ s cause, and setting forth the
gospel purely and sincerely, was such that he would neither for dread or meed, affection
or favour, to swerve at any time or in any point from the truth, as appeared by his
Th e sundry trials ; wherein neither favour of his prince, nor fear of the indignation of the
Cnamerem same, nor any other worldly respect, could alienate or change his purpose, grounded upon
defence of that infallible doctrine of the gospel. Notwithstanding, his constant defence of God s
Christ s truth
and gospel, truth was ever joined with such meekness toward the king, that he never took occasion
of offence against him.
At the setting forth 2 of the six Articles, mention was made before in the story of
king Henry s time, how adventurously this archbishop, Thomas Cranmer, did oppose
himself, standing, as it were, post alone against the whole parliament, disputing and
replying three days together against the said articles; insomuch that the king, when
neither he could mislike his reasons, and yet would needs have these articles to pass,
required him to absent himself for the time out of the chamber, while the act should
pass, as is already declared before. And this was done during yet the state and time of
the lord Cromwell s authority. And now that it may appear likewise that after the
decay of the lord Cromwell, yet his constancy in Christ s cause did not decay, you shall
hear what followed after.
For after the apprehension of the lord Cromwell, when the adversaries of the gospel
thought all things sure now on their side, it was so appointed amongst them, that ten
or twelve bishops, and other learned men, joined together in commission, came to the
said archbishop of Canterbury for the establishing of certain articles of our religion,
which the papists then thought to win to their purpose against the said archbishop.
For having now the lord Cromwell fast and sure, they thought all had been safe and
sure for ever: as indeed to all men s reasonable consideration, that time appeared so
dangerous, that there was no manner hope that religion reformed should any one w r eek
The longer stand, such accompt was then made of the king s untowardness thereunto : inso-
aione stotS- much that of all those commissioners, there was not one left to stay on the archbishop s
ethin
f 1 i.e. Boulogne, which was taken by the English after a siege in the year 1544.J
[ 2 At the time of setting forth, Foxe. Ed. 1583.J
OF THOMAS CRANMER. xvii
part, but ho alone against them all stood in defence of the truth; and those that he most
trusted to, namely, bishop Heath, and bishop Skippe, left him in the plain field : who
then so turned against him, that they took upon them to persuade him to their
purpose : and having him down from the rest of the commissioners into his garden at in
field. The
Lambeth, there by all manner of effectual persuasions entreated him to leave off his
overmuch constancy, and to incline unto the king s intent, who was fully set to have it J
otherwise than ho then had penned, or meant to have set abroad. When those two his tfv e P overthe
familiars, with one or two others his friends, had used all their eloquence and policy, gospel.
he, little regarding their inconstancy and remissness in God s cause or quarrel, said unto
them right notably : " You make much ado to have me come to your purpose, alleging The answer
. . of the arch-
that it is the kings pleasure to have the articles in that sort you have devised them ^ ish P ,
doctors Heath
to proceed; and now that you do perceive his highness, by sinister information, to be and skippe -
bent that way, you think it a convenient thing to apply unto his highness s mind. You
be my friends both, especially the one of you I did put to his majesty as of trust.
Beware, I say, what you do. There is but one truth in our articles to be concluded
upon, which if you do hide from his highness by consenting unto a contrary doctrine,
and then after in process of time, when the truth cannot be hidden from him, his
highness shall perceive how that you have dealt colourably with him, I know his grace s
nature so well," quoth the archbishop, " that he will never after trust and credit you, or
put any good confidence in you. And as you are both my friends, so therefore I will
you to beware thereof in time, and discharge your consciences in maintenance of the
truth." But all this would not serve, for they still swerved ; and in the end, by dis
charging of his conscience, and declaring the truth unto the king, God so wrought with
the king, that his highness joined with him against the rest ; so that the book of articles
passing on his side, he won the goal from them all, contrary to all their expectations ;
when many wagers would have been laid in London, that he should have been laid up
with Cromwell at that time in the Tower, for his stiff standing to his tackle. After
that day there could neither councillor, bishop, or papist, win him out of the king s
favour.
Notwithstanding, not long after that, certain of the council, whose names need not
to be repeated, by the enticement and provocation of his ancient enemy, the bishop
Winchester, and other of the same sect, attempted the king against him, declaring credit\vith f
plainly, that the realm was so infected with heresies and heretics, that it was dangerous
for his highness farther to permit it unreformed, lest peradventure by long suffering The arch-
such contention should arise and ensue in the realm among his subjects, that thereby SsedTo* 1 "
might spring horrible commotions and uproars, like as in some parts of Germany it *
did not long ago ; the enormity whereof they could not impute to any so much as to
the archbishop of Canterbury, who by his own preaching and his chaplains had filled
the whole realm full of divers pernicious heresies. The king would needs know his
accusers. They answered, that forasmuch as he was a councillor, no man durst take
upon him to accuse him ; but, if it please his highness to commit him to the Tower
for a time, there would be accusations and proofs enough against him, for otherwise
just testimony and witness against him would not appear; "and therefore your highness,"
said they, " must needs give us, the council, liberty and leave to commit him to durance."
The king perceiving their importune suit against the archbishop, but yet meaning
not to have him wronged and utterly given over unto their hands, granted to them
that they should the next day commit him to the Tower for his trial. When night
came, the king sent Sir Antony Deny about midnight to Lambeth to the archbishop, The king mt
willing him forthwith to resort unto him at the court. The message done, the arch- D !SL
, . . midnight for
ishop speedily addressed himself to the court, and coming into the gallery where the
rrn.Awi7.ij I l>
xv
THE LIFE, STATE, AND STORY
Th rd k 5id
supportation
archbishop.
The arch-
bishop s
The kingjs
The king
cTiuerb h ury f
The arch-
one of the
w h aTung. rdoor
th e c king tts
friend of the
walked and tarried for him, his highness said : " Ah, my lord of Canterbury, I
can tell you news. For divers weighty considerations it is determined by me and the
* n J J
council, that you to-morrow at nine of the clock shall be committed to the Tower, for
that you and your chaplains (as information is given us) have taught and preached, and
thereby sown within the realm, such a number of execrable heresies, that it is feared,
the whole realm being infected with them, no small contentions and commotions will
rise thereby amongst my subjects, as of late days the like was in divers parts of
Germany ; and therefore the council have requested me, for the trial of this matter, to
suffer them to commit you to the Tower, or else no man dare come forth as witness in
these matters, you being a councillor."
"When the king had said his mind, the archbishop kneeled down, and said : " I am
e
content, if it please your grace, with all my heart to go thither at your highness s
commandment, and I most humbly thank your majesty that I may come to my trial ;
for there be that have many ways slandered me, and now this way I hope to try
myself not worthy of such a report."
The king, perceiving the man s uprightness joined with such simplicity, said: "Oh
Lord, what manner a man be you ! what simplicity is in you ! I had thought that you
would rather have sued to us to have taken the pains to have heard you and your
accusers together for your trial without any such endurance. Do not you know what
state you be in with the whole w^orld, and how many great enemies you have? Do
you not consider, what an easy thing it is to procure three or four false knaves to
witness against you? Think you to have better luck that way than your master
Christ had ? I see it, you will run headlong to your undoing, if I would suffer you.
Your enemies shall not so prevail against you, for I have otherwise devised with myself
to keep you out of their hands. Yet, notwithstanding, to-morrow when the council
shall sit and send for you, resort unto them ; and if in charging you with this matter
they do commit you to the Tower, require of them, because you are one of them, a
councillor, that you may have your accusers brought before them, and that you may
answer their accusations before them without any further endurance, and use for yourself
as good persuasions that way as you may devise; and if no entreaty or reasonable
request will serve, then deliver unto them this my ring, (which then the king delivered
unto ^ e arcn kishop,) an d Sa 7 unto them: If there be no remedy, my lords, but that
l must needs to the Tower 5 tnen I revoke my cause from you, and appeal to the
king s own person by this his token unto you all : for," said the king then unto the
archbishop, " so soon as they shall see this my ring, they know it so well, that they
shall understand that I have resumed the whole cause into mine own hands and deter
mination, and that I have discharged them thereof."
The archbishop, perceiving the king s benignity so much to him wards, had much
ado to forbear tears. " Well," said the king, " go your ways, my lord, and do as I
have bidden you." My lord, humbling himself with thanks, took his leave of the king s
highness for that night.
On the morrow, about nine of the clock before noon, the council sent a gentleman
usher for the archbishop, who when he came to the council-chamber door, could not
k k* m kut of P ur P ose 5 as it seemed, was compelled there to wait among the pages,
lacke y s 5 and serving-men all alone. Doctor Butts, the king s physician, resorting that
way, and espying how my lord of Canterbury was handled, went to the king s highness
and said : " My lord of Canterbury, if it please your grace, is well promoted ; for now
he is become a lackey or a serving-man, for yonder he standeth this half-hour without
the council-chamber door amongst them." " It is not so," quoth the king, " I trow, nor
the council hath not so little discretion as to use the metropolitan of the realm in that
OF THOMAS CRANMER. Xlx
sort, specially being one of their own number; but let them alone," said the king, "and
we shall hear more soon."
Anon the archbishop was called into the council-chamber, to whom was alleged as The arch-
council.
him ; and in tin; end when he perceived that no manner of persuasion or entreaty could
serve, he delivered to them the king s ring, revoking his cause into the king s hands. The council
The whole council being thereat somewhat amazed, the earl of Bedford with a loud against the
5 9 arc-hbishon,
voice, confirming his words with a solemn oath, said : " When you first began this [h/tj ^
matter, my lords, I told you what would come of it. Do you think that the king
will suffer this man s finger to ache ? much more, I warrant you, will he defend his
life against brabbling varlets. You do but cumber yourselves to hear tales and fables
against him." And so incontinently, upon the receipt of the king s token, they all rose
and carried to the king his ring, surrendering that matter (as the order and use was)
into his own hands.
When they were all come to the king s presence, his highness with a severe coun- The king s
tenance said unto them : " Ah, my lords, I thought I had had wiser men of my SJgJjJ j} th
council than now I find you. What discretion was this in you, thus to make the arcnbish P-
primate of the realm, and one of you in office, to wait at the council-chamber door
amongst serving-men? You might have considered that he was a councillor as well
as you, and you had no such commission of me so to handle him. I was content
that you should try him as a councillor, and not as a mean subject. But now I
well perceive that things be done against him maliciously; and if some of you might
have had your minds, you would have tried him to the uttermost. But I do you all
to wit, and protest, that if a prince may be beholding unto his subject," (and so
solemnly laying his hand upon his breast, said,) " by the faith I owe to God, I take
this man here, my lord of Canterbury, to be of all other a most faithful subject unto
us, and one to whom we are much beholding," giving him great commendations other
wise. And with that one or two of the chiefest of the council, making their excuse,
declared, that in requesting his indurance, it was rather meant for his trial and his
purgation against the common fame and slander of the world, than for any malice
conceived against him. "Well, well, my lords," quoth the king, "take him and well
use him, as he is worthy to be, and make no more ado." And with that every man The lords of
caught him by the hand, and made fair weather of altogethers, which might easily p 1 ? 1 ^
bo done with that man.
And it was much to be marvelled that they would go so far with him, thus to
seek his undoing, this well understanding before, that the king most entirely loved The king a
him, and always would stand in his defence, whosoever spake against him ; as many gjj^jf
other times the king s patience was by sinister informations against him tried : inso
much that the lord Cromwell was evermore wont to say unto him : " My lord of The lord
J J Cromwell s
to the
xx THE LIFE, STATE, AND STORY
The true and took upon him the defence of that whole doctrine, that is, to refute and throw down
gorily doc-
ne c r P ra l presence ; secondly, the phantastical transubstantiation ; thirdly, the
* e forrti k by idolatrous adoration; fourthly, the false error of the papists, that wicked men do eat
bishnof the natural body of Christ; and lastly, the blasphemous sacrifice of the mass. Where
upon in conclusion he wrote five books for the public instruction of the church of
England, which instruction yet to this day standeth and is received in this church of
England.
Against these five books of the archbishop, Stephen Gardiner, the arch-enemy to
Christ and his gospel, being then in the tower, slubbereth up a certain answer, such
as it was, which he in open court exhibited up at Lambeth, being there examined
by the archbishop aforesaid, and other the king s commissioners in king Edward s
days, which book was entitled, "An Explication and Assertion of the True Catholic
Faith, touching the blessed Sacrament of the Altar, with a Confutation of a Book
written against the same."
tion e bT liC3 ~ Against this explication, or rather a cavilling sophistication of Stephen Gardiner,
Gardiner Doctor of Law, the said archbishop of Canterbury learnedly and copiously replying
mer"ardh- ;!n again, maketli answer, as by the discourse thereof renewed in print is evident to be
canterbury, seen to all such as with indifferent eye will read and peruse the same.
Besides these books above recited of this archbishop, divers other things there were
also of his doing, as the Book of Reformation, with the Book of Homilies, whereof
part was by him contrived, part by his procurement approved and published. W here
unto also may be adjoined another writing or confutation of his against eighty-
eight articles by the convocation devised and propounded, but yet not ratified nor
received, in the reign and time of king Henry 1 .
And thus much hitherto concerning the doings and travails of this archbishop of
Canterbury during the lives both of king Henry and king Edward his son; which
two kings so long as they continued, this archbishop lacked no stay of maintenance
against all his maligners.
After the death of king Edward, queen Mary coming now to the crown, and
being established in the possession of the realm, not long after came to London ; and
after she had caused first the two dukes of Northumberland and Suffolk, and their
two children, the lady Jane and the lord Guilford, both in age tender and innocent
of that crime, to be executed; she put the rest of the nobility to their fines, and forgave
them, the archbishop of Canterbury only except. Who, though he desired pardon by mean
of friends, could obtain none ; insomuch that the queen would not once vouchsafe to see
J-emerJjTos- hmi : foT a9 ^ Gi tlie ^ g rud S es against the archbishop, for the divorcement of her mother,
S Paridis, remained hid in the bottom of her heart. Besides this divorce, she remembered the state
mJSma- of religion changed : all which was reputed to the archbishop, as the chief cause thereof.
ASiieid. ?. While these things were in doing, a rumour was in all men s mouths that the
archbishop, to curry favour with the queen, had promised to say a Diriae mass after
the old custom, for the funeral of king Edward her brother. Neither wanted there
some, which reported that he had already said mass at Canterbury; which mass in
This doctor deed was said by doctor Thornton. This rumour Cranmer thinking speedily to stay,
bishop h of ave forth a writin g in his purgation ; the tenor whereof being set out at large in the
cnleTand Book of Acts and Monuments, I need not here again to recite.
teuton l er ~ This bill being thus written, and lying openly a window 2 in his chamber, cometh
in by chance Master Scory, bishop then of Rochester, who after he had read and
[ King Henry eight, Foxe, 1583.] [ Openly in a window, ibid.]
OF THOMAS CRANMER. xxi
perused the same, required of the archbishop to have a copy of the bill. The arch
bishop, when he had granted and permitted the same to Master Scory, by the occa
sion thereof Master Scory lending it to some friend of his, there were divers copies taken
out thereof, and the thing published abroad among the common people : insomuch
that every scrivener s shop almost was occupied in writing out the same; and so at
length some of those copies coming to the bishops hands, and so brought to the
council, and they sending it to the commissioners, the matter was known, and so he
commanded to appear.
AVhereupon Dr Cranmer at his day prefixed appeared before the said commissioners,
bringing a true inventory, as he was commanded, of all his goods. That done, a
bishop of the queen s privy council, being one of the said commissioners, after the
inventory was received, bringing in mention of the bill: "My lord/ said he, " there JSSlop after
is a bill put forth in your name, wherein you seem to be aggrieved with setting up of
the mass again : we doubt not but you are sorry that it is gone abroad."
To whom the archbishop answered again, saying : " As I do not deny myself to
be the very author of that bill or letter, so must I confess here unto you, con
cerning the same bill, that I am sorry the said bill went from me in such sort as it
did. For when I had written it, Master Scory got the copy of me, and is now come
abroad, and (as I understand) the city is full of it. For which I am sorry, that it
so passed my hands : for I had intended otherwise to have made it in a more large
and ample manner, and minded to have set it on Paul s Church door, and on the doors
of all the churches in London, with mine own seal joined thereto."
At which words, when they saw the constantness of the man, they dismissed him,
affirming they had no more at that present to say unto him, but that shortly he
should hear further. The said bishop declared afterward to one of Dr Cranmer s
friends, that notwithstanding his attainder of treason, the queen s determination at that
time was, that Cranmer should only have been deprived of his archbishoprick, and
have had a sufficient living assigned him, upon his exhibiting of a true inventory, with
commandment to keep his house without meddling with matters of religion. But how
that was true, I have not to say. This is certain, that not long after this he was
sent unto the tower, and soon after condemned of treason. Notwithstanding, the Cranmer con
demned ot
queen, when she could not honestly deny him his pardon, seeing all the rest were treason -
discharged, and specially seeing he last of all other subscribed to king Edward s re
quest, and that against his own will, released to him his action of treason, and accused Cranmer
released of
:him only of heresy : which liked the archbishop right well, and came to pass as he JSJSo" d
wished, because the cause was not now his own, but Christ s ; not the queen s, but hc
the church s. Thus stood the cause of Cranmer, till at length it was determined by
the queen and the council, that he should be removed from the Tower, where he was
prisoner, to Oxford, there to dispute with the doctors and divines. And privily word
was sent before to them of Oxford to prepare themselves, and make them ready to
dispute. And although the queen and the bishops had concluded before what should
become of him, yet it pleased them that the matter should be debated with argu
ments, that under some honest shew of disputation the murder of the man might be
covered. Neither could their hasty speed of revengement abide any long delay: and Cnmmer had
therefore in all haste he was carried to Oxford.
"What this disputation was, and how it was handled, what were the questions
and reasons on both sides, and also touching his condemnation by the university and
the prolocutor, because sufficiently it hath been declared in the story at large, we
mind now therefore to proceed to his final judgment and order of condemnation, which
xxii THE LIFE, STATE, AND STORY
was the twelfth day of September, anno 1556 ! , and seven days before the condemna
tion of bishop Ridley and Master Latimer.
of this con- After the disputations done and finished in Oxford, between the doctors of both
read^nth" universities, and the three worthy bishops, Dr Cranmer, Ridley, and Latimer, sen-
page 1554. tence condemnatory immediately upon the same was ministered against them by Dr
Weston and other of the university : whereby they were judged to be heretics, and
so committed to the Mayor and Sheriffs of Oxford, by whom he was carried to
Bocardo, their common gaol in Oxford.
In 2 this mean time, while the archbishop was thus remaining in durance, (whom
they had kept now in prison almost the space of three years,) the doctors and divines
of Oxford busied themselves all that ever they could about Master Cranmer, to have
him recant, assaying by all crafty practices and allurements they might devise, how
to bring their purpose to pass. And to the intent they might win him easily, they
had him to the dean s house of Christ s Church in the said university, where he lacked
no delicate fare, played at the bowls, had his pleasure for walking, and all other
things that might bring him from Christ. Over and besides all this, secretly and
sleightly, they suborned certain men, which, when they could not expunge him by
arguments and disputation, should by entreaty and fair promises or any other means
allure him to recantation : perceiving otherwise what a great wound they should
receive if the archbishop had stood stedfast in his sentence ; and again on the other
side, how great profit they should get, if he, as the principal standard-bearer, should
be overthrown. By reason whereof the wily papists flocked about him with threat-
ning, flattering, entreating, and promising, and all other means: especially, Henry
Sydall, and friar John, a Spaniard, de Villa Garcina, to the end to drive him, to the
uttermost of their possibility, from his former sentence to recantation: whose force
The arch- his manly constancy did a great while resist; but at last, when they made no end
tented to of calling and crying upon him, the archbishop being overcome, whether through
their importunity, or by his own imbecility, or of what mind I cannot tell, at length
gave his hand.
causes mov- It might be supposed that it was done for the hope of life, and better days to
bifhop^tT 11 " come. But as we may since perceive, by a letter of his sent to a lawyer, the most
time. cause why he desired his time to be delayed, was that he would make an end of
Marcus Antonius, which he had already begun : but howsoever it was, he recanted,
though plain against his conscience.
The queen s Mary the queen, having now gotten a time to revenge her old grief, received his
against* recantation very gladly; but of her purpose to put him to death she would nothing
relent. But taking secret counsel how to dispatch Cranmer out of the way, (who as
yet knew nothing of her secret hate, and looked for nothing less than death,) appointed
The queen doctor Cole, and secretly gave him in commandment, that against the 21st of March
with e doctor he should prepare a funeral sermon for Cranmer s burning, and so instructing hi]
cranmer s orderly and diligently of her will and pleasure in that behalf, sendeth him away.
Lord wm. of Soon after, the Lord "Williams of Thame, and the Lord Shandoys, Sir Thomas Brid^
shanToys, rd and Sir John Browne were sent for, with other worshipful men and justices, coi
Bridges, manded in the queen s name to be at Oxford at the same day, with their servant
Sir John
^pointed to and retinue, lest Cranmer s death should raise there any tumult.
Cole, the doctor, having his lesson given him before, and charged by her com
mandment, returned to Oxford ready to play his part, who, as the day of execution
So it is printed in ed. 1580, and in Foxe, ed. 1583, p. 1871.] [ 2 See Foxe, ed. 1583, p. 1884.]
OF THOMAS CRANMER. xxiii
drew near, even the Jay before he came into the prison to Cranmer, to try whether he
abode in the catholic faith, wjierein before he had left him. To whom when Cranmer
had answered, that by God s grace he would daily be more confirmed in the catholic
faith ; Cole, departing for that time, the next day following repaired to the archbishop
again, giving no signification as yet of his death that was prepared ; and therefore in
the morning, which was the 21st day of March, appointed for Cranmer s execution,
the said Cole coming to him asked, if he had any money. To whom when he answered
that he had none, he delivered him fifteen crowns to give the poor to whom he would :
and so exhorting him so much as he could to constancy in faith, departed thence about
his business, as to his sermon appertained.
By this partly, and other like arguments, the archbishop began more and more to
surmise what they went about. Then, because the day was not far past, and the
lords and knights that were looked for were not yet come, there came to him the
Spanish friar, witness of his recantation, bringing a paper with articles, which Cran
mer should openly profess in his recantation before the people, earnestly desiring that
he would write the said instrument with the articles with his own hand, and sign
it with his name : which when he had done, the said friar desired that he would nbMrnwth
the articles
write another copy thereof, which should remain with him: and that he did also. 1 with , hisown
1 * hands.
But yet the archbishop, being not ignorant whereunto their secret devices tended, and
thinking that the time was at hand, in which he could no longer dissemble the pro
fession of his faith with Christ s people, he put secretly in his bosom his prayer with
his exhortation, written in another paper, which he minded to recite to the people,
before he should make the last profession of his faith, fearing lest, if they had heard
the confession of his faith first, they would not afterward have suffered him to exhort
the people.
Soon after, about nine of the clock, the Lord Williams, Sir Thomas Bridges, Sir
John Browne, and the other justices, with certain other noblemen that were sent of
the queen s council, came to Oxford with a great train of waiting men. Also of the
other multitude on every side (as is wont in such a matter) was made a great con
course and greater expectation.
In this so great frequence and expectation, Cranmer at length cometh from the Doctor crau-
prison Bocardo unto St Mary s church (because it was a foul and a rainy day), the to doctor
chief church in the university, in this order. The mayor went before, next him the mon -
aldermen in their place and degree; after them was Cranmer brought between two
friars, which mumbling to and fro certain psalms in the streets, answered one ano
ther, until they came to the church door, and there they began the song of Simeon,
Nimc dimittis; and entering into the church, the psalm-saying friars brought him to
his standing, and there left him. There was a stage set up over against the pulpit, n^-tor cran-
of a mean height from the ground, where Cranmer had his standing, waiting until ^Sage! "
The lamentable case and sight of that man gave a sorrowful spectacle to all
Christian eyes that beheld him. He that late was archbishop, metropolitan and pri-
mato of England, and the king s privy councillor, being now in a bare and ragged
gown, and ill-favouredly clothed, with an old square cap, exposed to the contempt
of all men, did admonish men not only of his own calamity, but also of their state
and fortune. For who would not pity his case, and bewail his fortune, and might
not fear his own chance, to see such a prelate, so grave a councillor, and of so long
continued honour, after so many dignities, in his old years to be deprived of his
estate, adjudged to die, and in so painful a death to end his life, and now presently
from such fresh ornaments to descend to such vile and ragged apparel?
XXIV
THE LIFE, STATE, AND STORY
if cole gave
thisjudg-
mentupon
Cranmer
replnted, hacl
In this habit, when he had stood a good space upon the stage, turning to a pillar
near adjoining thereunto, he lifted up his hands to heaven, and prayed to God once
or twice : till at the length Dr Cole coming into the pulpit, and beginning his sermon,
entered first into mention of Tobias and Zachary. Whom after that he had praised
in the beginning of his sermon, for their perseverance in the true worshipping of God,
Doctor Cole s he then divided his w r hole sermon into three parts (according to the solemn custom
seimon di-
three "arts ^ the schools), intending to speak first of the mercy of God, secondly of his justice
to be shewed, and last of all, how the prince s secrets are not to be opened. And
proceeding a little from the beginning, he took occasion by and by to turn his tale
to Cranmer, and with many hot words reproved him, that once he being endued with
The sum and the favour and feeling of wholesome and catholic doctrine, fell into the contrary opinion
effect of
doctor cole s o f pernicious error, which he had not only defended by writings, and all his power,
but also allured other men to the like 1 with great liberality of gifts, as it were
appointing rewards for error ; and after he had allured them, by all means did cherish
them.
It were too long to repeat all things, that in long order were then pronounced.
The sum of this tripartite declamation was, that he said God s mercy was so tem
pered with his justice, that he did not altogether require punishment according to the
merits of offenders, nor yet sometimes suffered the same altogether to go unpunished,
of cole which yea, though they had repented : as in David, who when he was bidden choose of
always hath * _
er e ror ur and n three kinds of punishments Avhich he would, and he had chosen pestilence for three
days, the Lord forgave him half the time, but did not release all : and that the same
thing came to pass in him also, to whom although pardon and reconciliation was due
according to the canons, seeing he repented from his errors; yet there were causes
why the queen and the council at this time judged him to death; of which, lest he
should marvel too much, he should hear some.
First, that being a traitor, he had dissolved the lawful matrimony between the
king her father and mother; besides the driving out of the pope s authority, while he
was metropolitan.
Secondly, that he had been an heretic, from whom, as from an author and only
burned fountain, all heretical doctrine and schismatical opinions that so many years have pre-
do h ctoj S CoTe ld vailed in England, did first rise and spring : of which he had not been a secret
favourer only, but also a most earnest defender even to the end of his life, sowing
them abroad by writings and arguments, privately and openly, not without great
ruin and decay of the catholic church.
And further, it seemed meet, according to the law of equality, that as the death
of the Duke of Northumberland of late made even with Thomas More, chancellor,
that died for the church, so there should be one that should make even with Fisher
of Rochester ; and because that Ridley, Hooper, Farrar, were not able to make even
with that man, it seemed meet that Cranmer should be joined to them to fill up
this part of equality.
Beside these, there were other just and weighty causes, which seemed to the
queen and the council, which was not meet at that time to be opened to the common
people.
After this, turning his tale to the hearers, he bad all men beware by this man s
example, that among men nothing is so high, that can promise itself safety on the
earth, and that God s vengeance is equally stretched against all men, and spareth
none; therefore they should beware and learn to fear their prince. And seeing
be
ha\ e been
ere now
Lex npn
aequalitatis,
sea iniqui-
tatis.
No state in
this earth so
may fall.
[ l To do the like, Foxe, ed. 1583.J
OF THOMAS CRANMER. xxv
queen s majesty would not spare so notable a man as this, much less in the like
cause she would spare other men; that no man should think to make thereby any
defence of his error, either in riches or any kind of authority. They had now an
example to teach them all, by whose calamity every man might consider his own
fortune; who from the top of dignity, none being more honourable than he in the
whole realm, and next the king, was fallen into so great misery, as they might now
see; being a man of so high degree, some time one of the chiefest prelates in the
church, and an archbishop, the chief of the council, the second person in the realm
of long time, a man thought in greatest assurance, having a king on his side; not
withstanding all his authority and defence, to be debased from high estate to a low
degree; of a councillor to become a caitiff, and to be set in so wretched a state,
that the poorest wretch would not change condition with him ; briefly, so heaped
with misery on all sides, that neither was left in him any hope of better fortune,
nor place for worse.
The latter part of his sermon he converted to the archbishop ; whom he com- Doctor Cole
forted and encouraged to take his death well, by many places of scripture, as with thcaS e
these and such like : bidding him not mistrust, but he should incontinently receive take his
J > death pati-
that the thief did to whom Christ said, Hodie mccum eris in Paradiso; that is, "This entl y-
day thou shalt be with me in Paradise." And out of St Paul he armed him against
the terror of the fire, by this: Dominiis fidelis est, non sinet vos tentari ultra quam
ferre potestis; that is, "The Lord is faithful, which will not suffer you to be tempted icor. x.
above your strength :" by the example of the three children, to whom God made the
flame to seem like a pleasant dew: adding also the rejoicing of St Andrew in his
cross, the patience of St Laurence on the fire; assuring him that God, if he called
on him, and to such as die in his faith, either would abate the fury of the flame,
or give him strength to abide it.
He glorified God much in his conversion, because it appeared to be only his work, Doctor Co e
declaring what travail and conference had been with him to convert him, and all pre- t&S "
vailed not, till that it pleased God of his mercy to reclaim him and call him home, version! bi-t
that rejoicing
In discoursing of which place, he much commended Cranmer, and qualified his for-
mer doings, thus tempering his judgment and talk of him, that while the time (said
he) he flowed in riches and honour, he was unworthy of his life, and now that he
might not live, he was unworthy of death. But lest he should carry with him no
comfort, he would diligently labour, he said, and also he did promise in the name of n
all the priests that were present, immediately after his death there should be diriges,
masses, and funerals executed for him in all the churches of Oxford for the succour 80uL
of his soul.
Cranmer in all this mean time with what great grief of mind he stood hearing this
sermon, the outward shews of his body and countenance did better express than any
man can declare; one while lifting up his hands and eyes unto heaven, and then
again for shame letting them down to the earth. A man might have seen the very
image and shape of perfect sorrow lively in him expressed. More than twenty several The tears
times the tears gushed out abundantly, dropped down marvellously from his fatherly bish p-
face. They which were present do testify, that they never saw in any child more
tears, than brast out from him at that time, all the sermon while; but specially
when he recited his prayer before the people. It is marvellous what commiseration
and pity moved all men s hearts, that beheld so heavy a countenance and such abund
ance of tears in an old man of so reverend dignity.
Cole, after he had ended his sermon, called back the people that were readv to
depart, to prayers. " Brethren," said he, " lest any man should doubt of this man s
nd
masses pro-
xxvi THE LIFE, STATE, AND STORY
earnest conversion and repentance, you shall hear him speak before you; and there-
fore I pray you, Master Cranmer, that you will now perform that you promised
hh arehis no ^ l n a g> name ty> that you would openly express the true and undoubted pro
fession of your faith, that you may take away all suspicion from men, and that all
cranmer men may understand that you are a catholic in deed." " I will do it" (said the arch-
"illing to
f-Sh re h s ki sno p)> " an d wiik a good will ;" who by and by rising up, and putting off his cap,
began to speak thus unto the people :
The words " I desire you, well-beloved brethren in the Lord, that you will pray to God for me,
bishop to the to forgive me my sins, which above all men, both in number and greatness, I have
committed; but among all the rest, there is one offence, which of all at this time
doth vex and trouble me, whereof in process of my talk you shall hear more in
his proper place :" and then, putting his hand into his bosom, he drew forth his prayer,
which he recited to the people in this sense.
THE PRAYER OF DOCTOR CRANMER, ARCHBISHOP OF CANTER
BURY, AT HIS DEATH.
The prayer GOOD Christian people, my dearly beloved brethren and sisters in Christ, I beseech
bishop. you most heartily to pray for me to Almighty God, that he will forgive me all my
sins and offences, which be many without number, and great above measure. But
yet one thing grieveth ray conscience more than all the rest, whereof, God willing,
I intend to speak more hereafter. But how great and how many soever my sins be,
I beseech you to pray God of his mercy to pardon and forgive them all." And here,
kneeling down, he said : " O Father of Heaven : O Son of God, Redeemer of the
world : Holy Ghost, three persons and one God, have mercy upon me, most wretched
caitiff and miserable sinner. I have offended, both against heaven and earth, more
than my tongue can express. Whither then may I go, or whither should I fly?
To heaven I may be ashamed to lift up mine eyes, and in earth I find no place of
refuge or succour. To thee therefore, Lord, do I run : to thee do I humble my
self, saying: O Lord, my God, my sins be great, but yet have mercy upon me for
thy great mercy. The great mystery, that God became man, was not wrought for
little or few offences. Thou didst not give thy Son, heavenly Father, unto death
for small sins only, but for all the greatest sins of the world, so that the sinner return
to thee with his whole heart, as I do here at this present. Wherefore, have mercy
on me, God, whose property is always to have mercy; have mercy upon me, O
Lord, for thy great mercy. I crave nothing, Lord, for mine own merits, but for
thy name s sake, that it may be hallowed thereby, and for thy dear Son Jesus Christ s
sake: and now therefore, Our Father of heaven, hallowed be thy name," &c.
And then he rising said:
The last " Every man, good people, desireth at that time of their death to give some good
exhortation exhortation, that other may remember the same before their death, and be the better
bishop to the thereby : so I beseech God grant me grace, that I may speak something at this my
departing, whereby God may be glorified, and you edified.
"First, it is an heavy case to see that so many folk be so much doted upon
the love of this false world, and so careful for it, that of the love of God or the
Exhortation world to come they seem to care very little or nothing. Therefore this shall be my
of the work!, first exhortation, that you set not your minds overmuch upon this glosing world, but
upon God and upon the world to come; and to learn to know what this lesson
meaneth, which St John teacheth, That the love of this world is hatred against
God.
OF THOMAS CRANMER. xxvii
" The second exhortation is, that next, under God, you obey your king and queen Exhortation
to obedience.
willingly and gladly, without murmuring or grudging; not for fear of them only, but
much more for the fear of God: knowing that they be God s ministers, appointed
by God to rule and govern you; and therefore, whosoever resisteth them, resisteth
the ordinance of God.
" The third exhortation is, that you love altogether like brethren and sisters. For, Exhortation
to brotherly
alas ! pity it is to see what contention and hatred one Christian man beareth to another, l ve.
not taking each other as brother and sister, but rather as strangers and mortal ene
mies. But, I pray you, learn and bear well away this one lesson, to do good unto
all men, as much as in you lieth, and to hurt no man, no more than you would
hurt your own natural loving brother or sister. For this you may be sure of, that
whosoever hatcth any person, and goeth about maliciously to hinder or hurt him,
surely, and without all doubt, God is not with that man, although he think himself
never so much in God s favour.
" The fourth exhortation shall be to them that have great substance and riches Exhortation
t t to rich men
of this world, that they will well consider and weigh three sayings of the jjf^n *]
scripture. iP ub
" One is of our Saviour Christ himself, who saith : It is hard for a rich man to Luke xvm.
enter into the kingdom of heaven. A sore saying, and yet spoken of him that
knoweth the truth.
" The second is of St John, whose saying is this : lie that hath the substance 1 John m.
of this world, and secth his brother in necessity, and shutteth up his mercy from him,
how can he say that he loveth God?
" The third is of St James, who speaketh to the covetous rich man after this James v.
manner : Weep you and howl for the misery that shall come upon you : your
riches do rot, your clothes be moth-eaten, your gold and silver doth canker and
rust, and their rust shall bear witness against you, and consume you like fire : you
gather a hoard or treasure of God s indignation against the last day. Let them that
be rich, ponder well these three sentences : for if ever they had occasion to shew
their charity, they have it now at this present, the poor people being so many, and
victuals so dear.
" And now, forasmuch as I am come to the last end of my life, whereupon hangeth
all my life past, and all my life to come, either to live with my Master Christ for
ever in joy, or else to be in pain for ever with wicked devils in hell, and see before
me up ; I shall therefore declare unto you my very faith, how I believe, without
any colour or dissimulation: for now is no time to dissemble, whatsoever I have said
or written in time past.
"First, I believe in God the Father Almighty, Maker of heaven and earth, &c. Thearch-
And I believe every article of the catholic faith, every word and sentence taught by ciaceA the
J trueconfes-
our Saviour Jesus Christ, his apostles and prophets, in the new and old testament.
" And now I come to the great thing that so much troubleth my conscience more
than any thing that ever I did or said in my whole life, and that is, the setting abroad bishorTre-
of a writing contrary to the truth : which now here I renounce and refuse as things former re-
5 cantation,
written with my hand contrary to the truth which I thought in my heart, and written
for fear of death, and to save my life, if it might be ; and that is, all such bills and
papers which I have written or signed with my hand since my degradation ; wherein
I have written many things untrue. And forasmuch as my hand offended, writing
contrary to my heart, my hand shall first be punished therefore : for, may I come to
the fire, it shall be first burned.
xxviii THE LIFE, STATE, AND STORY
The arch- "And as for the pope, I refuse him as Christ s enemv and antichrist, with all his
bishop re- *
fuscththe f a l se doctrine.
nope as
eSyfami "And as for the sacrament, I believe as I have taught in my book against the bishop
The aS of Winchester ; the which my book teacheth so true a doctrine of the sacrament, that
ethtohis it shall stand at the last day before the judgment of God, where the papistical doc-
book written
chSr W n trine contrary thereto shall be ashamed to shew her face."
Here the standers by were all astonied, marvelled, were amazed, did look ono
upon another, whose expectation he had so notably deceived. Some began to ad
monish him of his recantation, and to accuse him of falsehood.
Briefly, it was a world to see the doctors beguiled of so great an hope. I think
there was never cruelty more notably or better in time deluded and deceived. For
it is not to be doubted but they looked for a glorious victory and a perpetual triumph
The papists by this man s retractation : who, as soon as they heard these things, began to let
in a great
th?re{T inst down ^ e ^ T ear8 to ra g e > ^ ret anc ^ " aa6 an( l so much the more, because they could
bishop. no reven g e their grief; for they could now no longer threaten or hurt him. For
the most miserable man in the world can die but once : and whereas of necessity he
must needs die that day, though the papists had been never so well pleased ; now,
being never so much offended with him, yet could he not be twice killed of them.
And so, when they could do nothing else unto him, yet lest they should say nothing,
they ceased not to object unto him his falsehood and dissimulation.
cranmer s Unto which accusation he answered : " Ah, my masters," quoth he, " do not you
papisu. take it so. Always since I lived hitherto I have been a hater of falsehood, and a
lover of simplicity, and never before this time have I dissembled :" and in saying this,
all the tears that remained in his body appeared in his eyes. And when he began
to speak more of the sacrament and of the papacy, some of them began to cry out,
yelp, and bawl; and specially Cole cried out upon him, "Stop the heretic s mouth,
and take him away."
And then Cranmer being pulled down from the stage, was led to the fire, accom-
from the panied with those friars, vexing, troubling, and threatening him most cruelly. " What
madness," say they, "hath brought thee again into this error, by which thou wilt
draw innumerable souls with thee into hell ? " To whom he answered nothing, but
directed all his talk to the people, saving that to one troubling him in the way he
spake, and exhorted him to get him home to his study, and apply his book diligently,
saying, " if he did diligently call upon God, by reading more he should get knowledge."
But the other Spanish barker, raging and foaming, was almost out of his wits, always
having this in his mouth: Non fecisti ? "didst thou it not?"
The arch- But when he came to the place where the holy bishops and martyrs of God, Hugh
the placeof Latimer and Ridley, were burnt before him for the confession of the truth, kneeling
down, he prayed to God ; and not long tarrying in prayers, putting off his garments
to his shirt, he prepared himself to death. His shirt was made long down to his
feet: his feet were bare: likewise his head, when both his caps were off, was so
bare, that not one hair could be seen upon it : his beard was long and thick, cover
ing his face with marvellous gravity. Such a countenance of gravity moved the hearts
both of his friends and of his enemies.
Then the Spanish friars, John and Richard, of whom mention was made before,
began to exhort him and play their parts with him afresh, but with vain and lost
labour: Cranmer, with steadfast purpose abiding in the profession of his doctrine,
gave his hand to certain old men, and other that stood by, bidding them farewell.
M. Fly re- And when he had thought to have done so likewise to Ely, the said Ely drew back
his hand to his hand and refused, saying, "it was not lawful to salute heretics, and specially
bishop.
OF THOMAS CRAXMER. xxix
such a one as falsely returned unto the opinions that he had forsworn ; and if he
had known before that he would have done so, he would never have used his com
pany so familiarly:" and chid those sergeants and citizens, which had not refused to
give him their hands. This Ely was a priest lately made, and student in divinity,
being then one of the fellows of Brazennose.
O
Then was an iron chain tied about Cranmer, whom when they perceived to be The arch
bishop tied to
more steadfast than that he could be moved from his sentence, they commanded the J he stake -
(ranmiT )>nt-
fire to be set unto him. And when the wood was kindled, and the fire began to
burn near him, stretching out his arm, he put his right hand into the flame : which
he held so steadfast and immoveable, (saving that once with the same hand he wiped
his face,) that all men might see his hand burned before his body was touched. His
body did so abide the burning of the flame, with such constancy and steadfastness,
that standing always in one place without moving of his body, he seemed to move
no more than the stake to which he was bound : his eyes were lifted up into heaven,
and oftentimes he repeated, his " unworthy right hand," so long as his voice would
suffer him: and using often the words of Stephen, "Lord Jesus, receive my spirit," h^SoS. 1
in the greatness of the flame, he gave up the ghost.
This fortitude of mind, which perchance is rare and not used among the Spaniards,
when friar John saw, thinking it came not of fortitude but of desperation, (although
such manner examples, which are of the like constancy, have been common here in
England,) ran to the lord Williams of Thame, crying that "the archbishop was vexed
in mind, and died in great desperation." But he which was not ignorant of the The friar s
lying report
archbishop s constancy, being unknown to the Spaniards, smiled only, and, as it were, of Cranraer -
by silence rebuked the friar s folly.
And this was the end of this learned archbishop, whom, lest by evil subscribing
he should have perished, by well recanting God preserved; and lest he should have
lived longer with shame and reproof, it pleased God rather to take him away, to the
glory of his name and profit of his church. So good was the Lord both to his
church in fortifying the same w T ith the testimony and blood of such a martyr: and
so good also to the man, with this cross of tribulation to purge his offences
in this world, not only of his recantation, but also of his standing
against John Lambert, and M. Allen, or if there were any other
with whose burning and blood his hands had been before
any thing polluted. But especially he had to rejoice that,
dying in such a cause, he was to be numbered
amongst Christ s martyrs, much more worthy
the name St Thomas of Canterbury
than he whom the pope
falsely before did
canonize.
The end of Cranmer s life, Archb. of Cant.
The following is the list of Archbishop Cranmer s writings, extracted from
Bishop Tanners Bibliotheca :
SCRIPSIT A Preface to the English Translation of the Bible, Strype in Vila
Cranmer. App. p. 241. A catechism of Christian doctrine, MDXLVIII. by Gualter Lynn.
Ternpore Edw. VI. typis vulgavit in 8vo. Instruction into the Christian religion, Pr.
cpist. " It is not unknown unto the hole." Idem hie liber cum Catechismo, quia saspe
mentionem facit verborum, "good children." The ordinances or appointments of the
reformed church. Hie liber fuit, The Book of Common Prayer, cum prefat. "There
was never any thing." A book of ordaining ministers. Idem cum, The form of
ordination, $c. A. MDL. A book concerning the Eucharist, with Luther. Eccle siastical Laws in the time of king Edward. Hie liber est Reformatio legum, fyc. a 32 delegatis composita, inter quos Cranmerus erat primarius. A defence of the catholic doctrine, Lib. v. Pr. pr. "Our Saviour Christ Jesus, according to the will." London, MDL. 4to. Emdas MDLVII. 8vo. Latine per Joh. Chekum, cui Archiepiscopus Latinam praafationem addidit ded. regi Edw. VI. pro cura dominici gregis, Lond. MDLIII. Vide hac versione Hospinian. Histor. Sacram. par. n. p. 246. a. Transtulit hunc librum etiam Johannes Young, Cantabr. The doctrine of the Lord s Supper, Lib. i. Against the error of transubstantiation, Lib. I. How Christ is present in the Lord s Supper, Lib. i. Concerning eating the Lord s Supper, Lib. I. Concerning the offering up of Christ, Lib. i. Haac sunt argumenta quinque librorum Defensionis Catholicce Doc- trince, 8$c. Responsionem ad sophisticam Gardineri cavillationem contra veram doc-
trinam de corpore et sanguine Christi in eucharistia, Lib. v. Anglice. Pr. "I thinke
it good, gentle reader," Lond. MDLI. 4to. MDLXXX. fol. Et Latine per Joh. Fox. MS.
penes Jo. Strype. Cui libro replicabat Steph. Gardiner sub nomine M. Ant. Constantii,
cui etiam libro Cranmer respondere voluit, nisi mors praavenisset. Tres tamen libros
responsorios contexuit, quorum duo priores Oxonise perierunt. A book of Christian
homelies. Est sc. prima pars homiliarum libri tempore Edw. VI. edit. A book in answer
to the calumnies of Richard Smith. Pr. " I have now obtained." Lond. MDLI. 4to.
MDLXXX. fol. Confutations of unwritten verities; written against Rich. Smith s book
De Veritatibus non scriptis, qui liber Latine scriptus, sed nunquam, ut mihi quidem
videtur, in ea lingua impressus fuit. Pr. translationis, "Ye shal put nothyng to the word."
Anglice per E.P. cum prefatione doctissima, Lond. MDLXXXII. 4to. Twelve books of
common places taken out of the doctors, concerning the unlawfulness of marrying the
brother s wife, Lib. n. Hie liber primus esse videtur, quern jussu regis Hen. VIII.
conscripsit. In MS. Cotton. Vespas. B. 5. sunt articuli xii., ex quibtis demonstratur
divortium inter Hen. VIII. et reginam Catharinam necessario esse faciendum. Pr.
"Affinitas." Against the pope s supremacy, Lib. n. Haec forte fuit declaratio episco-
porum, A. MDXXXVI. contra suprematum papas, et contra Poli Ecclesiastic am unionem
Against the pope s purgatory, Lib. n. Concerning justification, Lib. n. Hi duo ultimi
videntur esse tractatus hujus argument! ad finem libri, The institution of a Christian man.
Pious prayers, Lib. i. forte orarium sive libellus precationum a rege et clero editus,
A. MDXLV. Against the sacrifice of Mass ; and against the adoration of the bread,
Lib. i. Scriptus hie liber in carcere, et videtur esse pars prima Responsi ad Gardinerum,
sub nomine Constantii. XII Questions about alms, fasting, the mass, fyc. by archb.
Cranmer, MS. C. C. C. Cantabr. Misc. B. p. 231. His declaration concerning the
slanderous reports of his setting up mass again, Ibid. p. 321. et Strype in Vita Cranmer.
p. 305. Pr. "As the devil." Disputaliones Oxonice, April. 16. MDLIV. Fox. p. 1430, seqq.
LIST OF CRANMER S WRITINGS. xxxi
Submissions el recantationcs ejus VI. cum oratione ad populum ante mortem. Vis. ct
exam, per Edm. cpisc. London. Extant Angl. ct Latino London MDLVI. 4to. Protcsta-
tioncm contra jurisdictionem episcopi Romani. Extat in Condi. M. Brit, ct Hih.
Vol. III. p. 7^7- Mandatum dc fcsto S. Marci cvangclistce celebrando. Ibid. p. 820.
Aliud dc non celebrandis festis diebus in concil. provinc. abrogatis. Ibid. p. 827.
Literam commission alcm Kick, episcopo Dovor. Ibid. p. 828. seq. ct Strype in Vita
Cranmer. App. p. 41. Injunctions given to the diocese of Hereford. Ibid. p. 843.
Mandatum de nominibus beneficiatorum et benejiciorum. Ibid. p. 857. Statutum de
numero procuratorum curix Cant, confirmatum a T. C. Ibid. p. 858. seq. Conslitu-
tionem de moderato apparatu escarum. Ibid. p. 862. Mandatum pro orationibus pro
cessatione pluviaj. Ibid. p. 868. Epistolas varias. 1. M. Bucero post mortem Fagii,
MS. C. C. C. Cantabr. Miscell. II. p. 27. Epistola! dux ad M. Parkerum. Ibid.
IMisccll. I. 391. quarum una cxtat Strype in Vita Parker, p. 28. Epistola Lat. Jo.
Vadiano MDXXXVII., super controversia de coena Domini orta. Strype in Vila Cranm.
App. n. xxv. etiam edit, per Colomesium, Lond. MDCXCIV. 12mo. Epistola? VI. extant
ot altera ad doct. Martin, ct Story ex carcere Oxon. Pr. prima?, " It may please your
majesty." .... MDLVI. 8vo. Epistola ad Edwardum principem, Fox. 1395. Epistola
ad consilium sacrum e carcere Oxon. Fox. 1464. Epistolce XVII. Anglic^ et III.
Latina? extant apud Strype in Vita Cranmer. in Append, et in libro ipso VI. ejus
Epistola . Protestationem contra juramentum papa; prcestitum, Strype in Vita Cranm.
Append, n. v. Three discourses of faith, justification, and forgiveness of injuries,
occasioned upon his review of the king s book, intitl. Tbe erudition of a cbristian man.
Strype, Cranm. App. n. xxxr. Other discourses ; De consolatione Christianorum contra
metum mortis. Item, Exhortation to take adversity and sickness patiently. Ibid,
n. xxxir. Answers to the XV articles of the rebells, Devon. A. MDXLIX. Ibid. n. XL.
Notes for an homily against the rebellion. Ibid. n. XLI. Speech at the coronation of
k. Edward, Strype in Vita Cranmer. p. 144. Articles in the visitation of the diocese
of Canterbury, A. 2. Edw. VI. Pr. "First whether parsons, vicars." Extant in Collect,
canon. Sparrow Bal. VIII. 90. II. Holland. Herool p. 161.
A fuller account of the writings of Cranmer, with the list of those printed in
Dr Jenkyns s edition, will be given w T ith the biographical memoir in the other volume
of this collection.
UNTO
A CRAFTY AND SOPHISTICAL CAVILLATION,
DEVISED BY
STEPHEN GARDINER,
DOCTOIl OF LAW, LATE UISHOP OF WINCHESTER,
AGAINST THE TRUE AND GODLY DOCTRINE OF THE MOST HOLY
SACRAMENT OF THE BODY AND BLOOD OF OUR
SAVIOUR JESUS CHRIST.
BY THE REVEREND FATHER IN GOD
THOMAS CRANMER,
ARCIiniSH01> OF CANTERBURY, PRIMATE OF ALL ENGLAND, AND METROPOLITAN.
[CKANMKH/]
AN AVNSVVER
BY THE REVEREND FATHER
in God Thomas Archbyshop of Canterbury,
Primate of all England and Metropolitan,
Vnto a craftie and Sophisticall cauillation, deuised by
Stephen Gardiner Doctour of Law, late Byshop of Winchester
agaynst the true and godly doctrine of the most holy
Sacrament, of the body and bloud of our
Sauiour IESV CHRIST.
OTfrerem t* also, ass occasion $trntti>, atmstoerei sucfr ces of ttjt boofee of Bock Richard Smith, as map seeme anp tfcpng tx ortfrp tfte is also tfje true opg of tfje book forttten, anfc tn open (ftourt li, bg D. Stephen Gardiner, not one foorfc atfoefc or tftmtnts^^, but faptJfuIlB in all pointes agreegng fcottft tfje rigmall. antr t0rrcctelr bj? tfje jSagtr ^rt^figtf|)0ji at rfortr before Ijee ^at^ beautifielr Gardiner s tr0gnja;etf, tott!) aimui^ irtttjience atf be, bg ajpTginfl ^0tetf m tfje ^argent, antr mar&etf t0 flje IBoctourji Vagina : before toantetr in t^e e Irtecourrfe of t^e iSagtr ^rr^bB^oji^ Igfe, brteflg coIlecteJJ out of IjuS ^gitorg of tfje ^[cte^ an0 ^tonumente^, ano in tfje en0 iji atitrctr certaine ]$Jotetf, fco^eretn Gardiner faarieti, botl) from
Ijtm ielfe, antr otfjer pajjtslte^, flat^eretr bg
KeaB tnitt) SuUflemtnt, anU confem toit^ UiUflence. lapinfl astBe all affection on eftfjet partie, anU tfiou sftalt
eastlp pemaut (gooB ReaBtr) fioto slenter antt totafte tlje alleflattons antt perstoasions of tljt ^apistrs are, toi)ere=
tottt) ttiep floe atout to BefenUe tDett erroneous antt false Uoctrkie. antt to impuflne t$e trut$. Anno. M.D.LI.
AT LONDON
Printed by John Daye, dwellyng ouer Al
dersgate beneath S. Martines.
Anno. 1580.
Cum gratia 6? Priuilegio,
Regice Maiestatis.
[Prefixed to the edition of 15.51.]
I THINK it good, gentle reader, here in the beginning, to admonish thec of certain words
and kinds of speeches, which I do use sometimes in this mine answer to the late
bishop of Winchester s book, lest in mistaking thou do as it were stumble at
them.
First, this word "sacrament" I do sometimes use (as it is many times taken among sacr
writers and holy doctors) for the sacramental bread, water, or wine; as when they
say, that sacramentum est sacrce rei signum, "a sacrament is the sign of an holy
thing." But where I use to speak sometimes (as the old authors do) that Christ is
in the sacraments, I mean the same as they did understand the matter; that is to
say, not of Christ s carnal presence in the outward sacrament, but sometimes of his
sacramental presence. And sometime by this word "sacrament" I mean the whole
ministration and receiving of the sacraments, either of baptism, or of the Lord s
supper : and so the old writers many times do say, that Christ and the Holy
Ghost be present in the sacraments ; not meaning by that manner of speech, that
Christ and the Holy Ghost be present in the water, bread, or wine, (which be
only the outward visible sacraments,) but that in the due ministration of the sacra
ments according to Christ s ordinance and institution, Christ and his holy Spirit be
truly and indeed present by their mighty and sanctifying power, virtue, and grace,
in all them that worthily receive the same.
Moreover, when I say and repeat many times in my book, that the body of Christ s pre-
Christ is present in them that worthily receive the sacrament ; lest any man should godly re- "
mistake my words, and think that I mean, that although Christ be not corporally
in the outward visible signs, yet he is corporally in the persons that duly receive
them, this is to advertise the reader, that I mean no such thing; but my meaning
is, that the force, the grace, the virtue and benefit of Christ s body that was
crucified for us, and of his blood that was shed for us, be really and effectually
present with all them that duly receive the sacraments : but all this I understand
of his spiritual presence, of the which he saith, "I will be with you until the Matt. vi.
world s end ;" and, " wheresoever two or three be gathered together in my name, there Matt. xvm.
am I in the midst of them ;" and, " he that eateth my flesh and drinketh my blood, j hn vi.
dwelleth in me, and I in him." Nor no more truly is he corporally or really present
in the due ministration of the Lord s supper, than he is in the due ministration
of baptism ; [that is to say, in both spiritually by grace. And wheresover in the
scripture it is said that Christ, God, or the Holy Ghost is in any man, the same
is understood spiritually by grace.] 1
The third thing to admonish the reader of is this, that when I name Doctor The naming
of the late
Stephen Gardiner bishop of Winchester 2 , I mean not that he is so now; but foras- ^.
[N.B Wherever the asterisk is placed in the | bishoprick Feb. 14, 1550.; (Strype. Memorials of
margin, it is to signify that the side-note only i Cranmer, Vol. i. p. 322. Oxford ed. 1840.) but
occurs in the edition of 1580. The figures in the ! the positive deprivation did not take place till April
murgin denote the paging of the edition of 1580.] | 18, in the same year. ( Burnet. His. of Reforma-
f 1 This passage is only found in the edition of tion, Vol. n. p. 340. Oxford ed. 1829.) The
1580.] i sentence itself is preserved in Foxe s Acts and
[- Gardiner had been virtually deprived of his Monuments, Vol. it. pp. 738, 9, ed. 1631.]
12
4 A PREFACE.
much as he was bishop of Winchester at the time when he wrote his book against
me, therefore I answer his book as written by the bishop of Winchester, which
else needed greatly none answer for any great learning or substance of matter that
is in it.
The real pre- The last admonition to the reader is this, where the said late bishop thinketh
senee of
e ^atli sufficiently proved transubstantiation, (that is to say, that the sub-
stance of bread and wine cannot be in the sacrament, if the body and blood of
wiae." Christ were there, because two bodies cannot be together in one place,) although
the truth be, that in the sacrament of Christ s body there is corporally but the
substance of bread only, and in the sacrament of the blood the substance of wine
only, yet how far he is deceived, and doth vary from the doctrine of other pa
pists, and also from the principles of philosophy (which he taketh for the foun
dation of his doctrine in this point), the reader hereby may easily perceive. For
if we speak of God s power, the papists affirm, that by God s power two bodies
may be together in one place, and then why may not Christ s blood be with the
wine in the cup, and his flesh in the same place where the substance of the bread
is? And if we consider the cause wherefore two bodies cannot be together in
one place by the rules of nature, it shall evidently appear, that the body
of Christ may rather be in one place with the substance of the
bread, than with the accidents thereof, and so likewise his blood
with the wine. For the natural cause wherefore two bodies
cannot be together in one place (as the philosophers say) is
their accidents, their bigness, and thickness, and not
their substances. And then by the very order of
nature it repugneth more, that the body of Christ
should be present with the accidents of bread,
and his blood with the accidents of wine,
than with the substances either of bread
or wine. This shall suffice for the
thereto the preface in my
first book, which is
this :
(^Prefixed to the original edition of the " Defence of the True and Catholiek Doctrine
of the Sacrament," 1550.]
OUR Saviour Christ Jesus, according to the will of his eternal Father, when the
time thereto was fully accomplished, taking our nature upon him, came into this
world from the high throne of his Father, to declare unto miserable sinners good
news, to heal them that were sick, to make the blind to See, the deaf to hear,
and the dumb to speak, to set prisoners at liberty, to shew that the time of grace
and mercy was come, to give light to them that were in darkness and in the
shadow of death, and to preach and give pardon and full remission of sin to all
his elected. And to perform the same he made a sacrifice and oblation of his own
body upon the cross, which was a full redemption, satisfaction, and propitiation for
the sins of the whole world. And to commend this his sacrifice unto all his faithful
peoplo, and to confirm their faith and hope of eternal salvation in the same, he
hath ordained a perpetual memory of his said sacrifice, daily to be used in the
church to his perpetual laud and praise, and to our singular comfort and consola
tion ; that is to say, the celebration of his holy supper, wherein he doth not cease
to give himself, with all his benefits, to all those that duly receive the same
simper according to his blessed ordinance. But the Romish antichrist, to deface "The errone
ous doctrine
this great benefit of Christ, hath 1 that his sacrifice upon the cross is not sufficient obSfrm -Ttic
hereunto, without any other 2 sacrifice devised by him, and made by the priest, or same
else without indulgences, beads, pardons, pilgrimages, and such other pelfray, to
supply Christ s imperfection: and that Christian people cannot apply to themselves
the benefits of Christ s passion, but that the same is in the distribution of the
bishop of Rome; or else that by Christ we have no full remission, but be delivered
only from sin, and yet remaineth temporal pain in purgatory due for the same, to
be remitted after this life by the Romish antichrist and his ministers, who tako
upon them to do for us that thing, which Christ either would not or could not
do. () heinous blasphemy and most detestable injury against Christ ! O wicked
abomination in the temple of God! O pride intolerable of antichrist, and most mani
fest token of the son of perdition, extolling himself above God, and with Lucifer
exalting his seat and power above the throne of God! For he that taketh upon
him to supply that thing which he prctendeth to be imperfect in Christ, must
needs make himself above Christ, and so very antichrist. For what is this else,
but to be against Christ, and to bring him in contempt, as one that either for
lack of charity would not, or for lack of power he could not, with all his blood-
shedding and death, clearly deliver his faithful, and give them full remission of their
sins, but that the full perfection thereof must be had at the hands of antichrist
of Rome and his ministers ? What man of knowledge and zeal to God s honour TIW *tite .of
can with dry eyes see this injury to Christ, and look upon the estate of religion brought in by
brought in by the papists, perceiving the true sense of God s words subverted by
false glosses of man s devising, the true Christian religion turned into certain hypo-
1 hath (aught. Ed. 1551.] [ 2 another, 1531.]
A PREFACE.
critical and superstitious sects, the people praying with their mouths, and hearing
with their ears, they wist not what, and so ignorant in God s word, that they could
not discern the hypocrisy and superstition from true and sincere religion ? This was
of late years the face of religion within this realm of England, and yet rcmaineth
in divers realms. But thanks be to Almighty God and to the king s majesty, with
his father, a prince of most famous memory ! the superstitious sects of monks and
friars, that were in this realm, be clean taken away; the scripture is restored unto
the proper and true understanding ; the people may daily read and hear God s heavenly
word, and pray in their own language which they understand, so that their hearts
and mouths may go together, and be none of those people whom 1 Christ complained,
Matt. x\. saying : " These people honour me with their lips, but their hearts be far from me."
Thanks be to God! many corrupt weeds be plucked up, which were wont to rot the
flock of Christ, and to let the growing of the Lord s harvest.
nSsofsSi ^ ll ^ w ^at ava ileth it to take away beads, pardons, pilgrimages, and such other
like popery, so long as two chief roots remain unpulled up ? whereof, so long as they
remain, will spring again all former impediments of the Lord s harvest, and corruption
of his flock. The rest is but branches and leaves, the cutting away whereof is but
like topping and lopping of a tree, or cutting down of weeds, leaving the body standing
and the roots in the ground; but the very body of the tree, or rather the roots of
the weeds, is the popish doctrine of transubstantiation, of the real presence of Christ s
flesh and blood in the sacrament of the altar (as they call it), and of the sacrifice
and oblation of Christ made by the priest, for the salvation of the quick and the dead.
Which roots if they be suffered to grow in the Lord s vineyard, they will overspread
all the ground again with the old errors and superstitions. These injuries to Christ
* \viiatmov- be so intolerable, that no Christian heart can willingly bear them. "Wherefore, seeing
ed the author e J o
to write. that many have set to their hands, and whetted their tools, to pluck up the weeds,
and to cut down the tree of error, I, not knowing otherwise how to excuse myself
at the last day, have in this book set to my hand and axe with the rest, to cut
down this tree, and to pluck up the weeds and plants by the roots, which our hea
venly Father never planted, but were grafted and sown in his vineyard by his adver
sary the devil, and antichrist his minister. The Lord grant, that this my travail and
labour in his vineyard be not in vain, but that it may prosper and bring forth good
fruits to his honour and glory! For when I see his vineyard overgrown with thorns,
brambles and weeds, I know that everlasting woe appertained unto me, if I hold
my peace, and put not to my hands and tongue to labour in purging his vineyard.
God I take to witness, who seeth the hearts of all men thoroughly unto the bottom,
that I take this labour for none other consideration, but for the glory of his name,
and the discharge of my duty, and the zeal that I bear toward the flock of Christ.
1 know in what office God hath placed me, and to what purpose; that is to say,
to set forth his word truly unto his people, to the uttermost of my power, without
respect of person, or regard of thing in the world, but of him alone. I know what
account I shall make to him hereof at the last day, when every man shall answer
for his vocation, and receive for the same good or ill, according as he hath done. I
know how antichrist hath obscured the glory of God, and the true knowledge of his
word, overcasting the same with mists and clouds of error and ignorance through
false glosses and interpretations. It pitieth me to see the simple and hungry flock
of Christ led into corrupt pastures, to be carried blindfold they know not whither, and
to be fed with poison in the stead of wholesome meats. And moved by the duty,
1 of whom, 1551.]
A PREFACE. 7
office, and place, whereunto it hath pleased God to call me, I give warning in his A
name unto all that profess Christ, that they flee far from Babylon, if they will save ^J h r -
their souls, and to beware of that great harlot, that is to say, the pestiferous see of J? J{J L
Rome, that she make you not drunk with her pleasant w r ine. Trust not her sweet
promises, nor banquet not with her; for instead of wine she will give you sour dregs,
and for meat she will feed you with rank poison. But come to our Redeemer and
Saviour Christ, who refresheth all that truly come unto him, be their anguish and
heaviness never so great. Give credit unto him, in whose mouth was never found *I M J.
guile nor untruth. By him you shall be clearly delivered from all your diseases, of
him you shall have full remission a pcena et a culpa. He it is that feedeth
continually all that belong unto him, with his own flesh that hanged upon
the cross, and giveth them drink of the blood flowing out of his own
side, and maketh to spring within them water that floweth unto
everlasting life. Listen not to the false incantations, sweet
whisperings, and crafty juggling 8 of the subtle papists,
wherewith they have this many years deluded and
bewitched the world; but hearken to Christ,
give ear unto his words, which lead 3 you
the right way unto everlasting life,
there with him to live ever as
heirs of his kingdom.
AMEN.
JOHN VI.
It is the spirit that giveth life, the Jlesh profiteth nothing.
[* juggling*, 1551.] f 3 shall lead, 1551. J
I. PARKHURSTL*
ACCIPE przEclarum, Lector studiose, libclluni,
Qucm tibi Cranmcrus scripserat ante rogos.
Hie docta sanctam tractat rationc synaxin,
Insistcns, Patres quas docuerc, viis.
Hie, Gardncre, tuas phaleratas dctegit artcs,
Dctraliit et larvam, save tyrannc, tuam :
Atque tuo ipsius jugulum transvcrberat ensc,
Ut jaceas veluti sensibus absque fera.
Dcniquo rixosis hie obstruit ora Papistis,
Rixandi posset si tamen cssc modus.
8olvitur in cinercs corpus, mens scandit ad astra ;
Fama supcrstcs crit tempus in omnc mcmor.
H These verses are only in the edition of lofJU.J
CRAFTY AND SOPHISTICAL CAVILLATION,
DEVISED BY
M. STEPHEN GARDINER,
DOCTOR OF LAW, LATE BISHOP OF WINCHESTKll,
AGAINST THE TRUE AND GODLY DOCTRINE OF THE MOST HOLY SACRAMENT
OF THE HODY AND BLOOD OF OUR SAVIOUR CHRIST (CALLED BY HIM
"AN EXPLICATION AND ASSERTION THEREOF"), WITH AN ANSWER
UNTO THE SAME, MADE BY THE MOST REVEREND FATHER
IN GOD, THOMAS ARCHBISHOP OF CANTERBURY,
PRIMATE OF ALL ENGLAND AND METROPOLITAN.
THE TITLE OF THE BOOK OF STEPHEN GARDINER,
LATE BISHOP OF WINCHESTER :
AN EXPLICATION AND ASSERTION OF THE TRUE CATHOLIC FAITH,
TOUCHING THE MOST BLESSED SACRAMENT OF THE ALTAR,
WITH CONFUTATION OF A BOOK WRITTEN
AGAINST THE SAME. 1
THE ANSWER OF THOMAS ARCHBISHOP OF CANTERBURY, & c .
HERE before the beginning of your book you have prefixed a goodly title; but it
agrccth with the argument and matter thereof, as water agreeth with the fire. For
your book is so far from an explication and assertion of the true catholic faith in the
matter of the sacrament, that it is but a crafty cavillation and subtle sophistication, to
obscure the truth thereof, and to hide the same, that it should not appear. And in
your whole book, the reader (if he mark it well) shall easily perceive, how little learning
is shewed therein, and how few authors you have alleged, other than such as I brought
forth in my book, and made answer unto : but there is shewed what may be done by
fine wit and new devices to deceive the reader, and by false interpretations to avoid
the plain words of scripture and of the old authors.
Wherefore, inasmuch as I purpose, God willing, in this defence of my former book,
not only to answer you, but by the way also to touch D. Smith, 2 two things I would
wish in you both : the one is truth with simplicity ; the other is, that either of you
both had so much learning as you think you have, or else that you thought of yourself
no more than you have in deed. But to answer both your books in few words : the
one shewcth nothing else, but what railing without reason or learning, the other what
frowardness armed with wit and eloquence, be able to do against the truth. And
(Smith, because he would be vehement, and shew his heat in the manner of speech,
where the matter is cold, hath framed in a manner all his sentences throughout his
whole book by interrogations. But if the reader of both your books do no more, but
diligently read over my book once again, he shall find the same not so slenderly made,
but that I have foreseen all that could be said to the contrary; and that I have fully
answered beforehand all that you both have said, or is able to say.
I 1 * Made by Stephen, bishop of Winchester,
and exhibited by his own hand for his defence to
the King s Majesty s Commissioners at Lambeth."
Original edition.]
[ 2 Dr Smith s book was set forth under this
title : " A confutation of the true and Catholic
Doctrine, &c." Strype, Memorials of Cranmer. p.
10!. Oxford edition, 1840. App. Ixi. p. WO.l
10
THE FIRST BOOK
WINCHESTER.
Forasmuch as among other mine allegations for defence of myself in this matter, moved
against me by occasion of my sermon 1 made before the king s most excellent majesty, touching
partly the catholic faith of the most precious sacrament of the altar, which I see now im
pugned by a book set forth under the name of my lord of Canterbury s grace," I have thought
expedient for the better opening of the matter, and considering I am by name touched in the
*i would as said book, the rather to utter partly that I have to say by confutation of that book ; wherein
I think nevertheless not requisite to direct any speech by special name to the person of him,
^ iat " entitled author, because it may possibly be that his name is abused, wherewith to set
forth the matter, being himself of such dignity and authority in the commonwealth, as for that
respect should be inviolable. For which consideration, I shall in my speech of such reproof
as the untruth of the matter necessarily requireth, omitting the special title of the author of
the book, speak only of the author in general, being a thing to me greatly to be marvelled
at, that such matter should now be published out of my lord of Canterbury s pen ; but because
he is a man, I will not wonder, and because he is such a man, I will reverently use him,
and forbearing further to name him, talk only of the author by that general name.
CANTERBURY.
Tte craft of The first entry of your book sheweth to them that be wise, what they may look
m the begin for in the rest of the same, except the beginning vary from all that followeth. Now
the beginning is framed with such sleight and subtlety, that it may deceive the reader
notably in two things: the one, that he should think you were called into judgment
before the king s majesty s commissioners at Lambeth 2 for your catholic faith in the
both utterly untrue. For your book was made or ever ye were called before the said
commissioners; and after you were called, then you altered only two lines in the
beginning of your book, and made that beginning which it hath now. This am I able
to prove, as well otherwise, -as by a book which I have of your own hand- writing,
wherein appeareth plainly the alteration of the beginning.
And as concerning the cause wherefore ye were called before the commissioners,
whereas by your own importune suit and procurement, and as it were enforcing the
matter, you were called to justice for your manifest contempt and continual disobe
dience from time to time, or rather rebellion against the king s majesty, and were justly
deprived of your estate for the same, you would turn it now to a matter of the sacrament,
that the world should think your trouble rose for your faith in the sacrament ; which
was no matter nor occasion thereof, nor no such matter was objected against you,
wherefore you need to make any such defence. And where you would make that
matter the occasion of your worthy deprivation and punishment, (which was no cause
thereof,) and cloke your wilful obstinacy and disobedience (which was the only cause
thereof), all men of judgment may well perceive, that you could mean no goodness
thereby, neither to the king s majesty, nor to his realm.
But as touching the matter now in controversy, I impugn not the true catholic
3. faith which was taught by Christ and his apostles (as you say I do), but I impugn
the false papistical faith, invented, devised, and imagined by antichrist and his
ministers.
And as for further forbearing of my name, and talking of the author in general
(after that you have named me once, and your whole book is directed against my
book, openly set out in my name), all men may judge that your doing herein is not for
reverence to be used unto me, but that by suppressing of my name, you may the
more unreverently and unseemly use your scoffing, taunting, railing, and defaming
of the author in general; and yet shall every man understand that your speech is
directed to me in especial, as well as if you had appointed me with your finger. And
[ l Preached on St Peter s-day, June 29, 1548,
which he " chose, because the gospel agreed to his
purpose." The causes of accusation against him
are set forth in Burnet s Hist. Reform. Vol. n.
p. 340. Vol. i IT. p. 379. Oxford ed. 1829. See
Foxe s Acts and Monuments, Vol. n. p. 726, ed.
1031.]
[ 2 See p. 3, note 2.]
OF THE SACRAMENT. 11
your reverent using of yourself, before the king s highness commissioners of late, doth
plainly declare what reverent respect you have to them that be in dignity and authority
in the commonwealth.
WINCHESTER.
This author denieth the real presence of Christ s most precious body and blood in the * h
tacrament,
This author denieth trans instantiation.
This author denieth evil men to eat and drink the body and blood of Christ in the
sacrament.
These three denials only impugn and tend to destroy that faith, which this author term-
eth tlie popish to err in, calling now all popish that believe eitlter of these three articles by
hi in denied, tlie truth wJtereof shall hereafter be opened.
Now, because faith affirmeth some certainty: if we ask this author, what is his faith which * Because the
he calleth true and catholic, it is only this, as we may learn by his book, that in our Lord s taodaths
supper be consecrate bread and wine, and delivered as tokens only to signify Christ s body the catholic
and blood: he calleth them holy tokens, but yet noteth that the bread and wine be never
the holier : he saith nevertheless they be not bare tokens, and yet concludeth, Christ not to be ** what
spiritually present in them, but only as a thing is present in tJtat which signijieth it (which 2
is the nature of a bare token), saying in another place, there is nothing to be worshipped
for there is nothing present but in figure and in a sign : which whosoever saith, calleth the *Untrue re-
thing in deed absent. And yet the author saith, Christ is in the man that worthily receiveth,
spiritually present, who eateth of Christ s flesh and his blood reigning in Jieaven, whither the
good believing man ascendeth by his faith : and as our body is nourished with the bread
and wine received in the supper, so the true believing man is fed with the body and blood
of Christ. And this is the sum of the doctrine of that faith, which this author calleth the
true catholic faith.
CANTERBURY.
I desire the reader to judge my faith not by this short, envious, and untrue col
lection and report, but by mine own book, as it is at length set out in the first part,
from the 8th unto the 16th chapter.
And as concerning holiness 3 of bread and wine (whereunto I may add the water Bread, wine,
in baptism) how can a dumb or an insensible and lifeless creature receive into itself be not holy,
any food, and feed thereupon? No more is it possible that a spiritless creature should takm.
receive any spiritual sanctification or holiness. And yet do I not utterly deprive the
outward sacraments of the name of holy things, because of the holy use whereunto
they serve, and not because of any holiness that lieth hid in the insensible creature.
Which although they have no holiness in them, yet they be signs and tokens of the mar
vellous works and holy effects, which God worketh in us by his omnipotent power.
And they be no vain or bare tokens, as you would persuade, (for a bare token is 4.
that which betokcneth only and giveth nothing, as a painted fire, which giveth neither Sar^tokenl
light nor heat ;) but in the due ministration of the sacraments God is present, working
with his word and sacraments.
And although (to speak properly) in the bread and wine be nothing in deed to be
worshipped, yet in them that duly receive the sacraments is Christ himself inhabiting,
and is of all creatures to be worshipped.
And therefore you gather of my sayings unjustly, that Christ is in deed absent; for Christ jne-
l say (according to God s word and the doctrine of the old writers) that Christ is sacraments.
present in his sacraments, as they teach also that he is present in his word, when he
worketh mightily by the same in the hearts of the hearers. By which manner of
speech it is not meant that Christ is corporally present in the voice or sound of the
speaker (which sound perisheth as soon as the words be spoken), but this speech
meaneth that he worketh with his word, using the voice of the speaker, as his instrument
to work by; as he useth also his sacraments, whereby he worketh, and therefore is said
to be present in them.
[ a the holiness, 1551.]
12 THE FIRST BOOK
WINCHESTER.
*A catholic Now a catholic faith is an universal faith, taught and preached through all, and so
*Thisau- received and believed, agreeable and consonant to the scriptures, testified by such as by all
hath no ages have in their writings given knowledge thereof, which be the tokens and marks of a
true catholic faith, whereof no one can be found in the faith this author callcth catholic.
Untrue re- First, there is no scripture that in letter maintaineth the doctrine of this author s book.
Scripture in For Christ saith not that the bread doth only siqnifu his body absent, nor St Paul saith
letter favour- V V JJ V
eth not this not so in any place, nor any other canonical scripture declareth Christ s words so. As for
faith. the sense and understanding of Christ s words, there hath not been in any age any one
approved and known learned man, that hath so declared and expounded Christ s words in
his supper, that the bread did only signify Christ s body, and the wine his blood, as things
CANTERBURY.
My doctrine The first part of your description of a catholic faith is crafty and full of subtlety;
your own tie- for what you mean by "all" you do not express. The second part is very true, and
agreeth fully with my doctrine in every thing, as well in the matter of transubstantiation,
of the presence of Christ in the sacrament, and of the eating and drinking of him, as in
the sacrifice propitiatory. For as I have taught in these four matters of controversy,
so learned I the same of the holy scripture ; so is it testified by all old writers and
learned men of all ages ; so was it universally taught and preached, received and believed,
until the see of Rome, the chief adversary unto Christ, corrupted all together, and
by hypocrisy and simulation in the stead of Christ erected antichrist ; who, being the
son of perdition, hath extolled and advanced himself, and sitteth in the temple. of God,
as he were God himself, loosing and binding at his pleasure, in heaven, hell, and earth ;
condemning, absolving, canonising, and damning, as to his judgment he thinkcth
good.
But as concerning your doctrine of transubstantiation, of the real, corporal and
natural presence of Christ s body in the bread, and blood in the wine ; that ill men
5. do eat his flesh and drink his blood ; that Christ is many times offered ; there is no
scripture that in letter maintaineth any of them (as you require in a catholic faith),
but the scripture in the letter doth maintain this my doctrine plainly, that the bread
i Cor. x. remaineth, Panis quern frangimus, nonne communicatio corporis Christi est ? " Is not
the bread which we break the communion of Christ s body ?" And that evil men do
John vi. n t ea * Christ s flesh, nor drink his blood ; for the scripture saith expressly : " He
that eateth my flesh and drinkcth my blood, dwelleth in me and I in him," which is
not true of ill men. And for the corporal absence of Christ, what can be more plainly
Joimxvi. said in the letter than he said of himself, "that he forsook the world?" besides other
scriptures which I have alleged in my third book, the fourth chapter. And the
Hcb vii ix scripture speakctli plainly in the Epistle to the Hebrews, that Christ was never more
offered than once.
rhrist is spi- But here you take such a large scope, that you flee from the four proper matters
Sot. * that be in controversy, unto a new scope devised by you, that I should absolutely
deny the presence of Christ, and say, that the bread doth only signify Christ s body
absent ; which thing I never said nor thought. And as Christ saith not so, nor Paul
saith not so, even so likewise I say not so ; and my book in clivers places saith clean
contrary, that Christ is with us spiritually present, is eaten and drunken of us, and
dwelleth within us, although corporally he be departed out of this world, and is ascended
up into heaven.
WINCHESTER.
An isbuc. And to the intent every notable disagreement from the truth may the more evidently appear,
I will here in this place (as I will hereafter likewise when the case occurreth) join as it were
an issue with this author, that is to say, to make a stay with him in this point triable (as
they say) by evidence and soon tried. For in this point the scriptures be already by the
author brought forth, the letter whereof proveth not his faith. And albeit he travaileth and
bringeth forth the saying of many approved writers, yet is there no one of them that writeth
OF THE SACRAMENT. 13
in express words the doctrine of that faith, which this author calleth the faith catholic. And
to make the issue plain, and to join it directly, thus I say :
No author known and approved, that is to say, Ignatius, J olycarp, Justin, Irene, Ter- *NO writer
tullian, Cyprian, Chrysostom, Hilary, Gregory Nazianzen, Basil, Emissen, Ambrose, Cyril, tSettathfe
Jerome, Augustine, Damascene, TJieophylact, none of these hath this doctrine in plain terms, The S smn h <
that the bread only signijleth Christ s body absent ; nor this sentence, that the bread and thc lssue
wine be never the holier after consecration, nor that CJirist s body is none otherwise present
in the sacrament, but in a signijication ; nor this sentence, that the sacrament is not to be
worshipped, because there is nothing present but in a sign. And herein wftat the truth is,
iiuty soon appear, as it shall by their works never appear to have been taught and preached, *outwani
received and believed universally, and therefore can be called no catJtolic faith (that is to
say) allowed in the whole, through and in outward teaching, preached and believed.
CANTERBURY.
In your issues you make me to say what you list, and take your issue whore you J[[ 1 ur i < s l< JJ < t
list ; and then if twelve false varlets pass with you, what wonder is it ? But I will Catholic i.y
join with you this issue, that neither scripture nor ancient author writcth in express sedition.
words the doctrine of your faith. And to make the issue plain, and to join directly
with you therein, thus I say: that no ancient and catholic author hath your doctrine
in plain terms. And because I will not take my issue in bye matters (as you do), I
will make it in the four principal points, wherein we vary, and whereupon my book
resteth.
This therefore shall be mine issue : that as no scripture, so no ancient author known G.
and approved, hath in plain terms your transubstantiation : nor that the body and *
blood of Christ be really, corporally, naturally, and carnally under the forms of bread
and wine : nor that evil men do eat the very body and drink the very blood of Christ :
nor that Christ is offered every day by the priest a sacrifice propitiatory for sin.
Wherefore by your own description and rule of a catholic faith, your doctrine and
teaching in these four articles cannot be good and catholic, except you can find it in
plain terms in the scripture and old catholic doctors ; which when you do, I will hold
up my hand at the bar, and say, "guilty" : and if you cannot, then it is reason that you
do the like, per legem talionis.
WINCHESTER.
If this author, setting apart the word "catholic", would of his own wit go about to prove,
howsoever scripture hath been understanded hitherto, yet it should be understanded indeed as
he now teacheth, he hath herein divers disadvantages and hindrances worthy consideration,
which I will particularly note.
First, the prejudice and sentence, given as it were by his own mouth against himself, now A notable
in the book called the Catechism in his name set forth. ma" "to" be
Secondly, that about seven hundred years ago one Bertram (if the book set forth in his "y ",""
name be his) enterprised secretly the like, as appeareth by the said book, and yet prevailed J^S
not. Bertram
confes.-i il t<>
Thirdly, Berengarius, being indeed but an archdeacon, about Jive hundred years past, after -
he had openly attempted to set forth such like, doctrine, recanted, and so failed in his
purpose.
Fourthly, Wickliff, not much above an hundred years past, enterprised the same, whose
teaching God prospered not.
Fifthly, how Luther in his works handled them that would have in our time raised up Tiiis
the same doctrine in Germany, it is manifest by his and their writings; whereby appeareth Sine often
the enterprise that hath had so many overthrows, so many rebuts, so often reproofs, to be f|^ tct
desperate, and such as God hath not prospered and favoured to be received at any time
openly as his true teaching.
Herein whether I say true or no, let the stories try me; and it is matter worthy to be
noted, because Gamaliel s observation written in the Acts of the Apostles is allowed to AI-N \ .
marl-, how they prosper and go forward in their doctrine, that be authors of any neiu
teaching.
14
THE FIRST BOOK
CANTERBURY.
*My Cate
chism.
Bertram.
7.
Berengarius.
Wickliff.
Luther.
The papists
have been
the cause
whv the ca
tholic doc
trine hath
been hin
dered, and
good suc
cess these
late years.
I have not proved in my book my four assertions by mine own wit, but by the
collation of holy scripture, and the sayings of the old holy catholic authors. And as
for your five notes, you might have noted them against yourself, who by them have
much more disadvantage and hindrance than I have.
As concerning the Catechism by me set forth, I have answered in my fourth book,
the eighth chapter, that ignorant men for lack of judgment and exercise in old authors
mistake my said Catechism.
And as for Bertram, he did nothing else but, at the request of king Charles, set
out the true doctrine of the holy catholic church, from Christ unto his time, concerning
the sacrament. And I never heard nor read any man that condemned Bertram
before this time ; and therefore I can take no hindrance, but a great advantage at
his hands: for all men that hitherto have written of Bertram, have much commended
him. And seeing that he wrote of the sacrament at king Charles s request, it is not
like that he would write against the received doctrine of the church in those days.
And if he had, it is without all doubt that some learned man, either in his time or
sithence, would have written against him, or at the least not have commended him
so much as they have done.
Berengarius of himself had a godly judgment in this matter, but by the tyranny
of Nicholas the Second he was constrained to make a devilish recantation, as I
have declared in my first book, the seventeenth chapter.
And as for John Wickliff, he was a singular instrument of God in his time to set
forth the truth of Christ s gospel ; but antichrist, that sitteth in God s temple boasting
himself as God, hath by God s sufferance prevailed against many holy men, and
sucked the blood of martyrs these late years.
And as touching Martin Luther, it seemeth you be sore pressed, that be fain to
pray aid of him, whom you have hitherto ever detested. The fox is sore hunted that
is fain to take his burrow, and the wolf that is fain to take the lion s den for a shift,
or to run for succour unto a beast which he most hateth. And no man condemneth
your doctrine of transubstantiation, and of the propitiatory sacrifice of the mass, more
severely and earnestly than doth Martin Luther.
But it appeareth by your conclusion, that you have waded so far in rhetorick,
that you have forgotten your logic. For this is your argument: Bertram taught this
doctrine and prevailed not; Berengarius attempted the same, and failed in his purpose;
Wickliff entcrprised the same, whose teaching God prospered not; therefore God hath
not prospered and favoured it to be received at any time openly as his true teaching.
I will make the like reason. The prophet Osea taught in Samaria to the ten tribes
the true doctrine of God, to bring them from their abominable superstitions and ido
latry : Joel, Amos, and Micheas attempted the same, whose doctrine prevailed not ; God
prospered not their teaching among those people, but they were condemned with their
doctrine ; therefore God hath not prospered and favoured it to be received at any time
openly as his true teaching.
If you will answer (as you must needs do), that the cause why that among those
people the true teaching prevailed not, was by reason of the abundant superstition and
idolatry that blinded their eyes, you have fully answered your own argument, and
have plainly declared the cause, why the true doctrine in this matter hath not prevailed
these five hundred years, the church of Rome (which all that time hath borne the
chief swing) being overflown and drowned in all kind of superstition and idolatry, and
therefore might not abide to hear of the truth. And the true doctrine of the sacra
ment (which I have set out plainly in my book) was never condemned by no council,
nor your false papistical doctrine allowed, until the devil caused antichrist his son and
heir, Pope Nicholas the Second, with his monks and friars, to condemn the truth and
And where of Gamaliel s words you make an argument of prosperous success in
this matter, the scripture testifieth how antichrist shall prosper and prevail against
saints no short while, and persecute the truth. And yet the counsel of Gamaliel
OF THE SACRAMENT. 15
was very discreet and wise. For he perceived that God went about the reformation
of religion grown in those days to idolatry, hypocrisy and superstition, through tradi- 8.
tions of Pharisees; and therefore he moved the rest of the council to beware, that
they did not rashly and unadvisedly condemn that doctrine and religion which was
approved by God, lest in so doing they should not only resist the apostles, but God
himself. Which counsel if you had marked and followed, you would not have done
so unsoberly in many things as you have done.
And as for the prosperity of them that have professed Christ and his true doc
trine, they prospered with the papists as St John Baptist prospered with Herod, and
our Saviour Christ with Pilate, Annas, and Caiphas. Now which of these prospered
best, say you ? Was the doctrine of Christ and St John any whit the worse, because
the cruel tyrants and Jews put them to death for the same?
WINCHESTER.
But all this set apart, and putting aside all testimonies of the old church, and resorting * These
only to the letter of the scripture, there to search out an understanding, and in doing thereof * x^ js , Ily
to forget what hath been taught hitherto : how shall this author establish upon scripture that {jj^^^tii
lie ivould have believed ? What other text is there in scripture that encountereth with these {j[J JJj f ure
words of scripture, "This is my body," whereby to alter the signification of them ? There "Untrue re-
is ?io scripture saith, Christ did not give his body, but the figure of his body ; nor tJie giving "This author
of Christ s body in his supper, verily and really so understanded, doth not necessarily im- words of
pugn and contrary any other speech or doing of Christ, expressed in scripture. For the the ground of
great power and omnipotency of God excludeth that repugnance which man s reason would
deem, of Christ s departing from this world, and placing his humanity in the glory of his
Fatter.
CANTERBURY.
The scripture is plain, and you confess also that it was bread that Christ spake This is my
of when he said, " This is my body." And what need we any other scripture to JS^r *
encounter with these words, seeing that all men know that bread is not Christ s body, spm
the one having sense and reason, the other none at all ? Wherefore in that speech
must needs be sought another sense and meaning, than the \vords of themselves do
give, which is (as all old writers do teach, and the circumstances of the text declare)
that the bread is a figure and sacrament of Christ s body. And yet, as he giveth the
bread to be eaten with our mouths, so giveth he his very body to be eaten with our
faith. And therefore I say, that Christ giveth himself truly to be eaten, chewed, and
digested; but all is spiritually with faith, not with mouth. And yet you would bear
me in hand, that I say that thing which I say not; that is to say, that Christ did
not give his body, but the figure of his body. And because you be not able to confute
that I say, you would make me to say that you can confute.
As for the great power and omnipotency of God, it is no place here to dispute God s omni-
what God can do, but what he doth. I know that he can do what he will, both in ISTSV.
heaven and in earth, and no man is able to resist his will. But the question here is ***
of his will, not of his power. And yet if you can join together these two, that one
nature singular shall be here and not here, both at one time, and that it shall be
gone hence when it is here, you have some strong syment 1 , and be a cunning geome
trician ; but yet you shall never be good logician, that would set together two contra
dictories: for that, the schoolmen say, God cannot do.
WINCHESTER.
If this author without force of necessity would induce it, by the like speeches, as when 9
Christ said, "/ am the door," "I am thr ,/,.." " he is Helms," and such other; and because **? h * n l * r
it is a figurative speech in them, it may be so here, which maketh no kind of proof that speeches in
it is so here; but yet, if by way of reasoning I would yield to him therein, and call it *fhe faith of
a figurative speech, as he doth; wliat other point of faith is there then in the matter, but to but to believe
believe the story, that Christ did institute such a supper, wherein he gave bread and wine for ihe Lord s
a token of his boaij and blood, which is now after this understanding no secret mystery at ^o
[ l Cement.]
16
THE FIRST BOOK
it by this a ll^ or a ny ordinance above reason? For commonly men use to ordain in sensible things
derstamiinp. remembrances of themselves when they die or depart the country. So as in the ordinance of
madetoa this supper, after this understanding, CJirist shewed not his omnipotency, but only benevolence,
stipper!"or in that he loved us, and would be remembered of us. For Christ did not say, Whosoever eateth
John vi. jj^ s j fc en ea t e th m y body, or eateth my fiesh, or shall have any profit of it in special, but,
" Do this in remembrance of me."
CANTERBURY.
I make no such vain inductions, as you imagine me to do, but such as be established
by scripture and the consent of all the old writers. And yet both you and Smith
use such fond inductions for your proof of transubstantiation, when you say, God can
do this thing, and he can make that thing; whereof ye would conclude, that he doth
clearly take away the substance of bread and wine, and putteth his flesh and blood
in their places, and that Christ maketh his body to be corporally in many places
at one time; of which doctrine 1 you have not one iota in all the whole scripture.
And as concerning your argument made upon the history of the institution of
Christ s supper, like fond reasoning might ungodly men make of the sacrament of
baptism, and so scoff out both these high mysteries of Christ. For when Christ said
these words after his resurrection, " Go into the whole world, and preach unto all
people, baptizing them in the name of the Father, the Son, and the Holy Ghost :"
here might wicked blasphemers say, What point of faith is in these words, but to
believe the story, that Christ did institute such a sacrament, wherein he commanded
to give water for a token? which is now, after this understanding, no secret mystery
at all, or any ordinance above reason: so as in the ordinance of this sacrament, after
this understanding, Christ shewed not his omnipotence. For he said not then,
Whosoever receiveth this token of water, shall receive remission of sin, or the Holy
Ghost, or shall have any profit of it in especial, but, "Do this."
Injury to
baptism.
Matt. ult.
Mark ult.
WINCHESTER.
And albeit this author would not have them bare tokens, yet and 2 they be only tokens,
they have no warrant signed by scripture, for any apparel at all. For the sixth of John
speaketh not of any promise made to the eating of a token of Christ s flesh, but to the eating
of Christ s very fiesh, whereof the bread (as this author would have it) is but a figure in
Christ s words, when he said, " This is my body." And if it be but a figure in Christ s
words, it is but a figure in St Paul s words, when he said, " TJie bread which we break,
is it not the communication of Christ s body ?" that is to say, a figure of the communication
of Christ s body (if this author s doctrine be true), and not the communication indeed. Where
fore, if the very body of Christ be not in the supper delivered in deed, the eating there hath
no special promise, but only commandment to do it in remembrance. After which doctrine
why should it be noted absolutely for a sacrament and special mystery, that hath nothing
hidden in it, but a plain open ordinance of a token for a remembrance ; to the eating of
which token is annexed no promise expressly, nor any holiness to be accompted to be in the
bread or wine (as this author teacheth), but to be called holy, because tJiey be deputed to an
holy use ? If I ask the use, he declareth to signify. If I should ask what to signify f There
must be a sort of good words framed without scripture. For scripture ecrpresseth no matter
.of signification of special effect.
CANTERBURY.
?v3nan" ot ^ ^ S 11 ^ ^ or vour pleasure that the bare bread (having no further respect)
bare token, were but only a bare figure of Christ s body, or a bare token (because that term
liketh you better, as it may be thought for this consideration, that men should think
that I take the bread in the holy mystery to be but as it were a token of I recom
mend me unto you ), but if I grant, I say, that the bare bread is but a bare token
of Christ s body, what have you gained thereby? Is therefore the whole use of the
bread in the whole action and ministration of the Lord s holy supper but a naked or
nude and bare token? Is not one loaf being broken and distributed among faithful
people in the Lord s supper, taken and eaten of them, a token that the body of Christ
*Tokens be
but tokens,
howsoever
they be gar
nished with
gay wonls
without
scripture.
*Untrue re
port.
* Every spe
cial sacra
ment hath
promise
annexed and
hath a secret
hidden truth.
10.
[ ] doctrines, 1551. J
[ i.e. if.]
OF THE SACRAMENT. 17
was broken and crucified for them; and is to them spiritually and effectually given,
and of them spiritually and fruitfully taken and eaten, to their spiritual and heavenly
comfort, sustentation and nourishment of their souls, as the bread is of their bodies?
And what would you require more ? Can there be any greater comfort to a Christian
man than this? Is here nothing else but bare tokens?
But yet importune adversaries, and such as be wilful and obstinate, will never be
satisfied, but quarrel farther, saying, What of all this? Here be a great many of
gay words framed together, but to what purpose ? For all be but signs and tokens
as concerning the bread. Hut how can he be taken for a good Christian man, that
thinkcth that Christ did ordain his sacramental signs and tokens in vain, without
effectual grace and operation? For so might we as well say, that the water in bap
tism is a bare token, and hath no warrant signed by scripture for any apparel at all :
for the scripture spoaketh not of any promise made to the receiving of a token or
figure only. And so may be concluded, after your manner of reasoning, that in baptism
is no spiritual operation in deed, because that washing in water in itself is but a token.
But to express the true effect of the sacraments : As the washing outwardly in
water is not a vain token, but tcacheth such a washing as God workcth inwardly,
in them that duly receive the same; so likewise is not the bread a vain token, but
sheweth and preacheth to the godly receiver, what God worketh in him by his
almighty power secretly and invisibly. And therefore as the bread is outwardly eaten
indeed in the Lord s supper, so is the very body of Christ inwardly by faith eaten
indeed of all them that come thereto in such sort as they ought to do, which eating
nourisheth them into everlasting life.
And this eating hath a warrant signed by Christ himself in the sixth of John, A wan-ant
where Christ saith : " He that eateth my flesh and drinkcth my blood, hath life John vi.
everlasting." But they that to the outward eating of the bread, join not thereto an
inward eating of Christ by faith, they have no warrant by scripture at all, but the
bread and wine to them be vain, nude, and bare tokens.
And where you say that scripture expresseth no matter of signification fof] special ]].
effect in the sacraments of bread and wine, if your eyes were not blinded with popish
errors, frowardness, and self-love, ye might see in the twenty-second of Luke, where
Christ himself expresseth a matter of signification, saying : Hoc facite in mei commemo- Luke xxu.
rationem: "Do this in remembrance of me." And St Paul likewise, 1 Cor. xi., i cor. \\.
hath the very same thing ; which is a plain and direct answer to that same your last
question, whereupon you triumph at your pleasure, as though the victory were all
yours. For ye say, when this question is demanded of me, What to signify ? " Here
must be a sort of good words framed without scripture." But here St Paul answcreth
your question in express words, that it is the Lord s death that shall be signified, i cor. \\.
represented, and preached in these holy mysteries, until his coming again. And this
remembrance, representation and preaching of Christ s death, cannot be without special
effect, except you will say that Christ worketh not effectually with his word and
sacraments. And St Paul expresseth the effect, when he saith : " The bread which we i c<>r. x.
break is the communion of Christ s body." But by this place and such like in your
book, ye disclose yourself to all men of judgment, either how wilful in your opinion,
or how slender in knowledge of the scriptures you be.
WINCHESTER.
And therefore like as the teaching is new, to say it is an only figure, or only signi- * A new
fifth ; so the matter of signification must be newly devised, and new nine Jirtrr new hnttlfs, only figure.
find be thoroughly new, after fifteen hundred and fifty years, in the very year of jubilee (as
tiify were wont to call it) to be newly erected and builded in Englishmen s hearts.
beginneth to
be published
now.
CANTERBURY.
It seemeth that you be very desirous to abuse the people s ears with this term,
" new," and with the " year of jubilee," as though the true doctrine of the sacrament
by me taught should be but a new doctrine, and yours old (as tho Jews slandered Mark i.
]8 THE FIRST BOOK
the doctrine of Christ by the name of newness) ; or else that in this year of jubilee,
you would put the people in remembrance of the full remission of sin, which they
were wont to have at Rome this year, that they might long to return to Rome for
pardons again, as the children of Israel longed to return to Egypt for the flesh that
they were wont to have there.
But all men of learning and judgment know well enough that this your doctrine
is no older than the bishop of Rome s usurped supremacy, which though it be of good
age by number of years, yet is it new to Christ and his word. If there were such
darkness in the world now, as hath been in that world which you note for old, the
people might drink new wine of the whore of Babylon s cup, until they were as drunk
with hypocrisy and superstition, as they might well stand upon their legs, and no man
once say, black is their eye. But now, (thanks be to God!) the light of his word so
shineth in the world, that your drunkenness in this year of jubilee is espied, so that
you cannot erect and build your popish kingdom any longer in Englishmen s hearts,
without your own scorn, shame and confusion. The old popish bottles must needs
burst, when the new wine of God s holy word is poured into them.
WINCHESTER.
Which new teaching, whether it proceedeth from the spirit of truth or no, shall more
12. plainly appear by such matter as this author uttereth wherewith to impugn the true faith
taught hitherto. For among many other proofs, whereby truth after much travail in con-
* Tokens how tention at the last prevaileth and hath victory, tliere is none more notable, than when the
truth from very adversaries of truth (who pretend, nevertheless, to be truth s friends) do by some evident
untruth bewray themselves. According whereunto, when the two women contended before king
* i Kings iii. Solomon for the child yet alive, Solomon discerned the true natural mother from the other,
by their speeches and sayings; which in the very 1 mother were ever conformable unto nature,
and in the other, at the last evidently against nature. The very true mother spake always like
A lesson of herself, and never disagreed from tlie truth of nature, but rather than the child should be
judgment . killed (as Solomon threatened when he called for a sword) required 2 it to be given whole alive
to the other woman. Tlie other woman that was not the true mother cared more for victory
than for the child, and therefore spake that was in nature an evidence that she lied calling
herself mother, and saying, " Let it be divided" which no s natural mother could say of her
own child. Whereupon proceedeth Solomon s most wise judgment, which hath this lesson in
it, ever where contention is, on that part to be the truth, where all sayings and doings appear
uniformly consonant to the truth pretended; and on what side a notable lie appeareth, the rest
* Truth need- may be judged to be after the same sort. For truth needeth no aid of lies, craft, ,
lies. wherewith to be supported or* maintained. So as in the entreating of the truth of this high and
ineffable mystery of the, sacrament, on what part thou, reader, seest craft, sleight, shift, obliquity,
* Truth or i n an y one point an open manifest lie, there thou mayest consider, whatsoever pretence be
dtvand mpli maa ^ f truth, yet the victory of truth not to be there intended, which loveth simplicity, plainness,
plainness. direct speech, without admiztion of shift or colour.
CANTERBURY.
The church If either division or confusion may try the true mother, the wicked church of
not the true Rome (not in speech only, but in all other practices) hath long gone about to oppress,
<Xofie the confound and divide the true and lively faith of Christ, shewing herself not to be the
true mother, but a most cruel stepmother, dividing, confounding and counterfeiting
all things at her pleasure, not contrary to nature only, but chiefly against the plain
words of scripture.
* Absurda et For here in this one matter of controversy between you, Smith, and me, you
divide against nature the accidents of bread and wine from their substances, and the
substance of Christ from his accidents; and contrary to the scripture you divide our
eternal life, attributing unto the sacrifice of Christ upon the cross only the beginning
thereof, and the continuance thereof you ascribe unto the sacrifice of popish priests.
[ In the very true mother, 1551.] [ 8 No true natural mother, 1551.]
[* Required rather, 1551. J [ 4 Supported and maintained, 1551.]
OF THE SACUAMKXT. 19
And in the sacraments you separate Christ s body from hi.s spirit, affirming that in
baptism we receive but his spirit, and in the communion but his flesh: and that
Christ s spirit renewetli our life, but increaseth it not; and that his flesh increa>eth
our life, but givcth it not. And against all nature, reason, and truth, you confound
the substance of bread and wine with the sub.-tance of Christ s body and blood, in
such wi<e as you make but one nature and person of them all. And against scrip-
tun 1 and all conformity of nature, you confound and jumble so together the natural
members of Christ s body in the sacrament, that you leave no distinction, proportion,
nor fashion of man s body at all.
And can your church be taken for the true natural mother of the true doctrine
of Christ, that thus unnaturally speaketh, divideth, and confonndeth Christ s body? mother.
If Solomon were alive, he would surely give judgment that Christ should be taken 13.
from that woman, that speaketh so unnaturally, and so unlike his mother, and be
given to the true church of the faithful, that never digressed from the truth of God s
word, nor from the true speech of Christ s natural body, but speak according to the
same, that Christ s body, although it be inseparable, annexed unto his Godhead, yet it
hath all the natural conditions and properties of a very man s body, occupying one
place, and being of a certain height and measure, having all members distinct and set
in good order and proportion. And yet the same body joined unto his divinity, is
not only the beginning, but also the continuance and consummation of our eternal and
celestial life. By him we be regenerated, by him we be fed and nourished from
time to time, as he hath taught us most certainly to believe by his holy word and
sacraments, which remain in their former substance and nature, as Christ doth in his,
without mixtion or confusion. This is the true and natural speaking in this matter,
like a true natural mother, and like a true and right believing Christian man.
Marry, of that doctrine which you teach, I cannot deny but the church of Rome Rome is the
i i c ^ -i 11 -i -r -I i < mother of
is the mother thereof, winch in scripture is called Uabylon, because of commixtion the papistical
or confusion : which in all her doings and teachings so doth mix and confound
error with truth, superstition with religion, godliness with hypocrisy, scripture with
traditions, that she sheweth herself alway uniform and consonant, to confound all the
doctrine of Christ, yea, Christ himself, shewing herself to be Christ s stepmother, and
the true natural mother of antichrist.
And for the conclusion of your matter here, I doubt not but the indifferent reader
shall easily perceive what spirit moved you to write your book. For seeing that
your book is so full of crafts, sleights, shifts, obliquities, and manifest untruths, it
may be easily judged, that \\hatso\er pretence be made of truth, yet nothing is less
intended, than that truth should either have victory, or appear and be seen at all.
WINCHESTER.
And that thou, reader, mightest by these marks judge of that is here entreated by the author * The name
against the most blessed sacrament, I shall note certain evident and manifest untruths, which this great, where-
author is not afraid to utter, (a matter wonderful, considering his dignity, if he that is named be men to
the outhor indeed,) which should be a great stay of contradiction, if anything were to be regarded S1
against the truth.
First, I unll note unto tJte reader, how this author tcrmeth the faith of the real and substantial * An impu-
" dent untruth.
presence of Christ s body and blood in the sacrament to be the faith of the papists: which saying,
what foundation it hath, thou mayest consider of that followeth.
Luther, that professed openly to abhor all tht might be noted popish, defended stoutly the
presence of Christ s body in the sacrament, and to be present really and substantially, even wit ft
the same words and terms.
Bucer, that is here in England, in a solemn work that he writfth upon the Gospels,
professeth the same faith of the real and substantial presence of Christ s body in the sacra
ment, which he affirmeth to have been believed of all the church of Chr ^t frum the beginning
hitherto. * The faith of
Justus Jonas Jiath translated a catechism out of Dutch into Latin, t""g!tt in the city o/ mentinthe
Nuremberg in Germany, where Hosiander is chief preacher, in which catechism they be accounted pro^ethThhT
for no true chrislian men, that deny the presence of Chrisfs body in the sacrament. The words SLtMir.
9 9
20
THE FIRST BOOK
" really" and " substantially" be not expressed as they be in Bucer, but the word " truly" is
there, and, as Bucer saith, that is, substantially. Which catechism was translated into English
1-J. in this author s name about two years past.
Philip Melancthon, no papist nor priest, writeth a very wise epistle in this matter to
CEcolampadius, and signifying soberly his belief of the presence of Christ s very body in the
sacrament ; and to prove the same to have been the faith of the old church from the beginning,
allegeth the sayings of Irene,, Cyprian, Chrysostom, Hilary, Cyril, Ambrose, Theophylact, which
authors he esteemeth both worthy credit, and to affirm the presence of Christ s body in the
sacrament plainly without ambiguity. He answereth to certain places of St Augustine, and
saith all CEcolampadius enterprise to depend upon conjectures, and arguments applausible to
idle wits, with much more wise matter, as that epistle doth purport, which is set out in a book
of a good volume among tlie other epistles of CEcolampadius, so as no man may suspect anything
counterfeit in the matter.
One Hippinus, or CEpinus, of Hamburgh, greatly esteemed among tlie Lutherans, hath
written a book to the king s majesty that now is, published abroad in print, wherein much
inveighing against the church of Rome, doth in the matter of the sacrament write as followeth :
" Eucharistia is called by itself a sacrifice, because it is a remembrance of tlie true sacrifice
offered upon tlie cross, and that in it is dispensed tlie true body and true blood of Christ, which is
plainly the same in essence, that is to say substance, and tlie same blood in essence signifying,
though tlie manner of presence be spiritual, yet the substance of that is present, is the same with
that in heaven."
Erasmus, noted a man that durst and did speak of all abuses in the church liberally, taken
for no papist, and among iis so much esteemed, as his paraphrases of the gospel is ordered
com^endeth to be had in every church of this realm, declareth in divers of his works most manifestly his
the* work^ f^ith of the presence of Christ s body in the sacrament, and by his epistles recommendeth to
Aigerus upon fl^ world the work of Aigerus in that matter of the sacrament, whom he noteth well exercised
the sacra- J y J
ment. in the scriptures, and the old doctors, Cyprian, Hilary, Ambrose, Jerome, Augustine, Basil,
Christ hidden Chrysostom. And for Erasmus own judgment, lie saith we have an inviolable foundation of
signs r the Christ s own words, " This is my body" rehearsed again by St Paul : he saith further, the
* Erasmus body of Christ is hidden under those signs ; and sheweth also upon what occasions men have
repent, that erred in reading the old fathers, and wisheth that they which have followed Berengarius in
garius error, error xvould also follow him in repentance. I will not, reader, encumber thee with more words
of Erasmus.
* Peter Mar- Peter Martyr, of Oxford, taken for no papist, in a treatise he made of late of the sacrament,
lies impugn which is now translated into English, sheweth how as touching the real presence of Christ s body,
the sacra- it is not only the sentence of tlie papists, but of other also ; whom the said Peter nevertheless doth
with as many shifts and lies as he may impugn for that point, as well as he doth the papists for
transubstantiation, but yet lie doth not, as this author doth, impute that faith of the real presence
An issue. of Christ s body and blood to tlie only papists. Whereupon, reader, here I join with the author
an issue, that the faith of the real and substantial presence of Christ s body and blood in the
sacrament is not the device of papists, or their faith only, as this author doth considerately
slander it to be, and desire therefore that according to Solomon s judgment this may serve for a
* This author note and mark, to give sentence 1 for tlie true mother of tlie child. For what should this mean, so
theenvTous without shame openly and untruly to call this faith popish, but only with tlie envious word of
pistfopp P ess papist to overmatch the truth?
the truth.
CANTERBURY.
This explication of the true catholic faith noteth to the reader certain evident am
manifest untruths uttered by me (as he saith), which I also pray thee, good reader,
to note for this intent, that thou mayest take the rest of my sayings for true, which
he noteth not for false, and doubtless they should not have escaped noting as well as
the other, if they had been untrue, as he saith the other be. And if I can prove
these things also true, which he noteth for manifest and evident untruths, then me
thinketh 2 it is reason that all my sayings should be allowed for true, if those be proved
15. true which only be rejected as untrue. But this untruth is to be noted in him
generally, that he either ignorantly mistaketh, or willingly misreporteth almost all
that I say. But now note, good reader, the evident and manifest untruths which I
For to give sentence, 1551.]
[ 2 Me think, 1551.]
OF THE SACRAMENT. 21
utter, as he saith. The first is, that the faith of the real presence is the faith of
the papists. Another is, that these words, " My fle-h i< verily meat," I do translate
thus 3 : " My flesh is very meat." Another is, that I handle not sincerely the words
of St Augustine, speaking of the eating of Christ s body. The fourth is, that by
these words, " This is my body," Christ intendeth not to make the bread his body,
but to signify that such as receive that worthily be members of Christ s body.
These be the heinous and manifest errors which I have uttered.
A- touching the first, that the faith of the real and substantial presence of Christ s
body and blood in the sacrament is the faith of the papists, this is no untruth, but a
most certain truth. For you confess yourself, and defend in this book, that it is your
faith : and so do likewise all the papists. And here I will make an issue with you,
.
that the papists believe the real, corporal, and natural presence of Christ s body and blood
in the sacrament. Answer me directly without colour, whether it be so or not. If they
believe not so, then they believe as I do, for I believe not so : and then let them openly
confess that my belief is true. And if they believe so, then say I true when I say that it
is the papists faith. And then is my saying no manifest untruth, but a mere truth ;
and so the verdict in the issue passeth upon my side by your own confession.
And here the reader may note well, that once again you be fain to fly 4 for succour
unto M. 5 Luther, Bucer, Jonas, Melancthon, and CEpinus, whose names 6 were wont Luther,
to be so hateful unto you, that you could never with patience abide the hearing of Jonas.
them : and yet their sayings help you nothing at all. For although these men in
this and many other things have in times past, and yet peradventure some do (the
veil of old darkness not clearly in every point removed from their eyes), agree with
the papists in part of this matter, yet they agree not in the whole: and therefore
it is true nevertheless, that this faith which you teach is the papists faith. For if
you would conclude, that this is not the papists faith, because 7 Luther, Bucer, and
other, believe in many things as the papists do, then by the same reason you may
conclude that the papists believe not that Christ was born, crucified, died, rose again,
and ascended into heaven, which things Luther, Bucer and the other, constantly both
taught and believed: and yet the faith of the real presence may be called rather the
faith of the papists than of the other, not only because the papists do so believe,
but specially for that 8 the papists were the first authors and inventors of that faith,
and have been the chief spreaders abroad of it, and were the cause that other were
blinded with the same error.
But here may the reader note one thing by the way, that it is a foul clout that
you would refuse to wipe your nose withal, when you take such men to prove your
matter, whom you have hitherto accounted most vile and filthy heretics. And yet
now you be glad to fly 4 to them for succour, whom you take for God s enemies, and
to whom you have ever had a singular hatred. You pretend that you stay yourself
upon ancient writers : and why run you now to such men for aid, as be not only new,
but also as you think, be evil and corrupt in judgment ; and to such as think you,
by your writings and doings, as rank a papist as is any at Rome ?
And yet not one of these new men (whom you allege) do thoroughly agree with 1G.
your doctrine, either in transubstantiation, or in carnal eating and drinking of Christ s
flesh and blood, or in the sacrifice of Christ in the mass, nor yet thoroughly in the
real presence. For they affirm not such a gross presence of Christ s body, as cxpclleth
the substance of bread, and is made by conversion thereof into the substance of Christ s
body, and is eaten with the mouth. And yet if they did, the ancient authors that were
next unto Christ s time (whom I have alleged) may not give place unto these new men
in this matter, although they were men of excellent learning and judgment, howsoever
it liketh you to accept them.
But I may conclude that your faith in the sacrament is popish, until such time as
you can prove that your doctrine of transubstantiation and of the real presence was
I 3 1 translate thus, 1551.]
[ 4 Flee, 1551.]
[ 5 Martin Luther, 1551.J
[" Whose names before were wont, lool.]
[ 7 Because that Luther, 1551.]
[ 8 But for that specially, that the papists, lool.J
22 THE FIRST BOOK
universally received and believed, before the bishops of Rome defined and determined
the same. And when you have proved that, then will I grant that in your first note
you have convinced me of an evident and manifest untruth, and that I untruly charge
you with the envious name of a papistical faith.
But in your issue you term the words at your pleasure, and report me otherwise
than I do say : for I do not say that the doctrine of the real presence is the papists
* Mine issue, faith only, but that it was the papists faith, for it was their device. And herein will I
join with you an issue : that the papistical church is the mother of transubstantiation,
and of all the four principal errors which I impugn in my book.
WINCHESTER.
It shall be now to purpose to consider the scriptures touching the matter of tlie sacrament,
which the author pretending to bring forth faithfully as the majesty thereof requireth, in tlie
rehearsal of the words of Christ out of the gospel of St John, he beginneth a, little too low, and
passeth over that pertaineth to the matter, and therefore should have begun a little higher at this
[John vi.] clause : " And the bread which I shall give you is my Jlesh, which I will give for the life of the
world. The Jews therefore strived between themselves, saying, How can this man give his Jlesh to
be eaten ? Jesus therefore said unto them, Verily, verily I say unto you, Except ye eat the Jlesh
of the Son of man, and drink his blood, ye have no life in you. Whoso eateth my Jlesh, and
drinketh my blood, hath eternal life, and I will raise him up at the last day. For my Jlesh is
very meat, and my blood very drink. He that eateth my Jlesh, and drinketh my blood,
dwelleth in me, and I in him. As the living Father hath sent me, and I live by the Father :
even so he that eateth me shall live by me. This is the bread which came down from heaven.
Not as your fathers did eat manna and are dead. He that eateth this bread shall live for ever."
Here is also a fault in the translation of the text, which should be thus in one place : " For
my Jlesh is verily meat, and my blood is verily drink." In which speech the verb that coupleth
the words "Jlesh" and " meat" together, knitteth them together in their proper signification, so as
the Jlesh of Christ is verily meat, and not figuratively meat 1 , as the author would persuade.
And in time words of Christ may appear plainly, how Christ taught the mystery of the food of
his humanity, which he promised to give for food, even tlie same Jlesh that he said he would give
for the life of tlie world ; and so expresseth the first sentence of this scripture here by me wholly
brought forth, that is to say, " and tlie bread which I shall give you is my Jlesh, which I shall
give for the life of the world;" and so is it 2 plain that Christ spake of Jlesh in the same sense
that St John speaketh in, saying, " The word was made Jlesh," signifying by Jlesh the whole
Cyril and humanity. And so did Cyril agree to Nestorius, when he upon these texts reasoned how this
ms< eating is to be understanded of Christ s humanity, to which nature in Christ s person is properly
JT attribute to be eaten as meat spiritually to nourish man, dispensed and given in the sacrament.
And between Nestorius and Cyril was this diversity in understanding the mystery, that Nestorius
esteeming of each nature in Christ a several person, as it was objected to him, and so dissolving
tlie ineffable unity, did so repute the body of Christ to be eaten as the body of a man separate.
Cyril maintained the body of Christ to be eaten as a body inseparable, united to the Godhead, and
for the ine/able mystery of that union the same to be a Jlesh that giveth life. And then as Christ
saith, " If we eat not the Jlesh of the Son of man, we have not life in us" because Christ hath
ordered the sacrament of his most precious body and blood, to nourish such as be by his holy
in baptism Spirit regenerate. And as in baptism we receive the Spirit of Christ, for the renewing of our
chrSspirit Kfe) so ao we Mb sacrament of Christ s most precious body and blood receive Christ s very Jlesh,
In third s aild drink his ver # blood, to continue and preserve, increase and augment, the life received.
ceTve^rnesh And there f ore in the same f orm of words Christ spake to Nicodemus of baptism, that
contin ^ d iife ^ speaketh here of the eating of his body and drinking of his blood, and in both sacraments
giveth, dispenseth, and exhibiteth indeed, those celestial gifts in sensible elements, as Chrysostom
saith. And because the true, faithful, believing men do only by faith know the Son of man
to be in unity of person the Son of God, so as for the unity of the two natures in Christ, in
one person, the Jlesh of the Son of man is tlie proper Jlesh of the Son of God.
Saint Augustine said well when he noted these words of Christ, " Verily, verily, unless
ye eat the Jlesh of tlie Son of man," fyc., to be a figurative speech, because after the bare letter it
seemeth unprofitable, considering that Jlesh profiteth nothing in itself, esteemed in tlie own nature
[ These words, "and not figuratively meat," j [ And so it is, 1551.}
OF THE SACRAMENT. 23
alone ; but as the same flesh in Christ is united to the divine nature, so is it, as Christ said,
(after Cyril s exposition,) spirit and life, not changed into tJte divine nature of the spirit, but
for the ine/able union in the person of Christ thereunto. It is vivificatrix, as Cyril said, and
as the holy Epliesine council decreed : " A flesh giving life," according to Christ s words : " Who
eateth tny flesh, and drinketh my blood, hath eternal life, and I will raise him up at the latter
day." And then to declare unto us, how in giving this life to us Christ useth the instrument
of his very human body, it followeth : " For my flesh is verily meat, and my blood is verify
drink 3 ." So like as Christ sanctifleth by his godly Spirit, so doth he sanctify iis by his
godly flesh, and therefore repeateth again, to inculcate the celestial thing of this mystery, and
saith: "He that eateth my flesh, and drinketh my blood, dwelleth in me and I in him,"
which is tlie natural and corporal union between us and Christ. Whereupon followeth, that
as Christ is naturally in his Father, and his Father in him, so he that eateth verily the
flesh of Christ, lie is by nature in Christ, and Christ is naturally in him, and the worthy
receiver hath life increased, augmented, and conflrmed by the participation of the flesh ofCJirist.
And because of tlie ineffable union of the two natures, Christ said, " This is the food
that came down from heaven" because God (whose proper flesh it is) came down from heaven,
and hath another virtue than manna had, because this giveth life to them that worthily re
ceive it : which manna (being but a figure thereof) did not, but being in this food Christ s
very flesh, inseparably united to the Godhead, the same is of such efficacy, as he that worthily
i i/cff>, of it shall live for ever. And thus I have declared tlic sense of Christ s words, brought
forth out of the gospel of St John. Whereby appeareth, how evidently they set forth the doc
trine of the mystery of the eating of Christ s flesh, and drinking his blood in ttie sacrament,
ivhich mvst needs be understanded of a corporal eating, as Christ did after order in the in
stitution of the said sacrament, according to his promise and doctrine here declared.
CANTERBURY.
I fere before you enter into my second untruth (as you call it), you find fault by the
way, that in the rehearsal of the words of Christ, out of the Gospel of St John, I
begin a little too low. But if the reader consider the matter for the which I allege 18.
St John, he shall well perceive that I began at the right place where I ought to begin.
For I do not bring forth St John for the matter of the real presence of Christ in the
sacrament, whereof is no mention made in that chapter; and as it would not have
served me for that purpose, no more doth it serve you, although you cited the whole
gospel. But I bring St John for the matter of eating Christ s flesh and drinking his
blood, wherein I passed over nothing that pertaineth to the matter, but rehearse the
whole fully and faithfully. And because the reader may the better understand the
matter, and judge between us both, I shall rehearse the words of my former book,
which be these.
*THE supper of the Lord, otherwise called the holy communion or sacra- Joo k - ]
ment of the body and blood of our Saviour Christ, hath been of many men, The abuse of
and by sundry ways very much abused, but specially within these four or live supper.
hundred years. Of some it hath been used as a sacrifice propitiatory for sin,
and otherwise supcrstitiously, far from the intent that Christ did first ordain
the same at the beginning, doing therein great wrong and injury to his death
and passion. And of other some it hath been very lightly esteemed, or rather
contemned and despised as a thing of small or of none effect. And thus between
both the parties hath been much variance and contention in divers parts 4 of
Christendom. Therefore to the intent that this holy sacrament or Lord s supper
may hereafter neither of the one party be contemned or lightly esteemed, nor
of the other party be abused to any other purpose than Christ himself did
first appoint and ordain the same, and that so the contention on both parties
may be quieted and ended, the most sure and plain way is to cleave unto
[ 3 My blood verily drink, loftl.] j doctrine and use of the Sacrament of the Body and
* The title of this hook runs thus in the original Blood of our Saviour Christ."]
edition : " The first book is of the true and Catholic [ Places, 1551,
24 THE FIRST BOOK
holy scripture : wherein whatsoever is found, must be taken for a most sure
ground, and an infallible truth ; and whatsoever cannot be grounded upon the
same, touching our faith, is man s device, changeable and uncertain. And there
fore here are set forth the very words that Christ himself and his apostle St
Paul spake, both of the eating and drinking of Christ s body and blood, and
also of the eating and drinking of the sacrament of the same. First, as con-
chap. ii. cerning the eating of the body and drinking of the blood of our Saviour Christ,
the body of he speaketh himself in the sixth chapter of St John in this wise :
John vi. Verily, verily, I say unto you, except ye eat the flesh of the Son of man, and
drink his blood, you have no life in you. Whoso eateth my flesh and drinketh
my blood, hath eternal life, and I will raise him up at the last day. For my
flesh is very meat, and my blood is very drink. He that eateth my flesh, and
drinketh my blood, dwelleth in me and I in him. As the living Father hath sent
me, and I live by the Father, even so he that eateth me, shall live by me. This
is the bread which came down from heaven. Not as your fathers did eat manna,
and are dead. He that eateth this bread shall live for ever."
Here have I rehearsed the words of Christ faithfully and fully, so much as per-
taineth to the eating of Christ s flesh, and drinking of his blood. And I have begun
IQ neither too high nor too low, but taking only so much as served for the matter.
The second But here have I committed a fault (say you) in the translation, for "verily meat"
" veriiy translating " very meat." And this is another of the evident and manifest untruths
translating by me uttered, as you esteem it. "Wherein a man may see, how hard it is to escape
the reproaches of Momus. For what an horrible crime (trow you) is committed here,
* Origenes in to call " very meat" that which is " verily meat" ! As who should say, that " very
vii. Prop- meat" is not " verily meat," or that which is " verily meat" were not " very meat."
cuogiw ve- The old authors say " very meat," aXrjQrl^ /fycocm, verus cibus, in a hundred places.
And what skilleth it for the diversity of the words, where no diversity is in the
otus. ei Et fn sense ? and whether we say, " very meat," or " verily meat," it is a figurative speech
xii. baro in this place, and the sense is all one. And if you will look upon the New Testament
csca, e/Ln 5 - lately set forth in Greek by Robert Stevens, you shall see that he had three Greek
venuertpo- copies, which in the said sixth chapter of John have dXrjdrjs and not d\rj6w<;. So
in EccL cap. that I may be bold to say, that you find fault here where none is.
mu atcU And here in this place you shew forth your old condition (which you use much in
this book) in following the nature of a cuttle 1 . "The property of the cuttle," saith Pliny,
ug e ust p ?n US "is to cast out a black ink or colour, whensoever she spieth herself in clanger to be
111 taken, that the water being troubled and darkened therewith, she may hide herself and
so escape untaken." After like manner do you throughout this whole book ; for when
you see no other way to fly and escape, then you cast out your black colours, and mask
rap". 14. caro yourself so in clouds and darkness, that men should not discern where you be come,
dibtul^ttn- which is a manifest argument of untrue meaning: for he that meaneth plainly, speaketh
rnwtpotoT plainly ; et qui sophistice loquitur, odililis est^ saith the wise man. For he that
jn jScap.lx. speakcth obscurely and darkly, it is a token that he goeth about to cast mists before
raiwtdbut men s cyes * ua ^ they should not see, rather than to open their eyes that they may
fne^s venis clearly see the truth.
Thenature of And therefore to answer you plainly, the same flesh that was given in Christ s last
PuSlib. i\. supper was given also upon the cross, and is given daily in the ministration of the
*icS sacrament. But although it be one thing, yet it was diversely given. For upon the
rhrist is ve- cr ss Christ was carnally given to suffer and to die ; at his last supper he was spiritually
" iverTin the* gi vcn i n a promise of his death; and in the sacrament he is daily given in remembrance
btiVveTsni- ^ ^* s death. And yet it is all but one Christ that was promised to die, that died
ntuaiiy. indeed, and whose death is remembered; that is to say, the very same Christ, the
eternal Word that was made flesh. And the same flesh was also given to be spiritually
eaten, and was eaten in deed, before his supper, yea, and before his incarnation also.
[ Of the cuttle, 1551.]
OF THE SACRAMENT. 25
Of which eating, ami not of sacramental eating, he spake in the sixth of John : " My John vi.
flesh is very meat, and my blood is very drink. He that eateth my flesh, and drinketh
my blood, dwelleth in me, and I in him."
And Cyril, I grant, agreed to Nestorins in the substance of the thing that was cyrii.anathe-
eaten, (which is Christ s very flesh.) but in the manner of eating they varied. For
Nestorius imagined a carnal eating (as the papists do) with mouth, and tearing with
teeth. But Cyril in the same place saith, that Christ is eaten only by a pure faith,
and not that he is eaten corporally with our mouths, as other meats be, nor that he is
eaten in the sacrament only.
And it seemeth you understand not the matter of Nestorius, who did not esteem 20.
Christ to be made of two several natures and several persons, (as you report of him;)
but his error was, that Christ had in him naturally but one nature and one person,
affirming that he was a pure man, and not God by nature, but that the Godhead by
grace inhabited, as he doth in other men.
And where you say that in baptism we receive the spirit of Christ, and in the injury to
sacrament of his body and blood we receive his very flesh and blood ; this your saying
is no small derogation to baptism, wherein we receive not only the spirit of Christ,
but also Christ himself, whole body and soul, manhood and Godhead, unto everlasting
life, as well as in the holy communion. For St Paul saith, Quicunque in Christo oai. iii.
txrj>l!;<tfi estis, Christum induistis : "As many as be baptized in Christ, put Christ
upon them :" nevertheless, this is done in divers respects ; for in baptism it is done in
respect of regeneration, and in the holy communion in respect of nourishment and
augmentation.
But your understanding of the sixth chapter of John is such as never was uttered in tiic sixth
of any man before your time, and as declareth you to be utterly ignorant of God s John, Christ
mysteries. For who ever said or taught before this time, that the sacrament was the corporal cat-
cause why Christ said, "If we eat not the flesh of the Son of man, we have not lifejoiinvi
in us?" The spiritual eating of his flesh, and drinking of his blood by faith, by digesting
his death in our minds, as our only price, ransom, and redemption from eternal dam
nation, is the cause wherefore Christ said : " That if we eat not his flesh, and drink
not his blood, we have not life in us ; and if we eat his flesh, and drink his blood,
we have everlasting life." And if Christ had never ordained the sacrament, yet should
we have eaten his flesh, and drunken his blood, and have had thereby everlasting
life; as all the faithful did before the sacrament was ordained, and do daily when they
receive not the sacrament. And so did the holy men that wandered in the wilderness,
and in all their life-time very seldom received the sacrament; and many holy martyrs,
either exiled, or kept in prison, did daily feed of the food of Christ s body, and drank
daily the blood that sprang out of his side, or else they could not have had everlasting
life, as Christ himself said in the gospel of St John, and yet they were not suffered
with other Christian people to have the use of the sacrament. And therefore your
argument in this place is but a fallax a non causa, ut causa, which is another trick of
the devil s sophistry.
And that in the sixth of John Christ spake neither of corporal nor sacramental
eating of his flesh, the time manifestly sheweth. For Christ spake of the same present
time that was then, saying: "The bread which I will give is my flesh," and, "He John vi.
that eateth my flesh, and drinketh my blood, dwelleth in me, and I in him, and hath
everlasting life :" at which time the sacramental bread was not yet Christ s flesh. For
the sacrament was not then yet ordained ; and yet at that time all that believed in
Christ, did eat his flesh, and drink his blood, or else they could not have dwelled in
Christ, nor Christ in them.
Moreover, you say yourself, that in the sixth of St John s gospel, when Christ John vi.
slid, "The bread is my flesh," by the word "flesh" he meant his whole humanity,
(as is meant in this sentence, " The word was made flesh,") which he meant not in John i.
the word "body," when he said of bread, "This is my body;" whereby lie meant not - 1 *
his whole humanity, but his flesh only, and neither his blood nor his soul. And in
the sixth of John Christ made not bread his flesh, when he said, " The bread is my
ilesh -." but he expounded, in those words, what bread it was that he meant of, when
26 THE FIRST BOOK
he promised them bread that should give them eternal life. He declared in those
words, that himself was the bread that should give life, because they should not have
could not be understanded of the sacrament, nor of corporal eating with the mouth ;
but of spiritual eating by faith, as all the old authors do most clearly expound and
declare. And seeing that there is no corporal eating, but chewing with the teeth
or swallowing (as all men do know), if we eat Christ corporally, then you must
confess that we either swallow up Christ s flesh, or chew and tear it with our teeth,
(as pope Nicholas constrained Bcrengarius to confess,) which St Augustine saith is a
wicked and heinous thing. But in few words to answer to this second evident and
manifest untruth (as you object against me), I would wish you as truly to understand
these words of the sixth chapter of John, as I have truly translated them.
WINCHESTER.
Now, where the author, to exclude the mystery of corporal manducation, bringeth forth of
St Augustine such words as entreat of the effect and operation of the worthy receiving of
the sacrament; the handling is not so sincere as this matter requireth. For, as hereafter
shall be entreated, that is not worthily and well done, may (because the principal intent
faileth) be called not done, and so St Augustine saith : " Let him not think to eat the body
of Christ, that dwelleth not in Christ;" not because the body of Christ is not received, which
by St Augustine s mind evil men do to their condemnation, but because the effect of life
faileth. And so the author by sleight, to exclude the corporal manducation of Christ s most
precious body, uttereth such words, as might sound Christ to have taught the dwelling in
Christ to be an eating : which dwelling may be without this corporal manducation in him
that cannot attain tlie use of it, and dwelling in Christ is an effect of the worthy mandu
cation, and not the manducation itself, which Christ doth order to be practised in the most
precious sacrament institute in his supper. Here thou, reader, mayest see how this doctrine
of Christ (as I have declared it) openeth the corporal manducation of his most holy flesh,
and drinking of his most precious blood, which he gave in his supper under the form of
CANTERBURY.
The third un- This is the third evident and manifest untruth, whereof you note me. And be-
handiingthe cause you say that in citing of St Augustine in this place, I handle not the matter
Augustine. so sincerely as it requireth, let here be an issue between you and me, which of us
both doth handle this matter more sincerely; and I will bring such manifest evidence
for me, that you shall not be able to open your mouth against it. For I allege St
Augustine justly as he speaketh, adding nothing of myself. The words in my book
be these.
tat. xxvi!
"Of these words of Christ it is plain and manifest, that the eating of Christ s
body 1 , and drinking of his blood, is not like the eating and drinking of other
meats and drinks. For although without meat and drink man cannot live,
yet it followeth not that he that eateth and drinketh shall live for ever. But
as touching this meat and drink of the body and blood of Christ it is true,
22. both he that eateth and drinketh them hath everlasting life ; and also he
K ei de T ci- ct *^ at catct h an( * drinketh them not, hath not everlasting life. For to eat that
ci^S 2K meat an( l drink that drink, is to dwell in Christ, and to have Christ dwelling
in him; and therefore no man can say or think that he eateth the body of
Christ or drinketh his blood, except he dwelleth in Christ, and have Christ
dwelling in him. Thus have you heard of the eating and drinking of the
very flesh and blood of our Saviour Christ."
Thus allege I St Augustine truly, without adding any thing of mine own head, or
taking any thing away. And what sleight I used is easy to judge : for I cite di-
[ Flesh, 1551.]
OF THE SACRAMENT. 27
rectly the places, that every man may see whether I say true or no. And if it be
not true, quarrel not with me, but with St Augustine, whose words I only rehearse.
And that which St Augustine saith, spake before him St Cyprian, and Christ him
self also plainly enough ; upon whose words I thought I might be as bold to build
a true doctrine for the setting forth of (iod s glory, as you may be to pervert both
the words of Cyprian, and of Christ himself, to stablish a false- doctrine to the high
dishonour of God, and the corruption of his most true word. For you add this
word " worthily," whereby you gather such an unworthy meaning of St Augustine s Worthily,
words as you list yourself. And the same you do to the very words of Christ him
self, who speaketh absolutely and plainly, without adding of any such word as you
put thereto. What sophistry this is, you know well enough. Now if this be per
mitted unto you, to add what you list, and to expound how you list, then you
may say what you list without controlment of any man, which it seemeth you
look for.
And not of like sort, but of like evilness do you handle (in reprehending of my
second untruth, as you call it) another place of St Augustine in his book de doctrina August, de
C/trintMna, where he saith, that the eating and drinking of Christ s flesh and blood Christiana,
is a figurative .speech : which place you expound so far from St Augustine s mean- i;? "
ing, that whosoever looketh upon his words, may by and by discern that you do IK u ca2n.
not, or will not, understand him. But it is most like (the words of him being so
plain and easy) that purposely you will not understand him, nor nothing else that
is against your will, rather than you will go from any part of your will and re
ceived opinion. For it is plain and clear that St Augustine in that place speaketh
not one word of the separation of the two natures in Christ ; and although Christ s
flesh be never so surely and inseparably united unto his Godhead (without which
union it could profit nothing), yet being so joined, it is a very man s flesh, the
eating whereof (after the proper speech of eating) is horrible and abominable.
Wherefore the eating of Christ s flesh must needs be otherwise understanded, than
after the proper and common eating of other meats with the mouth, which eating
after such sort could avail nothing. And therefore St Augustine in that place de-
clareth the eating of Christ s flesh to be only a figurative speech. And he openeth
the figure so as the eating must be meant with the mind, not with the mouth, that
is to say, by chewing and digesting in our minds, to our great consolation and profit,
that Christ 2 died for us. Thus doth St Augustine open the figure and meaning of
Christ, when he spake of the eating of his flesh and drinking of his blood. And his
flesh being thus eaten, it must also be joined unto his divinity, or else it could not
give everlasting life, as Cyril and the council Ephesinc truly decreed. But St Au- 23.
gustine declared the figurative speech of Christ to be in the eating, not in the union.
And whereas, to shift off the plain words of Christ, spoken in the sixth of John,
" He that eateth my flesh, and drinketh my blood, dwelleth in me, and I in him," John \-i.
yon say that dwelling in Christ is not the manducation; you say herein directly
against St Cyprian, who saith, Quod mansio nostra in ipso sit manducatio, " That our Cyprian, in
dwelling in him is the eating :" and also against St Augustine, whose words be these : ranaDo-
Hoc est ergo mandttcare cscam illam^ et ilium lilere potum, in Christo manere, et Aug! injnn.
ill inn, nmnentem in se halere : " This is to eat that meat, and drink that drink, to lr
dwell in Christ, and to have Christ dwelling in him." And although the eating and
drinking of Christ be here defined by the effect, (for the very eating is the believing,)
yet wheresoever the eating is, the effect must be also, if the definition of St Augus
tine be truly given. And therefore, although good and bad eat carnally with their
teeth bread, being the sacrament of Christ s body ; yet no man eateth his very flesh,
which is spiritually eaten, but he that dwelleth in Christ, and Christ in him.
And where in the end you refer the reader to the declaration of Christ s words,
it is an evil sequel : you declare Christ s words thus, ergo, they be so meant. For
by like reason might Nestorius have prevailed against Cyril, Arius against Alex
ander, and the Pope against Christ. For they all prove their errors by the doctrine
[ ; M as crucified and died, lool.J
28 THE FIRST BOOK
of Christ after their own declarations, as you do here in your corporal manducation.
But of the manducation of Christ s flesh, I have spoken more fully in my fourth
book, the second, third, and fourth chapters.
Now before I answer to the fourth untruth which I am appeached of, I will
rehearse what I have said in the matter, and what fault you have found. My book
hath thus.
[Book i.] " Now as touching the sacraments of the same, our Saviour Christ did in
stitute them in bread and wine at his last supper which he had with his apostles,
The eating of tne night before his death, at which time, as Matthew saith, When they were
of e h^ C body nt eating, Jesus took bread, and when he had given thanks, he brake it, and gave
it to his disciples, and said, Take, eat : this is my body. And he took the
cup, and when he had given thanks he gave it to them, saying, Drink ye all
of this, for this is my blood of the new testament, that is shed for many for
the remission of sins. But I say unto you, I will not drink henceforth of
this fruit of the vine, until that day when I shall drink it new with you in
my Father s kingdom. :
This thing is rehearsed also of St Mark in these words.
M.irk xi\. " As they did eat, Jesus took bread, and when he had blessed, he brake it,
and gave it to them, and said, Take, eat : this is my body. And taking the cup,
Avhen he had given thanks, he gave it to them, and they all drank of it, and
he said to them, This is my blood of the new testament, which is shed for
many. Verily I say unto you, I will drink no more of the fruit of the vine,
until that day that I drink it new in the kingdom of God."
The evangelist St Luke uttereth this matter on this wise.
Lukcxxii. When the hour was come, he sat down, and the twelve apostles with him.
And he said unto them, I have greatly desired to eat this Pascha with you
before I suffer : for I say unto you, henceforth I will not eat of it any more,
- J - until it be fulfilled in the kingdom of God. And he took the cup, and gave
thanks, and said, Take this, and divide it among you : for I say unto you,
I will not drink of the fruit of the vine, until the kingdom of God come. And
he took bread, and when he had given thanks, he brake it, and gave it unto
them, saying, This is my body, which is given for you : this do in remem
brance of me. Likewise also when he had supped, he took the cup, saying, This
cup is the new testament in my blood, which is shed for you."
Hitherto you have heard all that the evangelists declare, that Christ spake
or did at his last supper, concerning the institution of the communion and
sacrament of his body and blood. Now you shall hear what St Paul saith
concerning the same, in the tenth chapter of the first to the Corinthians, where
he writeth thus :
i cor. x. j s not t h c CU p O f blessing, which we bless, a communion of the blood
of Christ ? Is not the bread, which we break, a communion of the body of
Christ ? We being many, are one bread, and one body : for we all are par
takers of one bread, and one cup."
And in, the eleventh he speaketh on this manner.
\ cor. M. " That which I delivered unto you I received of the Lord. For the Lord
Jesus the same night in the which he was betrayed took bread, and when
he had given thanks, he brake it, and said, Take, eat ; this is my body, which
is broken for you : do this in remembrance of me. Likewise also he took the
OF THE SACRAMENT. 29
cup, when supper was done, saying, This cup is the new testament in my
blood. Do this, as often as ye drink it, in remembrance of me : for as oft as
you shall eat this bread, and drink this cup, you shew forth the Lord s death
till he come. Wherefore whosoever shall cat of this bread, or drink of this
cup unworthily, shall be guilty of the body and blood of the Lord. But let
a man examine himself, and so eat of the bread, and drink of the cup. For
he that eateth and drinkcth unworthily, eateth and drinketh his own damnation,
because he makcth no difference of the Lord s body. For this cause many
arc weak and sick among you, and many do sleep."
By these words of Christ rehearsed of the evangelists, and by the doctrine
also of St Paul, which he confesseth that he received of Christ, two things
specially are to be noted.
First, that our Saviour Christ called the material bread which he brake, ch 2p .
his body; and the wine, which was the fruit of the vine, his blood. And yet
he spake not this to the intent that men should think that the material bread
is his very body, or that his very body is material bread ; neither that wine
made of grapes is his very blood, or that his very blood is wine made of grapes :
but to signify unto us, as St Paul saith, that the cup is a communion oficor. x.
Christ s blood that was shed for us, and the bread is a communion of his flesh
that was crucified for us. So that although in the truth of his human nature, Markuit.
Christ bo in heaven, and sitteth on the right hand of God the Father, yet
whosoever eateth of the bread in the supper of the Lord, according to Christ s
institution and ordinance, is assured of Christ s own promise and testament,
that he is a member of his body, and recciveth the benefits of his passion which
he suffered for us upon the cross. And likewise he that drinketh of that holy
cup in the supper of the Lord, according to Christ s institution, is certified by
Christ s legacy and testament, that he is made partaker of the blood of Christ
which was shed for us. And this meant St Paul, when he saith, " Is not the 25.
cup of blessing which we bless a communion of the blood of Christ? Is not
the bread which we break a communion of the body of Christ?" so that no
man can contemn or lightly esteem this holy communion, except he contemn
also Christ s body and blood, and pass not whether he have any fellowship
with him or no. And of those men St Paul saith, " that they eat and drink i cor. xi.
their own damnation, because they esteem not the body of Christ."
The second thing which may be learned of the foresaid words of Christ chap. v.
and St Paul is this : that although none eateth the body of Christ and drinketh
his blood, but they have eternal life, (as appeareth by the words before recited
of St John,) yet both the good and the bad do eat and drink the bread and
wine, which be the sacraments of the same. But beside the sacraments, the EVJI men do
good eat 1 everlasting life, the evil everlasting death. Therefore St Paul saith : ment,b5S
" Whosoever shall eat of the bread, or drink of the cup of the Lord unworthily, Christ -
he shall be guilty of the body and blood of the Lord." Here St Paul saith i cor. i.
hot, that he that eateth the bread, or drinketh the cup of the tLord unworthily,
eateth and drinketh the body and blood of the Lord; but, is guilty of the body
and blood of the Lord. But what he eateth and drinketh St Paul declareth,
saying : " He that eateth and drinketh unworthily, eateth and drinketh his
own damnation." Thus is declared the sum of all that scripture speaketh of
the eating and drinking both of the body and blood of Christ, and also of
the sacrament of the same.
And as these things be most certainly true, because they be spoken by Chap . .
[> Eateth, l;Vil.j
30
THE FIRST BOOK
These things
suffice for a
Christian
man s faith
concerning
this sacra
ment.
Chap. vn.
The sacra
ment which
was ordained
to make love
and concord
is turned into
the occasion
of variance
and discord.
Christ himself, the author of all truth, and by his holy apostle St Paul, as he
received them of Christ; so all doctrines contrary to the same be most certainly
false and untrue, and of all Christian men to be eschewed, because they be con
trary to God s word. And all doctrine concerning this matter, that is more
than this, which is not grounded upon God s word, is of no necessity, neither
ought the people s heads to be busied, or their consciences troubled with the
same. So that things spoken and done by Christ, and written by the holy
evangelists and St Paul, ought to suffice the faith of Christian people, as touch
ing the doctrine of the Lord s supper, and holy communion or sacrament of
his body and blood.
Which thing being well considered and weighed, shall be a just occasion to
pacify and agree both parties, as well them that hitherto have contemned or
lightly esteemed it, as also them which have hitherto for lack of knowledge
or otherwise ungodly abused it.
Christ ordained the sacrament to move and stir all men to friendship, love,
and concord, and to put away all hatred, variance, and discord, and to testify a
brotherly and unfeigned love between all them that be the members of Christ : but
the devil, the enemy of Christ and of all his members, hath so craftily juggled
herein, that of nothing riseth so much contention as of this holy sacrament.
God grant that, all contention set aside, both the parties may come to this
holy communion with such a lively faith in Christ, and such an unfeigned love
to all Christ s members, that as they carnally eat with their mouths this sacra
mental bread, and drink the wine, so spiritually they may eat and drink the
very flesh and blood of Christ which is in heaven, and sitteth on the right
hand of his Father ; and that finally by his means they may enjoy with
him the glory and kingdom of heaven ! Amen.
WINCHESTER.
26. Now let us consider the texts of the evangelists, and St Paul, which be brought in by the
author as followeth.
Matt. xxvi. " When they were eating, Jesus took bread, and when he had given thanks, he brake it,
giving it to his disciples, and said, Take, eat; this is my body. And he took the cup, and
when he had given thanks, he gave it to them, saying, Drink ye all of this ; for this is my
blood of the new testament, that is shed for many for tJie remission of sins. But I say unto
you, I will not drink henceforth of this fruit of the vine, until that day when I shall drink
it new with you in my Father s kingdom."
" As they did eat, Jesus took bread, and when he had blessed, fie brake it, and gave it to
them,, and said, Take, eat; this is my body. And taking the cup, when he had given thanks,
he gave it to them : and they all drank of it. And he said unto them, This is my blood of
the new testament, which is shed for many. Verily I say unto you, I will drink no more
of the fruit of the vine, until that day that I drink it new in the kingdom of God."
" When the hour was come, he sat down, and the twelve apostles with him; and he said
unto them, I have greatly desired to eat this Pascha with you, before I suffer : for I say unto
you, henceforth I will not eat of it any more, until it be fulfilled in the kingdom of God.
And he took the cup, and gave thanks, and said, Take this, and divide it among you : for I
say unto you, I will not drink of the fruit of the vine, until the kingdom of God come.
And he took bread, and xvhen he had given thanks, lie brake it, and gave it unto them, say
ing, This is my body which is given for you : this do in remembrance of m.e. Likewise also
when he had supped, lie took the cup, saying, This cup is the new testament in my blood,
which is shed for you."
i Cor. x. " Is not the cup of blessing which we bless a communion of tlie blood of Christ ? Is not
the bread which we break a communion of the body of Christ? We, being many, are one
bread, and one body ; for we are all partakers of one bread, and of one cup."
i Cor. xi. " That which I delivered unto you, I received of the Lord. For tJie Lord Jesus, the same
night in the ivhich he was betrayed, took bread, and when he had given thanks, he brake it, and
Mark xiv.
Luke xxii.
OF THE SACRAMENT.
:u
27-
said) Take, eat ; this is my body, which is broken for yon : do this in remembrance of me.
Likewise also he took the cup when supper vjas done, saying, This cup is the new testament
in my blood : do this, as often as ye drink it, in remembrance of me. For as often as you
shall eat this bread, and drink this cup, ye sJiew forth the Lord s death till Jte come. Where
fore whosoever shall eat of this bread, or drink of this cup unworthily, xhall be guilty of the
body and blood of tlie Lord. But let a man examine himself, and so eat of the bread, <in>f
ill-ink of the cup. For he that eateth and drinketh unworthily, eateth and drinketh his own
damnation, because he maketh no difference of the Lord s body. For this cause many are
weak and sick among you, and many do sleep."
After these texts brought in, the author doth in the fourth chapter begin to traverse Christ s The fourth
intent, that he intended not by these words, " Thin /* my body," to make the bread his body, by these
but to signify that such as receive that worthily be members of Christ s body. The catholic "v /^- y,,,*
church, acknowledging Christ to be very God and very man, hath from the beginning of these
texts of scripture confessed truly Christ s intent, and effectual miraculous work to make the
bread his body, and the wine his blood, to be verily meat and verify drink, using therein A/ .s bo<1 y-
humanity wJierewith to feed us, as he used the same wJierewith to redeem us; and as he doth
sanctify us by his holy Spirit, so to sanctify us by his holy divine flesh and blood ; and as
life is renewed in us by the gift of Christ s holy Spirit, so life to be increased in us by the
gift of his holy flesh. So he that believeth in Christ, and receiveth the sacrament of belief,
U hich is baptism, receiveth really Christ s Spirit: and likewise 1 he tliat, having Christ s Spirit,
receiveth also the sacrament of Christ s body and blood, doth really receive in the same, and also
effectually, Christ s very body and blood. And therefore Christ in the institution of this sacra
ment said, delivering that he consecrated : " This is my body," %c. And likewise of the cup :
" This is my blood," %c. And although to man s reason it seemeth strange that Christ, stand
ing or sitting at the table, sliould deliver tJiem his body to be eaten: yet when we remember
Christ to be very God, we must grant him omnipotent, and by reason thereof, repress in our
thoughts all imaginations how it might be, and consider Christ s intent by his will, preached
unto us by scriptures, and believed universally in his church. But if it may now be thought
seemly for us to be so bold, in so high a mystery, to begin to discuss Christ s intent: what
should move us to think that Christ would use so many words, without c/ectual and real
signification, as he rehearsed touching the mystery of this sacrament ?
First, in the slvth of John, when Christ had taught of the eating of him 2 , being the bread
descended from heaven, and declaring that eating to signify believing, whereat was no mur
muring, that then he should enter to speak of giving of his flesh to be eaten, and his blood to
be drunken, and to say that 3 he would give a bread, that is, his flesh, which he would give for
the life of the world. In which words Christ maketh mention of two gifts,- and therefore
as he is truth, must needs intend to fulfil them both. And therefore* as we believe the gift of
his flesh to the Jews to be crucified ; so we must believe the gift of his flesh to be eaten, and
of that gift, livery 5 and seisme 6 , as we say, to be made of him, that is in his promises faith
ful (as Christ is) to be made in both. And tlierefore when he said in his supper, " Take,
eat, this is my body," he must needs intend plainly as his ivords of promise required. And
tliese words in his supper purport to give as really then his body to be eaten of us, as he gave
hi* body indeed to be crucified for us; aptly nevertheless, and conveniently for each effect, and
therefore in manner of giving diversely, but in the substance of the same^ given, to be as his
words bear witness, the same, and tlierefore said, " This is my body that shall be betrayed
for you ;" expressing also the use, when he said, " Take, eat :" u hich words, in delivering of
material bread, had been superfluous ; for ivhat should men do with bread when they take it,
but cat it, specially wlien it is broken ?
But as Cyril saith : " Christ opened there unto them the practice of that doctrine he spake
of in the sixth of St John, and because he said he would give his flesh for food, which he
irmild give for the life of the world, he for fulfilling of his promise said: " Take, eat, this is
my body," u hich words have been taught and believed to be of effect, and operatory, and
Christ under the form of bread to have been 8 his very body. According whereunto St Paul
notrth the receiver to be guilty, when he doth not esteem it our Lord s body, wherewith it
pleascth Christ to feed such as be in him, regenerate, to the intent that as man was redeemed
[ "So he;" original ed. of Winchester s book.]
[ 2 Himself, 1551.J
[ a To say he would give, 1M1.]
[ 4 \VhcTeforc. lfM.]"
[ 5 Livery : i.e. the act of giving.]
[ 6 Seisme: i.e. seizin, the act of taking.]
f " The same body given, 1A51.J
[* Given, 1W1.]
32 THE FIRST BOOK
by Christ, suffering in the nature of his humanity, so to purchase for man the kingdom of
heaven, lost by Adam s fall. Even likewise in the nature of the same humanity, giving it to
be eaten, he ordained it 1 to nourish man, and make him strong to walk, and continue his
journey, to enjoy that kingdom. And therefore to set forth lively unto its the communication
of the substance of Christ s most precious body in the sacrament, and the same to be indeed
delivered, Christ used plain words, testified by the evangelists. St Paul also reJiearsed the
same words in tlie same plain terms in the eleventh to tJie Corinthians; and in the tenth,
giving (as it were) an exposition of the effect, useth the same proper words, declaring the effect
to be the communication of Christ s body and blood. And one thing is notable touching the
scripture, that in such notable speeches uttered by Christ, as might have an ambiguity, the
evangelists by some circumstance declared it, or sometime opened it by plain interpretation :
as when Christ said "he would dissolve the temple, and within three days build it again; *
tlie evangelist by and by addeth for interpretation : " This he said of the temple of his
body." And wJien Christ said, "He is Ellas" and "I am the true vine," the circumstance
of the text openeth tJie ambiguity.
* Neither st But to sliew that Christ should not mean of his very body when he so spake 2 , neither St
Paul nor the
Kvan geiists, Paul after, nor the evangelists in the place, add any words or circumstances, wliereby to take
words where- away the proper signification of the words " body" and " blood," so as the same might seem
away the sig- not in deed given (as the catholic faith teacheth), but in signification, as the author would have
bread and it. For, as for the words of Christ, "The Spirit giveth life, tlie flesh profiteth nothing," be
to declare the two natures in Christ, each in their property apart considered, but not as they
be in Christ s person united the mystery of which union such as believed not Christ to be
God could not consider, and yet to insinuate that unto tlie/m, Christ made mention of his
descension from heaven, and after of his ascension thither again, whereby they might under
stand him very God, whose flesh taken in the virgin s womb, and so given spiritually to be
eaten of tis, is (as I have before opened) vivifick, and giveth life.
And this shall suffice here to shew how Christ s intent was to give verily (as he did in
deed) his precious body and blood to be eaten and drunken, according as he taught them to
be verily meat and drink; and yet gave and giveth them so under form of visible creatures
to us, as we may conveniently and without horror of our nature receive them, Christ therein
condescending to our infirmity. As for such other wrangling as is made in understanding z
of tlie words of Christ, sliall after be spoken of by further occasion.
CANTERBURY.
*n T nfth u ? h N w we be come to the very pith of the matter, and the chief point whereupon
chrisHn- the whole controversy hangeth, whether in these words, " This is my body," Christ called
these words, bread his body : wherein you and Smith agree like a man and woman that dwelled in
" This is iny .
body," to Lincolnshire, as I have heard reported, that what pleased the one misliked the other,
bread his saving that they both agreed in wilfulness. So do Smith and you agree both in
The variance this point, that Christ made bread his body, but that it was bread which he called
and smith, his body, when he said, "This is my body," this you grant, but Smith denieth it.
smuh st ^ n( ^ t> ecause all Smith s buildings clearly fall down, if this his chief foundation be
overthrown, therefore must I first prove against Smith, that Christ called the material
bread his body, and the wine which was the fruit of the vine his blood. "For why
Christ called did you not prove this, my Lord?" saith Smith: "would you that men should take
body. you for a prophet, or for one that could not err in his sayings?"
First I allege against Smith s negation your affirmation, which, as it is more true
in this point than his negation, so for your estimation it is able 4 to countervail his
saying, if there were nothing else: and yet, if Smith had well pondered what I have
written in the second chapter of my second book, and in the seventh and eighth
chapters of my third book, he should have found this matter so fully proved, that
he neither is, nor never shall be able to answer thereto. For I have alleged the
scripture, I have alleged the consent of the old writers, holy fathers, and martyrs,
to prove that Christ called bread his body, and wine his blood. For the evangelists,
Matt. xxvi. speaking of the Lord s supper, say, that "he took bread, blessed it, brake it, and gave
Lukexxii. it to his disciples, saying, This is my body. And of the wine he said, Take this,
f 1 To be eaten, ordained to nourish, 1551.] [ 3 In the understanding, 1551.]
[" lie so spake these words in his supper, 1551.] [ 4 Is it able, 1551.]
OF THE SACRAMENT. 33
divide it among you, and drink it: this is my blood." I have alleged Irene 5 , saying ireneus.
that "Christ confessed bread to be his body, and the cup to bo his blood." I have
cited Tertullian, who saith in many places that " Christ called bread his body." I Tertuiuanus.
have brought in for the same purpose Cyprian, who saith that " Christ called such cyprianus.
bread as is made of many corns joined together, his body : and such wine he named
his blood, as is pressed out of many grapes." I have written the words of Epipha-
nius, which be these, that " Christ speaking of a loaf which is round in fashion, and
can neither see, hear, nor feel, said of it, This is my body. " And St Jerome, writing
ad Hedibiam, saith that "Christ called the bread which he brake his body." And
St Augustine saith, that " Jesus called meat his body, and drink his blood." And Augustinus.
Cyril saith more plainly, that " Christ called the pieces of bread his body." And c y rlllus
last of all I brought forth Theodorete, whose saying is this, that " when Christ gave Theodoretiw
the holy mysteries, he called bread his body, and the cup mixed with wine and
water he called his blood." All these authors I alleged, to prove that Christ called
bread his body, and wine his blood.
Which because they speak the thing so plainly as nothing can be more, and
Smith secth that he can devise nothing to answer these authors, like a wily fox, he
stealeth away by them softly, as he had a flea in his ear, saying nothing to all
these authors, but that they prove not my purpose. If this be a sufficient answer,
let the reader be judge; for in such sort I could 6 make a short answer to Smith s
whole book in this one sentence, that nothing that he saith proveth his puq^ose.
And as for proofs of his saying, Smith hath utterly none but only this fond reason:
us, because Christ added these words : " This is my body, which shall be given to
death for you." If such wise reason shall take place, a man may not take a loaf
in his hand made of wheat that came out of Dantzic, and say this is wheat that
grew in Dantzic, but it must follow, that the loaf grew in Dantzic. And if the
wife shall say, This is butter of my own cow, Smith shall prove by this speech
that her maid milked butter. But to this fantastical or rather frantic reason, I have
spoken more in mine answer to Smith s preface.
Howbeit, you have taken a wiser way than this, granting that Christ called
bread his body, and wine his blood: but adding thereto, that Christ s calling was
making. Yet here may they that be wise learn by the way, how evil-favouredly
you and Smith agree 7 among yourselves.
And forasmuch as Smith hath not made answer unto the authors by me alleged
in this part, I may justly require that for lack of answer in time and place where
he ought to have answered, he may be condemned as one that standeth mute. And
being condemned in this his chief demur, he hath after nothing to answer at all:
for this foundation being overthrown, all the rest falleth down withal.
the evident and manifest untruths, whereof you appeach me.
I perceive here how untoward you be to learn the truth, being brought up all
chief profession and study from your youth, and specially the canon law which
purposely corrupteth the truth of God s word, you should be much more apt to
understand and receive the secrets of holy scripture. But before those scales full
from your Saulish eyes, you neither can nor w r ill perceive the true doctrine of this
holy sacrament of Christ s body and blood. But yet I shall do as much as lieth
in me, to teach and instruct you, as occasion shall serve; so that the fault shall be
either in your evil bringing up altogether in popery, or in your dulness, or froward-
ness, if you attain not true 8 understanding of this matter.
[ 5 These references are given and verified in the
reprint of the " Defence of the Sacrament," which
is inserted in the body of this book (Book HI.
cap. 8.), and will be found in the "Confutation of
the second book against transubstantiation."]
[ 6 could 1, 1551.]
[ 7 do agree, 1551.]
[ 8 the true understanding, 1.151.J
[CRANMER. 1
34
THE FIRST BOOK
in the sacra
ment.
30.
Injury to
baptism.
Mine issue.
God s omni
potency.
Matt, xx vi.
Gen. i.
Where you speak of the miraculous working of Christ, to make bread his body,
y u mus t nrs t l earn that the bread is not made really Christ s body, nor the wine
his blood, but sacramentally. And the miraculous working is not in the bread, but
in them that duly eat the bread, and drink that drink. For the marvellous work
of God is in the feeding; and it is Christian people that be fed, and not the
And so the true confession and belief of the universal church, from the beginning,
is not such as you many times affirmed, but never can prove: for the catholic
church acknowledged no such division between Christ s holy flesh and his Spirit, that
life is renewed in us by his holy Spirit, and increased by his holy flesh ; but the true
faith confesseth that both be done by his holy Spirit and flesh jointly together, as
well the renovation, as the increase of our life. Wherefore you diminish here the
effect of baptism, wherein is not given only Christ s Spirit, but whole Christ. And
herein I will join an issue with you. And you shall find, that although you think
I lack law wherewith to follow my plea, yet I doubt not but I shall have help of
God s word enough, to make all men perceive that you be but a simple divine, so
that for lack of your proofs, I doubt not but the sentence shall be given upon my
side by all learned and indifferent judges, that understand the matter which is in
controversy between us.
And where you say that we must repress our thoughts and imaginations, and
by reason of Christ s omnipotency judge his intent by his will, it is a most certain
truth that God s absolute and determinate will is the chief governor of all things,
and the rule whereby all things must be ordered, and thereto obey. But where (I
pray you) have you any such will of Christ, that he is really, carnally, corporally, and
naturally, under the forms of bread and wine? There is no such will of Christ set
forth in the scripture, as you pretend by a false understanding of these words, "This
is my body." Why take you then so boldly upon you to say, that this is Christ s
will and intent, when you have no warrant in scripture to bear you ?
It is not a sufficient proof in scripture, to say, God doth it, because he can do
it. For he can do many things which he neither doth, nor will do. He could
have sent more than twelve legions of angels to deliver Christ from the wicked
Jews, and yet he would not do it. He could have created the world and all
things therein in one moment of time, and yet his pleasure was to do it in six days.
In all matters of our Christian faith, written in holy scripture, for our instruction
and doctrine, how far soever they seem discrepant from reason, we must repress our
imaginations, and consider God s pleasure and will, and yield thereto, believing him to
be omnipotent; and that by his omnipotent power, such things are verily so as holy
scripture teacheth. Like as we believe that Christ was born of the blessed virgin
Mary, without company of man: that our Saviour Christ the third day rose again
from death : that he in his humanity ascended into heaven : that our bodies at the
day of judgment shall rise again; and many other such like things, which we all that
be true Christian men, do believe firmly, because we find these things written in scrip
ture. And therefore we (knowing God s omnipotency) do believe that he hath brought
some of the said things to pass already, and those things that are yet to come, he
will by the same omnipotency without doubt likewise bring to pass.
Now if you can prove that your transubstantiation, your fleshly presence of Christ s
body and blood, your carnal eating and drinking of the same, your propitiatory
sacrifice of the mass, are taught us as plainly in the scripture, as the said articles
of our faith be, then I will believe that it is so in deed. Otherwise, neither I nor
any man that is in his right wits, will believe your said articles, because God is
omnipotent, and can make it so. For you might so, under pretence of God s omni
potency, make as many articles of our faith as you list, if such arguments might take
place, that God by his omnipotent power can convert the substance of bread and
wine into the substance of his flesh and blood : ergo he doth so indeed.
And although Christ be not corporally in the bread and wine, yet Christ used not
so many words, in the mystery of his holy supper, without effectual signification. For
he is effectually present, and effectually worketh not in the bread and wine, but in the
OF THE SACRAMENT. 35
godly receivers of them, to whom he giveth his own flesh spiritually to feed upon, and
his own blood to quench their great inward thirst.
And here I would wish you to mark very well one true sentence which you have Eating sjg.ij-
uttered by the way, which is, that Christ declared that eating of him signified believing, ing.
and start not from it another time. And mark the same, I pray thee, gentle reader.
For this one sentence assoileth almost all the arguments that ! brought by this lawyer,
in his whole book against the truth.
And yet to the said true saying you have joined another untruth, and have yoked them Three un-
i -n i 1 11 i i a i t truths uttered
both together in one sentence. bor when Christ had taught of the eating of him, being by you in
the bread descended from heaven, there was no murmuring thereat, say you. Which place.
your saying I cannot but wonder at, to see you so far deceived in a matter so plain
and manifest. And if I had spoken such an evident and manifest untruth, I doubt The first,
not but it should have been spoken of to Rome gates. For the text saith there plainly,
Mitrniuralxint Judwi de illo, quod dixisset, Ego sum panis vivus, qui de ccelo descendi: John \i.
"The Jews murmured at him because he said, I am the bread of life that came from
heaven. " But when you wrote this, it seemeth you looked a little too low, and should
have looked higher.
and meaning in this your book, if that be true which you said before, that ever where
contention is, on what part the reader seeth in any one point an open manifest lie, there
he may consider (whatsoever excuse be made of truth) yet the victory of truth not to
be there intended.
Another untruth also folio wcth incontinently, that when Christ said, "The bread The second,
which I will give you is my flesh, which I will give for the life of the world ; " in
these words, say you, Christ maketh mention of two gifts. But what be those two gifts,
I pray you ? and by what words is the diversity of those two gifts expressed ? If
the giving, as Smith saith, be giving to death, then those two gifts declare that Christ
died for us twice. And if one of Christ s gifts have livery and seisin, why hath not the
other likewise ? And when was then that livery and seisin given ? And if eating of
Christ be believing, as you said even now, then livery and seisin is given when we first
believe, whether it be in baptism, or at any other time.
But what you mean by these words, that Christ gave in his supper his body as
really to be eaten of us, as he did to be crucified for us, I understand not, except you
would have Christ so really eaten of his apostles at his supper with their teeth, as he
was after crucified, whipped, and thrust to the heart with a spear. But was he not
then so really and corporally crucified, that his body was rent and torn in pieces? And
was not he so crucified then, that he never was crucified after? Was he not so slain
then, that he never died any more 8 ? And if he were so eaten at his supper, then did 32.
his apostles tear his flesh at the supper, as the Jews did the day following ? And then
how could he now be eaten again ? or how could he be crucified the day following, if
the night before he were after that sort eaten all up ? But " aptly," say you, " and con
veniently." Marry, Sir, I thank you ; but what is that " aptly and conveniently," but
spiritually and by faith, as you said before, not grossly with the teeth, as he was crucified?
And so the manner was diverse, I grant, and the substance all one.
But when Christ said, " The bread which I will give is my flesh, which I will give The third,
for the life of the world," if he had fulfilled this promise at his supper, as you say he fulfilled not
did, then what needed he after to die that we might live, if he fulfilled his promise of tdVm "Tife
life at his supper ? Why said the prophets, that he should be wounded for our iniquities,
and that by his wounds we should be healed, if we had life, and were healed before he
was wounded ? Why doth the catholic faith teach us to believe that we be redeemed John vi.
by his blood-shedding, if he gave us life (which is our redemption) the night before he
shed his blood ? And why saith St Paul that there is no remission without blood-
shedding? Yea, why did he say 3 , Alsit mild gloriari, nisi in cruce? "God forbid
[ The edition of 1551 omits this paragraph
by Cranmer in the revision of the work.]
[ 2 no more, 1551.]
[ a did St Paul say, 1.V.1.J
THE FIRST BOOK
Rom. i.
Heb. ii.
Eph. i.
John iii.
Gal. ri.
Matt. xxvi.
Mark xiv.
Luke xxii.
1 Cor. x.
83.
A warrant
for apparel.
Christ s ambi
guous speech
es were not
always open
ed by the
evangelists.
Luke xii.
Luke ix.
John xii.
Matt. xiii.
Psal. Ixxvii.
" This is my
body", is no
proper
speech.
that I should rejoice, but in the cross only." Why did he not rather say, Absit mihi
gloriari, nisi in coena Domini* ? "God forbid that I should rejoice, but in the Lord s
supper :" whereat, as you say, the promise of life was fulfilled. This is godly doctrine
for such men to make, as being ignorant in God s word, wander in fantasies of their
own devices, and putantcs se esse sapientes, stulti facti sunt. But the true faithful
believing man professeth, that Christ by his death overcame him that was the author
of death, and hath reconciled us to his Father, making us his children, and heirs of his
kingdom ; that as many as believe in him should not perish, but have life everlasting.
Thus saith the true Christian man, putting his hope of life and eternal salvation neither
in Christ s supper, (although the same be to him a great confirmation of his faith,)
nor in any thing else, but with St Paul saith 8 , Mihi absit gloriari, nisi in cruce Domini
nostri Jesu Christi : " God save me that I rejoice in nothing, but in the cross of our
Lord Jesu Christ."
And when this true believing man cometh to the Lord s supper, and (according to
Christ s commandment) receiveth the bread broken, in remembrance that Christ s body
was broken for him upon the cross, and drinketh the wine in remembrance of the effusion
of Christ s blood for his sins, and unfeignedly believeth the same, to him the words
of our Saviour Christ be effectuous and operatory : " Take, eat ; this is my body, which
is given for thee : and drink of this, for this is my blood which is shed for thee, to the
remission of thy sins/ And as St Paul saith, " the bread unto him is the communion
of Christ s body, and the wine the communion of his blood." For the effect of his godly
eating (as you truly herein gather of St Paul s words) is the communication of Christ s
body and blood, but to the faithful receiver, and not to the dumb creatures of bread
and wine, under whose forms the catholic faith teacheth not the body and blood of
Christ invisibly to be hidden. And as to the godly eater (who duly esteemeth
Christ s body, and hath it in such price and estimation as he ought to have) the
effect is the communication of Christ s body; so to the wicked eater, the effect is
damnation and everlasting woe.
And now I am glad that here yourself have found out a warrant for the apparel
of bread and wine, that they shall not go altogether naked, and be nude and bare
tokens, but have promises of effectual signification, which now you have spied 3 out
both in the words of Christ and St Paul.
Now for the ambiguity of Christ s speeches, it is not always true, that such speeches
of Christ as might have ambiguity, the evangelists either plainly or by circumstances
open them. For Christ speaking so many things in parables, similes, allegories, meta
phors, and other tropes and figures, although sometime Christ himself, and sometime
the evangelists open the meaning, yet for the most part the meaning is left to the
judgment of the hearers, without any declaration. As when Christ said : " Gird your
loins, and take light candles in your hands." And when he said : " No man that
setteth his hand to the plough, and looketh behind him, is meet for the kingdom of
God." And when he said : u Except the grain of wheat falling upon the ground, die,
it remaineth sole." And as St Matthew saith : " Christ spake not to the people with
out parables, that the scriptures might be fulfilled, which prophesied of Christ, that
lie should open his mouth in parables."
And although some of his parables Christ opened to the people, some to his
apostles only, yet some he opened to neither of both, as can appear, but left them to
be considered by the discretion of the hearers. And when Christ called Herod a fox,
Judas a devil, himself a door, a way, a vine, a well ; neither he nor the evangelists
expounded these words, nor gave warning to the hearers that he spake in figures :
for every man that had any manner of sense or reason, might well perceive that
these sentences could not be true in plain form of words, as they were spoken. For
who is so ignorant, but he knoweth that a man is not a fox, a devil, a door, a
way, a vine, a well?
And so likewise when Christ brake the bread, and commanded his disciples to
I" 1 Nisi ccena dominica, 1551.]
[ 2 but saith with St Paul, 1551.]
I [ 3 espied, 1551.]
OF THE SACRAMENT. 37
eat it, and said, "This is my body;" and of the wine he said, "Divide it among
you, drink it, this is my blood:" no man that was there present was so fond, but
he knew well that the bread was not Christ s body, nor the wine his blood. And
therefore they might well know that Christ called the bread his body, and the wine
his blood for some figure, similitude, and property of the bread and wine unto his
flesh and blood : for as bread and wine be foods to nourish our bodies, so is the flesh
and blood of our Saviour Christ, (being annexed unto his deity,) the everlasting food
of our souls.
And although the evangelists in that place do not fully express the words in this
sense, yet adjoining the sixth chapter of John (speaking of the spiritual manducation
of Christ) to the circumstances of the text in the three evangelists, reciting Christ s
last supper, the whole matter is fully gathered, as old authors of the church have
declared. For do not the circumstances of the text, both before and after the eating
and drinking, declare that there is very bread and wine ? Is not that which is broken
and eaten bread? and that which is divided, drunken? And the fruit of the vine,
is it not very wine ? And doth not the nature of sacraments require that the sensible
elements should remain in their proper nature, to signify an higher mystery and
secret working of God inwardly, as the sensible elements be ministered outwardly? 34.
And is not the visible and corporal feeding upon bread and wine a convenient and
apt figure and similitude to put us in remembrance, and to admonish us how we
be fed invisibly and spiritually by the flesh and blood of Christ, God and man ? And
is not the sacrament taken away, when the element is taken away ? Or can the acci
dents of the element be the sacrament of substantial feeding? Or did ever any old
author say, that the accidents were the sacramental signs without the substances ?
But for the conclusion of your matter, here I would wish that you would once
truly understand me. For I do not say that Christ s body and blood be given to us
in signification, and not in deed. But I do as plainly speak as I can, that Christ s
body and blood be given to us in deed, yet not corporally and carnally, but spiritually
and effectually, as you confess yourself within twelve lines after.
WINCHESTER.
The author uttereth a great many words, from the eighth to the seventeenth chapter of the
first book, declaring spiritual hunger and thirst, and the relieving of the same by spiritual
feeding in Christ, and of Christ, as we constantly believe in him, to the confirmation of which
belief, the author would have the sacraments of baptism, and of the body and blood of Christ,
to be adminicles* as it were, and that we by them be preached unto, as in water, bread, and
wine, and by them all our sins 5 , as it were, spoken unto, or properly touched; which matter
in the gross, although there be some words by the way not tolerabk, yet if those words set
apart, the same were in the sum granted, to be good teaching and wholesome exhortation, it
containeth so no more but good matter not well applied. For the catholic church that professeth
the truth of the presence of Christ s body in the sacrament, would therewith use that declaration
of hunger of Christ, and that spiritual refreshing in Christ, with tJie effect of Christ s passion
and death, and the same to be the only mean of man s regeneration and feeding also, with
the differences of that feeding from bodily feeding, for continuing this earthly life. But this
toucheth not the principal point that should be entreated : whether Clirist so ordered to feed
such as be regenerate in him, to give to them in the sacrament the same his body, that he gave
to be crucified for us. The good man is fed by faith, and by merits of Christ s passion,
being the mean of the gift of that faith, and other gifts also, and by the suffering of the
body of Christ, and shedding of his most precious blood on the altar of the cross: which work
and passion of Christ is preached unto us by words and sacraments, and the same doctrine
received of us by faith, and the effect of it also. And thus far goeth the doctrine of this
author.
But the catholic teaching by the scriptures goeth fttrtlier, confessing Christ to feed such as
be regenerate in him^ not only by his body and blood, but also with his body and blood, delivered
in this sacrament by him in deed to us, which the, faithful, by Ms institution and commandment,
[ 4 adminicles; i.e. helps, supports.] [ 5 senses, 1551.]
38 THE FIRST BOOK
receive with their faith and with their mouth also, and with those special dainties be fed
specially at Christ s table. And so God doth not only preach in his sacraments, but also
worketh in them, and with them, and in sensible things giveth celestial gifts, after the doctrine
of each sacrament, as in baptism the Spirit of Christ, and in the sacrament of the altar the
very body and blood of Christ, according to tJie plain sense of his words which he spake : " This
is my body," c. And this is the catholic faith, against which, how the author will fortify
that he would have called catholic, and confute that he improveth, I intend hereafter more
particularly to touch in discussion of that is said.
CANTERBURY.
I mistrust not the indifferency of the reader so much, but he can well perceive
35. how simple and slender a rehearsal you have made here of my eight annotations, and
how little matter you have here to say against them, and how little your sayings re
And because this may the more evidently appear to the reader, I shall rehearse
my words here again.
chai> k vm. Although in this treaty of the sacrament of the body and blood of our
Saviour Christ, I have already sufficiently declared the institution and meaning
of the same, according to the very words of the gospel and of St Paul ; yet it shall
not be in vain somewhat more at large to declare the same, according to the
mind, as well of holy scripture, as of old ancient authors, and that so sincerely
and plainly, without doubts, ambiguities, or vain questions, that the very simple
and unlearned people may easily understand the same, and be edified thereby.
And this by God s grace is mine only intent and desire, that the flock
of Christ dispersed in this realm (among whom I am appointed a special pastor)
may no longer lack the commodity and fruit, which springeth of this heavenly
knowledge. For the more clearly it is understood 1 , the more sweetness, fruit,
comfort, and edification it bringeth to the godly receivers thereof. And to
the clear understanding of this sacrament, divers things must be considered.
chap. ix. First, that as all men of themselves be sinners, and through sin be in God s
hungerand 3 wrath, banished far away from him, condemned to hell and everlasting dam-
the soui. nation, and none is clearly innocent, but Christ alone : so every soul inspired
by God is desirous to be delivered from sin and hell, and to obtain at God s
hands mercy, favour, righteousness, and everlasting salvation.
Eph. if. And this earnest and great desire is called in scripture, " the hunger and
thirst of the soul :" with which kind of hunger David was taken, when he said :
rsai. xiii. "As an hart longeth for springs of water, so doth my soul long for thee,
rsai.ixiii. God." "My soul thirsteth 2 after God, who is the well of life. My soul thirsteth
for thee, my flesh wisheth for thee."
Rom. iv. And this hunger the silly poor sinful soul is driven unto by means of the
law, which sheweth unto her the horribleness of sin, the terror of God s indig
nation, and the horror of death and everlasting damnation.
Rom. viii. And when she seeth nothing but damnation for her offences by justice and
accusation of the law, and this damnation is ever before her eyes, then in this
great distress the soul being pressed with heaviness and sorrow, sceketh for
some comfort, and desireth some remedy for her miserable and sorrowful
estate. And this feeling of her damnable condition, and greedy desire of re
freshing, is the spiritual hunger of the soul.
And whosoever hath this godly hunger is blessed of God, and shall have
[ l understand, 1551.] [ 2 hath thhbted, 1551. j
OF THE SACRAMENT. 39
meat and drink enough, as Christ himself said : " Blessed be they that hunger Matt. v.
and thirst for righteousness, for they shall be filled full." And on the other
side, they that sec not their own sinful and damnable estate, but think them
selves holy enough, and in good case and condition enough, as they have no
spiritual hunger, so shall they not be fed of God with any spiritual food. For
as Almighty God feedeth them that be hungry, so doth he send away empty Lukci.
all that be not hungry.
But this hunger and thirst is not easily perceived of the carnal man. For
when he heareth the Holy Ghost speak of meat and drink, his mind is by
and by in the kitchen and buttery, and he tliinketh upon his dishes and pots, 3<3 -
his mouth and his belly.
But the scripture in sundry places useth special words, whereby to draw
our gross minds from the phantasying of our teeth and belly, and from this
carnal and fleshly imagination. For the apostles and disciples of Christ, when
they were yet carnal, knew not what was meant by this kind of hunger and
meat; and therefore when they desired him to eat, (to withdraw their minds
from carnal meat) he said unto them : "I have other meat to eat which you
know not." And why knew they it not? Forsooth, because their minds wercJ^mv.
gross as yet, and had not received the fulness of the Spirit. And therefore
our Saviour Christ, minding to draw them from this grossness, told them of
another kind of meat than they phantasied, (as it were) rebuking them, for that
they perceived not that there was any other kind of eating and drinking,
besides that eating and drinking which is with the mouth and throat. 3
Likewise when he said to the woman of Samaria, "Whosoever shall drink John i\.
of that water that I shall give him, shall never be thirsty again ; " they that
heard him speak those words, might well perceive that he went about to make
them well acquainted with another kind of drinking, than is the drinking with
the mouth and throat. For there is no such kind of drink, that with once
drinking can quench the thirst of a man s body for ever. Wherefore, in saying
he shall never be thirsty again, he did draw their minds from drinking with
the mouth unto another kind of drinking, whereof they knew not, and unto
another kind of thirsting, wherewith as yet they were not acquainted. And 4
also, when our Saviour Christ said, " He that cometh to me shall not hunger, John vi.
and he that believeth on me shall never be thirsty ;" he gave them a plain
watchword, that there was another kind of meat and drink than that where
with he fed them at the other side of the water, and another kind of hungering
and thirsting than was the hungering and thirsting of the body. By these
words therefore he drove the people to understand another kind of eating and
drinking, of hungering and thirsting, than that which belongeth only for the
preservation of temporal life.
Now then as the thing that comforteth the body is called meat and drink,
of a like sort the scripture calleth the same thing that comforteth the soul
meat and drink.
Wherefore as here before in the first note is declared the hunger and chap. x.
drought of the soul, so is it now secondly to be noted, what is the meat, drink, The spiritual
J food of the
and food of the soul. sou] -
The meat, drink, food, and refreshing of the soul is our Saviour Christ,
as he said himself: "Come unto me all you that travail and be laden, and Matt - xi -
I will refresh you." And, "If any man be dry," saith he, "let him come to John vii.
me and drink. He that believeth in me, floods of water of life shall flow out
[ 3 and the throat, 1551.] [ 4 Also when, 1551.]
40
THE FIRST BOOK
37.
[John vi.
155!.]
Gal. ii.
Chap. xi.
Christ far
excelleth all
of his belly." And, " I am the bread of life," saith Christ ; " he that cometh to
me, shall not be hungry : and he that believeth in me, shall never be dry."
For as meat and drink do comfort the hungry body, so doth the death of
Christ s body and the shedding of his blood comfort the soul, when she is
after her sort hungry. What thing is it that comforteth and nourisheth the
body? Forsooth, meat and drink. By what names then shall we call the
body and blood of our Saviour Christ (which do comfort and nourish the hungry
soul) but by the names of meat and drink? And this similitude caused our
Saviour to say : " My flesh is very meat, and my blood is very drink." For
there is no kind of meat that is comfortable to the soul, but only the death
of Christ s blessed body ; nor no kind of drink that can quench her thirst,
but only the blood-shedding of our Saviour Christ, which was shed for her
offences. For as there is a carnal generation, and a carnal feeding and nourish
ment; so is there also a spiritual generation, and a spiritual feeding.
And as every man by carnal generation of father and mother, is carnally
begotten and born unto this mortal life : so is every good Christian spiritually
born by Christ unto eternal life.
And as every man is carnally fed and nourished in his body by meat and
drink, even so is every good Christian man spiritually fed and nourished in his
soul by the flesh and blood of our Saviour Christ.
[And as the body liveth by meat and drink, and thereby increaseth and
groweth from a young babe unto a perfect man, (which thing experience
teacheth us;) so the soul liveth by Christ himself, by pure faith eating his
flesh and drinking his blood 1 .]
And this Christ himself teacheth us in this sixth 2 of John, saying : " Verily,
verily I say unto you, Except ye eat the flesh of the son of man, and drink
his blood, you have no life in you. Whoso eateth my flesh, and drinketh
my blood, hath eternal life, and I will raise him up at the last day. For
my flesh is very meat, and my blood is very drink. He that eateth my flesh,
and drinketh my blood, dwelleth in me, and I in him. As the living Father
hath sent me, and I live by the Father; even so he that eateth me, shall
live by me."
And this St Paul confessed 3 himself, saying : " That I have life, I have
it by faith in the Son of God. And now it is not I that live, but Christ
liveth in me."
The third thing to be noted is this, that although our Saviour Christ
resembleth his flesh and blood to meat and drink, yet he far passeth and
excelleth all corporal meats and drinks. For although corporal meats and
drinks do nourish and continue our life here in this world, yet they begin not
our life. For the beginning of our life we have of our fathers and mothers:
and the meat, after we be begotten, doth feed and nourish us, and so preserveth
us for a time. But our Saviour Christ is both the first beginner of our spiritual
life, (who first begetteth us unto God his Father,) and also afterward he is our
lively food and nourishment.
Moreover meat and drink do feed 4 and nourish only our bodies, but Christ
is the true and perfect nourishment both of body and soul. And besides that,
bodily food preserveth the life but for a time, but Christ is such a spiritual
and perfect food, that he preserveth both body and soul for ever ; as he said
[ l This passage is omitted in both the 1551 and
1580 editions, as well as in ed. Embd. 155J. It
is here inserted from the original edition of the
" Defence."]
[ 2 in the sixth of John, 1551.]
[ 3 confessed of himself, 1551.]
[ 4 doth, 1551. J
OF THE SACRAMENT. 41
unto Martha : " I am a resurrection 5 and life. He that believeth in me, although
he die, yet shall he live. And he that liveth and believeth in me, shall not
die for ever."
Fourthly it is to be noted, that the true knowledge of these things is chap.
the true knowledge of Christ, and to teach these things is to teach Christ. The sa
And the believing and feeling of these things is the believing and feeling
Christ in our hearts. And the more clearly we see, understand, and believe fjlth
these things, the more clearly we see and understand Christ, and have more
fully our faith and comfort in him.
And although our carnal generation and our carnal nourishment be known
to all men by daily experience, and by our common senses; yet this our spiritual
generation and our spiritual nutrition be so obscure and hid unto us, that
we cannot attain to the true and perfect knowledge and feeling of them,
but only by faith, which must be grounded upon God s most holy word and
sacraments.
And for this consideration our Saviour Christ hath not only set forth these 38,
things most plainly in his holy word, that we may hear them with our ears,
but he hath also ordained one visible sacrament of spiritual regeneration in
water, and another visible sacrament of spiritual nourishment in bread and
wine, to the intent, that as much as is possible for man, we may see Christ with
our eyes, smell him at our nose, taste him with our mouths, grope him with our
hands, and perceive him with all our senses. For as the word of God preached
putteth Christ into our ears, so likewise these elements of water, bread, and wine,
joined to God s word, do after a sacramental manner put Christ into our eyes,
mouths, hands, and all our senses.
And for this cause Christ ordained baptism in water, that as surely as
we see, feel, and touch water with our bodies, and be washed with water, so
assuredly ought we to believe, when we be baptized, that Christ is verily present
with us, and that by him we be newly born again spiritually, and washed from
our sins, and grafted in the stock of Christ s own body, and be apparelled,
clothed, and harnessed with him, in such wise, that as the devil hath no power
against Christ, so hath he none against us, so long as we remain grafted in
that stock, and be clothed with that apparel, and harnessed with that armour.
So that the washing in water of baptism is, as it were, shewing of Christ before
our eyes, and a sensible touching, feeling, and groping of him, to the confirmation
of the inward faith, which we have in him.
And in like manner Christ ordained the sacrament of his body and blood in
bread and wine, to preach unto us, that as our bodies be fed, nourished, and
preserved with meat and drink, so as touching our spiritual life towards God
we be fed, nourished, and preserved by the body and blood of our Saviour
Christ; and also that he is such a preservation unto us, that neither the devils of
hell, nor eternal death, nor sin, can be able to prevail against us, so long as
by true and constant faith we be fed and nourished with that meat and drink.
And for this cause Christ ordained this sacrament in bread and wine (which Hl g d <? &
Viet* de Sa
we eat and drink, and be chief nutriments of our body), to the intent that as 5J52*j
surely as we see the bread and wine with our eyes, smell them with our noses, <**- 3 -
touch them with our hands, and taste them with our mouths, so assuredly [Rabam<ie
ought we to believe that Christ is a spiritual 6 life and sustenance of our souls, Mm,uflT
like as the said bread and wine is the food and sustenance of our bodies. And "**sX *.
no less ought we to doubt, that our souls be fed and live by Christ, than
I am resurrection, 1551.] [ is our spiritual life, 1551.]
42 THE FIRST BOOK
that our bodies be fed and live by meat and drink. Thus our Saviour Christ,
knowing us to be in this world, as it were, but babes and weaklings in faith,
hath ordained sensible signs and tokens whereby to allure and to draw us to
more strength and more constant faith in him. So that the eating and drinking
of this sacramental bread and wine is, as it were, shewing 1 of Christ before our
eyes, a smelling of him with our noses, feeling 2 and groping of him with our
hands, and an eating, chewing, digesting, and feeding upon him to our spi
ritual strength and perfection.
chap. xiii. Fifthly, it is to be noted, that although there be many kinds of meats
tbktto? and drinks which feed the body, yet our Saviour Christ (as many ancient
ITrdainecUn authors write) ordained this sacrament of our spiritual feeding in bread and
w "in a e. al wine, rather than in other meats and drinks, because that bread and wine do
most lively represent unto us the spiritual union and knot of all faithful people,
39. as well unto Christ, as also among themselves. For like as bread is made
vSacS- of a great number of grains of corn, ground/ baken, and so joined together,
TniSvi. that thereof is made one loaf; and an infinite number of grapes be pressed
together in one vessel, and thereof is made wine ; likewise is the whole multi
tude of true Christian people spiritually joined, first to Christ, and then among
themselves together in one faith, one baptism, one Holy Spirit, one knot and
bond of love.
chap. xiv. Sixthly, it is to be noted, that as the bread and wine which we do eat
be turned into our flesh and blood, and be made our very flesh and very
blood, and so be 3 joined and mixed with our flesh and blood, that they be
ma( j e one w hole body together; even so be all faithful Christians spiritually
turned into the body of Christ, and so be 3 joined unto Christ, and also to
gether among themselves, that they do make but one mystical body of Christ,
i cor. x. as St Paul saith : " We be one bread and one body, as many as be partakers
of one bread and one cup." And as one loaf is given among many men, so
Dionysius, that every one is partaker of the same loaf; and likewise one cup of wine
EcAHier. .,..,, ff
cap. a. is distributed unto many persons, wnereoi every one is partaker ; even so our
Saviour Christ (whose flesh and blood be represented by the mystical bread
and wine in the Lord s supper) doth give himself unto all his true members,
spiritually to feed them, nourish them, and to give them continual life by
him. And as the branches of a tree, or member of a body, if they be
dead, or cut off, they neither live, nor receive any nourishment or sustenance
of the body or tree ; so likewise ungodly and wicked people, which be cut off
from Christ s mystical body, or be dead members of the same, do not spi
ritually feed upon Christ s body and blood, nor have any life, strength, or
sustentation thereby.
chap. xv. Seventhly, it is to be noted, that whereas nothing in this life is more ac-
inent^rnoveth ce ptable before God, or more pleasant unto man, than Christian people to live
friendship together quietly in love and peace, unity and concord, this sacrament doth
most aptly and effectuously move us thereunto. For when we be made all
partakers of this one table, what ought we to think, but that we be all mem
bers of one spiritual body, whereof Christ is the head ; that we be joined
together in one Christ, as a great number of grains of corn be joined to
gether in one loaf? Surely, they have very hard and stony hearts, which
with these things be not moved: and more cruel and unreasonable be they
than brute beasts, that cannot be persuaded to be good to their Christian bre
thren and neighbours, for whom Christ suffered death, when in this sacra-
[ a shewing, 1551.] [ 2 a feeling, 1551.] [ 3 be so, 1551.]
OF THE SACRAMENT. 43
mcnt they be put in remembrance that the Son of God bestowed his life for
his enemies. For we see by daily experience, that eating and drinking to
gether makcth friends, and continueth friendship : much more then ought the
table of Christ to move us so to do. AVild beasts and birds be made gentle
by giving them meat and drink : why then should not Christian men Avax
meek and gentle with this heavenly meat of Christ? Hereunto we be stirred
and moved, as well by the bread and wine in this holy supper, as by the
words of holy scripture recited in the same. Wherefore, whose heart soever
this holy sacrament, communion, and supper of Christ will not kindle with
love unto his neighbours, and cause him to put out of his heart all envy,
hatred, and malice, and to grave in the same all amity, friendship, and con
cord, he dcceiveth himself, if he think that he hath the Spirit of Christ
dwelling within him.
But all these foresaid godly admonitions, exhortations, and comforts, do
the papists (as much as licth in them) take away from all Christian people by
their transubstantiation.
For if we receive no bread nor wine in the holy communion, then all 40.
... i_ui i - i The doctrine
these lessons and comlorts be gone, which we should learn and receive by
eating of the bread, and drinking of the wine : and that fantastical imagi
nation giveth an occasion utterly to subvert our whole faith in Christ. For g
seeing that this sacrament was ordained in bread and wine (which be foods
for the body) to signify and declare unto us our spiritual food by Christ ;
then if our corporal feeding upon the bread and wine be but fantastical, (so
that there is no bread nor wine 4 there indeed to feed upon, although they appear
there to be,) then it doth us to understand, that our spiritual feeding in Christ
is also fantastical, and that indeed we feed not of him : which sophistry is
so devilish and wicked, and so much injurious to Christ, that it could not
come from any other person, but only from the devil himself, and from his
special minister antichrist.
The eighth thing that is to be noted is, that this spiritual meat of Christ s chap. xvr.
body and blood is not received in the mouth, and digested in the stomach. The spiritual
** r.it hiLj is with
(as corporal meats and drinks commonly be,) but it is received with a pure JJjJ^gJ? not
heart and a sincere faith. And the true eating and drinking of the said tctth>
body and blood of Christ is, with a constant and lively faith to believe, that
Christ gave his body, and shed his blood upon the cross for us, and that
he doth so join and incorporate himself to us, that he is our head, and we
his members, and flesh of his flesh, and bone of his bones, having him dwelling
in us, and we in him. And herein standeth the whole effect and strength of
this sacrament. And this faith God worketh inwardly in our hearts by his
holy Spirit, and confirmed! the same outwardly to our ears by hearing of his
word, and to our other senses by eating and drinking of the sacramental bread
and wine in his holy supper.
What thing then can be more comfortable to us, than to eat this meat,
and drink this drink? whereby Christ certified! us, that we be spiritually,
and truly, fed and nourished by him, and that we dwell in him, and he in
us. Can this be shewed unto us more plainly, than when he saith himself, John i.
" He that eateth me shall live by me ?"
Wherefore, whosoever doth not contemn the everlasting life, how can he
but highly esteem this sacrament ? How can he but embrace it as a sure
pledge of his salvation? And when he seeth godly people devoutly receive
| 4 bread and wine, l-jol.
44 THE FIRST BOOK
the same, how can he but be desirous oftentimes to receive it with them ?
Surely no man that well understandeth, and diligently weigheth these things,
can be without a great desire to come to this holy supper.
All men desire to have God s favour, and when they know the contrary,
that they be in his indignation, and cast out of his favour, what thing can
comfort them ? How be their minds vexed ! What trouble is in their con
sciences ! All God s creatures seem to be against them, and do make them
afraid, as things being ministers of God s wrath and indignation towards them,
and rest or comfort can they find none, neither within them, nor without them.
And in this case they do hate as well God, as the devil ; God, as an un
merciful and extreme judge, and the devil as a most malicious and cruel
tormentor.
And in this sorrowful heaviness, holy scripture teacheth them, that our
heavenly Father can by no means be pleased with them again, but by the
sacrifice and death of his only-begotten Son, whereby God hath made a per
petual amity and peace with us, doth pardon the sins of them that believe in
him, maketh them his children, and giveth them to his first-begotten Son
Christ, to be incorporate into him, to be saved by him, and to be made heirs
41. of heaven with him. And in the receiving of the holy supper of our Lord,
we be put in remembrance of this his death, and of the whole mystery of our
redemption. In the which supper is made mention of his testament, and of
the aforesaid communion of us with Christ, and of the remission of our sins
by his sacrifice upon the cross.
Wherefore in this sacrament, (if it be rightly received with a true faith,)
we be assured that our sins be forgiven, and the league of peace and the
testament of God is confirmed between him and us, so that whosoever by a
true faith doth eat Christ s flesh, and drink his blood, hath everlasting life
by him. Which thing when we feel in our hearts at the receiving of the
Lord s supper, what thing can be more joyful, more pleasant, or more com
fortable unto us ?
All this to be true is most certain by the words of Christ himself, when
he did first institute his holy supper, the night before his death, as it appeareth
Lukexxii. as well by the words of the evangelists, as of St Paul. "Do this," saith Christ,
icor. xi. "as often as you drink it, in remembrance of me." And St Paul saith : " As
LukxxiL often as you eat this bread, and drink this cup, you shall shew the Lord s
death until he come." And again Christ said : " This cup is a new testament
in mine own blood, which shall be shed for the remission of sins."
This doctrine here recited may suffice for all that be humble and godly,
and seek nothing that is superfluous, but that is necessary and profitable : and
therefore, unto such persons may be made here an end of this book. But
unto them that be contentious papists and idolaters, nothing is enough. And
yet, because they shall not glory in their subtle inventions and deceivable
doctrine (as though no man were able to answer them), I shall desire the
readers of patience to suffer me a little while, to spend some time in vain,
to confute their most vain vanities. And yet the time shall not be altogether
spent in vain, for thereby shall more clearly appear the light from the dark
ness, the truth from false sophistical subtleties, and the certain word of God
from men s dreams and fantastical inventions.
Although I need make no further answer, but the rehearsal of my words, yet
thus much will I answer, that where you say, that I speak some words by the way
not tolerable, if there had been any such they should not have failed to be expressed
and named to their reproach, as other have been. Wherefore the reader may take a
OF THE SACRAMENT. 45
day with you before he believe you, when you reprove me for using some .intoler
able words, and in conclusion name not one of them.
And as for your catholic confession, that Christ doth indeed feed such as be re
generated in him, not only by his body and blood, but also with his body and blood
at his holy table, this I confess also : but that he feedeth Jews, Turks, and infidels,
if they receive the sacrament, or that he corporally feedeth our mouths with his flesh
and blood, this neither I confess, nor any scripture or ancient writer ever taught;
but they teach that he is eaten spiritually in our hearts and by faith, not with mouth
and teeth, except our hearts be in our mouths, and our faith in our teeth.
Thus you have laboured sore in this matter, and spun a fair thread, and brought i n J r y *
tliis your first book to a goodly conclusion. For you conclude your book with bias- sacraments.
phemous words against both the sacrament of baptism and the Lord s supper, nig
gardly pinching God s gifts, and diminishing his liberal promises made unto us in 42.
them. For where Christ hath promised in both the sacraments to be assistant with
us whole both in body and Spirit (in the one to be our spiritual regeneration and
apparel, and in the other to be our spiritual meat and drink), you clip his liberal
benefits in such sort, that in the one you make him to give but only his Spirit, and
in the other but only his body. And yet you call your book an explication and assertion
of the true catholic faith.
Here you make an end of your first book, leaving unanswered the rest of my book. D. smith.
And yet, forasmuch as Smith busieth himself in this place with the answer thereof,
he may not pass unanswered again, where the matter requireth. The words of my
book be these.
But these things cannot manifestly appear to the reader, except the prin- [Book i.]
cipal points be first set out, wherein the papists vary from the truth of God s PoSpSS-
. , . , , , . a r. nal errors of
word, which be chiefly lour. the papists.
First, the papists say, that in the supper of the Lord, after the words of xhefmtisof
consecration, (as they call it,) there is none other substance remaining, but the of e clu5f. nce
substance of Christ s flesh and blood, so that there remaineth neither bread
to be eaten, nor wine to be drunken. And although there be the colour of
bread and wine, the savour, the smell, the bigness, the fashion, and all other
(as they call them) accidents, or qualities and quantities of bread and wine,
yet, say they, there is no very bread nor wine, but they be turned into the
flesh and blood of Christ. And this conversion they call " transubstantiation,"
that is to say, " turning of one substance into another substance." And although
all the accidents, both of the bread and wine, remain still, yet, say they, the
same accidents be in no manner of thing, but hang alone in the air, without
anything to stay them upon. For in the body and blood of Christ, say they,
these accidents cannot be, nor yet in the air; for the body and blood of Christ,
and the air, be neither of that bigness, fashion, smell, nor colour, that the
bread and wine be. Nor in the bread and wine, say they, these accidents
cannot be ; for the substance of bread and wine, as they affirm, be clean gone.
And so there remaineth whiteness, but nothing is white : there remaineth colours,
but nothing is coloured therewith : there remaineth roundness, but nothing is
round : and there is bigness, and yet nothing is big : there is sweetness, with
out any sweet thing ; softness, without any soft thing ; breaking, without any
tiling broken ; division, without anything divided : and so other qualities and
quantities, without anything to receive them. And this doctrine they teach
as a necessary article of our faith.
But it is not the doctrine of Christ, but the subtle invention of antichrist,
first decreed by Innocent the third, and after more at large set forth by school * i
authors, whose study was ever to defend and set abroad to the world all
I 1 The first is of transubstantiation, 1551.]
46
THE FIRST BOOK
43.
The second
is of the pre
sence of
Christ in the
sacrament.
such matters as the bishop of Home had once decreed. And the devil, by
his minister antichrist, had so dazzled the eyes of a great multitude of Christian
people in these latter days, that they sought not for their faith at the clear
light of God s word, but at the Romish antichrist, believing whatsoever he
prescribed unto them, yea, though it were against all reason, all senses, and
God s most holy word also. For else he could not have been very antichrist
indeed, except he had been so repugnant unto Christ, whose doctrine is clean
contrary to this doctrine of antichrist. For Christ tcachcth that we receive
very bread and wine in the most blessed supper of the Lord, as sacraments
to admonish us, that as we be fed with bread and wine bodily, so we be
fed with the body and blood of our Saviour Christ spiritually : as in our
baptism we receive very water, to signify unto us, that as water is an
element to wash the body outwardly, so be our souls washed by the Holy
Ghost inwardly.
The second principal thing, wherein the papists vary from the truth of
God s word, is this : They say, that the very natural flesh and blood of
Christ, which suffered for us upon the cross, and sitteth at the right
hand of the Father in heaven, is also really, substantially, corporally, and
naturally, in or under the accidents of the sacramental bread and wine, which
they call the forms of bread and wine. And yet here they vary not a
little among themselves, for some say, that the very natural body of Christ
is there, but not naturally, nor sensibly. And other say, that it is there
naturally and sensibly, and of the same bigness and fashion that it is in
heaven, and as the same was born of the blessed virgin Mary, and that it is
there broken and torn in pieces with our teeth. And this appeareth partly
by the school authors, and partly by the confession of Berengarius 1 , which
g- Nicholas the second constrained him to make, which was this : That of the
LegcRoffen.
sacraments of the Lord s table the said Berengarius should promise to hold
that faith which the said pope Nicholas and his council held, which was, that
not only the sacraments of bread and wine, but also the very flesh and blood
of our Lord Jesus Christ are sensibly handled of the priest in the altar, broken
and torn with the teeth of the faithful people. But the true catholic faith,
grounded upon God s most infallible word, teacheth us, that our Saviour Christ
(as concerning his man s nature and bodily presence) is gone up unto heaven,
* Christ is not and sitteth at the right hand of his Father, and there shall he tarry until the
corporal n ^^g en( ^ ^ what time he shall come again to judge both the quick and the
joimxvi. dead, as he saith himself in many scriptures: "I forsake the world," saith
Matt. xxvi. he, " and go to my Father." And in another place he saith : " You shall ever
borat r rr ~
have poor men among you, but me shall not you 2 ever have."
And again he
[ Ego Berengarius indignus sancti Mauri tii
Andegavensis ecclesise Diaconus cognoscens veram,
catholicam, et apostolicam fidem, anathematize
omnem haeresim, praecipue earn, de qua hactenus
inf amatus sum : quae astruere conatur panem et
vinum, qua2 in altari ponuntur, post consecrationem
solummodo sacramentum, et non verum corpus et
sanguinem Domini nostri Jesu Christi esse, nee
posse sensualiter, nisi in solo sacramento, manibus
sacerdotum tractari, vel frangi, aut tidelium denti-
bos atteri. Consentio autem sanctas Romanae et
apostolicae Sedi : et ore et corde profiteor de sacra-
mentis Dominicae mensae eandem h dem me tenere,
quam dominus et venerabilis Papa Nicolaus et
hasc sancta Synodus auctoritate evangelica et apos-
tolica tenendam tradidit, mihique firmavit : scilicet
panem et vinum, qurc in altari ponuntur, post con
secrationem non solum sacramentum, sed etiam
verum corpus et sanguinem Domini nostri Jesu
Christi esse, et sensualiter, non solum sacramento,
sed in veritate manibus sacerdotum tractari, frangi,
et h delium dentibus atteri : jurans per sanctam et
homousion Trinitatem, per haec sacrosancta Christi
evangelia. Eos vero, qui contra hanc h dem vene-
rint, cum dogmatibus et sectatoribus suis aeterno
anathemate dignos esse pronuntio. Quod si ego
ipse aliquando contra haec aliquid sentire aut prae-
dicare preesumpsero, subjaceam canonum severitati.
Lecto et perlecto sponte subscripsi. Corpus Juris
Canonici. Gratiani Decreti tertia pars. " De Con-
secrat." Dist. n. c. xlii. cols. 1932, 3. Ed. Lugd.
IfilS.j
[ 2 you shall not, 15fll.]
OF THE SACRAMENT.
47
44.
saith : "Many hereafter shall come and say, look here i> Christ, or look there Matt. xxiv.
he js, but believe them not." And St Peter saith in the Acts, that "heaven must Actsm.
receive Christ until the time that all tilings shall be rest on -si." And St Paul,
writing to the Colossians, agrceth hereto, saying: "Seek for tilings that becoi. m.
above, where Christ is sitting at the right hand of the Father." And St
Paul, speaking of the very sacrament, saith : " As often as you shall eat this i cor. XL
bread, and drink this cup, shew forth the Lord s death until he come." " Till
he come," saith St Paul, signifying that he is not there corporally present.
For what speech were this, or who useth of him that is already present to say,
"until he come?" For, "until he come 3 ," signifieth that he is not yet present.
This is the catholic faith, which we learn from our youth in our common
creed, and which Christ taught, the apostles followed, and the martyrs confirmed
with their blood.
And although Christ in his human nature, substantially, really, corporally,
naturally, and sensibly, be present with his Father in heaven, yet sacramentally
and spiritually he is here present 4 . For in water, bread, and wine, he is pre
sent, as in signs and sacraments ; but he is indeed spiritually in those faithful,
Christian people, which according to Christ s ordinance be baptized, or receive
the holy communion, or unfeignedly believe in him. Thus have you heard
the second principal article, wherein the papists vary from the truth of God s
word and from the catholic faith.
Now the third thing, wherein they vary, is this.
The papists say, that evil and ungodly men receive in this sacrament the
very body and blood of Christ, and eat and drink the selfsame thing that
the good and godly men do. But the truth of God s word is contrary, that
all those that be godly members of Christ, as they corporally cat the bread Chris t-
and drink the wine, so spiritually they eat and drink Christ s very flesh and
blood. And as for the wicked members of the devil, they eat the sacramental
bread, and drink the sacramental wine, but they do not spiritually eat Christ s
flesh, nor drink liis blood, but they eat and drink their own damnation.
The fourth thing, wherein the popish priests dissent from the manifest The fourth is
word of God, is this. They say that they offer Christ every day for remission mau3
of sin, and distribute by their masses the merits of Christ s passion. But the
prophets, apostles, and evangelists, do say that Christ himself in his own
person made a sacrifice for our sins upon the cross, by whose wounds all our
diseases were healed, and our sins pardoned ; and so did never no priest, man,
nor creature, but he, nor he did the same never more than once. And the
benefit hereof is in no man s power to give unto any other, but every man
must receive it at Christ s hands himself, by his own faith and belief, as the Abacuk ii.
prophet saith.
Here Smith findcth himself much grieved at two false reports, wherewith he saith D. smith,
that I untruly charge the papists. One, when I write that some say, that the very thatcSL b
natural body of Christ is in the sacrament naturally and sensibly ; which thing Smith the\
utterly denieth any of them to say, and that I falsely lay this unto their charge. And m<
moreover it is 5 very false, saith he, that you lay unto our charges, that we say, that
Christ s body is in the sacrament as it was born of the virgin, and that it is broken
and toni in pieces with our teeth. This also Smith saith 6 is a false report of me.
But whether I have made any untrue report or no, let the books be judges. As
eat and drink
[ 3 until I come, 1551.]
[ 4 He is here present in water, bread, and wine,
as in signs and sacraments, but he is indeed spiritu
ally in the faithful Christian people, 1551.]
[ 5 it is also very false, 1551. J
[ (! saith Smith, 1551.]
THE FIRST BOOK
A manifest,
falsehood in
op s book.
45.
ment aera "
touching the first, the bishop writeth thus in his book of the Devil s Sophistry, the
fourteenth leaf: "Good men were never offended with breaking of the host, which
they daily saw, being also persuaded Christ s body to be present in the sacrament
naturally and really." And in the eighteenth leaf he saith these words: "Christ,
God and man, is naturally present in the sacrament." And in ten or twelve places
of this, his last book, he saith, "that Christ is present in the sacrament naturally,
4 corporally, sensibly, and carnally, as shall appear evidently in the reading thereof."
So that I make no false report herein, who report no otherwise 1 than the papists have
written and published openly in their books.
And it is not to be passed over, but worthy to be noted, how manifest falsehood
is used in the printing of this bishop s book, in the one hundred and thirty-sixth leaf.
For where the bishop wrote (as I have two copies to shew, one of his own hand, and
another exhibited by him in open court before the king s commissioners), that Christ s
body in the sacrament is truly present, and therefore really present, corporally also,
and naturally ; the printed book now set abroad hath changed this word " naturally,"
and in the stead thereof hath put these words, "but yet supernaturally," corrupting
and manifestly falsifying the bishop s book 2 .
Who was the author of this untrue act, I cannot certainly define ; but if conjectures
may have place, I think the bishop himself would not command to alter the book in
the printing, and then set it forth with this title, that it was the same book that was
exhibited by his own hand, for his defence, to the king s majesty s commissioners at
Lambeth.
And I think the printer, being a Frenchman, would not have enterprised so false
a deed of his own head, for the which he should have no thanks at all, but be accused
of the author as a falsifier of his book.
Now forasmuch as it is not like, that either the bishop or the printer would play
any such pranks, it must then be some other, that was of counsel in the printing of
the book; which being printed in France (whither you be now fled from your own
native country), what person is more like to have done such a noble act than you ?
who being so full of craft and untruth in your own country, shew yourself to be no
changeling, wheresoever you be come. And the rather it seemeth to me to be you
than any other person, because that the book is altered in this word "naturally,"
upon which word standeth the reproof of your saying. For he saith that Christ is
in the sacrament "naturally," and you deny that any man so saith, but that Christ
is there "supernaturally." Who is more like therefore to change in his book "natu
rally" into "supernaturally" than you, whom the matter toucheth, and no man else?
But w r hether my conjectures be good in this matter I will not determine, but refer
it to the judgment of the indifferent reader.
Now as concerning the second untrue report, which I should make of the papists,
I have alleged the words of Berengarius recantation, appointed by pope Nicholas
the second, and written De eonsecrat. dist. 2, which be these, "that not only the sacra
ments of bread and wine, but also the very flesh and blood of our Lord Jesu Christ,
are sensibly handled of the priest in the altar, broken, and torn with the teeth of
the faithful people."
Thus the reader may see that I misreport not the papists, nor charge them with
any other words than they do write; that is to say, "that the body of Christ is
naturally and sensibly in the sacrament, and broken and torn in pieces with our teeth."
" But," saith Smith, " the meaning of Berengarius in his recantation was otherwise,
that the forms of bread 3 and wine are broken and torn with our teeth, but Christ is
received wholly, without breaking of his body, or tearing with our teeth." Well,
whatsoever the meaning of Berengarius was, his words be as I report ; so that I make
[ l none otherwise, 1551.]
[ 2 In the 1551 edition of Winchester s Expli
cation, p. 136, the passage is thus given : " It is
truly present, and therefore really present, corpo
rally also, and but yet supernaturally, with relation
to the truth of the body present, and not to the
manner of presence, which is spiritual." The
reader, however, is directed in the "certain faults
escaped in the printing," appended to the beginning
of the book, to read "naturally " for "supernatu
rally." Cranmer s version of these renderings, it
is evident, is the only one which can make the
sense clear and distinct.]
[ 3 the forms only of bread, 1551.]
OF THE SACRAMENT. 49
no false report of the papists, nor untruly charge them with that they say not. But
how should men know what the papists mean, when they say one thing, and mean
another? For Berrngarius said, "that not only the sacraments be broken and torn
with our teeth," and you say he meant contrary, " that only the sacraments be broken
and torn with our teeth." Bcrcngarius said, "that also the very flesh and blood of
Christ be broken and torn," and you say he meant clean contrary, "that the flesh
and blood of Christ be not broken and torn." Well, then would I fain learn, how
it may be known what the papists mean, if they mean yea, when they say nay, and
UK an nay, when they say yea.
And as for St John Chrysostom, and other old authors, by whom you would ex
cuse this manner of speech, they help you herein nothing 4 at all. For not one of them
speak after this sort that Berengarius doth. For although they say sometimes that ^6.
wr see Christ, touch him, and break him, (understanding that speech not of Christ
himself, but of the sacraments which represent him,) yet they use no such form of
speech as was prescribed to Berengarius, that we see, feel, and break, not only the
sacraments, but also Christ himself.
And likewise of Loth 5 , Abraham, Jacob, Joshua, Mary Magdalene, and the apostles,
whom you bring forth in this matter, there is no such speech in the scripture as
Berengarius useth. So that all these things be brought out in vain, having no colour
to serve for your purpose, saving that something you must say to make out your
book.
And as for all the rest that you say in this process, concerning the presence of
Christ visible and invisible, needeth no answer at all, because you prove nothing of
all that you say in that matter, w T hich may easily therefore 6 be denied by as good
authority as you affirm the same. And yet all the old writers that speak of the
diversity of Christ s substantial presence and absence, declare this diversity to be in
the diversity of his two natures, (that in the nature of his humanity he is gone
hence, and present in the nature of his divinity,) and not that in divers respects and
qualities of one nature he is both present and absent; which I have proved in my
third book, the fifth chapter.
And forasmuch as you have not brought one author for the proof of your saying,
but your own bare words, nor have answered to the authorities alleged by me in
the foresaid place of my third book, reason would that my proofs should stand and
have place, until such time as you have proved your sayings, or brought some
evident matter to improve mine. And this, I trust, shall suffice to any indifferent
reader, for the defence of my first book.
\\L\CIIESTER.
WJierein I will keep this order. First, to consider the third book, that speaketh against the
faith of the real presence of Christ s most precious body and blood in the sacrament: then
against the fourth, and so return to the second, speaking of transubstantiation, whereof to
talk, the real presence not being discussed, were clearly super/luotts. And finally, I will somewhat
say of the fifth book also.
CANTERBURY.
But now to return to the conclusion of the bishop s book. As it began with a why the or-
marvellotis sleight and subtlety, so doth he conclude the same with a like notable book JSJ
subtlety, changing the order of my books, not answering them in such order as I
wrote them, nor as the nature of the things requireth. For seeing that, by all men s
confessions, there is bread and wine before the consecration ; the first thing to be
discussed in this matter is, whether the same bread and wine remain still after the
consecration, as sacraments of Christ s most precious body and blood. And next, by
order of nature and reason, is to be discussed, whether the body and blood of Christ,
[ 4 nothing herein, 1551.] I [ 6 which may therefore easily, 1"51.J
[ i. e. Lot. ]
50 THE FIRST BOOK OF THE SACRAMENT.
represented by those sacraments, be present also with the said sacraments: and
what manner of presence Christ hath, both in the sacraments, and in them that
But for what intent the bishop changed this order, it is easy to perceive. For
he saw the matter of transubstantiation so flat and plain against him, that it was
47. hard for him to devise an answer in that matter, that should have any appearance
of truth, but all the world should evidently see him clearly overthrown at the first
onset. Wherefore he thought, that although the matter of the real presence hath no
truth in it at all, yet forasmuch as it seemed to him to have some more appearance
of truth than the matter of transubstantiation hath, he thought best to begin with
that first, trusting so to juggle in the matter, and to dazzle the eyes of them that
be simple and ignorant, and specially of such as were already persuaded in the matter,
that they should not well see nor perceive his legerdemain. And when he had won credit
with them in that matter, by making them to wonder at his crafty juggling, then
thought he, it should be a fit and meet time for him to bring in the matter of
transubstantiation. For when men be amazed, they do wonder rather than
judge: and when they be muffled and blindfolded, they cannot find the
right way, though they seek it never so fast, nor yet follow it, if it
chance them to find it ; but give up clearly their own judgment,
and follow whomsoever they take to be their guide. And so
shall they lightly follow me in this matter of transubstan
tiation, (thought the bishop,) if I can first persuade
them and get their good wills in the real presence.
This sleight and subtlety thou mayest judge
certainly, good reader, to be the cause,
and none other, wherefore the order
of my book is changed with
out ground or reason.
The end of the first book.
51
THE
CONFUTATION OF THE THIRD BOOK.
[WINCHESTER.]
IN the begvmwng of tJte third book, the author hath thought good to note certain differences, 48.
/ " /// also particularly consider. It folio weth in him thus. o3g.^luL
" They teach that Christ is in the bread and wine : but we say, according to the truth, that 155 *-]
he is in them that worthily eat and drink the bread and wine."
Note here, reader, even in tlie entry of the comparison of these di/erences, how untruly r The answer,
tJie true faith of the church is reported, which doth not teach that Christ is in the bread ai t l Jrn tr uere-
wine (which was the doctrine of Luther) ; but tlie true faith is, that Ctirisfs most precious 1>ort
body and blood is, by the might of his word and determination of his will, which he declareth
by his word, in his holy supper present under form of bread and wine. Tlie substance of which
natures of bread and wine is converted into his most precious body and blood, as it is truly
believed and taught in the catholic church, of which teaching this author cannot be ignorant.
So as tlie author of this book reporteth an untruth wittingly against his conscience, to say they
teach (calling them papists) that Christ is in the bread and wine, but they agree in form of
teaching with that tlie church of England teacheth at this day, in the distribution of the holy The teach-
communion, in that it is there said, the body and blood of Christ to be under the form of e "en at thU
bread and wine. And thus much serveth for declaration of the wrong and untrue report church of
of tlie faith of tlie catholic church, made of this autlior in the setting forth of this difference JJreeth with
on that part, which it pleaseth him to name papists. jjj** ^g^
And now to speak of the otJier part of the difference on tlie author s side, when he would papists .
ell what lie and his say, lie convey eth a sense cra/tily in words to serve for a difference, such Crafty con-
as no catholic man would deny. For every catholic teacher granteth, that no man can receive speech by
worthily Christ s body 1 and blood in the sacrament, unless he hath by faith and charity Christ
Iwelling in him. For otherwise, such one as hath not Christ in him, receiveth Christ s body
n the sacrament unworthily, to his condemnation. Christ cannot be received worthily, but *Worthy re-
nto his own temple, which be ye, Saint Paul saith; and yet, he that hath not Christ s Spirit Christ s pre-
n him, is not his. As for calling it bread and wine, a catholic man forbeareth not that amfbiootL
name, signifying what those creatures were before tlie consecration in substance. Wherefore 1 Cor. vi.
appeareth, how tlie author of this book, in the lieu and place of a difference, which he pretendeth
would shew, bringeth in that under a "but", which every catholic man must needs confess,
hat Christ is in them who worthily eat and drink the sacrament of his body and blood, or tlie
rread and wine, as this author speaketh.
But as 2 this author would have spoken plainly, and compared truly the difference of the *A difference
wo teachings, he should in the second part have said somewhat contrary to that the catholic contraries
church teacheth, which lie doth not; and therefore as he sheweth untruth in the first report,
so he slieweth a sleight and shift in the declaration of the second part, to say that repugneth
not to the Jirst matter, and that no catJwlic man will deny, considering the said two teachings
>e not of one matter, nor shoot not, (as one might say,) to one mark. For tlie Jirst part is
of the substance of tlie sacrament to be received, wliere it is truth, Christ to be present, God
and man. The second part is of Christ s spiritual presence in the man that receiveth, which
indeed must be in him before he receive the sacrament, or he cannot receive the sacrament
worthilt/, as before* is said, which two parts may stand well without any repugnancy ; and
so both the differences thus taught make but one catholic doctrine. Let utao what tke cnUMor
saith further.
CANTERBURY.
Now the crafts, wiles, and untruths of the first book being partly detected, after
I have also answered to this book, I shall leave to the indifferent reader to judge 49.
whether it be of the same sort or no. But before I make further answer, I shall
[ l Christ s precious body, 1551. J [* But and this author, 1551. J f 3 Afore, 1551.]
52 THE THIRD BOOK.
rehearse the words of mine own third book, which you attempt next, out of order,
fBookiii.n to impugn. My words be these:
Chap. i.
Now this matter of transubstantiation being, as I trust, sufficiently resolved,
(which is the first part before rehearsed, wherein the papistical doctrine varieth
from the catholic truth,) order reqtiireth next to entreat of the second part, which
is of the manner of the presence of the body and blood of our Saviour Christ in
the sacrament thereof; wherein is no less contention than in the first part.
For a plain explication whereof, it is not unknown to all true faithful
Christian people, that our Saviour Christ, (being perfect God, and in all things
equal and coetcrnal with his Father,) for our sakes became also a perfect
man, taking flesh and blood of his blessed mother and virgin Mary, and,
saving sin, being in all things like unto us, adjoining unto his divinity a
most perfect soul [and a most perfect body : his soul being endued with
life, sense, will, reason, wisdom, memory, and all other things required to
the perfect soul 2 ] of man: and his body being made of very flesh and
bones, not only having all members of a perfect man s body, in due order
and proportion, but also being subject to hunger, thirst, labour, sweat, wea
riness, cold, heat, and all other like infirmities and passions of a man, and
unto death also, and that the most vile and painful upon the cross ; and
after his death he rose again, with the selfsame visible and palpable body, and
appeared therewith, and shewed the same unto his apostles, and especially
to Thomas, making him to put his hands into his side, and to feel his wounds.
And with the selfsame body he forsook this world, and ascended into heaven,
Christ cor-^ (the apostles seeing and beholding his body when it ascended,) and now sit-
eendedimo teth at the right hand of his Father, and there shall remain until the last
heaven. o
day, when he shah 1 come to judge the quick and dead.
This is the true catholic faith, which the scripture teacheth, and the
universal church of Christ hath ever believed from the beginning, until
within these four or five hundred years last passed, that the bishop of Rome,
with the assistance of his papists, hath set up a new faith and belief of
their own devising, that the same body, really, corporally, naturally, and
sensibly, is in this world still, and that in an hundred thousand places at
one time, being inclosed in every pix, and bread consecrated.
chap. n. And although we do affirm (according to God s word), that Christ is in
ah 1 persons that truly believe in him, in such sort, that with his flesh and
blood he doth spiritually nourish 3 and feed them, and giveth them everlasting
life, and doth assure them thereof, as well by the promise of his word, as
by the sacramental bread and wine in his holy supper, which he did insti-
The differ- tute for the same purpose ; yet we do not a little vary from the heinous
the true and errors of the papists. For they teach, that Christ is in the bread and wine ;
papistical x L
cemiig e tS n ~ but we ^J (according to the truth), that he is in them that worthily eat and
Here it pleaseth you to pass over all the rest of my sayings, and to answer only
The first com- to the difference between the papists and the true catholic faith. Where in the first 4
ye find fault that I have untruly reported the papistical faith, (which you call 5 the
faith of the church,) which teacheth not, say you 8 , that Christ is in the bread and
wine, but under the forms of bread and ,wine. But to answer you 7 , I say, that the
[ l In the original edition this is the heading of
the third book : " The third book teacheth the
manner how Christ is present in his supper."]
[ 2 This passage appears only in the edition,
I r i51, being entirely omitted in that of 1580.]
[ 3 Nourish them, and, 1551. ]
[ 4 Wherein first ye find, 1551.]
P He calleth, 1551.]
[ G Saith he, 1551.]
OF THE PRESENCE OF CHRIST. 53
papists do teach, that Christ is in the visible signs, and whether they list to call
them bread and wine, or the forms of bread and wine, all is one to me; for the truth
is, that he is neither corporally in the bread and wine, nor in or under the forms and
figures of them, but is corporally in heaven, and spiritually in his lively members, 50.
which IK- his temples where he inhabiteth. And what untrue report is this, when I Misrcport c.f
Speak of bread and wine to the papists, to speak of them in the same sense that the *|" for thi
papists mean, taking bread and wine for the forms and accidents of bread and wine ? %<|res f
And yourself also do teach, to understand by the bread and wine, not their sub
stances, but accidents. And what have I offended then, in speaking to you after
vour own manner of speech, which yourself doth approve- and allow by and by after,
saying these words? "As for calling it bread and wine, a catholic man forl>careth not
that name." If a catholic man forbeareth not that name, and catholic men be true
men, then true men forbear not that name. And why then charge you me with an
untruth, for using that name, which you use yourself, and affirm catholic men to use ;
but that you be given altogether to find faults rather in other, than to amend your
own, and to reprehend that in me, which you allow in yourself and other, and pur
posely will not understand my meaning, because ye would seek occasion to carp and
controul ?
For else what man is so simple that readeth my book, but he may know well,
that I mean not to charge you for affirming of Christ to be in the very bread and
wine ? For I know that you say, there is neither bread nor wine, (although you say
untruly therein ;) but yet forasmuch as the accidents of bread and wine you call bread
and wine, and say that in them is Christ, therefore I report of you, that you say
Christ is in the bread and wine, meaning, as you take bread and w r ine, the accidents
thereof.
Yet I). Smith was a more indifferent reader of my book than you in this place, Smyth.
who understood my words as I meant and as the papists use, and therefore would
not purposely calumniate and reprehend that was well spoken. But there is no man
so dull as he that will not understand. For men know that your wit is of as good
capacity as D. Smith s is, if your will agreed to the same.
But as for any untrue report made by me herein willingly against my conscience
(as you untruly report of me), by that time 8 I have joined with you throughout your
book, you shall right well perceive, I trust, that I have said nothing wittingly, but
that my conscience shall be able to defend at the great day, in the sight of the
overliving God, and that I am able before any learned and indifferent judges to
justify by holy scriptures, and the ancient doctors of Christ s church, as I will appeal
the consciences of all godly men, that be any thing indifferent, and ready to yield to
the truth, when they read and consider my book.
And as concerning the form of doctrine used in this church of England in the The IXK* of
holy communion, that the body and blood of Christ be under the forms of bread and prayer.
wine, when you shall shew the place where this form of words is expressed, then shall
yon purge yourself of that, which in the meantime I take to be a plain untruth.
Now for the second part of the difference, you grant that our doctrine is true, Thr second
that Christ is in them that worthily eat and drink the Ijrcad and wine ; and if it pa
differ not from yours, then let it pass as a thing agreed upon by both parties. And
yet if I would captiously gather of your words, I could as well prove by this second
part, that very bread and wine be eaten 9 and drunken after consecration, as you could
prove by the first, that Christ is in the very bread and wine. And if a catholic ol.
man call that bread and wine 10 , (as you say in the second part of the difference,) what
meant you then in the first part of this difference, to charge me with so heinous a
crime (with a note to the reader), as though I had sinned against the Holy Ghost,
because I said, " that the papists do teach that Christ is in the bread and wine ? " Do
not you affirm here yourself the same that I report ? that the papists (which you call
the catholics), do not forbear to call the sacrament, (wherein they put the real and
By that time that I have, l-ViI. ] p Ed. 15.il, omit* the words : eaten and ".J
[ ln Called bread and wine, lool.]
54
THE THIRD BOOK.
*The differ
ence.
Repugnan
ces.
52.
corporal presence,) bread and wine? Let the reader now judge, whether you be caught
in your own snare or no. But such is the success of them that study to wrangle
in words, without any respect of opening the truth.
But letting that matter pass, yet we vary from you in this difference. For we
say not, as you do, that the body of Christ is corporally, naturally, and carnally,
either in the bread and w r ine, or forms of bread and wine, or in them that eat and
drink thereof. But we say, that he is corporally in heaven only, and spiritually in
them that worthily eat and drink the bread and wine. But you make an article
of the faith, which the old church never believed nor heard of.
And where you note in this second part of the difference a sleight and craft, as
you note an untruth in the first ; even as much craft is in the one as untruth in the
other, being neither sleight nor untruth in either of both. But this sleight, say you,
I use, putting that for a difference, wherein is no difference at all, but every catholic
man must needs confess. Yet once again, there is no man so deaf as he that will
not hear, nor so blind as he that will not see, nor so dull as he that will not under
stand. But if you had indifferent ears, indifferent eyes, and indifferent judgment, you
might well gather of my words a plain and manifest difference, although it be not
in such terms as contenteth your mind. But because you shall see that I mean no
sleight nor craft, but go plainly to work, I shall set out the difference truly as I meant,
and in such your own tenns as I trust shall content 1 you, if it be possible. Let this
therefore be the difference.
They say that Christ is corporally under, or in the forms of bread and wine: we
say, that Christ is not there, neither corporally, nor spiritually; but in them that worthily
eat and drink the bread and wune, he is spiritually, and corporally in heaven 2 .
Here, I trust, I have satisfied, as well the untrue report wittingly made, as you
say, in the first part of the difference against my conscience, as the craft and sleight
used in the second part. But what be you eased now by this ? We say as the scripture
teacheth, that Christ is corporally ascended into heaven, and nevertheless he is so 3 in
them that worthily eat the bread and drink the wine, given and distributed at his
holy supper, that he 4 feedeth and nourisheth them with his flesh and blood unto eternal
life. But we say not (as you do, clearly without ground of scripture), that he is cor
porally under the forms of bread and wine, where his presence should be without
any profit or commodity, either to us, or to the bread and wine.
And here in this difference, it seemeth that you have either clearly forgotten, or
negligently overshot yourself, uttering that thing unawares which is contrary to your
whole book. For the first part (which is of the being of Christ in the sacramental
bread and wine,) is of the substance of the sacrament to be received, say you, where
it is true, Christ to be present God and man. The second part, say you, which is
of the being of Christ in them that worthily eat and drink the bread and wine, is
of Christ s spiritual presence. Of your which words 5 I see nothing to be gathered,
but that as concerning his substantial presence, Christ is received into the sacramental
bread and wine; and as for them that worthily receive the sacrament, he is in them
none otherwise than after a spiritual presence: for else why should ye say, that the
second part is of Christ s .spiritual presence, if it be as well of his corporal, as of his 6
spiritual presence? Wherefore, by your own words, this difference should be under-
standed of two different beings of Christ, that in the sacrament he is by his substance,
and in the worthy receivers spiritually, and not by his substance ; for else the differences
repugn not, as you object against me. Wherefore either you write one thing and
mean another, or else, as you write of other, God so blindeth the adversaries of the
truth, that in one place or other they confess the truth unawares.
Now follow my words in the second comparison.
[ 1 trust to content you, lfifl.]
[ - He is spiritually, but not corporally, 1551.]
( 3 Ed. 1551, entirely omits the words, corpo
rally ascended into heaven, and nevertheless he
is so."]
f 4 Ed. 1551, omits the words "that he ", and
, adds, " in whom he is not in vain but, ".]
[ 5 Of which your words, 1551.]
[ Ed. 1551, omits "of his."]
OF THE PRESENCE OF CHRIST. 55
They say, that when any man cateth the bread, and drinketh the cup, Thcwc-ond
* * comparison.
Christ goeth into his mouth or stomach with the bread and wine, and no
further. But we say, that Christ is in the whole man, both in body and
soul of him that worthily cateth the bread, and drinketh the cup, and not
in liis mouth or stomach only.
WINCHESTER.
I n this comparison, tlie author termeth the true catJiolic teaching at his pleasure, to bring
it in contempt : which doing in rude speech would be called otherwise than I will term it.
Truth it is, as St Augustine saith, we receive in tlie sacrament tlie body of Christ with our
month; and such speech otJier use, as a book set forth in the archbishop of < <>/</- //,/> ry s
na,me, called a Catechism, willeth children to be taught that they receive with their bodily mouth
tin 1 body and blood of Christ : which I allege, because it sliall appear it is a teaching set forth
among us of late, as hath been also, and is by the book of common prayer, being tlie most Imr
catholic doctrine of the substance of tJie sacrament, in that it is there so catholicfy spoken of:
which book this author doth after specially allow, Jwwsoever all the sum of his teaching doth
/i/>rove it in that point. So much is he contrary to himself in this work, and here in this
place, not caring what lie saith, reporteth such a teaching in the first part of this difference,
as I have not lieard of before. There was never man of learning that I have read termed the
matter so, that Christ goeth into the stomach of the man that received^, and no further. For
that is written contra Stercoranistas, is nothing to this teaching; nor the speech of any gloss, *A sect re-
if there be any such, were herein to be regarded. The catholic doctrine is, that by the holy wen called
communion in the sacrament we be joined to Christ really, because we receive in the holy supper
the most precious substance of his glorious body, which is a flesh giving life. And that is not
digested into our flesh, but worketh in us and attempereth by heavenly nurture our body and
soul, being partakers of his passion, to be conformable to his will, and by such spiritual food
to be made more spiritual. In the receiving of which food in tlie most blessed sacrament, our
body and soul, in them that duly communicate, work together in due order, without other dis
cussion of the mystery than God hath appointed; that is to say, the soul to believe as it is
taught, and the body to do as God hath ordered, knowing that glorious flesh by our eating
cannot be consumed or suffer, but to be most profitable unto such as do accustome worthily to
receive tlie same. But to say that the church teacheth how we receive Christ at our mouth,
and he goeth into our stomach and no further, is a report which by the just judgment of
God is suffered to come out of the mouth of tlicm tliat fight against the truth in this most
high mystery.
Now where this author in the second part, by an adversative with a "but" to make the
comparison, telleth what lie and his say, he telfeth in Affect that which every catholic manmust needs 53.
<nnl doth confess. For such as receive Christ s most precious body and blood in the sacrament
worthily, they have Christ dwelling in them, who comforteth both body and soul; which the
church hath ever taught most plainly. So as this comparison of difference in his two parties
is made of one open untruth, and a trulh dugwttd, <ts though it were now first opened.
by this author and his; which manner of handling dcclareth what sleight <i.nd shift is iised
in the matter.
CANTERBURY.
In the first part of this comparison I go not about to term the true catholic faith,
for the first part in all the comparisons is the papistical faith, which I have termed
none otherwise than T learned of their own terming ; and therefore if my terming please
you not (as indeed it ought to please no man), yet lay the blame in them that were
the authors and inventors of that terming, and not in me, that against them do u.-e
their own terms, terming the matter as they do themselves, because they should not
find fault with me, as you do, that I term their teaching at my pleasure.
And as for receiving of the body of Christ with our mouths, truth it is, that St
Augustine, Ambrose, Chrysostom, and other use such speeches, that we receive the
body of Christ with our mouths, sec him with our eyes, feel him with our hands,
Weak him and tear him with our teeth, eat him and digest him. (which speech I have
[ Rcceiveth, 1551.]
56
THE THIRD BOOK.
The book of
common
prayer.
That the pa
pists say, that
Christ goeth
no further
than the
mouth or
stomach.
Thomas Bo-
naventura.
folio 64.
Hugo. Inno-
centius 111.
*Lib. cap. 15.
54.
The second
part.
Innoccntius
111.
also used in my catechism ;) but yet these speeches must be understand figuratively, (as
I have declared in my fourth book, the eighth chapter, and shall more fully declare
hereafter,) for we do not these things to the very body of Christ, but to the bread
whereby his body is represented.
And yet the book of common prayer neither useth any such speech nor giveth
any such doctrine, nor I in no point improve that godly book, nor vary from it. But
yet glad am I to hear that the said book liketh you so well, as no man can mislike
it, that hath any godliness in him joined with knowledge.
But now to come to the very matter of this article : it is marvel that you never
read, that Christ goeth into the mouth or stomach of that man that receiveth, and
no further, being a lawyer, and seeing that it is written in the gloss of the law, De
consecrat. dist. 2. Trilus gradibm, in these words : " It is certain that as soon as the
forms be torn with the teeth, so soon the body of Christ is gone up into heaven 1 ."
And in the chapter, Non iste*, is another gloss to the same purpose. And if you had
read Thomas de Aquino and Bonaventure, great clerks and holy saints of the pope s
own making, and other school-authors, then should you have known what the papists
do say in this matter. For some say, that the body of Christ remaineth so long as
the form and fashion of bread remaineth, although it be in a dog, mouse, or in the
jakes. And some say, it is not in the mouse nor jakes, but remaineth only in the
person that eateth it, until it be digested in the stomach, and the form of bread be gone.
Some say, it remaineth no longer than the sacrament is in the eating, and may be
felt, seen, and tasted in the mouth.
And this, besides Hugo, saith pope Innocentius himself, who was the best learned
and the chief doer in this matter of all the other popes. Read you never none of these
authors, and yet take upon you the full knowledge of this matter? Will you take
upon you to defen d the papists, and know not what they say ? Or do you know it,
and now be ashamed of it, and for shame will deny it ?
And seeing that you teach, that " we receive the body of Christ with our mouths,"
I pray you, tell whether it go any further than the mouth or no ? and how far it goeth ?
that I may know your judgment herein : and so shall you be charged no further than
with your own saying, and the reader shall perceive what excellent knowledge you
have in this matter.
And where you say, "that to teach that we receive Christ at our mouth, and he
goeth into our stomach, and no further, cometh out of the mouth of them that fight
against the truth in this most high mystery:" here, like unto Caiphas, you prophesy
the truth unawares. For this doctrine cometh out of the mouth of none, but of the
papists, which fight against the holy catholic truth of the ancient fathers, saying, that
Christ tarrieth no longer than the proper forms of bread and wine remain, which cannot
remain after perfect digestion in the stomach.
And I say not that the church teacheth so, as you feign me to say, but that the
papists say so. Wherefore I should 3 wish you to report my words as I say, and not
as you imagine me to say, lest you hear again (as you have heard heretofore), of your
wonderful learning and practice in the devil s sophistry.
Now as concerning the second part of this comparison, here you grant that my
saying therein is true, and that every catholic man must needs, and doth confess the
same. By which your saying, you must also condemn almost all the school-authors
and lawyers, that have written of this matter, with Innocent the third also, as men
not catholic, because they teach that Christ goeth no further, nor tarrieth no longer,
than the forms of bread and wine go, and remain in their proper kind.
[! "Certum est, quod species quam cito dentibus
teruntur, tarn cito in ccelum rapitur corpus Christi."
Corpus Juris Canonici : Decreti tertia pars : "de
consecrat." Dist. n. " Tribus gradibus^ 1 col. 1922.
Lugduni, 1618.]
[ 2 " Hug. species tamen bene vadunt in corpus.
Sect nunquid ibi est sacramentum ? Non, quia desi-
nit ibi esse corpus Christi: et tandiu est ibi sacra
mentum, quandiu est corpus Christi, Sed quandiu
hoc sit, id est, usque ad quern locum procedat per
gulam, nescio. Sed licet non sit sacramentum, cum
est in corpore, si tamen evomerit illud, cum venera-
tione est servandum, quia sacramentum fait." Ib,
Dist. IT. " Non isle panis," col. 1942. Ib.J
[ 3 Would, 1551.]
OF THE PRESENCE OF CHRIST. .57
And yet now your doctrine, as far as I can gather of your obscure \vords, is this :
that Christ is received at the month, with the forms of bread and wine, and gocth
with them into the >t<>inach. And although they go no further in their proper kinds,
yet there Christ leaveth them, and goeth himself further into every part of the man s
body, and into his soul also: which your saying seenx-th to me to be very strange.
For I have many times heard, that a soul hath gone into a body, but I never heard
that a body went into a soul. But I ween, of all the papists you shall be alone in
this matter, and find never a fellow to say as you do.
And of these things which I have here spoken, I may conclude, that this com
parison of difference is not made of an open untruth and a truth disguised, except
you will confess the papistical doctrine to be an open untruth.
Now the words of my third comparison be these.
They say, that Cbrist is received in the mouth, and cntcrcth in with
the bread and wine. We say that he is received in the heart, and cntcrcth
in by faith.
WINCHESTER.
Here is a pretty sleight in this comparison, where both parts of tJie comparison may be
understandcd on both sides, and tJierefore Jiere is by tJie author in this comparison no issue
joined. For tJte worthy receiving of Christ s body and blood in the sacrament is both with
mouth and heart; both in fact and faith. After which sort, St Peter in the last supper
received Christ s body, whereas in the same 4 Judas received it with mouth and in fact only;
whereof St Augustine speaketh in this wise: Non dicunt ista, nisi qui de mensa Domini 55.
vitum summit, sicut Petrus, non judicium, sicut Judas, et tamen ipsa utrique fuit una, August. >n-
sed non utrique valuit ad unum, quia ipsi non erant unum 5 . Which words be thus much lib. 2.Wp. 47.
to say : " That they say not so, (as was before entreated), but such as receive life of our Lord s
table, as Peter did, not judgment, as Judas, and yet the table was all one to them both; but
it was not to all one e/ect in them both, because tliey were not one." Here St Augustine
mouth only, and Christ entering in mystery only, doth not sanctify us, but is the stone of
stumbling, and our judgment and condemnation ; but if he be received with mouth and body,
vrith heart and faith, to such he bringeth life and nourishment. Wlierefore in this comparison,
the author hath made no di/erence, but with divers terms the catholic teaching is divided into
two members, with a " but," fashioned nevertheless in another phrase of speech than tlie church
hath used, which is so common in this author, that I will not hereafter note it any more for
a fault. But let its go further 6 .
CANTERBURY.
There is nothing in this comparison worthy to be answered; for if you can find
no difference therein, yet every indifferent reader can. For when I report the papists whether
7 J / 1 Christ be rr-
teaching, that they say Christ is received in the mouth, and entereth in with the ceivcd in lhc
scriptures and ancient writers), say that he is received in the heart, and entereth
in by faith, every indifferent reader understandeth this adversative upon our side, that
we say Christ is not received in the mouth, but in the heart, specially seeing that
in my fourth book, the second and third chapters, I make purposely a process thereof,
to prove that Christ is not eaten with mouths and teeth. And yet to eschew all
such occasions of sleight as you impute unto me in this comparison, to make the
comparison more full and plain, let this be the comparison,
They say that Christ is received with the mouth, and entereth in with the bread
and wine: we say that he is not received with the mouth, but with heart, and en- ThedifTcr-
tereth in by faith. And now, I trust, there is no sleight in this comparison, nor both *"
the parts may not be understand on both sides, as you say tliev might before.
And as for St Augustine, serveth nothing for your purpose, to prove that Christ s Augiut em
body is eaten with the mouth. For he speaketh not one word in the place by you lib 2. cap. 47.
! 4 In the same supper, l.V.l.l [> August. Opern, Tom. VIII. p. !</. Ed. Paris. l
[ fi Let us o further, 1,").}!.]
58 THE THIRD BOOK.
alleged, neither of our mouths, nor of Christ s body. But it seemeth you have so
fervent desire l to be doing in this matter, that you be like to certain men, which have
such a fond delight in shooting, that so they be doing, they pass not how far they
shoot from the mark. For in this place of St Augustine against the Donatists, he
shooteth not at this butt 2 , whether Christ s very natural body be received with our
mouths, but whether the sacraments in general be received both of good and evil. And
there he declareth, that it is all one water, whether Simon Peter, or Simon Magus
be christened in it ; all one table of the Lord, and one cup, whether Peter sup thereat,
or Judas; all one oil, whether David or Saul were anointed therewith. Wherefore
u he concludeth thus : Memento ergo sacramentis Dei nihil obesse mores malorum hominum,
lib. 2. cap. 47. q uo Ufa vel omnino non sint, vel minus sancta sint, sed ipsis malis hominibiis, ut hcec
fore," saith St Augustine, "that the manners of evil men hinder not the sacraments
of God, that either they utterly be not, or be less holy; but they hinder the
56. evil men themselves, so that they have the sacraments to witness of their damna
tion, not to help of their salvation." And all the process spoken there by St Augustine
is spoken chiefly of baptism, against the Donatists, which said, that the baptism was
naught, if either the minister or the receiver were naught. Against whom St Augustine
concludeth, that the sacraments of themselves be holy, and be all one, whether the
minister or receiver be good or bad. But this place of St Augustine proveth as well
your purpose, that Christ s body is received by the mouth, as it proveth that Paul s
steeple is higher than the cross in Cheap 4 . For he speak eth not one word of any of 5
them all. And therefore in this place where you pretend to shoot at the butt, you
shoot quite at rovers 6 , and clean from the mark.
Johnxiii. And yet if Judas received Christ with the bread, as you say, and the devil en
tered with the bread, as St John saith, then was the devil and Christ in Judas both
i cor. x. at once. And then how they agreed I marvel : for St Paul saith, that Christ and
Belial cannot agree. ! what a wit had he need to have, that will wittingly maintain
an open error, directly against God and his word, and all holy ancient writers !
Now followeth the fourth comparison in my book.
The fourth They say, that Christ is really in the sacramental bread, bemp- reserved
comparison.
a whole year, or so long as the form of bread remaineth : but after the
receiving thereof he flicth up, say they, from the receiver unto heaven, as
soon as the bread is chewed in the mouth, or changed in the stomach :
but we say, that Christ remaineth in the man that worthily receiveth it,
so long as the man remaineth a member of Christ.
WINCHESTER.
This comparison is like the other before, whereof the first part is garnished and embossed
with untruth ; and the second part is that the church hath ever taught most truly., and that all
must believe : and therefore that piece hath no untruth in the matter., but in tJie manner only,
being spoken as though it differed from the continual open teaching of the church, which is not
*Pugnatcum so. Wherefore in the manner of it in utterance signifietli an untruth, which in the matter
itself is nevertheless most true. For undoubtedly Christ remaineth in the man that worthily
receiveth tlie sacrament, so long as the man remaineth a member of Christ. In this first part
there is a fault in tlie matter of the speech ; for explication whereof I will examine it particu
larly. This author saith, " they say, that Christ is really in tlie sacramental bread, being reserved
an whole year, c" The church giving faith to Christ 7 s word, when lie said, " This is my body,"
$c., teacheth the body of Christ to be present in the sacrament under the form of bread; unto which words wlien we put the word " really," it serveth only to express that truth in open *christisthe words, ivhich was before 1 to be understanded in sense. For in Christ, who was the body of all the figures, the shadows and figures of the law, and who did exhibit and give in his sacraments of the P Fervent a desire, 1551. J [ 2 Butt : i. e. a mark.] [ 3 August. Opera, Tom. VII. p. 107. Ed. Paris. 1535.] In the Cheap, 1551.] Of none of, 1551.] [ fi At rovers: i.e. at random.] [ 7 Afore, 1551.] OF THE PRESENCE OF CHRIST. 59 new law tlie things promised in his sacraments of tlie old law, we must understand his words in the institution of his sacraments without figure, in tlie substance of the celestial thing of them : and tlierefore wlten he ordered his most precious body and blood to be eaten and drunken of us, under the forms of bread and wine ; we profess and believe, that truly he gave us his most precious body in the sacrament for a celestial food, to comfort and strengthen us in this miserable life. And for certainty of tlw truth of his work therein, we profess lie giveth us his body real/y, that is to say, in deed his body, the thing itself, which is the heavenly part of the * Really, that sacrament, called Eucliaristia : hni lnif tin- r/.s/7,/V form of bread and wine, and containing is> m invisibly tlie very body and blood of our Saviour Christ, which was not wont to be reserved otherwise, but to be ready for such as in danger of death call for it, and tlie same, so long as it may be used, is still tlie same sacrament, which only time altereth not. Whereof Cyril wrote 57. t<> this sense many hundred years past, and Hesychius also, and what ought to be done wlien Cyriiiusad by negligence of the minister it were reserved overlong. Marry, wJiere it liketh the author o/"episcopum. these differences, to say the church teacheth, Clirist to flee up from the receiver unto heaven, hffiSSu so soon as the bread is cJiewed in tlie mouth, or changed in the stomach, this manner of speech implieth as tliough Christ left the seat of his majesty in lieaven, to be present in the sacrament, which is most untrue. The church acknowledged, believeth, and teacheth truly, that Christ "Christ being sitteth on the right hand of his Father in glory, from whence he shall come to judge tlie world; sac-ramem, is and also teacheth Christ s very body and blood, and Clirist himself God and man, to be present time present in tlie sacrament, not by shifting of place, but by the determination of his will, declared in m scriptures, and believed of the catholic church ; which articles be to reason impossible, but possible to God omnipotent: so as being taught of his will, we should humbly submit all our senses and reason to the faith of his will and work declared in his scriptures. In tlie belief of which mysteries is great benefit and consolation, and in the unreverent search and curious discussion of tJiem, presumptuous boldness and wicked temerity. I know by ft it I/ Clirist to be present, but the particularity how lie is present, more than I am assured he is truly present, and tlierefore in substance present, I cannot tell; but present he is, and truly is, and verily is, and so in deed, that is to say, really is, and unfeignedly is, and therefore in substance is, and, as we term it, substantially is present. For all these adverbs, really, substantially, *Truiv. with the rest, be contained in the one word "is," spoken out of his mouth, that speaketh as *STbstanti- lie meaneth, truly and certainly, as Christ did, saying : " This is my body that shall be ally betrayed for you;" who then carried himself in his hands after a certain manner, as St Atinstine saith, which never man besides him could do, who in that his last supper gave himself Aupustin. to be eaten witltout consuming. Tlie ways and means whereof no man can tell, but humble spirits, as they be taught, must constantly believe it, without thinking or talking of flying, of stying s of Christ again unto heaven, where Christ is in the glory of his Father continually, and is nevertheless, because he will so be, present in tlie sacrament, wliole God and man, and dwell eth corporally in him that receiveth him worthily. Wherefore, reader, when thou shalt again well consider this comparison, thou shalt find * What is found in a true, how tlie first part is disguised with untrue report of the common teaching of the church, blind gloss, howsoever some gloss or some private teacher might speak of it; and the second part, such taken for the as hath been ever so taught. One thing I think good to admonish the reader, that whatsoever th^Jffih, I affirm, or precisely deny, I mean within tlie compass of my knowledge ; which I speak neverread of not because I am in any suspicion or doubt of that I affirm, or deny, but to avoid tlie Jh"if in man temerity of denying as " never," or affirming as " ever," which be extremities. And I mean S also of public doctrine by consent received, so taught, and believed, and not that any one ties man might blindly write, as uttering his fancy, as this author doth for his pleasure. TJiere l he V * t . ru ^ . _ j *or it makrtn followeth in the, author thus. him suspect of presump tion. CANTERBURY. Because this comparison, as you say, is like the other, therefore it is fully an- HOW long swered before in the other comparisons. And here yet again it is to be noted, that in all these four comparisons you approve and allow for truth the second part of the comparison which we say. And where you say that Christ undoubtedly remaineth in the man that worthily receiveth the sacrament, so long as that man remaineth a member of Christ: how agrceth this with the common saying of all the papists, that Christ is contained under the forms of bread and wine, and remaineth there no longer ["Stying: i.e. soaring, ascending.] ft) THE THIRD BOOK. than the forms of bread and wine remain? Wherefore in this point all the whole rout of the papists will condemn for untruth that w T hich you so constantly affirm to be undoubtedly true. 58. And when the papists teach, that the body of Christ is really in the sacrament under the form of bread, they speak not this, giving faith to Christ his words, as you say .they do, for Christ never spake any such w r ords ; and as for this saying of Metonymia. Christ, " This is my body," it is a figurative speech, called metonymia, when one thing is called by the name of another which it signifieth, and it hath no such sense as you pretend ; for there is a great diversity between these two sayings, " This is my body," and " the body of Christ is really in the sacrament under the form of bread." But the papists have set Christ s words upon the tenters 1 , and stretched them out so far, that they make his words to signify as pleaseth them, not as he meant. The fathers in And this is a marvellous doctrine of you, to say that Christ was the body of received the all the shadows and figures of the law, and did exhibit and give in his sacraments in their sacra- of the new law the things promised in the sacraments of the old law. For he is iij in ours, the body of all the figures, as well of the new law as of the old ; and did exhibit and give his promises in the sacraments of the old law, as he doth now in the sacraments of the new law. And we must understand the words spoken in the in stitution of the sacraments in both the laws, figuratively, as concerning the sacraments, and without figure, as concerning the things by them promised, signified, and exhibited : as in circumcision was given the same thing to them that is given to us in baptism, and the same by manna that we have at the Lord s table. Only this difference was between them and us, that our redemption by Christ s death and passion was then only promised, and now it is performed and past. And as their sacraments were figures of his death to come, so be our 2 figures of the same now past and gone. And yet it was all but one Christ to them and us 3 ; who gave life, comfort, and strength to them by his death to come, and giveth the same to us by his death passed. And he was in their sacraments spiritually and effectually present, and for so much truly and really present, that is to say, in deed, before he was born, no less than he is now in our sacraments present after his death and ascension into heaven. But as for carnal presence, he was to them not yet come: and to us he is come, and gone again unto his Father, from whom he came. Reservation. ^nd as f or the reservation of the sacrament, neither Cyril nor Hesychius speak Hesychius. an y W0 rd what ought to be done with the sacrament, when by negligence of the minister it were reserved over long. But Hesychius sheweth plainly, that nothing ought to be reserved, but to be burned whatsoever remained. And as for the " flying of Christ up into heaven, so soon as the bread is chewed in the mouth, or changed in the stomach," I say not that the church teacheth so, but that papists say so; which forasmuch as you say that it liketh me to report this most j)e consccrat. untruly, read what the gloss saith upon the chapter, Tribus gradibus, de Consecrat. /fribusgra- dlst. 2, and there you shall find these words : Certum cst, quod species quam cito dentibus teruntur, tarn cito in ccclum rapitur corpus Ckristi 4 . And if this gloss be false and erroneous, why was it published and set out by the authority of the papists ? Why hath it been written and printed in so many countries, and so many years without reproof, or any fault found therein by any man ? 59. But here may wise men learn to beware of your doctrine. For you reprove those papists which have written of this matter four or five hundred years past, and do invent a new device of your own. And therefore wise men, when they see you teach one doctrine, and the papists that were before your time teach another, they will believe none of you all. The benefit And where you say, that in the belief of this mystery is great benefit and con- fn tim JacvL solation : what benefit, I beseech you, is it to us, if Christ be really and corporally in the forms of bread and wine a month or two, or a year or two ? And if we receive him really and corporally with the bread and wine into our mouths or stomachs, [ Upon the tenters ; i.e. upon the stretch.] fa And to us, 1551.] [ e Ours, 1051.] [4 Vide supra, p. 50.] OF TIIK PRESENCE OF CHRIST. (il and no further, and there he tarrieth not in that sort, but departcth away from us by and by again, what great benefit or comfort, I pray you, is such a corporal presence unto us ? And yet this is the teaching of all the papists, although you seem to vary from them in this last point, of Christ s sudden departure. But when the matter shall bo throughly answered, I ween you will agree with the rest of the papists, that as concerning his carnal presence, Christ departeth from us, at the least when the forms of bread and wine be altered in the stomach. And then, I pray you, declare what comfort and benefit we have by this carnal presence, which by and by is absent, and tarrieth not with us ? Such comfort have weak and sick consciences at the papists hands, to tell them that Christ was with them, and now he is gone" from them. Nevertheless, in the belief of this mystery, (if it be understanded according to God s word,) is great benefit and consolation ; but to believe your addition unto God s word, is neither benefit nor wisdom. And I pray you, shew in what place the scripture saith, "that under the forms of bread and wine is the body of Christ, really, corporally, and naturally;" or else ac knowledge them to be your own addition, beside" God s word, and your stout assertion herein to be but presumptuous boldness and wicked temerity, affirming so arrogantly that thing, for the which you have no 7 authority of God s word. And where you seem to be offended with the discussion of this matter, what hurt, I pray you, can gold catch in the fire, or truth with discussing? Lies only fear dis cussing. The devil hateth the light, because he hath been a liar from the beginning, and is loth that his lies should come to light and trial. And all hypocrites and papists be of a like sort afraid, that their doctrine should come to discussing, whereby it may evidently appear that they be endued with the spirit of error and lying. If the papists had not feared that their doctrines should have been espied, and their opinions have come to discussing, the scriptures of God had been in the vulgar and English tongue many years ago. But, God be praised ! at the length your doctrine is come to discussing, so that you cannot so craftily walk in a cloud, but the light of God s word will always shew where you be. Our Saviour Christ, in the fifth of John, willeth us to search John \. the scriptures, and to try out the truth by them. And shall not we then with humble reverence search the truth in Christ s sacraments ? And if we cannot 8 tell how Christ is present, why do you then say, "that he is The manner substantially present, corporally present, naturally and carnally present?" And how sure be you, that Christ is in substance present, because he is truly present ? Are you assured that this your doctrine agreeth with God s word ? Doth 00. not God s word teach a true presence of Christ in spirit, where he is not present in his corporal substance ? As when he saith : " Where two or three be gathered Matt, xviii. together in my name, there am I in the midst of them." And also when he saith : "I shall be with you till 9 the end of the world." Was it not a true presence that Matt xxviii. Christ in these places promised? And yet can you not of this true presence gather such a corporal presence of the substance of Christ s manhood, as you unlearnedly, contrary to the scriptures, go about to prove in the sacrament. For when Christ said, "This is my body," it was bread, which is called 10 his body in a figurative speech, as all old authors 11 teach, and as I have proved in my third book, the eighth and eleventh chapters. And the manner how Christ carried himself in his own hands, St Augustine declareth it to be figuratively. And because you can find no repugnance between the two parts of this comparison, to make them more plain, I shall fill them up with more words, as I did the other comparisons before. This, therefore, shall be the comparison. They say, that Christ is really and corporally in the sacramental bread being re- The compari- served, so long as the form of bread remaineth, although it be an whole year and R0: more: but after the receiving thereof, he flieth up from the receiver into heaven, as soon as the bread is chewed in the mouth or digested in the stomach. But we say, [ 5 And now is gone, 1551.] [ 6 Besides, 1551.] [~ None, 1551.] [" And if vou cannot, 1551. [9 Until, 1551.] [> NVhich he called, 1551.] [" As all the old authors, 1551.] 62 THE THIRD BOOK. that after what manner Christ is received of us, in the same wise he remaineth in us, so long as we remain the members of Christ. And where in the end you admonish the reader, that whatsoever you affirm or precisely deny, you mean within the compass of your knowledge, and of public doctrine, and of doctrine by consent received : what do you here else, but devise cer tain sleights, and prepare for yourself privy holes to start out at, whensoever you should be taken with a manifest lie? So that you should not be compelled to abide by any word that you say. For by these crafty sleights and shifts, of the compass of your knowledge, and of public doctrine, and of doctrine by common consent received, you mean to say ever what you list. And though never so manifest a lie or untruth be laid to your charge, yet shall no man never be able to prove it so manifestly against you, but you shall have one of these three shifts to flee out at for your defence. Now followeth in my book the fifth comparison. They say, that in the sacrament the corporal members of Christ be not distant in place one from another, but that wheresoever the head is, there be the feet ; and wheresoever the arms be, there be the legs : so that in every part of the bread and wine is altogether whole head, whole feet, whole flesh, whole blood, whole heart, whole lungs, whole breast, whole back, and altogether whole, confused and mixed without distinction or diver sity. what a foolish and an abominable invention is this, to make of the most pure and perfect body of Christ such a confuse and monstrous body ! And yet can the papists imagine nothing so foolish, but all Christian people must receive the same as an oracle of God, and as a most certain article of their faith, without whispering to the contrary. 61. WINCHESTER. This is a marvellous rhetoric, and such as the author hath overseen himself in the utterance of it, and confesseth himself prettily abused, to the latter end of his years to have believed that he now calleth so foolish. But to the purpose. In the book of common prayer, now at this time set forth in this realm, " It is ordered to teach the people, that in each part of the bread consecrate, broken, is the whole body of our Saviour Christ, which is agreeable to the catholic doctrine." Upon occasion hereof, it liketh this author to multiply language by enumeration of parts ; and because reason without faith directeth the bodily eye to so little a visible quantity in the host, this author beareth in hand the catholic church to say and teach all that fond reason deviseth ; whereas the church in the doctrine of this mystery, denieth all that reason without faith deviseth : and therefore when we acknowledge by faith Christ s body present, although we say it is present truly, really, substantially, yet we say, our senses be not privy to that presence, or 1 the manner of it, but by instruction of faith ; and therefore we say Christ s body to be not locally present, not by manner of quantity, but invisible 2 , and in no sensible manner, but marvellously in a sacrament and mystery truly, and in such a spiritual manner as we cannot define and determine, and yet by faith we know his body present, the parts of which be in themselves distinct one from another, in their own substance, but not by circumscription of several places to be comprehended of our capacity ; which parts we can by no demonstration 3 place, nor by imagination displace, diminish, alter, or confound, as this author for his pleasure reporteth, who writeth monstrously in so high a mystery, and impu- Pugnatcum dently beareth in hand the catholic church to teach that he listeth to bear in hand, may by wanton reason be deduced of the teaching*; whereas all true Christian men believe simply Christ s words, and trouble not their heads with such consequences as seem to strive with reason. This is in tlie author no whispering, but plainly railing, wherein if he had remem bered himself well, he would not have spoken of all Christian men in the receipt of that he intendeth to disprove. And if he would say he spake it by an irony or scorn, yet it im- plieth that all had received that he thus mocketh, ivhich, after the sort he writeth, was never liis papistis. f 1 Nor, 1551.] [ 2 Invisibly, 1551.] [ 3 We cannot by demonstration, 1551.] [ 4 The original copy of Winchester s book reads, "of their teaching."] OF THE PRESENCE OF CHRIST. 63 devised by papist or other to be so taught, otherwise than as this author might read it, as an idle argument, to shew absurdity in reason. For in God s works, as tJie sacraments be, \vhat is re- we must think all seemliness in deed without deformity, even as we believe all God s judg- Christian nen ments just and true, altliough reason conclude in them evident iniquity. Mans reason, when ^SiSSf it seemeth most gallant, is fall of spots and folly. God s works be all seemliness, without l"^ in confusion, monster, or any such absurdity, as this author suppost th. Although I cannot in the sacraim-nt with the eye of my reason locally distinct Christ s liead from his foot, his /r /.s / ,<>, a //is arm. And where in the book of common prayer it is truly said, in each part <;/ (he bread consecrate broken to be Christ s whole body, if one of curiosity would question with me, and I of folly would answer him, first, where is Christ s head ? I should say, here, pointing with my finger, he would think it first, a little Jtead. Then he would ask, * I( ; is _ a _ foll y where is his foot ? and I should say there, and point in the same place again, for there is curious Ue- no,n other left. If he replied, that I pointed before the same for the head, might not the third, a catholic man, that stood by, trow you, wisely call us both mad, to go about to discuss that we must grant we see not; and when by faith we know only the being present of Christ s most precious body, then by blind reason to discuss tlie manner of being in the sit nn (ion of such parts as we do not see? Now if there came among us a fourth man as a mediator, and would do as king Alexander did, when he could not open the knot ofQ"" } ! n * Gordius, he did cut it with his sword, if this man should say, I will relieve this matter. *iaketh You, believe Christ s body is present indeed, really and substantially. Leave out "really and this faith of substantially," and say his body is present in signification, and then it may be easily conceived, Faith of God by reason, that Christ s body, being never so great, may be as well signified by a little piece of bread, cannot, by as by a great piece of bread: even as a man may write a great man s name, as well in small haveariy 14 * letters sliort, as in great letters at length. And to commend further his device unto us, would ^ ualification - percase 5 tell how many absurdities, as he thinketh, and inconveniences might be avoided by it. This fourth man I speak of, making himself a mediator, but in deed unmeet therefore, because In /Kith no participation with faith; yet if our religion and faith were man s invention, as that of Numa Pompilius was, he should not utter this his conceit all idly. For he speaketh of a 62. jolly easy way, without any mystery or marvel at all. But our faith is of Jiearing, as hath been preached continually from the beginning, grounded upon the most sure truth of the word of God, and tJierefore cannot be attempered as man would devise it, to exclude travail in carnal reason. For then ths Sabellians were to be hearkened unto, who by their heresy Sabeiiians. took away all the hard and difficile 6 questions in the mystery of tlie Trinity. The Arians also relieved much man s reason in consideration of Christ s death, denying Arians. him to be of the same substance with his Fatter, which was a pestilent heresy. Now in the sacrament to say, Christ s body is present only by signification, as it relieveth in some men s judgments the absurdities in reason, which ought not to be relieved, so it condemneth all the true public faith, testified in the church from the beginning hitherto, and sheweth the learned hly men to have wondered in their writings at that xuhich hath no wonder at all, to ordain one thing to be tlie signification of another, which is practised daily among men. But from the beginning the mystery of the sacrament hath been with wonder marvelled at, how Christ made bread hit body, and wine his blood, and under the figure of those visible creatures gave invisibly his precious body and blood presently there. And as he gave, saith St Bernard , JKT cam. ser. liis life for us, so he gave his fiesh to us, in that mystery to redeem us, in this to feed us. 31 Which doings of Christ we must understand to have been perfected, not in an imagination of i figure and signification, but really in very deed, truly and unfeignedly; not because we be lieve it so, but because he wrought it so; whose works we must believe to be most perfectly true, according to the truth of tJie letter, where no absurdity in scripture driveth us from it, howsoever it seem repugnant to our reason, be we never so wise and witty ; which man s reason noii -a-days inflamed with fury of language, is the only adversary against the most blessed t. /.<? // iti i i <n>i^<i,- by //><w Comparisons of differences throughly^ considered. CANTERBURY. Did not you believe, I pray you, many years together, that the bishop of Rome s Christ s vicar, and the head of his church ( s Percase : i.e. perchance, perhaps.] I ipse pascua est, ipse redemptio." Bernardus, su- ; fi Difficile: i.e. difficult.] I per Cant. Serm.xxxi. col.filU. Lutet. Paris. 1WO.] [ 7 " Animam pro illis, carnem illis. Illam in [ R Thoroughly, 1551.] pretium, istam in cibum. Res mira : ipse pastor, 64 THE THIRD BOOK. 1 Tim. i. 63. The book of common prayer. say e that sts bread. Thomas, 3. part. sum. q. 70 . art. 3. innocentius cap. 8. If you did not, you wittingly and willingly defended a false error in the open parliament. But sithens that time, you have called that belief, as it is indeed, very foolish. And if you confessed your ignorance in that matter, be no more abashed to confess it in this, if you have respect more unto God s truth, than to your own estimation. It is lawful and commendable for a man to learn from time to time, and to go from his ignorance, that he may receive and embrace the truth. And as for me, I am not, I grant, of that nature that the papists for the most part be, who study to devise all shameful shifts, rather than they will forsake any error wherewith they were infected in youth. I am glad to acknowledge my former ignorance (as St Paul, St Cyprian, St Augustine, and many other holy men did, who now be with Christ), to bring other to the knowledge of the truth, of whose ignorance I have much ruth 1 and pity. I am content to give place to God s word, that the victory may be Christ s. What a member had the church of God lost, if Paul would have been as froward as some papists be, that will stick to their error tooth and nail, though the scripture and ancient writers be never so plain and flat against them ! Although St Paul erred, yet because his error was not wilful, but of ignorance, so that he gave place to the truth when it was opened unto him, he became of a most cruel persecutor a most fervent setter forth of the truth, and apostle of Christ. And would God I were as sure that you be changed indeed in those matters of religion, wherein with the alteration of this realm you pretend a change, as I am glad even from the bottom of my heart, that it hath pleased Almighty God, in this latter end of my years, to give me knowledge of my former error, and a will to embrace the truth, setting apart all manner of worldly respects, which be special hinderances, that hold back many from the free profession of Christ and his word. And as for the book of common prayer, although it say, that in each part of the bread broken is received the whole body of Christ, yet it saith not so of the parts unbroken, nor yet of the parts or whole reserved, as the papists teach. But as in baptism we receive the Holy Ghost, and put Christ upon us, as well if we be christened in one dish full of water taken out of the font, as if we were christened in the whole font or river ; so we be as truly fed, refreshed, and comforted by Christ, receiving a piece of bread at the Lord s holy table, as if we did eat an whole loaf. For as in every part of the water in baptism is whole Christ and the Holy Spirit, sacramentally, so be they in every part of the bread broken, but not corporally and naturally, as the papists teach. And I bear not the catholic church in hand, as you report of me, that it saith and teacheth that whole Christ is in every part of the bread consecrated, but I say that the papists so teach. And because you deny it, read the chief pillars of the papists, Duns, and Thomas de Aquino, which the papists call St Thomas ; who say, that Christ is whole under every part of the forms of bread and wine, not only when the host is broken, but when it is whole also. "And there is no distance," saith he, "of parts one from another, as of one eye from another, or of the eye from the ear, or the head from the feet." These be Thomas s words : Christus totus est sub qualibet parte specierum panis et mni, non solum cum frangitur hostia, sed etiam cum integra manet. Nee est distantia partium ab invicem, ut oculi ab oculo, aut oculi ab aure, aut capitis a pedibus, sicut esl in aliis corporibus organicis. Talis enim distantia est in ipso corpore Christi vero, sed non prout est in hoc sacramento* . And not only the papists do thus write and teach, but the pope himself, Innocentius the f 1 Ruth: i.e. sorrow.] [ 2 CONCLTJSIO Cum corpus Christi sit in hoc Sacramento eo modo quo substantia est sub dimen- sionibus, manifestum est, totum Christum sub qua- libet parte specierum panis aut vim contineri, sive frangatur hostia, sive integra remaneat Et ideo manifestum est, quod totus Christus est sub qua- libet parte specierum panis, etiam hostia integra manente, et non solum cum frangitur Et ideo quia conversio substantiae panis directe terminatur ad substantiam corporis Christi, secundum cujus modum proprie et directe est in hoc Sacramento corpus Christi, talis distantia partium est quidem in ipso corpore Christi vero : sed non secundum hanc distantiam comparatur ad hoc sacramentum, sed secundum modum suae substantiae. Thos. Aquinas, Tertia pars. Quzest. Ixxvi. Art. iii. p. 190. Ed. Antwerp. 1624.] OF TI1K I HKSKNCK OF CHRIST. f>5 third. And so bear I in hand, or report of the papists nothing but that which they say indeed. And yet you say, the church saith not so; which I affirm also: and then it must needs follow, that the doctrine of the papists is not the doctrine of the church. Which papists, not by reason without faith, but against as well reason as faith, would direct our minds to seek in every little crumb of bread, whole Christ, and to find him in so many places there, as be small crumbs in the bread. And where you traverse the matter of the judgment of our senses herein, it is quite and clean from the matter, and but a crafty shift, to convey the matter to another thing that is not in question ; like unto crafty malefactors, which perceiving them selves to be sore pursued with a hound, make a new train to draw the hound to another fresh suit. For I speak not of the judgment of our senses in this matter, whether they perceive any distinction of parts and members or no; but whether in deed there be any such distinction in the sacrament or no, which the papists do deny. And therefore I say not untruly of them, that in the sacrament they say, "There is no distance of parts, one from another." And if the parts in their substance be distinct one from another, as you say, and be not so distinct in the sacrament, as Thomas saith, then must it follow that the 04. parts in their own substance be not in the sacrament. And if this distinction of parts be in the true body of Christ, and not in the sacrament, as Thomas saith, then fol- loweth it again, that the true body of Christ is not in the sacrament. And forasmuch as I speak not one word of the comprehension of our senses, to A subtil what purpose do you bring this in, if it be not to draw us to a new matter, to S avoid that which is in controversy ? You do herein as if James should buy of John a parcel of land, and by his attorney take state and possession therein; and after, John should traverse the matter, and say that there w T as never no state delivered, and thereupon join their issue; and when James should bring forth his witnesses for the state and possession, then should John run to a new matter, and say that James saw the 3 possession delivered : what were this allegation of John to the pur pose of the thing that was in issue, whether the possession were delivered indeed or no ? "Were this any other thing than to avoid the issue craftily by bringing in a new matter 4 ? And yet this shift is a common practice of you in this book, and this is another point of the devil s sophistry, wherein it is pity that ever such a wit as you have should be occupied. Again you say, that impudently I bear the catholic church in hand, to teach wanton that I list to bear in hand may by wanton reason be deduced of their teaching, whereas all true Christian men believe simply Christ s words, and trouble not their heads with such consequences. " This is in the author no whispering, but plain railing," say you. This is your barking eloquence, wherewith your book is well furnished : for as dogs bark at the moon without any cause, so do you in this place. For I do no more but truly report what the papists themselves do write, and no 5 otherwise; not bearing the catholic church in hand that it so teacheth, but charging the papists that they so teach ; not bearing the papists in hand what I list, or what by wanton reason may be deduced of their teaching, but reporting only what their own words and sayings be. And if they be no true Christian men that trouble their heads with such matters, Tnieeh as you affirm they be not, then was Innocent the third, the chief author of your doctrine both of transubstantiation and of the real presence, no true Christian man, as I believe well enough : then was your St Thomas no true Christian man : then Gabriel, Duns, Durand, and the great rabblement of the school-authors, which taught your doctrine of transubstantiation and of the real presence, were not true Christian men. And in few words to comprehend the whole, then were almost 8 none that taught that doctrine true Christian men, but yourself alone. For almost all with one consent do teach, that whole Christ is really in every part of the host. [ s Saw not, 1551.] [ 5 None otherwise, 1551.] [ 4 Of a new matter, 1551.] [" Then was almost, 15,51.] 06 THE THIRD BOOK. But your terms here of railing, mocking, and scorning, I would have taken patiently at your hand, if your tongue and pen had not overshot themselves in bragging so far, that the truth by you should be defaced. But now I shall be so bold as to send those terms thither, from whence they came. And for the matter itself, I am ready to join an issue with you, notwithstanding all your stout and boasting words. "But in God s works," say you, "as the sacraments be, we must think all seem- liness indeed without deformity." But what seemliness is this in a man s body, that 6-> the head is where the feet be, and the anus where the legs be ? which the papists do teach, and yourself seem to confess, when you say, that the parts of Christ s body be distinct in themselves, one from another in their own substance, but not by cir cumscription of several places. And yet you seem again to deny the same in your wise dialogue, or quadrilogue, between the curious questioner, the foolish answerer, your wise catholic man standing by, and the mediator. A dialogue. In which dialogue you bring in your wise catholic man to condemn of madness all such as say, that Christ s head is there where his feet be ; and so you condemn of madness not only all the scholastical doctors, which say that Christ is whole in every part of the consecrated bread, but also your own former saying, where you deny the distinction of the parts of Christ s body in several places. Wherefore the mediator seemeth wiser than you all, who, loosing this knot of Gordius, saith, that " Christ s body, (how big soever it be,) may be as well signified by a little piece of bread as by a great :" and so, as concerning the reason of a sacrament, all is one, whether it be an whole bread, or a piece of it, as it skilleth not whether a man be christened in the whole font, or in a part of the water taken out thereof. For the respect and consideration of the sacrament is all one in the less and more 1 . But this fourth man, say you, hath no participation with faith, condemning all the true public faith testified in the church from the beginning hitherto, which hath ever with wonder marvelled at the mystery of the sacrament, which is no wonder at all, if bread be but a signification of Christ s body. This is a wonderful saying of what is to be you, as of one that understood nothing utterly what a sacrament meaneth, and what ra- is to be wondered at in the sacrament. For the wonder is, not how God worketh in the outward visible sacrament, but his marvellous work is in the worthy receivers of the sacraments. The wonderful work of God is not in the water, which only washeth the body; but God by his omnipotent power worketh wonderfully in the receivers thereof, scouring, washing, and making them clean inwardly, and, as it were, new men and celestial creatures. This have all old authors wondered at ; this wonder passeth the capacities of all men s wits, how damnation is turned into salvation, and of the son of the devil condemned into hell is made the son of God and inheritor of heaven. This wonderful work of God all men may marvel and wonder at, but no creature is able sufficiently to comprehend it. And as this is wondered at in the sacrament of baptism, how he that was subject unto death receiveth life by Christ and his holy Spirit : so is this wondered at in the sacrament of Christ s holy table, how the same life is continued and endureth for ever by continual feeding upon Christ s fiesh and his blood. And these wonderful works of God towards us we be taught by God s holy word, and his sacraments of bread, wine, and water ; and yet be not these wonderful works of God in the sacraments, but in us. And although many authors use this manner of speech, that Christ maketh bread his body, and wine his blood, and wonder thereat; yet those authors mean not of the bread and wine in themselves, but of the bread and wine eaten and drunken of faithful people. For when Christ called bread his body, and wine his blood, he spake 6G. not those words to the bread and wine, but to the eaters and drinkers of them, saying, " Eat, this is my body ; drink, this is my blood :" signifying to them that worthily do eat that bread and drink that cup, that they be inwardly and invisibly fed with Christ s flesh and blood, as they outwardly and visibly receive the sacraments of them. To be short, here in this process you use plenty of words at your pleasure, to make the reader believe that I should suppose confusion, monstrousness, absurdity, [ The less and the more, 1551.] OF THE PRESENCE OF CHRIST. G7 and unseemliness to be in God s holy sacraments, where as I do no more but tell what monstrous absurdities and errors the papists do teach in the sacraments. But if the reader take good heed to your talk, he shall find that you, lacking good matter to answer this comparison, do fall unto railing, and enforce your pen to invent such stuff as might bring me into hatred undeserved ; which kind of rhetoric is called Canina facundia, and is used only of them that hunt for their own praise by the dispraise of their adversary, which is yet another trick of the devil s sophistry. And because you would bring me into more extreme hatred, you couple me with Sab?iiiug. Salx llius and Arrius, whose doctrines, as you say, were facile and easy, as here you confess mine for to be. But if all such expositions as make the scriptures plain should by and by be slanderously compared to the doctrines of Arrius and Sabellius, then, should all the expositions of the doctors be brought in danger, because that by their pains they have made hard questions facile and easy. And yet, whether the doctrine which I set forth be easy to understand or not, I cannot define, but it seemeth so hard that you cannot understand it; except you will put all the fault in your own wilfulness, that you can, and will not understand it. Now followcth the sixth comparison. Furthermore, the papists say, that a dog or a cat eateth 2 the body of Christ, if they by chance do eat the sacramental bread. We say, that no earthly creature can eat the body of Christ, nor drink his blood, but only man. WINCHESTER. I have read that some s entreat these chances of dogs and cats, but I never heard any of *The contra- that opinion*, to say or write so, as a doctrine, that a dog or a cat eateth the body of notedffor a" Christ, and set it forth for a teaching, as this author most impudently supposeth ; and I marvel much that such a word, and such a report, can come out of a Christian man s mouth, and therefore this is by the author a marvellous surmise, wJiereupon to take occa sion to bring the adversative " but" for the author s part, being such a saying on that side as all Christendom hath ever taught, that no creature can eat the body and drink the blood 5 q/ *Pugnatcum Christ, but only man. But this abominable surmised untruth in the former part of his 6 com- anspap parison, may be taken for a proof, whether such beastly asseverations proceed from the spirit of truth or no; and ivhetJier truth be there intended, where such blasphemy is surmised. But let us see tJte rest. CANTERBURY. Yet still in these comparisons you grant that part of the difference to be true which I affirm ; but you say that I report untruly of the papists, impudently bearing them in hand, to say such abominable and beastly asseverations as you never heard. Whereby appearcth your impudent arrogancy in denial of that thing which either you know whether a the papists do say, or you are in doubt whether they say or say not, having not read eauhe body what it is that they say. For why do they reject the Master of the Sentences in of this point, that he said, "a mouse or brute beast receiveth 7 not the body of Christ, 67. although they seem to receive it ? Wherein if you say, as the Master did, that Lib. 4. di- the mouse receiveth not the body of Christ, look for no favour at the papists hands, ermribus.foi but to be rejected as the Master was, unless they forbear you upon favour, and because that in other matters you have been so good a captain for them, they will pardon you this one fault. And so is this first part of the difference no untrue surmise of me, but a determination of the papists, condemning whosoever would say the contrary. And this is a common proposition among the school divines, that the body of Christ remaincth so long as the form of the bread is remaining, wheresoever it be, whereof Mar- [- Eat, 1551, and Orig. Ed.] [ 3 Some that, 1551.] [ 4 Of that abominable opinion, Orig. Ed. Win- Chester, 1551.] [ 5 Can eat the body and blood, 1551.] [ 6 Of this comparison, Orig. Ed. Winchester, 1551.] [ 7 Receive, 1551.] t>8 THE THIRD BOOK. Thomas, your St Thomas writeth thus : Quidam vero dixerunt^ quod quam primum sacramentum q. lui. art. in. sumitur a mure vel cane, desinit ibi csse corpus Christi. Sed hoc derogat veritati huju# sacramenti. Substantia enim panis sumpta a peccatore tamdiu manet, dum per calorem naturalem est in digestione : igitur tamdiu manet corpus Christi sub speciebus sacra- Peryn. nwntaUbus 1 . And Perin 2 , in his book printed and set abroad in this matter for all men to read, saith : " That although the mouse, or any other beast, do eat the sacra ment, yet nevertheless the same is the very and real body of Christ." And he asketh, "what inconvenience it is against the verity of Christ s real body in the sacrament, though the impassible body lie in the mouth or maw of the beast ? Is it not there fore the body of Christ ? Yes, undoubtedly," saith he. So that now these abominable opinions and beastly asseverations, (as you truly term them, meaning thereby to bite me, as appeareth,) be fit terms, and meet for the papists, whose asseverations they be. Now followeth the seventh comparison. They say, that every man, good and evil, eateth the body of Christ. We say, that both do eat the sacramental bread, and drink the wine; but none do eat the very body of Christ, and drink his blood, but only they that be lively members of his body. WINCHESTER. "A demur upon this issue. In this comparison the former part, speaking of such men as be by baptism received into Christ s church, is very true, confirmed by St Paul, and ever since affirmed in tlie church; in the proof whereof here in this book I will not travel, but make it a demur as it were in law, whereupon to try the truth of the whole matter. If that doctrine, catted by this author the doctrine of the papists, and is indeed the catholic doctrine, be not in this point true, let all be so judged for me. If it be true, as it is most true, let that be a mark whereby to judge the rest of this author s untrue asseverations. For undoubtedly St Augustine saith : con- " We may not of men s matters esteem the sacraments: they be made by him whose they be; but worthily used they bring reward, unworthily handled they bring judgment. He that dis- pertseth the sacrament worthily, and he that useth it unworthily, be not one; but that thing is one, whether it be handled worthily or unworthily, so as it is neither better ne worse, but *MarcusCon- life or death of them that use it." Thus saith St Augustine, and therefore be the receivers^ worthy or unworthy, good or evil, the substance of Christ s sacrament is all one, as being c, who worketh uniformly, and yet is not in all that receive of like effect, not of* any or diminution in it, but for the diversity of him that receiveth. So as the report made here of the doctrine of the catholic church under the name of papists is a very true report, and for want of grace reproved by the author as though it were no true doctrine. And the second part of the comparison on the author s side, contained under "we say" by them that in hypocrisy pretend to be truth s friends, containeth an untruth to the simple reader, and yet hath a matter of wrangling to the learned reader, because of the word " very" which, referred to the effect of eating the body of Christ, whereby to receive life, may be so spoken, that none receive the body of Christ with the very effect of life, but such as eat the sacrament spiritually, that is to say, with true faith worthily. And yet evil men, as idem fortasse sumuTU quod bruti in s<tcra- mentum tantum. The wnrd * Unfi f 1 Cranmer here, as above, p. 64, quotes the sub stance of Thomas Aquinas, rather than his exact words, which run thus: "Quidam antiqui errave- runt, dicentes, quod corpus Christi nee etiam sacra- mentaliter a peccatoribus sumitur, sed quam cito la biis peccatoris contingitur, tam cito sub speciebus sacramentalibus desinit esse corpus Christi. Sed hoc est erroneum : derogat enim veritati hujus sa cramenti, ad quam pertinet quod manentibus spe ciebus corpus Christi sub eis esse non desinat. Species autem manent, quamdiu substantia panis maneret, sibi ibi adesset. Manifestum est autem quod substantia panis assumpta a pecjcatore, non statim esse desinit, sed manet quandiu per calorem naturalem digeratur. Unde tamdiu corpus Christi sub speciebus sacramentalibus manet a peccatoribus sumptis." Tertia pars, p. 204. Art. iii. q. 80. Antverp. 1624.] [ 2 Dr Peryn was master of the Black-friars in Smithfield. He submitted to voluntary exile during the reign of Henry VIII. ; and after twenty years returned home in the reign of Mary, and opposed the reformed religion. He preached and published four sermons on the Eucharist. Vid. Strype s Eccl. Mem. Vol. in. Part 2. p. 116. Ed. Oxford, 1822. J [ 3 Receiver, 1551.] [ 4 For any alteration, 1551.] OF THK PKKSKNCE OF CHRIST. 69 Judas, receive the same very body, touching the truth of the presence thereof, that St Peter did. For in the substance of the sacrament, which is God s work, is no variety, who ordaineth ail (as afore) uniformly ; but in man is the variety, amongst whom he that receiveth wor thily Christ s body, receiveth life, and he that receiveth unworthily, receiveth condemnation. There followeth further. CANTERBURY. I thank you for this demur, for I myself could have chosen no better for my A purpose. And I am content that the trial of the whole matter be judged hereby, as you desire. You say, that "all that be baptized, good and evil, eat the body Christ;" and I say, only the good, and not the evil. Now must neither I nor you be judges in our own causes: therefore let Christ be judge between us both, whose judgment it is not reason that you refuse. Christ saith : " Whosoever eateth my flesh, and drinketh my blood, dwelleth in me, and I in joim vi. him. As the living Father hath sent me, and I live by the Father, even so he that eateth me shall live by me. This is the bread which came down from heaven : not as your fathers did eat manna, and are dead : he that eateth this bread shall live for ever." Now I ask you this question, Whether evil men shall live for ever? Whether they live by Christ ? Whether they dwell in Christ ? and have Christ dwelling in them ? If you say nay, (as you must needs if you will say the truth,) then have I proved my negative (wherein stood the demur), that ill men eat not Christ s body nor drink his blood; for if they did, then by Christ s own words they should live for ever, and dwell in Christ, and have Christ dwelling in them. And what proofs will you require more upon my part in this demur ? For if Christ be with me, who can be able to stand against me ? But you allege for you St Paul, who speaketh for you nothing at all. For the messenger will not speak against him that sent him. I know that St Paul in the eleventh to the Corinthians, speaketh expressly of the unworthy eating of the bread, but i Cor. xi. in no place of the unworthy eating of the body of Christ. And if he do, shew the place, or else the demur passeth against you, and the whole matter tried with me, by your own pact and covenant. And yet for further proof of this demur, I refer me to the 1st, 2nd, 3rd, 4th, and 5th chapters of my fourth book. And where you bring St Augustine to be witness, his witness in that place helpeth August, con- nothing your cause. For he speaketh there generally of the using of the sacraments lib. 2. cap. 07. well or ill, as the diversity of men be, rehearsing by name the sacrament of circum cision, of the paschal lamb, and of baptism. Wherefore if you will prove any real and corporal presence of Christ by that place, you may as well prove that he was cor porally present in circumcision, in eating of the paschal lamb, and in baptism, as in the Lord s supper. And here ye use such a subtilty to deceive the simple reader, that he hath good cause to suspect your proceedings, and to take good heed of you in all your writings, who do nothing else but go about to deceive him. For you conclude the matter of the substance of the sacrament, that the reader might think that place to speak only of the sacrament of Christ s body and blood, and to speak of the substance thereof, where St Augustine neither hath that word " substance," nor speaketh not one word specially of that sacrament ; but all his process goeth chiefly of baptism, which is all one, (saith St Augustine against the Donatists, which reproved baptism for the vice of the 69. minister,) whether the minister be good or ill, and whether he minister it to good or to ill. For the sacrament is all one, although the effect be diverse, to good and to evil. And as for them whom ye say that in hypocrisy pretend to be truth s friends, Truth s feign- all that be learned and have any judgment, know that it is the papists, which no few years past, by hypocrisy and feigned religion, have uttered and sold their lies and fables instead of God s eternal truth, and in the place of Christ have set up idols and antichrist. And for the conclusion of this comparison, in this word " very " you make such vry. a wrangling, (where none occasion is given,) as never was had before this time of any 70 THE THIRD BOOK. learned man. For who heard ever before this time that an adjective was referred to a verb, and not to his proper substantive, of any man that had any learning at all? And as for the matter of Judas is answered before. For he received not the August, in bread that was the Lord, as St Augustine saith, but the bread of the Lord. Nor 3 no man can receive the body of Christ unworthily, although he may receive un worthily the sacrament thereof. smith. And hitherto D. Smith hath found no fault at all in my comparisons, whereby the reader may see how nature passeth art, seeing here much more captiousness in a subtil sophistical wit, than in him that hath but learned the sophistical art. Now followeth the eighth comparison. The eighth They say, that good men eat the body of Christ and drink his blood, only at that time when they receive the sacrament. We say, that they eat, drink, and feed of Christ continually, so long as they be members of his body. WINCHESTER. What forehead, I pray you, is so hardened, that can utter this among them that know any thing of the learning of Christ s church ? In which it is a most common distinction, that there is three manner of eatings of Christ s body and blood: one spiritual only, which is *Three man- here affirmed in the second part of " we say," wherein the author and his say as the church gs> saith : another eating is both sacramentally and spiritually, which is when men worthily communicate in the supper : the third is sacramentally only, which is by men unworthy, *Causeof who eat and drink in the holy supper to their condemnation only. And the learned men in Christ s church say, that the ignorance and want of observation of these three manner of eatings causeth the error in the understanding of the scriptures and such fathers sayings, as have written of the sacrament. And when the church speaketh of these three manner of eatings, what an impudency is it to say, that the church teacheth good men only to eat the body of Christ and drink his blood, when they receive the sacrament, being the truth otherwise; and yet a diversity there is of eating spiritually only, and eating spiritually and sacramentally, because in the supper they receive his very flesh and 1 blood indeed, with the effects of all graces and gifts to such as receive it spiritually and worthily ; whereas out of the supper, when we eat only spiritually by faith, God that worketh without his sacraments, as seemeth to him, doth relieve those that believe and trust in him, and sufereth them not to be desti tute of that is necessary for them, whereof we may not presume contemning the sacrament, but ordinarily seek God, where he hath ordered himself to be sought, and there to assure ourse W f ^ s covenants and promises, which be most certainly annexed to his sacraments, We must, whereunto we ought to give most certain trust and confidence: wherefore to teach the spiritual in teaching, J J * exalt the sa- manducation to be equal with the spiritual manducation and sacramental also, that is to after their diminish the effect of the institution of tJie sacrament, which no Christian man ought to do. dignity. CANTERBURY. 70. Who is so ignorant that hath read any thing at all, but he knoweth that distinction of three eatings? But no man that is of learning and judgment, understandeth the Three man- three diverse eatings in such sort as you do, but after this manner : that some eat nerof eatings. on ry the sacrament of Christ s body, but not the very body itself; some eat his body and not the sacrament; and some eat the sacrament and body both together. The sacrament (that is to say, the bread) is corporally eaten and chewed with the teeth in the mouth : the very body is eaten and chewed with faith in the spirit. Un godly men, when they receive the sacrament, they chew in their mouths, like unto Judas, the sacramental bread, but they eat not the celestial bread, which is Christ. Faithful Christian people, such as be Christ s true disciples, continually from time to time record in their minds the beneficial death of our Saviour Christ, chewing it by faith in the cud of their spirit, and digesting it in their hearts, feeding and com- [ Very flesh and very blood, 1551.] OF THE PRESENCE OF CHRIST. 71 forting themselves with that heavenly meat, although they daily receive not the sacra ment thereof; and so they eat Christ s body spiritually, although not the sacrament thereof. But when such men for their more comfort and confirmation of eternal True sacra- life, given unto them by Christ s death, come unto the Lord s holy table; then, as hlg nU1 before they fed spiritually upon Christ, so now they feed corporally also upon the sacramental bread : by which sacramental feeding in Christ s promises, their former spiritual feeding is increased, and they grow and wax continually more strong in Christ, until at the last they shall come to the full measure and perfection in Christ. This is the teaching of the true catholic church, as it is taught by God s word. And therefore St Paul, speaking of them that unworthily eat, saith, that they eaticor. xi. the bread, but not that they eat the body of Christ, but their own damnation. And where you set out with your accustomed rhetorical colours a great impu- whether dency in me, that would report of the papists that good men eat the body of Christ and drink his blood only when they receive the sacrament, seeing that I know that the papists make a distinction of three manner of eatings of Christ s body, whereof one is without the sacrament : I am not ignorant indeed, that the papists grant a spiritual eating of Christ s body without the sacrament ; but I mean of such an eating of his body, as his presence is in the sacrament, and as you say he is there eaten, that is to say, corporally. Therefore to express my mind more plainly to you, that list not understand, let this be the comparison. They say that after such a sort as Christ is in the sacrament, and there eaten, The coin- so good men eat his body and blood only when they receive the sacrament. Q\Ve say, F that as they eat and drink Christ in the sacrament,] 2 so do they eat, drink, and feed upon him continually, so long as they be members of his body. Now the papists say, that Christ is corporally present in the sacrament, and is so eaten only when men receive the sacrament. But we say, that the presence of Christ in his holy supper is a spiritual presence : and as he is spiritually present, so is he spiritually eaten of all faithful Christian men, not only when they receive the sacra ment, but continually so long as they be members spiritual of Christ s mystical body. 71. And yet this is "really" also, (as you have expounded the word,) that is to say, Really, in deed and effectually. And as the Holy Ghost doth not only come to us in baptism, and Christ doth there clothe us, but they do the same to us continually so long as we dwell in Christ ; so likewise doth Christ feed us so long as we dw r eil in him and he in us, and not only when we receive the sacrament. So that as touching Christ himself, the presence is all one, the clothing all one, and the feeding all one, although the one for the more comfort and consolation have the sacrament added to it, and the other be without the sacrament. The rest that is here spoken is contentious wrangling to no purpose. But now cometh in Smith with his five eggs, saying that I have made here five smith. lies in these comparisons. " The first lie is," saith he, " that the papists do say, that good men do eat and drink Christ s body and blood only when they receive the sacrament :" which thing Smith saith the papists do not say, but that they then only do cat Christ s body and drink his blood corporally, which sufnceth for my purpose. For I mean no :J other thing, but that the papists teach such a corporal eating of Christ s body as endureth not, but vanisheth away, and ceaseth at the furthest within few hours after the sacrament is 4 received. But forasmuch as Smith agreeth here with you, the answer made before to you will serve for him also. And yet Smith here shall serve me in good stead against you, who have imputed unto me so many im pudent lies, made against the papists in the comparisons before rehearsed : and Smith saith that this is the first lie, which is in the eighth comparison. And so shall Smith, (being mine adversary and your friend,) be such a witness for me, as you cannot except against, to prove that those things which before you said were impudent lies, be no lies at all. For this "is the first lie," saith Smith ; and then my sayings before must be all true, and not impudent lies. [- The 15MO Ed. omits this sentence.] [ 4 Sacrament be received, 1551. [ 3 None other, 1551. J 72 TIIK THIRL) HOOK. Now to the ninth comparison. They say, that the body of Christ that is in the sacrament, hath his own proper form and quantity. We say, that Christ is there sacramentally and spiritually, without form or quantity. WINCHESTER. [The answer. In this comparison is both sleight and craft : in the first part of it, which is that " they say" Winch.1 551.] there is mention of the body of Christ, which is proper of the humanity of Christ. In the second iSy ifun- part, which is of "we say" there is no mention of Christ s body, but of Christ, who in his divine of r h t i* nded nature is understanded present without a body. Now the sacrament is institute of Christ s humanity, body and blood ; and because the divine nature in Christ continueth the unity with the body of Theunityof Christ, we must needs confess where the body of Christ is there is whole Christ, God and man. hood and* And wJien we speak of Christ s body, we must understand a true body, which hath both form Godhead. ^^ quantity ; and therefore such as confess the true catholic faith, they affirm of Christ s body all truth of a natural body, which although it hath all those truths of form and quantity, yet they say, Christ s body is not present after the manner of quantity, nor in a visible form, as it was conversant in this present life : but that there is truly in the sacrament the very true body of Christ, ivhich good men believe upon the credit of Christ that said so, and knowledge therewith the manner of that presence to be an high mystery, and the manner so spiritual, as the carnal man cannot by discourse of reason reach it, but in his discourse shall (as this author doth) think it a vanity and foolishness : which foolishness nevertheless overcometh the wisdom of the world. And thus have I opened what tliey say on the catholic part. A marvel- Noiv for the other part, whereof this author is, and with his faith "we say" the words seem to E author f imply, that Christ s human body is not in the sacrament, in that it is said, "Christ to be there scripture. sacramentally and spiritually, without form or quantity," which saying hath no scripture for it. 72. For tJie scripture speaketh of Christ s body ivhich was betrayed for us, to be given us to be eaten. institution of Where also Christ s divinity is present, as accompanying his humanity, which humanity is specially spoken of, the presence of which humanity wJien it is denied, then is there no text to n[ty! S saying. prow the presence of Christ s divinity specially, that is to say, otherwise than it is by his bod h l " ismy omnipotency present every wJiere. And to conclude this piece of comparison, this manner of speech was never, I think, read, that Christ is present in the sacrament without form or quantity. And St Paul speaketh of a form in the Godhead, Qui quum in forma Dei esset, " Who when he was in the form of God." So as if Christ be present in the sacrament without all form, then is he there neither as God nor man ; which is a stranger teaching than yet hath been heard or read of: but into such absurdities indeed do they fall, who entreat irreverently and untruly this high mystery. This is here worthy a special note, how by the manner of the speech in the latter part of this difference the teaching seemeth to be, that Christ is spiritually present * There. in the sacrament, because of the word "there" which thou, reader, mayest compare how it agreeth contrariety with the rest of this author s doctrine. Let us go to the next. in the author. CANTERBURY. Such is the nature of many, that they can find many knots in a plain rush, and doubts where no doubts ought to be found. So find you "sleight and craft," where I meant all things simply and plainly. And to avoid such sleight and craft as you gather of my words, I shall express them plainly thus. Th C compa- The papists say, that the body of Christ that is in the sacrament, hath his own proper form and quantity. We say, that the body of Christ hath not his proper form and quantity, neither in the sacrament, nor in them that receive the sacrament ; but is in the sacrament sacramentally, and in the worthy receivers spiritually, without the proper form and quantity of his body. This was my meaning at the first, and no man that had looked of this place indifferently, would have taken the second part of this comparison to be understanded of Christ s divine nature : for the bread and wme De sacraments of his body and blood, and not of his divinity, as Theodoretus saith ; and therefore his divine nature is not sacramentally in the sacrament, but his human nature only. And what manner of speech had this been, to say of Christ s divine nature, that it is in the sacrament without quantity, which hath in it no manner OF Till: I KINKNCK OF CHRIST. 73 of quantity wheresoever it be? And where I set forth these eomparisons to shew wherein we vary from the papists, what \ariance had been in this comparison, if I had understanded the first part of Christ s humanity, and the second of his divinity ? The reader by this one place, among many other, may easily discern, how captious you be to reprehend whatsoever I say, and to pervert every thing into a wrong sense : so that in respect of you, Smith is a very indifferent taker of my words, although D- smith, indeed he far passeth the bounds of honesty. But to come directly to the matter, if it be true that you say, that in the sacrament whether, tr Christ s body hath all the forms and quantities of a natural body, why say you then ""-nt, Christ that his body is not there present after the manner of quantity ? Declare what difference .s proper is between form and quantity, and the manner of quantity. And if Christ s body quantity. in the sacrament have the same quantity, that is to say, the same length, breadth, and thickness, and the same form, that is to say, the same due order and proportion ; of the members and parts of his body, that he had when he was crucified, and hath now in heaven, (as he hath by your saying here in this place,) then I pray you declare 73. further, how the length, breadth, and thickness of a man, should be contained in quantity within the compass of a piece of bread, no longer nor broader than one or two inches, nor much thicker than one leaf of paper : how an inch may be as long as an ell, and an ell as short as an inch : how length and roundness shall agree in one proportion ; and a thick and thin thing be both of one thickness : which you must warrant to be brought to pass, if the form and quantity of Christ s body be contained under the form and quantity of such bread and wine as we now use. But as Smith in the last comparison did me good service against you, so shall i>. smith, you in this comparison do me good service against him. For among the five lies wherewith he charges me in these comparisons, he accounteth this for one, that I report of the papists, that Christ s body in the sacrament hath his proper form and quantity, which you say is a truth. And therefore, if I make a lie herein, as Smith saith I do, yet I lie not alone, but have you to bear me company. And yet once again more may the reader here note, how the papists vary among themselves. And it is untrue that you say, that good men believe upon the credit of Christ, that there is truly in the sacrament the very true body of Christ. For Christ called bread his body, and wine his blood, (which, as the old authors say, must needs be understanded figuratively;) but he never said that his true body is truly in the sacrament, as you here report of him. And the manner of his presence you call so high a mystery, that the carnal man cannot reach it. And indeed, as you feign the matter, it is so high a mystery, that never man could reach it but yourself alone. For you make the manner of Christ being in the sacrament so spiritual, that you say his flesh, blood, and bones be there really and carnally; and yet you confess in your book, that you never read in any old author that so said. And this manner of handling of so pure a mystery is neither godly foolishness nor wordly, but rather a mere frenzy and madness. And although the scripture speak of Christ s body to be eaten of us, yet that is understanded of spiritual and not of corporal eating, and of spiritual not of cor poral presence. The scripture saith, that Christ hath forsaken 1 the world, and is John xvi. ascended into heaven. Upon which words St Augustine, Vigilius, and other ancient Lukexxi* authors do prove, that as concerning the nature of his manhood, Christ is gone hence, Al and is not here, as I declared in my third book, the 3rd, 4th, 5th, and 6th chapters. And where you think that this matter of speech was never read, that Christ is present in the sacrament without form or quantity, I am sure that it was never read in any approved author, that Christ hath his proper form and quantity in the sacrament. And Duns saith, " that his quantity is in heaven, and not in the sacra- scotus, 4. mont " Sent. Dist. ment - 10. q. 1. And when I say that Christ is in the sacrament sacramentally, and without form and quantity, who would think any man so captious, so ignorant, or so full [ l Ed. 1551 reads "forsaken;" Ed. 1580 reads "forespoken," which is evidently a misprint.] 74 THE THIRD BOOK. of sophistry, to draw my words to the form of Christ s divinity, which I speak most plainly of the form and quantity of his body and humanity ? as I have before declared. And although some other might be so far overseen, yet specially you ought not so to take my words ; forasmuch as you said not past sixteen lines before, that my words seem to imply, that I meant of Christ s human body. 74. And because it may appear how truly and faithfully you report my words, you AH. add this word " all," which is more than I speak, and marreth all the whole matter. And you gather thereof such absurdities as I never spake, but as you sophistically do gather, to make a great matter of nothing. There. And where of this word " there " you would conclude repugnance in my doctrine, that where in other places I have written that Christ is spiritually present in them that receive the sacrament, and not in the sacraments of bread and wine, and now it should seem that I teach contrary, that Christ is spiritually present in the very bread and wine ; if you pleased to understand my words rightly, there is no repug nance in my words at all. For by this w r ord "there," I mean not in the sacra ments of bread and wine, but in the ministration of the sacrament, as the old authors for the most part, when they speak of the presence of Christ in the sacrament, they mean in the ministration of the sacrament. Which my saying varieth from no doctrine that I have taught in any part of my book. Now followeth the tenth comparison. They say, that the fathers and prophets of the old testament did not eat the body, nor drink the blood of Christ. We say, that they did eat his body and drink his blood, although he was not yet born nor incarnated. WINCHESTER. *A riddle This comparison of difference is clerkly conveyed, as it were of a riddle, wherein nay and tmtrurf nay 3/^> when they be opened, agree and consent. The fathers did eat Christ s body and drink his beinHnap- blood in the 1 truth of promise, which was effectual to tJtem of redemption to be wrought, not in contrarils tw ^ ru ^ 1 f P r ^sence (as we do) for confirmation of redemption already wrought. They had a certain promise, and we a certain present payment : they did eat Christ spiritually, believing in him that was to come, but they did not eat Christ s body present in the sacrament, sacramentally and spiritually, as we do. Tlieir sacraments were figures of the things, but ours contain the very things. And therefore albeit in a sense to the learned men it may be verified, that tlie fathers did eat the body of Christ, and drink his blood ; yet there is no such form of ivords in scripture, and it is more agreeable to the simplicity of scripture, to say the fathers before Christ s nativity did not eat the body and blood of Christ, which body and blood Christ himself truly took of the body of the virgin Mary. For although St Paul, in the tenth to tlie Corinthians, be so understanded of some, as the fathers should eat the same spiritual meat, and drink the same spiritual drink that we do, to which understanding all do not agree, yet following that understanding, we may not *Augustinus. so press the words, as there should be no difference at all; and this one 2 difference St Augustine diffe^nce in noteth, how their sacraments contained the promise of that, which in our sacrament is given. st Augustine, y^ ^ saith : "And this is evident of itself, how to us in the holy supper Christ saith, This is my body that shall be betrayed for you ; take, eat : which was never said to the fathers, although their faith in substance agreed with ours, having all one Christ and Mediator, which they looked for to come, and we acknowledge to be already come." Come and to come, as St Augustine saith, differeth. But Christ is one, by whom all was created 3 , and man s fall repaired, from whom is all feeding, corporal and spiritual, and in whom all is restored in heaven and in earth. In this faith of Christ, the fathers were fed with heavenly spiritual food, which was the same with ours in respect of the restitution by Christ, and redemption by them hoped, which is achieved by tlie mystery of the body and blood of Christ; by reason whereof I deny not, but it may be said in a good sense, how they did eat the body and blood of Christ, before he was incarnate: but, as I said before, scripture speaketh not so, and it is no wholesome fashion of speech *Joan of at this time, which furthereth in sound to the ears of the rude tlie pestilent heresy wherein Joan of Kent s obsti nacy. [ In truth of promise, 1551.] [ 2 This one special difference, 1551.] [ 3 Create, 1551. J OF THE PRESENCE OF CHRIST. 75 Kent obstinately died, tliat is to say, that Christ took nothing of the virgin, but brought his body with him from above ; being a thing worthy to be noted, how the old heresy, denying tlie true taking of tlie flesh of Christ in tlie virgin s womb, at the same time to revive, when tlie true deliverance of Christ s flesh in the holy supper, to be of us eaten, is also denied. For as it is a mere truth without figure, and yet an high mystery, God s work in the incarnation of Christ, wherein our flesh was of Christ truly taken of the virgin s substance : so is it a mere truth, without figure, in tlie substance of the celestial thing, and yet an high mystery and God s work, in tlie giving of tlie same true flesh, truly to be in tlie supper eaten. Wlien I exclude figure in tlie sacrament, I mean not of the visible part, which is called a figure of tlie celestial invisible part, which is truly there without figure, so as by that figure is not impaired tlie truth of that presence; which I add to avoid cavillation. And to* make an end of this comparison, this I say, that this article declareth wantonness, to make a difference in words, where none is in the sense Noveity ct rightly taken, with a novelty of speech not necessary to be uttered now. speech. flesh k CANTERBURY. Note well here, reader, how the cuttle cometh in with his dark colours. Where I speak of the substance of the thing that is eaten, you turn it to the manner and circumstances thereof, to blind the simple reader, and that you may make thereof a riddle of yea and nay, as you be wont to make black white, and white black; or one thing yea and nay, black and white at your pleasure. But to put away your dark colours, and to make the matter plain, this I say, The fathers that the fathers and prophets did eat Christ s body and drink his blood in promise of redemption to be wrought, and we eat and drink the same flesh and blood in b confirmation of our faith in the redemption already wrought. But as the fathers did eat and drink, so did also the apostles at Christ s supper, in promise of redemption to be wrought, not in confirmation of redemption already wrought. So that if wrought and to be wrought make the diversity of presence and not presence, then the apostles did not eat and drink the flesh and blood of Christ really present, because the redemption was not then already wrought, but promised the next day to be wrought. And although before the crucifying of his flesh and effusion of his blood our re demption was not actually wrought by Christ, yet was he spiritually and sacra- mentally present, and spiritually and sacramentally eaten and drunken, not only of the apostles at his last supper before he suffered his passion, but also of the holy patriarchs and fathers before his incarnation, as well as he is now of us after his ascension. And although in the manner of signifying there be great difference between their The diversity sacraments and ours, yet, as St Augustine saith, both we and they receive one thing mcntsofthc in the diversity of sacraments 5 . And our sacraments contain presently the very things signified, no more than theirs did. For in their sacraments they were by Christ presently regenerated and fed, as we be in ours ; although their sacraments were figures of the death of Christ to come, and ours be figures of his death now past. And as it is all one Christ that was to be born and to die for us, and after ward was born indeed and died indeed, whose birth and death be now past ; so was the same Christ, and the same flesh and blood eaten and drunken of the faith ful fathers before he was born or dead, and of his apostles after he was born and before he was dead, and of faithful Christian people is now daily eaten and drunken after that both his nativity and death be past. And all is but one Christ, one flesh, and one blood, as concerning the substance, yet that which to the fathers was to come, is to us past. And nevertheless the eating and drinking is .all one; for neither the fathers did, nor we do eat carnally and corporally with our mouths, but both the fathers did, and we do eat spiritually by true and lively faith. The body Mt m . Tract. 70. [* So ed. 1551. In that of 1580 to is omitted.] [ 5 " Sacramenta ilia fuerunt : in signis diversa sum, sed in re qua: significatur paria sunt." August, in Joannem, Tract, xxvi. Pars ix. Ed. Basil, ap. Amerbach. 1506.] THE THIRD BOOK. The fathers did eat Christ s body and drink his blood be fore he was born. 1 Cor. x. August, de Util Peeni- ten. August, in Psal. Ixxvii. August, in Jran. Tract. 77. August, con tra Fausturn, lib. 19. cap. Ifi. et 20. cap. of Christ was and is all one to the fathers and to us, but corporally and locally he was not l yet born unto them, and from us he is gone, and ascended up into heaven. So that to neither he was nor is carnally, substantially, and corporally present, but to them he was, and to us he is spiritually present, and sacramentally also ; and of both sacramentally, spiritually, and effectually eaten and drunken, to eternal salva tion and everlasting life. And this is plainly enough declared in the scripture to them that have willing minds to understand the truth. For it is written in the old testament, Ecclus. xxiv. in the person of Christ thus : " They that eat me, shall yet hunger, and they that drink me shall yet be thirsty." And St Paul writeth to the Corinthians, saying : " Our fathers did all eat the same spiritual meat, and did all drink the same spiritual drink; and they drank of that spiritual rock that followed them, which rock was Christ." These words St Au gustine expounding, saith : " What is to eat the same meat, but that they did eat the same which we do? Whosoever in manna understood Christ, did eat the same spiritual meat that we do, that is to say, that meat which was received with faith, and not with bodies. Therefore to them that understood and believed, it was the same meat and the same drink. So that to such as understood not, the meat was only manna, and the drink only water; but to such as understood, it was the same that is now. For then was Christ to come, who is now come. To come and is come, be divers words, but it is the same Christ." These be St Augustine s sayings 2 . And because you say, "that it is more agreeable to the scripture to say, that the fathers before Christ s nativity did not eat the body and drink the blood of Christ"; 1 pray you, shew me one scripture that so saith. And shew me also one approved author that disallowed St Augustine s mind by me here alleged, because you say, "that all do not agree to his understanding." And in the seventy-seventh Psalm, St Augustine saith also : " The stone was Christ." Therefore the same was the meat and drink of the fathers in the mystery, which is ours; but in signification the same, not in outward form. For it is one Christ himself, that to them was figured in the stone, and to us manifestly appeared in flesh. And St Augustine saith plainly, " that both manna and our sacrament signifieth Christ, and that although the sacra ments were divers, yet in the thing by them meant and understand they were both like." And so after the mind of St Augustine it is clear, that the same things were given to the faithful receivers in the sacraments of the old testament that be given in the new : the same to them was circumcision, that to us is baptism ; and to them by manna was given the same thing, that now is given to us in the sacra mental bread. And if I would grant for your pleasure, that in their sacraments Christ was promised, and that in ours he is really given; doth it not then follow as well that Christ is given in the sacrament of baptism, as that he is given in the sacrament of his flesh and blood? And St Augustine, contra Faustum, esteemeth them mad, that think diversity between the things signified in the old and new testament, because the signs be diverse 3 ; and expressing the matter plainly, saith, "that the flesh and blood of our sacrifice before Christ s coming was promised by sacrifices of similitudes, in his passion was given indeed, and after his ascension is solemnly put in our memory by the sacrament 4 ." [ l Here again it is necessary to follow ed. 1551. The 1580 ed. omits not.] [ 2 " Eundem, inquit, cibum spiritalem mandu- caverunt. Quid est eundem, nisi quia eum quern etiam nos ? Quicunque in manna Christum intel- lexerunt, eundem quern nos cibum spiritalem man- ducaverunt : id est, qui fide capiebatur, non qui corpore hauriebatur Et eundem ergo cibum, eun dem potum, sed intelligentibus et credentibus. Non intelligentibus autem, illud solum manna, ilia sola aqua : credenti autem idem qui nunc. Tune enim Christus venturus, modo Christus venit. Venturus et venit, diversa verba sunt, sed idem Christus. * August, de Utilitate Pcenitentia?, Lib. i. Pars x.J [ 3 " Quanto errore delimit, qui putant signis sa- cramentisque mutatis, etiam res ipsas esse diver- sas." August, contra Faustum, Lib. xix. cap. xvi. Pars iv.] [ 4 "Hujus sacrificii caro et sanguis ante adven- tum Christi per victimas similitudinum promit- tebatur : in passione Christi per ipsam veritatem reddebatur : post ascensum Christi per sacramentum memoriae celebratur." Ibid. Lib. xx. cap. xxi.] or THE PKKsKxn: OF CHRIST. 77 And the thing which you say St Augustine 5 noteth to be given in the sacraments August, in of the new testament, and to be promised in the sacraments of the old, St Augustine expresseth the thing which he meant, that is to say, salvation and eternal life by C/hrist. And yet in this mortal life we have not eternal life in possession, but in promise, as the prophets had. But St Augustine saith, that we have the promise, because we have Christ already come, which by the prophets was promised before that he should come; and therefore St John the baptist was called more than a pro phet, because he said : " Here is the Lamb of God already present, which the prophets John i. taught us to look for until he came." The effect therefore of St Augustine s words plainly to be expressed, was this, that the prophets in the old testament promised a Saviour to come and redeem the world, which the sacraments of that time testified until his coming: but now he is already come, and hath by his death performed that was promised, which our sacraments testify unto us, as St Augustine declareth more plainly in his book, De fide ad Petrum, the 19th chapter 8 . So that St Augustine speaketh of the giving of Au^ist. AC Christ to death, (which the sacraments of the old testament testified to come, and cap. fy. ours testify to be done,) and not of the giving of him in the sacraments. And forasmuch as St Augustine spake generally of all the sacraments, therefore if you will by his words prove, that Christ is corporally in the sacrament of the holy communion, you may as well prove, that he is corporally in baptism ; for St Augustine speaketh no more of the one than of the other. But where St Augustine speaketh generally of all the sacraments, you restrain the matter particularly to the sacrament of the Lord s supper only, that the ignorant reader should think, that St Augustine spake of the corporal presence of Christ in the sacraments, and that only in the sacraments of bread and wine; whereas St Augustine himself speaketh only of our salvation by Christ, and of the sacraments in general. And nevertheless, as the fathers had the same Christ and Mediator that we have, (as you here confess,) so did they spiritually eat his flesh and drink his blood as we do, and spiritually feed of him, and by faith he was present with them, as he is with us, although carnally and corporally he was yet to come unto them, and from us is gone up to his Father into heaven. This, besides St Augustine, is plainly set out by Bertram above six hundred Bertram, years past, whose judgment in this matter of the sacrament although you allow not (because it utterly condemneth your doctrine therein,) yet forasmuch as hitherto his teaching was never reproved by none, but by you alone, and that he is commended of other as an excellent learned man in holy scripture, and a notable famous man, as well in living as learning, and that among his excellent works this one is specially praised, which he wrote of the matter of the sacrament of the body and 78. blood of our Lord, therefore I shall rehearse his teaching in this point, how the holy fathers and prophets, before the coming of Christ, did eat Christ s flesh and drink his blood : so that, although Bertram s saying be not esteemed with you, yet the indif ferent reader may see what was written in this matter, before your doctrine was in- [ 5 " Sacramenta non eadem, quia alia sunt sa- cramenta dantia salutem, alia promittentia Salvato- rem. Sacramenta novi testamenti dant salutem, sacramenta veteris testamenti promiserunt Salvato- rem. Cum ergo jam teneas promissa, quid quasris promittentia ? Salvatorem habens jam in hoc teneas promissa, non quod jam acceperimus vitam aeter- nam, sed quia jam venerit Christus, qui per prophe- tas praenunciabatur." August, in Psal. Ixxiii. Tom. VIII. p. 327. Ed. Paris. 1635.] [ 6 " Firmissime tene, et nullatenus dubites, ip- sum unigenitum Ueum, Verbum carnem factum, se pro nobis obtulisse sacrificium et hostiavn Deo in odorem suavitatis : cui cum Patre et Spiritu sancto a patriarchis, prophetis, et sacerdotibus tempore veteris testamenti animalia sacrificabantur; et cui mine, id est, tempore novi testamenti, cum Patre et Spiritu sancto, cum quibus illi est una divinitas, sacriricium panis et vini in fide et caritate sancta ecclesia catholica per universum orbem terrae offerre non cessat. In illis enim carnalibus victimis figu- ratio fuit carnis Christi, quam pro peccatis nostris ipse sine peccato fuerat oblaturus, et sanguinis quern erat effusurus in remissionem peccatorum nostrorum. In isto autem sacrificio gratiarum actio atque commemoratio est carnis Christi, quam pro nobis obtulit, et sanguinis quern pro nobis idem Deus effudit." August, de fide ad Petrum diaco- num, Cap. xix. Pars x. Basil, ap. Amerbach. 1506. In Ed. Paris. 1635. Tom. III. p. 391, 2. This trea tise is censured by Erasmus as spurious ; and the author is said to be Fulgentius Vid. Rived Critica Sacra, p. 389. Genev. 1626. " Coci censura Pa- trum," pp. 341, 2. Helm. 1683.J THE THIRD BOOK. Smith. vented. And although his authority be not received of you, yet his words may serve against Smith, who herein more learnedly, and with more judgment than you, ap pro veth this author. This is Bertram s doctrine 1 . " St Paul saith, that all the old fathers did eat the same spiritual meat, and drink the same spiritual drink. But peradven- ture thou wilt ask, which the same? Even the very same that Christian people do daily eat and drink in the church. For we may not understand divers things, when it is one and the self-same Christ, which in times past did feed with his flesh, and made to drink of his blood, the people that were baptized in the cloud and sea, in the wilderness, and which doth now in the church feed Christian people with the bread of his body, and giveth them to drink the flood of his blood. When he had not yet taken man s nature upon him, when he had not yet tasted death for the salvation of the w^orld, not redeemed us with his blood, nevertheless even then our forefathers, by spiritual meat and invisible drink, did eat his body in the wilderness and drink his blood, as the apostle beareth witness, saying: The same spiritual meat, the same spiritual drink/ For he that now in the church, by his omnipotent power, doth spiritually convert bread and wine into the flesh of his body, and into the flood of his own blood, he did then invisibly so work, that manna which came from heaven was his body, and the water his blood." Now by the things here by me al leged it evidently appeareth, that this is no novelty of speech to say, that the holy fathers and prophets did eat Christ s flesh, and drink his blood. For both the scrip ture and old authors use so to speak, how much soever the speech mislike them, that like no fashion but their own 2 . Joan of Kent. And what doth this further the pestilent heresy of Joan of Kent ? Is this a good argument? The fathers did eat Christ s flesh and drink his blood spiritually before he was born; ergo after he was not corporally born of his mother? Or be cause he was corporally born, is he not therefore daily eaten spiritually of his faithful people? Because he dwelt in the world corporally from his incarnation unto his as cension, did he not therefore spiritually dwell in his holy members before that time, and hath so done ever sithens, and will do to the world s end? Or if he be eaten in a figure, can you induce thereof that he was not born without a figure ? Do not such kind of arguments favour the error of Joan of Kent ? Yea, do they not manifestly approve her pestiferous heresy, if they were to be allowed? What man that meaneth the truth, would bring in such manner of reasoning to deface the truth? And yet it is not to be denied, but that Christ is truly eaten, as he was truly born; but the one corporally and without figure, and the other spiritually and with a figure. Now followeth my eleventh comparison. The eleventh comparison. They say, that the body of Christ is every day many times made, as often as there be masses said, and that then and there he is made of bread and wine. We say, that Christ s body was never but once made, and then not of the nature and substance of bread and wine, but of the sub stance of his blessed mother. I 1 " Cum cibus vel potus ille futuri corporis Christ! sanguinisque mysterium quod celebrat ecclesia praemonstraret, eandem tamen escam spiritualem manducasse, et eundem potum spiritualem bibisse patres nostros sanctus Paulus asseverat. Quaeris fortasse, quam eandem ? nimirum ipsam quam hodie populus credentium in ecclesia manducat et bibit. Non enim licet diversa intelligi, quoniam unus idemque Christus est, qui et populum in de- serto, in nube et in mari baptizatum sua carne pa- vit, suo sanguine tune potavit, et in ecclesia nunc credentium populum sui corporis pane, sui sanguinis unda pascit ac potat. Mirum certe, quoniam incom- prehensibile et inaestimabile : nondum hominem assumpserat, nondum pro salute mundi mortem degustaverat, nondum sanguine suo nos redemerat; et jam nostri patres in deserto per escam spiritualem potumque invisibilem ejus corpus manducabant, et ejus sanguinem bibebant, velut testis existit apostolus, clamans : eandem escam spiritualem manducasse, eundem potum spiritualem bibisse pa tres nostros. Ipse namque qui nunc in ecclesia omnipotent! virtute panem et vinum in sui corporis carnem et proprii cruoris undam spiritualiter con- vertit, ipse tune quoque manna de ccelo datum cor pus suum, et aquam de petra profusam proprium sanguinem invisibiliter operatus est." Bertram. Lib. de Corp. et Sang. Dom. Cap. xxii. xxiii. xxv. pp. 12 14.-Ed. Oxford, 1838.] P That like no fashion of speech but their own, 1551.] OF THE PRESENCE OF CHRIST. 79 WINCHESTER. The body of Christ is by God s omnipotency, who so < <>rkctli i,i liis wore?, made present 79. unto us at such time, as ttte church pray s it may please him so to do, which prayer is ordered Thebookof to be made in tfie book of common prayer now set forth 4 . Wherein we require of God, the prayerin this creatures of bread and wine to be sanctijied, and to be to us the body and blood of Christ, ra which tfiey cannot be, unless God worketh it, and make them so to be: in which mystery it was never taught, as this author willingly misreporteth, that Christ s most precious body is *christ s made of the matter of bread, but in that order exhibited and made present unto us, by con- sacrament i version of the substance of bread into his precious body; not a new body made of a new matter the matter of of bread and wine, but a new presence of the body, that is never old, made present tliere, tvliere the substance of bread and wine was before. So as this comparison of difference is mere wrangling, and so evident as it needeth no further answer but a note. Lo, how they be not ashamed to trifle in so great a matter, and without cause by wrong terms to bring the truth in slander, if it were possible. May not this be accounted as a part of God s punishment, for men of knowledge to write to the people such matter seriously, as were not tolerable to be by a sco/er devised in a play, to supply when his fellow had forgotten his part f CANTERBURY. Christ is present whensoever the church prayeth unto him, and is gathered to- <>vtlirr in his name. And the bread and wine be made unto us the body and blood of Christ, (as it is in the book of common prayer,) but not by changing the substance The book of of bread and wine into the substance of Christ s natural body and blood, but that in prayer, the godly using of them they be unto the receivers Christ s body and blood : as of some the scripture saith, that their riches is their redemption, and to some it is their Prov. xiii. damnation; and as God s word to some is life, to some it is death and a snare, aaiCtor. L the prophet saith. And Christ himself to some is a stone to stumble at, to some is a Jame^ i! raising from death, not by conversion of substances, but by good or evil use: tibatiuttulL thing which to the godly is salvation, to the ungodly is damnation. So is the water John xi. in baptism, and the bread and w T ine in the Lord s supper, to the worthy receivers Christ himself and eternal life, and to the unworthy receivers everlasting death and damnation, not by conversion of one substance into another, but by godly or ungodly use thereof. And therefore, in the book of the holy communion, we do not pray absolutely that the bread and wine may be made the body and blood of Christ, but that unto us in that holy mystery they may be so; that is to say, that we may so worthily receive the same, that we may be partakers of Christ s body and blood, *Domin. 3. and that therewith in spirit and in truth we may be spiritually nourished. And a s^ret. like prayer of old time were all the people wont to make at the communion of all Doming such offerings as at that time all the people used to offer, praying that their offerings obiata > sanc- might be unto them the body and blood of Christ. nob And where you say, " it was never taught as I say, that Christ s body is made SJJ of the matter of bread," you knowingly and willingly misreport me. For I say not of the matter of bread, but of bread ; which when you deny that the papists so chmtbe say, it seemeth you be now ashamed of the doctrine, which the papists have taught this four or five hundred years. For is it not plainly written of all the papists, both lawyers and school-authors, that the body of Christ in the sacrament is made of bread, and his blood of wine? And they say not that his body is made present of bread and wine, but is made of bread and wine. Be not their books in print ready to be shewed? Do they not say, that the substance of the bread neither re- maineth still, nor is turned into nothing, but into the body of Christ? And do not [ 3 Prayeth, 1551.] creatures of bread and wine, that they may be unto [ 4 Winchester here refers to these words in the us the body and blood of thy most dearly beloved first Service Book of Edward VI., in the prayer of Son Jesus Christ." In the second Service Book of consecration : " With thy holy Spirit and word Edward VI. the passage was changed, as it now vouchsafe to bless and sanctify these thy gifts and < stands.] THE THIRD BOOK. yourself also say here in this place, that the substance of bread is converted into Christ s precious body? And what is that else but the body of Christ to be made of bread, and to be made of a new matter * ? For if the bread do not vanish away into nothing, but be turned into Christ s body, then is Christ s body made of it ; and then it must needs follow that Christ s body is made of new 2 , and of another substance than it was made of in his mother s womb : for there it was made of her flesh and blood, and here it is made of bread and wine. And the papists say not (as you now would shift off the matter) that Christ s body is made present of bread, but they say plainly without addition, that it is made of bread. Can you deny that this is the plain doctrine of the papists, Ex pane Jit Corpus Christi, " Of bread is made the body of Christ," and that the substance of bread is turned into the substance thereof? And what reason, sentence, or English, could be in this saying, " Christ s body is made present of bread?" Marry, to be present in bread might be some sentence, but that speech will you in nowise admit. And this your saying here, if the reader mark it well, turneth over quite and clean Pugnatcum all the whole papistical doctrine in this matter of the sacrament, as well touching hu papistis. ^ransubstantiation, as a ] so the carnal presence. For their doctrine with one whole consent and agreement is this : That the substance of bread remaineth not, but is turned into the substance of Christ s body, and so the body of Christ is made of it. But this is false, say you, and " not tolerable to be by a scoffer devised in a place 3 , to supply when his fellow had forgotten his part." And so the whole doctrine of the papists, which they have taught these four or five hundred years, do you condemn with condign reproaches, as a teaching intolerable, not to be devised by a scoffer in a play. Why do you then take upon you to defend the papistical doctrine, if it be so intolerable ? Why do you not forsake those scoffers and players, which have juggled with the world so long, and embrace the most certain truth, that Christ s body is not made of bread ? And seeing that you embrace it here in this one place, why stand you not constantly therein, but go from it again in all the rest of your book, defending the papistical doctrine, clean contrary to yours in this point, in that they teach that Christ s body is made of bread ? And you vary so much from yourself herein, that although you deny the papists sayings 4 in words, that Christ s body is made of bread, yet in effect you grant and maintain the same, which you say is intolerable, and not to be devised by a scoffer in a play. For you say, that Christ calleth bread his body, and that his calling is making : and then if he make bread his body, it must needs follow that he maketh his body of the bread. Moreover, you say, that Christ s body is made present by Making by conversion, or turning of the substance of bread into the substance of his precious body; whereof must follow 5 , that his body is made of bread. For whensoever one substance is turned into another 6 , then the second is made of the first : as, because earth was turned into the body of Adam, we say that Adam was made of earth ; and that Eve was made of Adam s rib, and the wine in Galilee made of water, because the water was turned into wine, and the rib of Adam s side into the body of Eve. If the water had been put out of the pots, and wine put in for the water, we might have said that the wine had been made present there, where the water was before. But then we might not have said that the wine had been made of the water, because the water was emptied out, and not turned into wine. But when Christ turned the water into the wine, then by reason of that turning we say that the wine was made of the water. So likewise if the bread be turned into the substance of Christ s body, we must not only say that the body of Christ is present where the bread was before, but also that it is made of the bread, because that the substance of the bread is converted and turned into the substance of his body. Which thing the papists saw must needs follow, and therefore they plainly confessed that the body of Christ conversion. Gen. ii. John ii. 81. [ And to be made anew of a new matter, 1551.] P Is made new, 15f>l.] [ 3 Play, 1551. Evidently the correct reading. See Winchester in the preceding page.] [ 4 Saying, 1551.] [ Must also follow, 1551.] [ 6 Into another substance, 1551.] OF THE PRESENCE OF CHRIST. 81 was made of bread ; which doctrine, as you truly say in this place, is intolerable, and not to be devised by a scoffer in a play, when his fellow had forgotten his part. And yet you so far forget yourself in this book, that throughout the same, what soever you say here, you defend the same intolerable doctrine, not to be devised by a scoffer. And where Smith accounteth here my fourth lie, that I say, that the papists say, D. Smith. that Christ s body is made of bread and wine ; here Smith and you agree both together in one lie. For it is truth and no lie, that the papists so say and teach ; as Smith in other parts of his book saith, that Christ s body is made of bread, and that priests do make Christ s body. 7 My twelfth comparison is this. They say, that the mass is a sacrifice satisfactory for sin, by the de votion of the priest that offereth, and not by the thing that is offered. But we say, that their saying is a most heinous 8 , yea, and detestable error against the glory of Christ: for the satisfaction for our sins is not the devotion nor offering of the priest, but the only host and satisfaction for all the sins of the world is the death of Christ, and the oblation of his body upon the cross, that is to say, the oblation that Christ himself offered once upon the cross, and never but once, nor never any but he 9 . And there fore that oblation which the priests make daily in their papistical masses, cannot be a satisfaction for other men s sins by the priest s devotion : but it is a mere illusion, and subtle craft of the devil, whereby antichrist hath many years blinded and deceived the world. WINCHESTER. TJiis comparison is out of the matter of the presence of Christ s most precious body in the J e 5 g |* wcr - sacrament, which presence this author, in the first part of his comparison, seemeth by implication Winchester.] to grant, when he findeth fault that the priests devotion should be a sacrifice satisfactory, and not the thing that is offered ; which manner of doctrine I never read, and I think myself it ought to be improved 10 , if any such there be to make the devotion of the priest a satisfaction. For undoubtedly Christ is our satisfaction wholly and fully, who hath paid our whole debt *christ is our to God the Father, for the appeasing of his just wrath against us, and hath cancelled the bill sa( obligatory, as St Paul saith, that was against us. For further opening whereof, if it be asked how he satisfied; we answer as we be taught by the scriptures : By the accomplishment *HOW Christ of the will of his Father, in his innocent, willing, and obedient suffering 11 the miseries of thin world without sin, and the violent persecution of the world, even to the death of the cross, and shedding of his most precious blood. Wherein was perfected the willing sacrif.ce that he made of himself to God the Father for us, of whom it was written in the beginning of the book, that he should be the body and perfect accomplishment of all sacrifices, as of whom all other sacrifices before were shadows and figures. And here is to be considered, how the obedient will in Christ s sacrifice is specially to be 82. noted, who suffered because he would : which St Paul setteth forth in declaration of Christ s humility. And although that willing obedience was ended and perfected on the cross, to the which it continued from the beginning, by reason whereof the oblation is in St Pauls speech attributed thereunto: yet as in the sacrifice of Abraham, when he offered Isaac, the earnest will of offering was accounted for the offering indeed, whereupon it is said in scripture that Abraham offered Isaac, and the declaration of the will of Abraham is called the offering ; so the declaration of Christ 8 will in his last supper was an offering of him to God the Father, assuring there his apostles of his will and determination, and by them all the world-, that his body should be betrayed for them and us, and his precious blood shed for remission of sin, which his word he confirmed then with the gift of his precious body to be eaten, and his jure Inn* Mood to be drunken. In which mystery he declared his body and blood to be [ 7 Now my twelfth comparison, 1551.] [ 8 A most heinous lie, and detestable error, Orig. ed.] [ 9 Nor never none but he, 1551, and Orig. ed.] [ 10 I think it myself it ought to be improved, 1551, and Orig. ed. Winchester.] [ n In his innocent suffering, his willing and obedient suffering, 1551, and Orig. ed. Winch.] (3 I /" !> 4 XTHTTTT* I 82 THE THIRD BOOK. Christ s once offering Phil. ii. Bom. xii. 83. the very sacrifice of the world, by him offered to God the Father, by the same will that he said his body should be betrayed for us; and thereby ascertained us that to be in him 1 witting, that the Jews on the cross seemed to execute by violence and force against his will. And therefore as Christ offered himself on the cross, in the execution of the work of his will; so he offered himself in his supper, in declaration of his will, whereby we might be the more assured of the effect of his death, which he suffered willingly and determinately for the redemption of the world, with a most perfect oblation and satisfaction for the sins of the world, exhibited and offered by him to God the Father, for the reconciliation of man s nature to God s favour and grace. And this I write, because this author speaketh so precisely how Christ offered himself never but once. Whereby if he mean by once offering the whole action of our redemption, which was consummate and perfected upon the cross, all must confess the substance of that work of redemption by the oblation of Christ on the cross 2 to have been absolutely finished, and so once offered for all. But there is no scripture whereupon we might conclude, that Christ did in this mortal life, but in one particular moment of time, offer himself to his Father. For St Paul describeth it to the Philippians, under the word of humiliation, to have continued the whole time of Christ s conversation here, even to the death, the death of the cross. And that this obedience to God in humility is called offering, appeareth by St Paul, when he exhorted 3 us to offer our bodies, which meaneth a continual obedience in the observation of God s will, and he calleth oblationem gentium, to bring them to the faith*. And Abraham s willing obedience, ready at God s commandment to offer Isaac, is called the offering of Isaac, and is in very deed a true offering. And every man 5 offer eth himself to God when he yieldeth to God s calling, and presenteth himself ready to do God s will and commandment, who then may be said to offer his service, that is to say, to place his service in sight, and before him f before whom it should be done. And because our Saviour Christ, by the decree of the whole Trinity, took man s nature upon him, to suffer death for our redemption ; which death, in his last supper, he declared plainly he would suffer : we read in St Cyprian how Christ offered himself in his supper, ful filling the figure of Melchisedech, who by the offering of bread and wine signified that high mystery of Christ s supper, in which Christ, under the form of bread and wine, gave his very body and blood to be eaten and drunken, and in the giving thereof declared the determination of his glorious passion, and the fruit and effect thereof. Which doing was a sweet and pleasant oblation to God ttte Father, containing a most perfect obedience to God s will and pleasure. And in the mystery of this supper was written, made, and sealed, a most perfect testimony for an effectual memory of Clirist s offering of himself to his Father, and of his death and passion, with the fruit thereof. And therefore Christ ordained this supper to be observed and continued for a memory of his coming Q : so as we that saw not with our bodily eyes Christ s death and passion, may, in the celebration of the supper, be most surely ascertained of the truth out of Chrises own mouth, who still speaketh in the person of the minister of the church, " This is my body that is betrayed for you ; this is my blood that is shed for you in remission of sin :" and therewith maketh his very body and his precious blood truly present 7 , to be taken of us, eaten, and drunken. Whereby we be assured, that Christ is the same to us that he was to them, and useth us as familiarly as he did them; offereth himself to his Father for us as well as for them ; declareth his will in the fruit of his death to pertain as well to us as to them. Of which death we be assured by his own mouth, that he suffered the same to tlie effect he spake of; and by 8 the continual feeding in this high mystery of the same very body that suffered, and feeding of it without consumption, being continually exhibited unto us a living body and a lively blood, not only our soul is specially and spiritually comforted, and our body thereby reduced to more conformable obedience to the soul, but also we, by the partici pation of this most precious body and blood, be ascertained of the resurrection and regeneration of our bodies and fiesh, to be by God s power made incorruptible and immortal, to live, and have fruition in God, with our souls 9 for ever. Wherefore having this mystery of Christ s supper, so many trutJis in it, the church hath [ l Ascertained us to be in him, Grig. ed. Win- Chester.] [ 2 Of Christ s body on the cross, 1551.] [ 3 Exhorteth, Orig. ed. Winch.] [ 4 To faith. Ibid.] [ 5 And each man, 1551.] [ 6 A memory to his coming, 1551.] [ 7 His very body truly present, and his pre cious blood truly present, 1551.] [ 8 By supplied from Orig. ed. Winch. It is wanting in both editions of Cranmer.] [ 9 With our soul, 1551.] OF THE PRESENCE OF CHRIST. 83 celebrate them all, and knowledged them all of one certainty in truth, not as figures, but really "Truths and in deed 10 ; that is to say, as our bodies 11 shall be in the general resurrection regenerate in together. deed, so we believe we feed Jiere of Christ s body in deed. And as it is true that CJirists body in deed is betrayed for us, so it is true that he giveth us to eat his very body in deed. And as it is true that Christ was in earth, and did celebrate this supper: so it is true tJiat he com manded it to be celebrated by us till he come. And as it is true that Christ was very God omnipotent, and very man : so it is true that he could do that he affirmed by his word himself to do. And as he is most sincere truth: so may we be truly assured that he would, and did, as he said. And as it is true that he is most just : so it is true that he assisteth the doing of his commandment in the celebration of the holy supper. And therefore, as he is author of this most holy sacrament of his precious body and blood : so is he the maker of it, and is the invisible priest, who, as Emissene saith, by his secret power, with his word, changeth the visible Emissenus. creatures into the, substance of his body and blood. Wherein man, the visible priest and invisible minister, by order of the church, is only a dispenser of the mystery, doing and saying as the l^Cor. iv. Holy Ghost hath taught the church to do and say 12 . Finally, as we be taught by faith all these to be true : so when wanton reason (faith being asleep) goeth about by curiosity to impair any one of these truths, tlie chain is broken, the links sparkle abroad, and all is brought in danger to be scattered and scambled at. Truths have been abused, but yet they be true, as they were before; for no man can make that is true false: and abuse is man s fault, not the thing s 13 . Scripture in speech giveth to man as God s minister the name of that action which God specially worketh in that mystery. So it pleaseth God to honour the ministry of man in his church, by whom it also pleaseth him to work effectually. And Christ said, " They that believe in me, shall do the works that I do, and greater." Wlien all "Errors. this honour is given to man, as spiritually to regenerate, when the minister saith "I baptize tJtee," and to remit sin to such as fall ajler, to be also a minister in consecration of Christ s most precious body, with the ministration of other sacraments, benediction^, and prayer : if man should then wax proud, and glory as of himself, and extol his own devotion in these ministries ; such men should bewray tJieir own naughty hypocrisy, and yet thereby impair not the very dignity of the ministry, ne the very true fruit and effect thereof. And therefore when the church by the minister, and with the minister 15 , prayeth that the creatures of bread and wine, set on the altar (as the book of common prayer in this realm hath ordered), may be unto us the body and blood of our Saviour Christ; we require then the celebration of the same supper, which Christ made to his apostles, for to be the continual memory of his death, with all fruit and effect, such as the same had in the first institution. Wherefore when the minister pronounceth Christ s words, as spoken of his mouth, it is to be believed, that Christ doth now, as he did then. And it is to be noted, that altJiough in the sacrament of baptism the minister saith, "I baptize tJiee," yet in the celebration of his supper the words be spoken in Christ s person, as saying himself, " Tliis is my body that is broken for you," which is to us not only a memory, but an effectual memory, with the very presence of Christ s body and blood, our very sacrifice : who doing now, as he did then, offereth himself to his Father as he did then, not to renew that offering, as though it were imperfect, but *Onc offering continually to refresh us, that daily fall and decay. And as St John saith, " Christ is our many"** n advocate and entreateth for us," or pleadeth for us, not to supply any want on God s behalf, 1 Joh but to relieve our wants in edification, wherein the ministry of the church travailcth to bring man to perfection in Christ, which Christ himself doth assist, and absolutely perform in his 84. church, his mystical body. Now when we have Christ s body thus present in the celebration of the Jioly supper, and by Chrises mouth present unto us, saying, " This is my body which is betrayed for you" then have we Christ s body recommended unto us as our sacrifice, and a sacrifice propitiatory for all the sins of the world, being the only sacrifice of Christ s church, the pure and clean sacrifice ivhercof the prophet Malachi spake, and whereof the fathers in Mai. i. Christ s church have since the beginning continually written; tlie very true presence whereof, most constantly believed, hath increased from time to time such ceremonies as have been used in the celebration of that supper, in which by Christ s own mouth we be ascertained of his most glorious death and passion, and the self same body that suffered, delivered unto us in mystery, to be eaten of us, and therefore so to be worshipped and acknowledged of us as [ 10 But really in deed, 1551.] [ n As our body, 1551.] [ I2 To be done and said, 1551.] [ u Man s fault, and not the tilings, 1551.] [ u Benedictions, Orig. ed. Winch.] [ 15 Orig. ed. \Vinch. omits the words, and with the minister. ] [ 16 Of this supper, Orig. ed. Winch.] 62 84 THE THIRD BOOK. our very only sacrifice) in whom, by whom, and for whom, our other private gifts and sacrifices be acceptable, and no otherwise 1 . Errors. And therefore, as Christ declareth in the supper himself an offering, and sacrifice for our The whole sin, offering himself to his Father as our mediator, and so therewith recommendeth to his th "minuter, Father the church, his body, for which he suffereth : so tJie church at the same supper in their offering of lauds and thanks, with such other gifts as they have received from God, join tliemselves with their head Christ, presenting and offering him, as one by whom, for whom, w r hSein t i > s ry and in whom, all that by God s grace man can do well, is available and acceptable, shewed our an( % without whom nothing by us done can be pleasant in the sight of God. Whereupon this persuasion hath been duly conceived, which is also in the book of common prayer in the celebration of the holy supper retained, that it is very profitable at that time, when the memory of Chrisfs death is solemnized, to remember with prayer all estates of the church, and to recommend them to God, which St Paul to Timothy seemeth to require. At which time, as Christ signifieth unto us by the certainty of his death, and giveth us to be eaten, as it were in pledge, the same his precious body that suffered : so we, for declaration of our confidence in the death and sacrifice, do kindly remember with thanks his special gifts, and charitably remember the rest of the members of Christ s church with prayer, and, as we are able, should with our bodily goods remember at that time specially to relieve such as have need by poverty. And again, as Christ putteth us in remembrance of his great benefit, so we should throughly remember him for our part, with the true confession of this mystery, wherein is recapitulate a memorial of all gifts and mysteries that God in Christ hath wrought for us. In the consideration and estimation whereof, as there hath been a fault in the security of such as, so their names were remembered in this holy time of memory, they cared not how much they forgat themselves : so there may be a fault in such as, neglecting it, care not whether they be remembered there at all, and therefore would have it nothing but a plain eating and drinking. How much the remembrance in prayer may avail, no man can prescribe; but that it availeth, every Christian man must confess. Man may nothing arrogate to his devotion. But St James said truly, Multum valet ofatio justi assidua. It is to be abhorred to have hypocrites that counterfeit devotion, but true devotion is to be wished of God and prayed for, which is God s gift, not to obscure his glory, but to set it forth ; not that we should then trust in mens merits and prayers, but laud and glorify God in them; qui talem potestatem dcdit ho- minibus, one to be judged able to relieve another with his prayer, referring all to proceed from God, by the mediation of our Saviour and Redeemer, Jesus Christ. I have tarried long in this matter, to declare that, for the effect of all celestial or worldly gifts to be obtained of God in the celebration of Christ s holy supper, when we call it the communion, is now prayed for to be present, and is present, and with God s favour shall be obtained, if we devoutly, reverently, charitably, and quietly use and frequent the same, without other innovations than the order of the book prescribeth. Now to the last difference. James v. CANTERBURY. 85. How is " this comparison out of the matter of the presence of Christ s most precious body in the sacrament," when the papists say that the mass is not a sacrifice pro pitiatory, but because the presence of Christ s most precious body being presently there? And yet if this comparison be out of the matter (as you say it is), why do you then wrestle and wrangle with it so much? And do I "seem to grant the presence of Christ s body in the first part of my comparison," when I do nothing there but re hearse what the papists do say? But because all this process (which you bring in here out of tune and time) belongeth to the last book, I will pass it over unto the proper place, only by the way touching shortly some notable words. Although you "never read that the oblation of the priest is satisfactory by devo- t * on * *ke P r i es V 7 et nevertheless the papists do so teach, and you may find it in *keir * Thomas, both in his Sum, and upon the fourth of the sentences; whose words 2 3. 3 q.79.art. have been read in the universities almost these three hundred years, and never until this day reproved by any of the papists in this point. He saith: Quod sacrificium t 1 And none otherwise, 1551.] [ 2 Works, 1551.] [ 3 Hoc sacramentum simul est sacrih cium et sacramentum. In quantum vero est sacrificium habet vim satisfactivam, &c. Thomas Aquinas, Pars in. Qusest. Ixxix. Art. 5. p. 202. Antverp. 1624.] OF THE PRESENCE OF CHRIST. 85 saccrdotis habet vim satisfactivam, sed in satisfactione magis attenditur qffectus offe- rentis, quam quantitas oblationis. Ideo satufactoria cst illis pro quilus qffertur, vel etiam ojfcrcntilus, secundum quantitatem suce devotionis, et non pro tota poma. But here the reader may see in you, that the adversaries of the truth sometime be enforced to say the truth, although sometime they do it unawares ; as Caiaphas j h. xi. prophesied the truth, and as you do here confess, that Christ is our satisfaction wholly and fully. And yet the reader may note your inconstancy. For afterward, in the last book, you give Christ such a nip, that of that whole satisfaction you pinch half away from him, and ascribe it to the sacrifice of the priest, as I shall more fully declare in my answer to the last book. For you say there, " that the sacrifice of Christ giveth us life, and that the sacrifice of the priest continueth our life." And here, good reader, thou art to be warned, that this writer in this place gocth about craftily to draw thee from the very work of our full redemption, wrought by our Saviour Christ upon the cross, unto a sacrifice (as they say) made by him the night before at his last supper. And forasmuch as every priest (as the papists say) maketh the same sacrifice in his mass, therefore, consequently, it followeth by this writer, that we must seek our redemption at the priest s sacrifice. And so Christ s blessed passion (which he most obediently and willingly suffered for our salvation upon the cross,) was not the only and sufficient sacrifice for remission of our sins. The only will, I grant, both in good things and evil, is accepted 4 or rejected Th e dec before God, and sometime hath the name of the fact 5 , as the will of Abraham to cS^ offer his son is called the oblation of his son ; and Christ called him an adulterer in Jfl, t his heart, that desireth another man s wife, although there be no fact committed in f Heb. xi. Matt. v. And yet Abraham s will alone was not called the oblation of his son, but his will declared by many facts and circumstances : for he carried his son three days Gen. xxii. journey to the place where God had appointed him to slay and offer his son Isaac, whom he most entirely loved. He cut wood to make the fire for that purpose, he laid the wood upon his son s back, and made him carry the same wood wherewith he should be brent . And Abraham himself (commanding his servants to tarry at the 86. foot of the hill) carried the fire and sword, wherewith he intended (as God had com manded) to kill his own son, 7 whom he so deeply loved. And by the way as they went, his son said unto his father : " Father, see, here is fire and wood, but where is the sacrifice that must be killed ? " How these words of the son pierced the father s heart, every loving father may judge by the affection which he beareth to his own children. For what man would not have been abashed and stayed at these words? thinking thus within himself: "Alas! sweet son, thou dost ask me where the sacrifice is, thyself art the same sacrifice that must be slain, and thou (poor inno cent) carriest thine own death upon thy back, and the wood wherewith thyself must be brent. Thou art he whom I must slay, which art most innocent, and never offended." Such thoughts, you may be sure, pierced through Abraham s heart, no less than the very death of his son should have done : as David lamentably bewailed his son 2 Kings xii lying in the pangs of death, but after he was dead he took his death quietly and ^ comfortably enough. But nothing could alter Abraham s heart, or move him to dis obey God; but forth on he goeth with his son to the place which God had appointed, and there he made an altar, and laid the wood upon it, and bound his son, and laid him upon the heap of the wood in the altar, and took the sword in his hand, and lifted up his arm to strike and kill his son, and would have done so in deed if the angel of God had not letted 8 him, commanding bun in the stead of his son to take a ram that was fast by the horns in the briars. This obedience of Abraham unto God s commandment in offering of his son, declared by so many acts and cir cumstances, is called in the scripture the offering of his son, and not the will only. [ 4 Be accepted, 1551.] [ s Have the names of the fact, 1551.] [" Brent, i. e. burnt.] To kill his son, 1551.J Letted, i. e. hindered, prevented.] 8(5 THE THIRD BOOK. Nor the scripture calleth not the declaration of Christ s will in his last supper to suffer death by the name of a sacrifice satisfactory for sin, nor saith not that he was there offered in deed. For the will of a thing is not in deed the thing. And if the declaration of his will to die had been an oblation and sacrifice propitiatory for sin, then had Christ been offered not only in his supper, but as often as he declared his Matt. xx. w iH to die. As when he said, long before his supper many times, that he should be Lukexviii. betrayed, scourged, spit upon, and crucified, and that the third day he should rise John vi. John x. Heb. viii. 87. *Rom. vi. * Heb. vii. ix. Pet. iii. again: and when he bade them destroy the temple of his body, and he would build it up again within three days: and when he said that he would give his flesh for the life of the world, and his life for his sheep. And if these were sacrifices propitiatory or satisfactory for remission of sin, what needed he then after to die, if he had made the propitiatory sacrifice for sin already ? For either the other was not vailable thereto, or else his death was in vain, as St Paul reasoneth of the priests of the old law, and of Christ. And it is not read in any scripture, that Christ s will, declared at his supper, was effectuous and sufficient for our redemption, but that his most willing death and passion was the oblation sufficient to endure for ever and ever, world without end. But what sleights and shifts this writer doth use to wind the reader into his error, it is wonder to see, by devising to make two sacrifices of one will ; the one by declaration, the other 1 by execution ; a device such as was never imagined before of no man, and meet to come out of a fantastical head. But I say precisely, that Christ offered himself never but once, because the scripture so precisely and so many times saith so; and having the same for my warrant, it maketh me the bolder to stand against you, that deny that thing which is so often times repeated in scripture. And where you say, that "there is no scripture whereupon we might conclude that Christ did in this mortal life, but in one particular moment of time, offer himself to the Father :" to what purpose you bring forth this moment of time I cannot tell, for I made no mention thereof, but of the day of his death ; and the scripture saith plainly, that as it is ordained for every man to die but once, so Christ was offered but once ; and saith further, that sin is not forgiven but by effusion of blood, and therefore if Christ had been offered many times, he should have died many times. And of any other offering of Christ s body for sin, the scripture speaketh not. For although St Paul to the Philippians speaketh of the humiliation of Christ by his incarnation, and so to worldly miseries and afflictions, even unto death upon the cross ; yet he calleth not every humiliation of Christ a sacrifice and oblation for remis sion -of sin, but only his oblation upon Good Friday, which as it was our perfect redemption, so was it our perfect reconciliation, propitiation, and satisfaction for sin. And to what purpose you make here a long process of our sacrifices of obedience unto God s commandments, I cannot devise. For I declare in my last book, that all our whole obedience unto God s will and commandments is a sacrifice acceptable to God, but not a sacrifice propitiatory : for that sacrifice Christ only made, and by that his sacrifice all our sacrifices be acceptable to God, and without that none is acceptable to him. And by those sacrifices all Christian people offer themselves to God, but they offer not Christ again for sin; for that did never creature but Christ himself alone, nor he never but upon Good Friday. For although he did institute the night before a remembrance of his death 2 , under the sacraments of bread and wine, yet he made not at that time the sacrifice of our redemption and satisfaction for our sins, but the next day following. And the declaration of Christ at his last supper, that he would suffer death, was not the cause wherefore Cyprian said that Christ offered himself in his supper. For I read not in any place of Cyprian, to my remembrance, any such words that Christ offered himself in his supper; but he saith, that Christ Cyprianus, offered the same thing which Melchisedech offered 3 . And if Cyprian say in any place Heb. ix. *Ibidem. Phil. ii. [ J And the other, 1551.] [ 2 A sacrament of his death, 1551.] [ 3 Nam quis magis sacerdos Dei summi, quam Dominus noster Jesus Christus? qui sacrificiuni Deo patri obtulit, et obtulit hoc idem quod Mel chisedech obtulerat, id est, panem et vinum, suum scilicet corpus et sanguinem Cyprian, ad Cae- cilium, Epist. Ixiii. p. 143. Paris. 1574.] OF THE PRESENCE OF CHRIST. 87 that Christ offered himself in his supper, yet he said not that Christ did so for this cause, that in his supper he declared his death. And therefore here you make a deceitful fallax in sophistry, pretending to shew that thing to be a cause, which is not the true cause indeed. For the cause why Cyprian, and other old authors, say that Christ made an oblation and offering of himself in his last supper, was not that he declared there that he would suffer death, (for that he had declared many times before ;) but the cause was, that there he ordained a perpetual memory of his death, which he would all faithful Christian people to observe from time to time, remem bering his death, with thanks for his benefits, until his coming again. And there fore the memorial of the true sacrifice made upon the cross, as St Augustine saith, is August, ad called by the name of a sacrifice, as a thing that signifieth another thing is called J$3S. u
by the name of the thing which it signifieth, although in very deed it be not the same 4 .
And the long discourse that you make of Christ s true presence, and of the true 88.
eating of him, and of his true assisting us in our doing of his commandment, all these
be true. For Christ s flesh and blood be in the sacrament truly present, but spiritu
ally and sacramentally, not carnally and corporally. And as he is truly present, so
is he truly eaten and drunken, and assisteth us. And he is the same to us that he
was to them that saw him with their bodily eyes. But where you say, that he is
as familiar with us as he was with them, here I may say the French term which
they use for reverence sake, Save vostre grace. And he offered not himself then for
them upon the cross, and now offereth himself for us daily in the mass; but upon
the cross he offered himself both for us and for them. For that his one sacrifice of
his body, then only offered, is now unto us by faith as available as it was then for
them. " For with one sacrifice," as St Paul saith, " he hath made perfect for ever Hcb. x.
them that be sanctified."
And where you speak of the participation of Christ s flesh and blood, if you mean
of the sacramental participation only, that thereby we be ascertained of the regenera
tion 5 of our bodies, that they shall live, and have the fruition of God with our souls
for ever, you be in an horrible error. And if you mean a spiritual participation of
Christ s body and blood, then all this your process is in vain, and serveth nothing
for your purpose to prove that Christ s flesh and blood be corporally in the sacra
ment, under the forms of bread and wine, and participated of them that be evil, as
you teach; which be no whit thereby the more certain of their salvation, but of their icon xi.
damnation, as St Paul saith.
And although the holy supper of the Lord be not a vain or fantastical supper,
wherein things should be promised, which be not performed, to them that worthily
come thereunto, but Christ s flesh and blood be there truly eaten and drunken in deed ;
yet that mystical supper cannot be without mysteries and figures. And although we
feed in deed of Christ s body, and drink in deed his blood, yet not corporally, quanti
tatively, and palpably, as we shall be regenerated at the resurrection, and as he was
betrayed, walked here in earth, and was very man. And therefore, although the things
by you rehearsed be all truly done, yet all be not done after one sort and fashion;
but some corporally and visibly, some spiritually and invisibly. And therefore to all
your comparisons or similitudes here by you rehearsed, if there be given to every one
his true understanding, they may be so granted all to be true. But if you will link
all these together in one sort and fashion, and make a chain thereof, you shall far
pass the bonds of wanton reason, making a chain of gold and copper together, con
founding and mixing together corporal and spiritual, heavenly and earthly things, and
bring all to very madness and impiety, or plain and manifest heresy.
And because one single error pleaseth you not, shortly after you link a number A chain of
of errors almost together 6 in one sentence, as it were to make an whole chain of errors,
saying not only that Christ s body is verily present in the celebration of the holy
supper, meaning of corporal presence, but that it is also our very sacrifice, and sacri
fice propitiatory for all the sins of the world, and that it is the only sacrifice of the
[ 4 See the passage which is quoted at length I [ 5 Of our regeneration of our bodies, 1551.J
below, p. 124.] I [8 Together almost, 1551.]
88 THE THIRD BOOK.
Mai.i. church, and that it is the pure and clean sacrifice, whereof Malachi spake, and that
Christ doth now in the celebration of this supper as he did when he gave the same
89. to his apostles, and that he offereth himself now as he did then, and that the same
offering is not now renewed again. This is your chain of errors, wherein is not one
link of pure gold, but all be copper 1 , feigned, and counterfeit: for neither is Christ s
body verily and corporally present in the celebration of his holy supper, but spiritually ;
nor his body is not the very sacrifice, but the thing whereof the sacrifice was made ;
and the very sacrifice was the crucifying of his body, and the effusion of his blood
unto death. Wherefore of his body was not made a sacrifice propitiatory for all the
sins of the world at his supper, but the next day after upon the cross. Therefore
isai liii. saith the prophet, that we were made whole by his wounds : Livore ejtis sanati
sumus.
Nor that sacrifice of Christ in the celebration of the supper is not the only sacri
fice of the church, but all the works that Christian people do to the glory of God be
sacrifices of the church, smelling sweetly before God. And they be also the pure and
clean sacrifice whereof the prophet Malachi did speak. For the prophet Malachi spake
of no such sacrifices as only priests make, but of such sacrifice as all Christian people
make both day and night, at all times and in all places.
Nor Christ doth not now as he did at his last supper, which he had with his
apostles; for then, as you say, he declared his will, that he would die for us: and
if he do now as he did then, then doth he now declare that he will die for us
again.
But as for offering himself now as he did then, this speech may have a true sense,
being like to that which sometime was used at the admission of unlearned friars and
monks unto their degrees in the universities : where the doctor that presented them
deposed that they were meet for the said degrees, as well in learning as in virtue.
And yet that deposition in one sense was true, when indeed they were meet neither
in the one nor in the other. So likewise, in that sense Christ offereth himself now as
well as he did in his supper; for indeed he offered himself a sacrifice propitiatory for
remission of sin in neither of both, but only upon the cross, making there a sacrifice
full and perfect for our redemption, and yet by that sufficient offering made only at
Heb.vii. that time he is a daily intercessor for us to his Father for ever. Finally, it is not
true that the offering in the celebration of the supper is not renewed again. For the
same offering that is made in one supper is daily renewed and made again in every
supper, and is called the daily sacrifice of the church.
the very chain of Beelzebub, able to draw into hell as many as come within the com
pass thereof. And how would you require that men should give you credit, who
within so few lines knit together so many manifest lies ? It is another untruth also
which you say after, that Christ declared in the supper himself an offering and sacri
fice for sin ; for he declared in his supper, not that he was then a sacrifice, but that
a sacrifice should be made of his body, which was done the next day after, by the
voluntary effusion of his blood: and of any other sacrificing of Christ for sin the
scripture speaketh not. For although the scripture saith that our Saviour Christ is
a continual intercessor 2 for us unto his Father, yet no scripture calleth that intercession
90. a sacrifice for sin, but only the effusion of his blood, which it seemeth you make
him to do still, when you say that he suffereth ; and so by your imagination he should
now still be crucified, if he now suffer, as you say he doth. But it seemeth you
pass not greatly what you say, so that you may multiply many gallant words to
the admiration of the hearers. But forasmuch as you say that Christ offereth him
self in the celebration of the supper, and also that the church offereth him, here I
would have you declare how the church offereth Christ, and how he offereth him
self, and wherein those offerings stand, in words, deeds, or thoughts, that we may
know what you mean by your daily offerings of Christ. Of offering ourselves unto
God in all our acts and deeds, with lauds and thanksgiving, the scripture maketh
[ ! One link true gold, but all copper be, 1551.] [ 2 Is now a continual intercessor, 1551.]
OF THE PRESENCE OF CHRIST.
89
mention in many places : but that Christ himself in the holy communion, or that
the priests make any other oblation than all Christian people do, because these be
papistical inventions without scripture, I require nothing but reason of you, that you
should so plainly set out these devised offerings, that men might plainly understand
what they be, and wherein they rest. Now in this comparison, truth it is, as you say,
that you have spent many words, but utterly in vain, not to declare, but to darken
the matter. But if you would have followed the plain words of scripture, you needed
not 3 to have tarried so long, and yet should you have made the matter more clear a
great deal.
Now followeth my last comparison.
They say, that Christ is corporally in many places at one time, affirming The thir
that his body is corporally and really present in as many places as there
be hosts consecrated. We say, that as the sun corporally is ever in heaven,
and no where else, and yet by his operation and virtue the sun is here in
earth, by whose influence and virtue all things in the world be corporally
regenerated, increased, and grow to their perfect state ; so likewise our Saviour
Christ bodily and corporally is in heaven, sitting at the right hand of his
Father, although spiritually he hath promised to be present with us upon
earth unto tbe world s end. And whensoever two or three be gathered toge
ther in his name, he is there in the midst among them, by whose supernal 4 grace
all godly men be first by him spiritually regenerated, and after increase and
grow to their spiritual perfection in God, spiritually by faith eating his
flesh, and drinking his blood, although the same corporally be in heaven, far
distant from our sight.
WINCHESTER.
The true teaching is, that Christ s very body is present under the form of bread, in as [The answer.
many hosts as be consecrate, in how many places soever the hosts be consecrate, and is there Winchester.]
really and substantially, which words " really and substantially" be implied, when we say, truly Reaiiy, sub
present. The word "corporally" may have an ambiguity and doubleness in respect and rela- mnyl corpo-
tion : one is to the truth of the body present, and so it may be said, Christ is corporally rally
present in sacrament; if the word 5 corporally be referred to the manner of the presence, then
we should say, Christ s body were present after a corporal manner, which we say not, but Matmer of
in a spiritual manner ; and therefore not locally nor by manner of quantity, but in such presence>
manner as God only knoweth, and yet doth us to understand by faith the truth of the very
presence, exceeding our capacity to comprehend tlie manner " how." This is tJie very true *The true
teaching to affirm the truth of the presence of Christ s very body in the sacrament, even o/ 1 time of the
the same body that su/ercd, in plain, simple, evident terms and words, such as cannot by ^\^^\ y
cavillation be mistaken and construed, so near as possibly man s infirmity permitteth and in Jg sacra "
su/ercth. Now let us consider in what sort tJie author and his company, which he calleth 91.
"toe say," do understand the sacrament, who go about to express tJie same by a similitude
of the creature of tJie sun, " which sun," this author saith, " is ever corporally in heaven, and
no wJiere else, and yet by operation and virtue is here in earth : so Christ is corporally in
heaven, %c" In this matter of similitudes, it is to be taken for a truth undoubted, that there God s
is no creature by similitude, ne any language of man able to express God and his myste-
ries. For and things that be seen or heard might throughly express God s invisible myste-
ries, the nature whereof is that they cannot throughly be expressed, they were no mysteries : similitudes.
and yet it is true, that of things visible, wherein God worketh wonderfully, there may be
great resemblances 6 , some shadows, and as it were inductions, to make a man astonwd in
consideration of things invisible, when he seeth things visible so wonderfully wrought, and to
have so marvellous effects. And divers good catholic devout men have by divers natural
fhings gone about to open unto us the mystery of the Trinity, partly by the sun, as the au-
thorl doth in the sacrament, partly by Jire, partly by the soul of man, by the musician s
[ 3 You needed not indeed, 1551.J
[ 4 Supernal, i. e. heavenly.]
[ 5 Present in the sacrament, but if the word,
&c., 1551.]
[ 6 Some resemblances, 1551.]
[ 7 As this author, 1551.J
90
THE THIRD BOOK.
92.
science, the art, the touch with the player s fingers, and the sound of the chord, wherein wit !
hath all travailed the matter, yet remaineth dark, ne cannot be throughly set forth by any
similitude. But to the purpose of this similitude of the sun, which sun, this author saith, " is
only corporally in heaven, and no where else," and in the earth the operation and virtue of
tlie sun : so as by this author s supposal, the substance of the sun should not be in earth,
but only by operation and virtue: wherein if this author erreth, he doth the reader to un
derstand, that if he err in consideration of natural things, it is no marvel though he err
in heavenly things. For, because I will not of myself begin the contention with this author
of the natural work of the sun, I will bring forth the saying of Martin Bucer, now resi
dent at Cambridge, who vehemently, and for so much truly, affirmetli the true real presence
of Christ s body in the sacrament: for he saith, Christ said not, this is my spirit, this is
my virtue, but, " this is my body : " wherefore, he saith, we must believe Christ s body to be
there, tlie same that did hang upon the cross, our Lord himself, which in some part to de
clare, he useth the similitude of the sun for his purpose, to prove Christ s body present really
and substantially in the sacrament, where this author useth the same similitude to prove the
body of Christ really absent. I will write in Jiere as Bucer speaketh it in Latin, expound
ing the twenty-sixth chapter of St Matthew, and tJien I will put the same in English.
Bucer s words be these :
Ut sol vere uno in loco cceli visibilis circumscriptus est, radiis tamen suis prsesens
vere et substantialiter exhibetur ubilibet orbis: ita Dominus etiamsi circumscribatur
uno loco coeli arcani et divini, id est glorise Patris, verbo tamen suo et sacris symbolis
vere et totus ipse Deus et homo prsesens exhibetur in sacra coena, eoque substantialiter;
quam prsesentiam non minus certo agnoscit mens credens verbis his Domini et symbolis,
quam oculi vident et habent solem prsesentem demonstratum et exhibitum sua corporali
luce. Res ista arcana est, et novi Testamenti, res fidei : non sunt igitur hue admittendse
cogitationes de prsesentatione corporis, quse constat ratione hujus vitse etiamnum patibilis
et fluxse. Verbo Domini simpliciter inhserendum est, et debet fides sensuum defectui
prsebere supplementum. Which is thus much in English: "As the sun is truly placed de-
terminately in one place of the visible heaven, and yet is truly and substantially present by
means of his beams elsewhere in tJie world abroad: so our Lord, although he be compreliended
in one place of the secret and divine heaven, that is to say, the glory of his Father, yet
nevertheless by his word and holy tokens he is exhibit present truly whole God and man,
and therefore in substance in his holy supper; which presence man s mind, giving credit to
his words and tokens, with no less certainty acknowledged, than our eyes see, and have the
sun present, exhibited, and shewed with his corporal light. Tliis is a deep secret matter, and
of the new testament, and a matter of faith ; and therefore herein thoughts be not to be re
ceived of such a presentation of the body as consisteth in the manner of this life transitory,
and subject to su/er. We must simply cleave to the word of Christ, and faith must relieve
the default of our senses."
Thus hath Bucer expressed his mind, whereunto, because the similitude of the sun doth
not answer in all parts, he noteth wisely in the end, how this is a matter of faith, and
therefore upon the foundation of faith we must speak of it, thereby to supply where our
senses fail. For the presence of Christ, and whole Christ, God and man, is true, although
we cannot think of the manner "how." The chief cause why I bring in Bucer is this, to
shew how, in his judgment, we have not only in earth the operation and virtue of the sun,
but also the substance of the sun, by mean of the sun-beams, which be of the same substance
with the sun, and cannot be divided in substance from it ; and therefore we have in earth the
substantial presence of the sun, not only the operation and virtue. And howsoever the sun
above in the distance appeareth unto us of another sort, yet the beams that touch the earth
be of the same substance with it, as clerks say, or at the least as Bucer saith, whom I never
heard accompted papist ; and yet for the real and substantial presence of Christ s very body
in the sacrament, writeth pithily and plainly, and here encountereth this author with his simi
litude of the sun directly; wJiereby may appear, how much soever Bucer is esteemed other
wise, he is not with this author regarded in the truth of the sacrament, which is one of the
high mysteries in our religion. And this may suffice for that point of the similitude, where
this author would have Christ none otherwise present in the sacrament, than he promised to
be in the assembly of such as be gatliered together in his name: it is a plain abolition of the
mystery of tJie sacrament, in the words whereof Christ s human body is exhibit and made
[ l Wherein when wit, 1551.]
OF THE PRESENCE OF CHRIST. 91
present with his very Jlesh to feed us, and to that singular and special e/ect 2 tlie other pre
sence of Christ in the assembly made in his name is not spoken of; and it hath no appearance
of learning in scriptures, to conclude under one consideration a specialty and a generality.
And therefore it was well answered of him that said, " If I could tell reason, there were no August
faith:" if I could shew the like, it were not singular. Which both be notable in this sa- Sn
crament, where condemning all reason, good men both constantly believe that Christ sitteth on
the right hand of his FatJier, very God and man, and also without cliange of place doth
nevertheless make himself by his power present, both God and man, under the form of bread
and wine, at tlie prayer of tlie church and by tlie ministry of the same, to give life to such
as with faith do according to his institution in his holy supper worthily receive him, and to
the condemnation of such as do unworthily presume to receive him tJiere. For the worthy
receiving of whom we must come endued with Christ, and clothed with him seemly in that
garment, to receive his most precious body and blood, Christ whole God and man, whereby
Jie then dwelleth in us more abundantly, confirming in us the effects of his passion, and es
tablishing our hope of resurrection, then to enjoy the regeneration of our body, with a full
redemption of body and soul, to live with God in glory for ever.
CANTERBURY.
In this comparison I am glad that at the last we be come so near together ; for A concord
you be almost right heartily welcome home, and I pray you let us shake hands to- L" prince!"
gethcr 3 . For we be agreed, as me seemeth, that Christ s body is present, and the
same body that suffered : and we be agreed also of the manner of his presence. For
you say that the body of Christ is not present but after a spiritual manner, and so
say I also. And if there be any difference between us two, it is but a little and in
this point only : that I say that Christ is but spiritually in the ministration of tlie
sacrament, and you say that he is but after a spiritual manner in the sacrament.
And yet you say that he is corporally in the sacrament, as who should say that
there were a difference between spiritually, and a spiritual manner; and that it were
not all one, to say that Christ is there only after a spiritual manner, and not only
spiritually.
But if the substance of the sun be here corporally present with us upon earth, The presence
then I grant that Christ s body is so likewise: so that he of us two that erreth j n ofthesuu -
the one, let him be taken for a vain man, and to err also in the other. Therefore I 93.
am content that the reader judge indifferently between you and me, in the corporal
presence of the sun; and he that is found to err, and to be a fool therein, let him
be judged to err also in the corporal presence of Christ s body.
But now, master Bucer, help this man at need : for he that hath ever hitherto M. Eucer.
cried out against you, now being at a pinch driven to his shifts, crieth for help upon
you : and although he was never your friend, yet extend your charity to help him
in his necessity. But master Bucer saith not so much as you do : and yet if you
both said that the beams of the sun be of the same substance with the sun, who
would believe either of you both ? Is the light of the candle the substance of the
candle ? or the light of the fire the substance of the fire ? Or is the beams of the
sun any thing but the clear light of the sun? Now, as you said even now of me,
if you err so far from the true judgment of natural things, that all men may perceive
your error, what marvel is it if you err in heavenly things?
And why should you be offended with this my saying, that Christ is spiritually
present in the assembly of such as be gathered together in his name? And how can
you conclude hereof, that this is a plain abolition of the mystery of the sacrament,
because that in the celebration of the sacrament I say that Christ is spiritually
present? Have not you confessed yourself that Christ is in the sacrament but after
a spiritual manner? And after that manner he is also among them that be assembled
together in his name. And if they that say so do abolish the mystery of the sacra
ment, then do you abolish it yourself, by saying that Christ is but after a spiritual
[ 2 Special effect, which in the other, 1551.] p Together omitted, 1551.]
92 THE THIRD BOOK.
manner in the sacrament, after which manner you say also that he is in them that
be gathered together in his name, as well as I do, that say he is spiritually in both.
But he that is disposed to pick quarrels, and to calumniate all things, what can
be spoken so plainly, or meant so sincerely, but he will wrest it unto a wrong
sense? I say that Christ is spiritually and by grace in his supper, as he is when
two or three be gathered together in his name, meaning that with both he is spi
ritually, and with neither corporally; and yet I say not that there is no difference.
For this difference there is, that with the one he is sacramentally, and with the other
not sacramentally, except they be gathered together in his name to receive the sacra
ment. Nevertheless the selfsame Christ is present in both, nourisheth and feedeth both,
if the sacrament be rightly received. But that is only spiritually, as I say, and only
after a spiritual manner, as you say.
And you say further, that before we receive the sacrament, we must come endued
with Christ, and seemly clothed with him. But whosoever is endued and clothed with
Christ hath Christ present with him after a spiritual manner, and hath received Christ
whole both God and man, or else he could not have everlasting life. And therefore
is Christ present as well in baptism as in the Lord s supper. For in baptism be we
Gal. iii. endued with Christ, and seemly clothed with him, as well as in his holy supper we
eat and drink him.
WINCHESTER.
94. Thus I have perused these differences, which, well considered, methink sufficient to take away
and appease all such differences as might be moved against the sacrament, the faith whereof
hath ever prevailed against such as have impugned it. And I have not read of any that hath
written against it, but somewhat hath against his enterprise in his writings appeared, whereby
to confirm it, or so evident untruths affirmed, as whereby those that be as indifferent to the
truth as Salomon was in the judgment of the living child, may discern the very true mother
from the other, that is to say, who plainly intend the true child to continue alive, and who
could be content to have it be destroyed by division. God of his injinite mercy have pity on us,
and grant the true faith of this holy mystery uniformly to be conceived in our understandings,
and in one form of words to be uttered and preached, which in the book of common prayer
is well termed, not distant from the catholic faith in my judgment.
CANTERBURY.
Three parts You have so perused these differences, that you have made more difference than
ever was before : for where before there were no more but two parts, the true catholic
doctrine, and the papistical doctrine, now come you in with your new fantastical in
ventions, agreeing with neither part, but to make a song of three parts, you have
devised a new voluntary descant, so far out of tune, that it agreeth neither with the
tenor nor mean, but maketh such a shameful jar, that godly ears abhor to hear it.
For you have taught such a doctrine as never was written before this time, and uttered
therein so many untruths and so many strange sayings, that every indifferent reader
may easily discern that the true Christian faith in this matter is not to be sought at your
hands. And yet in your own " writings appeareth something to confirm the truth, quite
against your own enterprise," which maketh me have some hope, that after my answer
heard, we shall in the principal matter no more strive for the child, seeing that yourself
have confessed that Christ is but after a spiritual manner present with us. And there
is good hope that God shall prosper this child to live many years, seeing that now I
trust you will help to foster and nourish it up as well as I.
The true mo And yet if division may shew a step-mother, then be not you the true mother
chiki? fthe of the child, which in the sacrament make so many divisions. For you divide the
substances of bread and wine from their proper accidenccs, the substances also of
Christ s flesh and blood from their accidenccs, and Christ s very flesh sacramentally
from his very blood, although you join them again per concomitantiam ; and you divide
the sacrament so that the priest receiveth both the sacrament of Christ s body and
of his blood, and the lay people (as you call them) receive no more but the sacra
ment of his body, as though the sacrament of his blood and of our redemption
pertained only to the priests. And the cause of our eternal life and salvation you
OF THE PRESENCE OF CHRIST. 93
divide in such sort between Christ and the priest, that you attribute the beginning
thereof to the sacrifice of Christ upon the cross, and the continuance thereof you attri
bute to the sacrifice of the priest in the mass, as you do write plainly in your last book.
Oh ! wicked step-mothers, that so divide Christ, his sacraments, and his people !
After the differences followeth the third, fourth, fifth, arid sixth chapters of my
book, which you bind as it were altogether in one fardel 1 , and cast them quite away,
by the figure which you call "rejection," not answering one word to any scripture or 95.
old writer, which I have there alleged for the defence of the truth. But because the
render may see the matter plainly before his eyes, I shall here rehearse my words
Now to return to the principal matter, lest it might be thought a new device [Book in.]
of us, that Christ, as concerning his body and his human nature, is in heaven, cKcor-
and not in earth; therefore by God s grace it shall be evidently proved, that this Ken, and
is no new devised matter, but that it was ever the old faith of the catholic 00
church, until the papists invented a new faith, that Christ really, corporally,
naturally, and sensibly is here still with us in earth, shut up in a box, or
within the compass of bread and wine.
This ncedeth no better nor stronger proof than that which the old authors The proof
bring for the same, that is to say, the general profession of all Christian our^rffi-
pcople in the common creed, wherein, as concerning Christ s humanity, they common
bo taught to believe after this sort : That he was conceived by the Holy
Ghost,, born of the virgin Mary : that he suffered under Pontius Pilate : was
crucified, dead and buried : that he descended into hell, and rose again the
third day, that he ascended into heaven, and sittcth at the right hand of his
almighty Father, and from thence shall come to judge the quick and dead.
This hath been ever the catholic faith of Christian people, that Christ (as
concerning his body and his manhood) is in heaven, and shall there continue
until he come down at the last judgment.
And forasmuch as the creed makcth so express mention of the article of
his ascension, and departing hence from us, if it had been another article of
our faith, that his body tarricth also here with us in earth, surely in this
place of the creed was so urgent an occasion given to make some mention
thereof, that doubtless it would not have been passed over in our creed with
silence. For if Christ (as concerning his humanity) be both here, and gone
hence, and both these two bo articles of our faith, when mention was made
of the one in the creed, it was necessary to make mention of the other, lest
by professing the one we should be dissuaded from believing the other, being
so contrary the one to the other.
To this article of our creed accordeth holy scripture, and all the old ancient chap. \v.
doctors of Christ s church. For Christ himself said, "I leave the world, and go to
my Father." And also he said, "You shall ever have poor folks with you, but
you shall not ever have me with you." And he gave warning of this error
beforehand, saying that the time would come when many deceivers should be Matt. xxi
in the world, and say, " Here is Christ, and there is Christ, but believe them not,"
said Christ. And St Mark writeth in the last chapter of his gospel, that the Mark xvi
Lord Jesus was taken up into heaven, and sitteth at the right hand of his
Father. And St Paul exhorteth all men to seek for things that be above in coi. in.
heaven, " where Christ," saith he, " sitteth at the right hand of God" his Father.
Also he saith, that " we have such a bishop, that sitteth in heaven at the HCD. vm.
right hand of the throne of God s majesty;" and that he, " having offered Heb. x .
[ Fardel, i.e. a bundle.]
94
THE THIRD BOOK.
Chap. v.
96.
The proof
thereof by
ancient au
thors.
Origen. in
Matt. Horn.
33.
[1 John iv.]
Dardan.
epist. 57.
[Hunc lo
cum citat
Leo, epistola
probandum
in Christo
vera n for-
mam huma-
nam. Et in
tota epistola,
forma accipi-
tur pro sub-
stantia. Kci.
Einbd. 1557.]
one sacrifice for sins, sitteth continually at the right hand of God, until his
enemies be put under his feet as a footstool." And hereunto consent all the
old doctors of the church.
First Origen upon Matthew 1 reasoneth this matter, how Christ may be
called a stranger that is departed into another country, seeing that he is with
us alway unto the world s end, and is among all them that be gathered to
gether in his name, and also in the midst of them that know him not ; and
thus he reasoneth : If he be here among us still, how can he be gone hence
as a stranger departed into another country ? whereunto he answereth, that
Christ is both God and man, having in him two natures. And as a
man he is not with us unto the world s end, nor is present with all his faithful
that be gathered together in his name : but his divine power and spirit is
ever with us. Paul, saith he, was absent from the Corinthes in his body,
when he was present with them in his spirit : so is Christ, saith he, gone
hence, and absent in his humanity, which in his divine nature is every where.
And in this saying, saith Origen, we divide not his humanity, (for St John
writeth, that " no spirit that divideth Jesus can be of God,") but we reserve to
both his natures their own properties.
In these words Origen hath plainly declared his mind, that Christ s body
is not both present here with us, and also gone hence and estranged from us.
For that were to make two natures of one body, and to divide the body of
Jesus, forasmuch as one nature cannot at one time be both with us, and absent
from us. And therefore saith Origen, that the presence must be under-
standed of his divinity, and the absence of his humanity.
And according hereunto St Augustine writeth thus in an Epistle Ad Darda-
num : " Doubt not but Jesus Christ as concerning the nature of his manhood is
now there, from whence he shall come. And remember well and believe the pro
fession of a Christian man, that he rose from death, ascended into heaven,
sitteth at the right hand of his Father, and from that place, and none other,
shall he come to judge the quick and the dead. And he shall come, as the
angels said, as he was seen go into heaven, that is to say, in the same form
and substance, unto the which he gave immortality, but changed not nature.
After this form, (saith he, meaning his man s nature,) we may not think that
he is every where. For we must beware, that we do not so stablish
his divinity, that we take away the verity of his body 2 ." These be St Au
gustine s plain words. And by and by after he addeth these words : " The
Lord Jesus as God is every where, and as man is in heaven 3 ." And finally
he concludeth this matter in these few words : " Doubt not but our Lord Jesus
Christ is every where as God, and as a dAveller he is in man that is the temple
of God, and he is in a certain place in heaven, because of the measure of
a very body 4 ."
[ l Secundum hanc divinitatis suae naturam non
peregrinatur, sed peregrinatur secundum dispensa-
tionem corporis quod suscepit Haec autem dicen-
tes non solvimus suscepti corporis hominem, cum
sit scriptum apud Johannem, " Omnis spiritus qui
solvit Jesum, non est ex Deo :" sedunicuique sub-
stantiae proprietatem servamus Origen. in Matt,
cap. xxv. Tract. 33. Ed. Bened. Tom. III. p. 883.J
[ 2 Noli itaque dubitare ibi nunc esse hominem
Christum Jesum, unde venturus est, memoriterque
recole et fideliter tene Christianam confessionem, quo-
niam resurrexit a mortuis, ascendit in ccelum, sedet
ad dexteram Patris, nee aliunde quam inde venturus
est ad vivos mortuosque judicandos. Et sic venturus
est, ilia angelica voce testante, quemadmodum ire
visus est in ccelum, id est, in eadem carnis forma
atque substantia, cui profecto immortalitatem dedit,
naturam non abstulit. Secundum hanc formam non
est putandus ubique diffusus. Cavendum est enim,
ne ita divinitatem astruamus hominis, ut veritatem
corporis auferamus. August, de Praesentia Dei, ad
Dardanum, (Epist. Ivii.) Lib. i. cap.iii. Pars vui.
Basil, ap. Amerbach. 1506.]
[ 3 Una enim persona Deus et homo est, et
utrumque est unus Christus Jesus, ubique per id
quod Deus est, in ccelo autem per id quod homo.
Ibid. cap. iv.]
[ 4 Et ubique totum prjesentem esse (i. e. Chris-
OF THE PRESENCE OF CHRIST.
Tract. 3<l.
97.
And again St Augustine writeth upon the gospel of St John : " Our Saviour
& .1 TT
Jesus Christ," saith St Augustine, "is above, but yet his truth is here. His body
wherein he arose is in one place, but his truth is spread every where 5 ."
And in another place of the same book St Augustine expounding these Tract,
words of Christ, " You shall ever have poor men with you, but me you shall
not ever have," saith, that " Christ spake these words of the presence of his
body 6 . For," saith he, " as concerning his divine majesty, as concerning his
providence, as concerning his infallible and invisible grace, these words be fulfilled
which he spake, I am with you unto the world s end. But as concerning the
flesh which he took in his carnation 7 , as concerning that which was born of the
virgin, as concerning that which was apprehended by the Jews, and crucified
upon a tree, and taken down from the cross, lapped in linen clothes and
buried, and rose again, and appeared after his resurrection ; as concerning that 8
flesh, he said, You shall not ever have me with you. Wherefore seeing that
as concerning his flesh he was conversant with his disciples forty days, and
they accompanying, seeing, and not following him 9 , he went up into heaven,
both he is not here (for he sitteth at the right hand of his Father), and yet
he is here, for he departed not hence as concerning the presence of his divine
majesty. As concerning the presence of his majesty, we have Christ ever
with us; but as concerning the presence of his flesh, he said truly to his
disciples, Ye shall not ever have me with you. For as concerning the presence
of his flesh, the church had Christ but a few days; yet now it holdcth him fast
by faith, though it see him not with eyes." All these be St Augustine s words.
Also in another book 10 , entitled to St Augustine, is written thus : "We must
. .... .... Diviuitati
believe and confess that the Son of God (as concerning his divinity) is invisible,
without a body, immortal, and incircumscriptible : but as concerning his huma
nity, we ought to believe and confess that he is visible, hath a body, and is
contained in a certain place, and hath truly all the members of a man."
Of these words of St Augustine it is most clear, that the profession of
the catholic faith is, that Christ (as concerning his bodily substance and nature
of man) is in heaven, and not present here with us in earth. For the nature
and property of a very body is to be in one place, and to occupy one place,
and not to be everywhere, or in many places at one time. And though the
turn Jesum) non dubites tanquam Deum, et in
eodem templo Dei esse tanquam inhabitantem
Deum, et in loco aliquo cceli propter veri cor-
poris modum. Ibid. cap. xx.]
[ 5 Sursum est Dominus, sed etiam hie est ve-
ritas Dominus. Corpus enim Domini, in quo resur-
rexit, uno loco esse potest : veritas ejus ubique dif-
fusa est. August, in Evangelium Joannis, Tract.
xxx. Pars ix.]
[ 6 Loquebatur enim de praesentia corporis sui.
Nam secundum majestatem suam, secundum provi-
dentiam, secundum ineffabilem etinvisibilem gratiam
impletur quod ab eo dictum est, Ecce ego vobiscum
sum omnibus diebus usque ad consummationem sze-
culi. Secundum carnem vero quam verbum assump-
sit, secundum id quod de virgine natus est, secun
dum id quod a Judaeis comprehensus est, quod ligno
conlixus, quod de cruce depositus, quod linteis in-
volutus, quod in sepulchro conditus, quod in resur-
rectione manifestatus, non semper habebitis me
vobiscum. Quare ? Quoniam conversatus est se
cum discipulis suis, et eis deducentibus videndo,
non sequendo, ascendit in coelum, et non est hie.
Ibi enim sedet ad dexteram Patris: et hie est. Non
enimrecessitpraesentiamajestatis. Aliter. Secundum
praesentiam majestatis semper habemus Christum :
secundum praesentiam carnis recte dictum est disci-
pulis, Me autem non semper habebitis. Habuit
enim ilium ecclesia secundum praesentiam carnis
paucis diebus : modo fide tenet, oculis non videt.
Ibid. Tract. 1. Pars ix.J
[ 7 Incarnation, 1551.]
[ 8 The, 1551.]
[ 9 And following him, 1551. This is evidently a
misprint in that edition, which Cranmer appears to
have corrected as it was printed in the 1/580 edition,
since the words of Augustine are, " videndo, non
sequendo." See note 6.J
[ 10 Et idcirco eundem Dei filium secundum
substantiam divinitatis suae invisibilem et incor-
poreum et immortalem et incircumscriptum nos
credere et confiteri oportet. Juxta humanitatem vero
visibilem, corporeum, localem, atque omnia membra
humana veraciter habentem credere convenit et con
fiteri August, de Essentia Divinitatis, Pars x.
Ibid. This treatise is censured as spurious. Vid.
"James Corruptions of Scripture, Councils, and
Fathers." p. 53. Lond. 1843. Riveti Crit. Sacr.
p. 395. Geneva. 1026.]
96
THE THIRD BOOK.
Lib. ix.
cap. 21.
body of Christ after his resurrection and ascension was made immortal, yet this
nature was not taken away, for then, as St Augustine saith, it were no very body.
And further St Augustine sheweth both the manner and form how Christ is here
present with us in earth, and how he is absent, saying that he is present by his
divine nature and majesty, by his providence, and by grace ; but by his human
nature and very body he is absent from this world, and present in heaven.
Cyrillus likewise, upon the gospel of St John 1 , agreeth fully with St Augus-
ca P . 14. tine, saying : " Although Christ took away from hence the presence of his body,
yet in majesty 2 of his Godhead he is ever here, as he promised to his disciples
at his departing, saying, I am with you ever unto the world s end. "
And in another place of the same book St Cyril saith thus : " Christian
people must believe, that although Christ be absent from us as concerning his
body, yet by his power he governeth us and all things, and is present with all
them that love him. Therefore he said : Truly, truly I say unto you, where
soever there be two or three gathered together in my name, there am I in the
midst of them. For like as when he was conversant here in earth as a man,
yet then he filled heaven, and did not leave the company of angels; even
so being now in heaven with his flesh, yet he filleth the earth, and is in them
that love him. And it is to be marked, that although Christ should go away
only as concerning his flesh, (for he is ever present in the power of his divinity,)
yet for a little time he said he would be with his disciples 3 ." These be the words
of St Cyril.
St Ambrose also saith, that "we must not seek Christ upon earth, nor in
x. cap. 24. earth, but in heaven, where he sitteth at the right hand of his Father 4 ."
Gregoriusin And likewise St Gregory writeth thus: "Christ," saith he, "is not hero
us 01 " by the presence of his flesh, and yet he is absent no where by the
f Vid. Embd. * 1 .
tomihu us] P resence f his majesty ."
What subtlety, thinkest thou, good reader, can the papists now imagine to
defend their pernicious error, that Christ his human nature 6 is bodily here in
earth, in the consecrated bread and wine ; seeing that all the old church of
Christ believed the contrary, and all the old authors wrote the contrary ?
98. For they all affirmed and believed, that Christ, being but one person,
hath nevertheless in him two natures or substances, that is to say, the
nature of his Godhead, and the nature of his manhood. They say further-
[ l OvT(a 8ta/cei<ro /xe0a (ppovovvres opOtos, OTI KCLV
CK TOV Koa-fJLOv ye t;?]Tai Sid TJJJ/ trdpKa, Trapecrrai
TrdXiv ovdkv IJTTOV -rots ev UVTCO, Kal e7rt<rraTrj (rei
TOIS o Xois jj 0eia Te Kal a/ojOJ/Tos avrov Averts.
Cyril. Alex, in Evangelium Joannis. Lib. VI.
Tom. IV. p. 600. Ed. Aubert. Paris. 1638. But
Cranmer s quotation is evidently made from the
Latin edition, which reads as follows : Sed diligen-
ter hie animadvertendum, quod etsi corporis sui
praesentiam hinc subduxerit, majestate tamen divi-
nitatis semper adest : sicut ipse a discipulis abiturus
pollicetur : cce ego vobiscum sum omnibus diebus
usque ad consummationem saeculi. Tom. I. col.
323. Basil. 1566.]
[ 2 In his majesty, 1551.]
[ 3 AiaKel&Qai oe <5eu/ dvayKalov elvai (^rjfjLi TOI/S
oV ye <j>povov<riv 6p6a>s, Kal lopvfj.evi]v e^owi TJ/J/
TTICTTIU, o5s el Kal direcrTiV i]p.u>v Ttj arupKi^ TIJV TT/OOS
06oi/ Kal TraTepa o-reiXa/uei/os aVo^tj/uiai/, dXX ovv
TTJ Qeia SvvdfjLei TrepieTrei -ra frv/JLTravra, Kal (TV/JL-
Tols dyairtoa iv auTOf. Ata yap TOI TOUTO
e(f>aarKev Afjir^v, a /xrji/, Xeyw vjj.li>, OTTOV edv
s wcrt Suo ?; Tods eis TO C/JLOV ovo/ua, eKcl
cl/uLi kv uecrto auTtov. "Qcnrep ydp dvQpu>iroi<* CTI
<riw<5iarTw yuevos, Kal eTrl yijs uTrdp^uav /uera trap/cos,
e9rX?}|OOi; /u.ev ovpavoiis, (TVVTJV Se TOTC TO!S ayiots
a yyt Xois, ou/c ctTreXetTreTo T TWJ/ a j/to yjwpwv OVTOJ
Kal vvv virdp^tav ev ovpavols yueTct T;S idias aap-
/cos, TrXripol fiev T;V yi} v > crvvea-Tt Se -rols eavTOu
yvtoplfUHt, e-TriTij/oet ^e OTTWS, /CCUTOI Ka-rd fi6vi]i>
TI}V crapKa -^(opi^ea-Sai Trpoa&OKwv, (avvecrTL ydp
tjfjLlv Trj ^wdfjid T^S GCOTIJTOS did TravTos, ) eVt
fJiiKpov "xj)6vov /j.eQ TI/JLCOV e&ea Qai (pr)(ri. Ibid.
Lib. ix. cap. xxi. Tom. IV. p. 7470
[ 4 Ergo non supra terram, nee in terra, nee se-
cundum carnem te quaerere debemus, si volumus
invenire. Nunc enim secundum carnem jam non
novimus Christum. Denique Stephanus non supra
terram quaesivit, qui stantem te ad dexteram Dei
vidit Ambros. in Lucam, Lib. x. cap. xxiv.
Tom. III. p. 109. Colon. Agrip. 1616.]
[ 5 Non est hie, dicitur, per praesentiam carnis,
qui tamen nusquam deerat per praesentiam majesta-
tis Gregorii Papae Op. Homil. xxi. Tom. II.
p. 123. J. Antv. 1672.]
[ c That Christ in his human nature, 1551.]
OF THE PRESENCE OF CHRIST.
97
more, that Christ is both gone hence from us unto heaven, and is also here with
us in earth, but not in his human nature, (as the papists would have us to
believe,) but the old authors say that he is in heaven, as concerning his man
hood, and nevertheless both here and there, and every where, as concerning his
Godhead. For although his divinity be such, that it is infinite, without measure,
compass, or place, so that as concerning that nature he is circumscribed with no
place, but is every where, and filleth all the world : yet as concerning his human
nature, he hath measure, compass, and place, so that when he was here upon
earth, he was not at the same time in heaven ; and now that he has ascended
into heaven, as concerning that nature he hath now forsaken the earth, and is
only in heaven. For one nature that is circumscribed, compassed, and measured, chap. vi.
cannot be in divers places at one time. That is the faith 7 of the old catholic lannXbc in
church, as appeareth as well by the authors before rehearsed, as by these that a * one time.
hereafter followeth.
St Augustine, speaking that a body must needs be in some place, saith, that
if it be not within the compass of a place, it is nowhere ; and if it be nowhere,
then it is not 8 . And St Cyril, considering the proper nature of a very body,
said, that if the nature of the Godhead were a body, it must needs be in a
place, and have quantity, greatness, and circumscription 9 .
If then the nature of the Godhead must needs be circumscribed, if it were
a body, much more must the nature of Christ s manhood be circumscribed, and
contained within the compass of a certain place.
Didymus also, in his book de Spiritu Sancto, which St Jerome did translate,
proveth, that the Holy Ghost is very God, because he is in many places at one tojSb. Rt.
time, which no creature can be. For, saith he, all creatures, visible and invisible,
be circumscribed and environed either within one place, (as corporal and visible
things be,) or within the propriety of their own substance, (as angels and invisible
creatures be ;) so that no angel, saith he, can be at one time in two places. And
forasmuch as the Holy Ghost is in many men at one time, therefore, saith he,
the Holy Ghost must needs be God 10 .
The same affirmeth St Basil, that the angel which was with Cornelius, was
not at the same time with Philip ; nor the angel which spake to Zachary in the
altar, was not the same time in his proper place in heaven. But the Holy Ghost
was at one time in Habakkuk, and in Daniel in Babylon, and with Jeremy in
prison, and with Ezekiel in Chobcr; whereby he proveth that the Holy Ghost is
God 11 .
Wherefore the papists, (which say, that the body of Christ is in an infinite
number of places at one time.) do make his body to be God, and so confound the
[ 7 This is the faith, 1551, and Orig. ed.]
f 8 Nam spatia locorum tolle corporibus, nus-
quam erunt; et quia nusquam erunt, nee erunt.
Tolle ipsa corpora qualitatibus corporum, non erit
ubi sint, et ideo necesse est ut non sint August.
ad Dardanum, cap. viii. Pars vin. Basil, ap.
Amerbach. 1506.]
[ 9 Ei yap oXtus TO^IT/S re /cat /mepKTpov, /cat u>v
flfMTfOl </>atrii/, T; 0eta </>ucris dve\eTa.i, voeia-Qca /cat
(rtufia el de TOVTO, /cat ev TOTTW Tra i/Tcus TTOU, <cai
cv HeyeQei, /cat TTOO-W Cyril, cum Hermia Dialo-
gus de Trinitate, Lib. 11. (corpora non sunt sine
loco et circumscriptione). Tom. V. Pars i. p. 447.
Ed. Aubert. Paris. 1H38.J
[ 10 Ipse Spiritus sanctus, si unus de crcaturis
es-set, saltern circumscriptam haberet substantiam,
sicut universa qua: facta sunt. Nam etsi non circum-
IPII A VUTTD 1
scribantur loco et h nibus invisibiles creaturae, tamen
proprietate substantiae h niuntur. Spiritus autem
sanctus, cum in pluribus sit, non habet substan
tiam circumscriptam. Didymus de Spiritu Sancto,
Lib. i. cap. i. ad calcem Hieron. Ed. Villars.
Tom. IT. p. 105.]
[ n O yap TU> Ko/oi/tjXiw eirio-ra? ayyeXos ou/c
j)v ev TavTui /cat Trapd TW ^fiXiTnrw ovde o diro TOU
Qua"iaarTt]piov TU> liayjapia SiaXeyofievo^ /caTa TOV
ai>Tov Kaipov /cat ev ovpavta TijV ot/cetajMrrao ii
pov. TO fj.ev TOI TTveu/ma 6/j.ou TG Kai ev
evepyelv, /cat ev Aai/tijX CTTI TT/S Ba/3i/Xa)i/tas Treiri-
o-TCUTaf/cat ei/Tw /ca-rap/oa /cTTj [etptjTat] eti/at fiefd
lepe/miov, /cat fte-ra Ie^t/cn;\ tVi TOV \ofidp. Trvev-
fj.a yap Kvpiov TreTrX; /oti /ce TI]V oi/cou^tej/rji/. Basil,
de Spiritu Sancto, cap. xxii. Tom. II. p. 342.
Paris. 163J.]
THE THIRD BOOK.
two natures of Christ, attributing to his human nature that thing which belong-
eth only to his divinity ; which is a most heinous and detestable heresy.
Against whom writeth Fulgentius in this wise, speaking of the distinction
and diversity of the two natures in Christ :
"One and the self-same Christ," saith he, "of mankind was made a man,
compassed in a place, who of his Father is God, without measure or place. One
and the self-same person, as concerning his man s substance, was not in heaven,
when he was in earth, and forsook the earth when he ascended into heaven :
but as concerning his godly substance, which is above all measure, he neither left
99. heaven when he came from heaven, nor he left not the earth, when he ascended
into heaven: which may be known by the most certain word of Christ himself,
who, to shew the placing of his humanity, said to his disciples, I ascend up to
sakes, that you may believe, for I was not there. But to shew the unmcasurable
compass of his divinity, he said to his disciples, Behold, I am with you always
unto the world s end. Now how did he go up into heaven, but because lie is a
very man, contained within a place ? Or how is he present with faithful people,
but because he is very God, being without measure ] ?"
Of these words of Fulgentius it is declared most certainly, that Christ is not
here with us in earth but by his Godhead, and that his humanity is in heaven
only, and absent from us.
i^Lty- Yet the same is more plainly shewed, if more plainly can be spoken, by
Vigilius, a bishop and an holy martyr. He writeth thus against the heretic
Eutyches, which denied the humanity of Christ, holding opinion that he was
only God, and not man : whose error Vigilius confuting, proveth that Christ
had in him two natures joined together in one person, the nature of his Godhead,
and the nature of his manhood. Thus he writeth 2 :
nxiv. "Christ said to his disciples, If you loved me you would be glad, for I go
nxvi. unto my Father. And again he said, It is expedient for you that I go, for if
I go not, the Comforter shall not come unto you. And yet surely the eternal
Word of God, the virtue of God, the wisdom of God, was ever with his Father,
f 1 Unus idemque secundum carnem de matre
temporaliter natus, qui secundum divinitatem de
Patre pernianet sempiternus : unus idemque homo
localis ex homine, qui est Deus immensus ex Pa
tre : unus idemque secundum humanam substan-
tiam absens ccelo, cum esset in terra, et derelinquens
terram, cum ascendisset in ccelum ; secundum divi-
nam vero immensamque substantiam, nee ccelum
dimittens, cum de ccelo descendit, nee terram dese-
rens, cum ad ccelum ascendit. Quod ipsius Domini
certissimo potest cognosci sermone ; qui ut localem
ostenderet humanitatem suam, dicit discipulis suis,
Deum meum et Deum vestrum." De Lazaro quo-
que cum dixisset, " Lazarus mortuus est," ad-
junxit dicens : "Et gaudeo propter vos, ut credatis,
quoniam non eram ibi." Immensitatem vero suae
divinitatis ostendens discipulis dicit: "Ecce ego vo-
biscum sum omnibus diebus, usque ad consumma-
tionem sapculi." Quomodo autem ascendit in ccelum,
nisi quia localis et verus est homo ? aut quomodo
adest fidelibus suis, nisi quia idem immensus et
verus est Deus? Fulgent, ad Trasimundum Re-
gem. Lib. ii. cap. xiii. p. 107. Paris. 1684.]
[ 2 Ait discipulis suis, " Si diligeretisme, gaude-
Et iterum : " Expedit vobis ut ego earn ; si enim
ego non abiero, Paracletus ad vos non veniet." Et
certe verbum Dei, virtus Dei, sapientia Dei, semper
apud Patrem et in Patre fuit, etiam quando in nobis
nobiscum fuit. Neque enim cum terrena misericor-
diter incoluit, de ccelesti habitatione recessit. Cum
Patre enim ubique est totus pari divinitate, quern
nullus continet locus. Plena sunt quippe omnia
Filio, nee est aliquis locus divinitatis ejus pra?sentia
vacuus. Unde ergo et quo se iturum dicit, aut
sine dubio nunquam recessit ? Sed hoc erat ire ad
Patrem et recedere a nobis, auferre de hoc mundo
naturam quam susceperat ex nobis. Vides ergo ei-
dem naturae proprium fuisse, ut auferretur et abiret
a nobis, quae in fine tempormn reddenda est nobis,
secundum attestantium vocem angelorum, " Hie
Jesus, qui receptus est a vobis, sic veniet, quemad-
modum vidistis eum euntem in ccelum." Nam vide
miraculum, vide utriusque proprietatis mysterium:
Dei Filius, qui secundum humanitatem suam recessit
a nobis, secundum divinitatem suam ait nobis,
" Ecce ego vobiscum sum omnibus diebus usque
versus Eutychen, Lib. i. Tom. V. p. 712. Colon.
Agrip. 1618.]
OF THE PRESENCE OF CHRIST.
99
and in his Father, yea, even at the same time when he was with us, and in us.
For when he did mercifully dwell in this world, he left not his habitation in
heaven: for he is every where whole with his Father, equal in divinity, whom no
place can contain; for the Son filleth all things, and there is no place that lacketh
the presence of his divinity. From whence then, and whither did he say he
would go ? Or how did he say, that he went to his Father, from whom doubt
less he never departed ; but that to go to his Father, and from us, was to
take from this world that nature which he received of us? Thou seest therefore
that it was the property of that nature to be taken away and go from us, which
in the end of the world shall be rendered again to us, as the angels witnessed,
saying : This Jesus which is taken from you, shall come again like as you saw Acts L
him going up into heaven. For look upon the miracle, look upon the mystery
of both the natures: the Son of God, as concerning his humanity, went from us;
as concerning his divinity, he said unto us : Behold, I am with you all the Matt. uit.
days unto the world s end. "
Thus far have I rehearsed the words of Vigilius, and by and by he con-
cludeth thus 3 : " He is with us, and not with us. For those whom he left, and
went from them, as concerning his humanity, those he left not, nor forsook them
not, as touching his divinity. For as touching the form of a servant, which he
took away from us into heaven, he is absent from us; but by the form of God,
which goeth not from us, he is present with us in earth, and nevertheless, both
present and absent, he is all one Christ."
Hitherto you have heard Vigilius speak, that Christ, as concerning his bodily
presence and the nature of his manhood, " is gone from us, taken from us, is
gone up into heaven, is not with us, hath left us, hath forsaken us." But as
concerning the other nature of his deity, "he is still with us," so that he is both
" with us, and not with us, with us in the nature of his deity, and not with us
in the nature of his humanity." And yet more clearly doth the same Vigilius
declare the same thing in another place, saying 4 :
" If the word and flesh were both of one nature, seeing that the word is every
where, why is not the flesh then every where ? For when it was in earth, then
verily it was not in heaven : and now when it is in heaven, it is not surely in
earth. And it is so sure that it is not in earth, that as concerning it we look
for him to come from heaven, whom as concerning his eternal word we believe
to be with us in earth. Therefore by your doctrine," saith Vigilius unto Eutyches,
who defended that the divinity and humanity in Christ was but one nature, " either
the word is contained in a place with his flesh, or else the flesh is every where
[ 3 Sed et nobiscum est, et non est nobiscum.
Quia quos reliquit, et a quibus discessit humanitate
sua, non reliquit nee deseruit divinitate sua. Per
formamenim servi, quam abstulit a nobis in cerium,
absens est nobis : per formam Dei, quae non recedit
a nobis, in terris praesens est nobis ; tamen et prae-
sens et absens ipse unus idemque est nobis Ibid.]
[ 4 Si verbi et carnis una natura est, quomodo,
cum verbum ubique sit, non ubique inveniatur et
caro ? Namque quando in terra fuit, non erat utique
in coelo : et nunc, quia in ccelo est, non est utique
in terra, et in tantum non est, ut secundum ipsam
Christum spectemus venturum de coelo, quern se
cundum verbum nobiscum esse credimus in terra.
Igitur secundum vos, aut verbum cum carne sua
loco continetur, aut caro cum verbo ubique est,
quando una natura contrarium quid et diversum
non recipit in se ipsa. Diversum est autem et longe
dissimile circumscribi loco, et ubique esse ; et quia
verbum ubique est, caro autem ejus ubique non est,
apparet unum eundemque Christum utriusque esse
naturae ; et esse quidem ubique secundum naturam
divinitatis sure, et loco contineri secundum naturam
humanitatis suae : creatum esse, et initium non ha-
bere : morti subjacere, et mori non posse : quod
unum illi est ex natura verbi, qua Deus est, aliud ex
natura carnis, qua idem Deus homo est. Igitur unus
Dei Filius, idemque hominis factus Filius; habet
initium ex natura carnis suae, et non habet initium
ex natura divinitatis sua? : creatus est per naturam
carnis suae, et non est creatus per naturam divinita
tis suae : circumscribitur loco per naturam carnis
suae et loco non capitur per naturam divinitatis suae :
minor est etiam angelis per naturam carnis suae, et
a?qualis est Patri secundum naturam divinitatis
suae : mortuus est natura carnis suaa, et non est
mortuus natura divinitatis snap Ibid. Lib. iv.
p. 722.]
72
100.
100 THE THIRD BOOK.
with the word. For one nature cannot receive in itself two diverse and contrary
things. But these two things be diverse and far unlike, that is to say, to be
contained in a place, and to be every where. Therefore inasmuch as the word
is every where, and the flesh is not every where, it appeareth plainly, that one
Christ himself hath in him two natures ; and that by his divine nature he is
every where, and by his human nature he is contained in a place; that he is
created, and hath no beginning; that he is subject to death, and cannot die:
whereof one he hath by the nature of his word, whereby he is God, and the
other he hath by the nature of his flesh, whereby the same God is man also.
Therefore one Son of God, the self-same was made the son of man ; and he hath
a beginning by the nature of his flesh, and no beginning by the nature of his
Godhead. He is created by the nature of his flesh, and not created by the
nature of his Godhead. He is comprehended in a place by the nature of his
flesh, and not comprehended in a place by the nature of his Godhead. He is
inferior to angels in the nature of his flesh, and is equal to his Father in the
nature of his Godhead. He died by the nature of his flesh, and died not by the
nature of his Godhead. This is the faith and catholic confession, which the apo
stles taught, the martyrs did corroborate, and faithful people keep unto this day."
All these be the sayings of Vigilius, who according to all the other authors
before rehearsed, and to the faith and catholic confession of the apostles, martyrs,
and all faithful people unto his time, saith, that as concerning Christ s humanity,
when he was here on earth, he was not in heaven, and now when he is in
heaven, he is not in earth ; for one nature cannot be both contained in a place in
heaven, and be also here in earth at one time. And forasmuch as Christ is here
with us in earth, and also is contained in a place in heaven, he proveth thereby,
that Christ hath two natures in him, the nature of a man, whereby he is gone
from us, and ascended into heaven, and the nature of his Godhead, whereby he
is here with us in earth. So that it is not one nature that is here with us, and
that is gone from us, that is ascended into heaven and there contained, and that
is permanent here with us in earth. Wherefore the papists (which now of late
years have made a new faith, that Christ s natural body is really and naturally
present both with us both here in earth 1 , and sitteth at the right hand of his
Father in heaven,) do err in two very horrible heresies :
The one, that they confound his two natures, his Godhead and his manhood,
attributing unto his humanity that thing which appertaineth only to his divinity,
that is to say, to be in heaven, earth 2 , and in many places at one time. The
other is, that they divide and separate his human nature or his body, making of
101. one body of Christ two bodies and two natures, one which is in heaven, visible
and palpable, having all members and proportions of a most perfect natural
man ; and another which they say is in earth here with us, in every bread
and wine that is consecrated, having no distinction, form, nor proportion of
members: which contrarieties and diversities, as this holy martyr Vigilius saith,
cannot be together in one nature.
WINCHESTER.
These differences end in the forty -eighth leaf., in the second column. I intend now to touch the
further matter of the book with the manner of handling of it 3 , and where an evident untruth is,
there to join an issue, and where sleight and craft is, there to note it in the whole.
The matter of the book, from thence unto the fifty-sixth leaf, touching the being of Christ in
f 1 Both with us here in earth, 1551, and Orig. ed.] [ 2 In heaven and earth, 1551, Orig. ed.J
[ 3 Of the handling of it, 1551.]
OF THE PRESENCE OF CHRIST. 101
Iwaven and not in earth, is out of purpose superfluous. Tlie article of our creed that Christ
ascended to heaven, and sitteth on the right hand of his FatJier, hath been and w most con
stantly believed of true Christian men, which the true faith of Christ s real presence in tlte
sacrament doth not touch or impair. Nor Christ being whole God and man in the sacra
ment, is tliereby eitfter out of heaven, or to be said conversant in earth, became tlw conver- *christ s as-
sation is not earthly, but spiritual and godly, being the ascension of Christ, the end of his ^d^Thls
conversation in earth ; and tJierefore all that reasoning of the author is clearly void, to ^^r^ 110 "
travail to prove that is not denied, only for a sleight to make it seem as tfiough it were *sieight.
denied.
CANTERBURY.
Here is such a sleight used by you, as is worthy to be noted of all men. For I ^-^sicr
go not only about to prove in this place only that Christ, as concerning his human in g
nature, is in heaven, (which I know you deny not,) but I prove also that he is so in
heaven, that he is not in earth, which you utterly deny, and it is the chief point in
contention between us. But by this craft of appeaching me of sleight, that I go about
to prove that thing which you deny not, (which is untrue,) you have used such a sleight,
that you pass over eight leaves of my book together, wherein I prove that Christ, as
concerning his corporal presence, is not here in earth, and you answer not one word to
any of my arguments. And I pray thee note, good reader, what a strange manner of
sleight this is, to pass over eight leaves together clearly unanswered, and that in the
chief point that is in variance between us, under pretence that I use sleight, where
in deed I use none, but prove plainly that Christ is not bodily in heaven and in earth,
both at one time. If he had but touched mine arguments glancing by them, it had
been somewhat : but utterly to fly away 4 , and not once to touch them, I think thou
wilt judge no small sleight and craft therein. And methink in good reason, the
matter ought to be judged against him for default of answer, who being present
answereth nothing at all to the matter whereof he is accused; seeing that the law
saith : Qui facet, consentire mdetur.
Yet Smith is to be commended in respect of you, who attempteth at the least to smith.
see what shifts he could make to avoid my proofs, and busieth himself rather than
lie would stand mute, to say something to them. And yet in deed it had been as
good for him to have said nothing at all, as to say that which is nothing to the
purpose.
First to the scriptures by me alleged particularly, he utterly answereth nothing,
To Origen and St Augustine by name, and to all the other authors by me alleged,
he maketh this brief answer in general, that whatsoever those, authors say, they mean
no more, but that Christ is not here in earth visibly, naturally, and by circumscrip- smith s vain
tion, and yet nevertheless he is in the sacrament above nature, invisibly, and without
circumscription. This subtle distinction hath Smith devised, (or rather followeth other
papists therein,) to answer the authors which I have alleged. And yet of Smith s own
distinction it followeth, that Christ is not in the sacrament carnally and corporally.
For if Christ be in the sacrament but supernaturally, invisibly, and without circum
scription, then he is not there carnally and corporally, as St Augustine reasoncth ad
Dardanum 5 . But yet Smith only saith that the authors so meant, and proveth not
one word of his saying, supposing that the old holy writers be like to the papists,
which write one thing, and when they list not, or cannot defend it, they say they
mean another.
For those authors make no such distinction as Smith speaketh of, affirming divers
and contrary things to be in one nature of Christ in divers respects; but their dis
tinction is of the two natures in Christ, that is to say, the nature of his Godhead, and
the nature of his manhood. And they affirm plainly, that the diversity whereof they
spake cannot be in one nature, as you say it is, but must needs argue and prove
diversity of natures. And therefore by that diversity and instinction 6 in Christ they
prove against the heretics that Christ hath two natures in him; which were utterly
,
[ To flee away. K..M. ! [ 6 Sec note , P. 07.] [" Distinction, 1551.]
102 THE THIRD BOOK.
no proof at all, if one nature in divers respects might have that diversity: for the
that Christ had two natures, for one nature may have such diversity, if it be true
that Smith saith. And so Smith, with other papists which saith as he doth, putteth
a sword in the heretics hands to fight against the catholic faith. This, good reader,
thou shalt easily perceive, if thou do no more but read the authors which I have
in this place alleged.
And yet, for thy more ready instruction, I shall make a brief rehearsal of the
chief effect of them, as concerning this matter. To answer this question, how it can
^ sa ^ ^ ia ^ Christ is a stranger, and gone hence into heaven, and yet is also here
iSi us with us m earth, Smith and other papists resolve this matter by divers respects in
f us. 8 ne one nature of Christ ; but the old catholic writers which I alleged, resolve the matter
by two natures in Christ, affirming most certainly that such two diverse things cannot
navc pl acc both in one nature. And therefore say they, that Christ is gone hence
this matter. an( j j g a |3 Sen t i n his humanity, who in his deity is still here with us. They say also
that as concerning his man s nature, the catholic profession in our creed teacheth us
to believe that lie hath made it immortal, but not changed the nature of a very man s
body; for his body is in heaven, and in one certain place of heaven, because that
so requireth the measure and compass of a very man s body.
It is also, say they, visible, and hath all the members of a perfect man s body.
And further they say, that if Christ s body were not contained within the compass
of a place, it were no body, insomuch that if the Godhead were a body, it must
needs be in a place, and have quantity, bigness, and circumscription. For all crea-
103. tures, say they, visible and invisible, be circumscribed and contained within a certain
compass, either locally within one place, as corporal and visible things be, or else
within the property of their own substance, as angels and invisible creatures be. And
this is one strong argument whereby they prove that the Holy Ghost is God, because
he is in many places at one time, which no creature can be, as they teach. And
yet they say moreover, that Christ did not ascend into heaven but by his humanity,
nor is not here in earth but by his divinity, which hath no compass nor measure.
And finally they say, that to go to his Father from us, was to take from us that
nature which he received of us: and therefore when his body was in earth, then
surely it was not in heaven ; and now when it is in heaven, surely it is not in
earth. For one nature cannot have in itself two sundry and contrary things.
All things 1 here rehearsed be written by the old ancient authors which I have
alleged, and they conclude the whole matter in this wise, that this is the faith
and catholic confession, which the apostles taught, the martyrs did corroborate, and
faithful people keep unto this day. Whereby it appeareth evidently, that the doc
trine of Smith and the papists at that day was not yet sprung, nor had taken no root.
Wherefore diligently ponder and weigh, I beseech thee, gentle reader, the sayings
of these authors, and see whether they say, that one nature in Christ may be both
in heaven and in earth, both here with us and absent from us at one time; and
whether they resolve this matter of Christ s being in heaven and in earth, as Smith
doth, to be understand of his manhood in diversity of these respects visible and in
visible. And when thou hast well considered the authors sayings, then give credit
to Smith as thou shalt see cause.
But this allegation of these authors hath made the matter so hot, that the bishop
of Winchester durst not once touch it, and Smith, as soon as he had touched it,
felt it so scalding hot, that lie durst not abide it, but shrank away by and by for
fear of burning his fingers. Now hear what followeth further in my book.
chap. vn. But now ? seeing that it is so evident a matter, both by the express
th" papists, to words of scripture, and also by all the old authors of the same, that our Saviour
them tfie Christ (as concerning his bodily presence) is ascended into heaven, and is
"This is my not here in earth; and seeing; that this hath been the true confession of
body."
f 1 All these things, 1551. J
OF THE PRESENCE OF CHRIST. 103
the catholic faith ever since Christ s ascension ; it is now to be considered
what moved the papists to make a new and contrary faith, and what scrip
tures have they 2 for their purpose. What moved them I know not, but their
own iniquity, or the nature and condition of the sec of Rome, which is of
all other most contrary to Christ, and therefore most worthy to be called
the sec of antichrist. And as for scripture, they allege none but only one,
and that not truly understanded, but to serve their purpose wrested out of
tune, whereby they make it to jar and sound contrary to all other scriptures
pertaining to the matter.
"Christ took bread," say they, blessed, and brake it, and gave it to
disciplcs, saying, This is my body." These words they ever still repeat ISsu.
and beat upon, that Christ said, "This is my body." And this saying they
make their sheet-anchor, to prove thereby as well the real and natural pre
sence of Christ s body in the sacrament, as their imagined transubstantiation.
For these words of Christ, say they, be most plain and most true. Then 104.
forasmuch as he said, " This is my body," it must needs be true that that
thing which the priest holdcth in his hands is Christ s body. And if it be
Christ s body, then can it not be bread. Whereof they gather by their reason
ing, that there is Christ s body really present, and no bread.
Now forasmuch as all their proof hangeth only upon these words, "This The answer,
is my body:" the true sense and meaning of these words must be examined.
Hut, say they, what need they any examination ? what words can be more
plain, than to say, " This is my body ?"
Truth it is indeed, that the words be as plain as may be spoken ; but The internre
that the sense is not so plain, it is manifest to every man that weighcth words:
substantially the circumstances of the place. For when Christ gave bread body!-* n
to his disciples, and said, " This is my body," there is no man of any dis
cretion, that understandeth the English tongue, but he may well know by
the order of the speech that Christ spake those words of the bread, calling
it his body : as all the old authors also do affirm, although some of the papists
deny the same. Wherefore this sentence cannot mean as the words seem and
purport, but there must needs be some figure or mystery in this speech,
more than appcarcth in the plain words. For by this manner of speech plainly
understand without any figure, as the words lie, can be gathered none other
sense, but that bread is Christ s body, and that Christ s body is bread ; which
all Christian ears do abhor to hear. Wherefore in these words must needs be
sought out another sense and meaning than the words of themselves do bear.
And although the true sense and understanding of these words be suf- chap vm.
ficientlv declared before, when I spake of transubstantiation, yet to make the bread his
4. v body and
matter so plain that no scruple or doubt shall remain, here is occasion given
more fully to entreat thereof: in which process shall be shewed, that these
sentences of Christ, " This is my body," " This is my blood," be figurative
speeches. And although it be manifest enough by the plain words of the
gospel, and proved before in the process of transubstantiation, that Christ spake
of bread, when he said, " This is my body ;" likewise that it was very wine
which he called his blood ; yet lest the papists should say, that we suck
this out of our own fingers, the same shall be proved by testimony of the
old authors, to be the true and old faith of the catholic church : whereas
the school authors and papists shall not be able to shew so much as one
word of any ancient author to the contrary.
[- They have, 1551, and Grig, ed.]
104
THE THIRD BOOK.
Iren. contra
Valent. Lib.
iv. capp. 32.
34.57.
Lib. v.
Tertul.
Judseos.
105.
Cyprian,
Lib. i. Epist.
6.
Lib. ii. Epist.
3.
Epiphan. in
Ancorat.
Hedibiam.
First, Irenaeus, writing against the Valentinians, in his fourth book saith,
that "Christ confessed bread (which is a creature) to be his body, and the
cup to be his blood." And in the same book he writeth thus also : " The
bread wherein the thanks be given is the body of the Lord," And yet
again in the same book he saith, that Christ taking "bread of the same
sort that our bread is of, confessed that it was his body ; and that that
thing which was tempered in the chalice was his blood." And in the fifth
book he writeth further, "that of the chalice (which is his blood) a man is
nourished, and doth grow by the bread," which is his body 1 .
These words of Irenseus be most plain, that Chsist taking very material
bread, a creature of God, and of such sort as other bread is which we do
use, called that his body, when he said, " This is my body ;" and the wine
also which doth feed and nourish us, "he called his blood."
Tertullian likewise, in his book written against the Jews, saith that " Christ
called bread his body 2 ." And in his book against Marcion he oftentimes re-
peateth the self-same words.
And St Cyprian, in the first book of his epistles, saith the same thing, that
" Christ called such bread as is made of many corns joined together his body,
and such wine he called his blood, as is pressed out of many grapes, and made
into wine 3 ." And in his second book he saith these words : " Water is not the
blood of Christ, but wine 4 ." And again in the same epistle he saith, that " it
was wine which Christ called his blood; and that if wine be not in the chalice,
then we drink not of the fruit of the vine 5 ." And in the same epistle he saith,
that " meal alone, or water alone, is not the body of Christ, except they be both
joined together, to make thereof bread 6 ."
Epiphanius also saith that Christ, speaking of a "loaf which is round in
fashion, and cannot see, hear, nor feel, said of it : This is my body 7 ."
And St Jerome, writing ad Hedibiam, saith these words : " Let us mark
that the bread which the Lord brake, and gave to his disciples, was the body of
our Saviour Christ, as he said unto them : Take and eat; this is my body 8 . "
[ l Sed et suis discipulis dans consilium, primi-
tias Deo ofterre de suis creaturis, non quasi indi-
genti, sed ut ipsi nee infructuosi nee ingrati sint,
eum qui ex creatura est panis accepit, et gratias
egit, dicens : "Hoc est corpus meum." Et calicem
similiter, qui est ex ea creatura, quae est secundum
nos, suum sanguinem confessus est, et novi Testa
ment! novam docuit oblationem Irenams, contr.
Valent. Lib. iv. cap. 32, p. 323. Quomodo autem
constabit eis, eum panem in quo gratiae actae sint,
corpus esse Domini sui Quemadmodum enim qui
est a terra panis, percipiens invocationem Dei, jam
non communis panis est, sed eucharistia, ex duabus
rebus constans, terrena et ccelesti. Cap. 34. pp.
326, 7- Quando ergo et mixtus calix et factus pa
nis percipit verbum Dei, et fit eucharistia sanguinis
et corporis Christi, ex quibus augetur et consistit
carnis nostrae substantia. Lib. v. cap. ii. p. 397-
ed. Oxon. 1702.]
[ 2 Sic enim Christus revelavit, panem corpus
p. 196, et adversus Marcionem, Lib. iv. p. 458.
Lutetiae Paris. 1664.]
[ 3 Nam quando Dominus corpus suum panem
vocat demultorum granorum adunatione congestum ;
et quando sanguinem suum vinum appellat, de bo-
tris atque acinis plurimis expressum atque in unum
coactum. (Editio Erasmica in vinum). Cyprian.
ad Magnum. Lib. i. Epist. vi. p. 208. Paris.
1574.]
[ 4 Sanguis Christi non aqua est utique, sed vi
num Id. ad Csecilium. Lib. n. Epist. iii. p. 143.]
[ 5 Vinum fuisse, quod sanguinem suum dixit.
Quomodo autem de creatura vitis novum vinum cum
Christo in regno patris bibemus, si in sacrificio Dei
patris et Christi vinum non offerimus nee calicem
Domini dominica traditione miscemus ? Ib. p.
145.]
[ 6 Quomodo nee corpus Domini potest esse fa
rina sola, aut aqua sola, nisi utrumque adunatum
fuerit et copulatum, et panis unius compage solida-
tum Ib. 146.]
[f AvecrTt] ev TM ceiirvto, Kai e\a/3e T<z<5e* Kai
euYflc/oicrTjj<ras eiire, TOVTO /JLOV ecrri Tode Kai 6pu>-
uev OTI OVK Icrov ecfriv^ oiiSe O/ULOLOU, ov Ttj evadpKtp
CLKOVL, ov TTJ dopaTO) 0eoTT)Ti, ov TOIS yapaKTripai
TWV /j.$$Ji>v ; TO p.ev yap ea-Ti (TTpoyyvXaeide s Kai dvai(rQr)Tov, cos TT/OOS Tr\v Kvvafj.iv Kai j/OeAfjcrei/ ydpiTt, e nreiv, TOVTO [JLOV eo-ri To5e. Epiphanius, in Ancorato, Cap. Ivii. Tom. II. p. 60. Ed. Patav. Paris. 1622.] [ 8 Nos autem audiamus panem, quern fregit Dominus, deditque discipulis suis, esse corpus Domini Salvatoris, ipso dicente ad eos : " Accipite et comedite, hoc est corpus meum." Hieron. He- dibia;. Qufest. ii. Tom. III. p. 95. Francof. 1684.] OF THE PRESENCE OF CHRIST. 105 stiff s. And St Augustine also saith, " that although we may set forth Christ by Aug. deiriu mouth, by writing, and by the sacrament of his body and blood, yet we call 4. neither our tongue, nor words, nor ink, letters, nor paper, the body and blood of Christ ; but that we call the body and blood of Christ, which is taken of the fruit of the earth, and consecrated by mystical prayer." And also he saith : " Jesus called meat his body, and drink his blood 9 ." Moreover Cyril upon St John saith, that " Christ gave to his disciples cyriii. in pieces of bread, saying : Take, eat ; this is my body 10 . " *. M. Likewise Theodoretus saith : " When Christ gave the holy mysteries, he Theodoretus called bread his body, and the cup mixed with wine and water, he called his blood 11 ." By all these foresaid authors and places, with many more, it is plainly proved, that when our Saviour Christ gave bread unto his disciples, saying, " Take and eat ; this is my body ;" and likewise when he gave them the cup, saying, "Divide this among you, and drink you all of this, for this is my blood;" he called then the very material bread his body, and the very wine his blood. That bread, I say, that is one of the creatures here in earth among us, and that growcth out of the earth, and is made of many grains of corn beaten into flour, and mixed with water, and so baken and made into bread, of such sort as other our bread is, that hath neither sense nor reason, and finally that feedeth and nourisheth our bodies ; such bread Christ called his body, when he said, " This is my body :" and such wine as is made of grapes pressed together, and thereof is made drink, which nourish 12 the body, such wine ho called his blood. This is the true doctrine, confirmed as well by the holy scripture, as by all ancient authors of Christ s church, both Greeks and Latins ; that is to say, that when our Saviour Christ gave bread and wine to his disciples, and spake these words, " This is my body, this is my blood," it is very bread and wine which he called his body and blood. Now let the papists shew some authority for their opinion, either of scrip ture, or of some ancient author. And let them not constrain all men to follow their fond devices, only because they say it is so, without any other ground or authority, but their own bare words. For in such wise credit is to be given to God s word only, and not to the word of man. As many of them as I have read (the bishop of Winchester only excepted) do say, that Christ called not bread his body, nor wine his blood, when he said, " This is my body, this is my blood." And yet in expounding these words they vary among them selves ; which is a token that they be uncertain of their own doctrine. For some of them say, that by this pronoun demonstrative "this" Christ understood not the bread and wine, but his body and blood. And other some say, that by the pronoun "this" he meant neither the bread nor wine, nor his body nor blood; but that he meant a particular thing un- 100. [ 3 Potuit tamen significando predicate Dominum Jesum Christum, aliter per linguam suam, aliter per epistolam, aliter per sacramentum corporis et sanguinis ejus. Nee linguam quippe ejus, nee membranas, nee atramentum, nee significantes sonos lingua editos, nee signa literarum conscrip- ta pelliculis, corpus Christi et sanguinem dici- mus, sed illud tantum quod ex fructibus terras accep- tum et prece mystica consecratum. Augustin. de Trinitate. Lib. in. cap. 4. Pats v. Basil, ap. Amerbach. 1500.] [ 10 Tots yap ;<5tj ireirjo-Tei/fcoo-i <5ictK\a <ras r6v dpTov e<5i<5ou, \eytav AdfieTe, (]>dyere TOVTO to-Ti TO <rMfid fiov. Cyrill. in Joannem. Lib. iv. cap. 14. Tom. IV. p. 3(iO. Ed. Aubert. Paris. 1638. In the Latin version, fragmenta panis deriit.} [ H Ei/ 5t ye TTJ TWV /jLVffTiipitav irapaSocrei a-wfta TOV apTov e/caXeo-e, KOL alfjia TO Kpitfia Theo doretus in Dialogo 1. Tom. IV. p. 26. Halo* 1769-94.] [ 12 Nourisheth, lool, and Orig ed.] 106 THE THIRD BOOK. certain, which they call individuum vagum, or individuum in genere ; I trow some mathematical quiddity, they cannot tell what 1 . But let all these papists together shew any one authority, either of scrip ture or of ancient author, cither Greek or Latin, that saith as they say, that Christ called not bread and wine his body and blood, but individuum vagum ; and for my part I shall give them place and confess that they say true. And if they can shew nothing for them of antiquity, but only their own bare words, then it is reason that they give place to the truth confirmed by so many authorities, both of scripture and of ancient writers, which is, that Christ called very material bread his body, and very wine made of grapes his blood. Cyprianus dc Coena Do mini. WINCHESTER. After this the author occupieth a great number of leaves, that is to say, from the fifty - seventh leaf unto the seventy-fourth, to prove Christ s words, " This is my body," to be a flgu- rative speech. Sleight and shift is used in the matter, without any effectual consecution, to him that is learned. First, the author saith, Christ called "bread" his body, confessed 2 "bread" his body. To this is answered, Christ s calling is a making, as St Paul saith: Vocat ea quse non sunt, Bom. iv. tanquani ea qua? sint ; " He calleth that be not as they were." And so his calling (as Chry- Chrysost. in sostom 3 and the Greek commentaries say) is a making ; which also the catechism teacheth, iioin. cap. iv. translated by Justus Jonas in Germany, and after by this author in English. Tertullian adventu saith : " Christ made bread his body ;" and it is all one speech in Christ being God, declaring his ordinances, whether he use the word "call," or "make;" for in his mouth to call is to make 4 . Cyprian saith 5 according hereunto, how bread is by God s omnipotency made flesh : whereupon also this speech, Bread is flesh, is as much to say as made flesh; not that bread being bread is flesh, but that was bread is flesh by God s omnipotency; and so this author, entreating this matter as he doth, hath partly opened the faith of transubstantiation. For indeed bread being bread is not Christ s body, but that was bread is now Christ s body, because bread is made Christ s body, and because Christ called bread his body, which was in Christ to make bread his body. When Christ made water wine, the speech is very proper to say, water is made wine. For after like manner of speech we say, Christ justifleth a wicked man, Christ saveth sinners, and the physician hath made the sick man whole, and such diet will make an whole man sick. All these speeches be proper and plain, so as the construction be not made captious and sophistical, to join that was to that now is, forgetting the mean work. When Christ said, " This is my body," tJiere is no 1 necessity that the demonstration " this" should be referred to tJie outward visible matter, but may be referred to the invisible sub stance. As in the speech of God the Father upon Christ in baptism : " This is my Son." And here, wJien this author taketh his recreation to speak of the feigning of the papists, I shall join this issue in this place, that he understandeth not what he saith, and if his knowledge be no better than is uttered here in Hie pen, to be in this point clearly condemned of ignorance. An issue. 107. CANTERBURY. Here is another sleight, such as the like hath not lightly been seen. For where I wrote that when Christ said, "This is my body," it was bread that he called his body, you turn the matter to make a descant upon these two words, "calling" and [ The various opinions may be found collected by bishop Jewell in his Reply to Harding, Article 24. on Individuum vagum, p. 402, &c.] [ s Christ confessed bread, 1551.] [ 3 Bid. TOVTO oiide errcc, aai Trapdyovro s TO. OUK owra, ctXXa /caAoDvTos, TJJ/ TrAetWa evKoXiav <rjAwi/. uHTTrep yap, K. T. e Chrysost. in Epist. ad Rom. Horn. viii. Tom. IX. p. 504. Ed. Bened.] [ 4 Acceptum panem, et distribution discipulis, corpus ilium suum fecit, hoc est corpus meum dicendo, id est, figura corporis mei Tertullian. adversus Marcionem. Lib. iv. pp. 457, 8. Lu- tetiaj Paris. 1664.] [ 5 Panis iste quern Dominus discipulis porrige- bat, non effigie sed natura mutatus, omnipotentia verbi factus est caro Cyprian. (Arnoldi) De Ccena Domini, p. 468. Paris. 15J4.] [ 6 So as construction, but not made captious, Orig. ed. Winch.] [ 7 no inserted from edit. 1551.] OF THE PRESENCE OF CHRIST. 107 "making," that the minds of the readers should be so occupied witli the discussion of these two words, that in the meantime they should forget what thing it was that was called and made. Like unto men that dare larks 8 , which hold up an hoby, that the larks eyes being ever upon the hoby, should not see the net that is laid on their heads. And yet finally you grant that which Smith denieth, that it was bread which Christ called his body, when he said, "This is my body." And so that which was not his body in deed he called his body, who calleth things that be not, as Bom. iv. they were the things in deed. And if his calling be making, then his calling bread whether his body is making bread his body : and so is not only Christ s body made present, H\K be but also the bread is made his body, because it is called his body ; and so must m< bread be the thing whereof Christ s body is made: which before you denied in the eleventh comparison, calling that saying so foolish, that ft were "not tolerable to be devised by a scoffer in a play to supply when his fellow had forgotten his part." And thus should you conclude yourself, if Christ s calling were making, which in deed is not true : for then should Christ have made himself a vine, when he called John xv. himself a vine; and have made St John the blessed virgin Mary s son, when he called John xix. him her son ; and should have made his apostles vine-branches, when he called them John xv. so; and should have made Peter a devil, when he called him devil. Matt. xvi. After, when you come to make answer unto the authors cited by me in this place, first you skip over Irene, the eldest author of them all, because, I think, he is too ircnaus. hard meat for you well to digest, and therefore you will not once taste of him. In Tcrtulliaii and Cyprian you agree again, that when Christ said, " This is Tertuiiian. my body," it was bread that he called his body. And so when he said " this " he Whether meant the bread, making demonstration upon it : as before you have said more at cafied large in your book, which you named, "The Detection of the Devil s Sophistry 9 ." body 1 s And herein you say more truly than the other papists do, (which deny that the de monstration was made upon the bread,) although you say not true in the other part that Christ s calling was making. And if his calling be changing of the bread and making it the body of Christ, Conversion yet then it is not true to speak of the bread, and to say that it is the body of Christ, of waS" For when one thing is changed into another, the first still remaining, it may be said both that it is made the other thing, and that it is the other thing, (as when cloth is made a gown, we may say this cloth is made a gown, and also this cloth is a gown;) but when the former matter or state remaineth not, it may be said that it is made the other thing, but not that it is the other thing : as when Christ had turned *Jhn water into wine 10 . And likewise, although we say, a wicked man is made just, a sick man is made whole, or an whole man sick, yet it is no true speech to say a wicked man is just, a sick man is whole, or an whole man is sick ; because the former state remaineth not. And therefore, although it might in speech be allowed that the bread is made Christ s body, when the bread is gone, yet can it not be proper and approved speech to say, it is his body, except the bread remain still. For of that thing which is not, it cannot be said that it is Christ s body. For if it be his body, it must needs be by the rule of logic, a tertio adjacente ad sccundum adjacens. And I marvel how you have overshot yourself in this place, when you teach how and after what manner bread is made Christ s body. " Not that bread (say Christ s body you) being bread is his body, but that which was bread is now made his body : " {Tread.** whereof it followeth necessarily that his body is made of bread. For as the wine in j hn ii. the Cana of Galilee was made of water, when the substance of water was turned into the substance of wine ; so if in the sacrament the substance of bread be turned into the substance of Christ s body, then is his body in the sacrament made of bread : which 108. [ B To dare larks, i. e. to frighten in order to catch them. An hoby, i. e. a species of hawk.] | " Gardiner s " Detection of the Devil s So- phistrie, wherwith he robbcth the unlearned people of the true bylecf in the most blessed Sacrament of the aulter," was first published in lf>4r, and was replied to by Hooper and others before the publi cation of Cranmer s first book on the Sacrament.] [ 10 In Ed. 1551, after "as when Christ had turned water into wine," follow these words, " It was true to say water is made wine, but not to say water is wine." I 108 THE THIRD BOOK. Whether Christ called bread his body. Smith. 109. *Mine issue. Matt. xiv. in 1 the eleventh comparison you affirmed to be so foolish a saying, as were "not tolerable to be devised by a scoffer in a play to supply when his fellow had for gotten his part." Therefore I have not here "partly opened the faith of transubstantiation," as you say of me ; but you have here manifestly opened the wisdom of the papistical doctrine, which is more foolish than were to be devised by a scoffer in a play. But what need I much to contend with you in this place, seeing that you grant the thing for the which I cited all these authors, that is to say, that Christ called bread his body when he said, " This is my body ? " And in your "Detection of the Devil s Sophistry," as you call it, you say that Christ spake plainly, " This is my body," making demonstration of the bread when he said, " This is my body." But it seemeth you be sorry that you have granted so much, and that you spake those words unadvisedly, before you knew what the papists had written in this matter 2 ; and now, w T hen you perceive how far you vary from them, you would fain call your words back again, and prepare a way for the same, saying thus: ""When Christ said, This is my body, there is no necessity that the demonstration this should be referred to the outward visible matter, but may be referred to the invisible substance." In these your words it seemeth you begin to doubt in that thing which before you certainly affirm without all doubt. And when you have confessed the whole matter that I do here prove, which is only this, that Christ called bread his body, and wine his blood, when he said, " This is my body, this is my blood : " yet you conclude your answer with an issue of mine ignorance, that it is so great that I " understand not what I say, if my know ledge be no better than is uttered here in my pen." And yet my words be so plain, that the least child, as they say, in the town may understand them. For all my study is to speak plain, that the truth may be known, and not with dark speeches, as you do, to hide the truth. But when I had made a plain issue against all the papists in general, it had been your part to have joined in the said issue, and not to devise new issues. But because neither you nor Smith dare join with me in mine issue, I shall re peat mine issue again, and take it for confessed of you both, because neither of you dare say the contrary, and join an issue with me therein. My issue is this : " Let all the papists together shew any one authority, either of scripture or of ancient author, either Greek or Latin, that saith as they say, that Christ called not bread and wine his body and blood, but individuum vagum ; and for my part I shall give them place and confess that they say true. And if they can shew nothing for them of anti quity, but only their own bare words, then it is reason that they give place to the truth confirmed by so many authorities, both of scripture and of ancient writers, which is, that Christ called very material bread his body, and very wine made of grapes his blood." Now it shall not be much amiss to examine here the wise device of M. Smith, what he can say to this matter, that the opinion of divers doctors may be known, as well of Doctor Smith, as of Doctor Gardiner. " It is very false," saith Smith to me, " that you do say, that as these words This is my body do lie, there can be gathered of them none other sense, but that bread is Christ s body, and that Christ s body is bread. For there can no such thing be gathered of those words, but only that Christ gave his disciples his very body to eat, into which he had turned the bread, when he spake those words." First, Smith useth here a great and manifest falsehood in reciting of my sentence, leaving out those words, which should declare the truth of my saying. For I say, that by this manner of speech plainly understand without any figure, there can be gathered none other sense, but that bread is Christ s body. In which my sentence he leaveth out these words, "by this manner of speech plainly un derstand without any figure;" which words be so material, that in them resteth the pith and trial of the whole sentence. "VYhen Christ took the five loaves and two fishes, and looking up into heaven [ l Is in, edit. 1580. by a manifest error. J [ 2 In that matter, 1551.] OF THE PRESENCE OF CHRIST. 109 blessed them, and brake them, and gave them unto his disciples, that they should Mark yi. distribute them unto the people, if he had then said, Eat ; this is meat, which shall John vi. satisfy your hunger : by this manner of speech, plainly understand without any figure, could any other sense have been gathered, but that the bread and fishes which he gave them was meat? And if at the same time he had blessed wine, and commanding them to drink thereof, had said, "This is drink which shall quench your thirst:" what could have been gathered of those words, plainly understand without any figure, but that he called wine drink? So likewise when he blessed bread and wine, and gave them to his disciples, saying, "Eat, this is my body;" "Drink, this is my blood:" what can be gathered of this manner of speech, plainly understand without any figure, but that he called the bread his body, and wine his blood ? For Christ spake not one word there of any changing or turning of the substance of the bread, no more than he did when he gave the loaves and fishes. And therefore the manner of speech is all one, and the changing of the substances can no more be proved by the phrase and fashion of speech, to be in the one than in the other, whatsoever you papists dream of your own heads without scripture, that the substance of the bread is turned into the sub stance of Christ s body. But Smith bringeth here news, using such strange and novelty of speech, as Smith, other papists use not ; which he doth either of ignorance of his grammar, or else that he dissenteth far from other papists in judgment. For he saith, that Christ had 110. turned the bread when he spake these words, "This is my body." And if Smith remember his accidence, the preterpluperfect tense signifieth the time that is more than perfectly past; so that if Christ had turned the bread when he spake those words, then was the turning done before and already past, when he spake those words, which the other papists say was done after, or in the pronunciation of the words. And therefore they use to speak after this sort, that when he had spoken the w T ords, the bread was turned, and not that he had turned the bread when he spake the words. Another novelty of speech Smith useth in the same place, saying, that Christ called his body bread, because he turned bread into it ; it seemeth and appcareth still to be it, it hath the quality and quantity of bread, and because it is the food of the soul, as corporal meat is of the body. These be Smith s words, which if he understand of the outward form of bread, it is a novelty to say, that it is the food of the soul ; and if he mean of the very body of Christ, it is a more strange novelty to say, that it hath the quantity and quality of bread. For there was never man, I trow, that used that manner of speech, to say that the body of Christ hath the quantity and quality of bread, although the papists use this speech, that the body of Christ is contained under the form, that is to say, under the quantities and qua lities of bread. Now when Smith should come to make a direct answer unto the authorities of the old writers, which I have brought forth to prove that Christ called bread his body, when he said, "This is my body;" Smith answereth no more but this: "The doctors which you, my lord, allege here for you, prove not your purpose." Forsooth, a substantial answer, and well proved, that the doctors by me alleged prove not my purpose; for Smith saith so. I looked here, that Smith should have brought forth a great number of authors to approve his saying, and to reprove mine, specially seeing that I offered fair play to him, and to all the papists joined with him in one troop. For after that I had alleged for the proof of my purpose a great many places of old authors, both Greeks and Latins, I provoked the papists to say what they could to the contrary. "Let all the papists together," said I, "shew any one autho rity for them, either of scripture or ancient author, either Greek or Latin, and for my part I shall give them place. And if they can shew nothing for them of anti quity, then is it reason that they give place to the truth, confirmed by so many authorities, both of scripture and of ancient writers, which is, that Christ called very material bread his body, and very wine made of grapes his blood." Now I refer to thy judgment, indifferent reader, whether I offered the papists 110 THE THIRD BOOK. reason or no ; and whether they ought not, if they had any thing to shew, to have brought it forth here: and forasmuch as they have brought nothing, (being thus provoked with all their counsel,) whether thou oughtest not to judge, that they have nothing in deed to shew, which if they had, without doubt we should have heard of it in this place. But we hear nothing at all, but these their bare words, " Not one 111. of all these doctors saith as ye do, my Lord." Which I put in thy discretion, indif ferent reader, to view the doctor s words by me alleged, and so to judge. But they say not that there is only bread in the sacrament, saith Smith, and not Christ s body: what then? What is that to purpose here in this place, I pray you? For I go not about in this place to prove that only bread is in the sacra ment, and not Christ s body: but in this place I prove only, that it was very bread, which Christ called his body, and very wine which he called his blood, when he said, "This is my body, this is my blood:" which Smith with all his rablement 1 of the papists deny, and yet all the old authors affirm it with doctor Stephen Gar diner, late bishop of Winchester also, who saith, "that Christ made demonstration upon the bread, when he said, This is my body ." And as all the old authors be able to countervail the papists, so is the late bishop able to match Smith in this matter; so that we have, at the least, a Rowland for an Oliver. But shortly to comprehend the answer of Smith : where I have proved my sayings, a dozen leaves together, by the authority of scripture and old catholic writers, is this a suf ficient answer, only to say without any proof, that all my travail is lost ? and that all that I have alleged is nothing to the purpose ? Judge indifferently, gentle reader, whether I might not, by the same reason, cast away all Smith s whole book, and reject it quite and clean with one word, saying, " All his labour is lost, and to no purpose." Thus Smith and Gardiner being answered, I will return again to my book, where it followeth thus. chap. ix. Now this being fully proved, it must needs follow consequently, that this " Bread is my manner of speaking is a figurative speech. For in plain and proper speech, "wine is my it is not true to say that bread is Christ s body, or wine his blood. For blood " be Christ s body hath a soul, life, sense, and reason : but bread hath neither Toeat soul, life, sense, nor reason. Likewise in plain speech it is not true, that we eat Christ s body, and drink his blood. For eating and drinking, in their proper and usual signi fication, is with the tongue, teeth, and lips, to swallow, divide, and chaw in pieces : which thing to do to the flesh and blood of Christ, is horrible to be heard of any Christian. pX ^ ^ iat t ^ iese s P eecnes " To eat Christ s body and drink his blood," " to call bread his body, and wine his blood 2 ," be speeches not taken in the proper signification of every word, but by translation of these words, " eating" and speeches. "drinking," from the signification of a corporal thing to signify a spiritual thing; and by calling a thing that signifieth by the name of the thing which is signified thereby. Which is no rare nor strange thing, but an usual man ner and phrase in common speech. And yet, lest this fault should be im puted unto us, that we do feign things of our own heads without authority, (as the papists be accustomed to do,) here shall be cited sufficient authority, as well of scriptures 3 as of old ancient authors, to approve the same. LEtiYsk] First, when our Saviour Christ, in the sixth of John, said, that he was the bread of life, which whosoever did eat, should not die, but live for ever ; and that the bread which he would give us, was his flesh ; and therefore whosoever should eat his flesh, and drink his blood, should have everlasting [ l With all the rablement, 1551.] words, " to call bread his body, and wine his blood."] [ 2 Ed. 1551, and also the Orig. ed., omit these [ 3 As well of scripture, 1551, and Orig. ed.] OF THE PRESENCE OF CHRIST. Ill life ; and they that should not eat his flesh, and drink his blood, should not have everlasting life : when Christ had spoken these words, with many 112. more, of the eating of his flesh, and drinking of his blood, both the Jews, and many also of his disciples, were offended with his words, and said : " This is an hard saying. For how can he give us his flesh to be eaten?" Christ, perceiving their murmuring hearts, (because they knew none other eating of his flesh, but by chawing and swallowing,) to declare that they should not eat his body after that sort, nor that he meant of any such carnal eating, he said thus unto them : " What if you see the Son of man ascend up where he was before ? It is the spirit that givcth life, the flesh availeth IK idling: the words which I spake unto you be spirit and life." These words our Saviour Christ spake, to lift up their minds from earth to heaven, and from carnal to spiritual eating, that they should not phantasy that they should with their teeth eat him present here in earth : for his flesh so eaten, saith he, should nothing profit them. And yet so they should not cat him, for he would take his body away from them, and ascend with it into heaven ; and there by faith, and not with teeth, they should spiritually cat him, sitting at the right hand of his Father. And therefore, saith he, "The words which 1 do speak be spirit and life:" that is to say, arc not to be understand, that we shall eat Christ with our teeth, grossly and car nally, but that we shall spiritually and ghostly with our faith eat him, being carnally absent from us in heaven ; and in such wise as Abraham and other holy fathers did eat him, many years before he was incarnated and born, as St Paul saith : " That all they did eat the same spiritual meat that we i cor. x. do, and drink 4 the same spiritual drink ; that is to say, Christ." For they spiritually by their faith were fed and nourished with Christ s body and blood, and had eternal life by him, before he was born, as we have now, that come after his ascension. Thus have you heard the declaration of Christ himself, and of St Paul, that the eating and drinking of Christ s flesh and blood is not taken in the common signification, with mouth and teeth to eat and chaw a thing, being present, but by a lively faith in heart and mind to chaw and digest a thing, being absent, cither ascended hence into heaven, or else not yet born upon earth. WINCHESTER. In the sixtieth leaf the author entreatcth, whether it be a plain speech of Christ to say, "Eat and drink" speaking of his body and blood. I answer, the speech of itself is proper, commanding them present to eat and drink that is proponed for them: and yet it is not requi site (hat ttte nature of man should with like common effect work, in eating and drinking that heavenly meat and drink, as it doth in earthly and carnal mtats. In this mystery man doth as Christ ordained, that is to say, receive with his mouth that is ordered to be received with his mouth, granting it nevertheless of that <Iiiiuity nd estimation, that Christ s words affirm: <ni<l wliethcr lie so doth or no, Christ s ordinance is as it is in the substance of itself alone, whereof no good man judgeth carnally or grossly, ne discusseth tlie unfaithful question "how," which he cannot conceive, but leaveth ///< ////. s-s thereof, and doth as he is bidden. This m >i*tery receiveth no man s thoughts. Christ s Institution hath a property in it, which cannot IH discussed by man s sensual reason. Christ s words be spirit and life, which this author wresteth with his own gloss, to exclude the truth of the eating of Christ s Jlesh in his supper. [Terms meet And yet for a shift:, if a man would join issue with him, putteth to his speech the words how dog* "grossly" and "carnally," which words in such a rude understanding be tei*ms meeter to ex- paunches. press how dogs devour paunches, than to be inculkcd in speaking of this high mystery. Wherein ng j |Vj Drank, IM1, an&Orig. ed.j 112 THE THIRD BOOK. [An issue. Ed. 1551.] / will make the issue with this author., that no catholic teaching is so framed 1 with such terms, as though we should eat Christ s most precious body grossly, carnally., joining those words so together. For else "carnally" alone may have a good signification, as Hilary useth it: but contrariwise speaking in the catholic teaching of the manner of Christ s presence, they call it a spiritual manner of presence, and yet there is present by God s power the very true natural body and blood of Christ, whole God and man, without leaving his place in heaven : and in the holy supper men use their mouths and teeth, following Christ s commandment in the receiving of that holy sacrament, being in faith sufficiently instruct, that they cannot, ne do not tear, consume, or violate that most precious body and blood, but tmworthily receiving it, are cause of their own judgment and condemnation. The eating of Christ s body CANTERBURY. Eating and drinking with the mouth being so plain a matter, that young babes learn it, and know it before they can speak, yet the cuttle here with his black colours and dark speeches goeth about so to cover and hide the matter, that neither young nor old, learned nor unlearned, should understand what he meaneth. But for all his masking, who is so ignorant but he knoweth, that eating in the proper and usual signification is to bite and chaw in sunder with the teeth? And who knoweth not also, that Christ is not so eaten? Who can then be ignorant that here you speak a manifest untruth, when you say that Christ s body to be eaten is of itself a proper speech, and not figurative ? Which is by and by confessed by yourself, when you say that we do not eat that heavenly meat as we do other carnal meats, which is by chawing and dividing with the mouth and teeth. And yet we receive with the mouth that is ordained to be received with the mouth, that is to say, the sacra mental bread and wine, esteeming them nevertheless unto us, when we duly receive them, according unto Christ s words and ordinance. But where you say, that of the substance of Christ s body no good man judgeth carnally, ne discusseth the unfaithful question " how" : you charge yourself very sore in so saying, and seem to make demonstration upon yourself, of whom may be said, *Lukexix. Ex ore tuo te judico. For you both judge carnally in affirming a carnal presence, and a carnal eating; and also you discuss this question "how," when you say that Christ s body is in the sacrament really, substantially, corporally, carnally, sensibly, and naturally, as he was born of the virgin Mary, and suffered on the cross. And as concerning these words of Christ, " The words which I do speak be spirit and life;" I have not wrested them with mine own gloss, as you misreport, but I have cited for me the interpretation of the catholic doctors and holy fathers of the church, as I refer to the judgment of the reader. But you teach such a carnal and gross eating and drinking of Christ s flesh and blood, as is "more meet to express how dogs devour paunches, than to set forth the high mystery" of Christ s holy supper. For you say that Christ s body is present really, substantially, corporally, and carnally, and so is eaten ; and that we eat Christ s body as eating is taken in common speech : but in common speech it is taken for chawing and gnawing, as dogs do paunches: wherefore of your saying it folio weth, that we do so eat Christ s body, as dogs eat paunches; which all Christian ears abhor for to hear. But why should I join with you here an issue in that matter which I never spake ? For I never read, nor heard no man that said, saving you alone, that we do eat Christ grossly, or carnally, or as eating is taken in common speech without any figure ; but all that ever I have heard or read say quite clean contrary. But you, who affirm that we eat Christ carnally, and as eating is taken in common speech, (which is car nally and grossly to chew with the teeth,) must needs consequently grant, that we cat him grossly and carnally, as dogs eat paunches. And this is a strange thing to hear, that where before you said, that Christ is present but after a spiritual manner, now you my that he is eaten carnally. John vi. 114. [ So formed, Orig. eel. Winch.] OF THE PRESENCE OF CHRIST. 113 And where you say, that in the holy supper men use their mouth and teeth, truth it is that they so do, but to chaw the sacrament, not the body of Christ. And if they do not tear that most precious body and blood, why say you then that they eat the body of Christ, as eating is taken in common speech ? And wherefore doth that false papistical faitli of pope Nicholas, (which you wrongfully call catholic,) teach that Christ s body is torn with the teeth of the faithful? De Consecr. dist. 2. Ego 2 . J- Now follow the particular authorities which I have alleged for the interpretation of Christ s words, which if you had well considered, you would not have said, as you do, that I wrested Christ s words with mine own gloss. For 3 I begin with Origen, saying : And Origen, declaring the said eating of Christ s flesh and drinking his blood not to be understand as the words do sound, but figuratively, writeth thus upon these words of Christ : " Except you eat my flesh, and John vl drink my blood, you shall not bave life in you. 1 " Consider," saith Origen*, " that these things written in God s books are figures, and therefore examine and understand them as spiritual, and not as carnal men. For if you un derstand them as carnal men, they hurt you, and feed you not. For even in the gospels is there found letter that killeth. And not only in the old testament, but also in the new is there found letter that slayeth him, that doth not spiritually understand that which is spoken. For if thou follow the letter or words of this that Christ said, Except you eat my flesh, and drink my blood, this letter killeth." Who can more plainly express in any words, that the eating and drink ing of Christ s flesh and blood are not to be taken in common signification, as the words pretend and sound, than Origen doth in this place ? WINCHESTER. Now I will touch shortly what may be said to the particular authorities brought in by this author. Origen is noted (among other writers of the church) to draw the text to alle- Origenes. gories, who doth not thereby mean to destroy the truth of the letter, and therefore when he speaketh of a figure, saith not there is only a figure 5 , which exclusive "only" being away, (as it is not found by any author catholic taught that the speech of Christ of the eating of his flesh to be only a figure,) this author hath nothing avanced his purpose. As for spiritual understanding meaneth not any destruction of the letter where the same may stand with the rules of our faith 6 . All Christ s words be life and spirit, containing in the letter many times that is above our capacity, as specially in this place of the eating of his flesh, to discuss the particularities of "how;" and yet we must believe to be true that Christ saith, (although we cannot tell how:) for when we go about to discuss of God s mystery "how" then we fall from faith, and wax carnal men, and would have God s ways like ours. U5. CANTERBURY. Here may every man that readeth the words of Origen plainly see, that you seek in this weighty matter nothing but shifts and cavillations. For you have nothing answered [ 2 Ego Berengarius anathematize omnem I dicuntur. Si enim quasi carnales ista suscipitis, haeresin, quae astruere conatur panem et vinum, i laedunt vos, et non alunt. Est enim et in evangeliis qua in altari ponuntur, post consecrationem solum- i litera quae occidit : non solum in veteri Testamento modo sacramentum, et non verum corpus et sangui- | occidens litera deprehenditur. Est et in novo Tes- nem Domini nostri Jesu Christi esse, et non posse tamento litera, quae occidat eum, qui non spiritaliter sensualiter, nisi in solo sacramento, manibus sacer- dotum tractari vel frangi, aut tidelium dentibus at- teri. Decret. Gratian. Pars in. De Consecr. Dist. 2. col. 2021. Antv. 1573.] First, 1551.] [ 4 Agnoscite quia figurae sunt, quae in divinis voluminibus scripta sunt, et ideo tanquam spiritales et non tanquam carnales examinate et intelligite quae r, 1 8 quae dicuntur adverterit. Si enim secundum literam sequaris hoc ipsum quod dictum est, " Nisi man- ducaveritis carnem meam, et biberitis sanguinem meum," occidit haec litera. Origen. in Levit. Horn, vii. Tom. II. p. 225. ed. Bened.] [ 5 There is a only figure, 1551.] [ 6 The rule of our faith, Orig. ed. Winch.] 114 THE THIRD BOOK. directly to Origen, although he directly writeth against your doctrine. For you say that the eating of Christ s flesh is taken in the proper signification without a figure. Origen saith there is a figure. And Origen saith further, that it is only a figurative speech, although not adding this word "only," yet adding other words of the same effect. For he saith, that we may not understand the words as the letter soundeth : and saith further, that if we understand the words of Christ in this place as the letter soundeth, the letter killeth. Now who knoweth not, that to say these words, " not as the letter soundeth," and " the letter killeth," be as much to say, as only spiritually, and only otherwise than the letter soundeth? Wherefore you must spit upon your hands and take better hold, or else you cannot be able to pluck Origen so shortly from me. And I marvel that you be not ashamed thus to trifle with the ancient authors in so serious a matter, and such places, where the reader only look ing upon the author s \vords may see your dealing. The next is Chrysostom, whom I cite thus. And St John Chrysostom 1 affirmeth the same, saying, that "if any man understand the words of Christ carnally, he shall surely profit nothing thereby. For what mean these words, the flesh availeth nothing ? He meant not of flesh 2 , (God forbid !) but he meant of them that fleshly and carnally understood those things that Christ spake. But what is carnal understanding? To understand the words simply as they be spoken, and nothing else. For we ought not so to understand the things which we see, but all mysteries must be considered with inward eyes, and that is spiritually to understand them." In these words St John Chrysostom sheweth plainly that the words of Christ concerning the eating of his flesh and drinking of his blood, are not to be understand simply, as they be spoken, but spiritually and figuratively. WINCHESTER. Chrysostom St Chrysostom declareth himself, how mysteries must be considered with inward eyes, which is a spiritual understanding, whereby the truth of the mystery is not (as it were by a figurative speech) impaired, but with an humility of understanding in a certain faith of tJie truth marvelled at. And here the author of this book 3 useth a sleight to join figuratively to spiritually, as though they were always all one, which is not so. CANTERBURY. As you have handled Origen before, even so do you handle Chrysostom. Where fore I only refer the reader to look upon the words of Chrysostom recited in my book, who saith, that to understand the words of eating of Christ s flesh, simply as they be spoken, is a carnal understanding. And then can it be no proper speech, (as you say it is,) because it cannot be understand as the words be spoken, but must have another understanding spiritually. Then followeth next St Augustine, of whom I write thus r de d^ctrina 5 ^^ y e * mos * pl am ty f a ll other St Augustine doth declare this matter Christ. HD. 3. i n hi s hook De doctrina Christiana, in which book he instructeth Christian people how they should understand those places of scripture which seem hard and obscure. " Seldom," saith he, "is any difficulty in proper words, but either the circum stance of the place, or the conferring of divers translations, or else the original 116. [ ! Eav yap afiTO <rapKiKios Tts etcXa/foi, ovSt-v diroovdTO. T L ovv, OVK eo-ri tj <rap ainov <rdp; Kal <r(f>6Spa fj.ev ouv. Kal TTWS iiirev, t} <rup OVK (o<t>e\el ovocv; ov Trepl T^S eavrov <ra0Kos \eywv Ht\ yevoiTo d\\d irepl TU>V O-CT^KIKWS K\a/j.f3avov- Ttav TCL Xeyofjieva. T L Se to"ri TO yapKiKtos vorfcrai ; TO ctTrXaJs el? TO. irpoKeifieva opav, Kal fii) ir\eov TI (pavra^frrvai. TOVTO ydp eati crapKiKfos. XP^ ^ /urj OUTOJ icpiveiv TOIS bptap.evoLi, ctXXa iravra. fJLV<TTt]pia TOIS evSov 6<0aX;u.ots ydp earTi TTj/ev/iaTt/cws __ Chrysost. in Hom. xlvii. (al. 46.) Tom. VIII. p. Bened.] [ 2 Of his flesh, 1551, and Orig. ed.] [ 3 Of the book, Ori. ed. Winch.] Jaannem. 278. Ed. OF THE PRESENCE OF CHRIST. 115 tongue wherein it was written, will make the sense plain. But in words that be altered from their proper signification, there is great diligence and heed to be taken. And specially we must beware, that we take not literally any thing that is spoken figuratively : nor contrariwise, we must not take for a figure any thing that is spoken properly." "Therefore must be declared," saith St Augustine, " the manner how to discern a proper speech from a figurative. Wherein," saith he, "must be observed this rule, that if the thing which is spoken be to the furtherance of charity, then it is a proper speech, and no figure. So that if it be a commandment that forbiddeth any evil or wicked act, or commandeth any good or beneficial thing, then it is no figure. But if it command any ill or wicked tiling, or forbiddeth 4 anything that is good and beneficial, then it is a figurative speech. Now, this saying of Christ, Except ye eat the flesh of the Son of man, and drink his blood, you shall have no life in you/ seemeth to command an heinous and wicked thing : therefore it is a figure, commanding us to be partakers of Christ s passion, keeping in our minds, to our great comfort and profit, that his flesh was crucified and wounded for us 5 ." This is briefly the sentence of St Augustine in his book De doctrina Christiana. And the like he writeth in his book De catechisandis rudibus*, and in his book Contra adversarium legis et prophetarum~ , and in divers other places, which for tediousness I pass over. For if I should rehearse all the authorities of St Augustine and others, which make mention of this matter, it would weary the reader too much. Wherefore to all them that by any reasonable means will be satisfied, these things before rehearsed are sufficient to prove, that the eating of Christ s flesh and drinking of his blood is not to be understand simply and plainly (as the words do properly signify), that we do eat and drink him with our mouths : but it is a j * lib [ 4 forbid, 1551, and Orig. ed.] [ 5 Rarissime igitur et difficillime inveniri potest ambiguitas in propriis verbis, quantum ad libros divinarum scripturarum spectat, quam non aut cir- cumstantia ipsa sermonis qua cognoscitur scripto- rum intentio, aut interpretum collatio, aut praece- dentis linguae solvat inspectio. Sed verborum translatorum ambiguitates, de quibus deinceps lo- quendum est, non mediocrem curam industriamque desiderant. Nam in principle cavendum est, ne figuratam locutionem ad literam accipias. Neque illud quod proprio verbo significatur, refert ad aliam significationem.. Augustin. de Doctrina Christiana, Lib. in. Cap. iv. v. Pars iv. Basil, ap Amer- bach. 1500. Demonstrandus est igitur prius modus invenienda; locutionis, propriane an figurata sit. Ib. Cap. x. Servabitur ergo in locutionibus figuratis regula hujusmodi, ut tarn diu versetur diligenti con- sideratione quod legitur, donee ad regnum charitatis interpretatio perducatur. Si autem hoc jam proprie sonat, nulla putetur figurata locutio. Si praecep- tiva locutio est, aut flagitium aut facinus vetans, aut utilitatem aut beneficentiam jubens ; non est tigurata: si autem flagitium aut facinus videtur jubere, aut utilitatem aut beneficentiam vetare, tigurata est. Nisi manducaveritis, inquit, carnem Filii hominis et sanguinem biberitis, non habebitis vitam in vobis : facinus vel flagitium videter ju bere. Figura est ergo, pracipiens passioni Domini esse communicandum, et suaviter atque utiliter re- condendum in memoria, quod pro nobis caro ejus crucifixa et vulnerata sit. Ib. Cap. xv. xvi.J [ tt De sacramento sane quod accepit, cum ei bene commendatum fuerit, signacula quidem re- rum divinarum esse visibilia, sed res ipsas invisi- biles in eis honorari : nee sic habendam esse illam speciem benedictione sanctiticatam, quemadmodum habetur in usu quolibet. Dicendum etiam quid sig- nificet et sermo ille quern audivit, quid in illo con- diat [condatur], cujus ilia res similitudinem gerit. Deinde monendus est ex hac occasione, ut si quid etiam in scripturis audiat quod carnaliter sonet, etiam si non intelligit, credat tamen spiritale aliquid signi- ficari, quod ad sanctos mores futuramque vitam per- tineat. Hoc autem ita breviter discet, ut quicquid audierit ex libris canonicis, quod ad dilectionem Eeternitatis et veritatis et sanctitatis et ad dilecti onem proximi referre non possit, figurate dictum vel gestum esse credat ; atque ita conetur intelligere ut ad illam geminam referat dilectionem Augustin. de Catechizandis rudibus, Cap. xxvi. Pars iv.] [ 7 Sicut mediatorem Dei ethominum, hominem Christum Jesum, caniem suam nobis manducan- dam bibendumque sanguinem dan tern, fideli corde atque ore suscipimus : quamvis horribilius videatur humanam carnem manducare, quam perimere, et humanum sartguinem potare quam fundere : atque in omnibus sanctis scripturis, secundum sana? fldei regulam tigurate dictum vel factum si quid exponi- tur, de quibuslibet rebus et verbis qua sacris pagi- nis continentur, expositio ilia ducatur, non asper- nanter sed sapienter audiamus. Augustin. contra adversurium legis et Prophetarum, Lib. n. Cap. ix. Pars vi TI.] 82 116 THE THIRD BOOK. figurative speech spiritually to be understand, that we must deeply print and fruitfully believe in our hearts, that his flesh was crucified and his blood shed for our redemption. And this our belief in him is to eat his flesh and drink his blood, although they be not present here with us, but be ascended into heaven : as our forefathers before Christ s time did likewise eat his flesh and drink his blood, which was so far from them, that he was not yet then born. WINCHESTER. Augustinus. St Augustine, according to his rules of a figurative and proper speech, taketh this speech, "Except ye eat," c., for a figurative speech; because it seemeth to command in the letter carnally understanded an heinous and wicked thing to eat the Jlesh of a man, as man s carnal imagination conceiveth it: as appeared by the Capharnaites, who murmured at it. And therefore because only faithful men can by faith understand this mystery of the eating of Christ s fiesh in the sacrament, in which we eat not the carnal Jlesh of a common man, as the letter soundeth, but the very spiritual fiesh of Christ, God and man, as faith teacheth ; it is in that respect well noted for a figurative speech, for that it hath such a sense in the letter as is hidden from the unfaithful: so as the same letter being to faithful men spirit and life (who in humility of faith understandeth the same), is to the faithful 1 a figure, as 117. containing such a mystery as by the outward bark of the letter they understand not: upon which consideration it seemeth probable that the other fathers, also signifying a great secrecy in this mystery of the sacrament, wherein is a work of God ineffable, such as the ethnick ears could not abide, they termed it a figure, not thereby to diminish the truth of the mystery, as the proper and special name of a figure doth, but by the name of a figure reverently to cover so great a secrecy, apt only to be understanded of men believing : and therefore the said fathers, in some part of their works, in plain words express and declare the truth of the mystery, and the plain doctrine thereof according to the catholic faith, and in the other part pass it over with the name of a figure, which consideration in St Augustine s writings may be evidently gathered : for in some place no man more plainly openeth the substance of the sacrament than he doth, speaking expressly of the very body and blood of Christ contained in it ; and yet therewith in other places noteth in those words a figure, not thereby to contrary his other plain sayings and doctrine, but meaning by the word "figure" to signify a secret deep mystery hidden from carnal understanding. For avoiding and expelling of which carnality he giveth this doctrine here of this text: "Except ye eat," fyc., which, as I said before, in the bare literal sense implieth to carnal judgment other carnal circumstances to attain the same fiesh to be eaten, which in that carnal sense cannot be but by wickedness. But what is this to the obeying of Christ s commandment in the institution of his supper, when he himself 2 delivereth his body and blood in these mysteries, and biddeth " eat and drink ?" There can be no offence, to do as Christ biddeth, and therefore St Augustine s rule * Contrary, pertaineth not to Christ s supper, wherein when Christ willeth us to use our mouth, we ought to dare do as Jie biddeth ; for that is spiritual understanding, to do as is commanded without carnal thought or murmuring in our sensual device how it can be so. And St Augustine in the same place, speaking de communicando passionibus Christi, declareth plainly he meaneth of the sacrament. CANTERBURY. If thou takest not very good heed, reader, thou shalt not perceive where the cuttle becometh. He wrappeth himself so about in darkness, and he cometh not near the net by a mile, for fear he should be taken. But I will draw my net nearer to him that he shall not escape. I say that the words which Christ spake of the eating of his flesh and drinking of his blood were spoken by a figure, and he would avoid the matter by saying, that " those words have a spiritual mystery in them ;" which is most true, and nothing contrary to my saying, but confirmeth the same. For the words of eating and drinking be figurative speeches, because they have a secret and hid spiritual mystery in them, and cannot be taken otherwise than in that spiritual mystery, which is a [ Unfaithful, 1551. See p. J 18, at the beginning.] [ 2 When himself delivereth, 1551. J OF THE PRESENCE OF CHRIST. 117 figure. And, moreover, you plainly here confess, that to eat Christ s flesh and to drink his blood be figurative speeches. But you traverse the cause, wherefore they be figu rative speeches ; which is not material in this place, where my process is only to prove that they be figurative speeches. And forasmuch as you grant here all that I take upon me to prove, which is that they be figurative speeches, what ncedeth all this superfluous multiplication of words, when we agree in the matter which is here in question ? And as for the cause of the figure, you declare it far otherwise than St Augustine doth, as the words of St Augustine do plainly shew to every indifferent reader. For the cause, say you, is this, that "in the sacrament we eat not the carnal flesh of a common man, as the letter soundeth, but the very spiritual flesh of Christ, God and man, and in that respect it is well noted for a figurative speech." In which one sentence be three notable errors or untruths. The first is, that you say " the letter soundeth that we eat the carnal flesh of a common man ;" which your 1 18. saying the plain words of the gospel do manifestly reprove. For Christ, separating himself in that speech from all other men, spake only of himself, saying, " My flesh John vi. is very meat, and my blood is very drink : he that eateth my flesh and drinketh my blood, dwelleth in me and I in him." The second is, that you call the flesh of Christ a "spiritual flesh," as before you said that he is spiritually eaten. And so by your doc trine his flesh is spiritual, and is spiritually eaten, and all is spiritual : which hath need of a favourable interpretation, if it should be counted a sound and catholic teach ing. And if all be spiritual and done spiritually, what meaneth it then that in other places you make so often mention that he is present and eaten carnally, corporally, and naturally? The third is, that you say " the speech of Christ is noted figurative in respect of the eating of the flesh of a common man," which is utterly untrue. For the authors note not the figurative speech in that respect ; but as Christ spake of his own flesh joined unto his divinity, whereby it giveth life, even so do the authors note a figurative speech in respect of Christ s own flesh, and say thereof that the letter cannot be true without a figure. For although Christ be both God and man, yet his flesh is a very man s flesh, and his blood is truly man s blood, (as is the flesh and blood of his blessed mother,) and therefore cannot be eaten and drunken properly, but by a figure. For he is not meat and drink of the body, to be eaten corporally with mouth and teeth, and to be digested in the stomach : but he is the meat of the soul, to be received spiritually in our hearts and minds, and to be chawed and digested by faith. And it is untrue that you here say, that " the proper and special name of a figure diminislieth the truth of the mystery." For then Christ in vain did ordain the figures, if they diminish the mysteries. And the authors term it here a figure, not thereby to " cover the mystery," but to open the mystery, which was indeed in Christ s words by figurative speeches understand. And with the figurative speech were the ethnick and carnal ears offended, not with the mystery, which they understood not. And not to the ethnick and carnal, but to the faithful and spiritual ears, the words of Christ be figurative, and to them the truth of the figures be plainly opened and declared by the fathers : wherein the fathers be worthy much commendation, because they travailed to open plainly unto us the obscure and figu rative speeches of Christ. And yet in their said declarations they taught us, that these words of Christ, concerning the eating of his flesh and drinking of his blood, are not to be understanded plainly, as the words properly signify, but by a figurative speech. Nor St Augustine never wrote in all his long works, as you do, that Christ is in the -sacrament corporally, carnally, or naturally, or that he is so eaten, nor, I dare boldly say, he never thought it. For if he had, he would not have written so plainly, as he doth in the places by me alleged, that we must " beware that we take not literally any thing that is spoken figuratively." And specially he would not have expressed by name the words of " eating Christ s flesh and drinking his blood," and have said that they be figurative speeches. But St Augustine doth not only tell how we may not take those words, but also he declareth how we ought to take and under- 119. stand the eating of Christ s flesh and drinking of his blood, which, as he saith, is this : " To keep in our minds, to our great comfort and profit, that Christ was crucified and 118 THE THIRD BOOK. shed his blood for us, and so to be partakers of his passion. This," saith St Augustine, " is to eat his flesh and to drink his blood." And St Augustine saith not as you do, that Christ s words be "figurative to the unfaithful;" for they be figurative rather to the faithful than to the unfaithful. For the unfaithful take them for no figure or mystery at all, but rather carnally, as the Capernaites did. And there is indeed no mystery nor figure in eating with the mouth (as you say Christ s flesh is eaten), but in eating with the soul and spirit is the figure and mystery. For the eating and drinking with the mouth is all one to the faithful and unfaithful, to the carnal and spiritual, and both understand in like what is eating and drinking with the mouth. And therefore in no place do the doctors declare, that there is a figure or mystery in eating and drinking of Christ s body with our mouths, or that there is any truth in that mystery; but they say clean contrary, that he is not eaten and drunken with our mouths. And if in any place any old author write, that there is a figure or mystery in eating and drinking of Christ with August, de our mouths, shew the place if you will have any credit. St Augustine specially (whom verbis Domi- \ i T -, -.-r 7. in. serm. 33. you do here allege for your purpose) saith directly against you : Nohte parare fauces 25. " sed cor, " Prepare not your mouth or jaws, but your heart." And in another place he saith, Quid paras ventrem et dentem ? Crede et manducasti : " Why dost thou prepare thy belly and teeth? Believe, and thou hast eaten." But to avoid the saying of St Augustine by me alleged, you say that St Augus tine s rule pertaineth not to Christ s supper : which your saying is so strange, that you be the first that ever excluded the words of Christ from his supper. And St Augustine meant as well at the supper as at all other times, that the eating of Christ s flesh is not to be understanded carnally with our teeth (as the letter signi- fieth), but spiritually with our minds, as he in the same place declareth. And how can it be that St Augustine s rule pertaineth not to Christ s supper, when by the rule 1 he expoundeth Christ s words in the sixth of John, which you say Christ spake of his supper ? Did Christ speak of his supper, and St Augustine s words expounding the same pertain not to the supper? You make St Augustine an expositor like yourself, that commonly use to expound both doctors and scriptures clean from the purpose, either for that by lack of exercise in the scriptures and doctors you under stand them not, or else that for very frowardness you will not understand 2 any thing that misliketh you. And where you say that we must do as Christ commanded us, without carnal thought or sensual device, is not this a carnal thought and sensual device which you teach, that we eat Christ corporally with our teeth; and contrary to that which you said before, that Christ s body in the sacrament is a spiritual body, and eaten only spiritually? Now how the teeth can eat a thing spiritually, I pray you tell me. Now thou seest, good reader, what avail all those glosses of " carnal flesh and spiritual flesh," of "the flesh of Christ, and the flesh of a common man," of "a figure to the un faithful, and not to the faithful," that " the fathers termed it a figure, because else the 120. ethnick ears could not abide it," and "because they would reverently cover the mystery." And when none of these shifts will serve, he runneth to his sheet-anchor, that St Augustine s rule pertaineth nothing to Christ s supper. Thus mayest thou see, with what sincerity he handleth the old writers. And yet he might right well have spared all his long talk in this matter, seeing that he agreeth fully with me in the state of the whole cause, that to eat Christ s flesh and to drink his blood be figurative speeches. For he that declareth the cause why they be figurative speeches agreeth in the matter that they be figurative speeches. And so have I my full purpose in this article. Now hear what followeth in my book. chap. xi. The same authors did say also, that when Christ called the bread his m d &ood sis body, and the wine his blood, it was no proper speech that he then used; ? e eSes tive kut as a ^ sacraments be figures of other things, and ye have the very names J 1 By that rule, 1551.] [ 2 You will understand, 1551.] OF THE PRESENCE OF CHRIST. 119 of the things which they do signify ; so Christ instituting the sacrament of his most precious body and blood, did use figurative speeches, calling the bread by the name of his body, and the wine he called his blood, because it represented his blood. Tertullian herein writing against Marcion 3 , saith these words: "Christ did not reprove bread, whereby he did represent his very body." And in the LuHT* same book he saith, that Jesus "taking bread and distributing it amongst his disciples made it his body, saying, This is my body; that is to say," saith Tertullian, "a figure of my body." And therefore, saith Tertullian, "that Christ called bread his body, and wine his blood," because that in the old testament bread and wine were figures of his body and blood. WINCHESTER. Tertullian speaking of the representation of Christ s very body, in which place he termeth Tertuiiianus. * the same body," speaketh catholicly in such phrase as St Jerome speaketh : and then Ter- had left out tullian saith afterward, as this author therein truly bringeth him forth, that Christ made the bread his body, which bread was in the mouth of the prophet a figure of his body. Wtierefore it followeth by Tertullian s confession, when Christ made the bread his body, that Christ ended the figure, and made it the truth, making now his body that was before the figure of his body. For if Christ did no more but make it a figure still, then did he not make it his body, as Tertullian himself saith he did. And Tertullian therefore, being read thus, as appeareth to me most probable, that " tJiat is to say" in Tertullian should be only referred to the explication of tlie first " this ;" as when Tertullian had alleged Chrises words, saying " this is my body," and putteth to of his own, " that is to say, the figure of my body," these words, " that is to say," should serve to declare the demonstration " this " in this wise, " that is to say, this," which the prophet called the figure of the body, is now my body. And so Tertullian said before that Christ had made bread his body, which bread was a figure of his body with the prophet, and now endeth in the very truth, being made his body by con version (as Cyprian sheweth) of the nature of bread into his body. Tertullian reasoned against tlie Marcionists ; and because a figure in the prophet signifieth a certain unfeigned truth of that is signified, seeing Christ s body was figured by bread in the prophet Jeremy, it appeareth Christ had a true body; and that the bread was of Christ approved for a figure, he made now his very body 4 . And this may be said evidently to Tertullian, who reasoning against heretics useth tlie commodity of arguing, and giveth no doctrine of the sacrament to further this author s purpose. And what advantage slwuld tlie heretics have of Tertullian, if he should mean that these words, " This is my body," had only this sense, this is the figure of my body, having himself said before that Christ made bread his body? If so plain speech, to make bread his body, containeth no more certainty in understanding but the figure of a body, why should not they say, that a body in Christ should ever be spoken of a body in a figure, and so no certainty of any true body in Christ by Tertullian s words ? This place of Tertullian is no secret point of learning, and hath been of (Ecolampadius and other alleged, and, by other catholic men answered unto it ; whereof this author may not think now as upon a wrangling argument to satisfy a conjecture devised, thereby to confirm a new teaching. Finally, Tertullian termeth it not an only figure, which this author must prove,. or else he doth nothing. [ 3 Sed ille quidem usque nunc nee aquam repro- bavit nee panem, quo ipsum corpus suum reprae- sentat. Tertuiiianus, Adversus Marcionem. Lib. i. p. 372. Acceptum panem et distribution discipulis, corpus ilium suum fecit, l Hoc est corpus meum di- cendo, id est, tigura corporis mei. Figura autem non fuisset, nisi veritatis esset corpus. Ceterum vacua res, quod est phantasma, figuram capere non posset. Aut si propterea panem corpus sibi Hnxit, quia corporis carebat veritate : ergo panem debuit tradere pro nobis. Faciebat ad unitatem Marcionis, ut panis crucitigeretur. Cur autem panem corpus suum appellat, et non magis peponem, quern Mar- cion cordis loco habuit? Non intelligens veterem fuisse istam ftguram corporis Christi, dicentis per Hieremiam, "adversus me cogitaverunt cogitatum dicentes,Venite, conjiciamus lignum in panem ejus;" scilicet crucem in corpus ejus. Itaque illuminator antiquitatum quid tune voluerit significasse panem satis declaravit, corpus suum vocans panem. Ibid. Lib. iv. pp. 457, Paris. 1664.] [ 4 he made it now his very body, 1551.] 121- 120 THE THIRD BOOK. CANTERBURY. Tertullian^ Oh what a wrangling and wresting is here made ! what crooks be cast ! what only figure 3 " 1 leaping about is here, to avoid a foil ! And yet I refer to any indifferent man that shall read the place of Tertullian, to judge whether you have truly expounded him, or in the wrestling with him be quite overthrown, and have a flat fall upon your back. For Tertullian saith not, that the bread was a figure of Christ s body only in the prophet, as you expound Tertullian, but saith, " that bread and wine were figures in the old testament, and so taken in the prophets, and now be figures again in the new testament, and so used of Christ himself in his last supper." And where Tertullian saith, that Christ made bread his body, he expoundeth him self how Christ made bread his body, adding by and by these words, " that is to say, a figure of his body." But if thou canst forbear, good reader, (when thou readest the fond handling of Tertullian by this ignorant and subtle lawyer,) I pray thee laugh not; for it is no matter to be laughed at, but to be sorrowed, that the most ancient authors of Christ s church should thus be eluded in so weighty causes. O Lord, what shall these men answer to thee at the last day, when no cavillations shall have place ? These be Tertullian s words : " Jesus taking bread, and distributing it among his dis ciples, made it his body, saying, This is my body, that is to say, a figure of my body." Here Tertullian expoundeth not the saying of the prophet, but the saying of Christ, "This is my body." And where Tertullian hath but once the word "this," you say "the first this." And so you make a wise speech to say "the first," where is but one. And Tertullian speaketh of "this" in Christ s words, when he said, "This is my body ;" and you refer them to the prophet s words, which be not there, but be spoken of long after. And if you had not forgotten your grammar and all kind of speech, or else hurled away all together purposely to serve your own wilful device, you would have referred the demonstration 1 of his antecedent before, and not to a thing that in order cometh long after. And "bread" in the prophet was but a figurative speech, but in Christ s words was not only a figurative speech, but also a figurative thing; that is to say, very material bread, which by a figurative speech Christ ordained to be a figure and a sacrament of his body. For as the prophet by this word "bread" figured Christ s body, so did Christ himself institute very material bread to be a figure of his body in the sacrament. But you refer "this" to the bread in the prophet, which Christ spake, as Tertullian saith, of the bread in the gospel. And Christ s words must needs be understanded of the bread which he gave to his apostles, in the time of the gospel, after he had ended the supper of the law. And if Christ made the 122. bread in the prophet his very body, which was no material bread, but this word "bread," then did Christ make this word bread his body, and converted this word bread into the substance of his body. This is the conclusion of your subtle sophisti cation of Tertullian s words. Now, as concerning St Cyprian, whom you here allege, he spake of a sacramental, and not of a corporal and carnal conversion, as shall be plainly declared, when I come to the place of Cyprian, and partly I have declared already in mine other book. And Tertullian proved not in that place the verity of Christ s body by the figure of the prophet, but by the figure which Christ ordained of his body in his last supper. For he went not about to prove that Christ should have a body, but that he had then a true body, because he ordained a figure thereof, which could have had no figure, as Tertullian saith, if it had been but a fantastical body, and no true body in deed. Wherefore this which you say, in answering to the plain words of Tertullian, may be said of them that care not what they say ; but it cannot be " said evidently," that is spoken so sophistically. But "if so plain speech" of Tertullian, say you, that Christ "made bread his body, contain no more certainty in understanding but the figure of a body, why should not the body of Christ ever be taken for a figure, and so no certainty of any true body to The demonstrative, 1551.] OF THE PRESENCE OF CHRIST. 121 be in Christ?" This reason had been more fit to be made by a man that had lost both his wit and reason. For in this place Tertullian must needs be so understand, that by the body of Christ is understand the figure of his body, because Tertullian so expoumleth it himself. And must it be always so, because it is here so ? Must ever Christ s body be taken for a figure, because it is here taken for a figure, as Tertullian saith? Have you so forgotten your logic, that you will make a good argument, a particulari ad universale? By your own manner of argumentation, because you make a naughty argument here in this place, shall I conclude that you never make none good? Surely this place of Tertullian, as you have handled it, is neither secret nor manifest point either of learning, wit, or reason, but a mere so phistication, if it be no worse. What other papists have answered to this place of Tertullian, I am not igno rant, nor I am sure you be not so ignorant but you know that never none answered as you do. But your answer varieth as much from all other papists , as yours and theirs also do vary from the truth. Here the reader may note by the way, how many foul shifts you make to avoid the saying of Tertullian. First you say, that " bread was a figure in the prophet s mouth, but not in Christ s words." Second, that the thing which the prophet spake of was not that which Christ spake of. Third, that other have answered this place of Tertullian before. Fourth, that you call this matter but "a wrangling argument." Fifth, that if Tertullian call bread a figure, yet he "termeth it not only figure 8 ." These be your shifts. Now let the reader look upon Tertullian s plain words, which I have rehearsed in my book, and then let him judge whether you mean to declare Tertullian s mind truly, or no. And it is not requisite for my purpose to prove that bread is only a figure, for I take upon me there to prove no more but that the bread is a figure representing Christ s body, and the wine his blood. And if bread be a figure, and not only a figure, then must you make bread both the figure and the truth of the figure. Now hear what other authors I do here allege. And St Cyprian the holy martyr saith of this matter, that " Christ s blood is shewed in the wine, and the people in the water that is mixed with the wine ; 3. lb so that the mixture of the water to the wine signifieth the spiritual commixtion and joining of us unto Christ 3 ." By which similitude Cyprian meant not that the blood of Christ is wine, or the people water, but as the water doth signify and represent the people, so doth the wine signify and represent Christ s blood ; and the uniting of the water and wine together signifieth the uniting of Christian people unto Christ himself. And the same St Cyprian in another place, writing hereof, saith, that Dc unctione " Christ in his last supper gave to his apostles with his own hands bread and cl wine, which he called his flesh and blood ; but in the cross he gave his very body to be wounded with the hands of the soldiers, that the apostles might declare to the world, how and in what manner bread and wine may be the flesh and blood of Christ." And the manner he straightways declareth thus, that " those things which do signify, and those things which be signified by them, may be both called by one name 4 ." 123. [ 2 He termeth it not an only figure, 1551.] [ 3 Videmus in aqua populum intelligi, in vino vero ostendi sanguinem Christi. Quando autem in calice vino aqua miscetur, Christo populus adunatur, et credentium plebs ei, in quern credidit, copulatur et conjungitur Cyprian. Epist. Ixiii. Cscilio fratri. (Lib. 11. Epist. iii.) p. 146. Par. 1574.] [ 4 Dedit itaque Dominus noster in mensa, in qua ultimum cum Apostolis participavit convivium, pro- priis manibus panem et vinum : in cruce vero mani- bus militum corpus tradidit vulnerandum ; ut in Apostolis secretius impressa sincera veritas, et vera sinceritas, exponeret gentibus, quomodo vinum et panis caro esset et sanguis, et quibus rationibus causae effectibus convenient, et di versa nomina vel species ad unam reducerentur essentiam, et signifi- cantia et significata eisdem vocabulis censerentur. Cyprian. De unctione Chrismatis, p. 477- This 122 THE THIRD BOOK. Chrys. in Ps. xxii. J era. in Matt. xxvi. Ambros. de liis qui mys- teriis initian- tur, cap. ult. ])e Sacra- nientis, Lib. vi. cap. 1. Lib. iv. cap. 4. Lib. iv. cap. rUt nullus horror cru- oris sit : et pretium tamen opere- tur redemp- tionis. Emb. Ed. 1557.] 1 Cor. xi. 124. Here it is certain, by St Cyprian s mind, wherefore and in what wise bread is called Christ s flesh, and wine his blood ; that is to say, because that every thing that representeth and signifieth another thing, may be called by the name of the thing which it signifieth. And therefore St John Chrysostom saith, that " Christ ordained the table of his holy supper for this purpose, that in that sacrament he should daily shew unto us bread and wine for a similitude of his body and blood 1 ." St Jerome likewise saith upon the gospel of Matthew, that " Christ took bread, which comforteth man s heart, that he might represent thereby his very body and bloodV Also St Ambrose, if the book be his that is entitled De his qui mysteriis initiantur, saith, that " before the consecration another kind is named, but after the consecration the body of Christ is signified. Christ said his blood: before the consecration it is called another thing, but after the consecration is signified the blood of Christ 3 ." And in his book De Sacramentis, if that be also his, he writeth thus : " Thou dost receive the sacrament for a similitude of the flesh and blood of Christ, but thou dost obtain the grace and virtue of his true nature 4 ." "And receiving the bread, in that food thou art partaker of his godly substance." And in the same book he saith : "As thou hast in baptism received the similitude of death, so likewise dost thou in the sacrament drink the similitude of Christ s precious blood 5 ." And again he saith in the said book : " The priest saith, Make unto us this oblation to be acceptable/ which is the figure of the body and blood of our Lord Jesu Christ 6 ." And upon the epistle of St Paul to the Corinthians he saith, "that in eating and drinking the bread and wine, we do signify the flesh and blood, which were offered for us. And the old testament," he saith, "was instituted in blood, because that blood was a witness of God s benefit ; in signification and figure whereof we take the mystical cup of his blood, to the tuition of our body and soul 7 ." Of these places of St Chrysostom, St Jerome, and St Ambrose, it is clear, that in the sacramental bread and wine is not really and corporally the very Treatise is spurious Vid. James Corruptions of Scripture, &c. p. 19. Lond. 1843.] [ l The passage is not in the Greek of Chrysos tom. It stands as follows in the Homily, " incerto auctore," printed in the Latin edition of Chrysos tom, Paris. 1570. Tom. I. col. 720. Et quia istam mensam praeparavit servis et ancillis in conspectu eorum, ut quotidie in similitudinem corporis et san- guinis Christi panem et vinum secundum ordinem Melchisedech nobis ostenderet in sacramento, ita di- cit, Parasti in conspectu meo mensam adversus eos qui tribulant me,\ [ 2 Coenantibus autem eis, accepit Jesus panem, c. Postquam typicum pascha fuerat impletum, et agni carnes cum apostolis comederat, assumit panem, qui confortat cor hominis, et ad verum paschse transgreditur sacramentum ; ut quomodo in praefiguratione ejus Melchisedec, summi Dei sacer- dos, panem et vinum offerens fecerat, ipse quoque veritatem sui corporis et sanguinis reprsesentaret Hieronymus, Commentarii in Matt. Lib. iv. cap. 26. Tom. IX. p. 64. Francof. 1684.] [ 3 Ipse clamat Dominus Jesus ; Hoc est corpus meum. Ante benedictionem verborum ccelestium species nominatur, post consecrationem corpus Christi signih catur. Ipse dicit sanguinem suum. Ante consecrationem aliud dicitur, post consecra tionem sanguis nuncupatur. Ambros. de Initiandis. Tom. IV. p. 166. Ed. Colon. Agrip. 1616.] [ 4 Ideo in similitudine quidem accipis sacra mentum, sed vere naturas gratiam virtutemque con- sequeris : tu, qui accipis carnem, divinas ejus sub- stantiae in illo participaris alimento. De Sacram. Lib. vi. cap. i. Tom. IV. p. 176.] [ 5 Sicut enim mortis similitudinem sumpsisti, ita etiam similitudinem pretiosi sanguinis bibis Lib. iv. cap. iv. Tom. IV. p. 173.] [ 6 Dicit sacerdos : Fac nobis, inquit, hanc obla- tionem adscriptam, rationabilem, acceptabilem : quod sit in figuram corporis et sanguinis Domini nostri Jesu Christi. Ib. Lib. iv. cap. v. Tom. IV. p. 173.] [ 7 Quia enim morte Domini liberati sumus, hu- jus rei memores, in edendoet potando carnem et san guinem, quae pro nobis oblata sunt, significamus. Testamentum ergo sanguine coustitutum est, quia beneficii divini sanguis testis est. In cujus typum nos calicem mysticum sanguinis ad tuitionem cor poris et animae nostrae percipimus Id. in 1 Co rinth, xi. Tom. III. p. 184. But these commen taries are considered to be spurious.] OF THE PRESENCE OF CHRIST. 123 natural substance of the flesh and blood of Christ, but that the bread and wine signs and . .../. n figures have be similitudes, mysteries and representations, significations, sacraments, figures, the names of and signs of his body and blood : and therefore be called, and have the namo of vg{? thc> y his very body 8 , flesh, and blood. WINCHESTER. Cyprian shall be touched after, when we speak of him again. Cyprianus. Chrysostom shall open himself hereafter plainly. chrysostom. St Jerome speaketh here very pithily, using the word " represent" which signifieth a true Hieronym. real exhibition: for St Jerome speaketh of the representation of the truth of Christ s body, ^vhich truth excludeth an only figure. For Jiowsoever the visible matter of the sacrament be a figure, the invisible part is a truth : which St Jerome saith is here represented, that is to say, made present, which only signification doth not. St Ambrose shall after declare himself: and it is not denied, but the authors in speaking of Ambrosius. the sacrament used these words, "sign," "figure," "similitude," "token;" but those speeclies &r- *NO author elude not the verity and truth of tfie body and blood of Christ, for no approved author hath figure. this exclusion 9 , to say an only sign, an only token, an only similitude, or an only signifi cation, which is the issue with this author, CANTERBURY. Here you shift off St Cyprian and Chrysostom with fair promise to make answer Hieronymu*. to them hereafter, who approve plainly my saying, that the bread representeth Christ s body, and the wine his blood ; and so you answer here only to St Jerome. In answering to whom you were loth, I see well, to leave behind any thing that might have any colour to make for you, that expound this word " represent" in St Jerome to signify Kepresent. real exhibition. Here appeareth that ye can, when you list, change the signification of words, that can make vocare to signify facere, and facere to signify sacrijicare^ as you do in your last book. And why should you not then in other words (when it will serve for like purposes) have the like liberty to change the signification of words when you list? And if this word "represent" in St Jerome s words sig nify real exhibition, then did Melchisedech really exhibit Christ s flesh and blood, who, as the same St Jerome saith, did represent his flesh and blood by offering bread and wine. And yet in the Lord s supper, rightly used, is Christ s body exhibited indeed spiritually, and so really, if you take really to signify only a spiritual and not a Really, corporal and carnal exhibition. But this real and spiritual exhibition is to the receivers of the sacrament, and not to the bread and wine. And mine issue in this place is no more, but to prove that these sayings of Christ, "This is my body, this is my blood," be figurative speeches, signifying that the bread reprcscnteth Christ s body, and the wine his blood; which forasmuch as you confess, there needed no great contention in this point, but that you would seem in words to vary, where we agree in the substance of the matter, and so take occasion to make a long book, where a short would have served. And as for the exclusion 10 "only," many of the authors, as I proved before, have 125. the same exclusive, or other words equivalent thereto. And as for the sacramental signs, they be only figures. And of the presence of Christ s body yourself hath this exclusive, that Christ is but after a spiritual manner present, and I say he is but spi ritually present. Now followeth St Augustine. And yet St Augustine shewcth this matter more clearly and fully than any Augustim* of the rest, specially in an epistle which he wrote ad Bonifacium, where he gum. ^ [ 8 The Original ed., and that of 1551, omit the I [ 9 This exclusive, 1551.] word "body" in this sentence.] [ 10 The exclusive, 1551.] 124 THE THIRD BOOK. saith : " That a day or two before Good Friday, we use in common speech to say thus, To-morrow, or this day two days, Christ suffered his passion ; where in very deed he never suffered his passion but once, and that was many years past. Likewise upon Easter-day we say, This day Christ rose from death ; where in very deed it is many hundred years sithens he rose from death. Why then do not men reprove us as liars, when we speak in this sort, but because we call these days so, by a similitude of those days wherein these things were done in deed ? And so it is called that day, which is not that day in deed, but by the course of the year it is a like day. And such things be said to be done that day for the solemn celebration of the sacrament, which things in deed were not done that day, but long before. Was Christ offered any more but once? And he offered himself: and yet in a sacrament or representation, not only every solemn feast of Easter, but every day he is offered to the people ; so that he doth not lie that saith, He is every day offered. For if sacraments had not some similitude or likeness of those things whereof they be sacraments, they could in no wise be sacraments. And for their similitude and likeness, commonly they have the name of the things, whereof they be sacraments. Therefore, as after a certain manner of speech the sacrament of Christ s body is Christ s body, the sacrament of Christ s blood is Christ s blood ; so likewise the sacrament of faith is faith. And to believe is nothing else but to have faith ; and therefore when we answer for young children in their baptism, that they believe, which have not yet the mind to believe, we answer that they have faith, because they have the sacrament of faith. And we say also that they turn unto God, because of the sacrament of conversion unto God ; for that answer pertaineth to the cele bration of the sacrament. And likewise speaketh the apostle of baptism, saying, that by baptism we be buried with him into death : he saith not that we signify burial, but he saith plainly, that we be buried. So that the sa crament of so great a thing is not called but by the name of the thing itself 1 ." Hitherto I have rehearsed the answer of St Augustine unto Boniface, a learned bishop, who asked of him, how the parents and friends could answer for a young babe in baptism, and say in his person that he believeth and converteth unto God, when the child can neither do nor think any such things. W hereunto the answer of St Augustine is this: that forasmuch as baptism is the sacrament of the profession of our faith, and of our conversion unto [ l Nempe saepe ita loquimur, ut pascha pro- pinquante dicamus, crastinam vel perendinam Do mini passionem, cum ille ante tarn multos annos passus sit, nee omnino nisi semel ilia passio facta sit. Nempe ipso die Dominico dicimus, c Hodie Dominus resurrexit, cum ex quo resurrexit tot anni transierunt. Cur nemo tarn ineptus est, ut nos ita loquentes arguat esse mentitos, nisi quia istos dies secundum illorum quibus hajc gesta sunt similitu- dinem nuncupamus, ut dicatur ipse dies qui non est ipse, sed revolutione temporis similis ejus ; et dicatur illo die fieri, propter sacramenti celebra- tionem, quod non illo die, sed jam olim factuvn est ? Nonne semel immolatus est Christus in se ipso ? et tamen in sacramento non solum per omnes paschae solemnitates, sed omni die populis immo- latur, nee utique mentitur qui interrogatus eum responderit immolari. Si enim sacramenta quan- dam similitudinem earum rerum quarum sacra menta sunt non haberent, omnino sacramenta non essent. Ex hac autem similitudine plerumque etiam ipsarum rerum nomina accipiunt. Sicut ergo secundum quendam modum sacramentum corporis Christi corpus Christi est, sacramentum sanguinis Christi sanguis Christi est, ita sacramentum fidei fides est. Nihil est autem aliud credere quam fidem habere. Ac per hoc cum respondetur par- vulus credere, qui fidei nondum habet affectum, respondetur fidem habere propter fidei sacramentum, et convertere se ad Deum propter conversionis sacramentum, quia et ipsa responsio ad celebra- tionem pertinet sacramenti. Sicut de ipso baptismo Apostolus, < Consepulti, inquit, sumus Christo per baptismum in mortem. Non ait, sepulturam significavimus : sedprorsusait, Consepulti sumus. Sacramentum ergo tantae rei non nisi ejusdem rei vocabulo nuncupavit. Augustin. ad Bonifacium de Bapt. parvul. Epist. xxiii. Tom. II. p. 36. Paris. 1637.] OF THE PRESENCE OF CHRIST. 125 God, it bccometh us so to answer for young children coming thereunto, as to the 2 sacrament appcrtaineth, although the children in deed have no knowledge of such things. And yet in our said answers we ought not to be reprehended as vain men or liars, forasmuch as in common speech we use daily to call sacraments and figures by the names of the things that be signified by them, although they be not the same thing indeed. As every Good Friday, as often as it returneth from year to year, we call it the day of Christ s passion : and every Easter-day we call the day of his resurrection : and every day in the year, we say that 126. Christ is offered : and the sacrament of his body, we call it his body : and the sacrament of his blood, we call it his blood : and our baptism St Paul calleth our burial with Christ. And yet in very deed Christ never suffered but once, never arose but once, never was offered but once, nor in very deed in baptism we be not buried, nor the sacrament of Christ s body is not his body, nor the sacrament of his blood is not his blood. But so they be called, because they be figures, sacraments, and representations of the things themselves, which they signify, and whereof they bear the names. Thus doth St Augustine most plainly open this matter in his epistle to Bonifacius. Of this manner of speech, (wherein a sign is called by the name of s upe r Leviti the thing which it signifieth,) speaketh St Augustine also right largely in 57. his questions super Leviticum, et contra Adamantium, declaring how blood in scripture is called the soul. " A thing which signifieth," saith he, " is wont Lev. xvu. to be called by the name of the thing which it signifieth, as it is written in the scripture : The seven ears be seven years. The scripture saith not, Gen. \\\. signifieth seven years. And seven kine be seven years, 1 and many other like. And so said St Paul, that the stone was Christ, 1 and not that it i cor. x. signified Christ, but even as it had been he indeed, which nevertheless was not Christ by substance, but by signification. Even so," saith St Augustine, "because the blood signifieth and represented the soul, therefore in a sacra ment or signification it is called the soul 3 ." And contra Adamantium he contra Ada writeth much like, saying: "In such wise is blood the soul, as the stone p. is. was Christ; and yet the apostle saith not that the stone signified Christ, but saith it was Christ. And this sentence, blood is the soul/ may be under- Lev. xv.i. stand to be spoken in a sign or figure ; for Christ did not stick to say, This is my body, when he gave the sign of his body 4 ." Here St Augustine, rehearsing divers sentences, which were spoken figu ratively, that is to say, when one thing was called by the name of another, and yet was not the other in substance, but in signification, as "the blood is the soul ;" " seven kine be seven years ;" " seven ears be seven years ;" " the stone was Christ ;" among such manner of speeches, he rehearseth those [ 2 That, Orig. ed. and 1551.1 [ 3 Solet autem res qua; significat, ejus rei nomine quam significat nuncupari, sicut scriptum est, Septem spicas septem anni sunt. Non enim dixit, septem annos significant. Et septem boves septem anni sunt: et multa hujusmodi. Hinc est quod dictum est: Petra erat Christus. Non enim dixit, petra significat Christum, sed tanquam hoc esset, quod utique per substantiam non hoc erat, sed per significationem. Sic et sanguis, quoniam propter vitalem quandam corpulentiam animam significat, in sacramentis anima dictus est Augustin. super Levit. Lib. in. Quaest. Ivii. Tom. IV. p. 95.] [ 4 Sic est enim sanguis anima, quomodo petra erat Christus : de quibus [loquebatur] Apostolus cum haec diceret, nee tamen ait, petra significabat Christum, sed ait, petra erat Christus. Qua; rur- sus ne carnaliter acciperetur, spiritalem ille vocat : id est, earn spiritaliter intelligi docet. Possum etiam interpretari praeceptum illud in signo esse positum. Non enim Dominus dubitavit dicere, * Hoc est corpus meum, cum signum daret corporis sui. Ibid, contra Adamantium, cap. 12. pars iii. Basil, ap. Amerbach. 1506. The position of these quotations is reversed by Cranmer.] 126 THE THIRD BOOK. 127. words which Christ spake at his last supper, " This is my body." Which de- clareth plainly St Augustine s mind, that Christ spake those words figura tively, not meaning that the bread was his body by substance, but by sig nification. And therefore St Augustine saith, contra Maximinwn, that "in the sacra ments we must not consider what they be, but what they signify ; for they be signs of things, being one thing and signifying another 1 ." Which he doth shew specially of this sacrament, saying : " The heavenly bread, which is Christ s flesh, by some manner of speech is called Christ s body, when in very deed it is the sacrament of his body. And that offering of the flesh, which is done by the priest s hands, is called Christ s passion, death, and crucifying, not in very deed, but in a mystical signification 2 . WINCHESTER. As for St Augustine ad Bonifacium, the author shall perceive his fault at Martin Bucer s hand, who in his epistle dedicatory of his enarrations of the gospels, rehear seth his mind of St Augustine in this wise. Est (scribit divus Augustinus) secundum quendam modum sacramentum corporis Christi corpus Christi ; sacramentum sanguinis Christi sanguis Christi. At secundum quern modum ? Ut significet tantum corpus et sanguinem Domini absentia? Absit: honorari enim et percipi in symbolis visibilibus corpus et sanguinem Domini, idem passim scribit. These words of Bucer may be thus Englished : " St Augustine writeth : The sacrament of the body of Christ is after a certain manner the body of Christ, the sacrament of the blood of Christ, the blood of Christ. But after what manner? that it should signify only the body and blood absent ? Absit, in no wise ; for the same St Augustine writeth in many places, the body and blood of Christ to be honoured, and to be received in those visible tokens." Thus saith Bucer, who understandeth not St Augustine to say the sacrament of Christ s body, to be Christ s body after a certain manner of speech, as this author doth : nor St Augustine hath no such words, but only, secundum quendam modum, after a certain manner, whereunto to put " of speech" is an addition more than truth required of necessity. In these words of Bucer may appear his whole judgment concerning St Augustine, who affirmeth the very true presence of the thing signified in the sacrament ; which truth established in the matter, the calling it a sign, or a token, a figure, a similitude, or a shewing, maketh no matter when we understand the thing really present that is signified. Which and it were not indeed in the sacrament, why should it, after Bucer s true understanding of St Augustine, be honoured there? Arguing upon men s speeches may be without end; and the authors 3 upon diverse respects speak of one thing diversely. Therefore we should resort to the pith and knot of the matter, and see what they say in ex- shouid be pounding the special place, without contention, and not what they utter in the heat of their dispu- they expound tation, ne to search their dark and ambiguous places, whereivith to confound that they speak the matter _ T . 7 y * without openly and plainly. contention. CANTERBURY. M. Bucer. What need you to bring Martin Bucer to make me answer, if you could answer yourself ? But because you be ashamed of the matter, you would thrust Martin Bucer in your place, to receive rebuke 4 for you. But in this place he easeth you nothing at all; for lie saith no more but that the body and blood of Christ be exhibited unto the worthy receivers of the sacrament, which is true, but yet spiritually, not cor porally. [ HSEC enim sacramenta sunt, in quibus non quid sit, sed quid ostendant semper attenditur: quo- niam signa sunt rerum, aliud existentia, aliud sig- nificantia Ibid, contra Maximinum, Lib. HI. cap. 22. pars xi. Basil, ap. Amerbach. 1506.] [ 2 Sicut ergo ccelestis panis, qui vere Christus caro est, suo modo vocatur corpus Christi, cum revera sit sacramentum corporis Christi, illius vide- licet, quod visibile, palpabile, mortale in cruce est suspensum ; vocaturque ipsa immolatio carnis, quae sacerdotis manibus fit, Christi passio, mors, cruci- fixio, non rei veritate, sed significante mysterio. Corpus Juris Canonici. Gratiani Decreti, tert. pars. De consecrat. Dist. ii. " Hoc est." cap. xlviii. Tom. I. col. 1937. Lugd. 1618. Cranmer quoted this passage from the Corpus Juris Canonici, and not from Augustine.] [ 3 Thauctour, 1651.] [ 4 To receive the rebuke for you, 1551.] OF THE PRESENCE OF CHRIST. 127 And I never said that Christ is utterly absent, but I ever affirmed that he is truly The true and spiritually present, and truly and spiritually exhibited unto the godly receivers : onSt. but corporally is he neither in the receivers, nor in or under the forms of bread or wine, as you do teach clearly without the consent of master Bucer, who writeth no such thing. And where I allege of St Augustine, that the sacrament of Christ s body is called Christ s body, after a certain manner of speech, and you deny that St Augustine meant of a certain manner of speech, but saith only after a certain manner : read the place of St Augustine who will, and he shall find that he speaketh of the manner of speech, and that of such a manner of speech, as calleth one thing by the name of another, where it is not the very thing in deed. For of the manner of speech is all the process there, as appeareth by these his words: "A day or two before Good Friday, we use in common speech to say, To-morrow, or this day two days, Christ suffered, &c. Likewise upon Easter-day we say, This day Christ rose. And why do no men reprove us as liars, when we speak in this sort ? And we call those days so by a similitude, &c. And so it is called that day, which is not that day in deed. And sacraments commonly have the name of the things whereof they be sacraments. Therefore as after a certain manner the sacrament of Christ s body is Christ s body ; so likewise the sacrament of faith is faith. And likewise saith St Paul, that in baptism we be buried, he saith not that we signify burial, but he saith plainly that we be buried : so that the sacrament of so great a thing is called by the name of the thing." 128. All these be St Augustine s words, shewing how in the common use of speech one thing may have the name of another. Wherefore when Doctor Gardiner saith that St Augustine spake not of the manner of speech, thou mayest believe him hereafter as thou shalt see cause, but if thou trust his words too much, thou shalt soon be deceived. As for the real presence of Christ in the sacrament, I grant that he is really pre sent after such sort as you expound really in this place, that is to say, in deed, and Really, yet but spiritually. For you say yourself, that he is but after a spiritual manner there, and so is he spiritually honoured, as St Augustine saith. But as concerning heat of disputation, mark well the words of St Augustine, good reader, cited in my book, and thou shalt see clearly that all this multiplication of words is rather a juggling than a direct answer. For St Augustine writeth not in heat of disputation, but temperately and gravely, to a learned bishop, his dear friend, who demanded a question of him. And if St Augustine had answered in heat of disputation, or for any other respect otherwise than the truth, he had not done the part of a friend, nor of a learned and godly bishop. And whosoever judgeth so of St Augustine, hath small estimation of him, and sheweth himself to have little know ledge of St Augustine. But in this your answer to St Augustine, you utter where you learned a good part of your divinity, that is, of Albertus Pighius, who is the father of this shift, and Aibertus with this sleight eludeth St Augustine when he could no 5 otherwise answer: as 1 you do now shake off the same St Augustine, resembling as it were in that point the lively countenance of your father Pighius. Next in my book followeth Theodoret. And to this purpose it is both pleasant, comfortable, and profitable to read Theodoretus in his dialogues, where he disputeth and sheweth at length how the names of things be changed in scripture, and yet things remain still. And for example he proveth that the flesh of Christ is in the scripture sometime called a vail or covering, sometime a cloth, sometime a vestment, and sometime a stole : and the blood of the grape is called Christ s blood, and the names of bread and wine, and of his flesh and blood, Christ doth so change, that sometime he calleth his body corn or bread, and sometime rs none, 1551.] TO si sunt vera, corpus 128 THE THIRD BOOK. contrary he calleth bread his body. And likewise his blood sometime lie calleth wine, and sometime contrary he calleth wine his blood. For the more plain understanding whereof it shall not be amiss to re cite his own sayings in his foresaid dialogues, touching this matter of the holy sacrament of Christ s flesh and blood. The speakers in these dialogues be Orthodoxus, the right believer, and Eranistes, his companion, but not under standing the right faith. Orthodoxus saith to his companion : ] Dost thou not know that God calleth bread his flesh ? ERAN. I know that. ORTH. And in another place he calleth his body corn. ERAN. I know that also, for I have heard him say : " The hour is come that the Son of man shall be glorified," &c. " Except the grain of corn that falleth in the ground die, it remaineth sole; but if it die, then it bringeth forth much fruit." ORTH. When he gave the mysteries or sacraments, he called bread his body, and that which was mixt in the cup he called his blood. ERAN. So he called them. ORTH. But that also which was his natural body may well be called his body, and his very blood also may be called his blood. ERAN. It is plain. ORTH. But our Saviour without doubt changed the names, and gave to the body the name of the sign or token, and to the token he gave the name of the body. And so when he called himself a vine, he called blood that which was the token of blood. ERAN. Surely thou hast spoken the truth. But I would know the cause wherefore the names were changed. ORTH. The cause is manifest to them that be expert in true religion. For he would that they which be partakers of the godly sacraments, should not set their minds upon the nature of the things which they see, but by the changing of the names should believe the things which be wrought in them by grace. For he that called that, which is his natural body, corn and bread, and also called himself a vine, he did honour the visible tokens and signs with the names of his body and blood, not changing the nature, but adding grace to nature. ERAN. Sacraments be spoken of sacramentally, and also by them be manifestly declared things which all men know not. ORTH. Seeing then that it is certain that the patriarch called the Lord s body a vestment and apparel, and that now we be entered to speak of godly sacraments, tell me truly of what thing thinkest thou this holy meat to be a token and figure; of Christ s divinity, or of his body and blood? ERAN. It is clear that it is the figure of those things whereof it beareth the name. ORTH. Meanest thou of his body and blood? ERAN. Even so I mean. ORTH. Thou hast spoken as one that loveth the truth : for the Lord when he took the token or sign, he said not, This is my divinity ; but " This is my body," and " This is my blood." And in another place : " The bread which I will give is my flesh, which I will give for the life of the world." For- ERAN. These things be true, for they be God s words. " v Theodoretus, in Dialogo i. Tom. IV. pp. 25-27. Hate. 1709-94.] OF THE PRESENCE OF CHRIST. 129 130. All these writeth Theodoretus in his first dialogue. And in the second he writoth the same in effect, and yet in some thing 2 more plainly, against such heretics as affirmed, that after Christ s resurrection SEdff and ascension his humanity was changed from the very nature of man 3 and fatens mum turned into his divinity. Against whom thus he writeth 4 : i^T iwn ORTH. Corruption, health, sickness, and death, be accidents, for they Dialogue 2. go and come. ERAN. It is meet they be so called. ORTH. Men s bodies after their resurrection be delivered from corrup tion, death, and mortality, and yet they lose not their proper nature. ERAN. Truth it is. ORTH. The body of Christ therefore did rise quite clean from all cor- chnsf body glori- ruption and death, and is impassible, immortal, glorified with the glory offied^amhis God, and is honoured of the powers of heaven, and it is 5 a body, and hath the same bigness that it had 6 before. ERAN. Thy saying 7 seem true and according to reason ; but after he was ascended up into heaven, I think thou wilt not say, that his body was not turned 8 into the nature of his Godhead 9 . ORTH. I would not so say for the persuasion of man s reason : nor I am not so arrogant and presumptuous to affirm any thing which scripture passeth over in silence. But I have heard St Paul cry, "that God hath ordained Acts xvu. a day when he will judge all the world in justice by that man which he appointed before, performing his promise to all men, and raising him from death." I have learned also of the holy angels, that he will come after Acts i. that fashion, as his disciples saw him go to heaven. But they saw a nature of a certain bigness, not a nature which had no bigness. I heard further more the Lord say: "You shall see the Son of man come in the clouds heaven." And I know that every thing that men see hath a certain bigness : for that nature that hath no bigness cannot be seen. Moreover to sit in the throne of glory, and to set the lambs upon his right hand, and the goats upon liis left hand, signified! a thing that hath quantity and bigness. Hitherto have I rehearsed Theodoretus words, and shortly after Eranistes saith 10 : ERAN. We must turn every stone, as the proverb saith, to seek out the truth, but specially when godly matters be propounded. ORTH. TeU me then the sacramental signs which be offered to God by his priests, whereof be they signs, sayest thou ? ERAN. Of the Lord s body and blood. ORTH. Of a very body ? or not of a very body ? ERAN. Of a very body. ORTH. Very well, for an image must be made after a true pattern : for painters follow nature, and paint the images of such things as we see with our eyes. ERAN. Truth it is. ORTH. If therefore the godly sacraments represent a true body, then is the Lord s body yet still a body, not converted into the nature of his God head, but replenished with God s glory. [- Things, 1551, and Orig. ed.] I 3 Of a man, 1551, and Orig. ed.] . 4 Id. in Dialogo ii. Tom. IV. pp. 122, 3.] f 5 And yet it is, 1551, and Orig. ed.] [ (i Hath, 1551. The Orig. ed. reads with that of 1580.] [ 7 Sayings, 1551, and Orig. ed.] [ 8 Was turned, 1551, and Orig. ed.] [ 9 Of the Godhead, 1551, and Orig. ed.J [ 10 Theodoret. ubi supra, pp. 122, 3.] 130 THE THIRD BOOK. ERAN. It cometh in good time that thou makest mention of God s sacra ments; for by the same I shall prove that Christ s body is turned into another nature. Answer therefore unto my questions. ORTH. I shall answer. ERAN. What callest thou that which is offered before the invocation of the priest ? ORTH. We must not speak plainly ; for it is like that some be present which have not professed Christ. ERAN. Answer covertly. ORTH. It is a nourishment made of seeds that be like. ERAN. Then how call we the other sign ? ORTH. It is also a common name that signineth a kind of drink. ERAN. But how dost thou call them after the sanctification ? ORTH. The body of Christ, and the blood of Christ. ERAN. And dost thou believe that thou art made partaker of Christ s body and blood ? ORTH. I believe so. ERAN. Therefore as the tokens of God s body and blood be other things 131. before the priest s invocation, but after the invocation they be changed, and be other things ; so also the body of Christ after his assumption is changed into his divine substance. ORTH. Thou art taken with thine own net. For the sacramental signs go not from their own nature after the sanctification, but continue in their former substance, form, and figure, and may be seen and touched as well as before : yet in our minds we do consider what they be made, and do repute and esteem them and have them in reverence, according to the same things that they be taken for. Therefore compare their images to the pattern, and thou shalt see them like. For figure 1 must be like to the thing itself. For Christ s body hath his former fashion, figure, and bigness, and, to speak at one word, the same substance of his body : but after his resurrection it was made immortal, and of such power, that no corruption nor death could come unto it ; and it was exalted unto that dignity, that it was set at the right hand of the Father, and honoured of all creatures, as the body of him that is the Lord of nature. ERAN. But the sacramental token changeth his former name ; for it is no more called as it was before, but is called Christ s body. Therefore must his body after his ascension be called God, and not a body. [Jesus enim ORTH. Thou seemcst to me ignorant : for it is not called his body et^odieiiie only, but also the bread of life, as the Lord called it. So the body of Christ Embd UI Ed we ca ^ a g 0( % body, a body that giveth life, God s body, the Lord s body, our master s body ; meaning 2 that it is not a common body, as other men s bodies be, but that it is the body of our Lord Jesu Christ, both God and man. This have I rehearsed of the great clerk and holy bishop Theodoretus, whom some of the papists perceiving to make so plainly against them, have defamed, saying that he was infected with the error of Nestorius. Here the papists shew their old accustomed nature and condition, which is even in a manifest matter rather to lie without shame, than to give place unto the truth, and confess their own error. And although his adversaries 1 a figure, 1551.] [2 So the Orig. edit, and 1551 ; that of 1580 has name ning.] OF THE PRESENCE OF CHRIST. 131 falsely bruited such a fame against him, when he was yet alive, nevertheless [Quem Leo he was purged thereof by the whole council of Chalcedon, about eleven hundred SjJg^J]^ years ago. SEnSd. And furthermore in his book which he wrote against heresies, he specially fed> 1537>] condemncth Nestorius by name. And also all his three books of his dialogues before rehearsed he wrote chiefly against Nestorius, and was never herein noted of error this thousand year, but hath ever been reputed and taken for an holy bishop, a great learned man, and a grave author, until now at this present time, when the papists have nothing to answer unto him, they begin in excusing of themselves to defame him. Thus much have I spoken for Theodoretus, which I pray thee be not weary to read, good reader, but often and with delectation, deliberation, and good advertisement to read. For it containeth plainly and briefly the true instruction of a Christian man, concerning the matter, which in this book we treat upon. First, that our Saviour Christ in his last supper, when he gave bread and wine to his apostles, saying, " This is my body; this is my blood;" it was bread [Five win- which he called his body, and wine mixed in the cup which he called his blood : ? % noted ** in Theodoret. so that he changed the names of the bread and wine, which were the mysteries, Ed - 1351 -] sacraments, signs, figures, and tokens of Christ s flesh and blood, and called 132. them by the names of the things which they did represent and signify ; that is to say, the bread he called by the name of his very flesh, and the wine by the name of his blood. Second, that although the names of bread and wine were changed after sanctification, yet, nevertheless, the things themselves remained the selfsame that they were before the sanctification, that is to say, the same bread and wine in nature, substance, form, and fashion. The third, seeing that the substance of the bread and wine be not changed, why be then their names changed, and the bread called Christ s flesh, and the wine his blood? Theodoretus sheweth that the cause thereof was this, that we should not have so much respect to the bread and wine (which we see with our eyes, and taste with our mouths) as we should have to Christ himself, in whom we believe with our hearts, and feel and taste him by our faith, and with whose flesh and blood (by his grace) we believe that we be spiritually fed and nourished. These things we ought to remember and revolve in our minds, and to lift up our hearts from the bread and wine unto Christ that sitteth above. And because we should so do, therefore after the con secration they be no more called bread and wine, but the body and blood of Christ. The fourth, it is in these sacraments of bread and wine, as it is in the very body of Christ. For as the body of Christ before his resurrection and after is all one in nature, substance, bigness, form, and fashion ; and yet it is not called as another common body, but with addition, for the dignity of his exaltation, it is called a heavenly, a godly, an immortal, and the Lord s body : so likewise the bread and wine before the consecration and after is all one in nature, substance, bigness, form, and fashion ; and yet it is not called as other common bread, but for the dignity whereunto it is taken, it is called with addition, heavenly bread, the bread of life, and the bread of thanksgiving. The fifth, that no man ought to be so arrogant and presumptuous to affirm for a certain truth in religion any thing which is not spoken of in holy scripture. And this is spoken to the great and utter condemnation of 92 132 THE THIRD BOOK. the papists, which make and unmake new articles of our faith from time to time at their pleasure, without any scripture at all, yea, quite and clean contrary to scripture. And yet will they have all men bound to believe whatsoever they invent, upon peril of damnation and everlasting fire. And yet will they constrain 1 with fire and fagot all men to consent (contrary to the manifest words of God) to these their errors in this matter of the holy sacrament of Christ s body and blood : First, that there remaineth no bread nor wine after the consecration, but that Christ s flesh and blood is made of them. Second, that Christ s body is really, corporally, substantially, sensibly, and naturally in the bread and wine. Thirdly, that wicked persons do eat and drink Christ s very body and blood. Fourthly, that priests offer Christ every day, and make of him a new sacrifice propitiatory for sin. Thus for shortness of time I do make an end of Thcodoretus, with other old ancient writers, which do most clearly affirm that to eat Christ s body and to drink his blood be figurative speeches. And so be these sen- 133. tences likewise which Christ spake at his supper: "This is my body;" "this is my blood." WINCHESTER. Theodoretus. 77^ author bringeth in Theodoret, a Greek, whom to discuss particularly were long and tedious : one notable place there is in him which toucheth the point of the matter, which place Peter Martyr allegeth in Greek, and then translateth it into Latin, not exactly as other have done to the truth; but as he hath done, I will write here 2 . And then will I write the same, translated into English by one that hath translated Peter Martyr s book; and then will I add the translation of this author, and finally, the very truth of the Latin, as I will abide by, and join an issue with this author in it, whereby thou, reader, shalt perceive with what sin cerity things be handled. p. Martyr. Peter Martyr hath of Theodoret this in Latin, which the same Theodoret, in a disputation with an heretic, maketh the catholic man to say : Captus es iis quce tetenderas retibus. Neque enim post sanctificationem mystica symbola ilia propria sua natura egrediuntur ; manent enim in priori sua substantia, et figura, et specie, adeoque et videntur, et pal- pantur, quemaclmodum et antea. Intelliguritur autem quse facta sunt, et creduntur, et adorantur tanquam ea existentia, quse creduntur. He that translateth Peter Martyr in English, doth express these words thus : " Lo, thou art ndw caught in the same net which thou hadst set to catch me in. For those same mystical signs do not depart away out of their own proper nature after the hallowing of them. For they remain still in their former substance, and their former shape, and their former kind, and are even s as well seen and felt as they were afore. But the things that are done are understanded, and are believed, and are wor shipped, even as though they were in very deed the things that are believed." This is the common translation into English of Peter Martyr s book translated, which this author doth translate after his fashion thus: "Thou art taken vjith thine own net; for the sacramental signs go not from their own nature after the sanctijication, but continue in their former substance, form, and figure, and be seen and touched as well as before. Yet in our minds we do consider what they be made, and do repute and esteem them and have them in reverence according to the same things that they be taken for." Thus is the translation of this author. Mine English of this Latin is thus : " Thou art taken with the same nets thou didst lay forth. For the mystical tokens after tlie sanctijication go not away out of their proper nature. For they abide in their former substance, shape, and form, and so far forth, that they may be seen and felt as they might before. But they be understanded that they be made, and are believed, and are worshipped, as being the same things which be believed." This is my translation, who in the first sentence P And they would constrain, 1551, and Grig, ed.] I [ 3 Ever, 1551. Orig. ed. Winch, reads with ed. [ 2 I will write in here, 1551.] 1580.] OF THE PRESENCE OF CHRIST. 133 mem not to vary from the other tr<in-:l<iti<ms (<>"</,;,, >f the remain of substance, shape, form, or figure: I will use all those names. Jlut !,t the second part, where Theodoret speaketh of our belief what the tokens be made, and where he saith those tokens be worshipped, as being the same things which be believed, thou mayest see, reader, how this author flieth the words "believe" and "worship," which the common translation in English doth plainly and truly ejcpress, howsoever the translator 4 swerved by colour of the word tanquam, which there, after the Greek, signifieth the truth, and not the similitude only; like as St Paul, Vocat ca quse non sunt, tanquam sint, which is to make to be in deed, not as though they were. And tlie Greek is there oi/ra, as it is here coWep (Kflva oWa 5 . And it were an absurdity to believe things other wise than they be, as though they were, and very idolatry to worship wittingly that is not, as though it were in deed. And therefore in these two words, that they believed"! that tJiey be made <i,/ l be worshipped, is declared by Tficodoret his faith of the very true real presence of Christ s tih, tvhereunto tJie Deity is united, which flesh St Augustine, consonantly to this Tlieodoret, must be worshipped before it be received. The word "worshipping" put here in English is to c.rpress the word adorantur, put by Peter in Latin, signifying adoring, being the verb in Greek of such signification, as is used to express godly worship with bowing of the knee. Now, reader, what should I say by this author, that conveyeth tJiese two words of believing and worshipping, and instead of them cometh in with reverence, taking, reputing, and esteem ing? whereof thou mayest esteem how this place of Theodorct pincJied this author, who could 134. not but see that adoring of the sacrament signifieth the presence of the body of Christ to be adored, which else were an absurdity; and therefore the author took pain to ease it with other words of calling, believing, reputing, and esteeming, and for adoration, reverence. Con sider what praise this author giveth Theodoret, which praise condemneth this author sore. For Theodoret, in his doctrine, would h<xve us believe the mystery, and adore the sacrament, Adoration iclifi c, this author after in his doctrine professeth there is nothing to be worshipped at all. ment. If one should now say to me, " Yea, sir, but this Theodoret seemeth to condemn transubstan- tiation, because he speaketh so of the bread:" tfiereunto shall be answered when I speak of transubstantiation, which shall be after the third and fourth book discussed 8 . For before the truth of the presence of the substance of Christ s body may appear, what should we talk of transubstantiation ? I will travail no more in Theodoret, but leave it to thy judgment, reader, what credit this author ought to have, that handleth the matter after this sort. CANTERBURY. This bladder is so puffed up with wind, that it is marvel it brasteth not. But bo patient awhile, good reader, and suffer until the blast of wind be past, and thou shalt see a great calm, the bladder broken, and nothing in it but all vanity. There is no difference between your translation and mine, saving that mine is more plain, and giveth less occasion of error; and yours, as all your doings be, is dark and obscure, and containeth in it no little provocation to idolatry. For the words of Theodoret, after your interpretation, contain both a plain untruth and also manifest idolatry : for the signs and tokens which he speaketh of, be the very forms and sub stances of bread and wine. For the nominative case to the verb of adoring, in Theodoret, is not the body and blood of Christ, but the mystical tokens, by your own translation : which mystical tokens if you will have to be the very body and blood of Christ, what can be spoken more untrue or more foolish? And if you will have them to be wor shipped with godly worship, what can be greater idolatry? Wherefore I, to eschew such occasions of error, have translated the words of Theodoretus faithfully and truly as his mind was, and yet have avoided all occasions of evil : for tanqtiam, or wcnrcp 6K?i/a OI/TCC, signifieth not the truth, as you say, but is an adverb of similitude, as it is likewise in this place of St Paul : Vocat ca quw non sunt, tanquam sint. For St [ 4 that translator, lf)5l.] [ 5 The original of Theodoret is as follows : OP 9. Ea/Xtos uls- U(/>;i/es apKvaiv. oitde ydp /neTa Ton dyincr}i.oi> TO. f&tMTTucci vu/j.fio\a T/;S otv~e/s e^iGTCiTai <^>ucre(os. jiiti ei y ip CTTI TT/S Trportpas oucrms, KUI TOV erX /iuaTo?, *al TOU ci oous, KUI opctTci txrrt, KUI dirra, out KUI Trporepov iji;* i/oeiTai 6e (iirep tytWru, KUL Trio-reueTrti, KUI U>? t\6lJ/a OVTd aTTfp TTKTTfUfTai. ThCOdOTCt. ubi supra, p. 126.] [ 6 Grig. ed. Winch, omits the word "wittingly."] [ 7 they he believed, loal.] [ 8 Orig. ed. Winch, instead of, "which shall be after the third and fourth book discussed," reads, " which shall be the last."] 134 THE THIRD BOOK. Paul saith, " as though they were ;" which indeed were not, as he said the next word before, non sunt, " they be not." And nevertheless unto God all things be present ; and those things which in their nature be not yet present, unto God were ever present, Rev. xiii. in whom be not these successions of time, before and after : for Christ the Lamb in Psai. ixxxui. his present was slain before the world began ; and a thousand year to his eyes be but 2Pet.iii. as it were yesterday; and one day before him is as it were a thousand year, and a thousand year as one day. August, de And if you had read and considered a saying of St Augustine, De doctrina Christiana, Lib. iii. cap. Lib. in. cap. 9, you might have understand this place of Theodoret better than you do. " He serveth under a sign," saith St Augustine, " who wwketh or worshippeth any sign, not knowing what it signifieth. But he that worketh or worshippeth a pro fitable sign ordained of God, the strength and signification whereof he understandeth, 135. he worshippeth not that which is seen and is transitory, but rather that thing whereto all such signs ought to be referred." And anon after he saith further: "At this time when our Lord Jesus Christ is risen, we have a most manifest argument of our freedom, and be not burdened with the heavy yoke of signs which we understand not; but the Lord and the teaching of his apostles hath given to us a few signs for many, and those most easy to be done, most excellent in understanding, and in performing most pure; as the sacrament of baptism, and the celebration of the body and blood of our Lord, which every man when he receiveth knoweth whereunto they be re ferred, being taught that he worship not them with a carnal bondage, but rather with a spiritual freedom. And as it is a vile bondage to follow the letter, and to take the signs for the things signified by them ; so to interpret the signs to no profit, is an error that shrewdly spreadeth abroad 1 ." These words of St Augustine, being con ferred with the words of Theodoret, may declare plainly what Theodoret s meaning was. For where he saith that we may not worship with a carnal bondage the visi ble signs, (meaning of water in baptism, and of bread and wine in the holy communion,) when we receive the same, but rather ought to worship the things whereunto they be referred, he meant that although those signs or sacraments of water, bread, and wine ought highly to be esteemed, and not to be taken as other common water, baker s bread, or wine in the tavern, but as signs dedicated, consecrated, and referred to an holy use ; and by those earthly things to represent things celestial ; yet the very true honour and worship ought to be given to the celestial things, which by the visi ble signs be understand, and not to the visible signs themselves. And nevertheless, both St Augustine and Theodoret count it a certain kind of worshipping the signs, the reverent esteeming of them above other common and profane things, and yet the same principally to be referred to the celestial things represented by the signs ; and therefore saith St Augustine potius, "rather." And this worship is as well in the sacrament of baptism, as in the sacrament of Christ s body and blood. And there fore, although whosoever is baptized unto Christ, or eateth his flesh and drinketh his blood in his holy supper, do first honour him; yet is he corporally and carnally nei ther in the supper, nor in baptism, but spiritually and effectually. Now where you leave the judgment of Theodoret to the reader, even so do I also, not doubting but the indifferent reader shall soon espy, how little cause you have so to boast, and blow out your vain-glorious words as you do. But hear now what folio weth next in my book. f 1 Sub signo enim servit qui operatur aut vene- ratur aliquam rem significantem, nesciens quid sig- nificet : qui vero aut operatur, aut veneratur utile signum divinitus institutum, cujus vim significa- tionemque intelligit, non hoc veneratur quod videtur et transit, sed illud potius quo talia cuncta refe renda sunt Hoc vero tempore posteaquam resur- rectione Domini nostri manifestissimum indicium nostrae libertatis illuxit, nee eorum quidem signorum, quaejamintelligimus, operationegravionerati sumus; sed quaedam pauca pro multis, eademque factu fa- cillima, et intellectu augustissima, et observatione castissima ipse Dominus et apostolica tradidit dis- ciplina : sicuti est baptismi sacramentum, et cele- bratio corporis etsanguinis Domini. Quae unusquis- que cum percipit, quo ref erantur imbutus agnoscit, ut ea non carnali servitute, sed spiritali potius libertate veneretur. Ut autem literam sequi, et signa pro rebus qua? iis significantur accipere, servilis in- h rmitatis est ; ita inutiliter signa interpretari, male vagantis erroris est. Augustin. De doctrina Christiana, Lib. in. cap. J. Pars iv. Basil, ap. Amerbach. 1506.] OF THE PRESENCE OF CHRIST. 135 And marvel not, good reader, that Christ at that time spake in figures, chap. i. when he did institute that sacrament, seeing that it is the nature of all sacra- spl^heTbe not strange. ments to be figures. And although the scripture be full of schemes, tropes, and figures, yet specially it useth them when it speaketh of sacraments. When the ark, which represented God s majesty, was come into the army of the Israelites, the Philistines said that God was come into- the army. And isam.iv. God himself said by his prophet Nathan, that from the time that he had 2 Sam. vu. brought the children of Israel out of Egypt, he dwelled not in houses, but that he was carried about in tents and tabernacles. And yet was not God himself so carried about, or went in tents or tabernacles : but because the ark, which was a figure of God, was so removed from place to place, he 130. spake of himself that thing, which was to be understand of the ark. And Christ himself oftentimes spake in similitudes, parables, and figures ; Christ him- as when he said : " The field is the world, the enemy is the devil, the seed figuwtTve is the word of God;" "John is Elias;" " I am a vine, and you be the J[att xm. branches ; " " I am bread of life ; " " my Father is an husbandman, and he * oh x n vl x ;. hath his fan in his hand, and will make clean his floor, and gather the JjJJJ *|j wheat into his barn, but the chaff he will cast into everlasting fire;" "I have John iv. a meat to eat which you know not ; " " work not meat that perisheth, but na beo man" ducare oueiu that endureth unto everlasting life;" "I am a good shepherd;" "the Son J^J^ iti8 - of man will set the sheep at his right hand, and the goats at his left hand ; " jjjy * xv "I am a door, one of you is the devil;" "whosoever doeth my Father s will, John x. he is my brother, sister, and mother:" and when he said to his mother Malt. xii. and to John, " This is thy son," " this is thy mother." John xix. These, with an infinite number of like sentences, Christ spake in parables, metaphors, tropes, and figures. But chiefly when he spake of the sacraments, he used figurative speeches. As when in baptism he said, " that we must be baptized with the Holy Acts i. Ghost," meaning of spiritual baptism. And like speech used St John the Baptist, Ma - saying of Christ, " that he should baptize with the Holy Ghost and fire." And Christ said, " that we must be born again, or else we cannot see the John in. kingdom of God." And said also : " Whosoever shall drink of that water which John iv. I shall give him, he shall never be dry again. But the water which I shall ?aqu b al!Sm give him, shall be made within him a well, which shall spring into ever- ibidem. lasting life." And St Paul saith, " that in baptism we clothe us with Christ, Rom. vi. and be buried with him." This baptism and washing by the fire and the Holy Ghost, this new birth, this water that springeth in a man and floweth into everlasting life, and this clothing and burial, cannot be understand of any material baptism 2 , material washing, material birth, clothing, and burial ; but by translation of things visible into things invisible, they must be understand spiritually and figuratively. After the same sort the mystery of our redemption, and the passion of oui Saviour Christ upon the cross, as well in the new as in the old testa ment, is expressed and declared by many figures and figurative speeches. As the pure paschal lamb without spot signified Christ, the effusion ofihePas- thc lamb s blood signified the effusion of Christ s blood ; and the salvation C of the children of Israel from temporal death by the lamb s blood signified our salvation from eternal death by Christ s blood. And as Almighty God, passing through Egypt, killed all the Egyptians heirs in every house, and left not one alive, and nevertheless he passed by Of any baptism, 1551. J 136 THE THIRD BOOK. The Lord s Supper. 137. M.itt xxvi Exod. xii. Matt. xxvi. What figura tive spesches were used at Christ s last supper. Matt. xxvi. Mark xiv. Lukexxii. the children of Israel s houses, where he saw the lamb s blood upon the doors, and hurted none of them, but saved them all by the means of the lamb s blood ; so likewise at the last judgment of the whole world, none shall be passed over and saved but that shall be found marked with the blood of the most pure and immaculate Lamb, Jesus Christ. And forasmuch as the shedding of that lamb s blood was a token and figure of the shedding of Christ s blood then to come; and forasmuch also as all the sacraments and figures of the old testament ceased and had an end in Christ ; lest by our great unkindness we should peradventure be forgetful of the great benefit of Christ, therefore at his last supper, (when he took his leave of his apostles to depart out of the world,) he did make a new will and testament, wherein he bequeathed unto us clean remission of all our sins, and the everlasting inheritance of heaven. And the same he confirmed the next day with his own blood and death. And lest we should forget the same, he ordained not a yearly memory, (as the paschal lamb was eaten but once every year,) but a daily remembrance he ordained thereof in bread and wine, sanctified and dedicated to that purpose, saying : " This is my body ; this cup is my blood, which is shed for the remission of sins : do this in remembrance of me :" admonishing us by these words, spoken at the making of his last will and testament, and at his departing out of the world, (because they should be the better remembered,) that when soever we do eat the bread in his holy supper, and drink of that cup, we should remember how much Christ hath done for us, and how he died for our sakes. Therefore saith St Paul : "As often as ye shall eat this bread, and drink the cup, you shall shew forth the Lord s death until he come." And forasmuch as this holy bread broken, and the wine divided, do repre sent unto us the death of Christ now past, as the killing of the paschal lamb did represent the same yet to come ; therefore our Saviour Christ used the same manner of speech of bread and wine, as God before used the paschal lamb 1 . For as in the old testament God said, " This is the Lord s pass-by, or passover" ; even so saith Christ in the new testament, " This is my body ; this is my blood." But in the old mystery and sacrament the lamb was not the Lord s very passover or passing by, but it was a figure which repre sented his passing by : so likewise in the new testament the bread and wine be not Christ s very body and blood, but they be figures, which by Christ s institution be unto the godly receivers thereof sacraments, tokens, significations, and representations of his very flesh and blood ; instructing their faith, that as the bread and wine feed them corporally and continue this temporal life, so the very flesh and blood of Christ feedeth them spiritually, and giveth everlasting life. And why should any man think it strange to admit a figure in these speeches, " This is my body," " this is my blood ;" seeing that the communi cation the same night, by the papists own confessions, was so full of figura tive speeches ? For the apostles spake figuratively when they asked Christ, "where he would cat his passover or pass-by :" and Christ himself used the same figure, when he said : "I have much desired to eat this passover with you." Also, to cat Christ s body and to drink his blood, I am sure they will not say that it is taken properly, to eat and drink, as we do eat other meats and drinks. And when Christ said, " This cup is a new testament in my blood," here in one sentence be two figures : one in this word, " cup," which is not taken for the cup itself, but for the thing contained in the cup : another is in this word, [ Of the Paschal Lamb, 15ol.] OF THE PRESENCE OF CHRIST. 137 " testament ;" for neither the cup, nor the wine contained in the cup, is Christ s testament, but is a token, sign, and figure, whereby is represented unto us his testament, confirmed by his blood. And if the papists will say, as they say indeed, that by this cup is neither meant the cup, nor the wine contained in the cup, but that thereby is meant Christ s blood contained in the cup, yet must they needs grant that there is a figure. For Christ s blood is not in proper speech the new testament, but it is the thing that confirmed the new testament. And yet by this strange interpre- isa tation the papists make a very strange speech, more strange than any figurative speech is. For this they make the sentence : " This blood is a new testament in my blood." Which saying is so fond and so far from all reason, that the foolishness thereof is evident to every man. WINCHESTER. As for the use of figurative speeclies to be accustomed in scripture is not denied. But Philip Melancthon in an epistle to (Ecolampadius of the sacrament, giveth one good note of Meiancthon. observation in difference between the speeches in God s ordinances and commandments, and j n scripture! otherwise 2 . For if in the understanding 3 of God s ordinances and commandments figures may be often received ; truth shall by allegories be shortly subverted, and all our religion reduced spi to significations. There is no speech so plain and simple but it hath some piece of a figurative |*j speech, but such as expresseth the common plain understanding; and then the common use of Figurative tlie figure causeth it to be taken as a common proper speech. As these speecJies, " drink up tSm b m a ci this cup," or " eat this dish 4 ," is indeed a figurative speech, but by custom made so common P r P er - that it is reputed the plain speech, because it hath but one only understanding commonly received. And when Christ said, " This cup is tlie new testament" tJie proper speech thereof in letter hath an absurdity in reason, and faith also. But when Christ said, " TJiis is my body," although the truth of the literal sense hath an absurdity in carnal reason, yet hath it no absurdity in humility of faith, nor repugneth not to any other truth of scripture. And seeing it is a singular miracle of Christ wliereby to exercise us in the faith, understanded as the plain words signify in their proper sense, there can no reasoning be made of other figurative speeches to make this to be tJteir fellow and like unto them. No man denieth the use of figurative speeches in Christ s supper, but such as be equal with plain proper speech, or be expounded by other evangelists in plain spec,ch. CANTERBURY. I see well you would take a dung-fork to fight with, rather than you would lack a weapon. For how highly you have esteemed Melancthon in times past, it is not unknown. But whatsoever Melancthon saith, or howsoever you understand Melancthon, where is so convenient a place to use figurative speeches as when figures and sacraments be instituted ? And St Augustine giveth a plain rule how we may know when God s commandments be given in figurative speeches 5 , and yet shall neither the truth be subverted, nor our religion reduced to significations. And how can it be but that in the understanding of God s ordinances and commandments figures must needs be often received, (contrary to Mclancthon s saying,) if it be true that you say, " that there is no speech so plain and simple, but it hath some piece of a figurative speech?" But now be all speeches figurative, when it pleaseth you. What need I then to travail any more to prove that Christ in his supper used figurative speeches, seeing that all that he spake w r as spoken in figures by your saying? And these words " This is my body," spoken of the bread, and " This is my blood, [ 2 The epistle referred to appears to be that in- | cur earn deseramus." pp. 14, 15. The letter is serted in (Ecolampadii Dialogus, Quid de Eucharis- dated Spires, an. 1529.] tia veteres turn Graeci turn Latini senserint, Basil. 1590. " Nullam enim firm am rationem invenio, 4 me coiisdenti;i discedenti a, proprietate verborum satisfaciat Cum proprietas vcrborum cum nullo articulo h dei pugnet, nulla satis magna causa est [ 3 For if theunderstanding, 1551. Evidently an error of the press.] f 4 E ; it up this dish, 1551. Orig. ed. reads as cd. 1580.] [ 5 See before, p. 115, note 5.] 138 THE THIRD BOOK. 130. Chap. xni. Answer to the authori ties and ar guments of the papists. Chap. xiv. One brief answer to al! spoken of the cup, express no plain common understanding, whereby the common use of these figures should be equal with plain proper speeches, or cause them to be taken as common proper speeches : for you say yourself, " that these speeches in letter have an absurdity in reason." And as they have absurdity in reason, so have they "absurdity in faith." For neither is there any reason, faith, miracle, nor truth, to say that material bread is Christ s body. For then it must be true that his body is material bread, a conrersa ad convcrtentem ; for of the material bread spake Christ those words, by your confession 1 . And why have not these words of Christ, "This is my body," an absurdity both in faith and reason, as well as these words, "This cup is the new testament," seeing that these words were spoken by Christ as well as the other, and the credit of him is all one whatsoever he saith ? But if you will needs understand these words of Christ, " This is my body," as the plain words signify in their proper sense, (as in the end you seem to do, repugning therein to your own former saying,) you shall see how far you go, not only from reason, but also from the true confession of the Christian faith. Christ spake of bread, say you, " This is my body ;" appointing by this word " this" the bread : whereof followeth, as I said before, if bread be his body, that his body is bread: and if his body be bread, it is a creature without sense and reason, having neither life nor soul ; which is horrible of any Christian man to be heard or spoken. Hear now what followeth further in my book. Now forasmuch as it is plainly declared and manifestly proved, that Christ called bread his body, and wine his blood, and that these sentences be figurative speeches ; and that Christ, as concerning his humanity and bodily presence, is ascended into heaven with his whole flesh and blood, and is not here upon earth ; and that the substance of bread and wine do remain still, and be received in the sacrament, and that although they remain, yet they have changed their names, so that the bread is called Christ s body, and the wine his blood ; and that the cause why their names be changed is this, that we should lift up our hearts and minds from the things which we see unto the things which we believe and be above in heaven ; whereof the bread and wine have the names, although they be not the very same things in deed : these things well considered and weighed, all the authorities and arguments, which the papists feign to serve for their purpose, be clean wiped away. For whether the authors, which they allege, say that we do eat Christ s flesh and drink his blood ; or that the bread and wine is converted into the substance of his flesh and blood ; or that we be turned into his flesh ; or that in the Lord s supper we do receive his very flesh and blood ; or that in the bread and wine is received that which did hang upon the cross ; or that Christ hath left his flesh with us ; or that Christ is in us and we in him ; or that he is whole here and whole in heaven ; or that the same thing is in the chalice, which flowed out of his side ; or that the same thing is received with our mouth, which is believed with our faith ; or that the bread and wine after the consecration be the body and blood of Christ ; or that we be nourished with the body and blood of Christ ; or that Christ is both gone hence and is stih 1 here ; or that Christ at his last supper bare himself in his own hands : these and all other like sentences may not 2 be understanded of Christ s humanity literally and carnally, as the words in common speech do properly signify ; for so doth no man eat Christ s flesh, nor drink his blood, nor so is not the bread and wine 3 after the conse cration his flesh and blood, nor so is not his flesh and blood whole here in earth eaten with our mouths, nor so did not Christ take himself in his own hands. [ J By your own confession, 1551.] [2 Not omitted in edit. 1580.] [ 3 The Orig. ed. and ed. 1551, add the following words, " turned into his flesh and blood, nor we into him ; nor so is the bread and wine," and the passage then runs on as above, " after the consecration," &c.J OF THE PRESENCE OF CHRIST. 130 But these and all other like sentences, which declare Christ to be here in earth, and to be eaten and drunken of Christian people, are to be understanded either 140. of his divine nature, (whereby he is everywhere,) or else they must be under standed figuratively, or spiritually. For figuratively he is in the bread and wine, and spiritually he is in them that worthily eat and drink the bread and wine ; but really, carnally, and corporally, he is only in heaven, from whence he shall come to judge the quick and dead. This brief answer will suffice for all that the papists can bring for their purpose, if it be aptly applied. And for the more evidence hereof, I shall apply the same to some such places, as the papists think do make most for them, that by the answer to those places the rest may be the more easily answered unto. WINCHESTER. In the seventy -fourth Imf this author goeth about to give a general solution to all that may be said of Christ s being in earth, in heaven, or in the sacrament ; and giveth instructions Jiow tliese words of Christ s divine nature, figuratively, spiritually, really, carnally, corporally, may be placed : and thus lie saith: "Christ in his divine nature may be said to be in the earth, figuratively in tlie sacrament, spiritually in tlie man that receiveth, but really, carnally, cor porally, only in heaven." Let us consider tlie placing of tliese terms. When we say Christ is in his divine nature everywhere, is he not really also everywhere, according to the true Reaiiy. essence of his Godhead? in deed every where ? That is to say, not in fantasy, nor imagination, but verily, truly, and therefore really, as we believe, so in deed every wliere f And when Christ is spiritually in good men by grace, is not Christ in them really by grace ? but in fantasy and imagination? And tlierefore whatsoever this author saith, the word "really may not have such restraint to be referred only to heaven, unless the author would deny that substance of the God- liead, which as it compreJiendeth all, being incomprehensible, and is everywhere without limitation of place, so as it is, truly it is, in deed is, and therefore really is ; and therefore of Christ must be said, wlieresoever he is in his divine nature by power or grace, lie is there really, whether we speak of heaven or earth. As for the terms "carnally" and "corporally," as this author seemeth to use them in otlier Camaiiy. places of this book to express the manner of presence of tlie human nature in Christ, I marvel * Cor P raI| y- by what scripture he shall 4 prove that Christ s body is so carnally and corporally in lieaven. We be assured by faith, grounded upon tlie scriptures, of the truth of the being of Christ s Jlesh and body tliere, and tlie same to be a true Jlesh and a true body ; but yet in such sense as this author useth tlie terms carnal and corporal against tlie sacrament to imply a grossness, he cannot so attribute those terms to Christ s body in heaven. St Augustine after the gross sense of carnally, saith : " Christ reigneth not carnally in heaven." And Gregory Nazianzen saith : August, dc "Although Christ shall come in the last day to judge, so as he shall be seen; yet there is in him cngori Na- TIO grossness," he saith, and referreth the manner of his being to his knowledge only. "And our SptEmo! 6 resurrection," St Augustine saith, " although it shall be of our true Jlesh, yet it shall not be car nally." And when this author had 5 defamed as it were the terms "carnally" and "corporally," as terms of grossness, to whom he used always to put as an adversative the term "spiritually," as though carnally and spiritually might not agree in one; now for all that he would place them both in lieaven, where is no carnality, but all the manner of being spiritual, where is no grossness at all, the secrecy of the manner of which life is hidden from us, and such as eye hath not seen, or ear heard, or ascended into the heart and thought of man. I know these terms carnally and corporally may have a good understanding out of the HOW Christ mouth of him that had not defamed them with grossness, or made them adversaries to spiritual ; and a man may say CJirist is corporally in heaven because the truth of his body is there, and S carnally in heaven because his Jlesh is truly there : but in this understanding both the words heven - carnally and corporally may be coupled with the word spiritually, ivhich is against this author s teaching, who appointeth tlie word spiritually to be spoken of Christ s presence in the man that received the sacrament worthily, which speech I do not disallow; but as Christ is spiritually in the in i at that doth receive the sacrament worthily, so is he in him spiritually before he receive, or else 141. he cannot receive worthily, as I have before said. And by this appeareth how this autlwr, to [ 4 Will, 1551.] [ Hath, 1551. J 140 THE THIRD BOOK. frame his general solution,, hath used neitlier of the terms "really," "carnally," and "corporally 1 ," or " spiritually," in a convenient order, but hath in his distribution misused them notably. For * e ChnsUspre- Christ in his divine nature is really everywhere, and in his human nature is carnally and cor- sacrament porally, as these words signify substance of the flesh and body, continually in heaven to the day heaven. of judgment, and nevertheless after that signification present in the sacrament also. And in those terms in that signijication the fathers have spoken of the 2 effect of the eating of Christ in the sacrament, as in the particular solutions to the authors hereafter shall appear. Marry as touching the use of tJie word "jiguratively" to say that Christ is figuratively in the bread and wine, is a saying ii hich this author hath not proved at all, but is a doctrine before this divers times reproved, and now by this author in England renewed. CANTERBURY. Although my chief study be to speak so plainly that all men 3 may understand every thing what I say, yet nothing is plain to him that will find knots in a rush. For when I say that all sentences which declare Christ to be here in earth, and to be eaten and drunken of Christian people, are to be understanded either of his divine nature, (whereby he is everywhere,) or else they must be understanded figuratively or spiritually; (for figuratively he is in the bread and wine, and spiritually he is in them that worthily eat and drink the bread and wine; but really, carnally and corporally, he is only in heaven;) you have termed these my w^ords as it liketh you, but far otherwise than I either wrote or meant, or than any indifferent reader would have imagined. For what indifferent reader would have gathered of my words, that Christ in his divine nature is not really in heaven? For I make a disjunctive, wherein I declare a plain distinction between his divine nature and his human nature. And of his divine nature I say in the first member of my division, which is in the beginning of my aforesaid words, that by that nature he is everywhere. And all the rest that followeth is spoken of his human nature, whereby he is carnally and corporally only in heaven. Rcaiiy. And as for this word "really," in such a sense as you expound it, (that is to say, not in fantasy nor imagination, but verily and truly,) so I grant that Christ is really, not only in them that duly receive the sacrament of the Lord s supper, but also in them that duly receive the sacrament of baptism, and in all other true Christian people at other times when they receive no sacrament. For all they be the members of Christ s body, and temples in whom he truly inhabiteth, although corporally and really (as the papists take that word "really") he be only in heaven, and not in the sacrament. And although in them that duly receive the sacrament he is truly and in deed, and not by fancy and imagination, and so really, (as you understand " really,") yet is he not in them corporally, but "spiritually," as I say, and "only after a spiritual manner," as you say. carnally and And as for these words, "carnally" and "corporally," I defame them not; for I mean corpora ly. ^y carna iiy anc l corporally none otherwise than after the form and fashion of a man s body, as we shall be after our resurrection, that is to say, visible, palpable, and cir cumscribed, having a very quantity w T ith due proportion and distinction of members, in place and order, one from another. And if you will deny Christ so to be in heaven, 142. I have so plain and manifest scriptures against you, that I will take you for no Christian man, except that you revoke that error. For sure I am that Christ s natural body hath Grossly. such a grossness, or stature and quantity, if you will so call it, because the word gross- ness, grossly taken, as you understand it, soundeth not well in an incorruptible and immortal body. Marry, as for any other grossness, as of eating, drinking, and gross avoiding of the same, with such other like corruptible grossness, it is for gross heads to imagine or think either of Christ, or of any body glorified. Augustinus. And although St Augustine may say, that Christ reigncth not carnally in heaven, yet he saith plainly, that his body is of such sort that it is circumscribed and contained in one place. [ Carnally, corporally, or spiritually, 1551.] j the intermediate words.] [ Of the sacrament, Grig. cd. Winch, omitting i [ 3 So that all men, 1551.] OF THE PRESKXCi: OK CHRIST. 141 And Gregory Nazianzen meant that Christ should not come at the last judgment Nazianzcnus. in a corruptible and mortal flesh, as he had before his resurrection, and as we have in this mortal life, (for such grossncss is not to be attributed to bodies glorified ;) but yet shall he come with such a body as he hath since his resurrection, absolute and perfect in all parts and members of a man s body, having hands, feet, head, mouth, side and wounds, and all other parts of a man visible and sensible, like as we shall all appear before him at the same last day, with this same flesh in substance that we now have, and with these same eyes shall we see God our Saviour. Marry to what fineness and pureness our bodies shall be then changed, no man knoweth in the peregrination of this world, saving that St Paul saith, " that he shall change this vile body, that Phil. HI. he may make it like unto his glorious body." But that we shall have diversity of all members, and a due proportion of men s natural bodies, the scripture manifestly declareth, whatsover you can by a sinister gloss gather of Nazianzen to the contrary, that glorified bodies have no flesh nor grossness. But see you not how much this saying of St Augustine (that our resurrection shall not be carnally) maketh against yourself? For if we shall not rise carnally, then is not Christ risen carnally, nor is not in heaven carnally. And if he be not in heaven carnally, how can he be in the sacrament carnally, and eaten and drunken carnally with our mouths, as you say he is? And therefore, as for the terms "car nally and corporally," it is you that defame them by your gross taking of them, and not I, that speak of none other grossness, but of distinction of the natural and sub stantial parts, without the which no man s body can be perfect. And whereas here, in this process, you attribute unto Christ none other presence whether in heaven but spiritual, without all manner of grossness or carnality, so that all heaven hut manner of being is spiritual, and none otherwise than he is in the sacrament, here tua I join an issue with you for a joint, and for the price of a fagot. I wondered all this while that you were so ready to grant, that Christ is but after a spiritual manner in the sacrament; and now I wonder no more at that, seeing that you say he is but after a spiritual manner in heaven. And by this means we may say that he hath but a spiritual manhood, as you say that he hath in the sacrament but a spiritual body. And yet some carnal thing and grossness he hath in him, for he hath flesh and bones, which spirits lack ; except that to all this impiety you will add, 143. that his flesh and bones also be spiritual things, and not carnal. And it is not with out some strange prognostication, that you be now waxed altogether so spiritual. Now as concerning the word " figuratively," what need this any proof, that Christ Figuratively. is in the sacraments figuratively ? which is no more to say but sacramentally. And you grant yourself that Christ, under the figure of visible creatures, gave invisibly his precious body. And you say that Christ said, "This is my body," using the outward signs of the visible creatures. And this doctrine was never reproved of any catholic man, but hath at all times and of all men been allowed without contra diction, saving now of you alone. Now followeth my answer to the authors parti cularly. And first, to St Clement. My words be these. They allege St Clement, whose words be these, as they report : " The ch ap . xv. n ^ , , , The answer sacraments of Gods secrets are committed to three degrees : to a priest, a to ciemem, deacon, and a minister : which with fear and trembling ought to keep the leavings of the broken pieces of the Lord s body, that no corruption be found in the holy place, lest by negligence great injury be done to the portion of the Lord s body." And by and by followeth : "So many hosts must be offered in the altar as will suffice for the people. And if any remain, they must not be kept until the morning, but be spent and consumed of the clerks with fear and trembling. And they that consume the residue of the Lord s body may not by and by take other common meats, lest they should mix that holy portion with the meat, which is digested by the belly, and avoided by the fundament. Therefore if the Lord s portion be eaten in the morning, 142 THE THIRD BOOK. the ministers that consume it must fast unto six of the clock ; and if they do take it at three or four of the clock, the minister must fast until the evening/ Thus much writcth Clement of this matter : if the epistle which they allege were Clement s, (as in deed it is not, but they have feigned many things in other men s names, thereby to stablish their feigned purposes,) nevertheless whosesoever the epistle was, if it be thoroughly considered, it maketh much more against the papists than for their purpose. For by the same epistle appeareth evidently three special things against the errors of the papists. The first is, that the bread in the sacrament is called the Lord s body, and the pieces of the broken bread be called the pieces and fragments of the Lord s body, which cannot be understand but figuratively. The second is, that the bread ought not to be reserved and hanged up, as the papists everywhere do use. The third is, that the priests ought not to receive the sacrament alone, (as the papists commonly do, making a sale thereof unto the people,) but they ought to communicate with the people. And here is diligently to be noted, that we ought not unreverently and unadvisedly to approach unto this meat 1 of the Lord s table, as we do to other common meats and drinks, but with great fear and dread, lest we should come to that holy table unworthily, wherein is not only represented, but also spiritually given unto us, very Christ himself. And therefore we ought to come to that board of the Lord with all reve rence, faith, love, and charity, fear, and dread, according to the same. WINCHESTER. 144. Let us now consider what particular answers this author deviseth to make to the fathers of the church ; and first wliat he saith to St Clement s Epistle, his handling whereof is worthy to be noted. Clement. First, he saith the epistle is not Clement s, but feigned, as he saith many other things be for tlieir purpose, he saith, which solution is short and may be soon learned of naughty men, and naughtily applied further as they list. But this I may say, if this epistle were feigned of the papists, then do they shew themselves fools that could feign no better, but so as this author might of their feigned epistle gather three notes against them. This author s notes be these: first, " that the bread in the sacrament is called tlie Lord s body, and that the broken bread be called tlie pieces and fragments of the Lord s body." Mark well, reader, this note that speaketh so much of bread, where the words of tlie epistle in tlie part here alleged name no bread at all. If this author hath read so much mention of bread in another 2 part of the epistle, why bringeth he not that forth to fortify his note? I have read after the same 8 epistle, panes sanctuarii, but they would not help this author s note ; and yet for the other matter joined with them, tliey would slander another way. And therefore seeing this author hath left them out, I will go no further than is here alleged. TJie calling of bread by enunciation for a name is not material, because it signifieth that was, but in that is here alleged is no mention of bread to prove the note ; and to faithful men tlie words of the epistle reverently express the remain of the mysteries, in which when many hosts be offered in the altar, according to the multitude that should communicate, tJwse many hosts after consecration be not many bodies of Christ, but of many breads one body of Christ. And yet, as we teach in England now in the book of common prayer, in every part of that is broken is the whole body of our Saviour Christ. Man s words cannot suffice to express God s mysteries, nor can 4 utter them so, as froward reason shall not find matter to wrangle. And yet to stay reason may suffice, that as in one loaf of bread broken every piece broken is a piece of that bread, and every piece of the bread broken is in itself a whole piece of bread, and so whole bread, for every piece hath an whole substance of bread in it : so we truly speak of the host consecrated, to avoid [ l The meat, 1551, and Grig, ed.] [ 3 In the same, 1551.] [ 2 Any other, 1551.] [* Cannot, Orig. ed. Winch.] OF THE PRESENCE OF CHRIST. 143 tlie fantasy of multiplication of Christ s body, which in all the hosts, and all tJie parts of tiic hosts, is but one, not broken nor distribute by pieces, and yet in a speech, to tell and signify that is broken, called in name the leaving "pieces of the body," "portion of the body," "residue of the body ;" in which nevertheless each one piece is Christ s wJiole body. So as this speech having a f<inri , huth it of necessity to avoid the absurdity, whereby to signify a multitude of bodies, which is not so, and tlie sound of the speech Christian ears do abhor. But this I ask, where is the matter of this autJior s note, that bread is called Christ s body ? where there is no word of bread in the words alleged ; and if there were, as there it not, it were worthy no note at all. For that name is not abhorred, and the catholic faith t&icheth that the fraction is in tlie outward sign, and not in tlie body of Christ, invisibly present, and signified so to be present by that visible sign. Tfie second note of this author is touching reserving, which Clement might seem to deny, because he ordered the remain to be received of tlie clerks, thinking so best ; not declaring expressly that nothing might be reserved to the use of them that be absent. The contrary wliereof appeareth by Justin the Martyr 5 , Justin. Apoi. who testifieth a reservation to be sent to them that were sick, who and they dwell far from the church, as they do in some places, it may by chance in tJie way, or trouble in the sick man, tarry till tJie morning or it be received. And Cyril G writeth expressly, that in case it so doth, Cyriiiusad the, mystical benediction, by which terms he calleth the sacrament, remaineth still in force. When this author findeth fault at hanging up of the sacrament, he blameth only his own country and the isles liereabout; which fault Linehood" 7 , after he had travelled other countries Linehood found here, being tlie manner of custody in reservation otherwise used than in other parts, merit of \hIT~ 145. But one thing this author should have noted of Clement s words when lie speaketh of fearing p" and trembling, which and the bread were never tlie Iwlier, as this author teacheth, and but only a signification, why should any man fear or tremble more in tlieir presence than he doth wlien he lieareth of Christ s supper, tlie gospel read, or himself or any other saying his creed, which in words signify as much as tlie bread doth, if it be but a signification ? And Peter Martyr saith, that words signify more clearly than these signs do, and saith further PeterMartyr. in his disputation with Chedsay, that we receive the body of Christ, no less by words than ions speech of by tlie sacramental signs; which teaching if it were true, why should this sacrament be frttn- uniH/hcHfe bled at ? But because this author noteth the epistle of Clement to be feigned, I will not tartan then make with him any foundation of it, but note to the reader the third note, gathered by this ilke^himseif author of Clement s words, which is, "that priests ought not to receive alone," which the words of the epistle prove not. It sheweth indeed what was done, and how the feast is indeed prepared for the people as well as the priest. And I never read any thing of order in law or ceremony forbidding the people to com municate with the priest, but all the old prayers and ceremonies sounded as the people did communicate with the priest. And when the people is prepared for, and then come not, but fearing and trembling forbear to come, that then tlie priest might not receive his part alone, tlie words of this epistle shew not. And Clement, in that he speaketh so of leavings, seemeth to think of that case of disappointment of the people that should come, providing in that case tlie clerks to receive the residue ; whereby should appear, if there were no store of clerks, but only one clerk, as some poor churches have no more, then a man might rather make a note of Clement s mind, that in that case one priest might receive all alone 9 , and so upon a chance keep the feast alone. But whatsoever we may gather, that note of this author remaineth unproved, that tlie priest ought not to receive alone. And here I dare therefore join an issue with this author, that none of his three feigned notes An issue. is grounded of any words of this tliat he noteth a feigned epistle, taking only words 9 that he allegeth here. This author upon occasion of this epistle, which he calleth feigned, speaketh more reverently of the sacrament than he doth in other places, which methink worthy to be noted of me. Here he saith that very Christ himself is not only represented, but also spiritually given unto its |_ 5 Kal j; ia<orris Kai tj jU.cTa Xtjx|/ts diro Ttav evyapKTT^tievTtov e/cao-Tw yfwratj Kal TOIS ou irap- OVITI Sid TWV GicLKovtav TTffjLTreTcu. Just. Op. Par. 1742. Apol. i. (al. u.) 67. p. 83.] [ Anovu) <5 OTI ets dyiaafjLov dirpa.K.Tf iv <f>aaiv TJJI/ /JLV<TTIKI}V evXoyiav, ci a-TTo/it j/ot Xeii/rai/oi/ airri/s, eis CTepav li/iiepav. fjiaivovrai 5e TavTa XeyovTes. ov yap a\\oiovTai XpitrTOs, ou5t TO dyiov ai>Toi> at, a \\ j; T;> eii/Voyi as Svva- jftKf ear-rtv ev aura?. Ed. Aubert. Tom. VI. /it?, Kal J o)07rotos X a / ts Cyrillus, ad Calosyrium. p. 365. Ed. Par. 1638.] [ 7 Linehood or Lindwood compiled the Pro vincial Constitutions in the time of king Henry VI. and is referred to by Beal, clerk of the Council, as an authority, in Strype, Whitgift, II. p. 138.] [ 8 Receive alone, Grig. ed. Winch.] [ 9 The only words, 1551.] 144 THE THIRD BOOK. in this table ; for so I understand tlie word " wherein." And tJien if very Christ himself be represented and given in tlie table, the author meaneth not tJie material table, but by the word " table" the meat upon the table; as the word mensa, "a table" doth signify in tlie IQth of the Acts xvi. Acts, and the 10th of the Corinthians 1 . Now if very Christ himself be given in the meat, then is he present in the meat to be given. So as by this teaching very Christ himself is not only figuratively in the table, that is to say, the meat of the table, which this author now calleth repre senting, but is also spiritually given in the table, as these words sound to me. But whether this author will say very Christ himself is given spiritually in the meat, or by the meat, or with tlie meat, what scripture hath he to prove that he saith, if the words of Christ be only a figurative speech, and the bread only signify Christ s body ? For if the words of the institution be but in figure, man cannot add of his device any other substance or effect than the words of Christ purport : and so this supper, after this author s teaching in other places of his book, where he would have it but a signification, shall be a bare memory of Christ s death, and signify only such communication of Christ, as we have otherwise by faith in that benefit of his passion, without any special communication of tlie substance of his fiesli in this sacrament, being tlie same only a figure, if it were true that this author would persuade in the conclusion of this book, although by the way he saith otherwise, for fear percase and trembling, that he conceiveth even of an epistle which he himself saith is feigned. CANTERBURY. It is no marvel, though this epistle feigned by the papists many years passed do vary from the papists in these latter days. For the papistical church at the beginning was not so corrupt as it was after, but from time to time increased in errors and cor- 2 Tim. iii. ruption more and more, and still doth, according to St Paul s saying : " Evil men and deceivers wax ever worse, both leading other into error, and erring themselves." For at the first beginning they had no private masses, no pardons in purgatory, no reser vation of the bread ; they knew no masses of Scala Cceli^ no lady psalters, no transub- stantiation; but of later days all these, and an infinite number of errors besides, were invented and devised without any authority of God s word. As yourself have newly invented 2 a great sort of new devices contrary to the papists before your time, as that Christ is in the sacrament carnally and naturally; that the demonstration was made upon the bread when Christ said, " This is my body ;" that the word " satisfactory" signifieth no more but the priest to do his duty; with many other things, which here for shortness of time I will omit at this present, purposing to speak of them more hereafter. And the epistles of Clement were feigned before the papists had run so far in errors as they be now. For yet at that time was not invented, as I said, the error of transubstantiation, nor the reservation of the sacrament, nor the priests Clement s did not communicate alone without the people. But that the said epistle of Clement feigned. was feigned, be many most certain arguments. For there be five epistles of Clement so knit together, and referring one to another, that if one be feigned, all must needs be feigned. Now neither Eusebius in Ecclesiastica Historia, nor St Jerome, nor Gennadius, nor any other old writer, maketh any mention of those epistles ; which authors, in rehearsing what works Clement wrote, (not leaving out so much as one epistle of his,) would surely have made some mention of the five epistles, which the papists long before our time feigned in his name, if there had been any such in their time. Moreover those epistles make mention, that Clement at James s request wrote unto him the manner of Peter s death : but how could that be, seeing that James was dead seven years before Peter ? For James died the seventh year, and Peter the fourteenth year, of Nero the emperor. Thirdly, it is contained in the same epistles, that Peter made Clement his successor, which could not be true, forasmuch as next to Peter succeeded Linus, as all the his tories tell. Fourthly, the author of those epistles saith, that he made the book called Itinerarium [ l To the Corinth. 1-551.] [ 2 As yourself newly invented, 1551.] OF THE PRESENCE OF CHRIST. 145 dementis, which was but feigned in Clement s name, as it is declared, Dist. xv., Sancta*. And then it followeth likewise of the other epistles. Fifthly, the author of those epistles taketh upon him to instruct St James in the sacraments, and in all manner fashion 4 how he should use himself in his vocation, as he 5 should say, that James, who learned of Christ himself, knew not how to use himself in the necessary points of Christ s religion, except Clement must teach him. Sixthly, there be few things in those epistles that either be observed at this day, or were at any time observed sithens Christ s religion first began. Seventhly, a great number of scriptures in those epistles be so far wrested from the true sense thereof, that they have an evil opinion of Clement that think that he would do such injury to God s word. Eighthly, those epistles spake of palls, and archdeacons, and other inferior orders, 147. \\liic-li is not like that those things began so soon, but (as the histories 6 ) were in vented many years after Peter s time. And finally, in one of those epistles is contained a most pernicious heresy, that all things ought to be common, and wives also, which could not be the doctrine of Clement, being the most pestilent error of the Nicolaites, whom the Holy Ghost doth hate, as Rev. u. he testifieth in the Apocalypse. Now, all these things considered, who, having either wit or good opinion of the apostles and their disciples, can think that they should write any such epistles? But the epistle of St Clement, say you, speaketh not of bread. What was it then, clement I pray you, that he meant, when he spake of the broken pieces in the Lord s supper ? bread. If it were not bread, it must be some other thing which Christ did eat at that supper. Perad venture you will say, as some stick not to say now-a-days, that Christ had some other meat at that supper than bread, as, if he fared daintily, (which we never read,) you might imagine he had capon, partridge, or pheasant ; or, if he fared hardly, at the least you would say he had cheese to eat with his bread, because you will defend that he did not eat dry bread alone. Such vain phantasies men may have, that will speak without God s word, which maketh mention in that holy supper of nothing but of bread and wine. But let it be that Christ had as many dishes as you can devise, yet I trust you will not say, that he called all those his body, but only the bread. And so St Clement, speaking of the broken pieces of the Lord s body, of the residue and frag ments of the Lord s body, of the portion and leaving of the Lord s body, must needs speak all this of bread. And thus is it manifest false that you say, that the epistle of Clement speaketh nothing of bread. And then, forasmuch as he calleth the leavings of the same the broken pieces of the Lord s body, and the fragments and portion thereof he calleth the fragments and portion of the Lord s body, he sheweth that the bread remaincth, and that the calling thereof the Lord s body is a figurative speech. The body of Christ hath no fragments nor broken pieces, and therefore the calling here is so material, that it proveth fully calling of the matter, that to call bread Christ s body is a figurative speech. And although to avoid the matter you devise subtle cavillations, saying that calling is not material, because it signifieth that was; yet they that have understanding, may soon discern what a vain shift this is, imagined only to blind the ignorant reader s eyes. But if that which is bread before the consecration be after no bread, and if it be against the Christian faith to think that it is still bread, what occasion of error should this be, to call it still bread after consecration? Is not this a great occasion of error to call it bread still, if it be not bread still ? And yet in this place of Clement the calling can in no wise signify that was before consecration, but must needs signify that is after consecration. For this place speaketh of fragments, broken pieces, and leavings, which can have no true understanding before consecration, at what time there be yet no broken pieces, fragments, nor leavings, but be all done after consecration. [ 3 Item Ttinerarium nomine Petri Apostoli, quod appellatursancti dementis, Lib. vin. apocryphum. Corpus Juris Canonici. Gratian. Decreti Prima Tom. i. col. 57. Lugd. 1618.] [ 4 In all manner and fashion, 1551.] ~ 5 As who should say, 1551.] pars. Dist. xv. cap. 3. "8ancta Romana Ecclesia." I [ 6 As the histories tell, 1551.] [CRANMER.] . Q 146 THE THIRD BOOK. 148. Of reserva tion. Receiving with fear and trembling. Aug. 50, homiliatum Horn. -2(i. 149. But you wrangle so much in this matter to avoid absurdities, that you snarl your self into so many and heinous absurdities, as you shall never be able to wind yourself out. For you say that Christ s body, (which in all the hosts and in all the parts of the hosts is but one, not broken, nor distributed,) is called the leaving pieces of the body, portion of the body, residue of the body, and yet every piece is Christ s whole body ; which things to be spoken of Christ s body Christian ears abhor for to hear. And if you w T ill say that your book is false, that you meant all these leaving pieces, portion, and residue, to be understand of the hosts, and not of Christ s body, then you confess the hosts, which be broken, to be called by name the leavings or pieces of Christ s body, the portion of his body, the residue of his body, by a figurative speech, which is as much as I speak in my first note. And so appcareth how vainly you have travailed for the confutation of my first note. Now as touching the second note : Clement declarcth expressly, that nothing might be reserved. For where he saith, that " if any thing remain, it must not be kept until the morning, but be spent and consumed of the clerks;" how could he declare more plainly that nothing might be reserved, than by those words ? And as for Justin, he speaketh not one word of sick persons, as you report of him. And concerning Cyril ad Calosi/rium 1 , would to God that work of Cyril might come abroad ! for I doubt not but it would clearly discuss this matter ; but I fear that some papists will suppress it, that it shall never come to light. And where you say, that Linehood found fault with his own country of England, and blamed this realm because they hanged up the sacrament, contrary to the use of other countries ; you have well excused me that I am not the first finder of this fault, but many years ago that fault was found, and that it was not the use of other countries to hang it up. And yet the use of other countries was fond enough, even as they had charge and commandment from Innocentius III. and Honorius III. 2 And as for the receiving of the sacrament with fear and trembling, ought not they that be baptized in their old age, or in years of discretion, come to the water of baptism with fear and trembling, as well as to the Lord s supper ? Think you that Simon Magus was not in as great damnation for the unworthy receiving of baptism, as Judas was for the unworthy receiving of the Lord s supper ? And yet you will not say that Christ is really and corporally in the water, but that the washing in the water is an outward signification and figure, declaring what God worketh inwardly in them that truly be baptized. And likewise speaketh this epistle of the holy communion. For every good Christian man ought to come to Christ s sacraments with great fear, humility, faith, love, and charity. And St Augustine saith that the gospel is to be received or heard with no less fear and reverence than the body of Christ. Whose words be these : Interrogo vos, fratres et sorores, dicite mihi : Quid ? vobis plus esse videtur verbum Dei an corpus Christi ? Si vere vultis respondere, hoc utique dicere debetis, quod non sit minus verbum Dei quam corpus Christi. Et ideo quanta solicitudine observamus, quando nobis corpus Christi ministratur, ut nihil ex ipso de nostris manibus in terram cadat^ tanta solicitudine observemus^ ne verbum Dei quod nobis crogatur, dum aliquid aut cogitamus aut loquimur, de corde nostro pereat : quia non minus reus erit qui verbum Dei negli- genter audierit, quam ille qui corpus Christi in terram cadere sua negligentia per- miserit. " I ask this question of you, brethren and sistern," saith St Augustine, " answer me, Whether you think greater, the word of God, or the body of Christ ? If you will answer the truth, verily, you ought to say thus : That the word of God is no less than the body of Christ. And therefore with what carefulness we take heed, when the body of Christ is ministered unto us, that no part thereof fall out of our hands on the earth, with as great carefulness let us take heed, that the word of God which is ministered unto us, when we think or speak of vain matters, perish not out of our hearts. For he that heareth the word of God negligently shall be guilty of no less fault than he that suffereth the body of Christ to fall upon the ground through his I 1 This Treatise was published in 160o, with a translation in Latin by Bonavent. Vulcanius Vid. To. Geo. Walch. Biblioth. Patrist. p. 446.] [ 2 Decretal. Greg. Lugd. 1618. Lib. in. Tit. xliv. cap. i. and Tit. xli. cap. x.j OF THE PRESENCE OF CHRIST. 147 negligence." This is the mind of St Augustine. And as much we have in scripture for the reverent hearing and reading of God s holy word, or the neglecting thereof, as we have for the sacraments. But it seemcth by your pen and utterance of this matter, that you understand not The causes of the ground and cause, whereupon should arise the great fear and trembling in their tnmbUng. hearts, that come to receive the sacraments ; for you shew another consideration thereof than the scripture doth. For you seem to drive all the cause of fear to the dignity of the body of Christ, there corporally present and received ; but the scripture declareth the fear to rise of the indignity and unworthiness of the receivers. " lie that eateth and drinkcth unworthily," threateneth God s word, " eateth and drinketh his own damnation." And Centurio, considering his own unworthiness, was abashed to receive Christ into Matt. viii. his house, saying: " Lord, I am not worthy that thou shouldest come under the covering of my hotiso." And the same thing made Peter afraid to be near unto Christ, and to say : " Go from me, O Lord, for I am a sinner." And all Christian men ought not to Luke v. fear and tremble only, when they receive the sacraments, but whensoever they hear God s word, and thrcatenings pronounced against sinners. Now as concerning the third note, thou shalt sec plainly, good reader, that here 3 is The people received with nothing here answered directly, but mere cavillations sought, and shift to avoid. For the priests. if all the old prayers and ceremonies sound, as the people did communicate with the priest, (as you say they do, and so they do indeed, and that as well in the communion of drinking as eating,) then cither the people did communicate with them in deed, and received the sacrament under both the kinds, or else the prayers had been false, and the ceremonies frustrate and in vain. And is it like, that the priests in that time would have used unto God such untrue prayers, as should declare that the people did commu nicate with them, if in deed none did communicate with them ? as it should have been by your imagined chances and cases. But it appeareth by the words of the epistle, that the whole multitude of the people that was present did communicate at those days, so that the priest could not commu nicate alone, except he would communicate when no man was in the church. But by the answer of this sophistcr here in this place, thou mayest see an experience, good reader, whether he be as ready to see those things that make against him, as he is painful and studious to draw (as it were) by force all things to his purpose, to make 150. them, at the least, to seem to make for him, although they be never so much against him. As appeareth by all these his suppositions, that all the people which were pre pared for should in those days withdraw themselves from the communion, and not one of them come unto it ; that the clerks should receive all that was provided for the people; that one clerk should receive that which many clerks ought to have received. And so in conclusion by only his feigned suppositions he would persuade, that the priest should receive all alone. By such pretty cases, of the people disappointing the priests, and of lack of store of clerks, you might daily find 4 cavillations with all godly ordinances. For whereas God * The paschal ordained the paschal lamb to be eaten up clean in every house ; and where there were not enough in one house to eat up the lamb, they should call of their neighbours so many as should suffice to cat up the whole lamb, so that nothing should remain : here you might bring in your " upon a chance," that they that lacked company to cat up a whole lamb, dwelt alone far from other houses, and could not come together ; or could not get any such lamb as was appointed for the feast, or if their neighbours lacked company also. And what if they had no spit to roast the lamb? And whereas it was commanded, that they should be shoed, what if perchance they had no shoes? And if perchance a man s wife were not at home, and all his servants failed sick of the sweat or plague, and no man durst come to his house, then must he turn the spit himself, and eat the lamb all alone. Such chances you purposely devise, to establish your private mass, that the priest may cat all alone. But by such a like reason as you make here, a man might prove, that the priest should preach or say matins to himself alone, in case, as you say, that the people, which should come, would disappoint him. For what [ 3 That there is nothing L ol.] [ 4 Dayly, and find, 1551.1 102 148 THE THIRD BOOK. if the people disappoint the priest, say you, and come not to the communion ? What if the people disappoint the priest, say I, and come not to matins nor sermon ? shall he therefore say matins and preach, when no man is present but himself alone ? But your imagined case hath such an absurdity in it, as is not tolerable to be thought to have been in Christian people in that time, when Clement s epistles were written, that when all the people should receive the communion with the priest, yet not one would come, but all would disappoint him. And yet in that case I doubt not but the priest would have abstained from ministration unto more opportunity, and more access of Christian people, as he would have done likewise in saying of matins and preaching. Wherefore in your case I might well answer you, as St Jerome answered the argument Lib ir i ianum ma ^ e m ^ ne name of the heretic Jovinian, which might be brought against the com mendation of virginity, " What if all men would live virgins, and no man marry? how should then the world be maintained?" "What if heaven fall," said St Jerome? What if no man will come to the church ? is your argument ; for all that came in those days received the communion. What if heaven fall? say I. For I have not so evil opinion of the holy church in those days, to think that any such thing could chance among them, that no one would come, when all ought to have come. 151. Now when you come to your issue, you make your case too strait for me to " join an issue with you, binding me to the bare and only words of Clement, and refusing utterly his mind. But take the words and the mind together, and I dare adventure an issue to pass by any indifferent readers, that I have proved all my three notes. And where you say, that upon occasion of this epistle I speak more reverently of the sacrament than I do in other places : if you were not given altogether to calum niate and deprave my words, you should perceive in all my book through, even from the beginning to the end thereof, a constant and perpetual reverence given unto the sacraments of Christ, such as of duty all Christian men ought to give. Nevertheless you interpret this word " wherein" far from my meaning. For I mean not that Christ is spiritually either in the table, or in the bread and wine that be set upon the table ; but I mean that he is present in the ministration and receiving of that holy supper, according to his own institution and ordinance : like as in baptism, Christ and the Holy Ghost be not in the water, or font, but be given in the minis tration, or to them that be truly baptized in the water. Baresignifi- And although the sacramental tokens be only significations and figures, yet doth Almighty God effectually work, in them that duly receive his sacraments, those divine and celestial operations which he hath promised, and by the sacraments be signified. For else they were vain and unfruitful sacraments, as well to the godly as to the ungodly. And therefore I never said of the whole supper, that it is but a significa tion or a bare memory of Christ s death; but I teach that it is a spiritual refreshing, wherein our souls be fed and nourished with Christ s very flesh and blood to eternal life. And therefore bring you forth some place in my book, where I say that the Lord s supper is but a bare signification without any effect or operation of God in the same ; or else eat your words again, and knowledge that you untruly report me. But hear what followeth further in my book. Ignatius in Here I pass over Ignatius and Irenseus, which make nothing for the papists Ephesianos. opinions, but stand in the commendation of the holy communion, and in exhor- va b ienti C n ntra tation f &H men to the often and godly receiving thereof. And yet neither they, nor no man else, can extol and commend the same sufficiently, according to the dignity thereof, if it be godly used as it ought to be. WINCHESTER. TJiis author saitli Tie passeth over Ignatius and Irenceus; and why? Because they make nothing, lie saith, for the papists purpose. With the tvord "papist" the author playeth at his pleasure. But it shall be evident that Irene doth plainly confound this author s purpose, in the denial of the true presence of Christ s very flesh in the sacrament; who, although he use not the words " real and substantial," yet he doth effectually comprehend in his speech of the sacrament tJie virtue and strength of those words. And for the truth of tJte sacrament is OF THE PRESENCE OF CHRIST. 149 Irenceus specially alleged, insomuch as Melancthon, when he writeth to CEcolampadius, that Philip. Me- he will allege none but such as speak plainly 1 , he allegeth Irenrjeus for one, as appeareth by his said epistle to CEcolampadius. And CEcolampadius himself is not troubled so much with answering any other to shape any manner of evasion, as to answer Irenceus, in whom he notably stumbleth. And Peter Martyr, in his work, granteth Irenee to be specially alleged, to whom when lie goeth about to answer, a man may evidently see how he masketh himself. 152. And this autJior bringeth in Clement s epistle, of which no great count is made, although it be not contemned, and passeth over Irenceus, that speaketh evidently in the matter, and was as old as Clement, or not much younger. And because Ignatius was of that age, and is alleged by Tlteodoret to have written in his epistle ad Smyrnenses, whereof may appear his faith of the mystery of the sacrament, it shall serve to good purpose to write in tlie words of tlie same Ignatius here upon tlie credit of tlie said TJieodoret 2 , whom this author so much Theodoret. commendeth: tlie words of Ignatius be these: Eucharistias et oblationes non admittunt, quod non confiteantur eucharistiam esse carnem servatoris nostri Jesu Christi, quce pro peccatis nostris passa est, quam Pater sua benignitate suscitavit. Which words be thus much in English; " They do not admit eucharistias and oblations, because tltey do not confess eucharistiam to be the flesh of our Saviour Jesu Christ : which flesh suffered for our sins, which flesh the Father by his benignity hath stirred up." Tliese be Ignatius words, which I have not throughly Englished, because the word eucharistia cannot be well Englislied, being a word of mystery, and signifieth (as Irenceus openeth) both the parts of the sacrament, heavenly and earthly, visible and invisible. But in that Ignatius openeth his faith thus, he taketh 8 eucharistia to be the flesh of our Saviour Christ that suffered for us, he declareth the sense of Christ s words, " This is my body," not to be flgurative only, but to express the truth of the very flesh there given; and therefore (Ignatius saith) eucharistia is the flesh of our Saviour Christ, tlie same that suffered and the same that rose again. Which words of Ignatius so pithily open the matter, as they declare therewith tlie faith 4 also of TJieodoret that doth allege him, so as if the 5 author would make so absolute a work as to peruse all the fathers sayings, he should not thus leap over Ignatius, nor Irene neither, as I have before declared. But this is a colour of rlietoric called " rejection" of that is hard to answer, and is here a pretty shift or sleight, sieight wliereby thou, reader, mayest consider how this matter is handled. CANTERBURY. It shall not need to make any further answer to you here as concerning Irenaeus, Imt only to note one thing, that if any place of Irenams had served for your purpose, you would not have failed here to allege it. But because you have nothing that inakcth for you in deed, therefore you allege nothing in especial, (lest in the answer it should evidently appear to be nothing,) and so slide you from the matter, as though all men should believe you, because you say it is so. And as for the place of Irenee alleged by Melancthon in an epistle, CEcolampadius 6 irenee. (without any such troubling of himself as you imagine) maketli a plain and easy answer thereto; although Melancthon wrote not his said epistle to CEcolampadius, (as you, negligently looking upon their works, be deceived,) but to Fridericus Myconius. And P Nonnulli sine delectu maximum numerum i thon are from the 4th and 5th books contra Valenii- testimoniorum congesserunt, in quibus pleraque sunt ambigua et obseura : nos tantum ea recitavi- mus, quae videbantur esse quam maxime perspicua. JMelancth. Epist. Frid. Myconio. This Epistle is inserted in CEcolampadius s Dialogue referred to above, p. 137. The above quotation will be found in p. 33 of the edition there described. ] ca Trpocrfyopa.? OVK Tru*, OKI TO /I); ofj.o\oyeiv TI\V ev^apitTTiav <rdpKa eivai TOV 2a)Tjpos i//iwi/ Ii)<rov X/oio-roD, Trjv virep Theodoretus. Dialog, iii. Tom. IV. p. 231. Hahe. 17M-94.J [ 3 Thus as he taketh, 1551.] f 4 Therewith that faith, Orig. ed. Winch.] [ 5 So as if this author, 1551.] [ 6 The passages of Irenasus quoted by Melanc num : Irenasus dicit, Calicem eucharistias commu- nicationem sanguinis Domini, et panem quern frangimus communicationem corporis ejus. Item dicit : Calicem, qui est creatura, suum corpus con- firmavit, ex quo auget corpora nostra. Quando ergo et mistus calix et factus panis percipit verbum Dei, n t eucharistia sanguinis et corporis Christi, ex quibus augetur et subsistit carnis nostrae substantia. ...Idem et alio loco dicit : Quomodo dicunt carnem in corruptionem devenire, et non percipere vitam, quaa a corpore Domini et sanguine alitur ? The " plain and easy answer" of (Ecolampadius begins thus : At si ego essem Valentinus vel Manichaeus, nihil terrerer, si sic argueres : Panis est corpus Christi, vel, Christi corpus edimus carnaliter ; igitur resurrecturi sumus. Inutilis enim esset conse- quentia. (Ecolampad. Dialog, pp. 51, 52, 188, seqq.j * Ed. Patrum Apostol. Opera Tubings, 1842. (Hefele.) Ignatii Epist. ad Smyrnaeos, p. 172, for irpoa^opay OVK. reads npoa-ev an-eot-rat. 150 THE THIRD BOOK. the words of Irenee alleged by Melancthon mean in effect no more, but to prove that our bodies shall rise again, and be joined unto our souls, and reign with them in the eternal life to come. For he wrote against Valentine, Marcion, and other heretics, which denied the resurrection of our bodies, from whom it seemeth you do not much dissent, when you say that our bodies shall rise spiritually , if you mean that they shall rise without the form and fashion of men s bodies, without distinction and proportion of members. For those shall be marvellous bodies, that shall have no shape nor fashion of bodies, as you say Christ s body is in the sacrament, to whose body ours shall be like after the resurrection. 153. But to return to answer Irenee clearly and at large, his meaning was this, that called chSst" as the water in baptism is called aqua regenerans, " the water that doth regenerate," w inehu and yet it doth not regenerate in deed, but is the sacrament of regeneration wrought by the Holy Ghost, and called so to make it to be esteemed above other common waters: so Christ confessed the creatures of bread and wine, joined unto his words in his holy supper, and there truly ministered, to be his body and blood; meaning thereby, that they ought not to be taken as common bread, or as bakers bread, and Smyth. wine drunken in the tavern, (as Smith untruly jesteth of me throughout his book ;) but that they ought to be taken for bread and wine wherein we give thanks to God, and therefore be called euckaristia corporis et sanguinis Domini, "the thanking of Christ s body and blood," as Irenee termeth them; or mysteria corporis et sanguinis Domini, "the mysteries of Christ s 2 flesh and blood," as Dionysius calleth them; or sacramenta corporis et sanguinis Domini, "the sacraments of Christ s flesh and blood," as divers other authors use to call them. And when Christ called bread and wine his body and blood, why do the old authors change, in many places, that speech of Christ, and call them eucharistia, mysteria, et sacramenta corporis et sanguinis Domini, "the thanksgiving, the mysteries, and the sacraments of his flesh and blood," but because they would clearly expound the meaning of Christ s speech, that when he called the bread and wine his flesh and blood, he meant to ordain them to be the sacraments of his flesh and blood? according to such a speech as St Augustine expresseth, how the sacraments of Christ s flesh and blood be called his flesh and blood, and yet in deed they be not his flesh and blood, but the sacraments thereof, signifying unto the godly receivers, that as they corporally feed of the bread and wine, (which comfort 3 their hearts and continue this corruptible life for a season,) so spiritually they feed of Christ s very flesh, and drink his very blood. And we be in such sort united unto him, that his flesh is made our flesh, his holy Spirit uniting him and E P h. y. us so together, that we be flesh of his flesh, and bone of his bones, and make all cS,i! M one mystical body, whereof he is the head, and we the members. And as feeding, nourishing, and life, cometh from the head, and runneth into all parts of the body; so doth eternal nourishment and life come from Christ unto us completely and fully, as well into our bodies as souls. And therefore if Christ our head be risen again, then shall we that be the members of his body surely rise also; forasmuch as the i Cor. xv. members cannot be separated from the head, but seeing that as he is our head and eternal food, we must needs by him live with him for ever. This is the argument of Irenee against those heretics which denied the resurrection of our bodies. And these things the sacraments of bread and wine declare unto us : but neither the carnal presence, nor the carnal eating of Christ s flesh, maketh the things so to be, nor Irenee meant no such thing. For then should all manner of persons that receive the sacraments, have everlasting life, and none but they. Thus have I answered to Irenee plainly and shortly, and CEcolampadius needed not to trouble himself greatly with answering this matter. For by the corporal eating and drinking of Christ s flesh and blood, Irenee could never have proved the resur rection of our bodies to eternal life. PeterMartyr. And Peter Martyr 4 maketh the matter so plain, that he concludeth Irenosus words to make directly against the doctrine of the papists. P Spiritual, 1551.] . j-a Com forteth their hearts, and continueth, 1551.] [ His, 1551.] M Irenaus adversus ha?reticos Valentinianos, OF THE PRESENCE OF CHRIST. 151 The answer also is easily made to the place which you allege out of Ignatius, 154. where he calleth eucharistia the flesh of our Saviour Jesus Christ. For he mcancth fefissL] no more but that it is the sacrament of his flesh, or the mystery of his flesh, or, as Irenee said, eucharistia of his flesh, as even now I declared in mine answer to Irenee. And your long process here may have a short answ r er gathered of your own words. This word euch<tri*t nt, say you, "cannot be well Eu^lishi-d:" but the body of Christ is good and plain English ; and then if eucharistia be such a thing as cannot be well Englished, it cannot be called the body of Christ, but by a figurative speech. And how can you then conclude of Ignatius words, that " This is my body," is no figura tive speech ? It secmcth rather that the clean contrary may be concluded. For if these two speeches be like and of one sense, ("eucharistia is Christ s body," and "This i< my body,") and the first be a declaration of the second, is this a good argument, The first is a figure, ergo, the second is none ? Is it not rather to be gathered upon the other side thus, The first is a declaration of the second, and yet the first is a figure, ergo, the second is also a figure ? And that rather than the first ; because the declaration should be a more plain speech than that which is declared by it. And as for your " colour of rhetoric," which you call " rejection," it is so familiar with yourself, that you use it commonly in your book, when I allege any author, or speak any thing that you cannot answer unto. And yet one thing is necessary to admonish the reader, that Ignatius in this epistle entreateth not of the manner of the presence of Christ in the sacrament, but of the manner of his very body, as he was born of his mother, crucified, and rose again, appeared unto his apostles, and ascended into heaven: which things divers heretics said were not done verily in deed, but apparently to men s sights, and that in deed he had no such carnal and corporal body, as he appeared to have. And against such errors speaketh that epistle, and not of the real and corporal presence of Christ in the sacrament ; although eucharistia, or the sacrament, be ordained for a remembrance of that very body, and so hath the name of it, as the sacraments 5 have the names of the things which they signify. But by this so manifest writhing of the mind of Ignatius from that true sense 7 and purpose that was meant, to another sense and purpose that was not meant, may appear the truth of the papists, who wrast and misconstrue all old ancient writers and holy doctors to their wicked and ungodly purposes. Next in my book folio w T eth mine answer to Dionysius. Dionysius also, whom they allege to praise and extol this sacrament, (as The answer i T . . . to Dionysius indeed it is most worthy, being a sacrament of most high dignity and per- Jf ie ^J- fection, representing unto us our most perfect spiritual conjunction unto Christ, *? 3>a and our continual nourishing, feeding, comfort, and spiritual life in him,) yet he never said that the flesh and blood of Christ was in the bread and wine, really, corporally, sensibly and naturally, (as the papists would bear us in hand;) but he calleth ever the bread and wine signs, pledges, and tokens, declaring unto the faithful receivers of the same, that they receive Christ spiritually, and that they spiritually eat his flesh and drink his blood. And although the bread and wine be figures, signs, and tokens of Christ s flesh and blood, (as S. Dionyse calleth them, both before the consecration and after,) yet the Greek annotations upon the same Dionyse do say, that the very things themselves be above in heaven. 155. And as the same Dionyse maketli nothing for the papists opinions in this point 1 Panis terrenus, inquit, accepta vocatione a verbo Dei, non amplius est communis panis, sed edicitur eucharistia, quae constat ex duabus rebus, nimirum militudinem, ita corpora nostra illam sumentia, non sunt amplius ccrruptibilia Peter Martyr. De sacramento Eucharistia?, p. 94, 5. Tiguri. 1052.] terrena et ca lesti. In primis non negat eucharis- [ 5 As sacraments, 1551.] tiam panem esse, nisi ilium communem feceris. Postea dicit, ex duabus rebus constare, quarum una tcrrestris est, ut panis, alttra ccelestis, ut corpus Christi. Atque ut ex una purte retinetur veritas, scilicet quoad corpus Domini, ita in altera est con- servarsda, videlicet quoad panem. Et addit per si- Writing, 1551.] [~ From the true sense, 1551. J [ 8 This treatise is spurious ; for proof of which see "James Corruptions of Scripture," &c. p. 7> Ed. London. 1843.] 152 THE THIRD BOOK. of Christ s real and corporal presence, so in divers other things he maketh quite and clean against them, and that specially in three points ; in transubstantiation, in reservation of the sacrament, and in the receiving of the same by the priest alone. WINCHESTER. Dionysms. ^ s t ouc ji{ n g Dionysius, a wise reader may, without any note of mine, see how this author is troubled in him, and calleih for aid the help of him that made the Greek commentaries upon Dionysius, and pleadeth therewith the form of the words "really," "corporally," "sensibly," and "naturally" whereof two, that is to say, "really" and "sensibly," tlie old authors in syllables used not, for so much as I have read, but "corporally" and "naturally" they used speaking of this sacrament. TJiis Dionyse spake of this mystery after the dignity of it, not contending with any other for the truth of it as we do now, but extolling it as a marvellous high mystery, which, if the bread be never the holier, and were only a signification, (as this author teacJieth,) were no high mystery at all. As for the things of the sacrament to be in heaven, the church teacheth so, and yet the same things be in deed present in tlie, sacrament also, which is a mystery so deep and dark from man s natural capacity, as is only to be believed supernaturally, without asking of the question "how," wfiereof St Chrysostom maketh an exclamation in this wise: ff rea t benevolence of God towards us ! He that sitteth above with the Fatlier, at the same hour is holden here with the hands of all men, and giveth himself to tliem that will clasp and embrace him 1 ." Thus saith Chrysostom, confessing to be above and here the same things at once, and not only 2 in men s breasts but hands also, to declare tlie inward work of God, in the substance of the visible sacrament, whereby Christ is present in the midst of our senses, and so may be called sensibly present, although man s senses cannot comprehend and feel, or taste of him in their proper nature. But as for this Dionyse, he doth 3 , without argument, declare his faith in tlie adoration lie maketh of this sacrament, which is openly testified in his works, so as we need not to doubt* what his faith was. As for this author s notes, they be 5 descant voluntary G , without the tenor part, being belike ashamed to allege the text itself, lest his three notes might seem feigned without ground, as before in St Clement s epistle, and therefore I will not trouble the reader with tliem. " Lib. iii. 156. "Really "and "sensibly" be not found in any old author. CANTERBURY. I ask no more of the reader, but to read my book, and then to judge how much I am troubled with this author. And why may I not cite the Greek commentaries for testimony of the truth ? Is this to be termed a " calling for aid ?" Why is not then the allegation of all authors a calling for aid? Is not your doing rather a calling for aid, when you be fain to fly for succour to Martin Luther, Bucer, Melancthon, Epinus, Jonas, Peter Martyr, and such other, whom all the world knoweth you never favoured, but ever abhorred their names ? May not this be termed a " calling for aid," when you be driven to such a strait and need, that you be glad to cry to such men for help, whom ever you have hindered and defamed as much as lay in you to do? And as for pleading of those words, "really," "corporally," "sensibly," and "naturally," they be your own terms, and the terms wherein resteth the whole con tention between you and me: and should you be offended because I speak of those terms? It appeareth now that you be loth to hear of those words, and would very gladly have them put in silence, and so should the variance between you and me be clearly ended. For if you will confess, that the body of Christ is not in the sacra ment really, corporally, sensibly, and naturally, then you and I shall shake hands, and be both earnest friends of the truth. And yet one thing you do here confess, (which is worthy to be noted and had in memory,) that you read not in any old author, that the body of Christ is really and sensibly in the sacrament. And hereunto I add, that none of them say, that [ J ^Q TT;S Qeov cfri\ai;Qp<aTrias o /JLCTO. TOV Tra- T/OOS dvw /ca6)fjjuei/o<?, KCLTO. TTJV topav eKeivriv TWV uTTciv-rtjaif KaTcycTai Depart, /cat Sicwariv avTov -rots (3ov\o/jivois TrepnrTu^aa&ai /cat. TrepiXafielv Chrysostom. de Sacerdotio. Lib. in. Tom. I. p. 382. Ed. Bened.] [ 2 At once, not only, &c. 1551.] [ 3 For this, Dionyse doth, 1551.] [ 4 We need not doubt, 1551.] [ 5 Notes be descant, 1551.J [ Descant voluntary : i.e. a song or tune com posed in parts, played at will without any settled rule or rhythm.] OF THE PRESENCE OF CHRIST. 153 he is in the bread and wine corporally nor naturally. No, never no papist said, that Christ s body is in the sacrament naturally nor carnally, but you alone, (who be the first author of this gross error, which Smith himself condemneth, and denieth smith, that ever 7 Christian man so taught,) although some say that it is there "really," some "substantially," and some "sensibly." Now as concerning the high mystery which St Denys spcakcth of, he declareth the same to be in the marvellous and secret working of God in his reasonable creatures, (being made after his image, and being his lively temples, and Christ s mystical body,) and not in the unreasonable and unsensible and unlively creatures of bread and wine, wherein you say the deep and dark mystery standeth. But notwithstanding any holiness or godliness Holiness in wrought in the receivers of them, yet they be not the more holy or godly in themselves, merits, but be only tokens, significations, and sacraments of that holiness, * which Almighty God by his omnipotent power worketh in us. And for their holy significations they have the name of holiness* 8 , as the water in baptism is called aqua sanctificans, unda regenerans, " hallowing or regenerating water," because it is the sacrament of regenera tion and sanctification. Now as concerning Chrysostom s saying, that Christ is in our hands, Chrysostom Christ in our saith, (as I have rehearsed in my book,) not only that he is in our hands, but also hands> that we see him with our eyes, touch him, feel him, and grope him, fix our teeth in his flesh, taste it, break it, eat it, and digest it, make red our tongues, and dye them with his blood, c. ; which things cannot be understand of the body and blood of Christ but by a figurative speech, as I have more at large declared in my fourth book, the eighth chapter. And therefore St Augustine, De Verlis Domini sermone xxxiii. Au^istir. de saith clean contrary to Chrysostom, that we touch not Christ with our hands : "Non XuSnSSJT tanaimus Dominum" saith he. This speech therefore of Chrysostom declareth not the 33 " inward work of God in the substance of the visible sacrament, but signifieth what God worketh inwardly in true believers. And whereas you say, that my notes " be descant voluntary without the tenor part," I have named both the book and chapter where St Dionyse telleth, how the priest, when he comcth to the receiving of the sacraments, he divideth the bread in pieces, and distributeth the same to all that be present; which one sentence containeth suf ficiently all my three notes. So that if you be disposed to call my notes descant, there you may find the plain song or tenor part of them. And it is no marvel that you cannot judge well of my descant, when you see not, or will not see, the plain song, whereupon the descant was made. Now followeth Tertullian, of whom I write thus : 157. Furthermore they do allege Tertullian 9 , that he constantly affirmeth that in The answer the sacrament of the altar we do eat the body and drink the blood of our "**. Saviour Christ. To whom we grant, that our flesh cateth and drinketh the carnis - bread and wine, which be called the body and blood of Christ, because, as Tertullian saith, they do represent his body and blood, although they be not really the same in very deed. And we grant also, that our souls by faith do eat his very body and blood 10 , but that is spiritually, sucking out of the same everlasting life. But we deny that unto this spiritual feeding is requiring 11 any- real and corporal presence. And therefore this Tertullian speaketli nothing against the truth of our [ 7 Ever any, 1551. J [ 8 The words between asterisks are printed twice over by mistake in edit. 1580.] [ 9 Denique, cum anima Deo allegitur, ipsa est quae efficit, ut anima allegi possit. Scilicet caro abluitur, ut anima emaculetur. Caro ungitur, ut anima consecretur. Caro signatur, ut et anima muniatur. Caro manus impositione adumbratur, ut et anima spiritu illuminetur. Caro corpore et sanguine Christi vescitur, ut et anima de Deo sagi- netur. Non possunt ergo seperari in mercede, quas opera conjungit. Tertullian. De Resurrectione car nis, cap. 8, p. 330. Lutetia? Paris. 1604. Acceptum panem et distributum discipulis, corpus suum ilium fecit, Hoc est corpus meum dicendo, id est, figura corporis mei Cur autem panem corpus suum appellat, et non magis peponem, quern Marcion cordis loco habuit, non intelligens veterem fuisse istam h guram corporis Christi. Adv. Marcion. Lib. iv. cap. 40. J [ 10 And drink his blood, 1551, and Grig, ed.] [" Required, 1551, and Orig. ed.J 154 THE THIRD BOOK. catholic doctrine, but he speaketh many things most plainly for us, and against the papists, and specially in three points : First, in that he saith that Christ called bread his body. The second, that Christ called it so, because it represented his body. The third, in that he saith, that by these words of Christ, " This is my body," is meant, "This is a figure of my body." WINCHESTER. Of Tertullian I have spoken before, and so hath this author also * forgotten here one Tertuiiianus. notable thing in Tertullian., where Tertullian saith., that "Christ made the bread his body" not only called it so, as appear 2 by Tertullian s words, reported by this author before. This note that I make now of Tertullian maketh against this author s purpose, but yet it maketh with the truth, which this author should not impugn. The second note gathered of Tertul lian, by this author, is not true; for Christ called it his body, and made it his body, a Tertullian saith. And tJie third note of this author is in controversy of reading, and must be so understanded, as may agree with the rest of Tertullian s sayings, which, after my reading, doth evidently prove, and at the least doth not improve, the catholic doctrine of Christ s church universally received, although it improveth that which this author calleth here our catholic doctrine, most imprudently 3 and untruly reporting the same. CANTERBURY. I desire no more but that the reader will look upon the place of Tertullian before mentioned, and see what you speak there, and what is mine answer thereto, and so confer them together and judge. And that the reader will note also, that here covertly you have granted my first note, that Christ called bread his body, but so slyly, that the reader should not by your will perceive it. And where you deny my second note upon Tertullian, that Christ called it his body, because it represented his body, the words of Tertullian be these: "That Christ reproveth not bread, wherein he representeth his ow r n body 4 ." As for my third note, yet once again, reader, I beseech thee turn back and look upon the place, how this lawyer hath expounded Tertullian, if thou canst with patience abide to hear of so foolish a gloss. And where he saith that this author Tertullian "must be so understand as may agree with the rest of his sayings," would to God you would so do not only in Tertullian, but also in all other authors ! for then our controversy should be soon at a point. And it is a most shameless impudency of you, to affirm that the catholic church universally 158. teacheth that Christ is really, sensibly, corporally, naturally, carnally, and substantially, present in the visible forms of bread and wine, seeing that you cannot prove any one of these your sayings, either by scripture, or by the consent of the catholic church, but only by the papistical church, which now many years hath borne the whole swing. Now followeth Origen, to whom I answer thus. Moreover they allege for them Origen, (because they would seem to have Numeiv. many ancient authors favourers of their erroneous doctrine,) which Origen is most clearly against them. For although he do say, as they allege, that those things which before were signified by obscure figures, be now truly, in deed, and in their very nature and kind, accomplished and fulfilled; and for the declaration thereof he bringeth forth three examples, one of the stone that flowcth water, another of the sea and cloud, and the third of manna, which in the old testament did signify Christ to come, who is now come in deed, and is manifested and exhibited unto us, as it were face to face and sensibly, in his word, in the sacrament of regeneration, and the sacraments of bread and wine : [ l Also, and forgotten here, 1551.] | bavit Creatoris,....nec panem, quo ipsum corpus [ 2 May appear, 1551.] I suum reprassentat, etiam in sacramentis pvopriis [ 3 Impudently, 1551.] egens mendicitatibus Creatoris. Adv. Marcion. f 4 Sed ille quidem usque nunc nee aquam repro- ! Lib. I. cap, 14,] OF THE PRESENCE OF CHRIST. 155 yet Origcn meant not that Christ is corporally either in his word, or in the water of baptism, or in the bread and wine ; nor that we carnally and cor porally be regenerated and born again, or eat Christ s flesh and blood. For our regeneration in Christ is spiritual, and our eating and drinking is a spiritual feeding; which kind of regeneration and feeding required i no real and corporal presence of Christ, but only his presence in spirit, grace, and effectual operation. And that Origen thus meant that Christ s flesh is a spiritual meat, and his blood a spiritual drink, and that the eating and drinking of his flesh and blood may not be understand literally, but spiritually, it is manifested by Origen s own words, in his seventh homily upon the book called Leviticus ; where he in Levit. sheweth that those words must be understand figuratively, and whosoever un- derstandeth them otherwise, they be deceived, and take harm by their own gross understanding. WINCHESTER. Origen s words be very plain, and meaning also, which speak of manifestation and eocJii- Origenes. bition, which be two things to be verified three ways in our religion, that is to say, in the word, and regeneration, and the sacrament of bread and wine, as this author termeth it; ivhich Origen saith not so, but thus, " the fiesh of the word of God," not meaning in every of these after one sort, but after the truth of the scripture in each of them. CJirist in his word is manifested and exhibited unto us, and by faith, that is, of hearing, dwelleth in us spiritually; for so we have his Spirit. Of baptism St Paul saith, "as many as be baptized be clad in Christ." Now, in the sacrament of bread and wine, by Origen s rule, Christ xlmuttl be manifested and exhibited unto us after the scriptures, so as the sacrament of bread and wine should not only signify Christ, that is to say, preach him, but also exhibit him *Origen hath sensibly, as Origen s words be reported liere to be. So as Christ s words, " This is my faciSn.^but body," should be words not of figure or shewing, but of exhibiting Chrisfs body unto us, and L So/as he si-usiMy, as this author allojdh him, which should signify, to be received with our mouth, as fH\^ Christ commanded, when lie said, u Take, eat, fyc." diversely from tlie other two ways, in * Krrors - which by Christ s Spirit we be made participant of tJie benefit of his passion wrought in when I say ///x manlwod. But in this sacrament we be made participant of his Godhead, by his humanity Hood/ Y 1 exhibit unto us for food: and so, in this mystery, we receive him man and God; and in the JJJJJ 1 JJg ^j, other, by mean of his Godhead, be participant of tlie effect of his passion suffered in his manhood. & i )C aketh. In this sacrament Christ s manJiood is represented and truly present, whereunto the God head is most certainly united, whereby we receive a pledge of the regeneration of our fiesh, 15!). to be in the general resurrection spiritual with our soul, as we have been in baptism made spiritual by regeneration of tlie soul: ivhich in the full redemption of our bodies shall be made perfect. And therefore this author may not compare baptism, with the sacrament throughly; in ivhich baptism Christ? 8 manhood is not really present, although the virtue and effect of his most precious blood be there : but the truth of the mystery of this sacrament is to have Christ s body, his fiesh and blood, exhibited, luhereunto eating and drinking is, by Christ in his supper, appropriate. In which supper Christ said, " This is my body," which Bucer noteth; and that Christ said not, " This is my spirit" " This is my virtue." Wherefore, after Origen s teaching, if Christ be not only manifested, but also exhibited " sensibly" in the Sensibly. sacrament, then is he in the sacrament in deed, that is to say, "really;" and then is he there Substanti- * substantially," because the substance of the body is there ; and is tliere " corporally" also, corponiiy, l>"-">ise the very body is there; and "naturally," because the natural body is there; not un-** derttanding corporally and naturally in tlie manner of presence, nor sensibly neither. For then were the manner of presence within man s capacity, and that is false: and therefore tJie catholic teaching is, that the manner of Christ s presence in the sacrament is spiritual and supernatural, not corporal, not carnal, not natural, not sensible, not perceptible, but only spiritual, the "how" and manner ivhereof God knoweth; and we, assured by his word, know only the truth to be so, that it is there in deed, and therefore really to be also received with our hands and mouths; and so sensibly there, the body that suffered, and therefore his natural body there, the body of very fiesh, and therefore his carnal body, the body truly, and there fore his corporal body there. But as for the manner of presence, that is only spiritual, at I said before, and here in the inculcation of these words. I am tedious to a learned reader, but yet this author enforceth me thereunto, who with these words, "carnally" "corporally" "grossly" 156 THE THIRD BOOK. "sensibly? "naturally" applying tliem to the manner of presence, doth maliciously 1 and craftily carry away the reader from the simplicity of his faith ; and by such absurdities, as these words grossly understanded import, astonisheth tlie simple reader in consideration of the mat ter, and useth these words, as dust afore tlieir eyes, which to wipe away, I am enforced to repeat tJie understanding of these words oftener than elsewhere necessary. These things well considered, no man doth more plainly confound this author than this saying of Origen, as he allegeth it, whatsoever other sentences lie would pick out of Origen, when he useth liberty of allegories to make him seem to say otherwise. And as I have declared afore, to understand Christ s words spiritually, is to understand them as the Spirit of God hath taught tlie church, and to esteem God s mysteries most true in the substance of tlie thing so to be, although the manner exceedeth our capacities, which is a spiritual understanding of tlie same. And here also this author putteth in for "figuratively," " spiritually 2 ," to deceive the reader. CANTERBURY. You observe my words here concerning Origen so captiously, as though I had gone about scrupulously to translate his sayings word by word, which I did not ; but because they were very long, I went about only to rehearse the effect of his mind briefly and plainly, which I have done faithfully and truly, although you captiously carp and reprehend the same. And whereas, craftily to alter the sayings of Origen, you go about to put a diversity of the exhibition of Christ in these three things, in his word, in baptism, and in his holy supper, as though in his word and in baptism he were exhibited spiritually, and in his holy supper sensibly to be eaten with our mouths: this distinction you have dreamed in your sleep, or imagined of purpose. For Christ after one sort is exhibited 1GO. in all these three, in his word, in baptism, and in the Lord s supper; that is to say, spiritually, and for so much in one sort, as before you have confessed yourself. And Origen putteth no such diversity as you here imagine, but declareth one manner of giving of Christ unto us in his word, in baptism, and in the Lord s supper; that is to say, in all these three secundum speciem ; that as unto the Jews Christ was given in figures, so to us he is given in specie, that is to say, in rei veritate, in his very nature : meaning nothing else but that unto the Jews he was promised in figures, and to us, after his incarnation, he is married and joined in his proper kind, and in his words and sacraments as it were sensibly given. But howsoever I report Origen, you captiously and very untruly , do report me. For whereas I say, that in God s word, and in the sacraments of baptism and of the Lord s supper, Christ is manifested and exhibited unto us, as it were face to face and it were, sensibly, you, leaving out these words, " as it were," make a quarrel to this word "sensibly;" or rather, you make that word "sensibly" the foundation of all your weak building, as though there were no difference between " sensibly," and "as it were sensibly ;" and as it were all one thing a man to lie sleeping, and as he were sleeping; or dead, and as he were dead. Do not I write thus in my first book, "that the washing in the water of baptism is as it were a shewing of Christ be fore our eyes, and a sensible touching, feeling, and groping of him?" And do these words import that we see him and grope him in deed? And further I say, "that the eating and drinking of the sacramental bread and wine is as it were a shewing of Christ before our eyes, a smelling of him with our noses, and a feeling and groping of him with our hands." And do we therefore see him in deed with our corporal eyes, smell him with our noses, and put our hands in his side and feel his wounds? If it were so in deed, I would not add these words, " as it were." For what speech were this, of a thing that is in deed to say, " as it were ? " For these words, " as it were," signify that it is not so in deed. So now likewise in this place of Origen, where it is said, * that Christ in his words and sacraments is manifested and exhibited unto us, as it were face to face and sensibly," it is not meant that Christ is so exhi bited in deed face to face and sensibly, but the sense is clean contrary, that he is f 1 Grig. ed. Winch, omits the words "ma- I [ 2 For " spiritually," " figuratively," Orig. ed. liciously and."] Winch. J OF THE PRESENCE OF CHRIST. 157 not there given sensibly, nor face to face. Tims it appeareth how uprightly you handle this matter, and how truly you report my words. But the further you pro ceed in your answer, the more you shew crafty juggling, legerdemain, pass a God s name to blind men s eyes, strange speeches, new inventions, not without much impiety as the words sound, but what the meaning is no man can tell but the maker himself. But as the words be placed, it seemeth you mean, that in the Lord s supper we be not " made by Christ s Spirit participant of the benefit of his passion ;" nor by baptism or God s word we be not "made participant of his Godhead by his humanity:" and furthermore by this distinction, (which you feign without any ground of Origen,) we receive not "man and God" in baptism; nor in the Lord s supper we be not "by means of his Godhead made participant of the effect of his passion." In baptism also, by your distinction, we receive not " a pledge of the resurrection of our flesh," but in the Lord s supper ; nor Christ is not truly present in baptism. Which your said differ ences do not only derogate and diminish the effect and dignity of Christ s sacraments, 161. but be also blasphemous against the ineffable unity of Christ s person, separating his divinity from his humanity. Here may all men of judgment see by experience, how divinity is handled when it cometh to the discussion of ignorant lawyers. And in all these your sayings (if you mean as the words be), I make an issue * Three issue with you for the price of a fagot. And where you say, that " our flesh in the f general resurrection shall be spiritual," here I offer a like issue, except you under- An issue, stand a spiritual body to be a sensible and palpable body, that hath all perfect members distinct ; which thing in sundry places of your book you seem utterly to deny. And where you make this difference between baptism and this sacrament, that *The third in baptism Christ is not really present, expounding "really present" to signify no more m but to be in deed present, yet after a spiritual manner, if you deny that presence to be in baptism ; yet the third fagot I will adventure with you, for your strange and ungodly doctrine within twenty lines together ; who may in equality of error contend with the Valentines, Arians, or Anabaptists. But when you come here to your "lies" (declaring the words, "sensibly," "really," [* Adverb "substantially," "corporally," and "naturally"), you speak so fondly, unlearnedly, and "* ignorantly, as they that know you not might think that you understood neither grammar, English, nor reason. For who is so ignorant but he knoweth that adverbs that end in "ly" be adverbs of quality, and being added to the verb they express the manner, form, and fashion how a thing is, and not the substance of it? As speaking wisely, learnedly, and plainly, is to speak after such a form and manner as wise men, learned, and plain men, do speak : and to do wisely and godly is to do in such sort and fashion as wise and godly men do. And sometime the adverb "ly" signifieth the manner of a thing that is in deed, and sometime the manner of a thing that is not. As when a man speaketh wisely, that is wise indeed : and yet sometimes we say, " fools speak wisely ;" which although they be not wise, yet they utter some speeches in such sort as though they were wise. The king, we say, useth himself princely in all his doings, (who is a prince in deed,) but we say also of an arrogant, wilful, and proud man, that he useth himself princely and imperiously, although he be neither prince nor emperor : and yet we use so to speak of him, because of the manner, form, and fashion of using himself. And if you answer foolishly and unlearnedly, be you there fore a fool and unlearned ? Nay, but then your answers be made in such wise, manner, sort, and fashion, as you were neither learned nor wise. Or if you send to Rome or receive private letters from thence, be you therefore a papist? God is judge thereof; but yet do you popishly, that is to say, use such manner and fashion as the papists do. But where the fonn and manner lacketh, there the adverbs of quality in "ly" have no place, although the thing be there in deed. As when a wise man speaketh not in such a sort, in such a fashion and wise, as a wise man should speak, not withstanding that he is wise in deed, yet we say not that he speaketh wisely, but foolishly. And the godly king David did ungodly when he took Bersabe, and slew 2 Sam. xi. Urie her husband, because that manner of doing was not godly. So do all Englishmen understand by these words, "sensibly," "substantially," "corporally," "naturally," "car- 162. nally," "spiritually," and such like, the manner and form of being, and not the thing itself 158 THE THIRD BOOK. without the said forms and manners. For when Christ was born, and rose from death, and wrought miracles, we say not that he did these things naturally, because the mean and manner was not after a natural sort, although it was the selfsame Christ in nature. But we say that he did eat, drink, sleep, labour, and sweat, talk, and speak naturally, not because only of his nature, but because the manner and fashion Lukeiv. of doing was such as we use to do. Likewise when Jesus passed through the people, and they saw him not, he was not then sensibly and visibly among them ; their eyes being letted in such sort that they could not see and perceive him. And so in all the rest of your adverbs, the speech admitteth not to say that Christ is there sub stantially, corporally, carnally, and sensibly, where he is not after a substantial, cor poral, carnal, and sensual form and manner. This the husbandman at his plough, and his wife at her rock 1 , is able to judge, and to condemn you in this point, and so can the boys in the grammar-school, that you speak neither according to the English tongue, grammar, nor reason, when you say that these words and adverbs, "sensibly," "corporally," and "naturally," do not signify a corporal, sensible, and natural manner. I have been here somewhat long and tedious, but the reader must pardon me; for this subtile and evil device of your own brain, without ground or autho rity, containeth such absurdities, and may cast such mists before men s eyes to blind them that they should not see, that I am constrained to speak thus much in this matter, and yet more shall do, if this suffice not. But this one thing I wonder much at, that you being so much used and accustomed to lie, do not yet know what " ly " meaneth. But at length in this matter, (when you see none other shift,) you be fain to fly to the church for your shot-anchor 2 . And yet it is but the Romish church. For the old and first church of Christ is clearly against you. And Origen saith not as you do, that " to understand the said words of Christ spiritually is to understand them as the Spirit of God hath taught the church ; " but to understand them spiritually is to understand them otherwise than the words sound : " for he that understandeth them after the letter," saith Origen, "understandeth them carnally, and that under standing hurteth and destroy eth. For in plain understanding of eating and drinking without trope or figure, Christ s flesh cannot be eaten, nor his blood drunken." Next followeth in order St Cyprian, of whom I write thus : The answer And likewise meant Cyprian, in those places which the adversaries of the Lib. y n. r Epist. truth allege of him, concerning the true eating of Christ s very flesh and drinking of his blood. For Cyprian spake of no gross and carnal eating with the mouth, but of an inward spiritual and pure eating with heart and mind : which is to believe in our hearts that his flesh was rent and torn for us upon the cross, and his blood shed for our redemption ; and that the same flesh and blood now sittcth at the right hand of the Father, making continual intercession for us : and to imprint and digest this in our minds, putting our whole affiance and trust in him, as touching our salvation, and offering ourselves clearly unto him, to love and serve him all the days of our life ; this is truly, sincerely, and spiritually to eat his flesh, and to drink his blood. 163. And this sacrifice of Christ upon the cross was that oblation, which Cyprian Gen. ix. saith was figured and signified before it was done, by the wine which Noo Gen.xiv. drank, and by the bread and wine which Melchisedech gave to Abraham, and by many other figures which St Cyprian there rehearseth. And now when Christ is come, and hath accomplished that sacrifice, the same is figured, signified, and represented unto us by that bread and wine, which faithful people receive daily in the holy communion. Wherein like as with their mouths carnally they eat the bread and drink the wine, so by their faith [ ! Rock : i.e. a distaft , or staff , held in the hand, from which, in spinning, the wool was spun by twirling a spindle below. J f 2 Shot-anchor, the same as sheet-anchor.] OF THE PRESENCE OF CHRIST. 159 spiritually they cat Christ s very flesh and drink his very blood. And hereby it appeareth, that St Cyprian clearly affirmeth the most true doctrine, and is wholly upon our si sir. And against the papists he teacheth most plainly, that the communion ought to be received of all men under both kinds : and that Christ called bread his body, and \\iiio his blood: and that there is not transubstantiation, but that bread remaineth there as a figure to represent Christ s body, and wine to represent his blood, and that those which be not the lively members of Christ do eat the bread and drink the wine, and be not nourished 3 by them ; but the very flesh and blood of Christ they neither cat nor drink. Thus have you declared the mind of St Cyprian. Lib. uiri- WINCnESTKH. As touching Cyprian, this author maketh an exposition of his own device, which he would cypriamw. have taken for an answer unto him. Whereas Cyprian of all other, like as he is ancient i"/(/i!n two hundred and fifty years of Christ, so did he write very openly in tJie matter; and tliercfore Melancthon, in his epistle to (Ecolampadiue, did choose him for one whose words Meiancthon. in the affirmation of Chrises true presence in the sacrament had no ambiguity. And like judgment doth Ilippinus, in his book before alleged, give of Cyprianus faith in tJie sacra- Hippinus ment: which two I allege to countervail the judgment of this author, who speaketh of his own liead as it liketh him, playing with tJie words "gross" and "carnal," and using the word "repre sent," as tJuwgh it expressed a figure only. Hippinus, in tlw said book, allegeth Cyprian to say, (Lib. iii. ad Quirinum 4 ) "that tlte body of our Lord is our sacrifice in flesh " meaning, Cyprian, as Hippinus saitJi, " eucharistiam," wherein St Augustine, (as Hippinus saith further,) in the num . 1 Q prayer for his motJier, speaking of the bread and wine of eucharistia, saith, u that in it is dispensed the holy host and sacrifice, whereby was cancelled the bill obligatory that was against us." And farther, Ilippinus saith, that "the old men called the bread and wine of our Lord s supper a sacrifice, an host, and oblation, for that specially, because tJiey believed and taught the true body of Christ and his true blood to be distribute in the bread and wine of eucha ristia ;" and, as St Augustin saith, ad Januarium, " to enter in, and be received with the Augustinus. mouth, of them that eat." These be Hippinus very words, who, because he is, I think, in this author s opinion, taken for no papist, I rather speak in his words than in mine own, whom m another part of this work this author doth, as it were for charity, by name slander to be a papist. Wherefore the said Hippinus words shall be, as I think, more weighty to oppress this author s talk titan mine be; and therefore, howsoever this author handleth before the words of St Cyprian (de Unctiono Chrismatis), and tlie word "shewing" out of his epis- //<-.?, yet tJie same Cyprian s faith appeareth so certain otJierwise, as those places shall need no further answer of me here, having brought forth the judgment of Ilippinus and Melancthon how they understand St Cyprian s faith, which thou, reader, oughtest to regard more than the assertion of this author, specially when thou hast read how he hath handled Hilary, Cyril, Tlu ophylact, and Damascene, as I shall hereafter touch. CANTERBURY. Whether I " make an exposition of Cyprian by mine own device," I leave to the 104. judgment of the indifferent reader. And if I so do, why do not you prove the same substantially against me? For your own bare words, without any proof, I trust the indifferent reader will not allow, having such experience of you as he hath. And if Cyprian of all other had writ 5 most plainly against me, as you say without proof, Melancthon, who thinkcth that you would have omitted here Cyprian s words, and have fled to Epim Melancthon and Epinus for succour? [ 3 And be nourished, 1551, and Orig. eel.] [ 4 Cum timorcet honorc Euchdristiam accipien- flfnn. In Levitico : Anima autem quaecunque man- ducaverit ex came sacrificii salutaris, quod est Domini, ct immunditia ipsius super ipsum est, pcribit anima ilia de populo suo. Item ad Corin- thios prima : Quicunque ederit panem, aut biberit calicem Domini indigne, reus erit corporis et san- guinis Domini. Cyprian, "ad Quirinum," Lib. in. cap. 94. p. 390. Paris. 1574.J [ 5 Had written, 1551.] 160 THE THIRD BOOK. And why do you allege their authority for you, which in no wise you admit when they be brought against you? But it seemeth that you be faint-hearted in this matter, and begin to shrink ; and like one that refuseth the combat, and findeth the shift to put another in his place, even so it seemeth you would draw back your self from the danger, and set me to fight w r ith other men, that in the mean time you might be an idle looker on. And if you as grand captain take them but as mean soldiers to fight in your quarrel, you shall have little aid at their hands; for their writings declare openly that they be against you more than me, although in this place you bring them for your part, and report them to say more and otherwise than they say indeed. And as for Cyprian and St Augustine, here by you alleged, they serve nothing for your purpose, nor speak nothing against me, by Epinus own judgment. For Epinus saith, " That eucharistia is called a sacrifice, because it is a remembrance of the true sacrifice which was offered upon the cross, and that in it is dispensed the very body and blood, yea, the very death of Christ, (as he allegeth of St Augustine in that place,) the holy sacrifice whereby he blotted out and cancelled the obligation of death, which was against us, nailing it upon the cross, and in his own person won the victory, and triumphed against the princes and powers of darkness." This passion, death, and victory of Christ is dispensed and distributed in the Lord s holy supper, and daily among Christ s holy people. And yet all this requireth no corporal presence of Christ in the sacrament, nor the words of Cyprian ad Quirinum neither. For if they did, then was Christ s flesh corporally present in the sacrifice of the old testa ment fifteen hundred years before he was born; for of those sacrifices speaketh Cyprian ad that text alleged by Cyprian ad Quirinum, whereof Epinus and you gather these cap. 94. words, "that the body of our Lord is our sacrifice in flesh." And howsoever you wrest Melancthon or Epinus, they condemn clearly your doctrine, that "Christ s body is corporally contained under the forms or accidents of bread and wine." Next in my book is Hilarius. But Hilarius, think they, is plainest for them in this matter, whose words they translate thus 1 : The answer " If the word were made very flesh 2 , and we verily receive the word being de Trinitat e. flesh, in our Lord s meat, how shall not Christ be thought to dwell naturally in us ? who being born man, hath taken unto him the nature of our flesh, that cannot be severed, and hath put together the nature of his flesh to the nature of his eternity under the sacrament of the communion of his flesh unto us. For so we be all one, because the Father is in Christ, and Christ in us. Wherefore whosoever will deny the Father to be naturally in Christ, he must deny first 165. either himself to be naturally in Christ, or Christ to be naturally in him. For the being of the Father in Christ, and the being of Christ in us, maketh us to be one in them. And therefore if Christ have taken verily the flesh of our body, and the man that was verily born of the virgin Mary is Christ, and also we receive under the true mystery the flesh of his body, by means whereof we shall be one, (for the Father is in Christ, and Christ in us,) how shall that be called the unity of will, when the natural property, brought to pass by the sacrament, is the sacrament of unity?" f 1 Si enim vere Verbum caro factum est, et nos vere Verbum carnem cibo dominico sumimus, quo- modo non naturaliter manere in nobis existimandus est, qui et naturam carnis nostree jam inseparabilem sibi homo natus assumpsit, et naturam carnis suee ad naturam seternitatis sub sacramento nobis com- municandae carnis admiscuit? Ita enim omnes unum sumus, quia et in Christo Pater est, et Christus in nobis est. Quisquis ergo naturaliter Patrem in Christo negabit, neget prius non natu raliter vel se in Christo, vel Christum sibi inesse ; quia in Christo Pater, et Christus in nobis, unum in his esse nos faciunt. Si vere igitur carnem cor- poris nostri Christus assumpsit, et vere homo ille, qui ex Maria natus fuit, Christus est, nosque vere sub mysterio carnem corporis sui sumimus, et per hoc unum erimus, quia Pater in eo est, et ille in nobis, quomodo voluntatis unitas aperitur, cum naturalis per sacramentum proprietas perfectae sa- cramentum sit unitatis ? Hilarius De Trinitate. Lib. viii. pp. 133, 134. Ed. Basil. 1535.] [ 2 If the word was made verily flesh, 155 , and Orig. ed.J OF THE PRESENCE OF CHRIST. 161 Thus doth the papists, (the adversaries of God s word and of his truth,) allege the authority of Hilarius, cither perversely and purposely, as it seemeth, untruly reciting 3 him and wresting his words to their purpose, or else not truly understanding him. For although he saitli that Christ is naturally in us, yet he saith also that wo be naturally in him. And nevertheless, in so saying he meant not of the natural and corporal presence of the substance of Christ s body and of ours, (for as our bodies be not after that sort within his body, so is not his body after that sort within our bodies ;) but he meant, that Christ in his incarnation received of us a mortal nature, and united the same unto his divinity, and so be we naturally in him. And the sacraments of baptism and of his holy supper, (if we rightly use the same,) do most assuredly certify us, that we be partakers of his godly nature, having given unto us by him immortality and life everlasting ; and so is Christ naturally in us. And so be we one with Christ, and Christ with us, not only in will and mind, but also in very natural properties. And so concludeth Hilarius against Arius, that Christ is one with his Father, not in purpose and will only, but also in very nature. And as the union between Christ and us in baptism is spiritual, and requireth no real and corporal presence ; so likewise our union with Christ in his holy supper is spiritual, and therefore requireth no real and corporal presence. And therefore Hilarius, speaking there of both the sacraments, maketh no difference between our union with Christ in baptism, and our union with him in his holy supper : and saith further, that as Christ is in us, so be we in him ; which the papists cannot understand corporally and really, except they will say, that all our bodies be corporally within Christ s body. Thus is Ililarius answered unto, both plainly and shortly. WINCHESTER. Tliis answer to Hilary, in the seventy-eighth leaf*, requireth a plain, precise issue, worthy to be tried 5 apparent at hand. The allegation of Hilary touclieth specially me, who do say and maintain that I cited Hilary truly (as the copy did serve), and 6 translate him truly in English after the same words in Latin. This is one issue which I qualify with the copy, An issue. because I have Hilary now better correct, which better correction setteth forth more lively the truth, th tn the other did, and therefore that I did translate was not so much to the advantage of that I alleged Hilary for, as is that in the book that I have now better correct. Hilary s words in the book newly corrected be these: Si enim vere Verbum caro factum est, ct nos Hilarius. vcre Verbum carnem cibo dominico sumimus, quomodo non naturaliter manere in nobis existimandua cst : qui et naturam carnis nostrse jam inseparabilcm sibi homo natus as- BOmpserit 8 , ct naturam carnis sure ad naturam teternitatis sub sacramento nobis communi- camla} carnis admiscuit ? Ita cnim omnes unum sumus, quia et in Christo pater est, et Christus in nobis est. Quisquis ergo naturaliter Patrem in Christo negabit, neget prius non naturaliter vel se in Christo vel Christum sibi inesse, quia in Christo Pater et Christus in nobis unum in iis 9 esse nos faciunt. Si vere igitur carnem corporis nostri Christus sumpsit 10 , et vere homo ille qui ex Maria natus fuit Christus est, nosque vere sub mys- 160. terio carnem corporis sui sumimus, et per hoc unum erimus, quia Pater in eo est et illo in nobis, quomodo voluntatis unitas asseritur, cum naturalis per sacramentum proprietas perfects 11 sacramentum sit unitatis? My translation is this: "If the word was made verily Jl< fili, and we verily receive tlie word, being flesh, in our Lord s meat, how shall not Christ be thought to dwell naturally in us, who, being born man, hath taken unto him the nature of [ 3 Citing, 1551, and Orig. ed.] [ * i. e. of the original edition.] [ s and apparent, 1551.] [" Did, 1551.] I 7 A copy, 1551.] [CKAXMKK.] [* Iii Hilary, and in Orig. ed. Winch, "as- sumpsit."] [ In Hilary, "his."] [ 10 "Assumpsit," 1551, as in Hilary ] ["In Hilary, " perfectn."] 11 162 THE THIRD BOOK. Unity in faith. * Unity in baptism. * Unity in flesh. - Hilarius. 167. * Carnally. "Naturally. our flesh that cannot be severed, and hath put together the nature of his flesh to the nature of his eternity, under the sacrament of the communion of his flesh unto us ? for so we be all one, because the Father is in Christ, and Christ in us. Wherefore,, whosoever will deny Hie Father to be naturally in Christ, must deny, flrst, either himself to be naturally in Christ, or Christ not to be naturally in him ; for the being of the Father in Christ, and the being of Christ in us, ma,keth us to be one in them. And therefore, if Christ hath taken verily the flesh of our body, and the man that was born of the virgin Mary is verily Christ, and also we verily receive under a mystery the flesh of his body, by means ivhereof we shall be one, for the Father is in Christ, and Christ in its ; how shall that be called the unity of will, when the natural propriety brought to pass by the sacrament is the sacrament of perfect unity?" This translation differeth from mine otlier, whereat this author jindeth fault; but wherein? The word vero was in tlie oilier copy an adjective, and I joined it with mysterio, and there fore said " the true mystery:" which word " mystery" needed no such adjective " true," for every mystery is true of itself. But to say, as Hilary truly correct saith, " that we receive under the mystery, truly, the flesh of Christ s body," that word " truly," so placed, setteth forth lively tlie real presence and substantial presence of that is received, and repeateth again the same that was before said, to the more vehemency of it. So as this correction is better than my flrst copy, and according to this correction is Hilarius alleged by Melancthon to GEcolam- padius for the same purpose I allege him. Another alteration in the translation thou seest, reader, in the word perfectse, which in my copy was perfecta, and so was joined to proprietas, which now in the genitive case, joined to unitatis, giveth an excellent seme to the dignity of the sacrament, how the natural propriety by tlie sacrament is a sacrament of perfect unity, so as the perfect unity of us with Christ is to have his flesh in us, and to have Christ bodily and naturally dwelling in us by his manhood, as he dwelleth in us spiritually by his God head: and now I speak in such phrase as Hilary and Cyril speak, and use the words [as they use them,] l ivhatsoever this author saith, as I will justify by their plain words. And so I join now with this author an issue, that I have not perversely used the allega tion of Hilary, but alleged him, as one that speaketh most clearly of this matter; which Hilary, in his eighth book de Trinitate, entreateth how many divers ways we be one in Christ, among which he accompteth faith for one: then he cometh to the unity in baptism, where he handleth the matter above some capacities; and because there is but one baptism, and all that be baptized be so regenerate in one dispensation, and do the same thing, and be one in one, they that be one by the same thing be, as he saith, in nature one. From that unity in baptism he cometh to declare our unity with Christ in flesh, which he calleth the sacra ment of perfect unity, declaring how it is when Christ, who took truly our flesh mortal in the virgins womb, deliver eth us the same flesh glorified truly to be communicate with our flesh, ivhereby as we be naturally in Christ, so Christ is naturally in us : and when this is brought to pass, then the unity between Christ and us is perfected. For as Christ is natu rally in the Father of the same essence by the divine nature, [and God the Father naturally in Christ his Son, very God of the same essence in the divine nature:] 2 so we be naturally in Christ by our natural flesh which he took in tJie virgin s womb, and he naturally in us by the same flesh in him glorifled, and given to us, and received of us in the sacrament. For Hilary saith in plain words, how Christ s very flesh and Christ s very blood, received and drunken (accepta et hausta), bring this to pass. And it is notable, how Hilary compareth together the " truly" in Christ s taking of our flesh in tlie virgin s ivomb, with the " truly" of our taking of his flesh (in cibo dominico) in our Lord s meat: by which words he expresscth the sacrament, and after reproveth those that said, we were only united by obedience and will of religion to Christ, and by him so to the Father, as though by the sacrament of flesh and blood no propriety of natural communion were given unto us : whereas both by the honour given unto us we be the sons of God, and by the Son dwelling carnally in us, and we being corporally and inseparably unite in him, the mystery of true and natural unity is to be preached. These be Hilary s ivords. For this latter part, where thou nearest, reader, the Son of God to dwell carnally in us, not after man s gross imagination, for we may not so think of godly mysteries, but " carnally" is referred to the truth of Christ s flesh, given to us in this sacrament; and so is "naturally" to be understanded, that we receive Christ s natural flesh for the truth of it, as Christ received our natural flesh of the virgin, although ive receive Christ s flesh glorifled incorruptible, very spiritual, and in a spiritual manner delivered unto us. Here is mention made of the word " corporal ;" but I shall speak of that [ These words are omitted in the loHO. ed.J [ 2 This clause is found only in the Grig. ed. Winch.] OF THE PRESENCE OF CHRIST. lift in the discussion of Cyril. This Hilary was before St Augustine, and was known both of Mm and St Jerome, who called him Tuham Latini eloquii against the Arians. Never man found fault at this notable place of Hilary. Now let us consider how the author of this book forgetteth himself, to call Christ in us >*/f///v///y by his Godhead, which were then to make us all gods by nature, which is over-great an absurdity, and Christ in his divine nature dwelleth only in his Father naturally, and in us by grace. But as we receive him in tJie sacrament of his flesh and blood, if we receive him worthily, so dwelleth he in us naturally, for the natural 3 communication of our nature and his. And therefore, where this author reporteth Hilary to make no difference between our union to Christ in baptism, and in the supper, let him trust in 4 him no more that told him so: or if this author will take upon him as of his own knowledge, then I must 5 say, and (if he were another) would say, an answer in French, that I will not express. And hereupon will I join in 6 the issue, that in An uiue. Hil iry the matter is so plain otherwise than this author rehearseth, as it hath no colour of defence to the contrary. And what Hilary speaketh of baptism and our unity tlierein, I have before touched ; and this unity in flesh is after treated apart. What shall I say to this so manifest untruth, but that it conjirmeth that I have in other observed, how tfiere was never one of tJiem that I have read writing against the sacrament, but hath in his writings said somewhat so evidently in the matter, or out of the matter, dis crepant from truth, as might be a certain mark to judge tlie quality of his spirit f CANTERBURY. Here you confess that you cited Hilary untruly, but you impute the fault to your copy. What copy you had I know not, but as well the citation of Melancthon, as all the printed books that ever I saw, have otherwise than you have written; and therefore it seemcth that you never read any printed book of Hilarius. Marry it might be that you had from Smith a false copy written, who informed me that you had of smith, him all the authorities that be in your book : and having all the authorities that he had with great travail gathered, by and by you made your book, and stole from him all his thank and glory, like unto Esop s chough, which plumed himself with other birds feathers. But wheresoever you had your copy, all the books set forth by public faith have otherwise than you have cited. And although the false allegation of Hilary toucheth you somewhat, yet chiefly it toucheth Smith, who hath erred much worse in his translation than you have done, albeit neither of you both handle the matter sincerely and faithfully, nor agree the one with the other. But I trow it be your chance to light upon false books. For whereas in this sen tence, Quisquis ergo naturaliter Patrem in Christo negabit, negct prius naturaliter vel .< ni Christo, vel Christum sibi inesse, one false print for naturaliter hath non natu- >j n natura- ralitcr; it seemeth that you chanced upon that false print. For if you have found hter jg8 Hilary truly corrected, as you say you have, your fault is the more, that out of a true copy would pick out an untrue translation. And if you have so done, then by putting in a little pretty "not," where none ought to be, with that little pretty trip you have clean overthrown yourself. For if it be an error to deny that Christ is not naturally in us, (as it is rehearsed 7 for an error,) then must it be an error to affirm " that Christ is naturally in us." For it is all one thing to deny that he is not, and to affirm that "he is naturally in us." And so by your own translation you overthrow yourself quite and clean, in that you say in many places of your book, that "Christ is naturally in us," and ground your saying upon Hilary: whereas now, by your own translation, Hilary rejecteth that clearly as an heinous error. And as concerning this word " truly," it setteth not lively forth a real and sub- Truly, stantial presence, as you say it doth ; for Christ is truly in all his faithful people, and they 9 truly eat his flesh and drink his blood, and yet not by a real and corporal, but by a spiritual and effectual presence. And as concerning the word perfecta or perfecta 10 , in the print which I have of your Perfect*. [ 3 Mutual, Orig. ed. Winch.] [ 4 Trust him, 1551.] ^ 5 I would say, (if he were another,) an answer f 7 As it is here rehearsed, 1551.] [ 8 To deny, omitted in ed. 1580.J [ 9 There/1580.] in French, Grig. ed. Winch. J [ Perfecta or perfect, ed. 1551. J [ 6 Join the issue, 1551.] 112 1(54 THE THIRD BOOK. *Mine issue. John xiv. John v. John vi. Naturally. 109. book, is neither of both, but be left quite out. Nevertheless that fault I impute to no untruth in you, but rather to the negligence either of your pen or of the printer. But for the perfectness of the unity between Christ and us, you declare here the 1 perfect unity to be that which is but the one half of it. For the perfect unity of us with Christ is, not only to have Christ coqwrally and naturally dwelling in us, but likewise we to dwell corporally and naturally in him. And Hilary declareth the second part to pertain to our unity with Christ, as well as the first ; W 7 hich of sleight and policy you leave out purposely, because it declareth the meaning of the first part, which is not that Christ is in them that receive the sacrament, and when they receive the sacrament only, but that he naturally tarrieth and dwelleth in all them that per tain to him, whether they receive the sacrament or no. And as he dwelleth natu rally in them, so do they in him. And although you have excused your perversity by your false copy, yet here I will join an issue with you, that you did neither allege Hilary s words before truly, nor yet now do truly declare them. As for the first part, you have confessed your self that you were deceived by a false copy : and therefore, in this part, I plead that you be guilty by your own confession. And as concerning the second part, Hilary speaketh not of the unity of Christ with the sacrament, nor of the unity of Christ with us only when we receive the sacrament, nor of the unity of us with Christ only, but also with his Father ; by which unity we dwell in Christ and Christ in us, and also we dwell in the Father and the Father in us. For as Christ being in his Father, and his Father in him, hath life of his Father, so he being in us, and we in him, giveth unto us the nature of his eternity, which he received of his Father ; that is to say, im mortality and life everlasting, which is the nature of his Godhead. And so have we the Father and the Son dwelling in us naturally, and we in them, forasmuch as he giveth to us the nature of his eternity which he had of his Father, and honoureth us with that honour which he had of his Father. But Christ giveth not this nature of eternity to the sacrament, except you will say that the sacrament shall have ever lasting life ; as you must needs say, if Christ dwell naturally in it, after Hilary s manner of reasoning. For by the saying of Hilary, where Christ dwelleth, there dwelletl?. his Father, and givetb eternal life by his Son. And so be you a goodly saviour, that can bring to everlasting life both bread and drink, which never had life. But as this nature of eternity is not given to the sacrament, so is it not given to them that unworthily receive the sacrament, which eat and drink their own damnation. Nor it is not given to the lively members of Christ only when they receive the sacrament, but so long as they spiritually feed upon Christ, eating his flesh and drinking his blood, either in this life or in the life to come : for so long have they Christ naturally dwelling in them, and they in him. And as the Father naturally dwelleth in Christ, so by Christ doth he naturally dwell in us. And this is Hilary s mind, to tell how Christ and his Father dwell naturally in his faithful members, and w r hat unity we have with them, (that is to say, an unity of nature, and not of will only), and not to tell how Christ dwelleth in the sacrament, or in them that unworthily receive 2 it, that he dwelleth in them at that time only, when they receive the sacrament. And yet he saith that this unity of faithful people unto God is by faith taught by the sacrament of baptism and of the Lord s table, but wrought by Christ by the sacrament and mystery of his incarnation and redemption, whereby he humbled himself unto the lowliness of our feeble nature, that he might exalt us to the dignity of his godly nature, and join us unto his Father in the nature of his eternity. Thus is plainly declared Hilary s mind, who meant nothing less than, as you say, to entreat how many divers w r ays we be one in Christ, but only to entreat and prove that we be naturally in Christ, and Christ in us. And this one thing he proveth by our faith, and by the sacrament of baptism, and of the Lord s supper, and still he saith as well that we be naturally and corporally in him, as that he is naturally in us. And where you speak of the unity in baptism, and say that Hilary " handleth that matter above some capacities;" howsoever Hilary handleth the matter, you handle it f 1 Here to be the, edit. 1580.] [ 2 Receive the sacrament: or if they worthily receive it, that he dwelleth, &c., 1651.] OF THE PRESENCE OF CHRIST. Hi.") in such sort as I think passeth all men s capacities, unless yourself make a large com mentary thereto. For what these your words mean, "Because there is but one baptism, and all that be baptized be so regenerate in one dispensation, and do the same thing, and be one in one, they that be ono by the same thing be, as he saith, in nature one ;" and what that one thing is which they do that be baptized; 1 think no man can tell, except you read the riddle yourself. And now to your issue. If you can shew of the w r ords of Hilary in this place, that Christ is naturally in the sacraments of bread and wine, or in wicked persons, or in godly persons only when they receive the sacrament, then will I confess the issue to pass upon your side, that you have declared this author truly, and that he makcth most clearly for you against me. And if you cannot shew this by Hilary s words, then must you hold up your hand and say, " Guilty !" And yet furthermore, when Hilary saith that we be naturally in Christ, he meaneth not that our bodies be contained within the compass of his body, but that we receive 170. his natural eternity. And so likewise, when he saith that Christ dwelleth naturally and carnally in us, he meaneth not that his body is contained corporally within the compass of our mouths or bodies, (which you must prove by his plain words, if you will justify your issue, that he speaketh most clearly for you,) but he meaneth that Christ communi- cateth and giveth unto us the nature of his eternity or everlasting life. And he dwelleth in us by his incarnation, as St John saith : Verbum caro factum est, et habitamt in nobis, John i. " The word was made flesh, and dwelled in us." And as he may be said to dwell in us by receiving of our mortal nature, so may we be said to dwell in him by receiving the nature of his immortality. And "never man found fault," as you truly say, "at this notable place of Hilary ;" nor, again, never learned man hitherto expounded him as you do. And when I said that Christ is in us naturally by his Godhead, I forgat not what I said, as you say of me ; for I plainly expounded what I meant by naturally, that is to say, not by natural substance to make us gods, but by natural condition giving unto us immortality and everlasting life which he had of his Father, and so making us par takers of his godly nature, and uniting us to his Father. And if we attain to the unity of his Father, why not unto the unity of the Godhead, not by natural substance, but by natural propriety ? As Cyril saith that we be made the children of God and heavenly men by participation of the divine nature, as St Peter also teacheth. And so be we one 2 Pet. i. in the Father, in the Son, and in the Holy Ghost. And where you say that we " receive Christ in the sacrament of his flesh and blood, if we receive him worthily ;" here you have given good evidence against yourself, that we receive him not, and that he dwelleth not in us naturally, except we receive him worthily. And therefore where you say that there is " none that writeth against the truth in the sacrament, but he hath in his writings somewhat discrepant from truth, that might be a certain mark to judge his spirit;" this is so true, that yourself differ not only from the truth in a number of places, but also from your own sayings. And where you bid me " trust him no more that told me that Hilary maketh no difference between our union in Christ in baptism, and in his holy supper," it was very Hilary himself of whom I learned it, who saith that in both the sacraments the union is natural, and not in will only. And if you will say the contrary, I must tell you the " French answer" that you would tell me. And herein I will not refuse your issue. *Minc issue. Now come we to Cyril, of whom I write as folio weth. And this answer to 3 Ililarius will serve also unto Cyril, whom they allege The answer to speak after the same sort that Ililarius doth, that Christ is naturally in us. Lib.^ cai, . The words which they recite be these 4 : "We deny not," saith Cyril against the [ 3 Of, 1551, and Orig. ed.] [* "On fii-v yap <tct0t orei Ttj voov/mtvri Ka-rd T>JJ/ dydiri)v, opOjj TC Kai aoiao"rpo</>> TTt <TTei, ^iXptTa> TC nal etXiK pivet Xoyio"U6u avvevovfJLG&a rj/eujuttTiKcos TW XpitTTw, ourta/uuis e^ft/oi/ijcreTai Ttav rap 1 jj/xii/ fioy/j.d-r(ov o Xo yos trvvepov^v ydp on t f (Jid\a TOVTO <paaiv o,o6u>s TO 6e ye KUTC Xe yeii/, a>? ovSeis ;/LU" o-uvat^ei as T;/S Kara <r p\a TT/OOS avTov o \6yni t o\oH~\j /Ofts diracuv TCUS tfeo- Trvev<TTOL<i ypatf>a.l<} 67rio tt a/ueJ/. TTU>S yap an a juqW- \oyov, ; n s av o\a>s ei/ooiaaat TTOTC TWV eu (ppovflv etcoOoTwi/, ws J/iTreXos /ue i/ eo-ri /cuTa-rouTo X/nerroV >j/iels yap K\ijfjL(iT(av aTroreXoi/i/Tes &\>]u.a TI]V e avruv KOt Trap avrov a jj/ eis airrous Ko/nty/ie0a 1(56 THE THIRD BOOK. 171, 1 Cor. vi John vi. Jollll XY. Col. ii. In Jqhan. Lib. iv. cap. heretic, "but we be spiritually joined to Christ by faith and sincere charity; but that we should have no manner of conjunction in our flesh with Christ, that we utterly deny, and think it utterly discrepant from God s holy scrip tures. For who doubteth but Christ is so the vine-tree, and we so the branches, as we get thence our life ? Hear what St Paul saith : We be all one body with Christ, for though we be many, we be one in him : all we participate in one food. Thinketh this heretic that we know not the strength and virtue of the mystical benediction ? which when it is made in us, doth it not make Christ by communication of his flesh to dwell corporally in us ? Why be the members of faithful men s bodies called the members of Christ ? Know you not, saith St Paul, that your members be the members of Christ? And shall I make the members of Christ parts of the whore s body ? God forbid. And our Saviour also saith : He that eateth my flesh and drinketh my blood, dwelleth in me and I in him. " Although in these words Cyril doth say, that Christ doth dwell corporally in us when we receive the mystical benediction, yet he neither saith that Christ dwelleth corporally in the bread, nor that he dwelleth in us corporally only at such times as we receive the sacrament, nor that he dwelleth in us and not we in him; but he saith as well, that we dwell in him, as that he dwelleth in us. Which dwelling is neither corporal nor local, but an heavenly, spiritual, and supernatural dwelling, whereby so long as we dwell in him and he in us, we have by him everlasting life. And therefore Cyril saith in the same place, that Christ is the vine, and we the branches, because that by him we have life. For as the branches receive life and nourishment of the body of the vine, so receive we by him the natural property of his body, which is life and immortality, and by that means we, being his members, do live and are spiritually nourished. And this meant Cyril by this word " corporally," when he saith that Christ dwelleth corporally in us. And the same meant also St Hilarius by this word " naturally," when he said that Christ dwelleth naturally in us. And as St Paul, when he said that in Christ dwelleth the full divinity " corporally," by this word " corporally" he meant not that the divinity is a body, and so by that body dwelleth bodily in Christ. But by this word " corporally" he meant, that the divinity is not in Christ accidentally, lightly, and slenderly, but substantially and perfectly, with all his might and power : so that Christ was not only a mortal man to suffer for us, but also he was immortal God able to redeem us. So St Cyril, when he said that Christ is in us " corporally," he meant that we have him in us, not lightly and to small effect and purpose, but that we have him in us substantially, pithily, and effectually, in such wise that we have by him redemption and everlasting life. And this I suck not out of mine own fingers, but have it of Cyril s own express words, where he saith 1 : "A little benediction draweth the whole man to KaiTOL TOV IlauXou \eyovTO<s, Oi yap Travres ei/ crwud ea-fjicv ev X/OKTTW, on els ap-ros ol TroXXot e(Tfj.ev o t yap -TraWes e/c TOV eios ap-rou p.eTeyop.ev. XeyeTio yap TIS i//xtj/ TI}V ai-riav, Kal o^oacr/ceVa) irapeXQtav Trj? ^tu<7Ti/c?;s euXoyias TI}V duvau.iv. yiverai yap ev r\p.lv did T L ; lip ovyl Kal o-aiyuaTt/caJs tj/xli/ evoiKi^ovora TOV Xptcrroz/ TTJ /zet)e et /cat KOIVUO- via Ttjs a yias avTov (rap/cos; a XX ol/xat Xt yeti/ opflws* ypdfpei yap o IlauXos yeyevfjaQai TCI edvi] ffixra-wfia Kal o-v/z/ueVoxa /cat avyK\r]pov6/j.a Xpi- <TTov. a-va-ffda/Lia Toiyapovv KUTU TTO LOV direcpdvOt] TpoTrov ; ttu0eWa yap /j.eTaa-^e iv T?}S euXoyias T?/S p.$$GTiKris t ev 7T|Oos avTov yeyove <ru>p.a, KaQdirep
dfj.c\ei Kal TWV dyltav e/cao-Tos dtroGT6\<av. eirei
Std iroiav aiTiav /xe Xtj TOV X/>MTToS Ta oiKela,
u.d\\ov 8e Ta TrdvTtav, aJs UVTOV KaTtavo/maare /iteXrj ;
ypdfpei yap OUTOJS OVK oldaTe OTI TU /me Xrj vp.Cav
/xe Xrj Xpio-ToD tcrTLV ; a pas ovv Ta /xe X) TOV XpiarTov,
Troifjo co Tropvi)? fJLe\t] 5 /uLJ] yevoiTo aXXa Kal ai iros
6 <ro)Trj|O f o Tpwywv /mou TJJV <rap/ca, </>tj<ri, /cat irivwv
p.ov TO alfJLa, w e/xot /icWt, /ca yw ev avTw Cyrill.
In Joannem. Lib. x. cap. 13. Tom. IV. pp. 862, 3
Ed. Aubert. Paris. 1638.]
f 1 OUTWS oXty/o Tj) ird\iv eu\oyia avp/jrav \}p.<MV
els COUTJJI/ dvatpvpei TO aw/ma, Kal Trjs totas evepyeias
dvaTrXripol, OVTM TC ev T//U.IJ/ yiveTai X/OKTTOS, /cat
)/xets av Trd\iv ev avTw. Cyril, in Joannem. Lib.
iv. cap. 17- Ib. p. 365.]
OF THE PRESENCE OF CHRIST. 167
God, and fillcth him with his 2 grace, and after this manner Christ dwelleth in us,
and we in Christ."
But as for corporal eating and drinking with our mouths, and digesting with
our hodies, Cyril never meant that Christ doth so dwell in us, as he plainly
dorlareth. " Our sacrament," saith he, " doth not affirm the eating of a man, Anathema-
drawing wickedly Christian people to have gross imaginations and carnal fantasies inlohS.
of such things as be fine and pure, and received only with a sincere faith V i7. b
" But as two waxes, that be molten and put together, they close so in one, that
every part of the one is joined to every part of the other, even so," saith Cyril,
" he that recciveth the flesh and blood of the Lord, must needs be so joined
with Christ, that Christ must be in him, and he in Christ 4 ." 372
By these words of Cyril appeareth his mind plainly, that we may not
grossly and rudely think of the eating of Christ with our mouths, but with our
faith, by which eating, (although he be absent hence bodily, and be in the
eternal life and glory with his Father,) yet we be made partakers of his nature,
to be immortal, and have eternal life and glory with him.
And thus is declared the mind as well of Cyril as of Hilarius.
WINCHESTER.
The author saith, such answer as he made to Hilary will serve for Cyril; and indeed, to Cyril,
say truth, it is made after the same sort, and hath even such an error as the other had, saving
it may be excused by ignorance. For where the author travaileth here to expound the u ord
" corporally," which is a sore word in Cyril against this author, and therefore taketh labour
to temper it with the word corporaliter in St Paul, applied to the dwelling of the divinity
in Christ; and yet not content tJierewith, maketh further search, and would gladly have somewhat
to confirm his fancy oat of Cyril himself, and seeketh in Cyril where it is not to be found,
and seeketh not where it is to be found: (for Cyril telleth himself plainly, what he meaneth
by tJie word " corporally" which place and this author had found, he might have spared a
great many of words uttered by divination ; but then the truth of that place hindereth and
quaileth in manner all the book :) / will at my peril bring forth Cyril s own words truly upon
the 17 th chapter of St John.
Corporaliter Films per benedictionem mysticam nobis ut homo unitur, spiritualiter Lege Cyrii-
autem ut Deus 5 . Which be in English thus much to say : " The Son is unite as man cor- Lib. ix. cap.
porally to us by the mystical benediction, spiritually as God." These be Cyr rfs words, who ?n joan"can S
nameth the sacrament of the body and blood of Christ the mystical benediction, and sheu eth
in this sentence, how himself understandeth ttte words " corporally" and " spiritually ;" that
is to say, ivhen Christ uniteth himself to us as man, which he doth giving his body in this
sacrament to such as worthily receive it, then he dwelleth in them corporally, which Christ
was before in them spiritually, or else they could not worthily receive him to the effect of
that unity corporal and corporal dwelling; by which word "corporal" is understanded no
grossness at all, which the nature of a mystery &vcludeth, and yet keepeth truth still, being
the understanding only attained by faith. But ivliere the author of tJie book allegeth Cyril
[ 2 With grace, 1551, and Orig. ed.J j O.VTOV evpiaKeTai trvvuvaKipvdfievos uxnrep KO.I
[ A/) ovu, o5s CTepoif TLva uidv, /cat X/OICTTOI/ I dvafjuyvup.evo i avTW diet T//S yneTctXfj //ea>s, o5s ev
Trnpa TOV t(C Oeou \6yov, TOV (paivofievov elvai I Xpt<rTtj> p.tv aiiTov evpiaKeffQai, \piarTov oe ou
/cat fiovio TO T/;S aVoo-roXvs j ira Xu; ti> auroj. Id. in Joannem. Lib. iv. cap. ii.
x/jf//uia, OVK avtipwirofyayiav t lfiiav I Tom. IV. pp. 364, 5.]
O p-vaTt ipiov, Trayoicpras dvocriuis eis j [ 5 FiVeTai p.ev yap ev ityuJ b utos, (TW/JLUTIKCO^ /zej/
iTij\ous two ias TUIV TTi<rT6V<rdvT(jav TOV vovv
oyKr/molv ai/O/ofOTTti/ois vTro<f)epctv eiri^eiptJav, a
tos avQpajiro i, avvava.K.ipvdfJiv6<i TC KUI crvvevovfJLevo?
ot 6u/\oytas T?Js /nwo-TtK//*" WW^urmefit oe av Tra Xti/
Apologet. adv. Orient. Anath. xi. Def. Cyril.
Tom. VI. p. 193.J
[ 4 "Qcnrtp ydp fiTis Kijpov eTepw
irai/Tws O;TTOI/ Kai tTepov ev ert /oa) yeyouoTa KO.TO-
x//6Tai TOV avTov, oT.fj.ai, Tpoirov Kai o Ttjv adpKa
^ TOU <ra)T^jOos r^ifav X/ofo-ToD, Kai TTIVMV
Trpoa-\a.p.fidvTa.i ; Ib. | aJsGeos, T>; TOV ioiou Tri/et ^aros evepyeia, KO.I \dpiri
v TOTipiov al/ua, Ka6a <t>i}(nv auros, <iv w sir/oos
TO ev i )/J.lv dvaKTi^wv Trveuua TT/OOS KULVOTIJTU ^co?/v
Kai TT;S Betas avTov ^>u<rea)s noivtavovt Kat)to"ra s
ovv dpa T^S evoT)TOS t/fitoj/ TI^S Trpo
aTtpa oia<f>aivTai
B/oo)7ros, Beai oe ws 0eos evv-
(pva-iKfios Tta Iciw yei/i/rjTo/ot. Id. in Joan
. Lib. ix. cap. xlvii. Ib. pp. 1001,2.]
168
THE THIRD BOOK.
TU>V TTKTTGVOVTtoV VOVV,
173.
in words to deny the eating of a man, and to affirm the receiving in this sacrament to be only by
faith; it shall appear, I doubt not, upon further discussion, that Cyril saith not so, and
the translations of Cyril into Latin a/ler the print of Basil, in a book called " Antidotum"
and of whole Cyril s works printed at Cologne, have not in that place such sentence : so iis
following tlie testimony of those books set forth by public faith in two sundry places, I should
call the allegation of Cyril made by this author in this point untrue, as it is indeed in tfie
matter untrue. And yet because the original error proceedeth from CEcolampadius, it shall
serve to good purpose to direct the original fault to him ; as he well deserveth to be, as he is
noted guilty of it, whose reputation deceived many in the matter of the sacrament; and being
well noted how the same CEcolampadius corrupteth Cyril, it may percase somewhat work with
this author, to consider how he hath in this place been deceived by him. I will write here the
very words of Cyril in Greek, as tJiey be of CEcolampadius brought forth and published in
his name; wJiereby the reader that understandeth the Greek, as many do at this time, may judge
of CEcolampadius conscience in handling this matter. The words of Cyril be alleged of
CEcolampadius to be these in Greek : \p* ovv cos eTepov TIVO. vlov KOI Xpio~Tov Trapa TOV CK
6eov 6ebv \6yov TOV (paivop-evov eivai 5ta/3e/3ato{Wai, <u Kal TO TT/S aTrooroX^
aTTOtpaiWt TO p,vo"njpiov, irapicrTwv di>oo"/a>s fls
\oyio~p.ols dvQpaTTivois eVi^eipcoi , a p-ovrj Kal "^1X77 KOI
TTurrei Xa/i/Sai/tTai.
These ivords be by CEcolampadius translated in this wise : Nonne igitur eum qui videtur
filium et Christum, alium a Deo verbo, qui ex Deo esse amrmant, cui apostolatus functio
tributa sit? Non enim sacramentum nostrum hominis manducationem asserit, mentes
credentium ad crassas cogitationes irreligiose introtrudens, et humanis cogitationibus
subjicere enitens ea quse sola, et pura, et inexquisita fide capiuntur. This is CEcolam
padius translation of the Greek, as the same is by CEcolampadius alleged. Which, com
pared with the Greek, and the congruity and phrase of the Greek tongue considered, doth
plainly open a corruption in the Greek text. First, in the word diafifpaiovvTai, which should
be a participle in the singular number 6\a/3f/3atcoi>, as TrapiorcoV, and fTrixeip&v, all which
participles depend of the third person reproved of Cyril, and nominative case to the verb
djrocpaivfi, which hath the noun p-vo-Typiov his accusative case; for congruity will not suffer
to be tlie nominative case, as CEcolampadius maketh it, because irapio-T&v and
should then depend on it, which be the masculine gender, and /jLvo-Trjpiov the neuter:
and besides that, the sense hath so no good reason to attribute assertion to the mystery by
the way of declaration : the mystery of nature secret hath need of declaration, and maketh
none, but hideth rather; and the mystery cannot declare properly that should lead or subdue
men to vain imagination. But Cyril, intending to reprove the conclusion of him that attri-
buteth to that is seen in Christ the nature 1 (meaning the person of his humanity,) the office
of the apostle, and so tJiereby seemeth to make in Christ two several persons, esteeming that
ia/3e/3ai- is seen another son from the second person, sheweth how that man so concluding* doth affirm,
(i -TTochaivfi an ubsurdity, that is to say, declareth^ that mystery of our humanam commixtionem, for so
o/uLvirn- hath tlie public translation, and not dv6pu7ro(payiav, which should signify eating of a man,
as CEcolampadius would liave it, and cannot with this construction to make fj,vo"njpiov the
accusative case have any sense; and then that man so concluding may be said therewith
leading^ the mind of them that believe into slender and dark imaginations or thoughts, and
so\\ going about to bring under man s reasonings such things as be taken or understanded by
an only simple, bare, and no curious faith. And this is uttered by Cyril by interrogation,
*Ap ovv, which continueth unto tlie last word of all that is here written in Greek, ending in the
word \ap.@dvTai. But CEcolampadius, to frame these words to his purpose, corrupteth the
participle diafieficuwv, and maketh it Sta/3e/3aioi5i/Tcu, wliereby he might cut off the interroga
tive; and then is he yet fain to add evidently that is not in the Greek, a copulative causal
enim; and then when pvo-rripiov is, by the cutting off the interrogation and the addition of
enim, made the nominative case, then cannot Trapio-Twv and cVt^etpcoi/ depend of it, because
of the gender, and TO pvo-i^ptov, because of the article, determineth the principal mystery in
Christ s person; and after 3 public translation, it should seem the Greek word was not dvdpa>-
7ro<payiav, but avdptoTropiyiav, which in the public translation is expressed with these two
words, humanam commixtionem. 77m one place, and 4 there were no more like, may shew
i]fi<av.
Tn -
[ J " The nature of his humanity," omitting the
intermediate words, Orig. ed. Winch.]
at the side is only found in the
Orig. ed. Winch.]
[ 3 After the public, 1551.]
[ 4 And : here and elsewhere for i/.J
OF THE PRESENCE OF CHRIST. 160
with yjhat conscience (EcolcunpadUu bundled tJie matter of the sacrament, who was learned
in the Greek tongue, much exercised in trannl<iti<m*, and Jtad once written a grammar of
tlie Greek; and yet in this place abuseth himself and the reader in perverting Cyril against
all congruities of tJie speech, against the proper signijications of the words, against the con
venient connection of the matter, with depravation of the phrase and corruption of certain
words, all against tJie common and public translation ; and wlien he hath done all this, con-
cludeth in the end that lie hath translated the Greek faithfully, wJien there is by him used
no good faith at all, but credit and estimation of learning by him abused to deceive well-
t.u tiitmi simplicity, and serveth for some defence to such as be bold to use and follow his
authority in this matter : as the author of the book seemeth to have followed him herein, for
else t/te public authentic translations which be abroad, as I said, of tfie prints of Basil and
Cologne, have no such matter ; and tlierefore tlie fault of the author is to leave public truth
and search matter whispered in corners. But thus much must be granted, though in the prin
cipal matter, that in tlie mystery of the sacrament we must exclude all grossness, and yet for
t/te truth of God s secret work in tlie sacrament grant also, that 5 in such as receive the sacra
ment ^worthily, Clirist dwelleth in tliem corporally, as Cyril saith, and naturally and carnally, 174.
as Hilary saith. And with this true understanding, after the simplicity of a Christian faith,
which was in these fathers, Hilary and Cyril, tlie contention of these three envious words, in gross
capacities grossly taken, "natural," "carnal," and " corporal," which carnality hath engendered,
might soon be much assuaged: and this author aUo, considering with himself how much he hath
bi i ii, overseen in tlie understanding of them, and. the speciality in this place of himself and
CEoolampadius, might take occasion to repent and call home himself, who wonderfully wan-
dereth in this matter of the sacrament, and having lost his right way, breaketh up liedges, and
leapeth over ditches, with a wonderous travail to go whitJter lie would not, being not yet (as
appeareth) determined where he would rest, by tlie variety of his own doctrine, as may ap
pear in sundry places, if they be compared togetJier.
CANTERBURY.
I said very truly when I said, that such answer as I made to Hilary will servo
for Cyril; for so will it do indeed, although you wrangle and strive therein never so
much : for Cyril and Hilary entreat both of one matter, that we be united together
and with Christ, not only in will, but also in nature, and be made one, not only in
consent of godly religion, but also that Christ, taking our corporal nature upon him,
hath made us partakers of his godly nature, knitting us together with him unto his
Father and to his holy Spirit. Now let the indifferent reader judge whether you or
I be in error, and whether of us both hath most need to excuse himself of ignorance.
"Would God you were as ready humbly to yield in those manifest errors which be
proved against you, as you be stout to take upon you a knowledge in those things,
N\ herein ye be most ignorant ! But (piXavTia 6 is a perilous witch.
Now whereas I have truly expounded this word "corporally" in Cyril, when he saith Corporally,
that Christ dwelleth corporally in us, and have declared how that word " corporally," as
Cyril understandeth it, maketh nothing for your purpose, that Christ s flesh should be
corporally contained (as you understand the matter) under the form of bread, (for he
neither saith that Christ dwelleth corporally in the bread, nor that he dwelleth in
them corporally that be not lively members of his body, nor that he dwelleth in
his lively members at such time only as they receive the sacrament, nor that he dwelleth
in us corporally, and not we in him; but he saith as well that we dwell in him,
as that he dwelleth in us;) and when I have also declared that Cyril s meaning was
this, that as the vine and branches be both of one nature, so the Son of God, taking
unto him our human nature, and making us partakers of his divine nature, giving
unto us immortality and everlasting life, doth so dwell naturally and corporally
in us, and maketh us to dwell naturally and corporally in him; and where, as
I have proved this by Cyril s own words, as well in that place in his tenth book
upon St John s Gospel, the thirteenth chapter, as in his fourth book, the seventeenth
chapter; you answer no more to all this, but say that I "seek in Cyril where it is not
to be found, and seek not where it is to be found." A substantial answer, be you
sure, and a learned. For you do here like a keeper which I knew once, required to
[ s Orig. ed. Winch, omits the words, "grant also that."] [ 6 Self-love.]
170 THE THIRD BOOK.
follow a suit with his hound, after one that had stolen a deer; and when his hound
was in his right suit, and had his game fresh before him, and came near to the house
175. and place where the deer was indeed, after he had a little inkling that it was a special
friend of his that killed the deer, and then being loth to find the suit, he plucked
back his hound, being in the right way, and appointed him to hunt in another place
where the game was not, and so deceived all them that followed him, as you would
here do to as many as will follow you. For you promise to bring the reader to a
place where he shall find the meaning of this word "corporally;" and when he cometh
to the place where you appoint, the word is spoken of there, but the meaning thereof
is not declared, neither by you nor by Cyril in that place : and so the reader, by
your fair promise, is brought from the place where the game is truly indeed, and
brought to another place w r here he is utterly disappointed of that he sought for.
For where you send the reader to this place of Cyril, " The Son is united as man
corporally unto us by the mystical benediction, spiritually as God" : here indeed in this
sentence Cyril nameth this word "corporally," but he telleth not the meaning thereof,
which you promised the reader that he should find here.
Nevertheless Cyril meaneth no more by these words, but that Christ is united unto
us two manner of ways, by his body and by his Spirit. And he is also a band and
knot to bind and join us to his Father, being knit in nature unto both; to us as a
natural man, and to his Father as natural God, and himself knitting us and God his
Father together.
Cyril, in And although Cyril say that Christ is united unto us corporally by the mystical
fx. cap. 5. benediction, yet in that place the material 1 benediction may well be understand of his
incarnation, which as Cyril and Hilary both call "an high mystery," so was it to us a
marvellous " benediction," that he that was immortal God would become for us a mortal
man > which mystery St Paul saith was " without controversy great," and was hid from
* ne world, and at the last opened, that gentiles should be made partakers of the pro-
rationequa m ises in Christ, which by his flesh came down unto us.
But to give you all the advantage that may be, I will grant for your pleasure,
y "the mystical benediction" Cyril understood the sacrament of Christ s flesh and
blood, as you say, and that Christ is thereby united corporally unto us. Yet saith
not Cyril, that this unity is only when we receive the sacrament, nor extendeth to all
that receive the sacrament, but unto them that, being renewed to a new life, be made
partakers of the divine nature, which nature Cyril himself upon the sixth chapter of
John declareth to be life. But he speaketh not one word of the corporal presence of
Christ in the forms of bread and wine, nor no more cloth Hilary. And therefore I
may well approve that I said, that the answer made unto Hilary will very well also
serve for Cyril. And yet neither of them both hath one word that serveth for your
purpose, that Christ s flesh and blood should be in the sacrament under the forms of
And where you say that Christ uniteth himself to us as man, when he giveth his
body in the sacrament to such as worthily receive it, if you will speak as Cyril and
other old authors used to do, Christ did unite himself to us as man at his incarna
tion. And here again you give evidence against your own issue, affirming our unity
unto Christ no further than we receive the sacrament worthily. And then they that
receive it unworthily be not united corporally unto Christ, nor eat his flesh, nor drink
his blood ; which is the plain mind both of Hilary and also of Cyril, and directly with
the state of my fourth book, and against your answer to the same.
And here you, pretending to declare again what is meant by this word " corporal,"
do tell the negative, that there is " no grossness meant thereby," but the affirmative,
what is meant thereby, you declare not as you promised. But if you mean plainly,
speak plainly, whether Christ s body, being in the sacrament under the forms of bread
and wine, have head, feet, arms, legs, back and belly, eyes, ears and mouth, distinct
and in due order and proportion ? Which if he lack, the simplest man or woman
knoweth that it cannot be a perfect corporal man s body, but rather an imaginative
m natu 1 - 8
[> Mystical, 1551.]
OF THE PRESENCE OF CHRIST. 171
or phantastical body, as Marcion and Valentine taught it to he. Express here fully
and plainly what manner of body you call this corporal body of Christ.
And where you say that 1 " allege Cyril to deny in words the eating of a man,
and to affirm the receiving in this sacrament to be only by faith," and yet it shall
appear by further discussing 2 , say you, that Cyril saith not so : if you had not rubbed
shame out of your forehead, you would not have said that he saith not so, and be
taken with so manifest an untruth. For although you, like a grammarian, ruffle in
your cases, genders, numbers, and persons, and in matters of no learning trouble the
reader to shew yourself learned, corrupting the Greek, Latin, and English, to draw
them to your purpose; yet shall you never prove that Cyril speaketh of any other
eating of Christ, but by faith.
And to make the matter plain, which it seemeth you yet understand not, I shall
shortly rehearse, as well the argument of Nestorius as the answer of Cyril. Nesto- Nestorius.
rius, the heretic, said that Christ was but a pure man, and not God, and that he
had but a common body such as other men have, whereunto the Godhead was only
assistant, as it is to other men. And to prove the same, he alleged Christ s own
words, when he said : " He that eateth my flesh, &c." and "He that eateth me," and "As John vi.
the living Father sent me." And forasmuch as Christ said, that he had flesh, and
was eaten and sent, and God cannot be eaten nor sent, said Nestorius, therefore con
cluded he, that Christ was not God, but man, whose flesh might be eaten and sent :
whose gross argumentation Cyril confuting saith, "that by his rude reasoning of eat
ing, he draweth men s minds wickedly to fancy of the eating of man s flesh, (meaning
of the eating thereof with tooth and mouth,) and so to imagine carnally and grossly
such things of Christ as be understand to be done with an only and pure faith."
And as Nestorius made his argument of the eating of man s flesh, even so did Cyril
make his answer of the eating of the same, and not of the commixtion thereof. For
unto what purpose should commixtion serve in that place, and whereunto should Christ s
body be conmiixted ? Or why should Cyril charge Nestorius with commixtion in Christ,
seeing that he was charged with the clean contrary, as you say, that he separated
the natures in Christ, and did not confound and commixt them ? And furthermore,
the commixtion, they had foughten Andabatarum more, as the proverb saith, "like two
blind men, that when one striketh in one place, the other holdeth up his buckler to 177.
defend in another place." Therefore may all men judge, that have any judgment at
all, how unjustly you judge and condemn that godly and excellent learned man, CEco-
lampadius, for this word dv6p<a7ro<payiav, which you say would be aVfyjtoTro^iyi ai/, which
word in Greek I think was never read, nor hath in that place neither sense nor reason.
And what an heady and intolerable arrogancy is this of you, of your own vain con
jecturing to alter the Greek text without any Greek copy to ground yourself upon,
altering avSpwirofyayiav into dvdptairo/jiiyiav, and tiafieflaiovvrai into Bia/Se/JatoJi/, con
trary to the translations of CEcolampadius and Musculus, not " whispered in corners,"
as you with your railing w r ords w^ould defame the matter, but published abroad to the
world. And at the end you conclude altogether with interrogation, contrary to the
two translations which yourself do allege, being printed, the one at Basil and the other
at Cologne. And you, using such a licence to alter and change all things at your plea
sure, are offended with CEcolampadius for changing of any case, gender, number, verb
or participle, yea, for one tittle or prick of interrogation, which liberty hath ever been
suffered in all interpreters, so they went not from the true sense. But you can spy
a little mote in another man s eye, that cannot see a great block in your own.
Nevertheless, if I should divine without the book, as you do, I would rather think
that Siafieftaiovvrai should be %iaficf3atovTui, (for such small errors in one letter be
easily committed in the printing,) and then concluding with an interrogation, as you
would have it, the sense of the Greek should be this in English : " Doth not Nestorius
affirm, that he who was seen and sent is another Son and Christ beside the Word,
which is God of God ? Doth not he say, that our sacrament is the eating of a man,
unreverently leading faithful minds unto vain and gross imaginations, and going about
= Discussion, 1551.
172 THE THIRD BOOK.
to compass with man s phantasy those things which be received only with a pure and
simple faith ?" Where Cyril in these words reproveth Nestorius, in that lie said that
our sacrament is the eating of a man. Doth not he himself affirm the contrary, that
our sacrament is not the eating of a man, as I said in my book ? For else why
should he reprehend Nestorius for saying the contrary ? And doth not Cyril say also,
that this sacrament " is received only with a pure and simple faith ?" And yet you
find fault with me, because I say that Cyril affirmeth the receiving in this sacrament
to be only by faith ; which your saying being so manifest contrary to Cyril s words,
I refer me to the judgment of all indifferent readers, what trust is to be given to you
in this matter. And as for (Ecolampadius, if the printer in the stead of Trapto-roi/
made irapia-Twv^ and for eiri-^eipov printed eVi^e^toi/, which may soon chance in printing,
then may nvtrTrjpiov be the nominative case, notwithstanding all your vehement in
veighing and vain babbling against (Ecolampadius.
somewhat, saying that "in such as receive the sacrament worthily, Christ dwelleth
corporally, as Cyril saith; and naturally and carnally, as Hilary saith." This is the
third evidence which you give against yourself, signifying that Christ is not corpo
rally in them that receive not the sacrament worthily.
And here you begin to smack of some true understanding, when you say that
178. Christ dwelleth in them that worthily receive the sacrament, so that you would add
thereto, that he dwelleth not only in them when they receive the sacrament, but when
soever by a lively faith they spiritually eat his flesh and drink his blood.
And where you say, that " by the variety of my doctrine it appeareth that I am
not yet determined whither to go," you keep still your old conditions, and shew your
self to be always one man, in this point to charge other men with your own faults.
For whereas my doctrine is throughly uniform and constant, yours is so variable and
uncertain, that you agree with no man, nor with yourself neither, as I intend by
God s grace particularly to set out in the end of my book.
And in these two authors, Hilary and Cyril, you vary three times from your
answer unto my fourth book. For here you say no more, but that Christ is cor
porally in them that receive the sacrament worthily : and in the answer to my fourth
book you say, that he is corporally in all them that receive the sacrament, whether
it be worthily or unworthily.
Now followeth thus in my book.
And h erc ma y be we ^ enou gh passed over Basiiius, Gregorius Nyssenus, and
Gregorius Nazianzenus, partly because they speak little of this matter, and
partly because they may be easily answered unto, by that which is before de
clared and often repeated ; which is, that a figure hath the name of the thing
whereof it is the figure, and therefore of the figure may be spoken the same
thing that may be spoken of the thing itself. And as concerning the eating of
Christ s flesh and drinking of his blood, they spake of the spiritual eating and
drinking thereof by faith, and not of corporal eating and drinking with the
mouth and teeth.
WINCHESTER.
Basiiius, -4* f or Basil, Gregory Nyssen, and Gregory Nazianzen, this author saith they speak
nus 8 Grfo Se ^le of this matter, and indeed they spake 1 not so much as other do; but that they speak
Nazianzenus. j s not discrepant, nor contrarieth not that other afore them had ivritten. For in the old
riusTSer- church the truth of this mystery was never impugned openly and directly that we read of,
ed ai Wineh!] before Berengarius, Jive hundred years past, and secretly by one Bertram before that, but
Messaiiani only by the Messalians, who said the corporal eating did neither good nor hurt. The
Anthropo- Anthropomorphites also, who said the virtue of the mystical benediction endured not to
the next day, of whom Cyril speaketh, and the Nestorians by consecution of their learning,
that divided Christ s flesh from tJie deity. And where this author would have taken for a
true supposal, that Basil, Gregory Nazianzen, and Nyssen, should take the sacrament to be
*Oniy figurative only, that is to be denied. And likewise it is not true that this author teacheth,
[ Speak, Orig. cd. Winch.]
OF THE PRESENCE OF CHRIST.
173
that of the figure may be spoken the same thing that may be spoken of the (him/ itself.
And that I will declare thus. Of the thing /V>r//; th<it /*, Christ? s very body being present
in deed, it may be said, "Adore it, worship it there," which may not be said of tJie figure.
It may be said of tJie very thing being present there, that " it is a high miracle to be there"
" it is above nature to be there," " it is an high secret mystery to be there." But none of
these speeches can be conveniently said of the only figure, that it is such a miracle, so above
nature, so high a mystery to be a figure. And therefore it is no true doctrine to teach,
1 li il we may say the same of the figure, that may be said of tlie thing itself. And where
this author speaketh of the spiritual c>itin<i. <md corporal eating, he remaineth in his ignorance
what the word "corporal" meaneth, which I have opened in discussing of his answer to Cyril.
Faith is required in him that shall eat spiritually, and tlie corporal eating institute in Christ s
supper requireth the reverent use of man s mouth, to receive our Lord s meat and drink, his
own very fiesh and blood, by his omnipotency prepared in that supper, which not spiritually,
that is to say, not innocently 2 (as St Augustine 3 in one place evpoundeth "spiritually") received, >
bringeth judgment and condemnation, according to St Paul s words.
179.
August, in
Joan, tract,
xxvi.
CANTERBURY.
Where you say that " in the old church the truth of this mystery was never im
pugned openly," you say herein very truly ; for the truth which I have set forth, was
openly received and taught of all that were catholic without contradiction, until the
papists devised a contrary doctrine. And I say further, that the untruth which you teach,
was not at that time improved of no man, neither openly nor privily. For how could your
doctrine be impugned in the old church, which was then neither taught nor known ?
And as concerning Bertram, he did not write secretly ; for he was required by Bertram,
king Charles to write in this matter, and wrote therein as the doctrine of the church
was at that time, or else some man would have reprehended him, which never none
did before you, but make mention of his works unto his great praise and commendation.
And the Massalians were not reproved for saying, that "corporal eating doth neither xtessaiiai.i,
good nor hurt," neither of Epiphanius, nor of St Augustine, nor Theodoret, nor of any becurraHtt.
other ancient author that I have read. Marry, that the sacraments do neither good j?H?etu!"
nor hurt, and namely baptism, is laid unto the Massalians charge ; and yet the cor- iJb^vTSj .
poral receiving without the spiritual availeth nothing, but rather hurteth very much, U
as appeared in Judas and Simon Magus. And as for the three heresies of the Mas
salians, Anthropomorphites, and Nestorians 5 , I allow none of them, although you report
them otherwise than either Epiphanius or St Augustine doth.
And where you say that I "would have taken for a supposal, that Basil, Nazianzen,
and Nyssenc should take the sacrament to be figurative only," still you charge me untruly
with that I neither say nor think. For I knowledge, as all good Christian men do,
that Almighty God worketh effectually with his sacraments.
And where you report me to say another untruth, " that of a figure may be spoken
the same thing, that may be spoken of the thing itself," that I say true therein wit-
nesseth plainly St Augustine and Cyprian. And yet I speak not universally, nor
these examples that you bring make anything against my sayings. For the first
example may be said of the figure, if Dr Smith say true. And because you two *smith.
write both against my book, and agree so evil one with another, as it is hard for
untrue sayers to agree in one talc ; therefore in this point I commit you together, to
see which of you is most valiant champion. And as for your other three examples, it
is not true of the thing itself, that Christ s body is present in the sacrament " by miracle
or above nature," although by miracle and above nature he is in the ministration of his
holy supper among them that godly be fed thereat. And thus be your frivolous cavil-
And where you say that I am ignorant what this word, " corporal," meaneth,
[ 2 Innocently, Orig. ed. Winch.]
[ 3 Videte ergo, fratres, panem ccelestem spiri-
taliter manducare, innocentiam ad altare apportare.
Augustin. in Joan. Tractat. xxvi.]
[ 4 i. e. Fisher s (bishop of Rochester) book
against (Ecolampadius, De Veritate Corporis, &c.
Colon. 1527. The title of this 13th chapter is : Ex
esu victimarum veteris legis docemur Christi car-
nem corporaliter edendam esse.]
[ 5 An account of the Messalians, or Euchites,
may be found in Mosheim, Eccles. Hist. Cent. iv.
Chap. V. 24 ; of the Anthropomorphites, ibid.
Cent. x. Chap. V. 4; of the Nestorians, ibid.
Cent. v. Chap. V. 12.]
174 THE THIRD BOOK.
surely then I have a very gross wit, that am ignorant in that thing, which every
180. ploughman knoweth. But you make so fine a construction of this word " corporal,"
that neither you can tell what you mean yourself, nor no man can understand you,
as I have opened before in the discussing of Cyril s mind.
And as for " the reverent use of man s mouth " in the Lord s holy supper, the bread
and wine outwardly must be reverently received with the mouth, because of the things
thereby represented, which by faith be received inwardly in our hearts and minds, and
not eaten with our mouths, as you untruly allege St Paul to say, whose words be of
the eating of the sacramental bread, and not of the body of Christ.
Now followeth next mine answer to Eusebius Emissenus, who is as it were your
chief trust and sheet-anchor.
The answer Likewise Eusebius Emissenus is shortly answered unto : for he speaketh
1S * not of any real and corporal conversion of bread and wine into Christ s body
and blood, nor of any corporal and real eating and drinking of the same ; but
he speaketh of a sacramental conversion of bread and wine, and of a spiritual
eating and drinking of the body and blood. After which sort Christ is as well
present in baptism, as the same Eusebius plainly there declareth, as he is in
the Lord s table : which is not carnally and corporally, but by faith and spiri
tually. But of this author is spoken before more at large in the matter of
transubstantiation.
WINCHESTER.
Emissen. This author saith that Emissen is shortly answered unto, and so is he, if a man care not what
he saith, as Hilary ivas answered and Cyril, But else, there can no short or long answer con
found the true plain testimony of Emissen, for the common true faith of the church in the
sacrament. Which Emissen hath this sentence, " That the invisible priest, (by the secret power
with his word,) turneth the visible creatures into the substance of his body and blood, saying
thus: This is my body ; and again repeating the same sanctification, This is my blood.
Wherefore as at the beck of him commanding the heights of Jieavens, the deepness of the floods,
and largeness of lands were founded of nothing : by like power in spiritual sacraments, where
virtue commandeth, the effect of the truth serveth." These be Emissen s words 1 , declaring his
faith plainly of the sacrament, in such terms as cannot be wrested or writhed, who speaketh.
of a turning and conversion of the visible creatures into the substance of Christ s body and
blood: he saith not into the sacrament of Christ s body and blood, nor figure of Christ s body
and blood, whereby he should mean a only sacramental conversion, as this author would have
it ; but Tie saith, " into the substance of Christ s body and blood [declaring the truth of Christ s
body and blood 2 ] to be in the sacrament." For the words "substance" and "truth" be of one
strength, and shew a difference from a figure, wherein the truth is not in deed present, but signified
to be absent. And because it is a work supernatural, and a great miracle, this Emissen represseth
man s carnal reason, and succoureth the weak faith with remembrance of like power of God in
the creation of this world 3 , which were brought forth out of time by Emissen, if Christ s body
were not in substance present, as Emissen s words be, but in figure only, as this author teacheth.
Only. And where this author coupleth together the two sacraments, of baptism and of the body and blood
of Christ, as though there were no difference in the presence of Christ in either, he putteth himself
in danger to be reproved of malice or ignorance. For although these mysteries be both great,
and man s regeneration in baptism is also a mystery and the secret work of God, and hath
a great marvel in that effect ; yet it differeth from the mystery of the sacrament, touching the
181. manner of Christ s presence, and the working of the effect also. For in baptism our union
with Christ is wrought without the real presence of Christ s humanity, only in the virtue and
effect of Christ s blood, the whole Trinity there working as author, in ivhose name the sacra
ment is expressly ministered, where our soul is regenerate and made spiritual, but not our
body in deed, but in hope only that for the Spirit of Christ dwelling in us our mortal bodies
shall be resuscitate, and as we have in baptism been buried with Christ, so we be assured to
be partakers of his resurrection. And so in this sacrament we be unite to Christ s manhood
by this divinity. But in the sacrament of Christ s body and blood we be in nature united to
Christ as man, and by his glorified flesh made partakers also of his divinity ; which mystical
P Emissen s sayings, Orig. ed. Winch.] [ 3 Of the world, 1551.]
[ 2 Oiig. ed. Winch, inserts this passage.]
OF THE PRESI:\( i: OF CHRIST. 175
union represented unto us the high estate of our glorification, wherein body and soul shall in
tfie general resurrection, by a marvellous regeneration of the body, be made both spiritual,
the special pledge whereof we receive in this sacrament, and therefore it is the sacrament (as
Hilary saith) of perfect unity. And albeit the soul of man be more precious than the body,
and the nature of the Godhead in Christ more excellent than tfte nature of man in him glo
rified, and in baptism man s soul is regenerate in the virtue and effect of Christ s passion and
blood, Christ s Godhead present there without the real presence of his humanity ; although for
tltese respects the excellency of baptism is great ; yet because the mystery of the sacrament of
the altar, where Christ is present both man and God, in the e/ectual unity that is wrought
between our bodies, our souls and Christ s, in the use of this sacrament, signifieth the perfect
redemption of our bodies in the general resurrection, which shall be the end and consummation
of all our felicity. This sacrament of perfect unity is the mystery of our perfect estate, wtien
body and soul shall be all spiritual ; and hath so a degree of excellency, for the dignity that
is esteemed in every end and perfection: wherefore the word "spiritual" is a necessary word Spiritual,
n? tlt.is sacrament, to call it a spiritual food, as it is indeed, for it is to work in our bodies
a, spiritual effect, not only in our souls : and CJirisfs body and flesh is a spiritual body and
flesh 4 , and yet a true body and flesh. And it is present in this sacrament after a spiritual "Spiritual
manner, granted and taught of all true teachers, which we should receive also spiritually, which Spiritually.
is by having Christ before spiritually in us to receive it so worthily. Wherefore, like as in
tltf invisible substance of the sacrament there is nothing carnal but all spiritual, taking the
word "carnal" as it signifieth "grossly" in man s carnal judgment : so where the receivers
of ihat food bring carnal lusts or desires, carnal fancies or imaginations with tliem, they
receive the same precious food unworthily to their judgment and condemnation. For they judge
not truly, after the simplicity of a true Christian faith, of the very presence of Christ s body.
And this sufficeth to wipe out that this autJior hath spoken of Emissen against the truth.
CANTERBURY.
I have BO plainly answered unto Emissen in my former book, partly in this place,
and partly in the second part of my book, that he that readeth over those two places,
shall see most clearly that you have spent a great many of words here in vain, and need
no further answer at all. And I had then such a care what I said, that I said nothing
but according to Emissenus own mind, and which I proved by his own words. But
if you find but one word that in speech soundeth to your purpose, you stick to that
word tooth and nail, caring nothing what the author s meaning is.
And here is one great token of sleight and untruth to be noted in you, that you *A sleight,
write diligently every word so long as they seem to make with you. And when you
come to the very place where Emissen declareth the meaning of his words, there vou
leave all the rest out of your book, which cannot be without a great untruth and
fraud, to deceive the simple reader. For when you have recited these words of Emissen, 182.
" that the invisible priest by the secret power with his word turneth the visible creatures
into the substance of his body and blood," and so further as serveth to your affection,
w^hen you come even to the very place where Emissen declareth these words, there vou
leave and cut off your writing.
But because the reader may know what you have cut off, and thereby know
Emissen s meaning, I shall here rehearse Emissen s words which you have left out. " If
thou wilt know," saith Emissen 5 , "how it ought not to seem to thee a thing new and
[ 4 Orig. ed. Winch, omits the words " is a spi- I effectus. Quanta itaque et quani celebranda bene-
ritual body and flesh."] | ficia vis divinae benedictionis operetur, attende : et
[ 5 Item Eusebius Emisenns, 6. Recedat ergo j ut tibi novum et impossibile videri non debeat,
omne infidelitatis ambiguum : quandoquidem qui
auctor est muneris, ipse etiam testis est veritatis.
Nam invisibilis Sacerdos visibiles creaturas in sub-
stantiam corporis et sanguinis sui verbo suo secreta
potestate convertit, ita dicens, Accipite, et come-
ditc : hoc pfst oi hn corpus meum: et sanctificatione
repetita, Accipite, et bibite : hie est sanyuis metis.
Ergo sicut ad nutum prascipientis Domini repente
ex nihilo substiterunt excelsa coelorum, profunda
fluctuum, vasta terrarum : itapari potestate in spu
ritualibus sacramentis ubi praecipit virtus, servit
quod in Christi substantiam terrena et mortalia
convertuntur, teipsum, qui jam in Christo es re-
generatus, interroga: Dudum alienus a vita, pere-
grinus a misericordia, a salutis via intrinsecus mor-
tuus exulabas : subito initiatus Christi legibus, et
salutaribus mysteriis innovatus, in corpus ecclesiae
non videndo sed credendo transiluisti, et de filio
perdidonis adoptivus Dei filius fieri occulta puritate
meruisti : in mensura visibili permanens, major
factus es teipso invisibiliter, sine quantitatis aug-
mento: cum ipse atque idem esses, nmlto alter fidei
176
THE THIRD BOOK.
Truth.
Only.
183.
Errors.
impossible, that earthly and incorruptible things be turned into the substance of Christ,
look upon thyself which art made new in baptism. When thou wast far from life,
and banished as a stranger from mercy and from the way of salvation, and inwardlv
wast dead, yet suddenly thou begannest another new life in Christ, and wast made new
by wholesome mysteries, and wast turned into the body of the church, not by seeing,
but by believing ; and of the child of damnation, by a secret pureness thou wast made
the son of God. Thou visibly didst remain in the same measure that thou hadst be
fore, but invisibly thou wast made greater, without any increase of thy body. Thou
wast the self same person, and yet by increase of faith thou wast made another man.
Outwardly nothing was added, but all the change was inwardly. And so was man
made the son of Christ, and Christ formed in the mind of man. Therefore as thou,
putting away thy former vileness, didst receive a new dignity, not feeling any change
in thy body; and as the curing of thy disease, the putting away thine infection, the
wiping away of thy filthiness, be not seen with thine eyes, but believed in thy mind ;
so likewise when thou dost go up to the reverend altar to feed upon the spiritual meat,
in thy faith look upon the body and blood of him that is thy God, honour him,
touch him with thy mind, take him in the hand of thy heart, and chiefly drink him
with the draught of thy inward man." These be Emissen s own words. Upon which
words I gather his meaning in his former words by you alleged. For where you
bring in these words, " That Christ by his secret power with his word turneth the
visible creatures into the substance of his body and blood," straightways in these words by
me now rehearsed he sheweth, what manner of turning that is, and after what manner
the earthly and corruptible things be turned into the substance of Christ : " even so,"
saith he, "as it is in baptism," wherein is no transubstantiation. So that I gather his
meaning of his own plain words, and you gather his meaning by your own imagination,
devising such phantastical things as neither Emissen saith, nor yet be catholic.
And this word " truth " you have put unto the words of Emissen, of your own
head, which is no true dealing. For so you may prove what you list, if you may
words, "substance" and "truth," what should that help you? For Christ is in sub
stance and truth present in baptism, as well as he is in the Lord s supper; and yet is
he not there carnally, corporally, and naturally.
I will pass over here, to aggravate the matter, how untruly you add to my words
this word " only," in an hundred places, where I say not so : what true and sincere
dealing this is, let all men judge.
Now as concerning my coupling together of the two sacraments of baptism and
of the body and blood of Christ, Emissen himself coupleth them both together in this
place, and saith that the one is like the other, without putting any difference, even as
I truly recited him. So that there appeareth neither " malice nor ignorance" in me ; but
in you, adding at your pleasure such things as Emissen saith not, to deceive the
appeareth much shift and craft joined with untruth and infidelity.
For what Christian man would say, as you do, that Christ is not indeed, (which you
call " really,") in baptism ? Or that we be not regenerated, both body and soul, as
well in baptism as in the sacrament of the body and blood of Christ ? Or that in
baptism we be not united to Christ s divinity by his manhood ? Or that baptism
representeth not to us the high state of our glorification, and the perfect redemption of
our bodies in the general resurrection ? In which things you make difference between
baptism and the sacrament (as you call it) of the altar. Or what man that were
processibus extitisti : in exterior! nihil additum est,
et totum in interiori mutatum est : ac sic homo
Chiisti films effectus, et Christus in hominis mente
formatus est. Sicut ergo sine corporali sensu, prae-
terita utilitate deposita, subito novam indutus es
dignitatem : et sicut hoc, quod in te Deus Isesa
curavit, infecta diluit, immaculata detersit, non sunt
oculis nee sensibus tuis credita : ita cum reverendum
altare ccelestibus cibis satiandus ascendis, sacrum
Dei tui corpus et sanguinem fide respice, honora,
mirare, mente continge, cordis manu suscipe, et
maxime haustu interiore assume Corpus Juris
Canonici, Tom. I. Decreti tertia pars. " De Con-
secrat." Dist. i. cap. 35. "Quia corpus." col. 192<5-
28. Lugduni. 101H.J
OF THE PRESENCE OF CHRIST. 177
learned in God s word would affirm, that in the general resurrection our bodies and
souls shall be all spiritual ? I know that JSt Paul saith that in the resurrection our Spir.aai.
bodies shall be spiritual, meaning in the respect of such vileness, filthiness, sin, and cor
ruption, as we be subject unto in this mi.serable world : yet he saith not that our
bodies shall be all spiritual. For notwithstanding such spiritualness as St Paul speaketh
of, we shall have all such substantial parts and members as pertain to a very natural
man s body. So that in this part our bodies shall be carnal, corporal, real, and natural
bodies, lacking nothing that belongeth to perfect men s bodies. And in that 1 respect is
the body of Christ also carnal, and not spiritual. And yet we bring none other carnal
imaginations of Christ s body, nor mean none other, but that Christ s body is carnal in
this respect, that it hath the same flesh and natural substance which was born of the
virgin Mary, and wherein he suffered and rose again, and now sittcth at the right hand
of his Father in glory ; and that the same his natural body now glorified hath all the
natural parts of a man s body in order, proportion, and place distinct, as our bodies
shall be in these respects carnal after our resurrection. Which manner of carnalness
and diversity of parts and members if you take away now from Christ in heaven, and
from us after our resurrection, you make Christ now to have no true man s body, but a
fantastical body, as Marcion and Valentine did : and as concerning our bodies, you run
into the error of Origen, which fancied and imagined, that at the resurrection all things
should be so spiritual, that women should be turned into men, and bodies into souls.
And yet it is to be noted by the way, that in your answer here to Emissene, you
make " spiritually" and a " spiritual manner" all one.
Now followeth mine answer to St Ambrose in this wise.
And now I will come to the saying of St Ambrose, which is always in The answer
* m / to Arnbrosms
their mouths. " Before the consecration," saith he 2 , as they allege, " it is e n " a Lib
bread, but after the words of the 3 consecration it is the body of Christ." iv. &i>. 4.
For answer hereunto, it must be first known what consecration is.
Consecration is the separation of any thing from a profane and worldly use consecration,
unto a spiritual and godly use.
And therefore when usual and common water is taken from other uses, and * In iis * f -
feum. n.
put to the use of baptism in the name of the Father, and of the Son, and of the cap - 25
Holy Ghost, then it may rightly be called consecrated water, that is to say,
water put to an holy use.
Even so, when common bread and wine be taken and severed from other
bread and wine to the use of the holy communion, that portion of bread and
wine, although it be of the same substance that the other is from the which it is
severed, yet it is now called consecrated, or holy bread and holy wine.
Not that the bread and wine have or can have any holiness in them, but
that they he used to an holy work, and represent holy and godly things.
And therefore St Dionyse 4 called the bread holy bread, and the cup an holy
cup, as soon as they be set upon the altar to the use of the holy communion. 3 -
But specially they may be called holy and consecrated, when they be sepa
rated to that holy use by Christ s own words 5 , which he spake for that purpose,
saying of the bread, "This is my body," and of the wine, "This is my blood." Sl^ki*
So that commonly the authors, before those words be spoken, do take Lukexx
the bread and wine but as other common bread and wine ; but after those
words be pronounced over them, then they take them for consecrated and
Not that the bread and wine can be partakers of any holiness or godliness,
[> So ed. 1531. In 1580, the.] I Tom. IV. p. 1?3. Colon. Agrip. 1616.]
p Sed panis iste panis est ante verba sacramen- [ 3 Words of consecration, iool, and Orig. ed.]
torum ; ubi accesserit consecratio, de pane tit caro
Christi. Anibros. de Sacramentis, Lib. iv. cap. iv.
[ 4 Vid. supra, p. 151.]
[ 5 Of Christ s own words, 15C1, and Orig. ed.J
[CRAMMER.]
178
THE THIRD BOOK.
De his qui
mysteriis
imtiantur,
cap. ult.
De sacra
mentis, Lib.
v. cap. 4.
De sacra
mentis, Lib.
vi. cap. 1.
or can be the body and blood of Christ, but that they represent the very body
and blood of Christ, and the holy food and nourishment which we have by
him. And so they be called by the names of the body and blood of Christ,
as the sign, token, and figure is called by the name of the very thing which
it sheweth and signifieth.
And therefore as St Ambrose, in the words before cited by the adversaries,
saith, that " before the consecration it is bread, and after the consecration it is
Christ s body," so in other places he doth more plainly set forth his meaning,
saying these words : " Before the benediction of the heavenly words, it is
called another kind of thing ; but after the consecration, is signified the body
of Christ. Likewise before the consecration it is called another thing ; but after
the consecration it is named the blood of Christ 1 ." And again he saith : "When
I treated of the sacraments, I told you that that thing which is offered before the
words of Christ, is called bread ; but when the words of Christ be pronounced,
then it is not called bread, but it is called by the name of Christ s body 2 ."
By which words of St Ambrose it appeareth plainly, that the bread is
called by the name of Christ s body after the consecration ; and although it be
still bread, yet after consecration it is dignified by the name of the tiling which
it representeth : as at length is declared before in the process of transubstan-
tiation, and specially in the words of Theodoretus.
And as the bread is a corporal meat, and corporally eaten, so, saith St
Ambrose 3 , "is the body of Christ a spiritual meat, and spiritually eaten," and
that requireth no corporal presence.
Ambrosius.
"Consecra
tion.
185.
WINCHESTER.
As touching St Ambrose, this author taketh a great enterprise to wrestle with him, whose
plain and evident words must needs be a rule to try his other words by, if any might be
writhed. What can be more plainly spoken than St Ambrose speaketh, when he saith these
words? "It is bread before consecration, but after it is Christ s body 4 ." By the word "con
secration" is signified, as it is here placed, God s omnipotent work. Wherefore in this place
it comprehendeth as much as Emissene said in these words, " he converteth by the secret power
of his word." God is the worker, and so consecration signifieth the whole action of his omni-
potency in working the substance of this high mystery ; and therefore the definition of the word
" consecration" as it is generally taken, cannot be a rule to the understanding of it in this high
mystery, where it is used to express a singular work, as the circumstance of St Ambrose writing
folk declare. For as Philip Melancthon writeth to CEcolampadius, " St Ambrose would never
have travailed to accumulate so many miracles as he doth," speaking of this matter to declare
God s omnipotency, "and he had not thought the nature of bread to be changed in this mystery 5 ."
These be Melancthon s very words. Now to answer the question, as it were, at the word
Sacramental " change," this author shall come with a " sacramental change," which is a device in terms to
blind the rude reader. St Ambrose doth express plainly what the change is when he writeth
the words before rehearsed.
"It is bread before the consecration, but after it is the body of Christ." Can a change be more
plainly declared ? The near & way for this author had been to have joined Ambrose with
Clement, and called him, feigned by the papists, rather than after the effect of consecration so
opened by St Ambrose himself to travail to prove what it may signify, if it were in another
Melancthon.
change.
[* Ante benedictionem verborum ccelestium spe
cies nominatur, post consecrationem corpus Christ!
significatur. Ante consecrationem aliuddicitur, post
consecrationem sanguis nuncupatur. Ambros. de
Initiandis, cap. ult. Tom. IV. p. 16H.]
[ 2 Memini sermonis mei cum de sacramentis
tractarem. Dixi vobis quod ante verba Christi quod
offertur panis dicatur ; ubi Christi verba deprompta
fuerint, jam non panis dicitur, sed Christi corpus
appellatur. Quare ergo in oratione Dominica quae
postea sequitur, ait, Panem nostrum ? Panem qui-
dem dixit, sed e-n-iovcriov, hoc est supersubstantialem.
Id. de Sacramentis, Lib. v. cap. iv. Tom. IV. p. 175.]
[ 3 Id. Lib. vi. cap. i. Tom. IV. p. 176.]
[ 4 The body of Christ. Orig. ed. Winch.]
[ 5 Haec tarn longa recitatio exemplorum clare
ostendit auctorem [h.e. Ambrosium] sensisse, panem
non esse tantum signum, sed naturam panis mutari.
The quotation (as before observed, p. 149), is from
Melancthon s Letter to Myconius, p. 55. of (Eco-
[ Nearer, Orig. ed. Winch.]
OF THE PRESENCE OF CHRIST.
17<)
form of speech not understanded of tlie ptopU <<jendereth sunn 1 tompb that needeth not, being
no sound form of doctrine : for St Paul speaketh and teaclieth thus, that the creatures be sanctified i Tim. iv.
by the word of God and prayer ; and St Augustine writeth of sanctified bread to be given to them ment. et
tliat be catechised before they be baptized : and this author himself expoundeth St Cyprian in the
thirty-fifth leaf 7 of this book, how the divinity is poured into the bread sacramentally, which is
strange phrase ; not expressing there, Cyprian s mind, and far discrepant from tlie doctrine here.
And in anotJier place this author saith, that as liot and burning iron is iron still, and yet
hath the force of fire; so the bread and wine be turned into the virtue of Christ s flesh and
blood. By which similitude bread may conceive virtue, as iron conceiveth fire; and then as
we call iron burning and fiery, so we may call bread virtuous and holy, unless tlie author
would again resemble bread to a wJietstone, that may make sharp and have no sJiarpness in
it at all. WhicJi matter I declare thus to shew, tJiat as tJiis author dissenteth from truth
in other, so he dissenteth from that he uttereth for truth himself, and walketh in a maze, im
pugning the very truth in this sacrament, and would have that taken for a catholic doctrine
that is not one, and tJie same doctrine through this whole book, so far off is it from the wJtole
of Christian teaching. But now let us consider what speeches of St Ambrose this author
bringeth forth, ivherewith to alter the truth of the very plain proper speech of St Ambrose,
saying : " It is bread before the consecration ; and after it is Christ s body 8 ."
St Ambrose, as this author saith in another place, saith thus : " Before tlie benediction of
tlie heavenly words it is called another kind of thing ; but after the consecration is signified
the body and blood of Christ." And anotJier speech tJiu$: "Before the consecration it is called another thing ; but after the consecration it is named the blood of Christ." And yet a third speech, where the word " call " is used before and after both, as tJiou, reader, mayest see in this author s book, in tlie eighty-third leaf. Now, good reader, was there ever man so over seen as this author is, who seeth not St Ambrose in these three latter speeches to speak as plainly as in the first ? For in the last speech St Ambrose saith, it is called bread before the conse cration, and called the body of Christ after tlie consecration. And I would demand of this author, doth not this word "call" signify the truth that is bread in deed before the con secration ? which if it be so, why shall not the same word " call" signify also the very truth added to the words of the body of Christ after the consecration ? And likewise when he saith, speaking of the body of Christ, the word " signified" or " named," which is as much as " call." TJie body of Christ is signified there, for Christ said " This is my body,"$c., using the outward
signs of the visible creatures to signify the body and blood present, and not absent. Was not
Christ the true Son of God, because the angel said, " He shall be called tlie Son of God?" But Luke i.
in these places of St Ambrose, to express plainly what he meant by "calling," lie putteth that 180.
word " call" to the bread before the consecration, as well as to the body of Christ after the
consecration; thereby to declare how in his understanding the word 10 "call" signifieth as much
truth in the thing whereunto it is added after consecration as before ; and therefore as it is
by St Ambrose called bread before consecration, signifying it was so indeed, so it is " called,"
"signified" or "named", (which three thus placed be all one in effect,) the body of Christ after
tlie consecration, and is so in deed, agreeable to the plain speech of St Ambrose, where he saith :
"It is bread before consecration, and it is the body of Christ after consecration." As touching
the spirituality of the meat of CJirist s body I liave spoken before ; but where this author addeth,
" it requireth no corporal presence," he speaketh in his dream, being oppressed with sleep of
ignorance, and cannot tell what " corporal" meaneth, as I have opened before by the authority
of Cyril. Now let us see what this author saith to Chrysostom.
CANTERBURY.
It is not I that wrestle with St Ambrose, but you, who take great pain to wrest
his words clean contrary to his intent and meaning. But where you ask this question,
What can be more plain than these words of St Ambrose, " It is bread before conse- v/hether
cration, and after, it is Christ s body?" these words of St Ambrose be not fully so c5Sl5boci y .
plain as you pretend, but clean contrary. For what can be spoken either more un-
plain or untrue, than to say of bread after consecration, that it is the body of Christ,
unless the same be understand in a figurative speech? For although Christ s body,
as you say, be there after consecration, yet the bread is not his body, nor his body
is not made of it, by your confession. And therefore the saying of St Ambrose, that
it is Christ s body, cannot be true in plain speech. And therefore St Ambrose in the
[ 7 See below, Book 11. chap. 11.] [ Vide supra, p. 178.]
I But after, it is the body of Christ. Grig, ed. [ 10 This word, Grig. ed. Winch.]
\Vinch. I
180
THE THIRD BOOK.
A sacramen
tal change.
187.
Psal. xxxv.
August, de
peccatorum
meritis et
remiss.
Lib. ii. cap.
56.
Cyprianus.
same place, where he calleth it the body and blood of Christ, he saith, it is a figure
of his body and blood. For these be his words : Quod est figura corporis et sanguinis
Domini nostri Jesu Christi.
And as for the word "consecration," I have declared the signification thereof ac
cording to the mind of the old authors, as I will justify.
And for the writing of Melancthon to QEcolampadius, you remain still in your old
error, taking Myconius for QEcolampadius. And yet the change of bread and wine in this
sacrament, which Melancthon speaketh of, is a sacramental change, as the nature of a
sacrament requireth, signifying how wonderfully Almighty God by his omnipotency
worketh in us his lively members, and not in the dead creatures of bread and wine.
And the change is in the use, and not in the elements kept and reserved, wherein
is not the perfection of a sacrament. Therefore, as water in the font or vessel hath
not the reason and nature of a sacrament, but when it is put to the use of christening,
and then it is changed into the proper nature and kind of a sacrament, to signify the
wonderful change which Almighty God by his omnipotency worketh really in them
that be baptized therewith; such is the change of the bread and wine in the Lord s
supper. And therefore, the bread is called Christ s body after consecration, as St Am
brose saith, and yet it is not so really, but sacramentally. For it is neither Christ s
mystical body, (for that is the congregation of the faithful dispersed abroad in the
world,) nor his natural body, (for that is in heaven,) but it is the sacrament both of
his true natural body, and also of his mystical body, and for that consideration hath
the name of his body, as a sacrament or sign may bear the name of the very thing
that is signified and represented thereby.
And as for the foresaid books entitled to St Ambrose, if I joined Ambrose with
Clement, and should say that the said books entitled in the name of St Ambrose, de
sacramentis, et de mysteriis initiandis, were none of his, I should say but as I think,
and as they do think that be men of most excellent learning and judgment, as I de
clared in my second book, which speaketh of transubstantiation. And so doth judge
not only Erasmus, but also Melancthon (whom you allege for authority when he
maketh for your purpose), suspecteth the same. And yet I plainly deny not these
books to be his, (for your pleasure to give you as much advantage as you can ask,)
and yet it availeth you nothing at all.
But here I cannot pass over, that you be offended, because I say, that bread and
wine be called holy, when they be put to an holy use, not that they have any holi
ness in them, or be partakers of any holiness or godliness. I would feign learn of
Smith and you, when the bread and wine be holy. For before they be hallowed or
consecrated, they be not holy by your teaching, but be common baker s bread and
wine of the tavern; and after the consecration, there is neither bread or wine, as
you teach : at what time then should the bread and wine be holy ? But the creatures
of bread and wine be much bound unto you, and can no less do than take you for
their saviour. For if you can make them holy and godly, then shall you glorify
them, and so bring them to eternal bliss. And then you may as well save the true
labouring bullocks, and innocent sheep and lambs, and so understand the prophet,
Homines et jumenta sahabis^ Domine.
But " to admonish the reader," say you, " how the bread and wine have no holiness,
this fortune 1 of speech, not understand of the people, engendereth some scruple that
needeth not." By which your saying I cannot tell what the people may understand,
but that you have a great scruple that you have lost your holy bread. And yet
St Paul speaketh not of your holy bread, as you imagine, being utterly ignorant, as
appeareth, in the scripture; but he speaketh generally of all manner of meats, which
Christian people receive with thanksgiving unto God, whether it be bread, wine, or
water, fish, flesh, white meat, herbs, or what manner of meat and drink so ever it be.
And the sanctified bread, which St Augustine writeth, to be given to them that be
catechised, was not holy in itself, but was called holy for the use and signification.
And I express St Cyprian s mind truly, and not a whit discrepant from my doc
trine here, when I say, that the divinity may be said to be poured, or put sacramen-
Form, 1551.]
OF THE PRESENCE OF CHRIST. 181
tally into the bread ; as the Spirit of God is said to be in the water of baptism, when
it is truly ministered, or in his word when it is sincerely preached, with the Holy
Spirit working mightily in the hearts of the hearers. And yet the water in itself is
but a visible element, nor the preacher s word of itself is but a sound in the air, which
as soon as it is heard, vanisheth away, and hath in itself no holiness at all, although for
the use and ministry thereof it may be called holy. And so likewise may be said of 188.
the sacraments, which, as St Augustine saith, " be as it were God s visible word."
And whereas you rehearse out of my words in another place, that " as hot and Holy bread.
burning iron is iron still, and yet hath the force of fire, so the bread and wine be
turned into the virtue of Christ s flesh and blood :" you neither report my words truly,
nor understand them truly. For I declare, in my book, virtue to be in them that
there to signify might and strength, or force, as I name it, (w T hich in the Greek is
called 3ui/tt|uj<?, after w r hich sense we say, that there is virtue in herbs, in words, and
in stones,) and not to signify virtue in holiness, (which in Greek is called a^er/),
whereof a person is called virtuous, whose faith and conversation is godly. But you
sophistically and fraudulently do of purpose abuse the word "virtue" to another signifi
cation than I meant, to approve by my words your own vain error, that bread should
be virtuous and holy, making in your argument a fallax or craft, called equivocation.
For where my meaning is, that the death of Christ, and the effusion of his blood,
have effect and strength in them that truly receive the sacrament of his flesh and
blood, you turn the matter quite, as though I should say, that the bread were godly
and virtuous; which is a very frantic and ungodly opinion, and nothing pertaining to
mine application of the similitude of iron. But this is the mother of many errors,
both in interpretation of scriptures, and also in understanding of old ancient writers,
when the mind and intent of him that maketh a similitude is not considered, but
the similitude is applied unto other matters than the meaning was. Which fault may
be justly noted in you here, when you reason by the similitude of hot burning iron,
that bread may conceive such virtue as it may be called virtuous and holy. For
my only purpose was by that similitude to teach, that iron, remaining in his proper
nature and substance, by conceiving of fire may work another thing than is the na
ture of iron. And so likewise bread, remaining in his proper nature and substance,
in the ministration of the sacrament, hath another use than to feed the body. For
it is a memorial of Christ s death, that by exercise of our faith our souls may re
ceive the more heavenly food. But this is a strange manner of speech, (which nei
ther scripture, nor approved author ever used before you,) to call the sacramental
bread virtuous, as you do. But into such absurdities men do commonly fall, when
they will of purpose impugn the evident truth.
But " was there ever any man so overseen," say you, " as this author is ? Who
seeth not St Ambrose in these three latter speeches to speak as plainly as in the
first ?" Was there ever any man so destitute of reason, say I, but that he understand-
eth this, that when bread is called bread, it is called by the proper name, as it is Bread is
in deed ; and when bread is called the body of Christ, it taketh the name of a thing, Sl s^-h.
which it is not in deed, but is so called by a figurative speech ? And calling, say chrUt sbody,
you, in the words of Christ signifieth making, which if it signifieth when bread is lj^ec^. ra
your demand, why this word "call" in the one signifieth the truth, and in the other
not: because that the one is a plain speech, and the other a figurative. For else by
your 2 reasoning out of reason, when the cup which Christ used in his last supper was
called a cup, and when it was called Christ s blood, all was one calling, and was of 139.
like truth without figure : so that the cup was Christ s blood in deed.
And likewise when 3 the stone that flowed out water was called a stone, and when Numb. \\.
it was called Christ ; and the ark also when it was called the ark, and when it was j C
called God ; all these must be one speech and of like truth, if it be true which you
here say. But as the ark was an ark, the stone a stone, and bread very bread, and
the cup a cup, plainly without figurative speech ; so when they be called God, Christ,
or x>
] Sam>
[ 2 Our, 1580.] [ 3 When, omitted in 1580.]
182
THE THIRD BOOK.
John i.
Rev. per
totum.
Gen. xlix.
Rev. v.
John x. xiv.
John xii.
Corporal.
to Chrysosto-
inus.
190.
In Sermone
de eucha-
ristia in
Encieniis.
De Prodi-
tione Judsc.
the body and blood of Christ, this cannot be a like calling, but must needs be under
stand by a figurative speech. For as Christ in the scripture is called a lamb for his
innocency and meekness, a lion for his might and power, a door and way, whereby
we enter into his Father s house, wheat and corn for the property of dying before
they rise up and bring increase ; so is he called bread, and bread is called his body,
and wine his blood, for the property 1 of feeding and nourishing. So that these and
all like speeches, (where as one substance is called by the name of another substance
diverse and distinct in nature,) must needs be understand figuratively by some simili
tude or propriety of one substance unto another, and can in no wise be understand
properly and plainly without a figure. And therefore, when Christ is called the Son
of God, or bread is called bread, it is a most plain and proper speech; but when
Christ is called bread, or bread is called Christ, these can in no wise be formal and
proper speeches, (the substances and natures of them being so diverse,) but must needs
have an understanding in figure, signification or similitude, (as the very nature of all sa
craments require,) as all the old writers do plainly teach. And therefore the bread
after consecration is not called Christ s body, because it is so in deed; for then it
were no figurative speech, as all the old authors say it is.
And as for this word "corporal," you openly confessed your own ignorance in the
open audience of all the people at Lambeth : when I asked you, what corporal body
Christ hath in the sacrament, and whether he had distinction of members or no, your
answer was in effect that you could not tell. And yet was that a wiser saying than
you spake before in Cyril, where you said, that Christ hath only a spiritual body
and a spiritual presence, and now you say, he hath a corporal presence. And so
you confound corporal and spiritual, as if you knew not what either of them meant,
or wist not, or cared not what you said. But now I will return to my book, and
rehearse mine answer unto St John Chrysostom, which is this.
Now let us examine St John Chrysostom, who in sound of words maketh
most for the adversaries of the truth ; but they that be familiar and acquainted
with Chrysostom s manner of speaking, (how in all his writings he is full of
allusions, schemes, tropes, and figures,) shall soon perceive that he helpeth
nothing their purposes, as it shall well appear by the discussing of those places
which the papists do allege of him, which be specially two. One is In Sermone
de Eucharistia in Encceniis, and the other is De proditione Judce.
And as touching the first, no man can speak more plainly against them than
St John Chrysostom speaketh in that sermon. Wherefore it is to be wondered
why they should allege him for their party, unless they be so blind in their
opinion that they can see nothing, nor discern what maketh for them, nor what
against them. For there he hath these words : " When you come to these
mysteries," speaking of the Lord s board and holy communion, "do not think that
you receive by a man the body of God 2 / meaning of Christ. These be St John
Chrysostom s own words in that place.
Then if we receive not the body of Christ at the hands of a man, ergo, the
body of Christ is not really, corporally, and naturally in the sacrament, and so
given to us by the priest. And then it followeth that all the papists be liars,
because they feign and teach the contrary.
But in 3 this place of St Chrysostom is touched before more at length in
Wherefore now shall be answered the other place which they allege of
Chrysostom in these words 4 : " Here he is present in the sacrament and doth
[* Propriety, 1551.]
[ 2 Ato /cat Trpocrepyofjievoi fu] o>s e dvBpwTrov vo-
e fj.eTa.\a/uLftdve iv TOV 6etou trto /iaTos. Chrysost.
In sermone de eucharistia in Encaeniis. (Ed. Be-
ned. de Pcenitentia.) Horn. ix. Tom. II. p. 35<5,J
f 3 But this place, 1551, and Grig, ed.]
T 4 Tldpecrnv 6 Xpj<rro?. Kai vvv e/ceij/os o Tnu
rpaTre^av <$ta/co<r/irj<ras e/cet i/jj/, OUTOS /cat TOUTJJV diaKoa-fjLel vvv. ovoe yap dvQpurtros ewriv 6 TTOLWV TO. TrpoKcifJieva yevevdai <ruj/xa /cat aljua X/otcrrot; a XX airros 6 <TTau/>a>06ts inrep i]p.iav X/OKTTOS. \i]p(jav earT^Kev 6 te/oei/s, -ra /otj /xara <0ey- c/celi/a 1} de cvvanis /cat j X U / S T0 ^ e u eem. TOVTO uou to"ri TO awua, (hij<rt. TOVTO TO OF THE PRESENCE OF CHRIST. 183 consecrate, which garnished the table at the maundy or last supper. For it is not man which maketh of the bread and wine, being set forth to be consecrated, the body and blood of Christ; but it is Christ himself, which for us is crucified, that maketh himself to be there present. The words are uttered and pronounced by the mouth of the priest, but the consecration is by the virtue, might, and grace of God himself. And as this saying of God, Increase, be Gen. i. multiplied, and fill the earth, once spoken by God, took always effect toward generation ; even so the saying of Christ, This is my body, being but once Matt. xxvi. spoken, doth throughout all churches to this present, and shall to his last Luke xxii - coining, give force and strength to this sacrifice." Thus far they rehearse of Chrysostom s words. Which words, although they sound much for the purpose 5 , yet if they be throughly considered and con ferred with other places of the same author, it shall well appear that he meant nothing less than that Christ s body should be corporally and naturally present in the bread and wine, but that in such sort he is in heaven only ; and in our minds by faith we ascend up into heaven, to eat him there, although sacra- mentally, as in a sign and figure, he be in the bread and wine, (and so is ho also in the water of baptism;) and in them that rightly receive the bread and wine he is in a much more perfection than corporally, (which should avail them nothing,) but in them he is spiritually with his divine power, giving them eternal life. And as in the first creation of the world all living creatures had their first life by God^s only word, (for God only spake his word, and all things were created by and by accordingly,) and after their creation he spake these words, " Increase and multiply ;" and by the virtue of those words all things have Gen. i. gendered and increased ever since that time; even so after that Christ said, Matt. xxvi. " Eat, this is my body;" and "Drink, this is my blood: do this hereafter inLukexxYi. remembrance of me ;" by virtue of these words, and not by virtue of any man, the bread and wine be so consecrated, that whosoever with a lively faith doth eat that bread and drink that wine, doth spiritually eat, drink, and feed upon Christ sitting in heaven with his Father. And this is the whole meaning of St Chrysostom. And therefore doth he so often say that we receive Christ in baptism. And when he hath spoken of the receiving of lu m in the holy communion, by and by he speaketh of the receiving of him in baptism, without declaring any diversity of his presence in the one from his presence in the other. He saith also in many places, that "We ascend into heaven, and do eat Ad Popuiu Christ sitting there above." And where St Chrysostom and other authors do numHL. speak of the wonderful operation of God in his sacraments, passing all man s hannem. J( wit, senses, and reason, they mean not of the working of God in the water, IQI. bread, and wine, but of the marvellous working of God in the hearts of them that receive the sacraments ; secretly, inwardly, and spiritually transforming them, re newing, feeding, comforting, and nourishing them with his flesh and blood, through his most holy Spirit, the same flesh and blood still remaining in heaven. Thus is this place of Chrysostom sufficiently answered unto. And if any man require any more, then let him look what is recited of the same author before, in the matter of transubstantiation. prjp.a Lillet TCC irpOKeifjieva. Kal KaQdirep ij (pwvtj t-Keivrj tj \eyovcra, Ai>at/eo - 0e, Kai TT/\TJ- Ouj/eo-Oe, /cat TrXrjyowo-aTe TTJI; y^v, eppedij p.tv aVa, 5ta irai/Tos 5e TOU yj)6vov ylveTai epyui evdvva/mov<ra KUL 17 (jxavi] av-rri a.Tra]~ Xcx0ei<ra Ara6 /cao-rt;i/ TpaTre^av ev rats e/CK\r;<rtat9, t CKC IVOV tnj/j.epov, Kal MC X/K T^S OUTOU Trapovaiav, TTJV Qua-iav dirripTia-fjLevtji epyd^CTai. Chrysostom. de Proditione Judae, Horn. i. Tom. II. p. 384. Ed. Bened.J [ 5 For their purpose, 1551, and Orig. ed.] 184 THE THIRD BOOK. WINCHESTER. chrysostom. This author noteth in Chrysostom two places, and bringeth them forth, : and in handling the first place, declareth himself to trifle in so great a matter, evidently to his own reproof. For where, in the second book of his work, entreating transubstantiation, he would the same ivords of Chrysostom, by this form of speech in the negative, should not deny precisely ; and when Chrysostom saith, "Do not think that you by man receive the body of God, but that tve should not consider man in the receiving of it;" here this author doth allege these words, and reasoneth of them as though they were terms of mere denial. But I would ask of this author this question : If Chrysostom s faith had been, that we receive not the body of God in the sacrament verily, why should he use words idly to entreat of whom we received the body of God, which after this author s doctrine we receive not at all, but in figure ; and no body at all, which is of CJirist s humanity, being Christ, as this author teacheth, spiritually, that is, by his divine nature in him only that worthily receiveth, and in the very sacrament, as he con- cludeth in this book, only figuratively. Turn back, reader, to tlie thirty-sixth leaf in the author s book, and read it with this, and so consider upon what principle here is made an ergo. / will answer that place when I speak of transubstantiation, which shall be after answered to the third and fourth book, as the natural order of the matter requireth. Tlie second place of Chrysostom that this author bringeth forth, he granteth it soundeth much against him, and favoureth his adversaries, but with conferring and considering he trusteth to alter it from the true understanding. And not to expound, but confound the matter, he joineth in speech the sacrament of baptism with this sacrament, (which shift this author used untruly in Hilary,} and would now bear in hand, that the presence of Christ were none otherwise in this sacrament than in baptism, which is not so; for in this sa crament Christ s humanity and Godhead is really present, and in baptism his Godhead with the effectual virtue of his blood, in which we be washed, not requiring by scripture any real presence thereof for dispensation of that mystery, as I have before touched discussing chrysost.de the answer to Emissene 1 ; whereas Chrysostom speaking of this sacrament, whereof I have be- iu. cer fore spoken, and Melancthon alleging it to (Ecolampadius, saith thus : " The great miracle and great benevolence of Christ is, that he sitteth above with his Father, and is the same hour in our hands Jiere to be embraced of us." And therefore, where this author would note the wonder of God s work in the sacrament to be wonderful for the work and effect in man, this is one piece of truth; but in the sacrament of the body and blood of Christ, the old fathers wonder at the work in the sacrament, how bread is changed into the body of Christ, how Christ sitting in heaven, God and man, is also man and God in the sacrament, and being worthily received, dwelleth in such carnally and naturally, as Hilary saith, and corporally, as Cyril saith. How this can be no man can tell, no faithful man should ask; and yet it is the true catholic faith to be truly so wrought. For, as Emissene saith : " he An issue. that is the author of it, he is the witness of it." And therefore 1 will make it an issue with this author, that the old fathers, speaking of the wonderful operation of God in this sacrament, refer it not only to the virtue and effect of this sacrament, nor to the virtue specially, but chiefly to the operation of God in the substance of this sacrament, and the in Joan. sacrament self; for such a difference St Augustine maketh, saying : Aliud est sacramentum, ractat. 2fi. a |j u( j v j r ^ us gacramenti, " The sacrament is one, the virtue of the sacrament is another." Finally, in answering to Chrysostom, this author doth nothing but spend words in vain, to tlie more plain declaration of his own ignorance, or worse. CANTERBURY. As concerning Chrysostom, you have spent so many taunting and scornful words in waste, without cause, that I need to waste no words here at all to make you answer: but refer the reader to my book, the twenty-fifth leaf and thirty-sixth leaf, and to the thirty-second, thirty-third, and thirty-fourth leaf, where the reader shall find all that is here spoken fully answered unto 2 . Christ is But always you be like yourself, proceeding in amplification of an argument against tiv y present me, which you have forged yourself, and charge me therewith untruly. For I use not d this speech, that we receive not the body of God at all, that we receive it but in a figure. For it is my constant faith and belief, that we receive Christ in the sacra- f 1 Of Emissene, Orig. ed. Winch.] i second book "Of the Error of Transubstantiation," [ 2 All these references are to passages in the I as well as those alluded to above by Winchester.] OF THE PRESENCE OF CHRIST. 185 mcnt verily and truly; and this is plainly taught and set forth in my book. But that "verily" as I with Chrysostom and all the old authors take it, is not of such a sort as you would have it. For your understanding of " verily" is so Capernaical, so Vcriiy. gross, and so dull in the perceiving of this mystery, that you think a man cannot re ceive the body of Christ verily, unless he take him corporally in his corporal mouth, flesh, blood, and bones, as he was born of the virgin Mary. But it is certain, that Chrysostom meant not, that we receive Christ s body verily after such a sort, when he saith, "Do not think that you receive by a man the body of God." And yet, because I deny only this gross understanding, you misreport my doctrine, that I should say, we " receive not Christ at all, but in a figure, and no body at all :" wherein you untruly and slanderously report me, as my whole book and doctrine can witness against you. For my doctrine is, that the very body of Christ, which was born of the virgin Mary, and suffered for our sins, giving us life by his death, the same Jesus, as con cerning his corporal presence, is taken from us, and sitteth at the right hand of his Father; and yet is he by faith spiritually present with us, and is our spiritual food and nourishment, and sitteth in the midst of all them that be gathered together in his name. And this feeding is a spiritual feeding, and an heavenly feeding, far pass ing all corporal and carnal feeding; and therefore there is a true presence and a true feeding in deed, and not " in a figure only, or not at all," as you most untruly report my saying to be. This is the true understanding of the true presence, receiving and feeding upon the body and blood of our Saviour Christ, and not, as you deprave the meaning and true sense thereof, that the receiving of Christ truly and verily is the receiving corporally with the mouth corporal 3 , or that the spiritual receiving is to re ceive Christ only by his divine nature, which thing I never said nor meant. Turn, I pray thee, gentle reader, to the thirty-sixth leaf of my book, and note these words there, which I allege out of Chrysostom. " Do not think," saith he, " that you receive by a man the body of God." Then turn over the leaf, and in the twentieth line, note again my saying that, " in the holy communion Christ himself is spiritually eaten and drunken, and nourisheth the right believers." Then compare those sayings with this place of this ignorant lawyer, and thou shalt evidently perceive, that either he will not, 193. or cannot, or at the least he doth not understand what is meant in the book of common prayer, and in my book also, by the receiving and feeding upon Christ spiritually. But it is no marvel, that Nicodemus and the Capernaites understand not Christ, before they be born anew, and forsaking their papistical leaven, have learned another lesson of the Spirit of God, than flesh and blood can teach them. Much talk the pa pists make about this belief, that we must believe and have a stedfast faith, that Christ s body is corporally there, where the visible forms of bread and wine be: of which belief is no mention made in the whole scripture, which teacheth us to believe and profess, that Christ (as concerning his bodily presence) hath forsaken the world, and is ascended into heaven, and shall not come again until the restitution of all things that be spoken of by prophets. But whereas, in the feeding upon Christ s body and drinking of his blood, there is no mouth and teeth can serve, but only the inward and spiritual mouth of faith, there the papists keep silence like monks, and speak very little. And the cause why, is flesh and blood, which so blindeth all the Nicodemes and Capernaitcs, that they cannot understand what is spiritual nativity, spiritual circumcision, spiritual hunger and thirst, and spiritual eating and drinking of the fle.sli and blood of our Saviour Christ : but they hang all together so in the letter, that they cannot enter into the kingdom of the spirit ; which knowledge if that you had, you should soon perceive upon what principle my ergo were made. And where The order of you pervert the order of the books, setting the cart before the horse, that is to say, thc book> the third and fourth book before the second, saying that the natural order of the matter so requireth, here the reader may note an evident mark of all subtle papists, which is under the pretence and colour of order to break that order, whereby the falsehead of their doctrine should best be detected, and the truth brought to light. For when they perceive a window open, whereby the light may shine in, and the [ 3 Corporal mouth, lool.J 186 THE THIRD BOOK. 194. Chrysosto- nms. Dard. truth appear, then they busily go about to shut that window, and to draw the reader from that place to some mystical and obscure matter where more darkness is, and less light can be seen. And when, besides the darkness of the matter, they have by their subtle sophistry cast such a mist over the reader s eyes, that he is become blind, then dare they make him judge, be the matter never so untrue. And no marvel, for he is now become so blindfold and subject unto them, that he must say whatsoever they bid him, be it never so much repugnant to the evident truth. In such sort it is in the matter of the sacrament. For the papists perceiving that their error should easily be espied, if the matter of transubstantiation were first determined, the plain words of the scripture, the consent of ancient writers, the articles of our faith, the nature of a sacrament, reason, and all senses making so evidently against it, there fore none of the subtle papists will be glad to talk of transubstantiation, but they will always bear men in hand, that other matters must first be examined, as the late bishop doth here in this place. Now, in the second place of Chrysostom, where you say, that " in this sacrament Christ s humanity and Godhead is really present, and in baptism his Godhead with the effectual virtue of his blood, in which we be washed, not requiring by scripture any real presence thereof for the dispensation of that mystery," in this matter I have joined an issue with you before in the answer unto Origen, which shall suffice for answer here also. And where St John Chrysostom speaketh of " the great miracle of Christ, that he sitteth above with his Father, and is the same hour here with us in our hands," truth it is, that Christ sitteth above with his Father in his natural body, triumphant in glory, and yet is the same hour in our hands sacramentally, and present in our hearts by grace and spiritual nourishment. But that we should not think, that he is cor- August. ad porally here with us, St Augustine 1 giveth a rule in his epistle ad Dardanum, say ing: Cavendum est ne ita divinitatem astruamus hominis, ut veritatem corporis aufera- mus : "We must foresee that we do not so affirm the divinity of him that is man, that we should thereby take away the truth of his body." And forasmuch as it is against the nature and truth of a natural body to be in two places at one time, therefore you seem to speak against the truth of Christ s natural body, when yon teach that his body is in heaven naturally, and also naturally in the sacrament. For whosoever affirmeth that Christ s body is in sundry places as his Godhead is, seemeth August, ad to deify Christ s body by St Augustine s rule. But like as it is not to be thought, that Quicquid est in Deo, est putandum ubique ut Deus, " that whatsoever is in God, is every where as God is;" so must we not think that his body may be at one time every where, where his Godhead is. But Christ is, saith Augustine, Ubique per id quod est Deus, in ccelo autem per id quod est homo; "Every where in that he is God, but in heaven in that he is man." Wherefore his presence here of his body must be a sacramental presence ; and the presence of his divinity, of his grace, of his truth, of his majesty and power, is real and effectual in many places, according to his word. Now, as concerning your issue, I refuse it not, but say, that the great miracle whereat the Jews wondered, and which our Saviour Christ meant, and the old fathers speak of, is of the eating of Christ s flesh and drinking of his blood, and how by flesh and blood we have everlasting life. Now, if you can bring good testimony for you, that the sacrament eateth Christ s flesh and drinketh his blood, and that it shall live for ever, which never had life, and that God s operation and work is more in dumb creatures than in man, then I must needs and will confess the issue to pass with you. And when I hear your testimonies, I shall make answer; but before I hear them, I should do nothing else but spend words in vain, and beat the wind to no purpose. Now hear what I have answered to Theophilus Alexandrinus. The answer Yet furthermore, they bring for them Theophilus Alexandrinus, who, as In&xiv" 8 they allege, saith thus 2 : " Christ giving thanks, did break, which also we do, Dard. Wherein is the miracle. [* August, ad Dardanum. Pars vin. cap. iii.iv. Basil, ap. Amerbach. 1506.] vr TOV Xacre TOV ap-rov. oirep /cat jj/uets iroiovp.ev, eTTiXeyovres. TOVTO CCTTI TO crw/nd uou, TOVTO o vvu Xa/x/3a veT. ov yap dvri-rvirot TOV Kvptanov OF THE PRESENCE OF CHRIST. 187 adding thereto prayer. And ho gave unto them, saying, Take, this is my body ; this that I do now give, and that which ye now do take. For the bread is not a figure only of Christ s body, but it is changed into the very body of Christ. For Christ saith : The bread which I will give you is my flesh. 1 John vi. Nevertheless the flesh of Christ is not seen for our weakness, but bread and wine arc familiar unto us. And surely if we should visibly see flesh and blood, we could not abide it. And therefore our Lord, bearing with our weakness, doth retain and keep the form and appearance of bread and wine, but he doth turn the very bread and wine into the very flesh and blood of Christ." These be the words which the papists do cite out of Theophilus upon the ] ( J5. gospel of St Mark. But by this one place it appearcth evidently, either how negligent the papists be in searching out and examining the sayings of the authors, which they allege for their purpose, or else how false and deceitful they be, which willingly and wittingly have made in this one place, and as it were with one breath, two loud and shameful lies. The first is, that because they would give the more authority to the words by them alleged, they (like false apothecaries that sell quid pro quo) falsify the author s name, fathering such sayings upon Theophilus Alexandrinus 3 , an old and ancient author, which were indeed none of his words, but were the words of Theophylactus, who was many years after Theophilus Alexandrinus. But such hath ever been the papistical subtilties, to set forth their own inventions, dreams, and lies, under the name of antiquity and ancient authors. The second he or falsehood is, that they falsify the author s words and meaning, subverting the truth of his doctrine. For where Theophylactus, (accord ing to the catholic doctrine of ancient authors,) saith, that " almighty God, condescending to our infirmity, reserveth the kind of bread and wine, and yet turncth them into the virtue of Christ s flesh and blood ;" they say, that " he reserveth the forms and appearances of bread and wine, and turneth them into the verity of his flesh and blood ;" so turning and altering kinds into forms and appearances, and virtue into verity, that of the virtue of the flesh and blood they make the verity of his flesh and blood. And thus they have falsified as well the name as the words of Theophylactus, turning verity into plain and flat falsity. But to set forth plainly the meaning of Theophylactus in this matter. As hot and burning iron is iron still, and yet hath the force of fire ; and as the flesh of Christ still remaining flesh giveth life as the flesh of him that is God ; so the sacramental bread and wine remain still in their proper kinds, and yet to them that worthily eat and drink them they be turned not into the corporal presence, but into the virtue of Christ s flesh and blood. And although Theophylactus spake of the eating of the very body of Christ, and the drinking of his very blood, (and not only 4 of the figures of them,) and of the conversion of the bread and wine into the body and blood of Christ; yet he mcancth not of a gross, carnal, corporal and sensible conversion of the bread o O/OTOS aXX eis avTO e/cetvo TO cruj/ma TOV XpicrTou. Kcti o Kuptos yap Xeyei* o C/OTO? vv t-yaJ 6cu<ra>, j <rdp P.OV CO-T/J;. OVK elirej/, at/Trri/Tros ca-rt TT/S o-a/o/co s pov, aXX ; <rdp /mov ecrri Kai TTWS </>rj<rti/, ov yap o"a/o jcaOopa-rai ; did TI}V i}/JLTepav, a> dv- Qpojire, darOeveiav. eireidt] yap o fiev C/OTOS Kai o olj/os awqtft; jf/iij/, afyia oe TrpoKtifJievov Kai <rdpKa 6pu>m-es, OVK av jj i/eyK-a/nei/, aXX direvap- Ki](rafj.fv, td TOVTO crvyHaraaivwv i;iTv o 1- \dv6pwjros TO fj.ev eI<$O9 dp-rov Kai olvov <pv\aT-
Tfij eis dvva/j.iv 3e <ra/o/cos Kai ai /zaTos /ueTa-
(TTOL^fio i Theoph. in Marcum, cap. xiv. Tom. I.
p. 249. Ed. Venet. 1754.]
[ 3 Theophilus was Patriarch of Alexandria, A.D.
385. Theophylact was Archbishop of Bulgaria, A.D.
10/1. His Commentaries on the Gospels were ge
nerally supposed to be compiled from Chrysostom
and other of the fathers. Vid. Cave Hist. Lit. &c.J
[ 4 One, 1551 ; Orig. ed. reads with ed. 1580.]
188
THE THIRD BOOK.
and wine, nor of a like eating and drinking of his flesh and blood, (for so not
only our stomachs would yearn, and our hearts abhor to eat his flesh and to
drink his blood, but also such eating and drinking could nothing profit or avail
us ;) but he spake of the celestial and spiritual eating of Christ, and of a sacra
mental conversion of the bread, calling the bread not only a figure, but also the
body of Christ, giving us by these words 1 to understand, that in the sacrament
we do not only eat corporally the bread, (which is a sacrament and figure of
Christ s body,) but spiritually we eat also his very body, and drink his very
blood. And this doctrine of Theophylactus is both true, godly and comfortable.
WINCHESTER.
100.
Thcophyiact.
An issue.
Now followeth, as it is entitled, Theophylact, being the words in deed not of Tlieophylact,
as he writeth upon Mark, and therefore they were not alleged as his words, but as the words
of Theophilus Alexandrinus, wherein this author traverseth a falsehood on the alleger s part
to wrong name tlie author. In which allegation, I say, if there be a fault, as I know none,
it is no lie, but a probable error for a man to believe another better learned than himself;
and as I found it alleged I reported it again, so as having mine author learned whom I
followed, I am discharged of malice, being the author such whom I followed, as might pos
sibly have had such a work of Theophilus, containing those words as thev be alleged, the
negative whereof how this author should prove I cannot tell, because of the common saying,
Bernardus non vidit omnia ; and therefore, there may be a Theophilus Alexandrinus having
these words alleged in their form, for any demonstration this author can make to the con
trary. Whether there be or no any such to be shewed, it is not material, being so many testi
monies besides. As for Theophylact s words, I grant they be not, for he wrote his mind
more plainly in another place of his works, as I shall hereafter shew, and by the way make
an issue with this author, that no catholic writer among the Greeks hath more plainly set forth
the truth of the presence of Christ s body in tlie sacrament, than Theophylact hath; as shall
appear by and by, after I have noted to the reader this, how CEcolampadius of Germany,
SbyffiS?" about a two year before he impugned the truth of Christ s presence in the sacrament, he
lampadms. translated out of Greek into Latin the works of the said Theophylact, and gave the Latin
church thereby some weapon wherewith to destroy his wicked folly afterward, not unlike
the chance in this author, translating into English, two years by-past, the catechism of
Germany : and as CEcolampadius hath since his folly or madness against the sacrament
confessed, (as appeareth,) that he did translate Theophylact, so as we need not doubt of
it; so this author hath now in this work confessed the translation of the catechism, which
one in communication would needs have made me believe had been his man s doing, and
not his. Hear now, reader, liow plainly Theophylact speaketh upon the Gospel of St John,
expounding the sixth chapter 2 :
*Theophy- " Take heed that tlie bread which is eaten of us in the mysteries, is not only a certain
lact s words. ^ urai ^ n O f t j te jfogfo O f our Lord, but the Jlesh itself of our Lord; for lie said not, The
bread which I shall give is the Jigure of my Jlesh, but it is my Jlesh. For that bread, by
the mystical benediction, is transformed by the mystical words and presence of the Holy
Ghost into tJie Jlesh of our Lord. And it should trouble no man, that the bread is to be
believed Jlesh : for whilst our Lord walked in Jlesh and received nourishment of bread, that
bread he did eat was changed into his body, and was made like to his holy Jlesh ; and as
it is customably in man s feeding served to the sustentation and increase of it, therefore the
P Giving us those words, Orig. ed. Giving us
by those words, 1551.]
[ 2 Upo^X" oe on o apTos 6 ev TOIS /xucrr^ptots
v<p jj/jiwv ecrtftd/xei os ou/c dvTLTVTrov eerrt TT;? TOV
Kvplov trap/cos, a XX auT?j jj TOV Kvpiov <rdp.
ou yap elirev, on o apTos ov eyta 6a> (ra>, dvn-
TVTTOV can TT/S <rap/co s /uou, dXX j <rap /tzou
etrrt. /neTaTTOteiTat yap aVopp ijTois Xo yots o
apTos OUTOS out TTJS /j.vcrTiKri S eOXoyias, /cat CTTI-
e/>orrr)crea)S TOV dyiov Tri/eu/xaToe, et s cra p/ca TOV
Kvpiov. Kai /x| Tiva 6poerra> TO TOV dpTov <ra p/ca
TTio-Teueo-tiai, al yap TOI /cat ev crap/ci TreptTra-
TOVVTO-S TOV Kvp lOV, KUl T\\V ( UpTOV TpO(pl)v
Trpo&ie/jievov, o ap-ros e/ceii/os 6 eo-flto/xei/os ets aw/xa
avTov /xe-re/SaXXeTo, /cat <rvveu>[jioiovTo TIJ dyia
avTOv trap/a, /cat cts av^jjcnv Kai <ru<TTacriv crvve-
/Sa XXeTo /caxa TO dvQpwirivov hat vvv ouj/ 6 a pTos
eis <ra p/ca TOU Kup/ou p.6Taj3d\\eTaL. /cat Trais
(j)t](riv, ou^t /cat crap^ (fiaiveTai i ]/uuv, a XX a pTos j
did TO fjin i}u.d<s a fj6tecrt)at Trpos Tijjy fip(oaiv. ei
yuei> yap <ra p e</>aueTo, a t}3aJs dv oiexei/jieQa Trpos
TTJV ^ueTa Xrji|/ tj/, vvv oe TJJ jj/xeTepa doQeveia <rvy-
KaTafBalvovTos TOV Kuptou TotauTrj (puivfTai i i/juv
rj /txvo-Tt/ctj /Spaxrts, ot a eanv t] o-ui/;0tjs jj/xtf.
Theoph. in Joannem. cap. vi. Tom. I. p. 5U4.
Ed. Venet. 1J54.J
OF THE PRESENCE OF CHRIST. 189
bread now also is changed into the flesh of our Lord. And how is it then that it ap-
peareth not flesh but bread? That we should not loathe the eating of it; for if flesh did
appear, we should be unpleasantly disposed to the communion of it. Now our Lord conde
scending to our infirmity, the mystical meat appear eth such to us, as those we have been
accustomed unto." Hitherto I have faithfully expressed Tlieophylact s words out of Latin
of (Ecolampadius translation, without terming the substantial points otlierwise than the words
purport in Latin. By which may appear what was Theophylact & meaning, what doctrine
he giveth of the sacrament, and how his own words upon St Mark be to be understanded,
when he saith, Speciom quidem panis et vini servat, in virtutem autcm carnis et sanguinis
transelementat : in corrupting of which words this author maketh a great matter, when tliey \\-j t 1 .[.{[. ^
were not alleged for his; but as they be hi*, servarc spccicm may be well translate "form and
appearance," because upon St John, before alleged, he saith of the bread, "it appeareth."
And as for these words, " the virtue of Christ s flesh and blood," must be understanded to
agree with the plain place of Theophylact upon St John, and upon St Mark also, to signify not
only virtue, but verity of the flesh and blood of Christ. For if Tlieophylact by that speech meant
"the virtue of the body of Christ," and not tlie "verity of the very body" as this author saith
he did, why should Theophylact, both upon St Mark, and also upon St John, ask this question,
" Why doth not the flesh appear f " if himself by those words should teach there were only
present the virtue of the flesh ; who, and he had meant so, would not have asked the question ; j gg
or if he had, would have answered it thus accordingly, " There is no flesh in deed, but the
virtue of the flesh" and that had been a plain answer and such as he would have made. This
author will ask then, Wliy doth Theophylact use this phrase to say, " changed into the virtue
of tlie body of Christ?" Hereunto I answer, that this word "virtue" in phrase of speech
many times only fllleth the speech, and is comprehended in the signification of his genitive
following; and therefore, as Luke in the twenty-second chapter saith, a dextris virtutis Dei,
so in the Acts in the same sentence 3 is spoken a dextris Dei, both out of one pen ; and a dextris
virtutis Dei is no more to say than a dextris Dei; and so is virtutem carnis et sanguinis
no more to say but in carnem et sanguinem, which sentence the same Theophylact hath upon
St John before alleged, in this saying, " The bread is changed into flesh;" and in Mark in this
phrase, " into the virtue of flesh" being like these speeches, a dextris Dei, and a dextris virtutis
Dei. Which and it had liked this author to have considered, lie should have taken Theophylact s
speech as Theophylact understandeth himself, and said the words alleged in the name of
Theophilus Alexandrinus were not Theophylacfs words, and then lie had said for so much
true, (which would do well among,) and the words be not indeed Theophylact s ii ords, nor were not
alleged for his. Now when this author saith, " they were not Theophilus Alexandrinus s words;"
that is a large negative, and will be hardly proved otherwise than by addition of the author s
knowledge for any thing that lie can find, and so there shall be no absurdity to grant it. And thus
I return to mine issue with this author, that Theophylact himself hath no such meaning expressed
in words as this author attributed 11 unto him, but an evident contrary meaning, saving herein I
will agree with this author, that Tlieophylact meant not "grossly" "sensibly" and "carnally," as
tliese words sound in carnal men s judgments. For we may not so think of God s mysteries, the
work wliereofis not carnal nor corporal, for the manner of it; but the manner spiritual, and yet
in the sacrament of tlie body and blood of Christ, because Christ is in his very true flesh present,
he may be said so carnally present, and naturally, after Hilary, and corporally, after Cyril; c.im?iiiy,
understanding the words of tlie truth of that is present, Chrises very body and flesh, and
not of the manner of tlie presence, which is only spiritual, supernatural, and above man s
capacity : and therefore a high mystery, a great miracle, a wonderful work, which it is
wholesome to believe simply with a sincere faith, and dangerous to search and examine with
a curious imagination, such as idleness and arrogancy would tempt a man unto, and by
devising of a figure or metaphor bring it within the compass of our busy reason.
CANTERBURY.
This is a pretty sleight of you to pass over the author s name, saying that you
found it so alleged in an author, and tell not in what author. There is surely some
hid mystery in this matter, that you would not have his name known. For if you had
found any approved author who had fathered these words upon Theophilus Alexandrinus,
[ 3 In the Acts the same sentence, Orig. ed. Winch.] [ 4 Attributeth, Ori. ed. Winch.]
190 THE THIRD BOOK.
I doubt not but I should have heard him here named, it should have served so much
for your purpose. For to what purpose should you conceal his name, if you had any
such author? But shall I open the mystery of this matter? Shall I by conjectures
tell the author which you followed, as you by conjecture gathered of him the name
*Thomas in of Thcophilus ? Thomas de Aquino, in his Catena Aurca, citeth the words by you
alleged in these letters, " Theoph." ; which letters be indifferent, as well to Theophilus
as to Theophylact s, so that you might have christened the child whether you would
198. by the name of Theophilus or of Thcophylactus. And because Theophilus was a more
ancient author, and of more learning and estimation than was Theophylact, therefore the
name pleased you better, to give more credit to your sayings, and so of " Theoph."
you made the whole name " Theophilus." And because one Theophilus was a bishop
of Alexandria, you added as it were his surname, calling him " Theophilus Alexan-
drinus." And if Thomas was not the author which you followed in this matter,
Fisher, peradventurc it might be doctor Fisher, sometime bishop of Rochester, who, writing
in the same matter that you do, was, or would be deceived as you be. But what
author soever you followed, you shall not honestly shake off this matter, except you
tell his name. For else I will say that you be fain to bring in for you feigned
authors, whispered in corners. And yet, that Theophilus wrote not the words al
leged upon Mark, this is no small proof, that Theophylact hath the same sentences,
word by word, and that neither St Hierome, Gennadius, Eusebius, Trithemius, nor any
other that ever wrote hitherto, made ever any mention that Theophilus wrote upon
the gospel of St Mark.
And as concerning your issue, thus much I grant without issue, that no catholic
writer among the Greeks hath more plainly spoken for you than Theophylact hath ;
and yet when that shall be w^ell examined, it is nothing at all, as I have plainly de
clared, shewing your untruth as well in allegation of the author s words, as in falsi
fying his name.
Thecate- And as for " the catechism of Germany" by me translated into English, to this I
have answered before ; and truth it is, that either you understand not the phrase of
the old authors of the church, or else of purpose you will not understand me. But
hereunto you shall have a more full answer when I come to the proper place thereof,
in the fourth part of my book.
And as concerning the words of Theophylact upon the gospel of John, he speaketh
to one effect, and useth much like terms upon the gospels of Matthew, Mark, and
John, whereunto I have sufficiently answered in my former book. And because the
answer may be the more present, I shall rehearse some of my words here again.
" Although," said I, " Theophylactus spake of the eating of the very body of Christ,
and the drinking of his very blood, and not only of the figures of them, and of the
conversion of the bread and wine into the body and blood of Christ, yet he meaneth
not of a gross, carnal, corporal, and sensible conversion of the bread and wine, nor
of a like eating and drinking of his flesh and blood, (for so not only our stomachs
would yearn, and our hearts abhor to eat his flesh and to drink his blood, but also such
eating and drinking could nothing profit and avail us;) but he spake of the celestial
and spiritual eating of Christ, and of a sacramental conversion of the bread, calling
the bread not only a figure, but also the body of Christ; giving us by those words
to -understand, that in the sacrament we do not only eat corporally the bread, (which
is a sacrament and figure of Christ s body,) but spiritually we eat also his very body,
and drink his very blood. And this doctrine of Theophylactus is both true, godly,
and comfortable." This I wrote in my former book, which is sufficient to answer
unto all that you have here spoken.
199, And as concerning the bread that Christ did eat and feed upon, it was naturally
eaten, as other men eat, naturally changed, and caused a natural nourishment, and
yet the very matter of the bread remained, although in another form; but in them
that duly receive and eat the Lord s holy supper all is spiritual, as well the eating
as the change and nourishment, which is none impediment to the nature of bread,
but that it may still remain.
species for And where you come to the translation of this word fpftCMt, to signify " appearance,"
appearance.
OF THE PRESENCE OF CHRIST. 191
this is a wonderful kind of translation, to translate specie in "appearance," because
apparet is truly translated " appearcth : " with like reason aurum might be translated
" meat," because etlere signifieth " to eat."
And your other translation is no less wonderful, where you tuni the " virtue" of
Christ s body into the " verity." And yet to cloak your folly therein, and to cast a Verity for
mist before the reader s eyes, that he should not see your untruth therein, you say v
that by " virtue " in that place must be understanded " verity." First, whatsoever
be understand by the word "virtue," your faitli in translation is broken. For the
sense being ambiguous, you ought in translation to have kept the word as it is, leaving
the sense to be expended by the indifferent reader, and not by altering the word to
make such a sense as please you; which is so foul a fault in a translator, that if
CEcolampadius had so done, he should have been called a man faulty and guilty, a
corrupter, a deceiver, an abuser of other men, a perverter, a depraver, and a man
without faith : as he might be called that would translate verbum caro factum est,
"the second person became man;" which although it be true in meaning, yet it
is not true in translation, nor dcclarcth the faith of the translator.
But now as your translation is untrue, so is the meaning also untrue and uncx-
cusable. For what man is so far destitute of all his senses, that he knoweth not
a difference between the verity of Christ s body and the virtue thereof? Who can
pretend ignorance in so manifest a thing ? Doth not all men know, that of every thing
the virtue is one, and the substance another ? except in God only, who is of that
simplicity without multiplication of anything in him, or diversity, that his virtue,
his power, his wisdom, his justice, and all that is said to be in him, be neither qualities
nor accidents, but all one thing with his very substance. And neither the right hand
of God, nor the virtue of God, (which you bring for an example, and servcth to no
purpose, but to blind the ignorant reader,) be any thing else but the very substance
of God, (although in diversity of respects and considerations they have diversity of
names,) except you will divide the most single substance of God into corporal parts
and members, following the error of the Anthropomorphites. But the like is not in
the body of Christ, which hath distinction of integral parts, and the virtue also, and
qualities distinct from the substance.
And yet, if the example were like, he should be an evil translator, or rather a
corrupter, that for a dextris virtutis Dei would translate a dextris Dei, or contrariwise. A dextris Dei.
And therefore all translators in those places follow the words as they be, and be not tutulK! Vl
so arrogant to alter one title in them, thereby to make them one in words, although
the thing in substance be one. For words had not their signification of the substances,
or of things only, but of the qualities, manners, respects, and considerations. And 200.
so may one word signify divers things, and one thing be signified by divers words.
And therefore he that should for one word take another, because they be both re
ferred to one substance, as you have done in this place, should make a goodly piece
of work of it ; not much unlike to him that should burn his house, and say he made
it, because the making and burning was both in one matter and substance.
It is much pity that you have not bestowed your time in translation of good
authors, that can skill so well of translation, to make speciem to signify appearance,
and that take virtue sometime for verity, and sometime for nothing; and a dextris
rirfniis Dei to signify no more but a dextris Dei, and virtutem carnis to signify no
more but carnem, and virtutem sanguinis, sanguinem. And why not? seeing that
such words signify ad placitum, that is to say, as please you to translate them.
And it scemoth to be a strange thing, that you have so quick an eye to espy other
men s faults, and cannot see in Theophylact his plain answer, but to take upon you
to teach him to answer. For when he asketh the question, " Why doth not the flesh
appear ? " he should have answered, say you, " that the flesh is not there in deed,
but the virtue of the flesh :" I pray you, doth not he answer plainly the same in effect ?
Is not his answer to that question this, as you confess yourself, "that the forms of
bread and wine be changed into the virtue of the body of Christ ? " And what would
you require more ? Is not this as much to say, as the virtue of the flesh is there,
but not the substance corporally and carnally?
And yet another third error is committed in the same sentence, because one sen-
192 THE THIRD BOOK.
tence should not be without three errors at the least in your translation. For whereas
Theophylact hath but one accusative case, you put thereto other two more of your own
head. And as you once taught Barnes 1 , so now you would make Theophylact your
scholar, to say what you would have him. But that the truth may appear, what
Theophylact said, I shall rehearse his own words in Greek : a-vyKctTafiaiviav IJ/JLIV d (f>i\dv-
TO jjLev e?3o<? apTov KOtt oivov (frvXciTTei, els ^uva/juv 3e craoKo? /cat al/xaTO? /xera-
?; which words translated into Latin be these: Condescendens nobis lenignus
Deus speclem quidem panis et vini servat, in potestatem autem carnis et sanguinis trans-
elementat. And in English they be thus much to say : " The merciful God, conde
scending to our infirmity, conserveth still the kind of bread and wine, but turneth
them into the virtue of his flesh and blood." To this sentence you do add of your
own authority these words " the bread and wine," which words Theophylact hath not,
which is an untrue part of him that pretendeth to be a true interpreter. And by
adding those words, you alter clearly the author s meaning. For where the author s
meaning was, that we should abhor to eat Christ s flesh and drink his blood in their
proper form and kind, yet Almighty God hath ordained that in his holy supper we
should receive the forms and kinds of bread and wine, and that those kinds should
be turned (unto them that worthily receive the same) into the virtue and effect of
201. Christ s very flesh and blood, although they remain still in the same kind and form
of bread and wine. And so by him the nature and kind of bread and wine remain ;
and yet the same be turned into the virtue of flesh and blood. So that the word
" forms" is the accusative case, as well to the verb turneth, as to the verb conserveth :
accusative cases, that is to say, " bread and wine," besides Theophylact s words ; wherein
all men may consider how little you regard the truth, that to maintain your untrue
doctrine once devised by yourselves, care not what untruth you use besides to corrupt
all doctors, making so many faults in translation of one sentence.
And if the words alleged upon Mark were not Theophylact s words, but the words
of Theophilus Alexandrinus, as you say, at the least Theophylact must borrow them
of Theophilus, because the words be all one, sixteen lines together, saving this word
"verity," which Theophylact turneth into "virtue." And then it is to be thought that
he would not alter that word, (wherein all the contention standeth,) without some con
sideration. And specially when Theophilus speaketh of the verity of Christ s body,
as you say, if Theophylact had thought the body had been there, would he have
refused the word, and changed verity into virtue, bringing his own faith into suspi
cion, and giving occasion of error unto other?
And where, to excuse your error in translation, you say that the words by you
alleged in the name of Theophilus Alexandrinus be not Theophylact s words, and I
deny that they be Theophilus words; so then be they nobody s words, which is no
detriment to my cause at all, because I took him for none of my witness ; but it is
in a manner a clear overthrow of your cause, which take him for your chief and
principal witness, saying "that no catholic writer among the Greeks hath more plainly
set forth the truth of the presence of Christ s body in the sacrament than Theophy-
lactus hath," and hereupon you make your issue.
And yet have I a good cause to call them Theophylact s words, forasmuch as
I find them in his works printed abroad, saving one word which you have untruly
corrupted, because that word pleaseth you not. And yet am I not bound to admit
that your witness is named Theophilus, except you have better proofs thereof than
this, that one saith he hath him in a corner, and so allegeth him. It is your part
to prove your own witness, and not my part that stand herein only at defence. And
yet to every indifferent man I have shewed sufficient matter to reject him.
Hear now my answer to St Hierome.
The answer to Besides this, our adversaries do allege St Hierome 2 upon the epistle ad Titum,
Hieronymus
super epistol.
[* Vide Burnet s Hist, of the Reformation, Vol. i.
p. 592. Oxford, 1829, and Foxe s Acts and Monu
ments, Vol. n. p. 525. Lond. 1631.]
[ 2 Tantum interest inter propositions panes et
rornus Christi. Quantum inter umbram et corpora.
inter imaginem et veritatem, inter exemplaria futu-
rorum, et ea ipsa quas per exemplaria praefiguraban-
tur. Jerom. Comment, in Epist. ad Titum, cap. i.
8, 9. Tom. IX. p. 199. Ed. Francof. 1084.]
OF THE PRESENCE OF ( I IK 1ST. 193
that there is as great difference between the loaves called panes propositions,
and the body of Christ, as there is between the shadow 3 of a body and the body
itself; and as there is between an image and the thing itself, and between
an example of tilings to come and the things that be prefigured by them.
These words of St Hierorne, truly understand, serve nothing for the intent of
the papists. For he meant that the show-bread of the law was but a dark
shadow of Christ to come ; but the sacrament of Christ s body is a clear testi
mony that Christ is already come, and that he hath performed that which
was promised, and doth presently comfort and feed us spiritually with his
precious body and blood, notwithstanding that corporally he is ascended into 202.
heaven.
WINCHESTER.
This author travaileth to answer St Hierome, and to make him tlie easier for him to deal Hieronym.
with, he cutteth off that followeth in the same St Hierome, which should make the matter open
and manifest, how effectually St Hierome speaketh of the sacrament of Christ s body and blood.
" There is," saith St Hierome, " as great difference between tJte loaves called panes propositions,
and the body of Christ, as there is between tJte shadow of a body and the body itself; and as
there is between an image and the true thing itself, and between an example of things to come
and the things that be prefigured by them. Therefore as meekness, patience, sobriety, mode
ration, abstinence of gain, hospitality also, and liberality should be chiefly in a bishop, and
tuning all laymen an excellency in them; so there should be in him a special chastity, and
as I should say, chastity that is priestly, that he should not only abstain from unclean* work,
but also from the cast of his eye, and his mind free from error of thought, that should make
the body of Christ 5 ." These be St Hierome s words in this place. By the latter part whereof
OfptanA plainly how St Hierome meaneth of Christ s body in the sacrament, of which the
/ <>,i res that were panes propositions were a shadow, as St Hierome saith; that bread being
" the image, and this the truth," that " tJie example, and this that was prefigured." So as if
Christ s body in the sacrament should be there but figuratively, as this author teacJieth, then
were the bread of proposition figure of a figure, and shadow of a shadow, which is over
yrt t an absurdity in our religion. Therefore tliere cannot be a more plain proof to shew,
that by St Hierome s mind Christ s body is verily in the sacrament and not figuratively only,
ilmn when he noteth panes propositions to be the figure and the shadow of Christ s body in
the sacrament. For, as Tertullian 6 saith, figura non esset, nisi veritatis esset corpus: " The *TertuHianus
nlln r were not to be called a figure, if that 1 * answered unto it, were not of truth," which is Maidonem,
tin sense of Tertullian s words. And therefore St Hierome could with no other words have
expressed his mind so certainly and plainly, as with these, to confess tlie truth of Chris fs
body in the sacrament. And therefore regard not, reader, what this author saith: for St
/!/<Tome offirmeth plainly Christ s true body to be in the sacrament, the consecration whereof
although St Hierome attributeth to the minister, yet we must understand him, that he taketh
God for tlie author and worker, notwithstanding by reason of the ministry in the church tlie
doing is ascribed to man as minister, because CJirist said, Hoc facite, after which speech
x tli n.tion, remission of sin, and the work in other sacraments is attribute to the minister, being
ntntrtheleM the same the proper and special works of God.
And this I add, because some be unjustly o/ended to Jiear that man should make the body
of Christ. And this author findeth fault before at the word "making," which religiously
heard and reverently spoken should offend no man; for man is but a minister, wherein he
should not glory. And Christ maketh not himself of the matter of bread, nor maketh himself
so oft of bread a new body; but sitting in heaven doth, as our invisible priest, work in the
mtnwfery of the visible priesthood of his church, and maketh present by his omnipotemy his
glorified body and blood in this high mystery, by conversion of the visible creatures of bread
"<id icint; as Emissp.m saith, into the same. This author of this book, as thou, reader, mayest
[ 3 A shadow, 1551, and Orig. ed.]
4 An unclean work, Grig. ed. Winch.]
[ Quomodo itaque mansuetudo, patientia, so-
rietas, moderatio, abstinentia lucri, hospitalitas quo-
que, et benignitas, prascipue esse debent in episcopo,
et inter cunctos laicos coiitinentia : sic et castitas
ut non solum ab opere se immundo abstineat, sed
etiam a jactu oculi, et cogitationis errore, men*
Christi corpus confectura sit libera. Ib. p. 199.]
[ B Figura auteni non fuisset, nisi veritatis esset
corpus. Tcrtul. ad versus Marcionem. Lib. iv. p.
458. Ed. Lutet. Paris. 1>44.]
propna, et (ut Ha dixerim) pudicitia sacerdotalis, ; [ If that, that answered, &c. lool.]
194 THE THIRD BOOK.
perceive, applieth the figure of the breads, called panes propositionis, to the body of Christ to
come, whereas St Hierome calleth them the figure of Christ s body in the sacrament, and there
fore doth fashion his argument in this sense. If those breads, that were but a figure, required
so much cleanness in them that should eat them, that they might not eat of them, which a day
or two before had lien with their wives ; what cleanness is required in him that should make the
body of Christ! Whereby thou mayest see how 1 this author hath reserved this notable place of
St Hierome to the latter end, that thou shouldest in the end, as well as in the midst, see him
evidently snarled, for thy better remembrance.
CANTERBURY.
203. To these words of St Hierome I have sufficiently answered in my former book. And
now to add something thereto, I say that he meaneth not that panes propositionis be
figures of the sacrament, but of Christ s very body. And yet the same body is not
only in the sacrament figuratively, but it is also in the true ministration thereof spiri
tually present and spiritually eaten, as in my book I have plainly declared. But how
is it possible that Caius Ulpian, or Scevola, Batholus, Baldus or Curtius, should have
knowledge what is meant by the spiritual presence of Christ in the sacrament, and
of the spiritual eating of his flesh and blood, if they be void of a lively faith, feeding
and comforting their souls with their own works, and not with the breaking of the
body and shedding of the blood of our Saviour Christ ?
The meat that the papists live by is indulgences and pardons, and such other
remission of sins as cometh all from the pope, which giveth no life, but infecteth
and poisoneth : but the meat that the true Christian man liveth by, is Christ him
self, who is eaten only by faith, and so eaten is life and spirit, giving that life that
endureth and continueth for ever. God grant that we may learn this heavenly know
ledge of the spiritual presence, that we may spiritually taste and feed of this heavenly
food!
Now, where you say " that there cannot be a more plain proof to shew that Christ s
body is verily in the sacrament, and not figuratively only," than when St Hierome
noteth panes propositionis to be the figure and shadow of Christ s body in the sacra
ment. " For," as Tertullian saith, " the other were not to be called a figure, if that
which answereth to it were not of truth." Here your " for" is a plain fallax a non
causa ut causa 2 , and a wondrous subtlety is used therein. For where Tertullian proveth
that Christ had here in earth a very body, which Marcion denied, because that bread
was instituted to be a figure thereof, and there can be no figure of a thing that is
not, you allege Tertullian s words, as though he should say, that Christ s body is in
the sacrament under the form of bread; whereof neither Tertullian entreated in that
place, nor it is not required, that the body should be corporally where the figure is,
but rather it should be in vain to have a figure when the thing itself is present.
And therefore you untruly report both of St Hierome and Tertullian : for neither of
them both do say, as you would gather of their words, that Christ s body is in the
sacrament really and corporally.
whether the And where you say, " that Christ maketh not himself of the matter of bread,"
chnstbe either you be very ignorant in the doctrine of the sacrament, as it hath been taught
matterof he these five hundred years, or else you dissemble the matter. Hath not this been the
teaching of the school divines, yea, of Innocent himself, that the matter of this sacra
ment is bread of wheat, and wine of grapes? Do they not say, that the substance
of bread is turned into the substance of Christ s flesh, and that his flesh is made of
bread? And who worketh this, but Christ himself? And have you not confessed
all this in your book of the " Devil s Sophistry ?" Why do you then deny here that
which you taught before, and which hath been the common approved doctrine of the
204. papists so many years? And because it should have the more authority, was not
this put into the mass-books, and read every year, Dogma datur Christianity quod
in carnem transit panis, et vinum in sanguinem ? Now, seeing that you have taught
so many years, that the matter and substance of bread is not consumed to nothing,
[ Here, Orig. ed. Winch.] . [* Ad causam, 1551.]
OF THE PRESENCE OF CHRIST. 195
but is changed and turned into the body of Christ, so that the body of Christ is
made of it, what mean you now to deny that Christ is made of the matter of bread?
When water was turned into wine, was not the wine made of the water ? And when John H.
the rod was turned into a serpent, and water into blood, the earth into a man, and Qra. iL^
his rib into a woman, were not the woman, man, blood, and serpent, made of the
matter of the rib, the earth, the \vater, and the rod? And is not every thing made
of that which is turned into it ? As bread is made of corn ; wine of grapes ; beer of
water, hops, and malt; and so of all things like? And when you have confessed
yourselves, so many years past, that Christ is made of bread in the sacrament, what
moveth you now to say, that Christ maketh not himself of the matter of bread,
except that either you will say, that the priest doth it and not Christ, which were
an intolerable blasphemy; or that the truth is of such a nature that even the very
adversaries thereof, sometime un wares, acknowledge it ; or else that force of argu
ments constraineth you to confess the truth against your will, when you see none
other shift to escape? But if you take upon you to defend the received doctrine of
the papists, you must affirm that doctrine which they affirm, and say that bread in
the sacrament is the matter whereof Christ s body is made ; whereof must then needs
follow, ex consequents^ that he hath from time to time a new body, made of new
bread, besides the body which was incarnated, and never but once made, nor of none
other substance but of his mother. So that it is but a vain cavillation, only to elude
simple people, or to shift off the matter, to say, as you do, " that Christ is not made
of the bread, but is made to be present there." For then should he have said, " There
is my body," and not, "This is my body." And to be present requireth no new
making : but to be present by conversion requireth a new making : as the wine
that was bought at the marriage in the Cane of Galilee, if there were any such, w r as
present without conversion, and so without new making ; but the wine that was
made of water, was present by conversion, which could not be without new making.
And so must Christ s body be newly made, if it be present by corporal conversion
of the substance of bread into the substance of it. And now I refer to every
indifferent reader, to judge between us both, which of us is most snarled.
Now let us examine the other authors following in my book.
And the same is to be answered unto all that the adversaries bring of August!*
St Augustine, Sedulius, Leo, Fulgentius, Cassiodorus, Gregorius, and other, con- SJ?""
cerning the eating of Christ in the sacrament. caSonX
Which thing cannot be understanded plainly as the words sound, but figura
tively and spiritually, as before is sufficiently proved, and hereafter shall be more
fully declared in the fourth part of this book.
WINCHESTER.
Because this author, who hitherto hath answered none substantially, would nevertheless be seen 205.
to answer all, he windeth up six of them in one fardell, St Augustine, Sedulius, Leo, Fulgentius, August,*.
Cassiodonts, and Gregorius, and dispatcheth them all with an ut supra : and among thenil think i5i? lius
he would have knit up all the rest of the learned men of all ages, amongst whom I know none that &oru\
write as this author doth of the sacrament, or impugneth the catholic faith as this author doth by Grc s orius -
the envious name of papists. Since Christ s time there is no memory more than of six, that have 3
affirmed that doctrine, which this author would have called now the catholic doctrine, and yet not
written by them of one sort, neither received in belief in public profession; but secretly, when it
happened, begun by conspiration, and in the end ever hitherto extinct and quenched. First was
Bertram, then Berengarim, then Wiclif, and in our time, CEcolampadius, Zuinglius, and Joa-
rhlwns Vadiamts. I will not reckon Peter Martyr, because such as know him saith he is not Peter
learned; nor this author, because he doth but as it were translate Peter Martyr, saving he roveth at Martyr
solutions, as liketh his phantasy, as I have before declared. Which matter being thus, it is a
strange title of this book, to call it the true catholic doctrine.
f 3 Hath, lo.-.l.J
J3 2
19(5 THE THIRD BOOK.
CANTERBURY.
All that you have these many years gathered together for your purpose, or that
can be gathered, may be well trussed up in a very small fardell, and very easily
borne and carried away, for any weight that is therein. For your doings be like
to him, that would fain seem to have something, and having nothing else, filktli a
great mail full of straw, that men should think he carried something, where indeed a
little budget had been sufficient for so much in value.
And as for your own doctrine, it is so strange, that neither it agreeth with the
scripture, nor with the old catholic church, nor yet with the later 1 church or con
gregation of the papists : but you stand post alone, after the fall of the papistical
doctrine, as sometime an old post standeth when the building is overthrown.
And where you say, "that since Christ s time there is no more but six that
have affirmed the doctrine that I have taught ;" all that have been learned, and have
read the old authors of the catholic church, may evidently see the contrary, that
sithens Christ s time the doctrine of my book was ever the catholic and public re
ceived faith of the church, until Nicholas the second s time, who compelled Beren-
Herengarius. garius to make such a devilish recantation, that the papists themselves be now ashamed
of it. And since that time, have many thousands been cruelly persecuted only for
the profession of the true faith. For no man might speak one word against the bishop
of Rome s determination herein, but he was taken for an heretic, and so condemned,
as Wicliff, Huss, and an infinite number more. ^
Bertram. And as for Bertram, he was never before this time detected of any error that ever
I read, but only now by you. For all other that have written of him, have spoken
much to his commendation and praise. But I know what the matter is : he hath written
against your mind, which is a fault and error great enough.
As for Dr Peter Martyr, he is of age to answer for himself: but concerning him,
that told you that he was not learned, I would wish you to leave this old rooted fault
in you, to be light of credit. For I suppose, that if his learning that told you that
20(3. lie, and yours also, were set both together, you should be far behind Master Peter
Peter Martyr. Martyr. Marry, in words I think that you alone would overlay two Peter Martyrs;
he is so sober a man, and delighteth not in wasting of words in vain. And none
do say that he is not learned, but such as know him not, or be not learned them
selves, or else be so malicious or envious, that they wittingly speak against their
own conscience. And, no doubt, that man bringeth himself out of the estimation of a
learned man, which hath heard him reason and read, and saith that he is not learned. And
whosoever misreporteth him, and hath never heard him, may not be called so well momus
as sycophanta, whose property is to misrcport them whom they neither see nor know.
Now resteth only Damascene, of whom I write thus.
The answer But here John Damascene may in no wise be passed over, whom for his
authority the adversaries of Christ s true natural body do reckon as a stout
cap. 14. champion, sufficient to defend all the whole matter alone. But neither is the
[Quern for- r .
aSrhnum 1 au thority ot Damascene so great that they may oppress us thereby, nor his
re r m p na?un?fis words so plain for them, as they boast and untruly pretend. For he is
JiSnS" 1 but a young new author in the respect of those, which we have brought in for
Sducunt! our party. And in divers points he varieth from the most ancient authors,
L] (if he mean as they expound him;) as when he saith, that " the bread and wine
be not figures," which all the old authors call figures ; and that " the bread and
wine consume not, nor be avoided downward," which Origen and St Augustine
affirm ; or that " they be not called the examples of Christ s body after the
consecration," which shall manifestly appear false by the liturgy ascribed unto
St Basil.
And moreover the said Damascene was one of the bishop of Rome s chief
[ l Latter, 1551.]
OF THE PRESENCE OF CHRIST.
197
proctors against the emperors, and as it were his right hand, to set abroad
all idolatry by his own hand-writing. And therefore, if he lost his hand 2 , as
they say he did, he lost it by God s most righteous judgment, whatsoever they
feign and fable of the miraculous restitution of the same. And yet whatsoever
the said Damascene writeth in other matters, surely in this place, which the
adversaries do allege, he writeth spiritually and godly, although the papists
either of ignorance mistake him, or else willingly wrest him and writhe him to
their purpose, clean contrary to his meaning.
The sum of Damascene his doctrine in this matter is this 3 : That as Christ,
being both God and man, hath in him two natures; so hath he two nativities,
one eternal, and the other temporal. And so likewise, we, being as it were
double men, or having every one of us two men in us, the new man and the old
man, the spiritual man and the carnal man, have a double nativity ; one of our
first carnal father Adam, (by whom, as by ancient inheritance, cometh unto us
malediction and everlasting damnation,) and the other of our heavenly Adam,
that is to say, of Christ, by whom we be made heirs of celestial benediction and
everlasting glory and immortality.
And because this Adam is spiritual, therefore our generation by him must
TTOtfct Ta
Kal e\at
T)V ydpiv TOU
Tpov
[ 3 For the account of this restoration of Damas
cene s hand, vide Winchester s "Detection of the
Devil s Sophistry," f. 35.]
UTTCICJJ Snr\o1 rivei eoyxty Kai <ruy06Toi, eel
Kal Tfjy yeyy;)<Tiy onrX;/y elyat, b/JLoiia? Kal TI}V
(3p<a<riv (TvvdfToV j /JLev ovv ye j/yj(rts ii/nlv Si vSaTos
i;al TTvevfJiaTos SeooTai, </>;/ii 6e TOU dyiov fiaTT-
TitrfiaTOS j; oe fjptaariv, auTos o ap-ros T//S >??,
6 Kvpiov i]fJLu>u \t]crov<s X/OKTTOS, 6 tK TOU oupavov
KaTa/ia s __ Damascenus, de Fide Orth. Lib. iv.
cap. 14. Ed. Basil. 1559. Tom. I. p. 315.
"ApTOv <?fc Ktti olyos TrapaXauftdveTai olSe yap
o 6eo? Tjjy dvtiptairiviiv dadeveiav, cos TCC TroXXtt
Ta fiii Kara TJ/y <ruyj0eiay TCTpifiueva diroaTpt-
Gvcr^CQaivovcra- TTJ ovv <ruy>;0ei avyKa.Ta.fid-
Sid Ttav vmnfiS9 TT;S <ucrea>s
VGlV Kal UHTTTCp TTL TOU /3tt7T-
etfos diftpwiroi? vSaTi XoueaOat,
vveeve TM e\aiia KUI u^aTi
To?, Kal eiroijjo-ei/ avTto \ov-
OUTWS e7rei^j etJos TO?S dv-
pw-rroi<i dpTov e&dittv, votap TP Kal olvov TTii/eti/,
uvc cvev ai/ToIs TJJJ; avTov OeoTTjTa, Kal ireTrotrj-
SV auTa crwfJLa Kal dlfia auTou, t j/a Sid TWV aruv-
!S i7rt ; |0 fpixriu yevw/JLeQa.
oTJjTi, TO CK T^S
dyias irapQevov cfutfia, ov% OTL TO dva\tj(pQev
aoi/za e ovpavov KaTep-^fTai, d\X OTI CUTOS o
dpTOf Kal olvos /JLeTa-TTOiouvTai fh crw/ua ^ai al/ia
0fou. ei Ot- TO// TpoTrov eiri^TjTeTs iriaf yti/eroi,
dpKel croi a/couaai, OTI Sid Trvevp.aTO i dyiov, <a<nrep
/vai tK T//S ayias QCOTOKOV Sid -Trj/ev/uaTos dyiou
eavTio Kal ev eavTia o xvpios <rdpKa vire(rTi ]<jaTO
Kai tf\4ov ovoev yivtacTKOfjiev, aXX* OTI o X<>yos
TOU Qeou ciXt)0>fv e<rTi Kal evepyijs Kal TravTood-
i/ajuo9, o Ot TpoTros av^epevvt]TO^ ob y^elpov ce Kal
TOUTO clTrelv, OTI wairep </)uo-i/cais Sid T^S fipwcrew?
o tlpTOS, Kai o oTi/os Kal TO uotnp Sid T//S 7TO(reas, eis
irttfta Kal aljua TOU eadiovTos KalTrivovTO? /ueTa/3aX-
\orrai , Kal ov yivovTai tTepov crw/jia irapd TO irpoTe-
pov auTou (rw/jLa ol/Ttov o TI}S TTjOoOJaffus a/oTos oTvo s
T6 Kal vS<op Sid T//S eTTixXfjo-ecDS Kai e7ri</>oiTij crea)s
TOU ayiov Tri/eu/uaTos vTreptfcvux; p.eTairoioui>Tai ets
TO ffotfta TOV XpitTTOv Kal TO al/ma, Kal OVK elcrl <5uo,
a XX ey KOI TO aurd.
u/c <TTI TUTTOS o
Kal o oli/os TOU (ra/iaTOS Kai at /xaTos TOU \pi-
CTTOU ynj yevoiTO a XX auTO TO ffwint TOV Kvpiou
Teticco/jLtvoV) avTov TOV Kvpiov fiTrdyrov, TOUTO
/iou eo"Ti, ou TUTTOS TOU (Tto/zaTos, a XXa TO o"iyua
Kai ou TUTTOS TOU 7/iaTO9j aXXa TO aT/xa. - TI/HI/-
crwjiiey auTO Trdaij KatiapnUfit \lti>iKrj Tt vai trfd-
fjictTucfj cnrXo . i/ yttfj .CTTI. ai/H^axaeW
aVf/oa^ oe ^u<N..v ) .T,-/ii oi v ecrTt, aXX tl /
TTUpl OUTtoi Kal O dp^ifi T^S KOlVWVid? OVK
XtTos eTTJy, a XX JJJ/w/Lie yos OedrtjTi <rcu/u.a oe
}}v(ufJLCVOV HeoTtjTi ou ^ita (pva i i tcrTiv, aXXa ynia
^iey TOU crai ^LiaTos, TJ/S oe 7Jyaj/xe y>js avTu> 0eoT/Tos
CTepa UHTTS TO <TVVafJ.(pOTpOV OV fJLia 0U(71S,
a XXa ^uo. - Sw/xa e<TTi Kai al/za X/ot<rrou, ets
, ou SaTravaouevov, ov <t>Qeip6u.evov, OVK eis
va ^topouv, p.)} yevoiTO a XX eis T>;y tj/iwy
ovaiav Kal <rvvTrip\](nv, /iXa /3?js iravTooaTrov^ du.vv-
Tt ipiov, puTrov TrayTos KaSapTrfptoy. - OUTOS o
a/OTos ecrTiy j dirap^t] TOV u.e\\ovTO<s dpTov, os
t<TTty o eTriouo-tos T() ya/o eTTiouariov oijXoi, J
Toy /le XXoyTa, TOVTCCTTI. TOV TOV p.e\\ovTO<i alw-
yos, j Toy TT/OOS <TVVTi ipiio-iv T//S oufftas ;/ztuy X)U-
fiavofJLevov en-e ouy OUTOJS, eiTe OUTUJSTO TOU Kvpiov
crai^ia Trpoo~(pvu)S Xe ^QijtreTai Trvev/maydp "^woiroiovv
ecrTiv i] crdp TOV Kvpiov. SIOTI CK TOU wo7rotou
TrveiifjLaTo i (ruycXj/(/)6j" TO ya/o yeyevvt]u.fvov eK
Tov TryeujuaTos irvevp.d eori" TOUTO 6e Xeytu OUK
dvuipwv Tj/y TOU (TaifiaTO^ <^)u(rty, a XXa TO ^wo-
Trojoy Kai 6e?oy TOUTOU 8jXai(rai /3ouXd/ieyos. Ei
<5d Kai Ttyes dvTiTvtra TOV trcJ^aTOS Kai a i[Ji(tTos
TOV Kvpiov Toy apTov Kai Toy olvov eva Xecray, ous
6 Qeoffoopo? ffpij Ba<riXeio9, ou /meTa TO ayta<r0^yat
el-Troy, a XXa -rrpiy dyiafrQrjvai, auTijy TJI/ irpo<r-
<popdv OUTGO KaXecrayTcs. MeTa XtjiI^is oe XtytTaf
^i auT^s ya/o T?/? Irj^oi/ 06OTJJTO5 /zeTaXa/u/3a -
yo/xey. KOivcavia Sk XeyfTai TC Kal etrriy dX^IM
5ta TO KOivtavelv tj^ias ci auT;/s TO; X/OKTTW, Kai
HCTtxeiv avTov T^S <ra/oKo Te Kai TT;S OeoTrjTos*
Koivwveiv Si Kal evovtrdai a XX/Xois 6V avTtjs. eirel
ydp e eyos dpTov u.eTa\au(3dvou.ev ol -jra yTes ey
<roa/J.a \pi(rTov Kal ev alu.a, Kal dXX;Xajy /ue Xf}
yjyd/ie^a, <ruo-(ra>/uot XptaTOu x/)?//zaTt^oyres. Ib.
pp. 317, 18, 19.J
198 THE THIRD BOOK.
be spiritual, and our feeding must be likewise spiritual. And our spiritual
generation by him is plainly set forth in baptism; and our spiritual meat and
food is set forth in the holy communion and supper of the Lord. And because
our sights be so feeble that we cannot see the spiritual water wherewith we be
207. washed in baptism, nor the spiritual meat wherewith we be fed at the Lord s
table ; therefore to help our infirmities, and to make us the better to see the
same with a pure faith, our Saviour Christ hath set forth the same, as it were
before our eyes, by sensible signs and tokens, which we be daily used and
accustomed unto.
And because the common custom of men is to wash in water, therefore our
spiritual regeneration in Christ, or spiritual washing in his blood, is declared
unto us in baptism by water. Likewise our spiritual nourishment and feeding
in Christ is set before our eyes by bread and wine, because they be meats and
drinks which chiefly and usually we be fed withal ; that as they feed the body,
so doth Christ with his flesh and blood spiritually feed the soul.
And therefore the bread and wine be called examples of Christ s flesh and
blood; and also they be called his very flesh and blood, to signify unto us, that
as they feed us carnally, so do they admonish us, that Christ with his flesh and
blood doth feed us spiritually, and most truly, unto everlasting life.
And as Almighty God by his most mighty word and his holy Spirit and
infinite power brought forth all creatures in the beginning, and ever sithens hath
preserved them ; even so by the same word and power he worketh in us, from
time to time, this marvellous spiritual generation and wonderful spiritual nourish
ment and feeding, which is wrought only by God, and is comprehended and
And as bread and drink by natural nourishment be changed into a man s
body, and yet the body is not changed, but is the same 1 that it was before : so,
although the bread and wine be sacramentally changed into Christ s body, yet
his body is the same, and in the same place that it was before ; that is to say,
in heaven, without any alteration of the same.
And the bread and wine be not so changed into the flesh and blood of Christ
that they be made one nature, but they remain still distinct in nature; so that
the bread in itself is not his flesh, and the wine his blood, but unto them that
worthily eat and drink the bread and wine, to them the bread and wine be his
flesh and blood ; that is to say, by things natural, and which they be accustomed
unto, they be exalted unto things above nature. For the sacramental bread and
wine be not bare and naked figures, but so pithy and effectuous, that whosoever
worthily eateth them, eateth spiritually Christ s flesh and blood, and hath by
them everlasting life.
Wherefore, whosoever cometh to the Lord s table, must come with all
humility, fear, reverence, and purity of life, as to receive not only bread and
wine, but also our Saviour Christ, both God and man, with all his benefits, to
the relief and sustentation both of their bodies and souls.
This is briefly the sum and true meaning of Damascene concerning this
matter.
Wherefore, they that gather of him either the natural presence of Christ s
body in the sacraments of bread and wine, or the adoration of the outward and
visible sacrament; or that after the consecration there remaineth no bread, nor
wine, nor other substance, but only the substance of the body and blood of
Christ ; either they understand not Damascene, or else of wilful frowardness
[ l But the same, 1551, and Orig. ed.j
OF TJIK PRESENCE OF CHRIST. 199
they will not understand him : which rather seemeth to be true by such col
lections as they have unjustly gathered and noted out of him.
For although lie say that Christ is the spiritual meat; yet as in baptism the
1 loly Ghost is not in the water, but in him that is unfeignedly baptized ; so
Damascene meant not, that Christ is in the bread, but in him that worthily 208.
And though he say that the bread is Christ s body, and the wine his blood,
yet he meant not that the bread, considered in itself, or the wine in itself, being
not received, is his flesh and blood : but to such as by unfeigned faith worthily
the body and blood of Christ, because that such persons, through the working
of the Holy Ghost, be so knit and united spiritually to Christ s flesh and blood,
and to his divinity also, that they be fed with them unto everlasting life.
Furthermore, Damascene saith not that the sacrament should be worshipped
and adored, as the papists term it, which is plain idolatry ; but that we must
worship Christ, God and man. And yet we may not worship him in bread
and wine, but sitting in heaven with his Father, and being spiritually within
ourselves.
Nor he saith not, that there remaineth no bread nor wine, nor none
other substance, but only the substance of the body and blood of Christ ; but
he saith plainly, "that as a burning coal is not wood only, but fire and
wood joined together ; so the bread of the communion is not bread only, but
bread joined to the divinity." But those that say, that there is none other
substance but the substance of the body and blood of Christ, do not only
deny that there is bread and wine, but by force they must deny also, that
there is either Christ s divinity or his soul. For if the flesh and blood, the
soul and divinity, of Christ be four substances, and in the sacrament be but
two of them, that is to say, his flesh and blood, then where is his soul and
divinity ? And thus these men divide Jesus, separating his divinity from his
humanity : of whom St John saith : " Whosoever divideth Jesus, is not of i joi.n \\.
God, but he is antichrist."
And moreover, these men do separate Christ s body from his members
in the sacrament, that they leave him no man s body at all. For as
Damascene saith, that the distinction of members pertain so much to the in in>ro <\c
nature of man s 2 body, that where there is no such distinction, there is no cimsto
J . . . voluntatibus.
perfect man s body: but by these papists doctrine, there is no such distinc
tion of members in the sacrament; for either there is no head, feet, hands,
arms, legs, mouth, eyes, and nose at all ; or else all is head, all feet, all
hands, all arms, all legs, all mouth, all eyes, and all nose. And so they
make of Christ s body no man s body at all.
Thus being confuted the papists errors, as well concerning transubstan-
tiation, as the real, corporal, and natural presence of Christ in the sacrament,
which were two principal points purposed in the beginning of this work ; now
it is time something to speak of the third error of the papists, which is
concerning the eating of Christ s very body, and drinking of his blood.
\_Thus em/,-t/t t/n> f/nr./ Book 3 . }
[ a Of a man s body, lool, and Orig. Ecl.J [ 3 Grig. Ed.J
200 THE THIRD BOOK.
WINCHESTER.
Damascene. Last of all, the author busieth himself with Damascene, and goeth about to answer li n.t
by making of a sum ; which sum is so wrong accompted, that every man that readeth Da
mascene may be auditor to control it. And this will I say, Damascene writeth so evidently
in the matter, that Peter Martyr, for a shift, is fain to find fault in his judgment and
age ; and yet he is eight hundred years old at the least, and I say at the least, because he is
20t >- reckoned of some half as old again. And whatsoever his judgment were, he writeth (as
Melancthon saith) his testimony of the faith of the sacrament as it was in his time. I would
write in here Damascene s words, to compare them with tlie sum* collected by this author,
whereby to disprove his particulars plainly ; but tJie words of Damascene be to be read, trans
As for ttie "four substances" which this author by accompt numbereth of Christ, might have
been left unreckoned by tale, because among tliem that be faithful, and understand truly,
">***<>*># the substance of Christ s very body is, there is also understanded by concomitance
to be present tlw substance of Ids soul, as very man, and also of the Godfiead as very God.
And in the matter of the sacrament therefore, contending with him that would have the
substance of bread there, it may be said there is in the sacrament the only substance of Christ s
body, because the word "only" thus placed excludeth other strange substances, and not the
substances which without contention be known and confessed unite with Christ s body. And
so a man may be said to be alone in his house when he hath no strangers, although he hath
a number of his own men. And Erasmus noteth how the evangelist writeth Christ to have
.prayed alone, and yet certain of his disciples were there. And if in a contention raised,
wUther the father and son were both killed in such a field or no, I defended the father to
have been only killed there, and thereupon a wager laid, should I lose, if by proof it ap
peared, that not only the father, but also three or four of the father s servants were slain, but
the son escaped? And as in this speech the word "only" served to exclude that was in con-
tention, and not to reduce the number to one; no more is it in the speech that this author
ivould reprove, and therefore needed not to have occupied himself in the matter, wherein I heard
him once say in a good audience, himself was satisfied. In which mind I would he had
continued; and having so slender stuff as this is, and the truth so evident against him, not
to have resuscitate this so often reproved untruth, wherein never hitherto any one could prevail.
CANTERBURY.
As for Damascene neecleth no further answer than I have made in my former
book. But I pray the reader, that he will diligently examine the place, and so to
be an indifferent auditor betwixt us two.
Now when you be called to accompt for the number of substances in the sacrament,
I perceive by your wrangling, that you be somewhat moved with this audit, for be
cause you be called to accompt. And I cannot blame you, though it somewhat grieve
you; for it toucheth the very quick. And although I
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https://scicomp.stackexchange.com/questions/5549/how-does-the-performance-of-python-numpy-array-operations-scale-with-increasing/11451
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# How does the performance of Python/Numpy array operations scale with increasing array dimensions?
How do Python/Numpy arrays scale with increasing array dimensions?
This is based on some behaviour I noticed while benchmarking Python code for this question: How to express this complicated expression using numpy slices
The problem mostly involved indexing to populate an array. I found that the advantages of using (not-very-good) Cython and Numpy versions over a Python loop varied depending on the size of the arrays involved. Both Numpy and Cython experience an increasing performance advantage up to a point (somewhere broadly around $N=500$ for Cython and $N=2000$ for Numpy on my laptop), after which their advantages declined (the Cython function remained the fastest).
Is this hardware defined? In terms of working with large arrays, what are best practices that one should adhere to for code where performance is appreciated?
This question (Why isn't my Matrix-Vector Multiplication Scaling?) may be related, but I am interested in knowing more about how different ways of treating arrays in Python scale relative to each other.
• Have you tried numexpr? There's also, for example, this talk which points to blosc and CArray, all meant to speed things up further (and possibly bypassing memory bandwidth limitations). – 0 0 Aug 2 '13 at 9:24
• Can you post the code used to profile. There is probably a few things going on here. – meawoppl Dec 10 '13 at 17:52
I don't know how this benchmark was done, but probably with floating point numbers, that in Python default to doubles. The sizes correspond, respectively, to $4$ and $16 kB$. Those are reasonable values for L1 and L2 cache sizes of a (a bit old) AMD CPU. To be certain, I did my own benchmark:
def timeit(size):
t0 = time.time()
for _ in xrange(10):
np.random.random(size)
return time.time() - t0
sizes = np.logspace(1, 6, 40)
times = [timeit(s) for s in sizes]
There are a few things wrong with this benchmark, for a start, I am not disabling garbage collection and I am taking the sum, not the best time, but bear with me.
The time it takes is quite proportional to the size of the array, but there is a change in the slope around size $8000$. This is an array of $64 kB$, that is the size of the L1 cache of an i5 (my computer).
Should one worry about the cache size? As a general rule, I say no. Optimizing for it in Python means making the code much more complicated, for dubious performance gains. Don't forget that Python objects add several overheads that are difficult to track and predict. I can only think of two cases where this is a relevant factor:
• Basic operations on large arrays (like evaluate a polynomial), limited by memory bandwidth. Use Numexpr or (if the data is much bigger) Pytables. They are optimised to take the cache size into account amongst other optimisations.
• Performance critical code: if you want to squeeze every microsecond, you should not be using Python in the first place. Writing vectorized Cython and leaving the compiler do what it does best is probably the painless way to go.
In the comments, Evert mentioned CArray. Note that, even working, the development has stopped and it has been abandoned as a standalone project. The functionality will be included in Blaze instead, an ongoing project to make a "new generation Numpy".
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https://cyrusimap.org/imap/reference/manpages/usercommands/dav_reconstruct.html
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# dav_reconstruct¶
Rebuild the caldav and carddav database for a user/set of users.
## Synopsis¶
dav_reconstruct [ -C alt_config] [ -A <audit tool> ] [ -a ] <userid_list>
## Description¶
dav_reconstruct fixes up the dav internal sqlite database which is used for lots of the dav commands to make them more efficient.
Any corruption to the dav database can cause the wrong stuff to be returned via caldav/carddav. Using dav_reconstruct can correct these faults.
## Options¶
-C alt_config
Alternative config file with cyrus settings.
-a
Process all users on this store.
-A <audit tool>
Name of a program to take two sqlite databases and compare them. This option currently does not work.
userid_list
List of users whose cal/card dav information you need to fix.
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http://www.zora.uzh.ch/81691/
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# Distribution and use of knowledge under the “Laws of the web”
Falkinger, Josef (2007). Distribution and use of knowledge under the “Laws of the web”. CESifo Working Paper 2154, CESifo Group Munich.
## Abstract
Empirical evidence shows that the perception of information is strongly concentrated in those environments in which a mass of producers and users of knowledge interact through a distribution medium. This paper considers the consequences of this fact for economic equilibrium analysis. In particular, it examines how the ranking schemes applied by the distribution technology affect the use of knowledge, and it then describes the characteristics of an optimal ranking scheme. The analysis is carried out using a model in which agents’ productivity is based on the stock of knowledge used. The value of a piece of information is assessed in terms of its contribution to productivity.
Empirical evidence shows that the perception of information is strongly concentrated in those environments in which a mass of producers and users of knowledge interact through a distribution medium. This paper considers the consequences of this fact for economic equilibrium analysis. In particular, it examines how the ranking schemes applied by the distribution technology affect the use of knowledge, and it then describes the characteristics of an optimal ranking scheme. The analysis is carried out using a model in which agents’ productivity is based on the stock of knowledge used. The value of a piece of information is assessed in terms of its contribution to productivity.
Detailed statistics
Item Type: Working Paper 03 Faculty of Economics > Department of Economics 330 Economics English December 2007 09 Oct 2013 09:37 05 Apr 2016 17:02 CESifo Working Paper 31 Official URL. An embargo period may apply. http://www.cesifo-group.de/de/ifoHome/publications/working-papers/CESifoWP/CESifoWPdetails?wp_id=14557402
Permanent URL: https://doi.org/10.5167/uzh-81691
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http://software.imdea.org/projects/beaver/beaver.html
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Beaver: This is a tool for computing the over-approximate reach set of the parameterized linear dynamical system given by,
(t) = Ax(t), x(0) ∈ X0n, A ∈ Ω, t ∈ [0,T] (1)
within desired error tolerance ε > 0, where X0 and Ωn×n, are compact polyhedral sets, A is a n×n dimensional matrix and [0,T] is the time domain of interest. This tool computes the over approximate reach set in the form of SMT expressions in SMT Lib format. We use Z3-SMT solver for safety verification of system (1) from the given unsafe region.
Reach set: The state of the System (1) starting from an initial state x(0) ∈ X0 for a matrix A ∈ Ω at time t is given by the state transition function defined as:
Φ(x(0), A, t) = eAt x(0)
The reach set of the System (1) is given by,
ReachΦ(X(0), Ω, [0,T]) = {Φ(x(0), A, t) | x(0) ∈ X0, A ∈ Ω, t ∈ [0,T]}
Verification: This tool is useful for safety verification of the reach set of the parameterized linear dynamical system from the given unsafe region. It is shown in below figure.
In the above figure, if the Z3-SMT solver gives the output unsat, the ReachΦ (X(0), Ω, [0,T]) does not intersect with unsafe region, i.e. it is safe and if the output is sat, the ε-ball of reach set Bε (ReachΦ(X(0), Ω, [0,T])) intersects with the unsafe region i.e. it is Unsafe*. The Unsafe* guarantees that the reach set of the parameterized linear dynamical system is unsafe within the error tolerance ε > 0.
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http://mathhelpforum.com/algebra/163502-graphing-find-y-intercept-need-help.html
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Thread: graphing: find the y-intercept, need help!
1. graphing: find the y-intercept, need help!
So i have two point on my graph
(2,5) and (-3,-3)
the slope is
m=8/5
so y=8/5x + b
i take the first point
so 5= 8/5 (2) + b
5= 16/5 +b
afterwards... im stuck can somebody help me figure out the answers plx
2. Originally Posted by jingming90
So i have two point on my graph
(2,5) and (-3,-3)
the slope is
m=8/5
so y=8/5x + b
i take the first point
so 5= 8/5 (2) + b
5= 16/5 +b
$b = 5 - \frac{16}{5}$
common denominator?
3. would I still get the same answer if i use (-3,-3)
4. You should be getting the same answer, yes.
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http://www.zora.uzh.ch/52378/
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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-52378
# Fehr-Duda, Helga; Bruhin, Adrian; Epper, Thomas; Schubert, Renate (2008). Rationality on the Rise: Why Relative Risk Aversion Increases with Stake Size. Working paper series / Socioeconomic Institute No. 708, University of Zurich.
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## Abstract
How does risk tolerance vary with stake size? This important question cannot be adequately answered if framing effects, nonlinear probability weighting, and heterogeneity of preference types are neglected. We show that, contrary to gains, no coherent change in relative risk aversion is observed for losses. The increase in relative risk aversion over gains cannot be captured by the curvature of the utility function. It is driven predominantly by a change in probability weighting of a majority group of individuals who exhibit more rational probability weighting at high stakes. These results not only challenge expected utility theory, but also prospect theory.
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https://codereview.stackexchange.com/questions/182113/first-project-euler-solution
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First Project Euler solution
To continue learning I decided to try solving some of project Euler problems. Here is the first solution.
The things I'm interested the most from the review are:
• The performance of the code
• Overall review of the code structure, styling rules and naming conventions.
Problem: 1
Find the sum of all the multiples of 3 or 5 below 1000.
#----------------------------------------------------------------------------------
def calculate_the_sum(threshold = 10):
"""Calculates the sum of all multiples of 3 or 5
below the provided threshold.
Arguments:
type:<int> -Preforms the calculations on all values up to this value.
Return:
type:<int> -The sum of numbers that are multiples of 3 or 5..
"""
return sum(n for n in range(threshold) if n % 3 == 0 or n % 5 == 0)
#----------------------------------------------------------------------------------
def main():
threshold = 1000
print(' Calculates the sum of all numbers that are multiples of 3 or 5')
print(' The Sum of numbers below {} is: {}'.format(threshold,calculate_the_sum(threshold)))
#----------------------------------------------------------------------------------
if __name__ == "__main__":
main()
• Consider asking 5 separate questions. – vnp Dec 6 '17 at 6:06
• @vnp Should i split this post, or you meant that for the future posts i make ? – HelloWorld Dec 6 '17 at 12:11
• There is too little in common between the five problems; we want to evaluate your solution, not you as a programmer. Since there is currently one answer that addresses just Problem 1, I have removed 2–5. – 200_success Dec 6 '17 at 13:14
You can define a generic function to relate the sum for a given multiplier to the number of multiples below the threshold. This is shown in function calculate_sum3.
import time
def ntimerprinter(n):
"""Decorate the function to run it n times and print the time
"""
def inner(func):
def wrapper(*args, **kwargs):
before = time.time()
for _ in range(n):
result = func(*args, **kwargs)
after = time.time()
elapsed = after - before
print 'Run {0.__name__} {1} times in: {2} s'.format(func, n,
elapsed)
return result
return wrapper
return inner
@ntimerprinter(500)
def calculate_sum1(threshold=10):
"""Calculates the sum of all multiples of 3 or 5
below the provided threshold.
Arguments:
type:<int> -Preforms the calculations on all values up to this value.
Return:
type:<int> -The sum of numbers that are multiples of 3 or 5..
"""
return sum(n for n in range(threshold) if n % 3 == 0 or n % 5 == 0)
@ntimerprinter(500)
def calculate_sum2(threshold=10):
"""Calculates the sum of all multiples of 3 or 5 below threshold.
"""
return (sum(range(3, threshold, 3)) + sum(range(5, threshold, 5)) - sum(
range(15, threshold, 15)))
@ntimerprinter(500)
def calculate_sum3(threshold=10):
"""Calculates the sum of all 3 and 5 entire multiples below threshold
"""
# number of multiples below the threshold
n3 = int((threshold - 1) / 3)
n5 = int((threshold - 1) / 5)
n15 = int((threshold - 1) / 15)
# generic sum function for multipliers m and highest multiple n
msum = lambda m, n: m * (n + (n * (n - 1)) / 2)
# respective sums
sum3 = msum(3, n3)
sum5 = msum(5, n5)
sum15 = msum(15, n15)
return sum3 + sum5 - sum15
if __name__ == '__main__':
t = 100000
print calculate_sum1(t)
print calculate_sum2(t)
print calculate_sum3(t)
Results:
Run calculate_sum1 500 times in: 4.82500004768 s
2333316668
Run calculate_sum2 500 times in: 0.351000070572 s
2333316668
Run calculate_sum3 500 times in: 0.000999927520752 s
2333316668
Regarding docstring and naming, a few remarks:
First, all of these are important if you intend to share your code publicly. Anyway, you would be glad to follow conventions if this day comes later.
Accroding to PEP8 naming convention:
Function names should be lowercase, with words separated by underscores as necessary to improve readability.
Basically, you followed it but the the in calculate_the_sum is certainly useless. Also, your name lacks of meaning as it do not refer to a sum of multiples. More generally, people tends to give meaningful short name without underscore to public function while longer fully understandable name for private ones. But no rules here, what matters the most is readability and consistency in the way you name your function.
According to PEP257 Docstring Conventions:
Multi-line docstrings consist of a summary line just like a one-line docstring, followed by a blank line, followed by a more elaborate description.
So, it would be better if your summary fit in one line (<120 characters as should be any line in your code, <80 for purist). They are several docstring conventions and the most important once you picked one is to stick to it.
Finally, have a look at the zen of python (PEP20). These are illustrated in The hitchhiker's guide to python (with more detail in the paper book). Specifically, one important aphorism is "sparse is better than dense". Basically, make one statement per line, add inline comments and separate them form the code using blank lines and in your case, do not return a long formula. Split it into several components and return something that appears meaningful. There is no pride in having the shortest code. Python is all about the opposite. Actually, important library that are following this principle are easy to read (for instance: pandas.Series) and it is such a pleasure to read it like English, learning from it, reviewing it and collaborate.
For the first problem I suggest you some performance improvements. You can use inclusion-exclusion technique for this problem.
So first improvement
def calculate_the_sum(threshold = 10):
return(sum(range(3, threshold, 3)) + sum(range(5, threshold, 5)) - sum(range(15, threshold, 15)))
def main():
threshold = 1000000
print(' Calculates the sum of all numbers that are multiples of 3 or 5')
print(' The Sum of numbers below {} is: {}'.format(threshold,calculate_the_sum(threshold)))
if __name__ == "__main__":
main()
I have tested both solutions in ideone (Python 3) for threshold=1000000. Your solution ~ 0.20s. My ~ 0.05s.
Next – you can use well known formula for the sum of arithmetic progression.
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|
https://www.hpmuseum.org/forum/thread-9920.html
|
another interesting math riddle
01-13-2018, 01:37 AM
Post: #1
Don Shepherd Senior Member Posts: 724 Joined: Dec 2013
another interesting math riddle
145 = 1! + 4! + 5!
find three other numbers like that.
01-13-2018, 02:04 AM
Post: #2
Gerson W. Barbosa Senior Member Posts: 1,362 Joined: Dec 2013
RE: another interesting math riddle
1 = 1!
2 = 2!
Well, that’s 2/3 of the answers. In an examination that would grant me a C, wouldn’t it? :-)
01-13-2018, 06:02 AM
Post: #3
Joe Horn Senior Member Posts: 1,687 Joined: Dec 2013
RE: another interesting math riddle
UBASIC:
list
10 repeat:inc X0:X=X0:clr T
20 while X>0:X\=10:T+=!(res):wend
30 until T=X0:print T:goto 10
OK
run
1
2
145
40585
<0|ɸ|0>
-Joe-
01-13-2018, 06:14 AM
Post: #4
Don Shepherd Senior Member Posts: 724 Joined: Dec 2013
RE: another interesting math riddle
Joe, you got it.
I got this from a book, "The Penguin Dictionary of Curious and Interesting Numbers." At first I thought 40585 was wrong until I remembered that 0!=1 and not 0, another math oddity.
01-13-2018, 10:03 AM
Post: #5
Didier Lachieze Senior Member Posts: 1,242 Joined: Dec 2013
RE: another interesting math riddle
To find a limit to the numbers that could meet the criteria, we can compare the number of digits of a number to the number of digits of the maximum sum of its digits factorials.
On the Prime in the sequence app, entering U1(N)= CEILING(LOG(9!*N))-N and going to the NUM view tells us that any number with more 7 digits cannot meet the criteria as it is superior to the maximum sum of its digits factorials (9!*8 has only 7 digits and is lower than any 8-digit number) and that for 7 digit numbers only the ones below 9!*7 (2540160) are candidates.
So the following program returns all possible solutions :
Code:
EXPORT TST() BEGIN LOCAL n,r:={}; FOR n FROM 1 TO 9!*7 DO IF ΣLIST((ASC(STRING(n))-48)!)==n THEN r(0):=n END; END; RETURN r; END;
On my Prime rev C with the Beta 3 firmware it returns {1,2,145,40585} after 16'21".
There may be smarter and faster ways to check for all possible solutions.
01-13-2018, 12:47 PM
Post: #6
SlideRule Senior Member Posts: 1,255 Joined: Dec 2013
RE: another interesting math riddle
(01-13-2018 06:14 AM)Don Shepherd Wrote: … from … "The Penguin Dictionary of Curious and Interesting Numbers." …
page 140 ?
BEST!
SlideRule
01-13-2018, 03:34 PM
Post: #7
Don Shepherd Senior Member Posts: 724 Joined: Dec 2013
RE: another interesting math riddle
(01-13-2018 12:47 PM)SlideRule Wrote:
(01-13-2018 06:14 AM)Don Shepherd Wrote: … from … "The Penguin Dictionary of Curious and Interesting Numbers." …
page 140 ?
BEST!
SlideRule
yes, that's where I saw it.
01-13-2018, 05:28 PM
Post: #8
SlideRule Senior Member Posts: 1,255 Joined: Dec 2013
RE: another interesting math riddle
from the front cover insert of the Penguin Dictionary of Curious & Interesting Geometry
David Wells was born in 1940. He had the rare distinction
of being a Cambridge scholar in mathematics and
failing his degree. He subsequently trained as a teacher
and, after working on computers and teaching machines,
taught mathematics and science in a primary school and
mathematics in secondary schools. He continues to be
involved with education through writing and working
with teachers.
While at university he became British under-21 chess
champion, and in the middle seventies was a game inventor,
devising 'Guerilla' and 'Checkpoint Danger', a
puzzle composer, and the puzzle editor of Games and
Puzzles magazine. From 1981 to 1983 he published The
Problem Solver, a magazine of mathematical problems
for secondary pupils. He has published several books of
problems and popular mathematics, including Can You
Solve These? and Hidden Connections, Double
Meanings, and also publishes the journal Studies of
Meaning, Language and Change. He has written The
Penguin Dictionary of Curious and Interesting Numbers
and recently published a book comparing the psychology
of the Russians with that of the West.
sic: bold my emphasis
[attachment=5559] [attachment=5560]
BEST!
SlideRule
01-13-2018, 09:08 PM
Post: #9
olr Junior Member Posts: 12 Joined: Apr 2014
RE: another interesting math riddle
(01-13-2018 10:03 AM)Didier Lachieze Wrote: On my Prime rev C with the Beta 3 firmware it returns {1,2,145,40585} after 16'21".
There may be smarter and faster ways to check for all possible solutions.
Another approach is to go through all sorted lists containing up to 7 digits, calculate the "factorial sum" of the digits and compare the digits of the sum with those in the list. There are $$\sum_{j=1}^7 \binom{9+j}{j} = 19447$$ sorted lists with up to 7 digits. Hence only 19447 possibilities need to be checked (and not 2540160).
If we additionally take into account that at least three (of seven) digits need to be 9s in order to get a 7-digit factorial sum ( $$5\cdot 8!+2\cdot 9! = 927360$$ ), the number of sorted lists with seven digits decreases from 11440 down to 715. Therfore only a total of 8722 possibilities need to be checked.
The following program returns the result in 9 seconds on my Prime rev A (in 19 seconds if the 7-digit optimization is removed).
Code:
EXPORT TST() BEGIN // r result list // l list of digits // s factorial sum // n helper LOCAL r:= {}, l:= {0}, s, n; WHILE SIZE(l) <= 7 DO s:= ΣLIST(l!); IF EQ( l, SORT(ASC(STRING(s))-48) ) THEN // The sum of factorials contains exactly // the summed up digits r(0):= s; END; // get next list of digits // add 1 to the last digit, that is different from 9 // set succesor digits to the same value n:= SIZE(l); WHILE n > 0 AND l(n) == 9 DO n:= n-1; END; IF n > 0 THEN l(n):= l(n)+1; WHILE n < SIZE(l) DO // a digit is never smaller than its predecessor l(n+1):= l(n); n:= n+1; END; ELSE // all digits are 9s -> new digit l:= MAKELIST(0,X,1,SIZE(l)+1); END; // to get a 7-digit number at least three 9s are necessary // 8!*5 + 9!*2 = 927360 IF SIZE(l) == 7 THEN l(5):= 9; l(6):= 9; l(7):= 9; END; END; RETURN r; END;
01-13-2018, 10:29 PM
Post: #10
Didier Lachieze Senior Member Posts: 1,242 Joined: Dec 2013
RE: another interesting math riddle
(01-13-2018 09:08 PM)olr Wrote: Another approach is to go through all sorted lists containing up to 7 digits, calculate the "factorial sum" of the digits and compare the digits of the sum with those in the list.
Great solution and optimization !
01-14-2018, 07:10 AM
Post: #11
Joe Horn Senior Member Posts: 1,687 Joined: Dec 2013
RE: another interesting math riddle
(01-13-2018 10:03 AM)Didier Lachieze Wrote: ... any number with more 7 digits cannot meet the criteria as it is superior to the maximum sum of its digits factorials (9!*8 has only 7 digits and is lower than any 8-digit number) and that for 7 digit numbers only the ones below 9!*7 (2540160) are candidates.
That's true in base 10, but if we extend the riddle to larger bases, it allows the factorials to be larger. For example, both 1441 and 1442 are solutions in base 15:
#1441d = #661(15) = 6! + 6! + 1!
#1442d = #662(15) = 6! + 6! + 2!
Unfortunately there don't seem to be ANY solutions which include a digit > 9, regardless of base. Strange.
<0|ɸ|0>
-Joe-
01-14-2018, 10:22 AM
Post: #12
Gamo Senior Member Posts: 625 Joined: Dec 2016
RE: another interesting math riddle
Here another interesting math riddle.
12345 MOD 67890 = 12345
98765 MOD 43210 = 12345
Gamo
01-14-2018, 10:44 AM
Post: #13
grsbanks Senior Member Posts: 1,200 Joined: Jan 2017
RE: another interesting math riddle
(01-14-2018 10:22 AM)Gamo Wrote: Here another interesting math riddle.
12345 MOD 67890 = 12345
Err... Nothing surprising about that one.
X MOD Y = X for all cases where X < Y
01-17-2018, 11:59 PM
Post: #14
Didier Lachieze Senior Member Posts: 1,242 Joined: Dec 2013
RE: another interesting math riddle
(01-13-2018 09:08 PM)olr Wrote: The following program returns the result in 9 seconds on my Prime rev A (in 19 seconds if the 7-digit optimization is removed).
Code:
EXPORT TST() BEGIN // r result list // l list of digits // s factorial sum // n helper LOCAL r:= {}, l:= {0}, s, n; WHILE SIZE(l) <= 7 DO s:= ΣLIST(l!); IF EQ( l, SORT(ASC(STRING(s))-48) ) THEN // The sum of factorials contains exactly // the summed up digits r(0):= s; END; // get next list of digits // add 1 to the last digit, that is different from 9 // set succesor digits to the same value n:= SIZE(l); WHILE n > 0 AND l(n) == 9 DO n:= n-1; END; IF n > 0 THEN l(n):= l(n)+1; WHILE n < SIZE(l) DO // a digit is never smaller than its predecessor l(n+1):= l(n); n:= n+1; END; ELSE // all digits are 9s -> new digit l:= MAKELIST(0,X,1,SIZE(l)+1); END; // to get a 7-digit number at least three 9s are necessary // 8!*5 + 9!*2 = 927360 IF SIZE(l) == 7 THEN l(5):= 9; l(6):= 9; l(7):= 9; END; END; RETURN r; END;
I've made a few changes to your program and now it returns the result in less than 7 seconds.
Code:
EXPORT TST() BEGIN // r result list // l list of digits // s factorial sum // n helper LOCAL r:= {}, l:= {0}, k, s, n; WHILE SIZE(l) <= 7 DO s:= ΣLIST(l!); IF EQ( l, SORT(ASC(STRING(s))-48) ) THEN // The sum of factorials contains exactly // the summed up digits r(0):= s; END; // get next list of digits // add 1 to the last digit, that is different from 9 // set successor digits to the same value n:= (POS(l,9)-1) MOD (SIZE(l)+1); l(n):= (l(n)+1) MOD 10; //if n=0, add a 0 element to l FOR k FROM n TO SIZE(l)-1 DO // a digit is never smaller than its predecessor l(k+1):= l(k); END; // to get a 7-digit number at least three 9s are necessary // 8!*5 + 9!*2 = 927360 IF SIZE(l) == 7 THEN l:=CONCAT(l({1,4}),{9,9,9}); END; END; RETURN r; END;
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http://nodus.ligo.caltech.edu:8080/40m/?id=14120&sort=Category
|
40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
40m Log, Page 235 of 339 Not logged in
ID Date Author Type Category Subject
11313 Tue May 19 17:53:38 2015 ranaUpdateModern ControlBrushing up on Wiener Filtering
Good to see that misofw.m is still alive and well. Todo:
1. Apply weighting to the filter via time domain SOS prefiltering of the signals (see Jenne's code from the LLO Global FF paper)
2. Consider using some of the MC SUSPOS signals. Its not strictly legal, but I wonder if its responsible for out noise below 1 Hz.
3. Steve was in the midst of hooking up the Wilcoxones to get better subtraction at 5-15 Hz, but couldn't find cables. We need to hunt them down in W Bridge.
4. Attach one of the medium or big Lings to the MC2 chamber platform and see if we can do this in hardware without driving the suspension. WE want to use a DAC channel (from where?) and pipe it to the Ling using a medium high current drive. Might start with the 50 Ohm output of the SR560 and later use a BUF634 ala Crackle coil driver.
14603 Fri May 10 18:24:29 2019 gautamUpdateNoiseBudgetaligoNB
I pulled the aligoNB git repo to /ligo/GIT/aligoNB/aligoNB. There isn't a reqs.txt file in the repo so installing the dependencies on individual workstations to get this running is a bit of a pain. I found the easiest thing to do was to setup a virtual environment for the python3 stuff, this way we can run python2 for the cdsutils package (hopefully that gets updated soon). I'm setting up a C1 directory in there, plan is to budget some subsystems like Oplev, ALS for now, and develop the code for the eventual IFO locking. As a test, I ran the H1 noise budget (./aligonb H1), works, so looks like I got all the dependencies...
15047 Mon Nov 25 22:10:26 2019 shrutiUpdateNoiseBudgetDiagnostics
This is to help troubleshoot the excess noise measured earlier.
The following channels were measured at GPS times 1258586880 s and 1258597457 s, corresponding to low and high Power Recycling Gain (PRG) respectively.
Excess noise was seen between 25-110 Hz in the high PRG case when compared to the low PRG case in the following channels:
C1:LSC-CARM-IN1_DQ (shown in Attachment 1 where the reference is low PRG)
C1:ALS-Y_ERR_MON_OUT_DQ
C1:ALS-BEAT{X,Y}_FINE_PHASE_OUT_DQ
C1:SUS-ETM{X,Y} _SENSOR_{LL,LR,UL,UR}
C1:ALS-TRX_OUT_DQ
Surprisingly, it was also seen to a smaller extent in (refer Attachment 3)
C1:SUS-ITMX_SENSOR_{LL,LR,UL,UR}
A different type of noise spectrum, attributed to known electronic effects, was observed for
C1:SUS-ITMY_SENSOR_{LL,UL} (refer Attachment 2)
These did not show any significant change in the noise spectrum:
C1:LSC-DARM-IN1_DQ (shown in Attachment 1 where the reference is low PRG)
C1:ALS-X_ERR_MON_OUT_DQ
C1:ALS-TRY_OUT_DQ
C1:SUS-ITMY_SENSOR_{LL,LR,UL,UR}
C1:SUS-ITMY_SENSOR_{LR,UR} (refer Attachment 2)
C1:LSC-PO{X,Y}11_I_ERR_DQ
Attachment 1: LSC.pdf
Attachment 2: ITMY.pdf
Attachment 3: ITMX_L.pdf
15300 Tue Apr 7 15:30:40 2020 JonSummaryNoiseBudget40m noise budget migrated to pygwinc
In the past year, pygwinc has expanded to support not just fundamental noise calculations (e.g., quantum, thermal) but also any number of user-defined noises. These custom noise definitions can do anything, from evaluating an empirical model (e.g., electronics, suspension) to loading real noise measurements (e.g., laser AM/PM noise). Here is an example of the framework applied to H1.
Starting with the BHD review-era noises, I have set up the 40m pygwinc fork with a working noise budget which we can easily expand. Specific actions:
• Updated the 40m fork to the latest pygwinc version (while preserving the commit history).
• Added a directory ./CIT40m containing the 40m-specific noise budget files (created by GV).
• Added an ipython notebook CIT40m.ipynb at the root level showing how to generate a noise budget.
• Integrated our DAC and seismic noise estimators into pygwinc.
• Marked the old 40m NB repo as obsolete (last commit > 2 yrs ago). Many of these noise estimates are probably stale, but I will work with GV to identify which ones can be migrated.
I set up our fork in this way to keep the 40m separate from the main pygwinc code (i.e., not added to as a built-in IFO type). With the 40m code all contained within one root-level directory (with a 40m-specific name), we should now always be able to upgrade to the latest pygwinc without creating intractable merge conflicts.
16152 Fri May 21 12:12:11 2021 PacoUpdateNoiseBudgetAUX PDH loop identification
[Anchal, Paco]
We went into 40m to identify where XARM PDH loop control elements are. We didn't touch anything, but this is to note we went in there twice at 10 AM and 11:10 AM.
16975 Wed Jul 6 19:58:16 2022 PacoSummaryNoiseBudgetXARM noise budget
[Anchal, Paco, Rana]
We locked the XARM using POX11 and made a noise budget for the single arm displacement; see Attachment #1. The noise budget is rough in that we use simple calibrations to get it going; for example we calibrate the measured error point C1:LSC-XARM_IN1_DQ using the single cavity pole and some dc gain to match the UGF point. The control point C1:LSC-XARM_OUT_DQ is calibrated using the actuator gain measured recently by Yuta. We also overlay an estimate of the seismic motion using C1:PEM-SEIS_BS_X_OUT_DQ (calibrated using a few poles to account for stack and pendulum), and finally the laser frequency noise as proxied by the mode cleaner C1:IOO-MC_F_DQ.
A couple of points are taken with this noise budget, apart from it needing a better calibration;
1. Overall the inferred residual displacement noise is high, even for our single arm cavity.
1. By looking at the sim OLTF in foton, it seemed that the single arm cavity loop TF could easily become unstable due to some near-UGF-funkiness likely from FM3 (higher freq boost), so we disabled the automatic triggering on it; the arm stayed locked and we changed the error signal (light blue vs gold (REF1) trace)
2. The arm cavity is potentially seeing too much noise from the IMC in the 1 to 30 Hz band in the form of laser frequency noise.
1. Need IMC noise budget to properly debug.
3. At high frequency (>UGF), there seem to be a bunch of "wiggles" which remain unidentified.
1. We actually tried to investigate a bit into these features, thinking they might have something to do with misalignment, but we couldn't really find significant correlation.
RXA edit:
1. we also noticed some weirdness in the calibration of MC_F v. Arm. We think MC_F should be in units of Hz, and Paco calculated the resulting motion as seen by the arm, but there was a factor of several between these two. Need to calibrate MC_F and check. In principle, MC_F will show up directly in ALS_BEATX (with the green PDH lock off), and I assume that one is accurately calibrated. Somehow we should get MC_F, XARM, and ALS_BEAT to all agree. JC is working on calibrating the Mini-Circuits frequency counter, so once that is done we will be in good shape.
2. we may need to turn on some MC_L feedback for the IMC, so that the MC length follows the NPRO frequency below ~20 Hz.
3. Need to estimate where the IMC WFS noise is in all of this. Does it limit the MC length stability in any frequency band? How do we determine this?
4. Also, we want to redo this noise budget today, whilst using AS55 instead of POX. Please measure the Schnupp asymmetry by checking the optimum demod phase in AS55 for locking Xarm v Yarm.
Attachment 1: xarm_nb_2022_07.pdf
5 Fri Oct 19 16:11:38 2007 pkpOtherOMCOMC PZT response
Sam and I locked the laser to the OMC cavity and looked at the error signal as a function of the voltage applied to the OMC PZT.
Here are two plots showing the response as a function of frequency from 1 kHz to 100 kHz and another high-res response in the region of 4.5 kHz to 10 kHz.
Attachment 1: fullspec.jpg
Attachment 2: 4.5to10.jpg
Attachment 3: 4.5to10.pdf
Attachment 4: fullres.pdf
6 Sat Oct 20 11:54:13 2007 waldmanOtherOMCOMC and OMC-SUS work
[Rich, Chub, Pinkesh, Chris, Sam]
Friday the 18th was a busy day in OMC land. Both DCPDs were mounted to the glass breadboard and the OMC-SUS structure was rebuilt to the point that an aluminum dummy mass is hanging, unbalanced. The OSEMs have not be put on the table cloth yet, but everything is hanging free. As for the DCPDs, if you recall one beam is 3mm off center from the DCPD tombstone. Fortunately, one DCPD is nearly 3mm offcenter from the case in the right direction, so the errors nearly cancel. The DCPD is too high, so the beam isn't quite centered, but they're close. We'll get photos of the beam positions in someday. Also, the DC gain between the two PDs is, at first glance, different by 15%. DCPD1, the one seen in transmission has 315 mV of signal while DCPD2 has 280 mV. Not sure why, could be because of beam alignment or tolerances in the Preamp or the angle incident on the diode or the QE of the diodes. The glass cans have *not* been removed.
8 Mon Oct 22 19:27:14 2007 pkpOtherOMCPZT calibration/ transfer function.
We measured the PZT transfer function by comparing the PZT response of the circuit with the cavity in the loop, with that of the circuit without the cavity in the loop. Basically measure the transfer function of the whole loop with the laser/PZT and Op-amps in it. Then take another measurement of the transfer function of everything else besides the PZT and from both these functions, we can calculate the PZT response.
The calibration was done by using the error signal response to a triangular wave of volts applied to the PZT. A measurement of the slope of the error signal , which has three zero-crossings as the cavity sweeps through the sidebands, gives us the Volts/Hz response. In order to derive a frequency calibration of the x axis, we assume that the first zero crossing corresponds to the first side band (-29.5 MHz) and the third one corresponds with the other sideband (+29.5 MHz). And then by using the fact that we know the response of the cavity to a constant frequency shift, we can use the Volts/Hz measurement to calculate the Volts/nm calibration. The slope that was calculated was 3.2e-6 V/Hz and using the fact that the cavity is 1 m in length and the frequency is 1064 nm, we get a calibration of 0.9022 V/nm.
Attachment 1: calib.pdf
Attachment 2: calibpzt2.pdf
Attachment 3: all2.pdf
Attachment 4: noPZT2.pdf
9 Tue Oct 23 09:01:00 2007 ranaOtherOMCPZT calibration/ transfer function.
Are you sure that the error signal sweep is not saturated on the top ends? This is usually the downfall
of this calibration method.
14 Thu Oct 25 17:52:45 2007 waldmanOtherOMCOMCs with QPDs
[Rich, Chub, Pinkesh, Sam]
Yesterday we got the QPD, OTAS, and PZT cabling harness integrated with the OMC. We found a few things out, not all of them good. The QPDs went on no problem and could be fairly well aligned by hand. We "aligned" them by looking at all four channels of the QPD on the scope and seeing that there is signal. Since the beam is omega = 0.5 mm, this is a reasonable adjustment. We then connected the OTAS connector to the OTAS and found that the heater on the OTAS was bonded on about 30 degrees rotated from its intended position. This rotated the connector into the beam and caused a visible amount of scattering. This wasn't really a disaster until I removed the connector from the heater and broke the heater off of the aluminum parts of the OTAS. Two steps backwards, one step forward. After the OMC, OMC-SUS integration test we will re-bond the heater to the aluminum using VacSeal. In the meantime, the OMC has been moved to Bridge 056 for integration with the OMC-SUS. More on that as we make progress.
16 Thu Oct 25 23:35:36 2007 waldmanOtherOMCHang the OMC!
[Pinkesh, Sam]
We tried, convicted and hung the OMC today. The OMC was found guilty of being overweight, and unsymmetrically balanced. The unsymmetry was kind of expected and was corrected with a hefty stack of counterweights positioned over the counterweighting holes. The stacks will be measured at some future date and correctly sized objects machined. The overweightness showed up when the level hanging breadboard was about 5 mm low. This showed up in the board height above the table as well as the OSEM flag positions within their holes. The problem was remedied with a liposuction of the intermediate mass. We removed both small vertical cylinder weights that Chris added, and then we removed the heavy steel transverse weight that can be used to adjust the tip around the long axis (I forgot what its called).
The top of the breadboard ended up about 154 mm off the table. The breadboard is 39 mm thick, and the optics are centered (30 - 12.7) = 17.3 mm below the surface for a as hanging beams height of 154 -39 - 17.3 = 97.7 mm or about an 0.150 inches lower than we were aiming for. Can I get a refund?
We screwed up in multiple ways:
• The slotted disks that capture the wires do not have the alignment bore used to center the wire in the hole
• We didn't correctly route the far field QPD cable so it runs funny
• We didn't have a tool which could be used to get two of the DCPD preamp box mounting screws (which are M3's chub!)
• We don't have the cable clamps to tie off the electrical cables to the intermediate mass
• We don't have any of the cabling from the OMC-SUS top to the rack so we can't test anything
• We haven't uploaded pretty pictures for all to see
We left the OMC partially suspended by the OMC-SUS and partly resting on the installation lab jacks which are currently acting as EQ stops. After we fix the cabling we will more permanently hang it. PS, It looks like the REFL beam extraction will be tricky so we need to get on that....
Attachment 1: IMG_1483.jpg
Attachment 2: IMG_1481.jpg
19 Fri Oct 26 17:34:43 2007 waldmanOtherOMCOMC + earthquake stops
[Chub, chris, Pinkesh, Sam]
Last night we hugn the OMC for the first time and came up with a bunch of pictures and some problems. Today we address some of the problems and, of course, make new problems. We replaced the flat slotted disks with the fitted slotted disks that are made to fit into the counterbore of the breadboard. This changed the balance slightly and required a more symmetric distribution of mass. It probably did not change the total mass very much. We did find that the amount of cable hanging down strongly affected the breadboard balance and may also have contributed to the changing balance.
We also attached earthquake stops and ran into a few problems:
• The bottom plate of the EQ stops is too thick so that it bumps into the tombstones
• The vertical member on the "waist" EQ stops is too close to the breadboard, possibly interfering with the REFL beam
• The "waist" EQ stops are made from a thin plate that doesn't have enough thickness to mount helicoils in
• Helicoil weren't loaded in the correct bottom EQ stops
• The DCPD cable loops over the end EQ stop looking nasty but not actually making contact
However, with a little bit of jimmying, the EQ stops are arrayed at all points within a few mm of the breadboard. Meanwhile, Chub has cabled up all the satellite modules and DCPD modules and Pinkesh is working on getting data into the digital system so we can start playing games. Tonight, I intend to mount a laser in Rana's lab and fiber couple a beam into the 056 room so we can start testing the suspended OMC.
20 Fri Oct 26 21:48:40 2007 waldmanConfigurationOMCFiber to 056
I set up a 700 mW NPRO in Rana's lab and launched it onto a 50m fiber. I got a few mW onto the fiber, enough to see with a card before disabling the laser. The fiber now runs along the hallway and terminates in rm 056. Its taped down everywhere someone might trip on it, but don't go out of your way to trip on it or pull on it because you are curious. Tomorrow I will co-run a BNC cable and attenuate the NPRO output so it can only send a few mW and so be laser safe. Then we can try to develop a procedure to align the beam to a suspended OMC and lock our suspended cavity goodness.
Notes to self: items needed from the 40m
• ND10 and ND20 neutral density filter
• EOM and mount set for 4 inch beam height
• Post for fiber launch to get to 4 inch
• Mode matching lens at 4in
• 3x steering mirror at 4in
• RF photodiode at 4in
• Post for camera to 4in
• Light sheild for camera
• Long BNC cable
Some of these exist at 056 already
21 Sat Oct 27 19:00:44 2007 waldmanConfigurationOMCHanging, locked OMC with REFL extracted.
I got the OMC locked to the fiber output today. It was much more difficult than I expected and I spent about 30 minutes or so flailing before stopping to think. The basic problem is that the initial alignment is a search in 4-dimensional space and there is naturally only one signal, the reflected DC level, to guide the alignment. I tried to eyeball the alignment using the IR card and "centering" the beams on mirrors, but I couldn't get close enough to get any light through. I also tried to put a camera on the high reflector transmission, but with 1.5 mW incident on the cavity, there is only 1.5 microwatts leaking through in the best case scenario, and much, much less during alignment.
I resolved the problem by placing a high reflector on a 3.5 inch tall fixed mount and picking off the OMC transmitted beam before it reaches the DC diodes. I took the pickoff beam to a camera. The alignment still sucked because even though the beam cleanly transmitted the output coupler, it wasn't anywhere close to getting through the OTAS. To resolve this problem, I visually looked through the back of M2 at M1 and used the IR card to align the beam to the centers of each mirror. That was close enough to get me fringes and align the camera. With the camera aligned, the rest was very easy.
I restored the PDH setup we know and love from the construction days and locked the laser to the OMC with no difficulty. The laser is in Rana's lab so I send the +/- 10V control signal from the SR560 down a cable to 058E where it goes into the Battery+resistor box, the Throlabs HV amplifier, and finally the FAST channel of the NPRO. BTW, a simple experiment sows that about 35 +/- 3 V are required to get an FSR out of the NPRO, hence the Thorlabs HV. The EOM, mixer, splitter, etc is on the edge of the table.
With this specific OMC alignment, ie. the particular sitting on EQ stops, it looks like all of the ghost beams have a good chance of coming clear. I can fit a 2 inch optic in a fixed mount in between the end of the breadboard and the leg of the support structure. A picture might or might not be included someday. One of the ghost beams craters directly into the EQ stop vertical member. The other ghost barely misses M2 on its way down the length of the board. In its current configuration, the many REFL beam misses the leg by about 1.5 inches.
25 Mon Oct 29 11:07:22 2007 waldmanSoftware InstallationOMCSoftware install on OMS
[Alex, Sam]
We spent a little time this morning working on OMS and getting things restarted. A few changes were made. 1) We put openmotif on OMS so that the burtrb doesn't throw that crappy libXm any more. 2) We upgraded OMS to a 32 kHz sampling rate from 2 kHz. All the filters will have to be changed. We also added a PDH filter path to maybe feedback PDH signals cuz that will be cool. Maybe someday I will write up the very cool channel adding procedure.
26 Mon Oct 29 12:20:15 2007 waldmanConfigurationOMCChanged OMS filters
I changed the OMS configuration so that some of the OMC-SUS LED channels go to a breakout box so that we can input the PDH error signal. After lunch, we will try to lock the cavity with a PDH error signal and digital filters. Then its on to dither locked stuff. Note that this LED business will have to be changed back some day. For now, it should be extremely visible because there are dangling cables and a hack job interface lying around.
27 Mon Oct 29 23:10:05 2007 waldmanConfigurationOMCLost in DAQspace
[Pinkesh, Sam]
In setting up a Digital based control of the hanging OMC, we naively connect the Anti-Imaging filter output to an Anti-Aliasing input. This led to no end of hell. For one thing, we found the 10 kHz 3rd order butterworth at 10 kHz, where it should be based on the install hardware. One wonders in passing whether we want a 10 kHz butter instead of a 15 kHz something else, but I leave that for a later discussion. Much more bothersome is a linear phase shift between output and input that looks like ~180 microseconds. It screams "What the hell am I!?" and none of us could scream back at it with an answer. I believe this will require the Wilson House Ghost Busters to fully remedy on the morrow.
Attachment 1: SS.pdf
Attachment 2: SS.gif
37 Wed Oct 31 09:45:28 2007 waldmanOtherOMCResolution to DAQland saga
[Jay, Sam]
We did a rough accounting for the linear delay this morning and it comes out more or less correct. The 10 kHz 3rd order butterworth AA/AI filter gives ~90 degrees of phase at 6 kHz, or 42 microseconds. Taken together, the two AA and AI filters are worth 80 microseconds. The 1.5 sample digital delay is worth 1.5/32768 = 45 microseconds. The remaining 160 - 125 = 35 microseconds is most likely taken up by the 64 kHz to 32 kHz decimation routine, assuming this isn't accounted for already in the 1.5 sample digital delay.
It remains to be seen whether this phase delay is good enough to lock the laser to the OMC cavity
42 Wed Oct 31 23:55:17 2007 waldmanOtherOMCQPD tests
The 4 QPDs for the OMC have been installed in the 056 at the test setup. All 4 QPDs work and have medm screens located under C2TPT. The breadboard mounted QPDs are not very well centered so their signal is somewhat crappy. But all 4 QPDs definitely see plenty of light. I include light and dark spectra below. QPDs 1-2 are table-mounted and QPD 2 is labeled with a bit of blue tape. QDPs 3-4 are mounted on the OMC. QPD3 is the near field detector and QPD4 is the far field. In other words, QPD3 is closest to the input coupler and QPD4 is farthest.
Included below are some spectra of the QPDs with and without light. For QPDs 1 & 2, the light source is just room lights, while 3&4 have the laser in the nominal OMC configuration with a few mWs as source. The noise at 100 Hz is about 100 microvolts / rtHz. If I recall correctly, the QPDs have 5 kOhm transimpedance (right Rich?) so this is 20 nanoamps / rtHz of current noise at the QPD.
Attachment 1: QPD_SignalSpectrum.pdf
Attachment 2: QPD_SignalSpectrum.gif
43 Thu Nov 1 01:28:04 2007 waldmanOtherOMCFirst digital lock of OMC
[Pinkesh, Sam]
We locked a fiber based NPRO to the suspended OMC tonight using the TPT digital control system. To control the laser frequency, we took the PZT AI output and ran it on a BNC cable down the hallway to the Thorlabs HV box. The Thorlabs is a singled ended unit so we connected the AI positive terminal only and grounded the BNC to the AI shield. We could get a -6 to 1.5 V throw in this method which fed into the 10 k resisotr + 9 V battery at the input of the HV box. The HV out ran to the NPRO PZT fast input.
We derived our error signal from a PDA255 in reflection with a 29.5 MHz PDH lock. The signal feeds into one of the unused Tip/Tilt AA channels and is passed to the PZT LSC drive through the TPT_PDH1 filter bank. In the PZT_LSC filter we put a single pole at 1 Hz which, together with the phase we mentioned the other night (180 degrees at 3 kHz) should allow a 1 kHz-ish loop. In practice, as shown below, we got a 650 Hz UGF with 45 degrees of phase margin and about 6 dB of gain margin.
The Lower figure shows the error point spectrum with 3 settings. REF0 in blue shows lots of gain peaking at 1.5 kHz-ish, just where its expected - the gain was -40. The REF1 has gain of -20 and shows no gain peaking. The current trace in red shows some gain peaking cuz the alignment is better but it also has included a 1^2:20^2 boost which totally crushes the low frequency noise. We should do a better loop sweep after getting the alignment right so we can see how much boost it will really take.
Just for fun, we are leaving it locked overnight and recording the PZT_LSC data for posterity.
Attachment 1: 071101_PZT_firstLoopSweep.pdf
Attachment 2: 071101_PZT_firstLoopSweep.gif
Attachment 3: 071101_OMC_FirstLock_spectra.pdf
Attachment 4: 071101_OMC_FirstLock_spectra.gif
58 Fri Nov 2 12:18:47 2007 waldmanSummaryOMCLocked OMC with DCPD
[Rich, Sam]
We locked the OMC and look at the signal on the DCPD. Plots included.
Attachment 1: 071102_OMC_LockedDCPD.gif
Attachment 2: 071102_OMC_LockedDCPD.pdf
59 Sat Nov 3 16:20:43 2007 waldmanSummaryOMCA good day's work
I followed up yesterday's test of the PZT with a whole mess of characterizations of the PZT control and finished the day by locking the OMC with a PZT dither lock and a 600 Hz loop. I haven't analyzed any of the data yet, so its not calibrated in physical units and etc. etc. etc. Since a lot of the sweeps below are of a "drive the PZT, look at the PDH signal" nature, a proper analysis will require taking out the loop and calibrating the signals, which alas, I haven't done. Nonetheless, I include all the plots because they are pretty. The files included below are:
• DitherLock_sweep: Sweep of the IN2/IN1 for the dither lock error point showing 600 Hz UGF
• HiResPZTDither_sweep: Sweep of the PZT dither input compared to the PDH error signal. I restarted the front end before the sweep was finished accounting for the blip.
• HiResPZTDither_sweep2: Finish of the PZT dither sweep
More will be posted later.
Attachment 1: 071103_DitherLock_sweep.png
Attachment 2: 071103_DitherLock_sweep.pdf
Attachment 3: 071103_HiResPZTDither_sweep.png
Attachment 4: 071103_HiResPZTDither_sweep.pdf
Attachment 5: 071103_HiResPZTDither_sweep2.png
Attachment 6: 071103_HiResPZTDither_sweep2.pdf
60 Sun Nov 4 23:22:50 2007 waldmanUpdateOMCOMC PZT and driver response functions
I wrote a big long elog and then my browser hung up, so you get a less detailed entry. I used Pinkesh's calibration of the PZT (0.9 V/nm) to calibrate the PDH error signal, then took the following data on the PZT and PZT driver response functions.:
• FIgure 1: PZT dither path. Most of the features in this plot are understood: There is a 2kHz high pass filter in the PZT drive which is otherwise flat. The resonance features above 5 kHz are believed to be the tombstones. I don't understand the extra motion from 1-2 kHz.
• Figure 2: PZT dither path zoom in. Since I want to dither the PZT to get an error signal, it helps to know where to dither. The ADC Anti-aliasing filter is a 3rd order butterworth at 10 kHz, so I looked for nice flat places below 10 KHz and settled on 8 kHz as relatively harmless.
• Figure 3: PZT LSC path. This path has got a 1^2:10^2 de-whitening stage in the hardware which hasn't been digitally compensated for. You can see its effect between 10 and 40 Hz. The LSC path also has a 160 Hz low path which is visible causing a 1/f between 200 and 500 Hz. I have no idea what the 1 kHz resonant feature is, though I am inclined to point to the PDH loop since that is pretty close to the UGF and there is much gain peaking at that frequency.
Attachment 1: 071103DitherShape.png
Attachment 2: 071103DitherZoom.png
Attachment 3: 071103LSCShape.png
Attachment 4: 071103DitherShape.pdf
Attachment 5: 071103DitherZoom.pdf
Attachment 6: 071103LSCShape.pdf
Attachment 7: 071103LoopShape.pdf
63 Mon Nov 5 14:44:39 2007 waldmanUpdateOMCPZT response functions and De-whitening
The PZT has two control paths: a DC coupled path with gain of 20, range of 0 to 300 V, and a pair of 1:10 whitening filters, and an AC path capacitively coupled to the PZT via a 0.1 uF cap through a 2nd order, 2 kHz high pass filter. There are two monitors for the PZT, a DC monitor which sniffs the DC directly with a gain of 0.02 and one which sniffs the dither input with a gain of 10.
There are two plots included below. The first measures the transfer function of the AC monitor / AC drive. It shows the expected 2 kHz 2d order filter and an AC gain of 100 dB, which seems a bit high but may be because of a filter I am forgetting. The high frequency rolloff is the AA and AI filters kicking in which are 3rd order butters at 10 kHz.
The second plot is the DC path. The two traces show the transfer function of DC monitor / DC drive with and with an Anti-dewhitening filter engaged in the DC drive. I fit the antidewhite using a least squares routine in matlab constrained to match 2 poles, 2 zeros, and a delay to the measured complex filter response. The resulting filter is (1.21, 0.72) : (12.61, 8.67) and the delay was f_pi = 912 Hz. The delay is a bit lower than expected for the f_pi = 3 kHz delay of the AA, AI, decimate combination, but not totally unreasonable. Without the delay, the filter is (1.3, 0.7) : (8.2, 13.2) - basically the same - so I use the results of the fit with delay. As you can see, the response of the combined digital AntiDW, analog DW path is flat to +/- 0.3 dB and +/- 3 degrees of phase.
Note the -44 dB of DC mon / DC drive is because the DC mon is calibrated in PZT Volts so the TF is PZT Volts / DAC cts. To calculate this value: there are (20 DAC V / 65536 DAC cts)* ( 20 PZT V / 1 DAC V) = -44.2 dB. Perfect!
I measured the high frequency response of the loop DC monitor / DC drive to be flat.
Attachment 1: 07110_DithertoVmonAC_sweep2-0.png
Attachment 2: 071105_LSCtoVmonDC_sweep4-0.png
Attachment 3: 07110_DithertoVmonAC_sweep2.pdf
Attachment 4: 071105_LSCtoVmonDC_sweep4.pdf
79 Wed Nov 7 14:01:31 2007 waldmanOmnistructureOMCFrequency and Intensity noise
One of the biggest problems I had using the PZT to lock was excessive noise. I did a little noise hunting and found that the problem was the cable running from the rack to the laser fast input. As a reminder, the laser has a 4 MHz / volt fast input. We require about 300 MHz to go one FSR, so there is a Thorlabs HV box between at the NPRO fast input which takes 0-10 V -> 0-150 V. The 150 V HV range is worth about 600 MHz of NPRO frequency.
OLD SETUP: Single side of DAC differential (10 Vpp) -> 9V in series with 10 kOhm -> 10 kOhm input impedance of Thorlabs HV -> NPRO
We used the single side of the DAC differential because we didn't have a differential receiver. This turned out to be a bad idea because the cable picks up every 60 Hz harmonic known to man kind.
NEW SETUP: Digital conditioning -> DAC differential (digitally limited to 0 - 1 V) -> SR560 in A-B mode gain 10 (0 - 10 V output)-> Thorlabs HV -> NPRO.
This has almost no 60 Hz noise and works much, much better. Moral of the story, ALWAYS USE DIFFERENTIAL SIGNALS DIFFERENTIALLY !
Note that I may be saturating the SR560 with 10 V output, Its spec'd for 10 Vpp output with 1 VDC max input. I don't know whether or not it can push 10 V out....
82 Thu Nov 8 00:55:44 2007 pkpUpdateOMCSuspension tests
[Sam , Pinkesh]
We tried to measure the transfer functions of the 6 degrees of freedom in the OMS SUS. To our chagrin, we found that it was very hard to get the OSEMs to center and get a mean value of around 6000 counts. Somehow the left and top OSEMs were coupled and we tried to see if any of the OSEMs/suspension parts were touching each other. But there is still a significant coupling between the various OSEMs. In theory, the only OSEMS that are supposed to couple are [SIDE] , [LEFT, RIGHT] , [TOP1, TOP2 , TOP3] , since the motion along these 3 sets is orthogonal to the other sets. Thus an excitation along any one OSEM in a set should only couple with another OSEM in the same same set and not with the others. The graphs below were obtained by driving all the OSEMS one by one at 7 Hz and at 500 counts ( I still have to figure out how much that is in units of length). These graphs show that there is some sort of contact somewhere. I cant locate any physical contact at this point, although TOP2 is suspicious and we moved it a bit, but it seems to be hanging free now. This can also be caused by the stiff wire with the peek on it. This wire is very stiff and it can transmit motion from one degree of freedom to another quite easily. I also have a graph showing the transfer function of the longitudnal degree of freedom. I decided to do this first because it was simple and I had to only deal with SIDE, which seems to be decoupled from the other DOFs. This graph is similar to one Norna has for the longitudnal DOF transfer function, with the addition of a peak around 1.8 Hz. This I reckon could very be due to the wire, although it is hard to claim for certain. I am going to stop the measurement at this time and start a fresh high resolution spectrum and leave it running over night.
There is an extra peak in the high res spectrum that is disturbing.
Attachment 1: shakeleft.pdf
Attachment 2: shakeright.pdf
Attachment 3: shakeside.pdf
Attachment 4: shaketop1.pdf
Attachment 5: shaketop2.pdf
Attachment 6: shaketop3.pdf
Attachment 7: LongTransfer.pdf
Attachment 8: Shakeleft7Nov2007_2.pdf
Attachment 9: Shakeleft7Nov2007_2.png
86 Fri Nov 9 00:01:24 2007 waldmanOmnistructureOMCOMC mechanical resonances (Tap tap tappy tap)
[Pinkesh, Aidan, Sam]
We did a tap-tap-tappy-tap test of the OMC to try to find its resonances. We looked at some combination of the PDH error signal and the DCPD signal in a couple of different noise configurations. The data included below shows tapping of the major tombstone objects as well the breadboard. I don't see any strong evidence of resonances below the very sharp resonance at 1300 Hz (which I interpret as the diving board mode of the breadboard). If I get free, I 'll post some plots of the different breadboard resonances you can excite by tapping in different places.
(The "normalized" tapping response is abs(tap - reference)./reference.)
Attachment 1: Fig1.png
Attachment 2: Fig2.png
Attachment 3: Fig4.png
Attachment 4: Fig2.pdf
Attachment 5: Fig1.pdf
Attachment 6: Fig4.pdf
Attachment 7: ResonanceData.zip
87 Fri Nov 9 00:23:12 2007 pkpUpdateOMCX and Z resonances
I got a couple of resonance plots going for now. I am still having trouble getting the Y measurement going for some reason. I will investigate that tommorow. But for tonight and tommorow morning, here is some food for thought. I have attached the X and Z transfer functions below. I compared them to Norna's plots - so just writing out what I was thinking -
Keep in mind that these arent high res scans and have been inconviniently stopped at 0.5 Hz .
Z case --
I see two small resonances and two large ones - the large ones are at 5.5 Hz and 0.55 Hz and the small ones at 9 Hz and 2 Hz respectively. In Norna's resonances, these features arent present. Secondly, the two large peaks in Norna's measurement are at 4.5 Hz and just above 1 Hz. Which was kind of expected, since we shortened the wires a bit, so one of the resonances moved up and I suppose that the other one moved down for the same reason.
X case --
Only one broad peak at about 3 Hz is seen here, whereas in Norna's measurement, there were two large peaks and one dip at 0.75 Hz and 2.5 Hz. I suspect that the lower peak has shifted lower than what I scanned to here and a high res scan going upto 0.2 Hz is taking place overnight. So we will have to wait and watch.
Pitch Roll and Yaw can wait for the morning.
Attachment 1: Xtransferfunc.pdf
Attachment 2: Ztransferfunc.pdf
93 Mon Nov 12 10:53:58 2007 pkpUpdateOMCVertical Transfer functions
[Norna Sam Pinkesh]
These plots were created by injected white noise into the OSEMs and reading out the response of the shadow sensors ( taking the power spectrum). We suspect that some of the additional structure is due to the wires.
Attachment 1: VerticalTrans.pdf
99 Wed Nov 14 07:48:38 2007 nornaOmnistructureOMCOMC Cable dressing
[Snipped from an email]
1) Last Friday Pinkesh and I set the OMC up with only the top three OSEMs and took a vertical transfer function. We had removed the other OSEMs due to difficulty of aligning all OSEMs with the weight of the bench etc bringing the top mass lower than the tablecloth can accommodate. See attached TF.Clearly there are extra peaks (we only expect two with a zero in between) and my belief is that at least some of them are coupling of other degrees of freedom caused by the electrical wiring. Pinkesh and I also noticed the difficulty of maintaining alignment if cables got touched and moved around. So.....
2) Yesterday Dennis and I took a look at how much moving a cable bundle around (with the peak shielding) changed the DC alignment. In a not too precise experiment ( using HeNe laser reflecting off the bench onto a surface ~ 1 metre away) we saw that we could reposition the beam one or two mm in yaw and pitch. This corresponds to ~ one or two mrad which is ~ the range of the OSEM DC alignment. We discussed possibility of removing the cabling from the middle mass, removing the peak and taking it from the bench directly to the structure above. I asked Chub if he could make an equivalent bundle of wires as those from the two preamps to see what happens if we repeat the "moving bundle" experiment. So...
3) Today Chub removed the cabling going to the preamps and we replaced it with a mock up of wire bundle going directly from the preamps to the structure above. See attached picture. The wires are only attached to the preamp boxes weighted down with masses but the bundle is clamped at the top. We repeated the "wiggle the bundle" test and couldnt see any apparent movement ( so maybe it is at most sub-mm). The cable bundle feels softer.
The next thing Chub did was to remove the second bundle ( from photodiodes, heater, pzt) from its attachment to the middle mass and strip off the peek. It is now also going to the top of the structure directly. The whole suspension now appears freer. We discussed with Dennis the "dressing " of the wires. There are some minor difficulties about how to take wires from the bright side to the dark side, but in general it looks like that the wires forming the second "bundle" could be brought to the "terminal block" mounted on the dark side and from there looped up to the top of the structure. We would have to try all this of course to see the wiring doesnt get in the way of other things (e.g. the L and R OSEMs). However this might be the way forward. So...
4) Tomorrow Pinkesh and I will check the alignment and then repeat the vertical transfer function measurement with the two bundles as they are going from bench to top of structure. We might even do a horizontal one if the middle mass is now within range of the tablecloth.
We can then remove preamp cables completely and lay the second bundle of cables on the optical bench and repeat the TFs.
The next thing will be to weigh the bench plus cables. This will allow us to
a) work out what counterbalance weights are needed - and then get them manufactured
b) firm up on how to handle the extra mass in terms of getting the masses at the correct height.
And in parallel Chub will work on the revised layout of cabling.
Looking a little further ahead we can also get some stiffness measurements made on the revised bundle design ( using Bob's method which Alejandro also used) and fold into Dennis's model to get some sanity check the isolation.
I think that's it for now. Comments etc are of course welcome.
Norna
Attachment 1: OMC-11-13-07_011.jpg
Attachment 2: VerticalTrans.pdf
102 Wed Nov 14 16:54:54 2007 pkpUpdateOMCMuch better looking vertical transfer functions
[Norna Pinkesh]
So after Chub did his wonderful mini-surgery and removed the peek from the cables and after Norna and I aligned the whole apparatus, the following are the peaks that we see.
It almost exactly matches Norna's simulations and some of the extra peaks are possibly due to us exciting the Roll/longitudnal/yaw and pitch motions. The roll resonance is esp prominent.
We also took another plot with one of the wires removed and will wait on Chub before we remove another wire.
Attachment 1: VerticalTransPreampwireremovedNov142007.pdf
Attachment 2: VerticalTranswiresclampedNov142007.pdf
105 Thu Nov 15 17:09:37 2007 pkpUpdateOMCVertical Transfer functions with no cables attached.
[Norna Pinkesh]
The cables connecting all the electronics ( DCPDs, QPDs etc) have been removed to test for the vertical transfer function. Now the cables are sitting on the OMC bench and it was realigned.
Attachment 1: VerticaltransferfuncnocablesattachedNov152007.pdf
179 Fri Dec 7 11:33:24 2007 waldmanOmnistructureOMCPZT wiring
The 2 pin LEMO connector has got an unmarked pin and a pin marked by a white half-circle.
The unmarked pin is connected to the side of the PZT attached to the mirror.
The marked pin is connected to the side of the PZT attached to the tombstone.
206 Thu Dec 20 19:05:34 2007 waldmanHowToOMCHOWTO build front ends
For instance, to build the TPT front end code.
• go to /cvs/cds/advLIGO on the TPT machine
• do make clean-tpt tpt install-tpt
• do rm /cvs/cds/caltech/chans/daq/C2TPT.ini (this step is needed because the DAQ install code isn't quite right at the time of this writing.
• do make install-daq-tpt
• run starttpt to restart the tpt computer.
Enjoy.
207 Thu Dec 20 19:10:03 2007 waldmanUpdateOMCStressful reattachment of heater
Photos may follow eventually, but for now here's the rundown. I scraped the heater clean of the thermal epoxy using a clean razor blade. Then I stuffed a small piece of lint free cloth in the OTAS bore and wrapped the OMC in tin foil. With a vacuum sucking directly from the face of the OTAS, I gently scraped the glue off the OTAS aluminum. I wiped both the OTAS and the heater down with an isoproponal soaked lint-free cloth. I put a thin sheen of VacSeal on the face of the heater, wiping off the excess from the edges with a cloth. Then I clamped the heater to the OTAS using 2" c-clamps from the tombstone back to the heater front, making sure the alignment of the OTAS was correct (connector on the absolute bottom, concentric with the OTAS outer diameter). I added a second clamp, then beaded the outside of the joint with a little bit extra VacSeal, just for kicks. I'll leave it covered at least overnight, and maybe for a day or two.
sam
1888 Tue Aug 11 23:55:04 2009 rana, richSummaryOMCQuantum Efficiency and Dark Current measurements of eLIGO Photodiodes
Rich Abbott, Rana
Summary: We found that the 3mm InGaAs photodiodes from eGTRAN which are being used for the DC Readout in eLIGO are bad. The QE is ~50%. We will have to replace them ASAP.
Valera and Nic Smith have pointed out out a factor of ~2 discrepancy between the estimated power transmission to the dark port in H1 and L1. So we decided to measure the QE of the accused diodes.
The data of the QE and dark current are attached here.
We used a 1064 nm CrystaLaser (which does not have a very stable power output). We attenuated the light with an ND1.0 for all measurements.
The photocurrent is estimated by reading out the voltage across one leg of the differential drive of the DC PD preamp. The photocurrent goes across a 100 Ohm resistor and then through 2 gain of 1 stages to get to this testpoint, so the overall transimpedance gain is 100 Ohms for this measurement.
By far, the Ophir power meter is the biggest source of error. Its absolute calibration is only 5% and the variation across the sensor face is ~5%. There are some hot and not hot spots on the face which can make even more variation, but we tried to avoid these.
We also inserted the power meter very close to the time when we read the voltage, so that the photocurrent and power estimates are made within 10 seconds of each other. This should reduce the error from the laser's power fluctuations.
All diodes still had the glass case on. We measured the reflected power to be ~5-7% of the incident power. This reflected power is NOT accounted for in these estimates.
Punch line: The eGTRAN diodes that we currently use are definitely bad. The JDSU and EG&G 2mm diodes have a better QE. We should immediately purchase 3 mm versions and get them cut and measured to be ready for the Sep. 1 commissioning surge.
Attachment 1: IMG_0135.png
1958 Thu Aug 27 16:14:28 2009 steveSummaryOMCburned photodiode
Old -pre 6/2009 LLO DCPD 3 mm od GTRAN photodiode
Attachment 1: 20090827_173252.jpg
Attachment 2: 20090827_170802.jpg
2095 Thu Oct 15 02:38:10 2009 rana, robUpdateOMCDark Port Mode Scan using the OMC
Bottom trace is proportional to the OMC PZT voltage - top trace is the transmitted light through the OMC. Interferometer is locked (DARM- RF) with arm powers = 80 / 100. The peaks marked by the cursors are the +(- ?) 166 MHz sidebands.
Attachment 1: OMC-ModeScan_091015.png
8849 Mon Jul 15 16:44:46 2013 AlexUpdateOMCOMC North Safety
[Eric Alex]
We are planning on testing our laser module soon, so we have added aluminum foil and a safety announcement to the door of OMC North. The safety announcement is as pictured in the attachment.
Attachment 1: photo_2_(1).JPG
14022 Tue Jun 26 20:59:36 2018 aaronUpdateOMCprep for vent in a couple weeks
I checked out the elog from the vent in October 2016 when the OMC was removed from the path. In the vent in a couple weeks, we'd like to get the beam going through the OMC again. I wasn't really there for this last vent and don't have a great sense for how things go at the 40m, but this is how I think the procedure for this work should approximately go. The main points are that we'll need to slightly translate and rotate OM5, rotate OM6, replace one mirror that was removed last time, and add some beam dumps. Please let me know what I've got wrong or am missing.
[side note, I want to make some markup on the optics layouts that I see as pdfs elsewhere in the log and wiki, but haven't done it and didn't much want to dig around random drawing software, if there's a canonical way this is done please let me know.]
Steps to return the OMC to the IFO output:
1. Complete non-Steve portions of the pre-vent checklist (https://wiki-40m.ligo.caltech.edu/vent/checklist)
2. Steve needs to complete his portions of the checklist (as in https://nodus.ligo.caltech.edu:8081/40m/12557)
3. Need to lock some things before making changes I think—but I’m not really sure about these, just going from what I can glean from the elogs around the last vent
1. Lock the IMC at low power
2. Align the arms to green
3. Lock the arms
4. Center op lev spots on QPDs
5. Is there a separate checklist for these things? Seems this locking process happens every time there is a realignment or we start any work, which makes sense, so I expect it is standardized.
4. Turn/add optics in the reverse order that Gautam did
1. Check table leveling first?
2. Rotate OM5 to send the beam to the partially transmissive mirror that goes to the OMC; currently OM5 is sent directly to OM6. OM5 also likely needs to be translated forward slightly; Gautam tried to maintain 45 deg AOI on OM5/6.
3. A razor beam dump was also removed, which should be replaced (see attachment 1 on https://nodus.ligo.caltech.edu:8081/40m/12568)
4. May need to rotate OM6 to extract AS beam again, since it was rotated last time
5. Replace the mirror just prior to the window on the AP table, mentioned here in attachment 3: https://nodus.ligo.caltech.edu:8081/40m/12566
1. There is currently a rectangular weight on the table where the mirror was, for leveling
5. Since Gautam had initially made this change to avoid some backscattered beams and get a little extra power, we may need to add some beam dumps to kill ghosts
1. This is also mentioned in 12566 linked above, the dumps are for back-reflection off the windows of the OMC
6. Center beam in new path
7. Check OMC table leveling
8. AS beam should be round on the camera, with no evidence of clipping on any optics in the path (especially check downstream of any changes)
14051 Wed Jul 11 15:57:00 2018 aaronUpdateOMCReviving OMC electronics
Gautam showed me the electronics racks for the OMC PZTs and DAQ. I'm in the process of chasing down what channels we need, and confirming that we'll be able to plug the old antialiasing/imaging boards into the current DAC/ADC boards. I found what I think was Rob Ward's simlink model for the omc, located at
Channels in this model:
• 27 or 29 total ADC channels are used (depending whether we keep 2 spare adc chans)
• 4 each go to ASC_QPD1/2 (8 chans total)
• 5 go to TRANS_PD1, TRANS_PD2, REFL_PD, TRANS_PD1_UF, TRANS_PD2_UF. These PD are used for ASC and LSC.
• 2 go to the LSC, one each for DVMDC, DVMAC, X3DC, and X4DC
• 12 go to the ASC_PZT
• 2 go to the SPARE_ADC (not sure what this is)
• I think these channels are (or were at some point) defined in memory by /cvs/cds/caltech/chans/ipc/G1.ipc
• I found this from elog 2860; it mentions that these should eventually be migrated over to a file C1.ipc, but I don't see any OMC channels in that file or any of the 'old' C1.ipc files, so I suppose it never happened or they were removed later
• During this vent, we won't have ASC, so
• 10 or 14 DAC channels are used (depending whether we keep 4 spare dac chans)
• 2 from the LSC, one for CLK_OUT and one for "LSC"
• 8 from ASC, including P1A, P1B, P2A, P2B, P1OSC, Y1OSC, P2OSC, Y2OSC
• I think these channels are (or were at some point) saved to frames due to /cvs/cds/caltech/chans/daq/C1OMC.ini, which I found from elog 2073
• At some point, the 33MHz mod depth was controlled by one of the spare OMC chans, C1:OMC-SPARE_DAC_CH_15. See elog 2126. I assume this is no longer the case, since c1omc is defunct.
• Durnig this vent, we won't have ASC and don't need to CLK_OUT the LSC, so we may just need one DAC channel
As of at least Nov 2009, the .par file for the OMC was located at /cvs/cds/gds/param/tpchn_C2 (see elog 2316)
Electronics inventory:
• Kepco HV supply, "OMC-L-PZT", labels indicate it goes to 250V, needs to be tested ("TESTED OK 2014OCT12")
• Tip/Tilt Piezo Driver, LIGO D060287
• HV Piezo Driver, LIGO D060283
• QPD Whitening Board, D060214
• LIGO D050374/D050387
• LIGO D050368/D050373
Need to check:
• Can the ADC/DAC adapter boards (eg D0902006) drive whatever ~10V control signal we need across ~10m of SCSI cable?
•
14052 Wed Jul 11 16:23:21 2018 aaronUpdateOMCCoordination of the Output Mode-cleaner Mirror Insertion Expedition (COMMIE)
I started this document on my own with notes as I was tracing the beam path through the output optics, as well as some notes as I started digging through the elogs. Let's just put it here instead....
1. Beam from AS port into OMMT
2. Reflect off OM5-PJ
1. TO DO: check that the PZT works
2. 40/P/F/L, 1525-45-P
3. Pick off from OMPO
1. TO DO: determine how much power is needed for the pick off, choose an appropriate optic (for this vent probably 50-50 is fine)
2. The PO beam goes to OM6
4. Reflect off MMT1???
1. TO DO: determine if this mirror has a PZT, get it working
1. Has a PZT?
2. Which PZT channel on the DAQ?
3. Is there a cable going to from the DAC to the PZT?
4. Is the PZT functional?
5. How many PZTs does this mirror actually have?
2. TO DO: determine the real name of this optic, find its recent history in the elog
3. TO DO: determine the correct telescope parameters to optimally couple into the mode cleaner given the following:
4. TO DO: look up how the radius of curvature (RC) of the OMC has changed, and therefore what telescope parameters are necessary
5. Focused by MMT2???
1. TO DO: determine if this mirror has a PZT
1. Has a PZT?
2. Which PZT channel on the DAQ?
3. Is there a cable going to from the DAC to the PZT?
4. Is the PZT functional?
5. How many PZTs does this mirror actually have?
2. TO DO: determine the real name of this optic, find its recent history in the elog
6. Columnated by MMT3???
1. TO DO: determine if this mirror has a PZT
1. Has a PZT?
2. Which PZT channel on the DAQ?
3. Is there a cable going to from the DAC to the PZT?
4. Is the PZT functional?
5. How many PZTs does this mirror actually have?
7. Steered by MMT4???
1. TO DO: determine the real name of this optic
2. TO DO: why is this optic so small? Looks different from the rest, maybe weird space constraint
8. Steered by MMT5???
1. TO DO: why is this optic so large compared to OMMT4?
2. TO DO: is there a more space efficient way of steering this beam, or even some way that avoids having to steer with three distinct optics
9. Steered by MMT6???
1. TO DO: Can this optic be removed with some clever new beam path?
10. Cleaned by the OMC
1. TO DO: Where does the promptly reflected beam from OMC1 go after it exits the chamber?
2. TO DO: check the PZTs
1. Has a PZT?
2. Which PZT channel on the DAQ?
3. Is there a cable going to from the DAC to the PZT?
4. Is the PZT functional?
5. How many PZTs does the OMC actually have?
3. TO DO: Determine if a new OMC configuration would be more ideal for the squeezing experiment
1. This is a large task, not part of this immediate vent
4. TO DO: What is done with the OMC reflection? What is done with the transmission?
5. TO DO: Check the logs about how the OMC had been in use; should be mostly from rob ward
11. Reflected beam goes to the next chamber
12. Transmitted beam is split by OM7???
1. TO DO: find the actual name of this optic
2. TO DO: why does this have the R/T that is does?
13. Reflected beam goes to my OMPD
1. TO DO: figure out what this PD is used for, and whether we even need it
1. I think this might be the camera mentioned in 40m elog 21
2. Elog 42 says the 4 QPDs for the OMC have meds screens located under C2TPT—is this a clue for channel names?
14. Transmitted beam is reflected to the next chamber by OM8???
1. TO DO: determine the name of this optic
2. TO DO: Where does this beam go? What is it used for?
1. Transmission through OM5? Probably don’t need…
2. OMMT1 transmission
3. OMMT steering mirror transmissions
4. OMC transmissions? Probably not?
5. OMPD transmission?
6. OM8 transmission
7. Green scattering off of the window where the beam goes after GR_SM5
8. Backscatter from the OMC prompt reflection to the window
9. Backscatter from the OMC reflection to the window
10. Backscatter from the MC beam off the window (this beam just travels through this chamber, interacts with no optics; there is also what looks like a small blue beam on this diagram, so maybe need to dump that backscatter too)
11. Backscatter from the PO beam from OM6 going through the chamber window
12. Backscatter from IM1 out the window
13. There is a small blue beam from OMMT3 that goes through this window as well, I’m not sure exactly what is is from or for, or if it is physical (there are a few of these strange blue lines, i'm probably just misreading the diagram)
16. TESTS TO DO
1. Characterize the PZT control
2. Lock the OMC with a PZT dither lock
1. Eg elog 59
3. “Tap-tap-tappy-tap test” to find resonanes
1. Look at combination of PDH error signal and DCPD signal???
2. See elog 86 for results from initial OMC install—Nov 2007
4. Check wiggling wires, etc
5. TFs to check? Vertical TF?
6. OMC Length check— see for eg elog 768
1. Mode matching calculation for new radius of curvature optics—see elog 1271
1. The current MMT is not the optimal configuration even for the old Rc (see 3077 and 3088)
• Entry 590 has a labelled picture of the optics setup with OMC
• Mention of omcepics at elog 894
• Some important changes happened in elog 1823
• 1''->2'' mirror out of the vacuum--I should check whether this is still there, or if it has been moved
• [many more changes.....]
• There were at one time 2 cameras monitoring OMCT and R (see 4492, 4493)
• Some OMC PZT HV supply info is at elog 4738, 4740...
• There are some photos of the OMC table at elog 5120, and a note about moving some optics
• Not strictly about the OMC, but I really like Suresh's diagram 6756, I'll make something similar for the OMC electronics
• although it is about adding the tip tilt electronics, which I think required a new flange for the OMC chamber
• OMC stage 1 and 2 are the steering mirrors going into the OMC, and were controlled by EPICS chans (6875, 6884)
• these PZT HV supplies lived in OMC_SOUTH (or maybe 1Y3? see elog 6893), the driver in OMC_NORTH (LIGO-D060287)
• Photos of these supplies in 7696
• There are pictures of the OMC and its PZTs in 7401
• The OMC HV supply was moved to power a different set of PZTs (see 7603)
• Talk of replacing the PZTs with picomotors or tip/tilts in 7684
• More pictures of the OMC table before the OMC was 'removed' are here (8114) and in 12563/12571 Gautam links to a Picassa album with pictures from just before the beam was diverted
14060 Thu Jul 12 21:16:25 2018 aaronUpdateOMCChecking OMC Electronics
In preparation for tomorrow's vent, I'm checking some of the OMC-related electronics we plan to use.
# First up is the HV Piezo Driver (D060283).
(well, technically the first up was the Kepco HV power supply... but I quickly tested that its output works up to 300V on a multimeter. The power supply for OMC-L-PZT is all good!)
According to the DCC, the nominal HV supply for this board is 200V; the board itself is printed with "+400V MAX", and the label on the HV supply says it was run at 250V. For now I'm applying 200V. I'm also supplying +-15V from a Tektronix supply.
I used two DB25 breakout boards to look at the pins for the DC and AC voltage monitors (OMC_Vmon_+/-, pins 1/6, and OMC_Vmon_AC+/-, pins 2 and 7) on a scope. I hooked up a DS345 function generator to the piezo drive inputn (pins 1,6). According to the 2013 diagram from the DCC, there is just one drive input, and an alternative "dither in" BNC that can override the DAC drive signal. I leave the alternative dither floating and am just talking to the DAC pins.
Aspects of the system seem to work. For example, I can apply a sine wave at the input, and watch on the AC monitor FFT as I shift the frequency. However, anything I do at DC seems to be filtered out. The DC output is always 150V (as long as 200V comes from the supply). I also notice that the sign of the DC mon is negative (when the Vmon_+ pin is kept high on the scope), even though when I measure the voltage directly with a multimeter the voltage has the expected (+) polarity.
A few things to try:
• The DC_Readout electronics scheme on the wiki has separate oscillator and control inputs. This diagram has lied to us in the past and is older, and the traces on top of the breadboard seem to only go to pins 1 and 6, but I'm going to first try to apply a voltage across pins 2 and 7 in case there actually is a separate control I'm ignoring.
• Driving on these pins seems to do nothing
On further investigation this was the key clue. I had the wrong DCC document, this is an old version of this board, the actual board we are using is version A1 of D060283-x0 (one of the "other files")
Gautam and Koji returned at this point and we started going through the testpoints of the board, before quickly realizing that the DC voltage wasn't making it to the board. Turns out the cable was a "NULL" cable, so indeed the AC wasn't passing. We swapped out the cable, and tested the circuit with 30V from the HV supply to trim the voltage reference at U14. The minimum voltage we could get is 5V, due to the voltage divider to ground made by R39. We confirmed that the board, powered with 200V, can drive a sine wave and the DC and AC mons behave as expected.
14072 Sat Jul 14 16:04:34 2018 aaronUpdateOMCChecking OMC Electronics
# Next check is the DCPD/OMMT Satellite Box
I traced a cable from the OMC electrical feedthrough flanges to find the DCPD/OMMT Satellite Box (D060105). I couldn't find the DCC number or mention of the box anywhere except this old elog.
Gautam and I supplied the box with power and tested what we think is the bias for the PD, but don't read any bias... we tracked down the problem to a suspicious cable, labelled.
We confirmed that the board supplies the +5V bias that Rich told us we should supply to the PDs.
We tested the TFs for the board from the PD input pins to output pins with a 100kHz low pass (attached, sorry no phase plots). The TFs look flat as expected. The unfiltered outputs of the board appear bandpassed; we couldn't identify why this was from the circuit diagram but didn't worry too much about it, as we can plan to use the low passed outputs.
Attachment 1: Screenshot_2018-07-14_17.53.40.png
Attachment 2: Screenshot_2018-07-14_17.57.17.png
14095 Sat Jul 21 01:14:02 2018 gautamUpdateOMCPZT Jena driver board check
[Aaron, gautam]
We did a quick check of this board today. Main takeaways:
• There are two voltages (HV pos and HV neg) that are output from this unit.
• Presumably, these goto different piezoelectric elements, referenced to ground. Are there any spec sheets for these describing the geometry/threshold voltages?
• The outputs are:
• $\mathrm{HV_{+}} = 10(V_{\mathrm{DAC}}+V_{\mathrm{offset}}), \mathrm{HV_{-}} = 10(-V_{\mathrm{DAC}}+V_{\mathrm{offset}})$
• So with $V_{\mathrm{offset}} = 7.5 \mathrm{V}$, we expect to be able to use +/- 7.5 V of DAC range.
• The trim pot had to be adjusted to realize $V_{\mathrm{offset}} = 7.5 \mathrm{V}$.
• I assume 150V is some kind of damage threshold of the PZT, so there is no benefit to using 10V offset voltage (as this would result in 200 V at full range DAC voltages).
With the correct $V_{\mathrm{offset}} = 7.5 \mathrm{V}$, we expect 0V from the DAC to result in 0 actuation on the mirror, assuming that an equal 75V goes to 2 PZTs mounted diametrically opposite on the optic. Hopefully, this means we have sufficient range to scan the input pointing into the OMC and get some sort of signal in the REFL signal (while length PZT is being scanned) which indicates a resonance.
We plan to carve out some IFO time for this work next week.
14120 Tue Jul 31 22:50:18 2018 aaronUpdateOMCOMC Expected Refl Signal
I learned a lot about lasers this week from Siegman. Here are some plots that show the expected reflectivity off of the OMC for various mode matching cases.
The main equation to know is 11.29 in Siegman, the total reflection coefficient going into the cavity:
$R=r-\frac{t^2}{r}\frac{g(\omega)}{1-g(\omega)}$
Where r is the mirror reflectivity (assumed all mirrors have the same reflectivity), t is the transmissivity, and g is the complex round-trip gain, eq 11.18
$g(\omega)=r_1r_2(r_3...)e^{-i\phi}e^{-\alpha_0p}$
The second exponential is the loss; in Siegman the \alpha_0 is some absorption coecfficient and p is the total round trip length, so the product is just the total loss in a round trip, which I take to be 4*the loss on a single optic (50ppm each). \phi is the total round trip phase accumulation, which is 2\pi*detuning(Hz)/FSR. The parameters for the cavity can be found on the wiki.
I've added the ipynb to my personal git, but I can put it elsewhere if there is somewhere more appropriate. I think this is all OK, but let me know if something is not quite right.
Attachment 1: omcRefl.pdf
14159 Mon Aug 13 20:21:10 2018 aaronUpdateOMCNew DAC for the OMC
[aaron, gautam]
We finished up making the new c1omc model (screenshot attached).
The new channels are only four DAC for ASC into the OMC, and one DAC for the OMC length:
C1:OMC-ASC_PZT1_PIT
C1:OMC-ASC_PZT1_YAW
C1:OMC-ASC_PZT2_PIT
C1:OMC-ASC_PZT2_YAW
C1:OMC-PZT
The model compiles and we can change the channel values, so we are all set to do this OMC scan on the software side.
Attachment 1: c1omcSCREENSHOT.png
14163 Tue Aug 14 23:14:24 2018 aaronUpdateOMCOMC scanning/aligning script
I made a script to scan the OMC length at each setpoint for the two TTs steering into the OMC. It is currently located on nodus at /users/aaron/OMC/scripts/OMC_lockScan.py.
I haven't tested it and used some ez.write syntax that I hadn't used before, so I'll have to double check it.
My other qualm is that I start with all PZTs set at 0, and step around alternative +/- values on each PZT at the same magnitude (for example, at some value of PZT1_PIT, PZT1_YAW, PZT2_PIT, I'll scan PZT2_YAW=1, then PZT2_YAW=-1, then PZT2_YAW=2). If there's strong hysteresis in the PZTs, this might be a problem.
14213 Sun Sep 23 20:15:35 2018 KojiSummaryOMCMontecarlo simulation of the phase difference between P and S pols for a modeled HR mirror
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https://www.openscience.fr/Numero-1-552
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# Vol 11 - Numéro 1 (Mai 2020)
## Articles parus
Solutions régulières pour l’équation relativiste de Boltzmann dans le domaine de Yang-Mills
We consider in this work the Boltzmann equation in the presence of a Yang-Mills fields in temporal gauge, which generalizes to the non-Abelian case the electromagnetic field. We prove, using the method presented by N. Noutchegueme and R. D. Ayissi [2], a local in time existence and uniqueness theorem for the regular solutions.
Une nouvelle caractérisation des anneaux semi-réguliers commutatifs
A commutative ring R is called J-rad clean in case, for any r ∈ R, there is an idempotent e ∈ R such that r−e ∈ U(R) and re ∈ J(R), where U(R) and J(R) denote the set of units and the Jacobson radical of R, respectively. Also, a ring R is called semiregular if R/J(R) is regular in the sense of von Neumann and idempotents lift modulo J(R). We demonstrate that these two concepts are, actually, equivalent and we portray a portion of the properties of this class of rings. In particular, as a direct application, we prove that the commutative group ring RG is J-rad clean if, and only if, R is a commutative J-rad clean ring and G is a torsion abelian group, provided that J(R) is nil.
Produits de Complexes Rectangulaires et Matrices aléatoires hermitiennes
Very recently, it has been shown for products of real matrices with anti-symmetric matrices of even dimension that the traditional harmonic analysis on matrix groups developed by Harish-Chandra et al. needs to be modified when considering the group action on general symmetric spaces of matrices. In the present work, we consider the product of complex random matrices with Hermitian matrices, in particular the former can be also rectangular while the latter has not to be positive definite and is considered as a fixed matrix as well as a random matrix. This generalises an approach for products involving the Gaussian unitary ensemble (GUE) and circumvents the use there of non-compact group integrals. We derive the joint probability density function of the real eigenvalues and, additionally, prove transformation formulas for the bi-orthogonal functions and kernels.
Fonctions ∗-LIE supérieurement dérivables sur les ∗-anneaux
In this paper, it is shown that, if R is a ∗-ring containing a nontrivial self adjoint idempotent which admits a ∗-Lie higher derivable mapping L={Ln}n∈N, then there exists an element ZX,Y (depending on X and Y) in the center Z(R) such that Ln(X+Y)=Ln(X)+Ln(Y)+ZX,Y.
### Autres numéros :
2020
Volume 20- 11
Numéro 1 (Mai 2020)
Numéro 2 (Septembre 2020)
À paraître
2021
Volume 21- 12
Numéro 1 (Janvier 2021)
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https://judithcurry.com/2012/02/24/why-target-heartland/
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# Why target Heartland?
Update: Email from Joseph Bast, President of Heartland Institute, appended at the end of the post.
So, imagine you are a climate scientist and climate change ideologue, and want to “take down” the single organization (or individual) that is doing the most damage to the movement (i.e. with the end result of thwarting CO2 emissions/stabilization policy). Who would you target?
Scientists seem to persist in thinking the problem is the public’s understanding of climate science; if they only understood infrared radiative transfer, they would be on board with the inevitable policy prescription from that scientific understanding. This is the so-called “deficit model,” which has been shown in numerous studies not to be a factor (this has been discussed on some of the Climate Etc. communications threads).
But lets accept the deficit model for a moment. In the U.S. anyways, who (individual organization) has been most effective at challenging the IPCC consensus science in the public debate on climate change?
Peter Gleick seems to think it is Heartland Institute. Even among the libertarian think tank/advocacy groups, Heartland would not be at the top of my list. What about Cato/Pat Michaels? GWPC/Bennie Peiser? CEI/Chris Horner?
What about bloggers such as Anthony Watts and Steve McIntyre?
What about skeptical scientists such as Richard Lindzen and Roy Spencer?
And what of the people in the (relative) middle, e.g. Revkin, Curry, Pielkes, Randy Olson?
Was Heartland singled out because Gleick thought they were doing something unethical?
Several issues came up my NPR interview yesterday, which are worth mentioning on this topic:
The moderator, Larry Mantle asked this question of Mandia (paraphrased to the best of my recollection): “Isn’t this a dog bites man story? Didn’t we already know this? Why should we be surprised if an advocacy receives money from donors, and uses it to pay people to write educational materials that express their viewpoint?” Isn’t this the story told by Naomi Oreskes in Merchants of Doubt? Can’t you find most of this information on sourcewatch?
I made a statement something like this: “Gleick pointed a big gun at a small target and ended up shooting himself.” It seems to me that Gleick’s understanding of the lack of action on CO2 policy has its roots in the deficit model, and that Heartland was making the most outrageous scientific statements, and doing things that seemed ‘scientific’ like running conferences and publishing the NIPCC. But I suspect most of the public has never heard of Heartland or the NIPCC? The end result of this episode is that Heartland will become known to many more people.
Back to my original question:
So, imagine you are a climate scientist and climate change ideologue, and want to “take down” the single organization (or individual) that is doing the most damage to the movement (i.e. with the end result of thwarting CO2 emissions/stabilization policy). Who would you target?
And of course all this begs the question of why we don’t have CO2 stabilization policies, which is mostly about economics, politics, values.
Email from Joseph Bast
From: “Joseph Bast”
To: [email protected]
Sent: Friday, February 24, 2012 1:58:19 PM
Subject: Why was Heartland targeted?
Dear Dr. Curry,
I read with interest your post, “Why Heartland?” Thankfully, I can’t read Peter Gleick’s mind, but I suspect he targeted us because we have done so very much to document and rebut the assumptions and exaggerations of the global warming alarmists. Please let me describe some of the ways we’ve done that, and you decide.
We send publications to every national, state, and 8,400 county and local officials in the U.S. on average about once a week. 79% of state legislators say they read at least one of our publications. “Environment & Climate News,” one of six monthly publications we produce, is read by 57% of state legislators, a higher percentage than read the New York Times. It has been published continuously for 15 years, and every issue features the work of leading climate realists. No other organization produces a regular publication that reaches more people with this message.
Many policymakers and other opinion leaders in the U.S. and around the world recognize the names of (to use those in your list) Pat Michael, Chris Horner, Anthony Watts, Steve McIntyre, Richard Lindzen, and Roy Spencer only because they read their work or about their work in Environment & Climate News.
ECN is just the tip of the iceberg. You know about our International Conferences on Climate Change (ICCCs) – six held since 2008, total attendance of more than 3,000 people. The press and online coverage of these conferences was greater than anything else done by climate realists, and the videos of the presentations posted online have been viewed hundreds of thousands of times. The personal connections created among scientists from all around the world created a genuine social movement in favor of a more realistic understanding of climate change.
You’ve commented favorably on Climate Change Reconsidered. Is there any book from the realist perspective that compares to it in terms of comprehensive coverage of the issues in the debate or citations to peer-reviewed literature? Someone sent me the following numbers about the 2009 edition: 37 contributing authors, 880 pages, 344 chapters and sections,and 4,235 source citations. The 2011 interim report was only about 400 pages long … I haven’t counted chapters and sources, but it too is much more comprehensive than anything else written from our perspective. Don’t get me wrong, I love the books from Pat Michaels and others and we promote them when we can. But Climate Change Reconsidered is the big reference book that the realist movement needed and didn’t have until we came along and helped create it.
In addition, we’ve distributed more than a million DVDs, nearly 2 million short booklets and reprints, and 200,000 copies of a New York Times best-seller. Most were sent to educators, opinion leaders, and policymakers over the course of the past five years. We deliberately bypassed the mainstream media, for reasons made obvious by their coverage of the Fakegate scandal. Our strategy worked. All surveys show informed opinion has moved decidedly in the direction of climate realism and away from alarmism.
Our science director Jay Lehr and senior fellow James Taylor criss-cross the country giving talks and participating in debates on climate change. Lehr often speaks two and three times a week to audiences reaching up to 1,000 and more, almost invariably getting standing ovations. He usually speaks to groups meeting in areas outside major metropolitan areas and university thought bubbles. He says “out there,” nobody “believes” in global warming anymore.
Not all that we’ve done should have escaped your attention. We ran full-page and smaller ads in the Wall Street Journal, New York Times, USA Today, and elsewhere … often featuring pictures of the scientists you mentioned and I list above, many of them challenging Al Gore to debate is critics.
As you can tell, I’m very proud of what The Heartland Institute has been able to do on a budget that is a mere fraction of what other organizations spend … and I should add that climate change is just one of five major topic areas we address. We are proud to provide a forum for the thousands of scientists and policy experts who actually understand climate change – how complex it is, how much we don’t know, and the difference between scientific knowledge and scientific forecasting — and don’t just “believe” it in. Together, we are making genuine contributions to the international scientific debate, changing public opinion, and improving public policy.
Thank you for your own fine efforts in this difficult debate, I hope to see you at our next ICCC, and best regards,
P.,S. – feel free to post this on your site or not. If you don’t, though, I think I’d like to post this on one of Heartland’s sites, perhaps removing the reference to you at the beginning, so please let me know one way or the other.
Joe
JC reflection: With virtually no effort on my part (beyond reading an email, cutting and pasting into the blog post), I have uncovered “juicier stuff” about Heartland than anything Gleick uncovered. Okay, maybe the HI are actually the baddest guys in town from the perspective of the alarmists. The irony of Gleick committing professional seppuku over getting information about stuff that is either generally known or suspected or regarded as no big deal. When all he had to do was ask Joseph Bast some questions, and he would have told him all sorts of things (just not the names of the donors, which aren’t all that interesting anyways.)
### 756 responses to “Why target Heartland?”
1. Punksta
I would try and target the people who expose the pervasive dishonesty in the whole CAGW movement and argument.
• Yes, Punksta, that is exactly what was done.
Probably motivated to immediate action, like Watergate, by the:
a.) Impending election
b.) Collapsing economy
c.) Absence of Green jobs
d.) And H-fusion reactors
Anticipated and foolishly promised from computer model predictions!.
• Dr. Peter Gleick was probably easy to manipulate, as were Al Gore, Rajendra Pachauri, James Hansen, Michael Mann, Phil Jones and others who have endorsed the standard models of Earth’s climate, economics and Earth’s heat source – the Sun – standard models officially approved for computer calculations.
What a sad, sad state of affairs. Computers – a great tool – were used to destroy so many branches of science – Climatology, Economics, Nuclear, Particle, Planetary and Solar Physics!
• Bruce
Al Gore – his lies single handedly galvanized an opposition.
Michael Mann and the Team – If your core religion has as its core tenet a huge lie like the Hockey Stick, nothing your fellow cult members say can be believed until that lie is admitted to and all proponents shamed out of the church.
Andy Revkin type fake journalists. They can always be counted on to make stuff up which galvanizes anyone who can google for 10 seconds to prove it is a lie.
The BBC. The Guardian etc all. All lies. All the time and easily refutable.
BEST – for telling a big lie and then showing up with crappy data later that proves nothing.
• The current game plan: Retain power past the next election !
The alternative is very bleak for the US NAS, the UK RS, the UN IPCC, mainstream news media including BBC and PBS, and once reputable research journals – like Nature, Science, PNAS, MPRS, etc
• cwon14
I hear you Bruce but why should we be concerned about how the “cause” is doing at all. I want it annihilated don’t you?
The post is another false narrative written for the benefit of believers who are suffering “Post Gleick Traumatic Syndrome” (PGTS). Self-hatred and fingerpointing is no surprise in the AGW movement, I just refuse to validate this talking point. The post is nonsense for a purpose, refocus warming prattle to carry on for the next battle.
2. hunter
If I cared about integrity, I would demand a clean house first.
If I cared about controlling the message, I would do exactly as the consensus does.
There is no target, in reality. There is only integrity and honesty.
• Punksta
I think Hunter is on the money here – if I was a knowledgeable climate scientist who believed CAGW, my priority would be a clean-up.
Radically reform or abolish the IPCC, oust or discipline the Climategate crooks and the likes of Gleick, etc etc. It’s the presence of so much blatant deceit with narry a word from the rank and file that most hampers acceptance of the CAGW thesis – the deafening silence.
• hunter
Punsta,
Thanks.
The social dysfunction of AGW is really deep. read the rationalizations of Gleick from the true believers. They are becoming disassociated from reality.
• Number One (#1) Priority: [Not Integrity] Retain Power !
Politicians – and puppet “scientists” – are as simple-minded as bureaucrats in revealing their motives.
How can world leaders and their puppets retain power now? . . .
Thirty-eight (38) years after uniting nations against an imaginary “common enemy” – global climate change – by basing policies on adjustable computer models of nature instead of experimental observations of nature after ~1971?
An election is coming; The public wants to know:
1. Was AGW abated by moving industries overseas to emit CO2?
2. Where are all the Green jobs we promised the public?
3. Where are the H-fusion reactors we promised them?
4. When is economic recovery coming?
• Actually the rank and file seem to be waking up a little: “you have to stoop to those crooks level” blather to justify Gleik. Lots of reaffirming AGW much like Dorothy in her ruby slippers crying, “There’s no place like home. There’s NO place like home…” If I just say it enough it will be true, “ohhhh, global warming is man made. Global warming IS man-made.” Now that’s the great scientific method right? Or was it Huxley or Orwell IPCC learned from? 10,000 repititions of a lie while sleeping makes 1 truth in the morning. Sorry if this is a bit scattered, been watching the AGWist priests exhorting the faithful.
• cwon14
Hunter,
What if they “cleaned house”? Who or what would be left as a first question?
The “cause” should be annihilated, that’s justice. If they choose to die in the bunker whose fault is this?
The should be a Nuremberg type of science trial (hopefully better and less political than the first one) at the end of the day but I doubt we will live to see it.
3. Who does most damage to the climate movement? Michael Mann, Phil Jones, Jim Hansen, Peter Gleick, Al Gore, Rajendra Pachauri (not necessarily in that order)
• Latimer Alder
All of the above
:-)
• These are all Big Brother’s puppets. So are:
1. The Nobel Prize Committee that awarded them for deceit.
2. Agencies (NASA, EPA, DOE) that gave public funds to them.
3. Politicians that directed this misuse of public funds to deceive.
Undamaged so far are world leaders who secretly decided thirty-eight (38) years ago, in fear of mutual nuclear annihilation, to Unite Nations against an imaginary “common enemy” – “Global Climate Change” – and base future government policies on
b.) Experimental observations and measurements on nature.
How did it work? No better in economics than in climatology.
That is why our economy is collapsing, the public is darn mad, politicians are running scared, and agencies that exposed government deceit are under attack.
Unfortunately it will probably get much worse. It is easier to push a camel through the “eye of a needle” than a proud politician into an admission of powerlessness over Nature.
There is no “easier, softer way” out of the current situation.
• Unfortunately, this is probably true
• Brian H
Why “unfortunately”? On balance, I think it’s both fortunate and inevitable.
• Peter Davies
Possibly because there may well be AGW happening but false science is not the way to explore the cause and extent of this phenomenon.
• “tragically” is better — tragic in the sense that they work hard and achieve the opposite of what they seem to want to achieve
• Their fatal flaw IMO is failure to understand their enemy (Sun Tzu’s argument), thinking they were fighting another tobacco war
• curryja
Re: “Their fatal flaw IMO is failure to understand their enemy”
Might not the greater challenge be whether whether I know myself? e.g. do I really seek wisdom and to follow the scientific method?
Proverbs 27:17 ESV
Iron sharpens iron,
and one man sharpens another.
1 Thessalonians 5:21 ESV
but test everything; hold fast what is good.
Do you see a man who is wise in his own eyes?
There is more hope for a fool than for him.
Proverbs 28:26 ESV
Whoever trusts in his own mind is a fool, but he who walks in wisdom will be delivered.
Ecclesiastes 7:5 ESV
It is better for a man to hear the rebuke of the wise than to hear the song of fools.
2 Chronicles 12:14 ESV
And he did evil, for he did not set his heart to seek the LORD.
Psalm 101:5 ESV
Whoever slanders his neighbor secretly I will destroy. Whoever has a haughty look and an arrogant heart I will not endure.
Proverbs 6:16-19 ESV
There are six things that the Lord hates,
seven that are an abomination to him:
haughty eyes, a lying tongue,
and hands that shed innocent blood,
a heart that devises wicked plans,
feet that make haste to run to evil,
a false witness who breathes out lies,
and one who sows discord among brothers.
Proverbs 17:3 ESV
The crucible is for silver, and the furnace is for gold,
and the Lord tests hearts.
Proverbs 24:17 ESV
Do not rejoice when your enemy falls,
Psalm 26:2 ESV
Prove me, O LORD, and try me; test my heart and my mind.
Am I prepared for those tests? Do I delight in what God delights in or not? Or will I also be found to be arrogant?
• David Springer
You left out the most important:
Proclaim Liberty Throughout All the Land unto All the Inhabitants Thereof. Leviticus 25:10
It can be found in Independence Hall, Philidelphia, engraved on The Liberty Bell which is just down the street from where the Tun Tavern was located. The Tun Tavern is, among other things, the first recruitment center for the United States Marine Corps and is regarded as its birthplace. Hoo Rah!
• David Hagen:
Might not the greater challenge be whether whether I know myself? e.g. do I really seek wisdom and to follow the scientific method?
With you on that David.
Proverbs 24:17 ESV
Do not rejoice when your enemy falls,
Selected from your selection of scriptures, because this speaks to all of us dissenters right now as Gleick himself stumbles.
Am I prepared for those tests? Do I delight in what God delights in or not? Or will I also be found to be arrogant? [pointing back to Dr K’s latest and greatest]
The most pertinent and challenging Christian message I’ve heard all year.
• Markus Fitzhenry
Ya wouldn’t think the bloke who penned this was a Christian, would ya.
• sharper00
If you replace those individuals with another personality that produces the same results would the damage lessen or be eliminated?
Is the problem Michael Mann or the hockey stick that Michael Mann produces? Would skeptics accept that the modern era is warmer than Medieval times if it came from someone else.
1. A different scientist would produce different results. That suggests the problem is not the people but the work the people produce.
2. A different scientist would produce the same results but somehow be better received. This is problematic because it paints skeptics as focussing entirely on personalities and ignoring reality, is the solution really to satisfy their personality requirements instead of keeping the focus on reality?
Furthermore, do we want the best scientists or the nicest scientists?
Do we want the best scientists or the most media savvy scientists?
These seem like important issues for the “Climate science is technically correct but skeptics are justified in ignoring that because the scientists are mean” position.
As for Gleick, people sometimes do very very odd things that defy explanation unless you know them well.
• Punksta
The problem isn’t that climate scientists are “mean”, Sharperoo. It’s that they are unquestionably dishonest.
• hunter
shaper00,
You do not have the best scientists, you have the most ideologically extreme leading your movement straight over a cliff.
• @sharperoo
Faster-than-light neutrinos are a good example. Spectacular result, world wide attention, and in the end that had to admit to a fault.That’s science. I’m sure the cable guy nearly died of embarrassment.
Mann’s hockey stick is spectacular too (albeit less so), and its faults are clear to all. However, by refusing to admit his errors, Mann portrays himself as an ideologue and taints his peers in the process.
• Latimer Alder
Gleick’s actions do not defy explanation at all. They are very easy to explain.
He has let his own extremely elevated opinion of his own cleverness and importance seduce him into believing that He can do wrong as long as He believes it to be in a just cause. For example he sees nor reason to read book before slagging it off, he sees no reason not to embellish/manufacture stuff about his opponents. He knows that in His cause, all transgressions will be overlooked.
Sadly for him, but hilariously for the rest of us, He has come up against a very salutary recognition that He is the only one who shares the idea of Gleick as The Force Of Good. And that ethics and stuff that He is so keen on lectuing others about also apply to Him.
Seems to me that there are plenty of others with similar ego complexes in the climatology world. Perhaps the awful example of Gleick’s complete stupidity and fall from Self-Described Hero to Zero in less than a week will give them the focus they need to rein in their worst excesses
• sharper00
@Richard S.J. Tol
“Mann’s hockey stick is spectacular too (albeit less so), and its faults are clear to all. However, by refusing to admit his errors, Mann portrays himself as an ideologue and taints his peers in the process.”
A different scientist would change our understanding of global climate over the last one to two thousand years yes/no?
You’re are continuing to conflate the scientists with the work they produce and I think it’s critically important to make a distinction between these.
Would the GISS temperature record change if Hansen were replaced? Would the CRU temperature record change if Jones were replaced?
• Tom
“Faster-than-light neutrinos are a good example…”
Mr. Richard Tol, shouldn’t we wait to see the final results of the tests first to see if this was just a ‘bug’? I thought that the tests were to be finished sometime in June?
• @Sharperoo
You missed my point entirely.
No one can evaluate every scientific claim at its merit. Many cannot evaluate any claim. Therefore, trust is important. My confidence in high energy physics was boosted this week (no need to wait till June, @Tom) even though I would not recognize a Higgs boson if it bit me in the nose.
I have a background in statistics so I can and I have evaluated Mann’s past work: It’s sloppy if not incompetent. I therefore discount Mann’s future work. That is not very scientific of me, but I have better things to do than keep an eye on the learning curve of someone who is not my student.
• sharper00
@Richard Tol
“Therefore, trust is important.”
I observed a lot of skeptics trusted Richard Muller to produce an independent temperature record.
When Richard Muller produced a temperature record that did not give the answer skeptics wanted I observed that they no longer trusted him.
“I have evaluated Mann’s past work: It’s sloppy if not incompetent. “
I do not trust you, Richard Tol, or any single individual. I do however place trust in both scientific process to work things out over time and in collections of scientists to spot incompetence/sloppiness over time.
• The faster-than-light neutrino is a great example. The initial announcement was very cautious and included commitments to track down possible error and reproduce the result, the first of which they did.
Why the first announcement at all? It was bound to leak and create a furor. Better to announce the anomaly with caveats.
Why so long between announcements? IMO, a deeply-buried fault is difficult and time-consuming to find and confirm.
Science well-done. Kudos!
• harrywr2
Shaperoo,
If your basic claim is ‘the highest quality scientific evidence we have says we must take X action’ then you have to throw anyone on your side that does ‘sloppy work’ or makes statements that are only ‘weakly’ supported by ‘the highest quality science’ under the bus.
As soon as one single fact that your cause espouses to be ‘correct’ is proven false then you can’t blame the public for asking the question What else did they get wrong?
• The problem isn’t that climate scientists are “mean”, Sharperoo. It’s that they are unquestionably dishonest.
All of them?
And are all climate skeptics honest?
If so, a simple test for honesty would be to ask about AGW. :)
• MattStat/MatthewRMarler
1. A different scientist would produce different results. That suggests the problem is not the people but the work the people produce.
2. A different scientist would produce the same results but somehow be better received.
There is a third and greatly more reasonable answer: a different scientist would have responded more favorably to the critiques of the original hockey stick paper that were written by McIntyre and McKittrick and others, acknowledged the good critiques openly, and made the appropriate corrections citing the help from M&M (M&M’s work itself had some problems.) Having done so, a different scientist would have written more consistently about the different time series, not Mann’s contradictory claims between papers and blogs that Steve McIntyre has documented at ClimateAudit. A different scientist would have made all code and data available on line from the start, rather than maintaining the oblique reference to online sources, a practice that continued right up through the debate in the Annals of Applied Statistics, vol 5, number 1, March 2011, pages 1 – 123 (see especially the rejoinder, starting on p. 99.)
It is the open process that makes the scientific enterprise more reliable than the scientists themselves, and it has been that open process that Mann has subverted.
• MattStat/MatthewRMarler
Richard S. J. Tol: I have a background in statistics so I can and I have evaluated Mann’s past work: It’s sloppy if not incompetent.
On that you and I agree, but in Mann’s defense I would like to assert that much innovative work is sloppy. Some of the innovative work of Robert Millikan and Margaret Mead was sloppy (worse has been claimed, but I personally come down on the side of sloppiness rather than deceit.) Those are only 2 of many examples. The tragedy and loss to science in this case was that Mann and co-authors were so close-minded and contradictory about repairing the flaws in their work when the flaws were pointed out to them.
• MattStat/MatthewRMarler
sharperoo: I do not trust you, Richard Tol, or any single individual. I do however place trust in both scientific process to work things out over time and in collections of scientists to spot incompetence/sloppiness over time.
The obvious question then: On balance, are you satisfied with Mann’s “[working] things out over time and in collections of scientists to spot incompetence/sloppiness” in the work on the hockey stick? I think he has seriously hurt his credibility where he might instead of built it up.
• sharper00
@MattStat
” a different scientist would have…”
Ok so given all of the things this other hypothetical scientist did: What’s changed?
Does the skeptical blogosphere now accept the MWP as cooler than modern times?
Do the many many many claims of fraud in the temperature record disappear?
Assume those scientists do everything you suggest and more but still produce the same answers as today, are those answers then found to be acceptable?
If so you’re suggesting the entirety of climate change skepticism is based on a personality clash.
If not you want to change the answers by changing the people, will you know you have the “right people” only when they produce the “right answers”?
• MattStat/MatthewRMarler
sharperoo: Does the skeptical blogosphere now accept the MWP as cooler than modern times?
Do the many many many claims of fraud in the temperature record disappear?
Assume those scientists do everything you suggest and more but still produce the same answers as today, are those answers then found to be acceptable?
1. not yet; it looks to me like the totality of the evidence comes down against your claim;
2. most of them related to Mann. note how many of the claims of “fraud” in Mann’s case came after he decided not to acknowledge the work of M&M
3. you are supposing what can’t be known, but it is most unlikely, on present evidence (reviewed, for example, in the Annals of Applied Statistics Statistics debate that I cited; see also the supporting online material) that the original MBH98, and the hockey stick that adorned the IPCC website for a few years, are now supported. So which “answers” are you supposing to be the “same”?
• sharper00
@MattStat
“So which “answers” are you supposing to be the “same”?”
It is with some frustration I note that both you and Richard Tol are extremely reluctant to address the issue of whether you think different people will provide the same answers differently or different answers.
I think my question is fairly clear cut and requires little clarification nor do I know why you’re invoking MBH98 when it has been superseded by later work.
So I ask again, if you replace Mann does the state paleoclimate, as understood by other paleoclimate experts, change?
If you replace Hansen does the GISS temperature record change?
If you replace Jones does the CRU temperature record change?
• Billy Ruff'n
@ Shaperoo
” I do however place trust in both scientific process to work things out over time and in collections of scientists to spot incompetence/sloppiness over time.”
Trust process? Is it not human to put a finger up to sense the direction of the wind and to “pick your battles” wisely? It takes courage to go against the flow — and how much courage to you see in the AGW crowd?
• MattStat/MatthewRMarler
sharperoo: It is with some frustration I note that both you and Richard Tol are extremely reluctant to address the issue of whether you think different people will provide the same answers differently or different answers.
You are trying to make a point without writing out what it is. For the questions that had clear interpretations, we provided answers.
• sharper00
@Billy Ruff’n
“It takes courage to go against the flow “
How many scientists became famous for “going with the flow”? The answer is none. Within science you acquire notice, prestige and career advancement by not going with the flow.
All of the thousands of scientists regularly accused of remaining silent about the fraud in the temperature record or that greenhouse physics just doesn’t work could all become famous next week by highlighting just that.
@MattStat
“You are trying to make a point without writing out what it is. For the questions that had clear interpretations, we provided answers.”
I have stated my point openly and invited both you and Richard Tol to contradict my point by answering questions which would reveal me to be wrong.
Both of you evaded those questions and now you evade yet again, indicating my point is correct.
• Berényi Péter
sharper00 wrote:
>
> different / same results
You miss the point entirely. Science is not about results, it is about methods applied to get said results.
If you divine somehow the very same results the next guy arrives at using careful observation, experimentation, logical analysis-synthesis, mathematical modelling, prediction and empirical verification, your results are still absolutely pseudo-scientific, unreliable and fraudulent, while his work, if all details are published, can be checked by anyone having the right educational background.
In this sense, the hockey-sticky exploit, based on a few bristlecone pines and a flawed statistical method, is a prime example of scientific abuse.
• sharper00
@Berényi Péter
“In this sense, the hockey-sticky exploit, based on a few bristlecone pines and a flawed statistical method, is a prime example of scientific abuse”
And yet oddly every reconstruction verifies Mann’s results – that the modern era is warmer than the MWP. A variety of authors, methods and proxy data have been used.
The skeptics do not accept these results. I’m told that if we just swap out Mann and replace him with someone else they will. I do not find this credible or likely.
• Markus Fitzhenry
“And yet oddly every reconstruction verifies Mann’s results – that the modern era is warmer than the MWP.”
BS.
• MattStat/MatthewRMarler
sharperoo: I have stated my point openly and invited both you and Richard Tol to contradict my point by answering questions which would reveal me to be wrong.
Both of you evaded those questions and now you evade yet again, indicating my point is correct.
I reference MBH98 and The Annals of Applied Statistics, the beginning and a more recent contribution of Mann to obfuscating his work. You ought to read the Annals of Applied Statistics articles, the supporting online materials, to understand more about how Mann in particular does not aim for the highest standard.
• MattStat/MatthewRMarler
sharperoo: And yet oddly every reconstruction verifies Mann’s results – that the modern era is warmer than the MWP. A variety of authors, methods and proxy data have been used.
The skeptics do not accept these results. I’m told that if we just swap out Mann and replace him with someone else they will. I do not find this credible or likely.
Mann’s results, that he modern era is warmer than the MWP, has not been confirmed.
If someone told you that “if we just swap out Mann etc “, then you should quote that someone. That someone is wrong. It is Mann’s results, along with Mann himself, that are disputed (Annals of Applied Statistics again: vol 5, number 1, pp 1 – 123, plus supporting onlin material, March 2011.)
• Tom
I can hardly wait until the census is complete and we know the real size of both tribes. I don’t think the AGW tribe is as big as their crowd thinks. We will all know the reality of this situation very soon, I hope. Time is very overrated by the way…
Correct. I came into this issue wishing to understand the debate having zero scientific background. While I couldn’t dispute any positions about their science, what struck me like cold water in the face, was the attitudes of those in the climate establishment. Based on my experience of simply working with people in large organizations, something did not sit well with their behavior. Watching the “body language” and responses to differing views set off the BS meter and confidence in their theories dropped like a bucket of bricks soon after.
• Dennis:
I came to the debate having a bachelor degree in science, and not knowing more, I just accepted that the greenhouse effect was obvious. I soon found out what was considered the greenhouse effect in global warming theory was not at all the greenhouse effect commonly understood to be occuring in an actual greenhouse.
Then I found that CO2 is not considered the actual greenhouse gas, but rather it is water vapor, which is supposed to increase due to the increase of heat caused by an original heating of the CO2, by an effectual ration of 19 to 1.
Then as you experienced, I noticed the response to any skeptical thought or ideas was anaphalactic. The phrase “thou doth protest too much” came to mind.
The vitriole that came from a few humble questions, made me even more suspicious about what underlay their ‘science’.
Then I saw the Great Global Warming Hoax documentary, and saw there that the debate was not over, that there were perfectly credible and educated researchers who had a difference of opinion.
My conclusion, albeit still open to change, is that the majority of climate scientists and the public have an opinion similar to many doomsday cults of the past. I think Michael Criton has made the best argument and comparison to commonly accepted ‘truths’ of the scientific community, that were later found to be incorrect; most recently the stomach ulcer causes actually discovered against the entire gastroenterological medical community. (it was found to be an infection, not stress or bad food) Another may be the statin/cardiovascular/cholesterol disease theory.
I feel there are far too many holes in Climate Science as its conclusions of today.
(I heard that any field of endeavor that feels it necessary to append the word “science” to its moniker, may not be so scientific.)
• Robin Melville
Ditto, except I came into this issue from a Public Health research background where “noble cause corruption” is also rife. It’s a tough thing to have some pretty core beliefs tumbled by exposure to the real debate. I suspect that when the history of these times is written the doom-laden and almost hysterical public memes at the turn into the third millennium will seem as quaint and bizarre as the superstitious frenzy to which Europe succumbed at the end of the first.
• cwon14
Why is there a climate movement at all? What are its true roots and goals?
At NPR, a partisan left-wing media organization and fanatical AGW supporter as a rule has been running disinformation and false narratives as above for days regarding Gleick. Heartland exists in part as an offset to this reality, they fill a void. It’s why they are targeted by a usual suspect in Gleick or for that matter NPR.
The trouble here is the misuse of the word “Ideologue” when the debate is so much easier and more accurately defined;
https://judithcurry.com/2010/11/07/no-ideologues-part-iii/#comment-175222
We know what the word “Ideologue” means in this world Dr. Curry. In the case of AGW the debate can’t be advanced while trying to obfuscate the very specific ideology of the advocates themselves at the highest ranks of science communities. It should be about advancing the debate not selling the results (AGW CO2 mitigation policy for example) you and the core AGW advocate community might wish.
“And of course all this begs the question of why we don’t have CO2 stabilization policies, which is mostly about economics, politics, values.”
A good part of the public has it figured out. We don’t like the “climate movements” politics, values or economics. The science was reduced to a facade long ago. This is more of the same here if skeptics accept this narrow and politcally correct protocal of accepting generic terms about “ideology” instead of getting to the heart of the matter of what that is with “Michael Mann, Phil Jones, Jim Hansen, Peter Gleick, Al Gore, Rajendra Pachauri” not to forget NPR, NYTimes (MSM in general), Greenpeace, IPCC, WWF, the U.N. or U.S. Democratic party that embraces the “cause”. What about yourself Dr. Curry? Why can’t the agw movement be identified in simple and accurate terms? Why do we need this massive investment in euphemisms under “ideology” when most understand it exactly as I and many describe it?
Skeptic or moderator alike, it’s a politically correct protocal that assists the AGW movement. You should object if only for ethical reason. The protocal is unethical.
• steven mosher
Good question Richard.
I have to say that the one that does the most damage is Mann.
Why? because his paleo argument, as it stands, really contributes very little to our understanding of sensitivity. Yet, too much brand equity has been invested in the hockey stick. So, its an argument that if won, adds nothing, and if lost, tarnishes the brand ( not the science) tremendously.
• sharper00
” So, its an argument that if won, adds nothing”
It’s almost as if scientists don’t behave according to the political ideologies attributed to them.
• Why? because his paleo argument, as it stands, really contributes very little to our understanding of sensitivity.
If you’re referring to modern sensitivity, Steven, I would agree because it is so strongly influenced by the high rate of global warming, creating a huge gap between theoretical and observed sensitivity. The argument that humankind rode out the MWP without a sweat, so to speak, is invalidated by the point that we weren’t subjected to the rapid change we experienced during the past half-century.
Even if it was hotter then, which itself is still hotly argued today, it’s irrelevant to the current situation because not just humankind but all life on Earth is being given considerably less time to adapt to the modern rate of change.
But in that case I would say McIntyre did as much or more damage than Mann, by throwing down the wrong glove and thereby starting a pointless war. As experience has shown it is very difficult to make convincing arguments about the exact height of the MWP based on what center(s) to use when comparing principal components.
Neither side however has claimed that medieval temperatures collided with the peak of the Medieval Warming Period at the breakneck speed of jousting medieval knights on horseback. It would have been so much easier, to say nothing of avoiding a controversy that has stirred up so much hatred of each side for the other, had McIntyre made the simple and noncontroversial point that Mann’s research was irrelevant to modern times.
Who did more damage is like asking whether God is Christian or Muslim. It depends who you ask.
• maksimovich
The argument that humankind rode out the MWP without a sweat, so to speak, is invalidated by the point that we weren’t subjected to the rapid change we experienced during the past half-century.
Your proposition contradicts your own argument, in so far that the rapid change (inverse excursion) in the transition from the MWP to the LIA was also over a small temporal period and had great societal implications eg Nunn
Within the last millennium there was a marked contrast in
many Pacific Basin societies between what might be termed
‘times of plenty’ during the Medieval Warm Period
(approximately A.D. 700–1250) and ‘times of less’ during
the Little Ice Age (approximately A.D. 1350–1800). The
transition between the Medieval Warm Period and the Little
Ice Age has been named the ‘A.D. 1300 Event’ and has been
identified as a time of rapid cooling, sea-level fall, and
cultural change. Specifically, it is clear that the societal
disruption associated with the A.D. 1300 Event was due
largely to a massive and rapid reduction of the food
resource base on which many Pacific communities had
come to depend during the preceding Medieval Warm
Period
• Billy Ruff'n
@Vaugahn Pratt
“The argument that humankind rode out the MWP without a sweat, so to speak, is invalidated by the point that we weren’t subjected to the rapid change we experienced during the past half-century.
Even if it was hotter then, which itself is still hotly argued today, it’s irrelevant to the current situation because not just humankind but all life on Earth is being given considerably less time to adapt to the modern rate of change.”
Come on! How about the “rapid change” comparing 2010 winter to 2011 winter in New England? Yeah, I know it’s just weather, but you were talking about “rate of change”. When I compare the number of birds at my back yard feeder, the number of rabbits, squirrels and chipmunks running around this year to last, I’d say nature has adapted very well to the extremely rapid warming we’ve experienced in the last 12 months.
• Steven Mosher (Feb. 24, 2012 at 12:29 pm) and Vaughan Pratt (Feb 24, 2012 at 1:51 pm):
If, by “the sensitivity,” you mean “the equilibrium climate sensitivity” (TECS) then the concept that you reference by this phrase is scientifically illegitimate for the value of TECS is not observable and thus speculations regarding this value lie outside science. If not, what do you mean by “the sensitivity”?
• Markus Fitzhenry
‘speculations’
The discourse that garners such terminology is Rhetoric.
We will never be able to communicate to Vaughan in the language of Logic.
Mosher is OK, he is not too bent, just a bit of a smartie at times. Eh Mosher?
• Your proposition contradicts your own argument, in so far that the rapid change (inverse excursion) in the transition from the MWP to the LIA was also over a small temporal period and had great societal implications eg Nunn
Maksimovich, your point that rapid changes are harmful (in your MWP-LIA example, decreasing rather than increasing temperatures) is the same one I’m making. How can that be an objection to my point that “The argument that humankind rode out the MWP without a sweat, so to speak, is invalidated”?
The central point here is that rapid change is bad. My complaint is that McIntyre continues to ignore this. You’re agreeing with me that rapid change is bad.
• We will never be able to communicate to Vaughan in the language of Logic.
Are you saying you’re illogical, Markus?
• If, by “the sensitivity,” you mean “the equilibrium climate sensitivity” (TECS) then the concept that you reference by this phrase is scientifically illegitimate for the value of TECS is not observable and thus speculations regarding this value lie outside science.
Thank you, Terry! I’ve been having a terrible time trying to convince people of this. The term has come to be used so frequently as to acquire a life of its own. It’s like belonging to a community that speaks of God in every second sentence and as a result cannot imagine a world without God.
• MattStat/MatthewRMarler
Richard S. J. Tol Who does most damage to the climate movement? Michael Mann, Phil Jones, Jim Hansen, Peter Gleick, Al Gore, Rajendra Pachauri
That is an intriguing post. I think you could make a good case for that.
I have been planning for a while to cut down on my posting and to post under my name, Matthew R. Marler. Here is my LinkedIn public profile:
This is a good time to start.
I have been involved in research, which you could call the edge between knowledge and ignorance. In my posts I have generally focused on: (1) approximations whose accuracy for the purposes at hand has not been demonstrated; (2) questions whose answers are not known (hypotheses with little or no evidentiary support); and (3) inaccuracies in model results due to random variation in observations that gets incorporated into the parameter estimates (what statisticians generally specialize in.)
• I would add Trenberth to your list, Richard … But, in any event …At this point, I’m beginning to wonder if perhaps they have been competing to see who can build the biggest mountain out of the smallest molehill!
They’ve had two years to re-evaluate their outreach and PR efforts, and it would appear that they have learned absolutely nothing.
All they seem capable of doing is ignoring the “problem” in the hope that their silence – along with repetition of their constant refrain of “we must decarbonize now” – will make it disappear.
• Sam NC
Yes. Trenberth has definitely done a lot of misinformation back radiation to students in his Global Annual Mean Energy article more than a decade ago with the publish by the AMS. AMS helped the spread of misinformation so far not retreating that article.
• lolwot
• SamNC
• I would say the greatest damage to the climate movement has been done not by one person, but the frequency with which single weather events have been attributed by some climate scientists and some journalists to AGW. So last year’s blizzards were AGW, and this year’s warm winter is AGW, and last year’s Texas drought was AGW, and last year’s floods in Vermont were AGW. It’s become a joke, such that people — many people, most completely uninvolved in the climate science discussion — will look out at the snow, and joke ‘global warming!’
I know the arguments that AGW causes extreme weather events (and the counter-arguments that this is wrong or alternatively essentially unprovable), but for popular consumption it’s a very dangerous argument, because people are smart enough to figure out that a theory that can account for everything is unfalsifiable and unscientific, even if they’ve never heard of Karl Popper.
• people are smart enough to figure out that a theory that can account for everything is unfalsifiable and unscientific, even if they’ve never heard of Karl Popper.
But Gerard, there is an easy way to falsify this theory. If increasing CO2 is supposed to be making the weather fluctuate more violently, and it returns to the relatively calm state it was in before 1960, as we would all love it to do, then you have your falsification right there!
If on the other hand it continues to get more and more violent, then those of you continuing to say there’s nothing out of the ordinary with the weather will look more and more stupid with every passing year, because what the so-called alarmists were warning about will be coming to pass and you will be refusing to acknowledge that it is happening. Your head will be in the sand.
In the parable of the boy who cried wolf, the wolf eventually put in an appearance.
• Brian H
“If on the other hand it continues to get more and more violent”
Say what? Frequency of virtually every major storm type from tornado to sandstorm has been dropping for some time. ACE is declining.
Dollar damages due to expansion of expensive coastal developments (ironically encouraged by the drop in landfalling hurricanes?) are rising, but that’s not the weather or climate’s fault.
Cooling will steepen the tropic/pole heat gradient, though, and bring back “violent climate”. But it will prove the opposite of the CO2-forcing hypothesis.
4. I find the question akin to asking “If you wanted to thwart the worldwide conspiracy of hidden reptilian overlords, who would you target”
But in the spirit of the question, Steve McIntyre. Very powerful to discredit someone who focuses on relevant technical matters and plays with such a straight bat.
Note that I don’t accept that even if you were to uncover SM was lavishly funded by Big Oil behind the scenes it would make a blind bit of difference to the analyses, but the question is one of the sizzle and not real bacon.
5. Brian H
Gleick and other warmists claim, and seem to believe, that there is an “extremely well-funded and organized” anti-science campaign directed against them. That they can’t seem to find any overt examples of its operation is very frustrating.
Because, of course, there is no such campaign, the funding of skeptic analysis, commentary, and research is spotty and minuscule, and there is thus no target. So they blast away at random.
6. Louise
“Was Heartland singled out because Gleick thought they were doing something unethical?”
They were singled out because somebody sent Peter Gleick the ‘Strategy Document’ for that organisation and not any other. That you ignore this implies you think he was lying. Do you?
• Markus Fitzhenry
Oh come on Louise, Peter Gleick stole the documents because his style of AGW climate science is on its knees and they are panicking. Simple, there is no conspiracy against them. Doesn’t need to be they are being dishonest enough to hang themselves.
• People send me all sorts of stuff, most of it lands in the garbage. Whether Peter Gleick is lying or not i have no idea, but I have to say that what he says doesn’t have much credibility at this point.
And if I did receive what Gleick says he received in the mail, and I was concerned about something (e.g. Wojick’s education plan), I would have contacted Heartland or Wojick for information.
The simplest thing would have been for Gleick to accept Heartland’s invitation to speak, then discuss this in person.
• Robert in Calgary
Goodness, Dr. Curry, those aren’t the sort of answers Louise wants to hear!
Judith,
You may remember in a previous post using the words “thank you hacker/whistleblower”, thereby not only condoning the release of the “climategate” emails but apparently condoning someone committing a serious criminal offence (computer hacking), worse than what Gleick did, in order to obtain them.
If it turned out that the mails were indeed obtained via computer hacking would you in fact condone the actions of the hacker?
• Ged
Hacking is actually less of a legal offense than impersonating for the purpose of fraud, from my understanding. But laws change all the time, so that may not be true.
Still, everything about CRU points directly to an insider with Admin privileges and access to the physical backup tapes for the servers. The e-mails were also different from this, as those were intercommunications through public property, not private budget, employee, and donor information.
Remember, CRU is public and public money, Heartland is private and private money. Very different issue legally and morally as well.
• Hacking is actually less of a legal offense than impersonating for the purpose of fraud, from my understanding.
Oh great, another bush lawyer.
Fraud is illegal. Impersonating a police officer is illegal. These terms are well defined in law. What does the law define as “hacking?”
• Gleick’s behaviour on other media (Amazon book reviews, Twitter) leave me with the opinion that he has a somewhat flexible relationship with objective truth where he thinks it’s justified.
It also seems to have been the writing style in the alleged fake document that alerted people to his.
I’d estimate there’s a decent chance he’s lying about everything – he’s already admitted to lying to get the documents.
• Latimer Alder
Do I think Peter Gleick is lying?
Yep. Through his frigging teeth!
He has already admitted to lying about his identity to obtain the unfaked documents. I see absolutely no reason to believe that he isn’t lying this time.
• Hey, Latimer, you should play Angry Birds more. :) Take it out on those pigs instead of on live human beings who have emotions like yours.
Well, somewhat like yours. You have all the self-righteous anger of Joan of Arc with none of her eloquence:
I could let the banners and the trumpets and the knights and soldiers pass me and leave me behind as they leave the other women, if only I could still hear the wind in the trees, the larks in the sunshine, the young lambs crying through the healthy frost, and the blessed blessed church bells that send my angel voices floating to me on the wind. But without these things I cannot live; and by your wanting to take them away from me, or from any human creature, I know that your counsel is of the devil, and that mine is of God.
The “from any human creature” is a nice touch. Can’t get more self-righteously angry than that. Make a note.
• hunter
Dr. Pratt,
Your post seems non-responsive to Latimer’s remark. Is it OK to doubt your fellow Bay Area academic just a wee bit?
• Your post seems non-responsive to Latimer’s remark.
On the contrary, hunter, I would say that the only reasonable response to a remark made in anger is to point out the anger and wait for it to subside. Engaging the angry in rational conversation is an exercise in futility.
• Latimer Alder
@vaughan
No anger here, mon brave. I have no spare emotional bandwidth to be angry since I am still laughing so much that it almost hurts.
I just love to learn of self-appointed egotistical tubthumpers brought down by their own deep character flaws. It is made even better when their buddies – rather than shutting up in the hope that it will all be soon forgotten – pile on into vapid and futile defences. Not content with the main man making a public idiot of himself they rush to join him.
One day perhaps I’ll be angry. But not just yet. Having far too much fun right now
• coniston
Dr Pratt,
As we are attempting to be accurate here….those words are GB Shaw’s not direct quotes from St Joan.
• Weird, I’d written something about how I was setting the bar a tad high by setting Shaw as a standard but I must have accidentally deleted it or something. Sorry about the inaccuracy.
• hunter
Louise,
Keep repeating this line of rationalization.
It is wondermus.
• DocMartyn
Louise, on what basis do you have to support the claim
‘somebody sent Peter Gleick the ‘Strategy Document’ for that organisation and not any other’?
• Bill
1. It looks very much like the fake “Strategy” document was written by someone other than a true skeptic since it uses terms and beliefs that are pro-CAGW caricatures of what skeptics actually believe.
It also does not have an author, is not signed, has a few careless mistakes in it and does not feel like something one would send to the board as it is not very professional. See The Atlantic for some articles by an unbiased journalist on her views on this.
2. Whoever wrote it had access to the 4-5 other Heartland documents so it was either written beforehand by someone who had the documents or afterwards once the documents were in “warmist” hands. If whoever gave Gleick the memo had the documents, why did they not just send them to him so he did not have to break several laws in order to get them?
3. The fake document was scanned and handled differently than the others and has a date on it (electronically) the day before Gleick sent them to his accomplices (just had to throw that in there) and was done in the Pacific time zone (perhaps at Gleick’s Pacific Institute??) Not proof but interesting.
4. The fake memo prominently mentions Gleick and his Forbes columns like he is really on skeptics minds when in fact he is pretty far down the list. (Yes, there is an official secret enemies list and on it are listed all the trillions of dollars that all the evil corpurashions are paying me and all who post on skeptical blogs). It’s a true conspiracy!!!! RUN!
5. It also uses words and punctuation that Gleick likes to use, again ones none of us would ever use to characterize our own positions. And some of the mistakes I mentioned in 1. actually are misleading in the way that Gleick in print actually thinks things work. Saying Koch gave 200K when in fact it was 25K and then not realizing that this was for health care issues, so why would someone able to secretly contact half the board put the wrong number about the wrong topic in a memo that was supposed to be on climate strategy? What it does, if one does not know the truth, is paint a picture Gleick already subscribes to, that validates in his mind the idea that evil energy companies are backing skeptics.
• Ron DeWitt
A point that you didn’t mention is that both the purported independent writer of the strategy memo and Gleik (in his “verifying”) made the same errors regarding the Koch $200K donation. Coincidence? This, to me, is a strong indication that they were not independent. • max re: #4 But HI invited Gleick to participate in a debate, so Gleick was on HI’s radar as an important and influential person. HI is only about obscuring the science and not interested in honest debate so it would only invite a influence-less fool with no persuasive ability to a debate. But HI invited Gleick, who HI considers important enough to warrant neutralization, to be the fool in a one-sided “debate”. Sorry, my mind is having problems following the logic. This comes from a theory I have that the 13Jan2012 invitation to debate might have been the catalyst which caused Gleick to target Heartland. I’m not sold on the idea, but it should be worthy of consideration. If we accept that Geick received an anonymous memo purportedly from HI at about the same time as the debate invitation, then the contents of the memo would have been worthy of investigation. Contrariwise if Gleick were the source of the ‘anonymous’ memo then the HI invitation alone might have been enough to prompt him to acquire the documents and write the memo. • David Jay YES!!! • chuckr Lying is a habitual behavior, just as is honesty. When people are faced with stressful or uncomfortable situations their habitual nature will take over. That’s why you can change your golf swing but revert to old habits at the most inconvenient times. There is zero chance, IMO, that Gleick does not have a long history of dishonesty. When he was frustrated or angry with Heartland he resorted to what for him has become second nature. This is how he deals with difficult situations. He then rationalizes the method . Everything Gleick says should be viewed with extreme skepticism. • Peter317 Why do you imagine they sent it to Gleick only? They would have gotten a lot more mileage out of it by sending it to other people. Just askin’ • GeneDoc Yes Louise, he is lying. He lied to Heartland to steal their confidential documents. He lied to the people he sent the documents to. Why would you believe his “explanation” for the forged document? Read his statement. It’s a carefully parsed, lawyer-assisted explanation that does not equate the “received” document with the forged one. Also look at the timing. He impersonated a board member almost immediately after turning down Heartland’s invitation to their donor dinner. Of course he’s lying. Of course he forged the Strategy Document. He’s simply trying not to go to jail or to minimize the damages that he will have to cough up. 7. Punksta Does anyone actually still believe Gleick is capable of being truthful on such matters ? • Latimer Alder And why should we believe that this recent ‘transgression’ by the hapless Gleick is the only one of its kind? He has been active for some while establishing himself as a noisy and bumptious cheerleader for the alarmist cause. Are we sure that all his previous utterances and declarations are untainted by a similar failure in his moral compass? 8. The end result of this episode is that Heartland will become known to many more people. You bet. Who would you target? That’s a good one. Their problem is they don’t have a target. They try to fabricate it, Big Oil, libertarians, smokers (ha), conservative morons, etc. But it is just a fairy tale about the “good” against the “bad”. Stuff for kids. If I had to single out one, being so difficult, NIPCC doesn’t seem a too bad choice for me. And that’s Heartland. 9. Peter Davies I consider the organisation that is doing the most damage to the AGW cause is the IPCC itself and the individual who has the most influence in creating doubt about the AGW concensus would have to be Professor Freeman Dyson. However, if I were to be on the side of AGW, I would do my utmost to ensure that the science behind the AGW hypothesis is verified and validated and made the subject of the most intense peer review process ever conducted. I say this because I truly think that human activity is causing some climate change beyond normal natural fluctuations but the extent is still to be satisfactorily quantified. • +1 • I was tempted to say the IPCC but Peter Davies got there first. I think you are asking the wrong people – most of the denizens of your blog would find it very difficult to put themselves in the position of a fanatic like Gleick. The reason Gleick chose to try to attack Heartland is because of his recent personal history with them. See the Jan 12 Forbes article by Heartland’s James Taylor, criticising an earlier ‘rant’ by Gleick. Gleick responded in the comments, returning the word ‘rant’ but his arguments were shredded by a reply from Taylor. This seems to be what caused Gleick to go off the rails and produce the fake memo referring to Forbes, Taylor and Gleick. Judy’s point towards the end is not new but is worth repeating: these organisations like Heartland and GWPF only get noticed when the zealots attack them. • Bob Koss Paul, You beat me to it. Those are also my thoughts. Gleick’s inherent hubris couldn’t stand the idea of someone having the audacity to challenge his version of reality. I have little doubt he was obsessively stewing about it for a considerable length of time just hoping for a way to damage Taylor. When Jim Lakely emailed an invitation to debate Taylor and started out by saying “I’ve enjoyed the lively discussion via dueling Forbes.com columns and replies between you and James Taylor.” His obsessive mindset took it as a mocking statement. It then became an I’m going to show these bastards a thing or two situation to him. It may have started even earlier than those two columns for all I know. Simply having to compete with someone writing from a different perspective in the same publication may have already had him wound up tight. I’m no psychologist, but that is the way I see it. YMMV • kcom I think Bob Koss nails it. This explains everything, including why Heartland specifically: I have little doubt he was obsessively stewing about it for a considerable length of time • Ian Blanchard Dr Gleick forgot the wise words of Terry Pratchett: Personal is not the same as important • Personal is not the same as important Quite right. That’s certainly how Newt Gingrich feels about his intimate relationships vs. his public persona. • Anteros Peter Davies/Judith – I’m not sure I agree. It is so easy to criticise the IPCC. What are you criticising? It’s structure? The average scientist that devotes a lot of time to it? The reviewers like Anthony Watts and Steve Macintyre? It’s mandate? Its attempt at summing up the current state of climate science? If anyone steps back and asks what sort of organisation and product would the relevant bodies come up with, it would be the IPCC. Of course it is politicised. Of course it over-eggs the pudding [see FAR predictions] Of course it makes some mistakes. But to believe that the IPCC is the biggest impediment to the AGW cause is, frankly, delusional. Think back 25 years and ask in what meaningful way it could have been any different. It’s a big, messy, imperfect body that many people hate in principle – which seems to me to be 95% (ish) of the problem. But as Richard Tol has pointed out, it isn’t going to go away any time soon. *** My response to one of Judith’s questions (and Richard Tol’s list) is to ask who do the most to damage the anti-CAGW cause? Some might mention Moncton but I think he is at most a buffoon. For Americans it might be Senator Inhofe. For me, in the UK, it is hate-filled Delingpole with his mantra that the opposition are all “eco-Nazis”. If anyone makes me want to disavow being a sceptic it is him. • kim Monckton has his high horse, Delingpole his deadly wit, and Inhofe his basket of roses, but you go to war with the warriors you have. ============== • cwon14 Delingpole “hate-filled”? You seem to be missing the point of either NPR or Gleick for example. If you want to see “hate” go to an OWS, G-8 or AGW rally. AGW is a hate based movement, Delingpole exposes it perhaps crudely but is far more accurate then the sort of poltically correct prattle standards of discussing abstracts about “ideology” that go on here. All so that you, Joshua, Robert, Martha, WHT to name a few might not have their fantasy of themselves as “objective” not disturbed? Or is to maintain Dr. Curry’s gutless Switzerland status during the climate war? I’m leary of anything that describes “all” as you accuse but don’t convince me regarding Delingpole. Still he’s far closer to the truth than Dr. Curry who goes through every language contortion imaginable to protect the warming establishment of being exposed for their political fingerprint which Inhofe, Monckton and Delingpole recognize. Bedwetting skeptics only help the “cause” by accepting false narratives and conventions. • cwon14 said; ‘All so that you, Joshua, Robert, Martha, WHT to name a few might not have their fantasy of themselves as “objective” not disturbed? Or is to maintain Dr. Curry’s gutless Switzerland status during the climate war?’ Perhaps the comparison to Switzerland is more apt than you realised. Switzerland was accidentally bombed once, and suffered considerable hardship for much of the war. Gutless?: Certainly not. I can do no better than to quote this blurb from the cover of the book ‘Refuge from the Reich’-this comment by James Hutson director Library of congress; ‘A fast paced account of the experiences of Amercan Airmen forced down in neutral Switzerand during world war 2. …this little known story becomes a testimonial to the courage of the American flyers and of their swiss hosts whose defiance of Hitler provided a refuge for the distressed aviators.’ I recommend the book, it might provide a better perception of Switzerland than you seem to have. . Judith displays considerable courage in providing a safe haven for those of us fighting against the current consensus. She deserves our thanks rather than the sniping and questioning of her motives that seems to be her reward. tonyb • nutso fasst Perhaps Senator Inhofe is playing the same role Senator McCarthy played with Communism: give the opposition the moral high ground relative to yourself. Assuming you were an anti-communist who thought McCarthy was spouting a counter-productive hate-filled mantra in opposition to communism, would you then want to disavow being anti-communist? • AGW is a hate based movement So eco-Nazis, right, cwon14? (Don’t be shy, you can say it.) 10. Bruce Anderson I think Steve Mosher nailed it at CA: “his motive is anger. Like many who set fires. Anger and revenge. The humiliation he suffered at Judith’s and WUWT. Taylor’s refusal to listen to the macarthur genius. The crime is not about the science. not about the cause. The motive, the governing emotion, is anger and revenge. Brought on by humiliation, fanned by pride. It’s personal. It’s always personal. People tend to look for political motivations or the cause as a motivation. Those are the rationalizations, NOT the motive.” This wasn’t a well thought out plan to discredit the skeptical movement by targeting the main player….it was personal. Bruce • Garry No doubt about it, this was hardly a random act. Very personal indeed. And what may have pushed him over the edge was the series of emails between Gleick and Jim Lakely of Heartland immediately surrounding Gleick’s impersonation and document theft. It was all detailed by Steve McIntyre at Climate Audit yesterday: http://climateaudit.org/2012/02/23/heartlands-invitation-to-gleick-details/ • steven mosher Thanks Bruce. I also happen to believe climategate was personal as well. These violations are almost always personal, of course “politics” and “causes” provide good cover for the motive. But it’s personal. Look for people whose intellectual pride has been wounded. Getting away with the crime would restore their wounded self image. • Tim Interesting. Do you think that is what motivated FOIA? You have mentioned clues to his/her identity but I must confess that I have not been able to keep up. • Ged I love your analysis, Steven. You could totally write a detective’s novel, or become a private investigator yourself! 11. Paul Why target the Heartland? Because he had been interacting with the Heartland and declined their invitation to a Heartland conference. His offered reason for declining (among others) was lack of clarity on funding! The Heartland was on his mind as was funding. He chanced his arm with a request and got a result. I think Lucia (or someone on her blog) asked the question if Peter Gleick has, as yet, an undiognosed pyschological condition. This is a good question. Doing this and thinking he coudl get away with it, smacks of someone who has taken leave of their senses. Paul • Punksta The Heartland was on his mind as was funding. Never seems to occur to or trouble them that funding for the CAGW cause is orders of magnitude larger, and that the provider of these vast funds – the state – has a massive vested interest in a finding ifo CAGW. • Brian H Any funding for the deniers is too much. That it is sufficient to derail their Choo-Choo gravy train, potentially, must mean that it is massive and devilishly well targetted. Thus the persistent, repetitive rhetoric, and efforts to locate and eliminate the sources. • kcom That it is sufficient to derail their Choo-Choo gravy train, potentially, must mean that it is massive and devilishly well targetted. Or, alternatively, that its target is extremely rickety and vulnerable. But they can’t admit that one in public. • DeNihilist Paul, actually, reading Glieck’s lawyers response to Heartlands’ annoucment that they have involved the FBI, I am tending to think the Glieck set himself up on purpose to try to get to discovery, thinking that his team will be able to rummage through all of Heartlands’ docs and be able to publish them all! From what I understand though of the process, which is not much, if this is what he intended, he may have blown it again. • This train of thought does not pass the smell test. It presumes thoughtful planning and execution. It is unlikely Gleick would voluntary and permanently destroy his stature in a multitude of commitee’s and organizations in a Kamikaze attempt at rooting out the secrets of Heartland. Perhaps if Gleick suffered from a martyrdoom illusion and believed that Heartland was the personification of evil on Earth, and he had to destroy himself in order to save the Planet, the Children, the Trees, then maybe…..but do ya really think so? 12. If I was a climate scientist, one who really knows what he’s doing, I would be aware that I was wrong. Most of them are at this state. What would I do? Easy: start doing what I started more than 4 years ago: getting the truth out… Ecotretas • DocMartyn actually, the first one to bolt has the most to gain. It is a scientific version of ‘Prisoners Dilemma’. The climate reconstructionists know the tree/cave/pollen/verve e.t.c. series that have been ‘eliminated’ from global reconstructions. Like reshuffling a stacked deck it would be rather easy to show up/down swings. The first AGW based scientist to break ranks will bring all the others down. I would expect them to do a world wide pollen temperature reconstruction and then exclaim, we were all fooled by tree-rings. • oxonmoron Ahem Ecotretas. Actually Richard Lindzen is a very distinguished climate scientist. His recent lecture to Brit parliamentarians is a blistering expose which, surprise surprise was received very well. There are others as reputable who have bucked the “cause”. It’s not about the science. 13. kch The difficulty in finding an appropriate target comes from the very nature of the skeptical/lukewarmer side of this. It’s too amorphous, too wide-spread, too grass roots. There is no one individual or organization that that seems recognized as the ‘leader’, hence no natural target. The targeting then becomes more about the personal beliefs and anger of the attacker – not the prominence of the attacked – which is why the choice of evil overlord du jour often seems a little strange. 14. As others have said, the answer to “who would you target” is the same as “who has done the most damage to the credibility of climate science”. You could easily name the usual suspects (in no particular order): Mann, Hansen, Jones, IPCC, Gleick (a rising star), Pauchari and on and on it goes. But all the prominent skeptics could disappear tomorrow, and the questionable science/advocacy would remain as the low hanging fruit for new critics. The problem isn’t the critics, the problem is that there are so many obvious criticisms. 15. MDR Who to target? Maybe the whole Tea Party or the GOP, as we all miss a better one. That was a very, very well proposed question. • hunter MD, Which comes back tot he political nature of the AGW movement. And it is a nature that the AGW faithful are very reluctant to acknowledge in themselves, but obsessed with attributing to others. 16. Joe's World Judith, Fanaticism to one’s cause is usually the downfall of that cause. The incredible bias to anything outside of the single minded view by experts that MUST NEVER be questioned. This is making all of science be questioned. • hunter Joe, that is the single best thing you have ever posted. • billc joe’s pretty insightful when he’s not talking about models • kim Yup, billc, and I’d about half bet he’s got it figured out, just can’t get it out. =================== 17. Speed Imagine you are a flat earther and want to take down the single organization that is doing the most damage to your movement. Who would that be? If it was 1492 or so, Chris Columbus would be a good target along with a few Viking offspring. But now, it’s too late. Same for global warmers. • DocMartyn This is completely incorrect. Columbus was vilified not because he thought the Earth was a sphere, but because he thought the size of the sphere was far to small. He hoped that by sailing the Atlantic he would reach the most eastern coast of China. He didn’t, he hit the Americas. He was informed time and again that he could not reach China, BECAUSE THE SIZE OF THE GLOBE HAD BEEN CALCULATED MORE THAN A THOUSAND YEARS BEFORE. Columbus faked his calculation to arrive at a small Earth, not a spherical one. Those who had studied classical Greek texts could read the calculations performed that showed that the Earth was a much larger sphere than the one Columbus had concluded. It is a myth that Columbus overturned the ‘flat-Earthers’, instead he proved the big-spherer’s correct. He did not get to China. Note that on arrival to the Americas he carried a letter to present to the Grand Khan and his Arabic interpreter had a problem with the natives. On return from his first voyage he attempted to persuade everyone he had landed in Japan. • Speed DocMartyn: Sit down and take three deep breaths. This isn’t about Christopher Columbus. It’s a story to illustrate a point: there is no way to prove that the earth is flat and there is no way for Peter Gleick et al to prove today that we are destined to suffer greatly in an overheated Earth. There is neither a big boogey man nor a “single organization” to take down. They are simply wrong and are destined to be marginalized just like the flat earthers. The Flat Earth Society (also known as the International Flat Earth Society or the International Flat Earth Research Society) is an organization that seeks to further the belief that the Earth is flat instead of an oblate spheroid. (Wikipedia) • Gdn From various sources, including NASA: http://www-spof.gsfc.nasa.gov/stargaze/Scolumb.htm The Greek philosopher Aristotle (384-322 BC) argued in his writings that the Earth was spherical, because of the circular shadow it cast on the Moon, during a lunar eclipse. Another reason was that some stars visible from Egypt are not seen further north Eratosthenes (ˌɛrəˈtɒsθɪˌniːz) — n ?276–?194 bc , Greek mathematician and astronomer, who calculated the circumference of the earth by observing the angle of the sun’s rays at two different locations at the same time. He also invented a method for listing the prime numbers that are less than any given number. The Arab Khalif El Ma’mun, who ruled in Baghdad from 813 to 833, sent out two teams of surveyors to measure a north-south baseline and from it also obtained the radius of the Earth. Columbus had an estimate of his own. Dr. Fischer found his claim to be based on incorrect units of distance. Columbus used an erroneous estimate by Ptolemy, who based it on a later definition of the stadium, and in estimating the size of the settled world he confused the Arab mile, used by El Ma’mun, with the Roman mile on which our own mile is based. 18. Tom Choularton The reason Heartland was targeted I suggest is that he received one or more internal leaks from Heartland containing their plans and list of sponsors. He then decided to find out whether these are genuine. That is what he says and I have no reason to doubt it. • hunter Tom, Gleick is like a defendant who, after being caught, admits to having the jewelry from the victim’s house but promises he did not assault her. And besides, she was a known slut anyway. • Wow. Tom Choularton is a professor at Manchester University. He says there is no reason to doubt Gleick’s word. One can only hope that Tom is misinformed and hasn’t looked into the story. • kim That’s just his cover, Paul. Actually, he’s a bot escaped from a Pink Panther film. ======== • David Jay “That is what he says and I have no reason to doubt it” snigger…guffaw…LOL…ROFLMAO Tom, Tom. Tom, you really should be doing stand-up comedy 19. DocMartyn I think it reveals an underlying Marxists mindset. The ides that the great mass of people ‘the proletariat’ do not act in their own best interest, such as embracing communism, is to their having a ‘False consciousness’. The Marxist view is that the majority of people develop a ‘false consciousness’ because the capitalist controlled media constantly feed the population is misleading information. Thus, organizations like Heartland are the tip of the capitalist spear in the climate wars. Capitalists, especially big oil, must use front organizations that deliberately and systematically mislead the public and stop them understanding the obvious consequences of fossil fuel usage. Thus, the people are sheep and whilst the long term target of political action should be replacing the Shepard, in the short term you should try to kill his dog. Heartland is the embodiment of evil in a Marxist analysis, a think-tank is the machine that delivers false information to the proles and stop them revolting against the political/societal organization. • MDR I don’t agree with the Marxist mindset, but with a broader notion of many activists that “the system does not work, let’s fight consolidated power with any means available; our actions are justified by our moral superiority”, which is quite common in the far left. (And I mention the far left because it might be taken seriously, in oposition to the far right, which is mostly a criminal justice issue). • billc I agree with your first paragraph, I don’t understand your second. I would classify myself as center-left if it matters. Of course the center moves around. • Robin Melville The first paragraph’s ok. MDR nails the operational modes of the tiny muddled rump of far-left groups shattered by Reagan/Thatcher and the collapse of the USSR (which they strongly opposed, by the way). The second para implies that a Marxist would support anti-AGW campaigns. Marx and Engels mourned the replacement of diverse and complex social relations by the simple payment of a cash sum (e.g. wages). But they recognised that capitalism had unleashed unparalleled productivity which had the prospect of allowing beneficial living standards for all (as opposed to the “idiocy of rural life” which green campaigners seem to wish for us). Their complaint was that the workers who created this wealth were alienated from its fruits. Marxists can’t be against industrialism — their supposed agency of change is the industrial working class. They are, however, opposed to capitalism. 20. Ian Blanchard It’s a good question. From a scientific viewpoint, I think that the AGW promoters would actually do a lot to help their cause by engaging with the likes of Lindzen and McIntyre and disengaging from the likes of Romm, DeSmog and even some of the more mainstream media who publicise the most extreme catastrophe stories. As a climate change ideologue, I’d probably look to shut down WUWT, not because it is necessarily the technically best or most balanced source of information (too many contributors are primarily political rather than technical), but because it is probably the most widely read. The problem with that strategy now though is that the climate blogosphere is a bit of a hydra, and decapitating one site would only see the commenters migrate to another of similar beliefs. Of course being at the skeptical end of the luke-warming spectrum, I don’t have to worry about such things. • hunter Ian, If they engage, they lose. AGW believers do not even admit that they have an extreme view of cliamte risk. They deny that AGW is about a climate catastrophe. They assert that if CO2 has any impact at all, then they are correct in everything they claim. Set aside the loons who think CO2 is not a ghg. Most skeptics understand ghg, and understand at least the concepts of CO2. Most skeptics doubt the system is as sensitive as the AGW leadership claims. And skeptics are happy to point out that the AGW consensus claims things that are not so. But that is job of skeptics. AGW believers, unlike mature believers, simply attack those pointing out the problems, and go to a seemingly endless series of conferences, with fellow believers, to talk about how to communicate to the unwashed, and apparently from Gleick’s example and the climategate evidence, and sadly the reaction of true believers, to do whatever strikes their fancy to silence the denialist scum. 21. The sceptical movement is a many headed hydra, with most of the heads disagreeing with each other as to the extent or otherwise of the AGW proposition, which is at the same time our greatest strength and our greatest weakness. So to do real damage a substantial number of heads would need to be cut off. On this side of the pond I would see Heartland as being irrelevant and too right wing for many peoples tastes, and I wouldn’t bother trying to behead it. I would put WUWT at the top of the list of those to ‘take down’ in a general sense, but strategically I would target people like Judith. I consider her to be by no means a sceptic-although many warmists perceive her as such-and bringing her firmly back into the all embracing arms of the IPCC would, I suspect, cause the sceptics considerable dismay, although not dealing a fatal blow by any means. tonyb • hunter tonyb makes a great point: The real targets of AGW orthodoxy enforcers is those who have been within the temple, so to speak, and yet choose to deny the faith. Anthony Watts was given, by accident, full access to some of Phil Jones raw papers and data. What did he do, this most wicked of denialists? He studiously avoided using the access, contacted Dr. Jones and those who controlled the access, and advised them of the breach in security. And he kept it quiet. What would a Gleick do if he could have gotten into Dr. Curry’s, Dr. Spencer’s, or Lindzen’s private e-mail or notes? 22. Who does most damage to the climate movement? Mother Earth has kept the temperature well inside the range of the past ten thousand years. Mother Earth has done the most damage to the climate movement! • Bill She prefers to be called Gaia. • kim And, she’s been scorned by unwary modelers. =========================== • Who does the most damage? Is it not those who worship creation rather than the Creator? • David Springer Actually David I think the creation worshippers as you call them are acting in better faith as stewards than those you associate with who seem to believe that nature belongs to them rather than having its care entrusted to them. http://www.frontlinemin.org/environment.asp A Biblical View of the Environment by D. Massimiliano Lorenzini • David Springer Thanks for the article ref. Curious. How can those who do not believe in a creator have have “its care entrusted to them”? I do not understand why you accuse regarding “who seem to believe that nature belongs to them “. For the standards for being stewards of the earth, see The Cornwall Alliance See also: Pollution and the Death of Man, By Francis A. Schaeffer, Udo W. Middelmann Crossway, 2011. The ethical priority is to first care for children, widows, orphans and the poor. Contrast: “The Destruction of Nature in the Soviet Union” Boris Komarov 1978 (review) 23. Roddy Campbell We can’t know, but I think he went after HI at least in part because of the exchange of posts on Forbes. eg see this one by HI’s Taylor. http://www.forbes.com/sites/jamestaylor/2012/01/12/please-global-warming-alarmists-stop-denying-climate-change-and-science/ You can’t but laugh, Taylor is very effective, and if I was Gleick I think I would have exploded at being so effectively mocked. Be sure to read the exchange of comments between Taylor and Gleick below. Opening sentence: “Every now and then I read a blog post that melts my heart. I truly feel the pain, anguish and anger of the writer. I may not always agree with the writer’s point of view, but I empathize with the writer’s pain nonetheless.” • very good article at forbes, thanks for the link • Roddy Campbell Glad you enjoyed it. • Brian H In Comments, Gleick responded. Notable was his repetition of the phrase “makes my head explode”. Little did he know … >:) • kim Ooh, he’ll be a marvelously self-insightful patient. I think talk therapy, though, not drug therapy. ================= • Thanks Roddy It is insightful relative to FakeGate to see Gleick’s focus on: Fourth Place: The Koch Brothers for funding the promotion of bad climate science Fourth place goes to fossil-fuel billionaires Charles and David Koch of Koch Industries, Inc., who provide substantial funding to groups and politicians who deny the science of climate change. . . . and the Heartland Institute for “Arcticgate” As the Arctic ice disappears before our eyes, . . . and for the Heartland Institute’s promulgation of – and refusal to correct – those errors when they were uncovered. • Jim D From the comments we find that Taylor isn’t a denier himself as he believes in global warming and that human influence has been significant, so where is the argument, and wouldn’t Heartland be upset about this admission from one of its own? If human influence has been significant already and less than 20% of the CO2 increase expected by 2100 has been experienced so far, why not consider some action to slow this other even more significant 80+% down? • Roddy Campbell Jim D, you’ve lost me there. Most ‘sceptics’ believe in AGW, we believe in GHG’s, warming, and human influence. That would seem to be Taylor’s position, although HI do run the ‘it’s all a Commie plot’ meme as well.. ‘Where is the argument’? The arguments are over how much, how fast, what are the impacts (WGII), what should we do about it, what the uncertainties really are, is reality matching models, if not then can we rely on their projections. Putting it crudely, it’s not remotely inconsistent to believe in AGW but not in CAGW. (There are many sub-arguments, like is there any point the EU spending$100’s of billions mitigating when it has zero impact on global ppm unless the Chinese and Indians stop doing what they’re doing right now – but that’s for another day, maybe.)
• Jim D
Roddy, you see the slippery slope Taylor puts himself on by admitting that the human influence on global warming is already significant. The AGW effect has barely started and is already significant. I think Heartland should throw him out for expressing such a view. This is tongue-in-cheek by the way, as I expect many other Heartland people think this way, even if they don’t admit it publicly.
• Roddy Campbell
Nope, still lost. I haven’t read everything HI have written about everything climatic/consequential, but I see no inconsistency.
(He doesn’t specify whether the human contribution is via GHGs or other anthropogenic factors (Pielke Sr has a lot to say on that). Nor does he say that the quantum of human-induced rise itself is significant.)
For example, if we knew it was going to warm by another 1c in the next, whatever, 75 years, on average, over the whole world, because of AGW, that says very little about CAGW.
• Jim D
Put it this way. The IPCC also think a significant amount of the warming we have already had is man-made, just like Taylor. Yet, his organization is taking this on. Are they pouring millions of dollars every year into better defining the meaning of “significant” in this sentence? The donors may not be happy if that is what their money is going for.
24. Diogenes
Willis Eschenbach and Lord Monckton.
Anybody who can encapsulate the near-total lack of observance of the scientific method in such glorious prose is a formidable adversary.
Scientists are in broad agreement that the earth has been slowly warming for about three centuries. We don’t know why, which should give us a clue about the depth of our understanding of the climate.
More to the point, there is no agreement about such basic, rudimentary, fundamental, all-important questions as the sign and size of the cloud feedbacks. A change of 2% in cloud cover would wipe out any CO2 effect. Since we don’t understand the clouds, that most basic and critically important part of climate science, the idea that we understand why the earth is currently warming, or the idea that we can forecast climate a hundred years in advance, is hubris of the first order. We don’t know why it warmed in Medieval times. We don’t know why it warmed in Roman times. We don’t know why it has warmed since the “Little Ice Age”. We don’t understand the climate, and you folks’ claims that you do understand it well enough to make century-long forecasts just makes rational, reasonable people point and laugh.
-Willis Eschenbach
• David Springer
Get a room.
And an editor. Sheesh, D-G, I’d have to work to be that prolix.
• A physicist
Shall we try to fix the unmatched HTML italics in the above post?
• A physicist
To other fixes: I’d have to have to work to be that prolix. Or, I’d have to have to work to be that prolix. Otherwise, I give up! :)
• kcom
Shall we try to fix the unmatched HTML italics in the above post?
Yes, we should.
• kcom
How’s that?
• kcom
Now?
25. Kip Hansen
From an ethics point of view, I would first target the cabal of scientists that have publicly promoted, and performed, unethical acts in their effort to ‘get the world to take action on climate change’. Public polling shows that the man on the street (some unfortunately large percentage) has vaguely heard that ‘some climate scientists have cooked the books and fudged their results’ [this includes exaggerating risks and effects of CO2]. . Our thus affected man on the street has now a prejudice against further claims of the same type, no matter how accurate. The Gleick incident has now hammered another nail in this coffin.
History of scandals has shown that ‘cover-ups’ always backfire in the end. The Climategate whitewashes have not fooled the man in the street — especially in the US — he knows a cover-up when he sees it. See the polls.
What does work — all too well in some cases, IMHO — is full public confession, naming names, dates, and details.
If I were the ethics adviser for ‘Climate Scientists Without Borders’ [a hypothetical group representing Climate Science as a whole], I would tell them they must:
1) Out any and all instances of blatant falsehoods, exaggerations, use of scare tactics (ala Mike Crichton), etc with a Public Confession document. It might be called ‘The Real State of Climate Knowledge” and point out these past offenses, naming names and details.
2) Point out misconceptions foisted on the public by weak or outright bad papers that do not stand on scientific merits — Mann’s Hockey Stick papers, warming antarctic, or whatever. A list of papers that should be withdrawn or corrected by their authors might be a good place to start.
3) A straightforward statement on the uncertainty issues of climate and climate prediction, similar to Curry’s four variable problem post.
4) A statement of what other serious theories regarding recent climate changes are on the table — some have been presented here at Climate Etc.
5) A confession that many have been doing lots of science seriously compromised by confirmation bias, due to funding pressures.
6) A realistic statement of what we know and what we don’t know.
This list is speculative and Climate Scientists Without Borders would have to make up their own list — it might look something like the above.
Now this sounds like what the man on the street thought he’d be getting from the IPCC, except for the mea culpas.
In the sort of mess climate science finds itself, the ethical prescription is: Confess publically, out the bad apples, tell the truth as best as can be done, promise to do better — then Do Better.
• Andrew Russell
Great suggestions! Although I have little hope we will see those implemented any time soon.
One suggestion: Instead of “Climate Scientists Without Borders”, I would recommend “Climate Scientists Without Boundary Conditions”. :-)
I’ll join! Where’s the Paypal link?
• Sam NC
Paypal charges big fees!
26. “What ultimately makes Gleick a truly pathetic figure is that what he did, even if it had been successful, would have had no discernible effect on the final outcome of the war, except possibly hastening it. There’s simply no way that a vitriolic squabble between a cabal of activists and an institute the ordinary person had never heard of, was going to reverse the declining belief in the threat of global warming.”
http://thepointman.wordpress.com/2012/02/21/fakegate-claims-its-first-scalp/
In terms of target selection, the Heartland Institute is well down the list of cost effective targets.
Pointman
• > In terms of target selection, the Heartland Institute is well down the list of cost effective targets.
This begs two questions:
1. Could you explain by cost effectiveness?
2. What would be your top 5 list of “cost effective targets”?
• Typo:
> 1. Could you explain by cost effectiveness?
• Hi Willard. You make up your list of potential targets. For each one, you assess what would be the best and worst possible outcome in terms of impact on them and yourself. If you pick out a high impact target, you must expect to pay some cost, in terms of material or personnel, for attacking it. You pick the target with the biggest impact, which has an acceptable cost.
HI was a low impact target with a huge cost either way. Dumb.
Pointman
• WUWT has to be the biggest impact target by far.Nothing else comes anywhere near it.
Pointman
• Pointman,
Thanks for sharing.
• cwon14
Good to see you here Pointman. Your other related link should be viewed by all;
http://thepointman.wordpress.com/2010/12/07/the-death-of-the-agw-belief-system/
Dr. Curry is still on stage #3 with a tinge of stage #1. Maybe you can explain why skeptics paradoxically support those symptoms as well here?
Is there anything other than a cynical reason that Dr. Curry denies the specific political fingerprint of the AGW belief system?
• Hi cwon14, too many loaded questions for me, I’m afraid. What I would say is that Gleick, unlike Judith, is a fanatic whose stage# 2 anger and desperation totally blinded him. He wanted to find some huge well-financed conspiracy at the HI and when the documents he stole didn’t support that expectation, he couldn’t stop himself.
Pointman
• cwon14
Can you explain Dr. Curry’s refusal to politically ID the “cause” and its primary support network? You’re not saying she does this accurately are you?
Why is this assumed “loaded”? You can say whatever you want, I respect your opinion.
• Hi cwon14. I’m not sure Judith has said either way whether “the cause” is political, though to mind it certainly is. I’m an occasional visitor to this blog, so if colours have been nailed to the mast, give me the relevant quote.
Even if you take the view that Judith is of the warmist persuasion, she is providing the only venue where both sides can meet in some civilised fashion and at least exchange opinions without heavy censorship or knee-jerk banning. It was an initative that wasn’t very popular with the warmist propaganda machine and especially with fanatics like Gleick – witness the occasional clumsy attacks on her integrity.
I consider any level-headed venue like this an asset and don’t realistically expect its host to convert to my viewpoint, nice though that might be.
Pointman
• Pointman,
I don’t expect Dr. Curry to convert. When I do discuss something of importance I expect the obvious to be acknowledged. AGW and Green movements are left-wing in nature at this point of history. She can’t bring herself to say this. Why? It’s a very deep politically correct code that is followed here.
I really do want your opinion Pointman or anyone who can explain a good reason for the obfuscation of something very basic that is acknowledged in coded speak all the time by Dr. Curry herself. It helps feed the “it’s about science” mantra of the AGW movement that deserves no respect at all. She is feeding a monster, why should I respect that at all? Why should you?
27. Climate Scientist: “It is a Travesty that Earth Temperature does not show the warming.
Rocket Scientists: “It is a Travesty the Climate Models do not show the lack of warming”
Look at the massive snows that an open Arctic produces and open your minds to the data that shows there is a lid on Earth Temperature.
You cannot warm the Earth in the face of the Arctic Ocean Effect Snow Machine.
• David Springer
Yes. I’ve written about how Arctic sea ice acts essentially like the thermostat in a water-cooled internal combustion engine. Sea ice is a fantastic insulator for the water beneath. It blocks a great deal of conductive heat loss, almost all radiative heat loss, and the really big Kahuna 100% of evaporative heat loss. When it gets a little warmer in the NH tropics a little more heat is transported to the Arctic for disposal. The extra heat melts a little more ice and the cooling system effectively increases its capacity. The thermostat in an ICE (internal combustion engine) works in the same fashion. Warmer water from the engine block causes metal in the thermostat to expand which widens the opening allowing more water to move from block to radiator for disposal. The Arctic sea ice has an additional mechanism in that it effectively creates a greater surface area where cooling takes place as the water temperature increases.
The reason we’re having a deep La Nina IMO this year is a consequence of the El Nino in 1998. If you look at Artic sea ice extent you’ll note a step change reduction in 1999. This was the pulse of warm water from the 1998 El Nino arriving in the Arctic and transferring energy into latent heat of melting. The Arctic ‘radiator’ thus became about 10% more efficient (10% reduction in ice extent) over the next several years peaking in 2007 and now those chickens are coming home to roost in the form of a cold pulse making its way along the ocean floor back down to the tropics.
There are very reasonable explanations for just about everything we observe but you’ll never find them if you’re consumed with blaming everything on anthropogenic CO2. AGW is a land-only effect and while that’s where we live and breathe the earth is a water world and that is what rules the global climate. The ocean is responsible for the climate while the atmosphere is responsible for the weather. Climate boffins are focused on the wrong thing. Heck they don’t even focus on the surface… the start at the top atmosphere and work their way down. TOA is the gas tank and exhaust pipe. All the interesting stuff takes place in the engine and where the rubber meets the road.
• Markus Fitzhenry
I liked that David. ICE.
I think you left out the condenser (pressure) evaporator (tropopause) and air cooled radiator, (stratosphere). Of course the gas goes thru two filters (Mesospause & Tropopause).
Of course is a perpetual system as the cooled air falls back by gravity until insolation and the force of pressure keeps the ICE happening.
Climate science is not complex if your are looking at correct physics. The confusion comes in when Climate science claims cold warms hot, (backradiation).
There are several machinations that describe energy budgets, another good one is the refrigerator.
• Markus Fitzhenry
Sorry David,
I left out the electrical circuit that can conceptually include electromagnetism, into Climate system.
• Arctic Sea Ice is the Thermostat of Earth.
• David Springer
Keep in mind there’s a dearth of insolation at high latitudes so albedo becomes increasingly less important so snow cover over land doesn’t mean as much. The ocean also reflects increasingly more as the angle of the sun gets lower so albedo importance diminishes there too. Inside the Arctic the big factor is sea ice extent because that makes a huge difference by blocking radiative and evaporative cooling and not conducting particularly well either.
Also the transport mechanisms moving energy from tropics to poles goes faster with rising temperature difference between tropics and poles. When the Arctic sea ice ‘thermometer’ opens up it works to reduce the oceanic conveyor belt volume as the temperature differential between tropics and pole is reduced. These are all fairly simple heat engines using water as the working fluid. This particularly familiar territory for engineers because heat engines using water as working fluid is where you start learning about engineering. It’s no coincidence that ‘engineer’ starts out with the word ‘engine’. If Carnot Efficiency, for example, isn’t something you immediately recognize and understand then you won’t understand the earth’s energy budget or how the weather is generated from soup to nuts. The work produced by all these heat engines IS the weather. CO2 is at least a second order detail when the ocean presents a largely liquid surface and an infinite amount of evaporation. When evarporation gets restricted then radiative cooling becomes far more important and that’s when non-condensing greenhouse gases become critical. They’re a last line of defense against really radically plunging temperatures once water starts getting frozen out of the air and oceans covered with ice. Many believe non-condensing GHGs and soot from volcanos are what build up over millions of years to melt a snowball (or slushball if you prefer) earth.
What’s truly remarkable when you think about it is how all these self-regulating heat engines work together to produce such a remarkably stable climate that sometimes persists in more or less the same steady with no major perturbations for tens and hundreds of millions of years at a stretch. If it was something you asked an engineer to design he’d be hard pressed to come up with anything more stable or resistant to perturbation. The arrangment of continents is likely the largest driver of change because they can cover/uncover the polar radiators and also block or facilitate the oceanic conveyor belt. The slow movement of the continents and more or less haphazard distribution thus allow very very long periods of climate stability at one or the other of the two great attractors – melted or frozen.
• DocMartyn
The ratio of land (or even shallow water) to water would have a big impact and moving water around, so does land separating the Atlantic and Pacific. Having land at the poles must have a huge impact.
• The snow is a result of the open Arctic, but the snow falls at lower latitudes and increases Albedo where it does make a difference.
LOOK AT THE DATA. Low Arctic Sea Ice is always followed by high Snow Extent. This does keep Earth from ever getting too warm.
28. Ian Blanchard
As I wrote at RPjr’s blog:
The problem here is that Gleick and many contributors to the more alarmist blogs (DeSmog particularly) appear to believe their self-constructed narrative of the ‘skeptic / denier’ has to be true.
They seem to find it impossible to consider that reasonably intelligent and scientifically literate people can see the same data about recent warming and the future projections and honestly hold the opinion that it is not an existential crisis about which something has to be done now. Therefore anyone who disagrees with them MUST be in the pay of big business and part of the denial machine whose sole purpose is to spread disinformation. As such, any action against them is justified and justifiable, even when it turns out that the ‘well-funded’ organisation promoting the disinformation has a lower annual budget than the IPCC’s annual travel expences budget (and apparently none of it comes from ‘Big Oil’)…(originally continued)
29. Gary
Actually, this is a silly question. The battle is asymmetrical. Take off one small head and two grow in it’s place. The Lilliputian side is diverse and nimble; the Gulliver side is monotone and ponderous. Not to mention, deceptive by couching a political argument – global wealth redistribution – in scientific clothing. The Lilliputians rightly feel put upon and deceived. They’re fighting on their own turf, not trying to conquer foreign territory. They may be subdued in places, but not defeated by temporary losses.
30. hunter
The biggest opponent the AGW true believer must assault is reality.
• MDR
Probably AGW community will need a whole Matrix to stick with their plan.
31. Veritas
This is slightly off topic and I apologize but the thought occurred to me as I was reading the post. How can an issue be so polarizing when everyone is looking at the same data? For the most part, we are all rational and intelligent people, some with advanced degrees in a wide variety of disciplines and yet there are two very different conclusions about the meaning of the data. The amount of passion, sometimes anger, is fairly astounding. Sadly it has become politicized and rationality has given way to irrationality. Heartland was obviously weighing heavy on Dr. Gleick’s mind and he let his emotions get the better of him. However, he broke the law and should suffer the consequences.
For those of you who believe in AGW, have you done anything to mitigate your carbon footprint? Have you altered your lifestyle in any way or are you waiting until everyone is *made* to do so, in the hope of saving the planet? Lead by example and others may follow. Lead by mandate and others will refuse.
• Jim
Veritas,
From my limited point of view, the dichotomy you mention is the difference between those people who see things ‘the way that things are’ and those people who see ‘the way that things ought to be’.
I think it can be seen in a slight way on this blog as the difference of opinion between people with an enterprise background and people with an academic or political background. As an example, from another thread, some one suggested the idea that the IPCC is dealing with such an important and expensive issue that strict codified conflict of interest rules need to be part of the IPCC process. The people with an enterprise background instantly recognize a concept and rules and laws that they comply with every day. People with a reformatory or progressive point of view, often I think academics and activists, see Wall Street and K Street (American examples) as examples that show that rules prohibiting conflicts of interest are only deceptions. Both points of view are true.
On the issue of this thread, and to answer your question, my background of engineering and enterprise makes me most susceptible to the ideas of the McIntyres, Moshers and McArtles; they know accountability the way I know it. I also see that the students, professors and activists and politicals don’t understand that idea of accountability at all. And there are ideas of theirs that I don’t begin to understand.
• “there are two very different conclusions about the meaning of the data”
There are many more than two different conclusions about the meaning of the data
My conclusion is that when earth is warm and the Arctic is open, it snows more and earth cools. When earth is cold and the Arctic is closed, it snows less and earth warms. This is more reasonable than any of the other conclusions out there, but there are many more than two.
32. I think Gleick’s targeting was perfect. He shot himself in the foot.
When you catch your partner in bed with another, the first question you ask is “How COULD you betray my trust in you like this!?”
The second question you ask, and it’s the one that lingers the longest, is “HOW LONG has this been going on?”
So it was with Climategate, it is with Gleick. For those who have been shocked and disappointed by Gleick’s deceit, it is the question which nags at them now.
• Ian Blanchard
Simon
He certainly confirmed one metaphorical conundrum:
It is possible to shoot yourself in the foot while jumping the shark ;-)
33. Garry
If I were a fanatic as detailed by Bertrand Russell (see Anthony Watts’ recent post on this topic), and I was obsessed with exposing the “big oil funding” of a hated demonic organization that opposes my views, *and* that organization has a member writing a column in the same national magazine as myself – often directly mocking my published views, *and* that same organization was in the process of inviting me to debate “for entertainment” at their big oil-funded conference, then I might be more than irritated. I might consider this organization to be evil, and my constant nemesis, and worthy of retaliation.
Peter Gleick did not choose HI randomly. He was clearly obsessed with HI and its views and its members and its covert “big oil” funding. There was some kind of massive evil at work, and it was directed at him very personally. Each of of the 10 components of Bertrand Russell’s prescription for fanaticism were now in place.
At some point along the way, Gleick’s rationality broke down completely.
• Anteros
Garry –
If you think back to his heaping vitriol on a book he’d never even read, I’d say he’s been running low on rationality for a long time.
34. Michael Larkin
He who knows the truth, has no need to target those who don’t. He just needs to say his truth and welcome any and all attempts to disprove it.
The consensualists could chop off hydra heads from now till the cows come home, but more would just grow to replace them, on and on and on until the real truth beccomes known. Whatever it is, sooner or later that will happen.
Whatever, I think currently the most effective single source of sceptical information is WUWT. I don’t believe that anyone could bring Anthony Watts down because I’m convinced of his integrity even though I don’t necessarily agree with all his postings.
35. Diogenes
Andrew W. Montford’s The Hockey Stick Illusion: Climategate and the Corruption of Science has been very effective at summarizing and conveying the methods, data, and activities of paleoclimatology. His description of climatology and the Herculean efforts of Steve McIntyre in a manner accessible to laypeople reached a sizeable audience.
Then, there are the efforts and commentaries of individual scientists such as Dr. Jonathan Jones of Brasenose College, Oxford and our gracious hostess. Dr. Curry’s testimony and courage as a firsthand witness to the substitution of certainty for uncertainty has been influential.
The author of the comment below is Dr. Jonathan Jones, professor of physics at Brasenose College, Oxford University.
Richard, I can’t answer for our host, but you have to remember why some of us got involved in the climate wars in the first place.
For me this has never really been about climate itself. I don’t find climate partcularly interesting; it’s one of those worthy but tedious branches of science which under normal circumstances I would happily leave to other people who like that sort of thing. My whole involvement has always been driven by concerns about the corruption of science.
Like many people I was dragged into this by the Hockey Stick. I was looking up some minor detail about the Medieval Warm Period and discovered this weird parallel universe of people who apparently didn’t believe it had happened, and even more bizarrely appeared to believe that essentially nothing had happened in the world before the twentieth century. The Hockey Stick is an extraordinary claim which requires extraordinary evidence, so I started reading round the subject. And it soon became clear that the first extraordinary thing about the evidence for the Hockey Stick was how extraordinarily weak it was, and the second extraordinary thing was how desperate its defenders were to hide this fact. I’d always had an interest in pathological science, and it looked like I might have stumbled across a really good modern example.
You can’t spend long digging around the Hockey Stick without stumbling across other areas of climate science pathology. The next one that really struck me was the famous Phil Jones quote: “Why should I make the data available to you, when your aim is to try and find something wrong with it”. To any practising scientist that’s a huge red flag. Sure we all feel a bit like that on occasion, but to actually say something like that in an email is practically equivalent to getting up on a public platform and saying “I’m a pathological scientist, and I’m proud.”
Rather naively I initially believed that Phil Jones was just having a bad day and had said something really stupid. Surely he couldn’t really think that was acceptable? And surely his colleagues would deal with him? But no, it turned out that this apalling quote was only the most quotable of several other remarks, and he really was trying to hide his data from people who might (horror of horrors) want to check his conclusions.
That’s when I got involved in my FOI request. And consequently got exposed to the full horror of “big climate”, as clear an example of politicised and pathological science as I have ever seen. And then came Climategate 2009, and “hide the decline”. All downhill from there.
When will I be done with climate? Quite simply when it stops being a pathological science and starts acting according to the normal rules and conventions of scientific discourse. At that point I will, I’m afraid, simply lose interest in the whole business, and leave it to the experts to get on with their stuff, just as I leave most of the rest of science to the appropriate experts.
To put it another way, I will be done with climate once I can trust that Richard Betts can be left to do good work on his own. I absolutely trust you to get on with doing good stuff under normal circumstances. But I’m afraid I don’t trust you to do good work under current pathological conditions, because you don’t stand up against the all too obvious stench emanating from some of your colleagues.
For me the Hockey Stick was where it began, and probably where it will end (and I will daringly suggest that the same thing might be true for our host). The Hockey Stick is obviously wrong. Everybody knows it is obviously wrong. Climategate 2011 shows that even many of its most outspoken public defenders know it is obviously wrong. And yet it goes on being published and defended year after year.
Do I expect you to publicly denounce the Hockey Stick as obvious drivel? Well yes, that’s what you should do. It is the job of scientists of integrity to expose pathological science, and it is especially the job of scientists in closely related fields. You should not be leaving this to random passing NMR spectroscopists who have better things to do. But I’m afraid I no longer expect you to do so. The opportune moment has, I think, passed. And that is why, even though we are all delighted to have you here, and all enjoy what you have to say, some of us get a trifle tetchy from time to time.
You ask us to judge you by AR5, and in many ways that is a reasonable request. Many of us will judge it by the handling of paleoclimate, not because this is all that important an aspect of the science, but rather because it is a litmus test of whether climate scientists are prepared to stand up against the bullying defenders of pathology in their midst. So, Richard, can I look forward to returning back to my proper work on the application of composite rotations to the performance of error-tolerant unitary transformations? Or will we all be let down again?
Dec 3, 2011 at 6:11 PM | Jonathan Jones
http://bishophill.squarespace.com/blog/2011/12/2/tim-barnett-on-the-hockey-stick.html
• thanks very much for this link, it is a classic
• Michael Larkin
+1
• Punksta
Re: the Jonathan Jones quote.
Yes, the real issue isn’t that scientist X or scientist Y went off the rails; this is par for the course in human affairs.
It’s that the climate establishment by and large do and say nothing about it.
This tacit acceptance of corruption means the profession as a whole simply cannot be trusted now.
Which will be doubly bad if it one day it becomes clear CAGW is in fact true. The sooner there is a radical clean-up the better.
• Jim
Jonathan Jones does exemplify scientific integrity. I wish we could all agree that it is the foundation that we must start from to address these issues…
36. Chris D.
The answer to your question is obvious. The activist movement sees the science education of American youth as a strategic backstop for future action on climate. If the battle is stalemated today, then look to the youth for hope – our future leaders. Heartland posed a strategic threat by possibly helping orchestrate legislation and curricula intended to undermine the activist position that consensus = scientific certainty. This drove Gleick over the edge. The devil made him do it.
37. AngusPangus
Who would you target? Who is responsible for the thwarting for CO2 emissions/stabilisation policies.
The answer is simple. People. Everyone, everywhere.
A climate change ideologue/activist is selling a product – a low carbon world that we must buy now, before it’s too late. Trouble is, nobody wants to buy their product and they can’t understand why. So they cast around looking for who’s to blame, whose fault it is. And they see glimpses of hidden enemies everywhere. Big oil. Neo-cons. Right wing nutters. Capitalists. Etc. etc. The simple truth is, nobody wants to buy their product for the simple reason that their product is crap.
It’s like they’ve spent a lifetime developing the world’s best chocolate teapot then put everything they’ve got into manufacturing millions of the things in the expectation that everyone will want one. But nobody will. “Oh noes”, they cry. “Why is no-one buying our most excellent chocolate teapots??!!” They then determine that the problem is Big Ceramic and Big Stainless Steel, the people behind other kinds of tea pot. They must have putting out lies and misinformation about the chocolate teapots!! Nobody stops to think “Hang on, is what we’re selling any good?” They are in fact incapable of asking themselves that question because, quite simply, they have far too much invested in the chocolate teapot project. It can’t be the project itself, to blame, it must be “enemies”.
Now, back to climate change. Our friends want to sell an extraordinarily expensive product in order to solve a currently non-existent problem. We are almost 25 years – a quarter of a century – down the road from James Hansen’s famous “projections”. Sure, according to averaged, world-wide records it got a bit warmer and then stopped, but ask any sane middle-aged person whether they feel that their local climate has changed in any kind of devastating way in their lifetime, and they will say no. And if there haven’t been any noticeable changes in the last 25 years, why should people expect any in the next 25 years? If warming is supposed to happen at an ever-accelerating rate, why has EXACTLY THE OPPOSITE happened since 1988?
And even if some of us are concerned this problem may manifest itself at some point in the near-ish future, there is no assurance that this very expensive product will do what it is supposed to do. Untold billions have been spent over the past 25 years chasing a “low carbon” pipe-dream. Where has it gotten us? Despite all the windmills, solar panels, bio-fuel plants, carbon taxes and energy efficiency measures ad nauseum, by how much have we reduced worldwide CO2 emissions over the last 25 years? By a big, fat, diddly-squat. They’ve gone up. In fact, emissions went up by a massive 6% in 2010 alone. In the UK, we have an EU-imposed target to achieve 20% of our energy from renewables by 2020. In 2010, we managed a massive 0.3% increase on the previous year, an increase to a dizzyingly-high 3.3%. We will get nowhere near 20% by 2020. How much CO2/temperature stabilisation are we achieving for our billions of investment? Zero. Or as near as makes no difference.
The thing is, ordinary people are not stupid, despite what certain elite academics may think. They would not buy a chocolate teapot because they just know that it’s useless. They won’t buy an uber-expensive carbon reduction problem because (a) they know from experiencing weather and climate first-hand that things aren’t changing very much and (b) they know that emission reduction targets are pie-in-the-sky unachievable, so the product won’t work anyway. It’s a non-functioning solution to a non-existent problem,a s far as the ordinary person is concerned. They’re not intereseted in “the science”. Failures in “communicating science” are just a side-show, a distraction. A way of avoiding talking about the fact that some folks have invested everything in developing the world’s worst product.
I wouldn’t buy a chocolate teapot unless you frog-marched me to the chocolate teapot store at gunpoint. Would you?
So you see, a climate change ideologue/activist will ultimately only ever be able to achieve his or her objectives by targeting the people. All people, everywhere. They could only ever get their way by coercion and force. If you think that that is over the top, consider that James Lovelock and others have already floated the idea that perhaps a “suspension of democracy” is necessary in order to achieve a low carbon world. Fortunately, I think that they have lost so much ground over the last few years that that will now be impossible.
• Anteros
AndyPandy –
Well said. I agree about targeting ‘everybody’, although Gleick [apparently pronounced Glick in the US – who’d have guessed?] had personal, delusional reasons to sacrifice himself by going after Heartland.
38. stan
The problems for the CAGW scientists is the lack of an adult in their midst. That can’t be solved by taking down someone else. In fact, the quest to take someone down is just another example of the need for an adult.
39. Bernie
Judy:
This is an interesting question but, for me, it misses the fundamental dilemma facing those who believe that continued large scale fossil fuel usage creates significant climate risks – namely they offer no coherent solution except reversing industrialization. Attacking any of their “enemies” fails because of the absence of realistic and viable alternatives.
To date, those with mindsets like Gleick tried to ignore all the skeptics – WWUT and Climate Audit are still absent from CAGW sites like RealClimate and avoid engaging with competent skeptics or even competent luke warmers. Then they tried to tie prominent skeptics with evil “fossil” industry funding, launching PR attacks on the scientific integrity of leading skeptics and closing down access to peer reviewed journals. Some of these efforts partially succeeded but the recent climategate emails revealed the scope, tenuousness and mendacity of these strategies and the revelations as to the role of environmental advocacy groups in the IPCC has left them without real alternatives except to find the PR equivalent of a “smoking gun”. In reality substantial funding of skeptics by the fossil fuel industry would amount in PR terms to a “smoking gun”. The target of opportunity therefore is the fossil fuel industry. Gleick’s illegal and delusional efforts is in line with this option but is much more personal. So long as prominent skeptics are free of fossil fuel funding this strategy will not work – by definition.
If I wanted to quieten the critics I would propose realistic and economically viable alternative solutions. The bind for evironmentalists is that the obvious Nuclear solution has for years been even more “evil” than fossil fuels.
Without realistic altrernatives, skepticism will prevail and the only option left to the fanatical warmists is a Stalinesque strategy of exiling opponents. The inflammatory rhetoric of Romm, Hansen, McKibben and Gleick fits this latter model. If skeptics are committing “crimes against humanity” all actions are legitimate. Lenin et al certainly believed this to be the case. Fortunately this strategy has a little historical baggage that will be hard to hide.
I think the neo-Malthusians were looking for a bunch of oil industry money or a big bad oilman to confirm that Heartland’s climate program was just greed vs. goodness. Really pretty much the opposite was uncovered. The big donor does not fit the profile the critics are looking for either.
41. pokerguy
Gleick reminds me of one of those secretly gay polticians who builds a career around pushing homophobic policies. Gleick knows who he is deep inside….someone who lies and cheats and reviews books he’s never read. So what does he do? He hides his own shame and self-loathing by preaching to the world on the importance of ethics in science. Surely that way, no one will suspect who he really is…a fraud and dissembler par excellence.
Why did he go after Heartland? I think because they invited him to debate, something he couldn’t risk doing. He knows the science is weak. He’s no dummy, So what does he do? He gets back at them for making him feel cowardly and crummy about himself.
It’s really a pathetic tale. I see no mystery, once one understands the nature of the man’s personality.
• BrendanR
I was reading that email chain where HI invited him and he ultimately declined and something struck me… That long one from HI about why they don’t share their donor list and therefore not going to do so for him. There’s a popular internet meme at some sites called “Challenge Accepted”, and a part of me wonders if his ego was just big enough that he thought, well, let’s just see about that…
• Jim
An other example are the TV evangelists who get caught with their trousers down. ;-)
42. http://www.ncdc.noaa.gov/sotc/
Earth Temperature Data shows no warming for 15 years.
CO has gone up for those same 15 years.
When computer model forecasts disagree with actual data, guess which one is always right.
• Tom Choularton
Judith,
This post illustrates the obvious problem with the views of many of your posters on this site. You say that understanding raditive transfer in the atmopshere would make no difference. However, if you read many of the posts here or indeed essays on sites like WUWT it is very clear that the basic science is not understood and many points made which we both know are simply wrong.
The science of climate change seems to be a matter of better education in science first rather than general debate. The places to debate the science are the scientific journals (as happens). The politics of implementation of mitigation is a very different matter but in my view the science comes first. ‘Sceptical ‘ blogs etc are targetting the science with a clear intention to confuse those who don’t understand it, I am sure you know that.
• AngusPangus
Tom,
with respect, your post illustrates the obvious problem with the views of many of the posters sites such as Realclimate. Confusion of science has got nothing whatsoever to do with the lack of traction of carbon reduction policies. Although WUWT is a very popular site of its type, hardly anybody, as a percentage of actual population, reads it.
People don’t want to “solve” dangerous climate change because they do not see, do not experience, any evidence of dangerous climate change. Back in the 90’s, climate change mitigation was gaining support, gaining populairty. Why? Simple – it was actually getting warmer. In the UK, we had some nice warm summers and springs. Winters were milder – we hardly saw any snow for years. CAGW was credible. People talked about shifting crop production to allow for a warmer climate – establishing olive groves in southern England etc.
But this didn’t continue. According to CAGW orthodoxy, the changes would accelerate if nothing was done. But they didn’t. Warming stopped or even reversed, according to people’s actual experiences. Snow returned in the UK with a venegence, year after year, not just a one-off. Summers disappeared and instead we seemed to get one long autumn. People saw that the idea of, for example, growing mediterranean crops in the UK was absurd. And, accordingly, support for climate change policies faded away.
Ordinary people do not look to the science or the data sets to inform them about climate change. They look to their own experiences of the weather today, yesterday, and throughout their lives. No amount of communicating “climate change: it’s worse than we thought” will make them believe something that they know, from their own first hand experience, is not true.
• Even if we have 100% worldwide consensus on the science (e.g. WG1), we still need to decide what is “dangerous” (IMO the climate community has failed pretty miserably in this regard), and what the best policy responses are (e.g. economically, politically and technically viable). So everyone know the basic science and agreeing on it doesn’t really help very much when it comes to policy.
• Peter Davies
AngusPangus makes the point that people needs to see it and/or feel it before they will believe anyone who says that climate change is dangerous. This proposition is absolutely correct and reflective of basic human nature.
Unfortunately for mainstream climate scientists, the predicted warming did not eventuate over the past 15 years or so. Hence any correctly conducted poll of the people will show a clear majority who do not believe that dangerous climate change is occuring around them.
• John Whitman
Peter Davies | February 24, 2012 at 7:38 pm |
AngusPangus makes the point that people needs to see it and/or feel it before they will believe anyone who says that climate change is dangerous. This proposition is absolutely correct and reflective of basic human nature.
[ . . . ]
– – – – – –
Peter Davies/AngusPangus,
If you are saying that most human beings alive on the planet (and say for past several hundred years) are non-conceptual/anti-conceptual and essentially limited to being sensate/perceptual beings, then I think you are vitally in error. There may be conceptual error that is widespread but that does not mean non-conceptual.
John
• David Young
Choularton, I’m not sure there is much evidence that the skeptical blogs are “targetting [sic] the science with a clear intention to confuse …” Judith has made her views clear many times. Just as there are members of the peanut gallery at Real Climate that believe all sorts of conspiracy theories about “BIG OIL”, so this site has uninformed people. Many of us, however, understand the physics and have scientifically valid concerns. My concern is the level of accuracy of the GCM’s and the weak constraints given by simpler energy balance models. If you read a little of the recent thread on ergodicity, you will get a flavor for these issues. Just in case you are not aware of it, numerical solution of PDE’s and the Navier-Stokes equations is a well developed field where the level of rigor is much higher than in climate science. I suggest a perusal of International Journal for Numerical Methods in Fluids for some background information.
• Peter Davies
John, only as far as the weather is concerned because climate to most people is just weather, averaged out, and pertaining to their geographic area.
• John Carpenter
AngusPangus,
Most people who espouse the ‘consensus’ view miss this point because they do not see the forest through the trees. It could be the single major reason they have what they call a ‘communication problem’.
• Jim
Tom Choularton,
You are correct, only a small minority understand raditive transfer. The thing that the majority that don’t understand raditive transfer DO understand (and the minority may not understand) is there are no possible means short of Godwin-esque totalitarianism that will keep extract able carbon fuels in the ground unextracted when poor peoples of the world wish to use those fuels to improve their condition thru the use of those fuels.
• Brian H
Judith;
“So everyone know the basic science and agreeing on it doesn’t really help very much when it comes to policy.”
You continue to assume that there is ANY actual problem that requires a policy response. The only policy change now required by a proper assessment of the “basic” science is to immediately defund all mitigation programs and refund the real science that has been exsanguinated by crimatologists and their enablers.
• Punksta
Tom Choularton : The science of climate change seems to be a matter of better education in science first rather than general debate. The places to debate the science are the scientific journals (as happens).
This post illustrates the obvious problem with the views of many naive observers – a complete failure to grasp that the journals etc have been reduced to tools advocacy.
• Judith
What do you believe is the ‘proper’; level for co2? Presumably you must believe it is the supposed pre-industrial level of 280ppm.
Supplementary question; Presumably in theory that would mean that if we tried to achieve the ‘proper’ level our temperatures would drop by 1 degree C?
tonyb
• Rob Starkey
In order to answer the question if climate change is dangerous, the question needs to be asked much more specifically. The question is dangerous to whom and specifically why.
That Imo is the real question that needs to be answered in order for governments to implement sensible policies. In order to answer those questions science needs to develop reliable models that can be demonstrated to provide outputs that come close to meeting observed results at a more regional level.
Currently, I just do not understand people like Chris Close and Gavin trying to argue that observations do not matter or should not be believed and that we should accept the outputs of models that do not match observations. I also cannot accept the idea that it is too difficult/ impossible to make models that can accurately predict 5 or 20 years into the future, but we should accept that the same models are accurate 100 years into the future.
People seem to like to argue about fairly unimportant minor points, when in fact until someone can demonstrate that they have developed model(s) that can reasonably accurately forecast conditions at a regional level, all is being accomplished is cheap talk. The proof in demonstrating that the climate science is really understood is models that work!
• simon abingdon
“I also cannot accept the idea that it is too difficult/ impossible to make models that can accurately predict 5 or 20 years into the future, but we should accept that the same models are accurate 100 years into the future”.
Come on Rob, be reasonable. The seasons are predictable; next week’s weather not.
• Furthermore predicting 5 years to the future might mean predicting year 2017, while predicting 100 years to the future might mean predicting the average of years 2100-2019.
The latter may well be easier than the former, but that’s certainly not obvious either. The point is that it’s wrong to say either way without further evidence.
• .. 2100-2119 ..
43. SuperMandia explains the rationale in this post
http://profmandia.wordpress.com/2012/02/23/do-not-take-your-eyes-off-lex-luthor-heartland-institute/
Global Warming: Man or Myth? Do Not Take Your Eyes off Lex Luthor (Heartland Institute)
• Brian H
What an amazing post. Slobbering adulation of Saint Peter, and imprecations against the evil subversives at Heartland. I thought it was a parody at first …
• Bob Ludwick
Unfortunately Brian H, we are now at the point in the ‘climate science debate’ (among others) where straight forward reporting, parody, satire, and just plain bald faced lying are indistinguishable without doing a good deal of research to determine just which case obtains. And even then is is sometimes difficult.
• Bob Koss
I guess that tells us all we have to know about Mandia. LIfe to him is like a comic book. Filled with outlandish caricatures of real people and things with a bright lines dividing good and evil, true or false. No wonder he runs around in tights with a cape and hipboots carrying a hockey stick. Just the type of person I want to save me from my wicked co2 burning ways.
• cwon14
Is Supermandia a right or left-wing site?
• Scott Basinger
Wing-nut.
• Sorry Judith
You have got hold of the wrong end of the stick with the Mandia article. Scott is actually organising a new University course on Satire and this was his first-and very good- attempt at writing course material.
Tomorrows satirical subject matter “Are the IPCC the finest organisation ever to grace the World?”
tonyb
• DCA
That says a lot…. or shall I say not?
• Don
I just commented there:
“Scott, you and your colleagues are always accusing Heartland of stifling debate, yet you never accept their open challenges to debate. Gleick apparently didn’t have the cojones to do so, even though accepting Heartland’s offer would have given him the opportunity to attend their headline event and speak personally with all those shadowy donors he’s so obsessed with unmasking. Sounds like a job for SuperMandia! If you are right and they are wrong it should be a cakewalk!”
Theo Goodwin also has a comment awaiting moderation. We shall see how moderate their moderation is…
• gcapologist
While I find this whole thing simply sickening, I must comment on this quote contained in your link “Heartland Institute is threatening the education and future of our children!”
The educational materials have yet to be produced. So where’s the threat?
A scientist protesting science curricula he hasn’t seen (or even yet exists)?
How on earth did PG win his reputation?
I think perhaps the hallowed academic halls need some cleaning.
• Brian H
You left an italics tag open, Judith.
44. GregS
“So, imagine you are a climate scientist and climate change ideologue, and want to “take down” the single organization (or individual) that is doing the most damage to the movement (i.e. with the end result of thwarting CO2 emissions/stabilization policy). Who would you target?”
My first answer would be Anthony Watts. After all, his website has the most reach.
But would going after the organization or individual who does the most damage be the best strategy? Think more along the lines of The Art of War. Think strategy.
Is it better to attack your opponent’s army or the agricultural areas that sustains their army? Is it better to bomb your opponent’s factories or the ball-bearing plant that keep their machinery spinning?
From Gleick’s emails to Heartland, he clearly is trying to expose and cut-off what he believes to be the source of funding that is keeping his opponents going.
By publishing Heartland’s internal documents, he might have accomplished his strategic goal – but then “Reality just wasn’t good enough”.
• Let me add a couple of other relevant examples:
1) Ploesti refineries (1943) and other oil sources in Europe.
2) Interdiction of oil tankers from Indonesia and Burma in the Pacific.
In the end, the magnificent jet technology of Germany had no fuel, the Japanese battleship Yamato had fuel enough for a one-way trip to Okinawa and fuel shortages hampered air defense.
How is this relevant? Fossil fuels are essential to this nation’s economy and defense (70%). The EPA, denied cap-and-trade, announced it would default to bureaucratic “Command-and Control”.
Garrett, Major, and AP. “Administration Warns of ‘Command-and-Control’ Regulation Over Emissions.” News. FOXNews.com, December 9, 2009. http://www.foxnews.com/politics/2009/12/09/administration-warns-command-control-regulation-emissions/
45. wilbert
we have a new instrument in the AGW pseudo-science .
What is a Gleickometer ?
• Punksta
… new instrument in the AGW pseudo-science … What is a Gleickometer ?
It measures the noble-cause conviction emanating from truebelievers as they sing in their Gleick Clubs.
• Nice!
I hope that in the future, when people study noble cause corruption, that Peter Glieck’s face is prominently displayed, along with the true story of what happened in Fakegate.
• hunter
+10.
And the AGW extremists are definitiley pegging the Gleickometer.
• Andrew Russell
Punksta: “It measures the noble-cause conviction emanating from truebelievers as they sing in their Gleick Clubs.”
Why o why did I, on first reading, see “Chicago Cubs” in place of “Gleick Clubs”? And I’m not even a baseball fan or live in Chicago…
Do Cubs fans suffer from “noble-cause conviction”? :-)
• SamNC
Gleickometer – needs to define max & min scale with pointer at mid third.
• David Jay
but…but… I always thought a Gleickometer measured glycogen.
46. Mark M
J C says- “And of course all this begs the question of why we don’t have CO2 stabilization policies, which is mostly about economics, politics, values.” Out here in CA we have a few CO2 stabilization policies in place. As to the effectiveness of our efforts Bill Slaton (Sacramento Municipal Utilities District) recently recommended that our approach in the electrical market should be modified as noted here-
Episode 126 [Watch online»] – Bill Slaton. An electrifying conversation about energy.
http://www.kvie.org/programs/kvie/studiosacramento/default.htm
Essentially he would like the regulators and legislatures to stop micro managing things as it’s not cost effective. I concur with Bill Slaton that our exclusion of large hydro from the RE calculations is rather odd…………… If we didn’t have the large hydro exclusion SMUD would already have 40% carbon neutral electrical energy generation.
Gleek may have viewed Heartland as an Easier Target. Like a bomber out on a mission he was instructed to drop “somewhere” and do some damage. And maybe his “intelligence” about the matter wasn’t so good.
Andrew
48. Wagathon
Why target Joe the Plumer?
49. Wagathon
… or, Joe the Plumber for that matter.
50. Wagathon
Given the evidence there can be little doubt that global warming is nothing more than a hoax and a scare tactic. The null hypothesis that climate change is the result of natural causes has never been rejected. Everything else is dogma.
51. Respectfully, it is too late to target a single individual or organization. The word is out by too many people and organizations, to too many citizens.
The unfortunate Gleick has shot himself in the foot with a muzzle-loader. When he looks in his cartridge case, he finds only spitballs. :-)
• It is Dr. Ravetz’s “Extended Peer Community” in operation.
52. Norm Kalmanovitch
All physical scientific evidence refutes the ridiculous notion of AGW and the consensus based on climate models of the GCM genre which themselves are incapable either of depicting the effect from CO2 or projecting global temperature in any way shape or form.
This is why the global temperature is not mentioned because none of the five global temperature datasets show any definitive global warming since 1998 let alone the rapid increase in global temperature predicted by the models that should have occurred with the rapid increase in CO2 emissions during the past dozen years.
The only argument left is the consensus argument and the Hartland Institute is at the forefront of exposing the consensus argument as fraudulent with such things as the 31000 signatures to the Oregon Declaration which dwarfs the 2500 claimed support of the IPCC or the 212 scientists who signed the 2007 Bali Declaration in suppoert of the IPCC 2007 4AR five years after HadCRUT3 showed that the world was already cooling!
Since science is the pursuit of truth and AGW advocacy is anything but; it stands to reason that all efforts to keep the debate out of the scientific arena must be made by the global warming orthodoxy to keep the fraud alive.
Or maybe this is part of AGW Climbdown. Hard to know with these people. ;)
Andrew
54. Wagathon
Why was William Gray targeted. Why was the label ‘denier’ hung around his neck like the scarlet letter?
Too many in academia are deniers of a simple fact: the need for honesty in science has never been greater; and, why do these deniers continue to hide from that? The credibility of those who proclaimed ‘consensus’ went down the drain with their targeting of skeptical scientists.
The AGW True Believers by their actions have voted against the need for honesty in science. The Medium is the Message: the ‘votes’ by those in academia in support of those who oppose the scientific method is their scarlet letter.
55. Herman Alexander Pope and hunter got in ahead of me. The problem for the proponents of CAGW is that the target that is the real and only problem is unassailable. That target is the hard, measured, observed, independently replicated data. If we skeptics are correct, and we are, then in the end the observed data will prove that we are correct.
Assuming this is going to happen sometime, then just like if you are running a marathon, you need to take a first step, eventually we will see something in the data that is going to prove that CAGW is wrong. Maybe we are starting to see this, in the “brightness” temperature at 600 mbars. This is currently setting records for the calendar date, since data became available in 2003. Will this trend continue? Is this the beginning of the end for CAGW? We have no idea. It depends on what Mother Nature gives us. But stay tuned.
56. David Springer
You don’t need a graduate degree in atmospheric physics to know when someone is trying to pull the wool over your eyes. Never underestimate the general public’s ability to differentiate between sincerity and deceit. This is a skill so essential to survival in the human species that recognizing deceit is probably as instinctual as the ability to recognize the shapes of spiders and snakes.
http://www.sciencedaily.com/releases/2008/02/080227121840.htm
“Evolution Of Aversion: Why Even Children Are Fearful Of Snakes”
Mitt Romney is currently conducting an experiment in whether there’s enough money in the world to subvert the instinctual recognition of a snake. ;-)
57. Jarmo
I nominate Earth.
Stubbornly refuses to co-operate with science.
• GeneDoc
+1
• SamNC
Nice!
58. dp
You target low hanging fruit. Or more coarsely, baby bison tastes just as good as adult bison but are less dangerous to put on the plate, so you focus on them. A quirk of fate put Heartland Institute in Peter’s reach and he tried to take it down. Not because it was the best or biggest, or even the most desirable. He did what any scavenger would do – he went for what was available. It turned out to be a bite larger than he could chew, to continue mixing the metaphor.
59. hunter
The AGW true believers apparently have, by their sad reaction to Gleick’s failings, helped Gleick make some more very poor decisions:
“Gleick’s lawyer John Keker, “Heartland no doubt will seek to exploit Dr. Gleick’s admitted lapse in judgement in order to further its agenda in the ongoing debate about climate change, but if it wants to pursue this matter legally, it will learn that our legal system provides for a level playing field.” Keker added, “Dr. Gleick looks forward to using discovery to understand more about the veracity of the documents, lay bare the implications of Heartland’s propaganda plans and, in particular, determine once and for all who is truly behind Heartland and why.”
from a post @ Feb 24, 2012 at 10:34 AM | Mac
• P.E.
IOW, “pay no attention to the man behind the curtain”. There are limits to discovery, and who’s paying for Heartland is completely irrelevant to the question before the court. The won’t have to disclose anything that’s not germane to Gleick’s defense, and that isn’t. It doesn’t matter if Lucifer Q. Satan is funding Heartland, Gleick still broke the law, and still committed tort. That guy’s blustering.
• SamNC
Using public funds engaging illegal activities and deceits, punish them to the extent of the law permitted!
• cwon14
Hunter,
Gleick himself, with many believers are deep into PGTS (Post Gleick Traumatic Syndrome). Aside from doubling Heartland donations it’s the best possible outcome. It’s like the Battle of Cannae with a “cause” in the middle of field.
You can’t fix stupid, you can only benefit by it from others. He’s going to try to use the court to prove Heartland’s position is “propaganda”? He’ll be looking for a friendly “peoples” court in Kalifornia I presume?
A. First amendment anyone?
B. PRIVATE assembly and rights?
What planet are these people from? What country is this?
Comrade Gleick is in for some serious hurt here.
60. pokerguy
“What an amazing post. Slobbering adulation of Saint Peter, and imprecations against the evil subversives at Heartland. I thought it was a parody at first …”
Which is why they are in fact *beyond* parody. They have no idea how crazy they sound.
61. Jarmo
Seriously speaking, taking down sceptics or organizations would not make any difference.
The US Senate unanimously rejected Kyoto in 1997, not because of Heartland or any sceptical scientist, but because the requirement to cut emissions would have damaged the US economy.
China and India loved Kyoto because they do not have to cut emissions. Major European nations went along because their emissions were going down after 1990 anyway.
Sceptics are a convenient scapegoat but the fact is that unless Mother Nature starts to show serious signs of distress, taxpayers and governments are unwilling to dole out thousands of billions.
And then there is Russia…. they are looking forward to a warming planet. Canada won’t be hurt either.
62. Dagfinn
My answer is that Heartland is probably the perfect choice, but I have a completely different explanation. At least I haven’t seen anyone else mention it.
If I am an AGW campaigner with no scruples, I don’t want to “take down” any opponent in anything like a literal way. I want to attack the opponent that best fits my preferred stereotype for all my opponents, those I label “deniers”. This is the best way to discredit the opposition and maintain my alleged moral and intellectual superiority. So clearly, anyone who is right-wing and can be associated with private donors giving money to skeptics is fine. And of course, I do not want them to go away. I want them to stay so that can keep using them in this way. Heartland is excellent, and so is Fred Singer who is one of Naomi Oreskes’ main “villiains”.
As for others who do not fit the stereotype, I (the hypothetical AGW campaigner) prefer to ignore them or to pretend that they agree with me. Attempts to attack them will get them attention and threaten the black and white distinction between good guys and bad guys. Leave Revkin, Curry etc. alone.
So, in this model, it’s not about getting rid of the opposition, it’s about defining who the participants are in a way that makes the idea of a war between angels and demons as credible as possible.
• hunter
Dagfinn,
Excellent points. Gleick was working with the NCSE to do just that, by confusing creationism and cliamte skepticism in the public sqaure and in school education.
The curriculum being developed by HI, while it would have been very limited in scope, was a counter to the lie Gleick was trying to sell.
So Peter was not simply acting out of outraged nobel cause corruption. He was worried about even a bit of competition.
• Heartland is obviously the biggest demon in the game. That is why I made my proposal to them in the first place. And NCSE has clearly just got a lot of money for its new climate thrust, since they are all over this story. They are quoted in most attack articles and I was invited to debate them on public radio, which I declined to do. If non-profits count as commercial enterprises under the law then the theft and release of those documents has commercial law implications. Fascinating.
• Theo Goodwin
“Excellent points. Gleick was working with the NCSE to do just that, by confusing creationism and cliamte skepticism in the public sqaure and in school education.”
Right on the money. Gleick, and Mandia writing in his defense, believe that they can recreate for AGW what they see as the victory against creationism. And after the AGW victory comes what?
• gcapologist
Definitely a big difference between the “controversy” of evolution science and climate science. NCSE lost my respect when they made the announcement they picked up the climate cause.
It is a matter of losing trust. I felt the same way when the Nobel committee gave the peace prize to Gore and Obama.
• interesting perspective
• Anteros
Dagfinn
Very convincing, although I don’t think there is quite as much deviousness as you might think. My guess is that the average Gleickian ideologue actually believes that Heartland are a specific incarnation of the devil. And that’s before you even mention the climate. I think climate is only peripheral to Gleick’s ideology [and many other people’s, on both extremes]
• cwon14
1+
Now if you could only break the convention and mention the ideology by name Anteros. “That ideology that can’t be named”? “The dark lord”?
• stan
Of course. Gleick desires to do good. He supports certain policies. People who oppose his policies must not desire to do good. Therefore those opponents must be evil.
Childish thinking? Sure. But it’s everywhere you look. See e.g. the thinking behind What’s the Matter with Kansas? [Since GOP policies supposedly only favor the rich, everyone who isn’t rich should vote for Dems. So the non-rich who vote for the GOP are obviously dupes.] The idea that someone might have legitimate reasons to disagree about what is the right policy to ‘do good’ never occurs to them.
• Dagfinn
Anteros,
It’s interesting to consider what the difference might be in practice between actually believing your opponent is the devil and just pretending for propaganda purposes. Not much, I think. When faced with the devil, you want to destroy him completely, which may be in conflict with I said about want to keep the opponent around for the next attack. On the other hand, you can’t kill the devil, and climate scientists probably know that Heartland won’t lose support from their existing supporters because no matter what they do. So it comes down to changing the hearts and minds of everybody else.
And that means persuading everybody that the opponent is in fact the devil and that you are the hero. Then the same style of manipulation applies, including using tricks that may seem unethical otherwise. There are no equal terms. You may demonize your opponent since he is fact in evil. But if he demonizes you, it’s unethical and proves how bad he is.
• Dagfinn
There is also the “false balance” ideology, which entails demanding dominance based on the alleged total wrongness of the opponent. This requires an opponent that fits the stereotype.
• cwon14
Very lucid Dagfinn. Keep in mind a good part of the population understands the would-be pompous “angels” in our society as the ultimate evil.
I can’t help but think of someone blowing a whistle, waving a baton and aiming the troop right at machine guns. Gleick and his tribe are goiong to get slaughtered.
Better read Pointman’s piece on the death of movements if you haven’t already;
http://thepointman.wordpress.com/2010/12/07/the-death-of-the-agw-belief-system/
This is a classic end of age event.
• Hi Dagfinn. I think HI in combination with the particular attack method chosen, was the worst possible choice.
“When you actually think it through, as he should have done, it was inevitable that Fakegate would be exposed as bogus but that was bound to happen some time after the whole of the alarmist propaganda machine had committed itself to supporting what was going to be an easily exposed fiction. The big damage was always going to be to their credibility, if not their wallets.”
http://thepointman.wordpress.com/2012/02/21/fakegate-claims-its-first-scalp/
Pointman
• John Carpenter
Dagfinn, your perspective illustrates a good, advanced strategy… but I’m afraid it’s a little too clever to believe PG or any other CAGW advocate could come up with it… too visionary of an idea for them.
• Jim
Dagfinn,
I don’t think that it is correct to characterize Gleick as being some one “with no scruples”. I think that is an exaggeration, and does no good as an explanation of what he did.
I think that the explanation that some one suggested way up above in the thread, the personal animus between Gleick , Taylor and Heartland at the Forbes, and frustration and ego in the same, is sufficient explanation of his actions. There’s no point ion invoking monsters when they’re not needed.
• Dagfinn
Jim,
I wasn’t characterizing Gleick, I was thinking in terms of a hypothetical “climate change ideologue”, which was what Judith asked for.
Your explanation may be right. Also, there is little or no conflict between that and mine. Both could be the case to some extent.
• Jim,
Some of what you say might be true of Gleick himself. As for many of the baggage carriers in the eco-left movement I can’t make that much of an excuse since the event took place. I’m thinking of the usual suspects in the media and NPR in particular. Gleick as provoked hero by evil GOP operatives (Heartland) meme came out as second nature.
Both Revkin and Gleick only offered the most half-truth apologies on the 15th or so. Both have walked it back since then and seem much less contrite. The “Gleick as victim” meme has amazing traction in the MSM fringe at the moment. At first I thought it might only be a few dollars and some political humiliation to eat for the “cause”. Now the stakes are raised by this full-blown “The Rosenberg’s are American Heros” defense as if we haven’t seen this sort of thing a hundred times in the past fifty years or so. Now it’s in the hands of the most corrupt and political Eric Holder FBI and Justice department since the Nixon years (in fact worse). The case is only getting bigger not smaller. It’s open and shut, it crossed state lines, it involves AML and Patriot acts statutes, Identity theft is involved. Every bit of the law in recent years have focused on these areas or are recently created.
He’s playing the martyr along with the tribe. Next to the “cause” these laws are traffic violations has been the party line. Gleick was driving too fast and said he was sorry. Case closed. AGW is mass murder on the part of the GOP and Heartland, we can’t forget that. I now have to see “a perp walk” and watching this administration corrupt itself yet again is expected by both Gleick and myself. It could well become a monster event given time. Sure, ego and general arrogance go with the AGW culture but it’s not the only force at work. There may be some optimal time for him to cave in his mind, in the mean time it’s the business of inventing political crimes (Heartland evil) and selling them to the AGW mob well represented on this board.
• Jim
cwon14,
You say ‘baggage carriers’ , I say ‘rent seekers’, let’s call the whole thing off…(sung to the well known tune.)
Thank you for the quote of Alinski below, I never would have seen it, had you not posted it.
WRT the Soviet spies, that is maybe the only time in history that I have seen a full measure of satisfaction. With the fall of the USSR, and the publication of the American Communist Party minutes and KGB American files, and Venona decryptions, the truth was finally outed.
63. Edim
I think Hanlon’s razor applies here.
http://en.wikipedia.org/wiki/Hanlon's_razor
64. Mark Kantor
Apologies for being potentially off-topic, but for those of you with an interest in the legal aspects of climate change and regulatory policy, a number of organizations are offering 8:30 am – 12 noon program on March 1 here in Washington DC entitled “Debrief of the DC Circuit’s Oral Arguments on EPA’s GHG Rulemakings March 1, 2012” (http://www.facebook.com/events/370847879593650/).
[Full Disclosure: I have nothing to do with this event or the co-sponsoring organizations, nor do I have any details except for the information in this post.]
“The U.S. Court of Appeals for the District of Columbia Circuit will hear two days of oral argument to review four of EPA’s greenhouse gas emissions rules: the “timing” rule, the “tailoring” rule, the “endangerment” rule, and the “tailpipe” rule. These four rules are EPA’s response to Massachusetts v. EPA and represent the bedrock of EPA’s regulation of greenhouse gas emissions under the Clean Air Act (CAA).
The court’s rulings on these four rules have the potential to halt, delay, modify, or greatly increase the scope of greenhouse gas regulation under the CAA. The stakes are among the highest in recent environmental litigation.”
Details of the program are below and at the weblink. Attendance is free either in-person or by teleconference, but you must register in advance. Particularly of interest to lawyers and public policy specialists – Please RSVP by February 27, 2012 to [email protected] with name, affiliation, and whether in-house or teleconference attendance.
The event is con-sponsored by the Environmental Law Institute, Jones Day, International Emissions Trading Association, Georgetown Climate Center and the DC Bar Environment, Energy, and Natural Resources Section. Details below.
Subject: REMINDER: Debrief of the DC Circuit’s Oral Arguments on EPA’s GHG Rulemakings March 1, 2012
Thursday, March 1, 2012
8:30 a.m. – 12:00 p.m.
Jones Day Washington
Reception Entrance
300 New Jersey Avenue, N.W.
Washington, D.C. 20001
Teleconference Available
Co-sponsored by the Environmental Law Institute, Jones Day, International Emissions Trading Association, Georgetown Climate Center, and the DC Bar Environment, Energy, and Natural Resources Section
The U.S. Court of Appeals for the District of Columbia Circuit will hear two days of oral argument to review four of EPA’s greenhouse gas emissions rules: the “timing” rule, the “tailoring” rule, the “endangerment” rule, and the “tailpipe” rule. These four rules are EPA’s response to Massachusetts v. EPA and represent the bedrock of EPA’s regulation of greenhouse gas emissions under the Clean Air Act (CAA).
The court’s rulings on these four rules have the potential to halt, delay, modify, or greatly increase the scope of greenhouse gas regulation under the CAA. The stakes are among the highest in recent environmental litigation.
Join our distinguished panelists, many of whom participated in the arguments, as they describe and dissect the previous days’ oral arguments and discuss the implications of the potential outcomes.
8:00 a.m. Breakfast Served
8:30 a.m. Welcome & Overview of Oral Arguments
Kevin Holewinski, Partner, Jones Day
Gabriel Pacyniak, Institute Associate, Georgetown University Climate Center
9:00am Panel I: Discussion of the oral arguments’ main sticking points and highlights
John Cruden, President, Environmental Law Institute (moderator)
Tim Webster , Partner, Sidley Austin LLP
Earle Duncan Getchell, Commonwealth of VA (invited)
Meleah Geertsma, Attorney, NRDC
Tracy Triplett, Assistant Attorney General, Massachusetts (invited)
10:15 a.m. Coffee Break
10:30 a.m. Panel II: Scenarios and implications: the impact of potential outcomes
David Hunter, US Director, International Emissions Trading Association (moderator)
Rob Brenner, Senior Fellow, Nicholas Institute, Duke University; Former EPA Director of the Office of Policy Analysis and Review at the Office of Air and Radiation (invited)
William Brownell, Partner, Hunton and Williams
Megan Ceronsky, Attorney, Environmental Defense Fund
Kyle Danish, Member, Van Ness Feldman
11:45 a.m. Closing Remarks
Henry Derwent, President and CEO, International Emissions Trading Association
12:00 p.m. Concludes
Please RSVP by February 27, 2012 to [email protected] with name, affiliation, and whether in-house or teleconference attendance.
• For some unknown reason I’m on Cato Institutes mailing list and have received couple of messages on another event on the same subject also on March 1.
• Mark Kantor
Way off topic, but lots of events here in DC that day. If you have no interest in this climate/regulatory event or the unidentified Cato event , the DC Bar International Dispute Resolution Committee (of which I am chair) is also co-sponsoring an 8:30-10:00 a.m. breakfast program on the same day (March 1st), to provide a “quick response” assessment of the February 28th oral argument before the U.S. Supreme Court in Kiobel v. Royal Dutch Petroleum. In that case, the Supreme Court will be considering the controversial decision of the Second Circuit Court of Appeals, which ruled that the Alien Tort Statute (which allows lawsuits in U.S. courts for violations of international law) does not create a legal basis for such suits against corporations. The registration link is http://wfls.us2.list-manage.com/track/click?u=526d87115e123966065f5b998&id=4fd4f1b0e9&e=aae5d361ea, which will take you to the Washington Foreign Law Society’s registration page.
No more off-topic stuff from me today – thanks for your patience.
• Mark, thanks much for these updates
• Should be inconclusive but fun, since both sides are well represented if everyone shows up. I am hoping that the Court remands the endangerment finding on the grounds that EPA did no analysis of its own. But that Court is a crap shoot. I used to cover oral arguments and the outcome has nothing to do with the questions asked by the Justices.
• Rob Starkey
Mark
That ruling is key to US policy in the US
65. David Bailey
Why Heartland?
My feeling is that some in the CAGW movement are getting really desperate. Recently there have been a number of prominent scientists coming out against CAGW, the global temperature curve remains flat, a prominent CAGW supporter has changed ‘sides’ in Germany, and has written a book about the IPCC……..
My guess is that Gleick wanted to create a positive new story (from his perspective) – anything, absolutely to distract the press from probing deeper into what we all know is a very deep can of worms!
When CAGW is fully exposed, there will be a huge crash in support for science (unfortunately not just climate science), with politicians wanting to blame the scientists for persuading them to waste billions of pounds. It is going to become very nasty!
I’d imagine some of those responsible must be starting to sweat – and maybe lose their senses. After all, they know that all the evidence showing that researchers acted in bad faith, is right there waiting to be GOOGLed! I know I would feel pretty quesy if I had been part of the CAGW scam!
• Edim
Yes, desperation too. They must be praying for some warming, don’t they?
• Jim
I think the answer to “why Heartland?” is simply Gleick and Taylor on the Forbes blog. That the escalation of insults, slights and invitations leads to Twinkies-style “temporary insanity” seems very understandable to me. (No violence is implied by me with the Dan White Twinkies-defense reference, I’m only suggesting the idea of temporary irrational behavior.)
66. Why Heartland? Because Mother Nature, who is also not cooperating with the narative, doesn’t issue board minutes or have corporate sponsors you can attack.
67. I would think by this time Gore and those who knell to his holy altar might be thinking of re-opening Jonestown.
• SamNC
Colossal believer suicides or murders!
68. pokerguy
I’m still waiting for one of those who think Gleick deserves to be sainted for stealing (and forging) documents from a private institution, to explainwhat we know now that we didn’t know before about HI, except that they actually have very little money to throw around relatively speaking, and less still from oil companies…
And more importantly, what is Heartland doing that is anyway illegal or unethical.
Still waiting….
Still waiting….
69. Craig Moore
Attempting to take down Heartland reminds me of the “war” mentality to bomb Hanoi into submission so that the people will embrace American democracy. Utter arrogance and misreading of the situation.
Gleick et al. can’t sell their message because they can’t address the needs of their audience. People are concerned about food, water, shelter, clothing, jobs, and quality of life. They don’t care about “infrared radiative transfer” when they don’t see how it improves their access to basic needs and enjoyment of life. “Progressive” abstractions just don’t motivate them to risk what’s important in their daily lives. All that’s left for the gleikers, who can’t win the hearts of the people, is to get them to “hate” the other side. Just won’t work in the long run.
• Tom
hmmm, it’s a ‘we have met the enemy and we are them moment’, What’s next? We will win.
The end result of this episode is that Heartland will become known to many more people.
Sure, just as the result of climategate was that CRU became known to many more people. Not all publicity is good publicity.
• Punksta
True enough – not all publicity is good publicity. A minor difference being that the formerly unknown CRU was shown to be nest of unrepentant fraudsters, whereas nothing even approaching that has been revealed about Heartland.
• Hopefully some teachers now know that help may be on the way.
• Rob Starkey
David
With all due respect- it remains to be scene if what you will put together is help or not. It all depends upon what you put together.
• Rob, I think the simple fact that there is a legitimate scientific debate will be useful news to many. We take the debate for granted here, but many people do not know it exists. The details are not important; it is the fact of the debate that matters.
• Latest shock news: Heartland’s education chief says as he prepares his material for schools:
The details are not important
Doesn’t that say it all.
Only kidding David. Carry on.
• SamNC
David,
When will it be ready? You seemed to have a lot of time here. LOL.
• Latimer Alder
But if you are a privately funded institution reliant on donations, it only takes a few who learn about you and decide to give a bob or two to change your fortunes substantially.
And if your main aim is to bring publicity to your views then a good dose of public loathing from the committed alarmists must be like manna from heaven.
So from Heartland’s view this is a win all round.
The man gleick really has let his massive ego lead him and his cause into a grave miscalculation. What a ‘banker’…….
71. “Who would you target?”
I thought for sure I would be the first to make this nomination but it appears that others have beaten to the punch.
The organization that has done the most to mint new sceptics, at least among the technically informed, is RealClimate.org.
A little more seriously, as person who has a background in applied statistics, I first became interested in climate issues by reading climateaudit.org. Although climateaudit obviously limits its discussion to a narrow aspect of climate science, it was the interactions between climateaudit.org and realclimate.org, that peaked my interest in seeing what lay under other rocks in the field of climate science. Thus, a sceptic was born.
• Actually I have a new idea: Steve Mosher, he is getting too good at this :)
• hunter
Yes. go after the kung fu master.
• Scott Basinger
I don’t know if I was in their position that I would want to take on Mosher. The speed at which he went ‘Gleick is that you?’ was pretty astounding.
• Pouncer
Yes, that’s who (what) did it for me…
I think I posted — asked — a simple question about some detail or another on the hockey stick. “What is ‘red noise?’ or some such. Yes, a phrase picked up almost at random from background chatter.
The question was deleted.
Twice.
Shortly after I found Climate Audit where the phrase had apparently originated.
Oh.
• Jim
pauldd,
I agree with you in your assessment of RealClimate.org, that it disappoints the technically experienced types of peoples. I don’t know if it “minted” me, but I first went there as a person concerned by AGW, and I was disillusioned by the lack of rigor. As with you, that peaked my interest in looking under the rocks of the orthodoxy.
• Jim
PS
Climate Audit was the antidote. McIntyer’s application of ordinary quality assurance practices was instantly understandable to me. That the scientists argued against QA was an eye-opener to me.
72. Why Heartland?
This may be of interest: http://nigguraths.wordpress.com/2012/02/22/fakegate-heartland-delegitimization/
Political conservatives have always been shooed away from the environmental arena.The objective is to prevent them from obtaining a foothold. If rational environmental debate were to take place, a) many of the supposed wicked issues would disappear thereby taking down those who depend on them for political sustenance, and, b)it would deprive issue entrepreneurs and pioneers, of dominance in that area.
The present situation is squarely to be blamed on (a) the success of political conservatism in ensuring economic progress, thereby depriving political left of virtually all oxygen in this area (as in, no credible lefty argues for a traditional left position), and (b) the failure of political conservatism in not caring for science and allowing ‘science’ to be completely hijacked by the political left, to be used as a tool and flag-standard.
• cwon14
Shub,
There is a loss of “turf” element in this event. The Green movement is in world of the their own results with massive financial and government backed losses for example. Going more radical is a way to rally their peers some of who are wavering. It is an election year of course.
Gleick now needs a pardon from a friendly Whitehouse. He better hope for a speedy trial and conviction and or an Obama win. He might spend more time in jail in the latter case waiting for January 2017 for the political payback pardons are likely to issued if Obama wins. Then of course he wants the longest possible trial, appeal etc. to reduce jail time.
What people away from finance may not realize is how the recent law is so much worse for Gleick on Identity Theft on many levels including the Patriot Act and anti-money laundering standards. He’s toast in a legal sense. His potential sentence is over 20 years. In California he would have been better off with manslaughter or 2nd degree murder. Identity Theft is a federal crime. It might not end up in California courts which he is praying to Gaia for every night.
73. Jeff
“So, imagine you are a climate scientist and climate change ideologue, and want to “take down” the single organization (or individual) that is doing the most damage to the movement (i.e. with the end result of thwarting CO2 emissions/stabilization policy)” And why would you ever imagine that this activity was as or more important than working on evidence supporting your position? And why would you consider that “having a position” was more important than the objective pursuit of information? The answer to that is that ethics, values and morays have all become (or been revealed as being) quite confused.
• Personally, I can’t imagine it, but Peter Gleick seems to have. Trying to understand this. So far the only thing that makes sense is to support the merchant of doubt meme, but i still can’t reconcile this with the Gleick’s act of professional seppuku.
• cwon14
You are living in a bubble if I’m to accept these words at face value Dr. Curry.
AGW for the most part (in the largest sense) is an ideological movement. Gleick is gambling on a political reward as a “get out of jail free card”, he’s already dead in court. His odds aren’t bad, this is among the most corrupt White House’s in history and the killer crime in a jail sense is Identity Theft. A Federal Crime with William Holder justice department, the most politically corrupt in history bar none. He makes himself a hero to the Obama clan is his best chance in his eyes, it suits his ego as well. We may have yet to see the largest collective crime in this event yet, Gleick has chances with this administration.
As for a professional career and reputation? How much worse is this than the TEAM itself that made plenty of the same trades or worse for the “cause”? He’s almost retired as a scientist for a long time. He gets to join the deified of the American left like Ethel and Julius Rosenberg, Jim Hansen, The Hollywood Ten. How are you missing this (or pretending to)? The AGW fanatics don’t care about their “professions”. Do you think NPR cares about “journalism” over this event? Have you heard the levels of “good cause” rationalizations as a Gleick defense going on there?
What kind of world do you think we are living in Dr. Curry? Why are you allowed to pretend when the world and nation suffers from this sort of fiction? There was time when the elite would police the mob, now they are the mob.
Jeff, “quite confused”??
There is nothing confused about it. Gleick and his followers know exactly what they are doing. By pretending otherwise you are subsidizing the behavior. Dr. Curry does this all the time, don’t be a minion you should object.
“Trying to understand this”? Gleick is like a brick thrown through a window at a “Peace rally”. How culturally biased and accomodative to your peers and political/cultural cousins can you be? It’s shameful. The Gleick defense plan is offensive on every level, it’s easy to understand, the politics behind are easy to identify as well. It will be what it will be regardless of what I say or even you say. You should take a moral position even if it is hard culturally. Enough of the “trying to understand” though, it just isn’t this hard to understand and I can’t believe you really don’t.
• Roddy Campbell
cwon14 – you’re sounding bit like …… Gleick. take a chill pill.
• Roddy, I have a good cause. -:)
• Put the scanner down, cwon. :)
• Jim
Judith,
Gleick couldn’t have intended the outcome, so “professional seppuku” seems too much like hyperbole.
I don’t think that he was rational, for that short time. I think that is the truthful part of his ‘confession’, that he was blinded by animus. That his subsequent actions were a stupid, irrational mistake.
What will be interesting to see is what happen in the future. If he is honest in his contrition, and he labors honestly in the public eye for a long time, I think that he can redeem himself. He is a very able person. If he continues to conceal and dissemble, well… we’ve all seen that before…
• He didn’t think he would be caught just as the CG 1 and 2 leaker was not caught.
Moshpit zeroing in on him within hours completely upset his plans and dreams. Everything since has been damage control. Everything.
• gcapologist
A few possibilities: cognitive dissonance, projection, feelings of moral superiority, personality disorder….
• GaryM
“The answer to that is that ethics, values and morays have all become (or been revealed as being) quite confused.”
What do eels have to do with it?
Oh, “mores.” Never mind.
• Andrew Russell
Channeling Emily Littela? :-)
74. The general positions of Peter Gleick and Heartland Institute have been for longclear enough for those who have followed the debate. Thus people will see HI in the same position they did before and in part that applies also to Gleick, but only in part.
Concerning the activities and funding of the Heartland Institute, there’s only one issue that has really come out – the project of David Wojick. The attention given to that project may really have a significant effect. It’s likely that various counteractions will be prepared and the outcome of the project will be strongly attacked and discredited, if there will finally be on outcome. This by itself may have been enough for justifying the choice for Gleick, although the Forbes contributions by both sides are a more likely reason.
• hunter
Pekka,
I think that we should recall that Peter Gleick and the NCSE was busy fabricating a science curriculum designed to confuse creationsim with cliamte skepticism.
NCSE is vastly more well funded, has much more access to school rooms, and was deliberately setting out misrepresent the debate as strongly as possible.
If we are going to talk about politicizationin the classroom, let’s chit chat.
• Looking for motivation it’s not necessary to present judgments on their activity. In any case Gleick was certainly convinced that the HI / Wojick project has been set up to discredit valid understanding. The main claim of my previous message is that on this issue, his activity may, indeed, have had real effect – perhaps a larger effect than could have been reached attacking other targets.
• Rob Starkey
Hunter
Good point.
Trying to compare the teaching of religious positions vs. evolution to the teaching of the uncertainty about the validity of the IPCC’s conclusions seems to be a political attempt to discredit those who do not accept the IPCC’s position.
• Gene
It’s likely that various counteractions will be prepared and the outcome of the project will be strongly attacked and discredited, if there will finally be on outcome. This by itself may have been enough for justifying the choice for Gleick, although the Forbes contributions by both sides are a more likely reason.
If his intention was to discredit the Heartland curriculum, then Gleick could well have handed them a golden opportunity since the curriculum doesn’t exist. Whipping up an outline that shows disagreements and uncertainties in a factual, politically neutral manner would allow Heartland the opportunity to portray Gleick (and by implication, those associated with him) as extremists.
This is why the only sane answer to Dr. Curry’s question above is “no one”. Absent a 100% guaranteed kill shot, you risk immense blowback with a stunt like this.
• hunter
Pekka,
Setting aside your seeming calmness in the face of Gleick’s efforts to mislead students irt climate skepticism by means of a lie, I would agree with your other point that this will have larger impacts than anticipated. HI’s membership and donations are up, and more people will understand and agree with their message that something is terribly wrong with the AGW movement.
• Pekka, you are half right. There is no question that my product will be attacked by the warmers. if it ever comes out, but it would have been anyway, so sounding the alarm serves little purpose. I doubt it will be discredited in other than their eyes, if I do the job well. Note that there is no actual project at this time. It was just a proposal.
In fact some of the hate publicity has actually been positive as these things go, in that I have been able to squeeze my message through the negative green filter. Keep in mind that half the readers in the USA don’t believe CAGW. Many are angry that it is being taught. They do not read this green stuff verbatim. If I get a good quote in edgewise it may be the whole story in their eyes. I think a lot of people are now looking forward to what I may produce. Alerting them may prove to have been quite useful.
• David,
I understand well that the scene is different in USA from what we have here in Finland or most of Europe. On the US scale I must be strongly on the warmist side, but perhaps not so certainly here or in EU more generally. Accepting most of the main stream climate science, but being skeptical on EU policies might be considered a rather strongly deviating view here.
• hunter
David,
It is astonishing to me that the extremists are so crazed on this as to be this upset over a proposal that you develop an idea that they do not approve of, sight unseen.
• Jim
Pekka,
It surprises me what you say; “Accepting most of the main stream climate science, but being skeptical on EU policies might be considered a rather strongly deviating view here.”
That being skeptical of the not-too-effective EU intervention policies is a “deviating view” is unfortunate! I think that many of the posts that you have had here are very rational and reasoned. I’m disappointed that your ideas are deviant, over there.
75. P.S. to my earlier post…leave the children and elderly behind.
76. John Whitman
I have a question regarding Mandia’s view of professional ethics based on this statement of his:
Scott Mandia a leader of the Climate Science Rapid Response Team is quoted as follows:
“Peter Gleick, a scientist who is also a journalist, just used the same tricks that any investigative reporter uses to uncover the truth. He is the hero and Heartland remains the villain. He will have many people lining up to support him.”
– – – – –
So given Mandia’s position on the Gleick Hoax above, I pose this question.
Does Scott Mandia’s statement mean that both he and the CSRRT members that he speaks for, if he or they were in a position to be aware in advance of Gleick’s plan to perpetrate the HI hoax, would he or they have supported the perpetration of Gleick’s plan?
By Mandia’s own statement above, he seems to infer it would be good to help this ‘hero’ (Gleick) in the perpetration of his efforts to harm the villain (HI). Mandia seems to infer it would not have been wrong to help Gleick in doing that acceptable (to Mandia) investigative journalism. Mandia seems to infer that many people would have been found to help Gleick’s hoax plan.
John
• hunter
If John Whitman is as poorly informed on claimte as he is on journalism 101, he is facing a much bigger problem than Peter Glecik.
• John Whitman
hunter,
Why?
John
• hunter
John,
Sorry, John: I meant to say that if Scott Mandia is as uninformed on journalismn as he is on cliamte science or ethics then he is facing muhc bigger problems than just Gleick.
Sorry. i was typing too fast and did not in any way mean to imply somethingnegative about you.
• John Whitman
hunter,
No problem. I have done errors by fast / heated typing before.
You surprised me though. Your comment was so out of character for you. : )
John
• Bob Ludwick
Just as a matter of curiosity, why does Climate Science need an official Climate Science Rapid Response Team?
Is this common to all scientific and technical fields fields? Is there a Physics Rapid Response Team or a Chemistry Rapid Response Team or a Mechanical Engineering Rapid Response Team or a Mathematics Rapid Response Team?
• My question exactly. What is the purpose? It’s not science, that’s for sure.
It does a bear a close resemblence to the Bill Clinton presidential campaign. Clinton camp maintains a rapid response team In other words, it’s pure politics. The whole global warming thing is run on a political model, not a scientific method model. It’s yet another embarrassment for climate science in their claims that they’re simply scientists and we should trust them.
And, of course, who did Peter Gleick hire to help him with his self-inflicted troubles? A couple of Clinton partisans. Again, the model is political, not scientific.
• Don
As a mechanical engineer, I can confirm that there IS a Mechanical Engineering Rapid Response Team that mobilizes upon hearing that there is cake in the break room.
• Scott Basinger
Same rapid cake response team in electrical engineering. Weird.
• Don
Exactly, Scott, hence the need for rapid deployment!
77. There is 2 huge assumptions:
1. That the motive was purely political, not personal
2. The target was one selected by thoughtful consideration, not opportunity.
I believe there are good reasons to doubt both these assumptions.
• Indeed, based on Gleick’s statements the target was selected when he received the forged strategy plan and he just wanted to follow up on it. Opportunity creates many a crime.
• I think it is more likely that he was annoyed about his conflicts with Heartland at Forbes, at the fact that the WSJ published a letter by 16 skeptics but refused to publish the letter than he had authored and organized signed by 255 warmists, and so on.
I think the opportunity, or the idea, arose, because of the email exchange with Heartland when they invited him to a debate. He obtained information in that exchange which he leveraged to use for phishing.
• kcom
Spot on, Copner. But I would change the word “annoyed” to something much stronger. As characterized upthread, I think his emotions run much hotter than that. The earlier poster said he was probably “stewing” after all those perceived slights and I bet that was true. It was that strength of emotion that allowed him to plow ahead, in a fit of pique, with his irrational, ultimately self-injuring plan before better sense could prevail. As mentioned above, I think his motivation was as much (and probably more) personal than political at the point he finally pulled the trigger and implemented his plan.
“He obtained information in that exchange which he leveraged to use for phishing.”
That was pretty slimy, wasn’t it.
• Jim
Copner,
You are correct about both assumptions!
The simple, self confessed motive is the true part, maybe the only true part, of the confession.
78. David Springer
“In the U.S. anyways, who (individual organization) has been most effective at challenging the IPCC consensus science in the public debate on climate change?”
The White House. In a rare display of non-partisan consensus Clinton, Bush, and Obama have all rejected the Kyoto Protocol.
• Rob Starkey
Also a good point as it was a bad treaty. Then again, what percentage of the world’s population did accept that treaty?
• David Springer
Someone’s probably going to object and say Clinton signed it. The presidents merely paid it lip service for brownie points with their peers in other nations knowing full well the U.S. was never going to ratify the treaty. I remember back in the 1990’s Scientific American publishing an article explaining why. In the original draft countries got credits for carbon sinks including forests. The U.S. had been on a tear at home and across the world planting trees and working to limit destruction of rain forest. It stood to get so much in the way of carbon credits there was little need to reduce carbon emissions. The UNFCC however recognized this and since as we all know this has never been about CO2 but rather about the wealth and power of the United States which is dependent on fossil fuel consumption the UNFCC effectively eliminated the carbon credits for reforestation and that killed it for the U.S. No president was going to fight for what was clearly not in the best interests of the United States.
• John R T
Thank you for noting UNFCC contributions.
1+
79. Steve Milesworthy
“So, imagine you are a climate scientist and climate change ideologue, and want to “take down” the single organization (or individual) that is doing the most damage to the movement”
The question is puerile. Gleick is an individual who has clearly let Heartland get to him. Characterising the event as an attempt by “climate scientists” as a group to target denialist institutions is just silly.
As you say:
“Scientists seem to persist in thinking the problem is the public’s understanding of climate science.”
I agree with that. You don’t solve that with direct action.
• hunter
Steve,
• kcom
“Characterising the event as an attempt by “climate scientists” as a group”
Please show where that was done. I don’t see a plural (scientists) anywhere in the original question you quoted.
80. gbaikie
“So, imagine you are a climate scientist and climate change ideologue, and want to “take down” the single organization (or individual) that is doing the most damage to the movement (i.e. with the end result of thwarting CO2 emissions/stabilization policy). Who would you target?”
Al Gore.
81. kramer
And of course all this begs the question of why we don’t have CO2 stabilization policies, which is mostly about economics, politics, values.
IMO, that is exactly what this is about.
In the 1969 book ‘Resources and Man’ by the National Academy of Sciences-National Research Council, it says in the introduction:
“Man must look with equal urgency to his nonrenewable resources–to mineral fuels, to metals, to chemical, and to construction materials.
“These are the heritage of mankind. Their overconsumption or waste for the temporary benefit of the few who currently possess the capability to exploit them cannot be tolerated.
I have also found a number of other references from different sources (the UN for example) from the ’70s that echo the same thing.
One of the common themes I have found in these books and papers I’ve read is that developing countries need access to these natural resources in order to grow their economies so they can end their poverty. Another theme I’ve gotten from what I’ve read is that modern economies tend to result in more women working and hence they’ll have less kids. Less kids means less population growth, and population growth is another issue that has come up repeatedly in what I’ve read.
I believe they are using CO2 and grossly exaggerating the consequences of it in order to force us to use less natural resources so that the rest of the world can use more of them.
And whose ‘values?’ Those of the left? Certainly looks like it to me…
82. pokerguy
J.C wrote: “…trying to understand this.”
I just don’t think it’s all that hard. I’m sometimes accused of too readily “psychoanalyzing” people, but I’m comfortable doing it when the pieces fall into place so neatly, as they do in this case. At least in my opinion.
No longer in question is the fact that Gleick is not an honest man. Sure, sure, it’s possible this is his one and only ethical lapse, but how likely is that? When someone gets charged with a DUI, we generally assume that it’s much more likely than not that he’s done it many times before..
What do people often do when they feel ashamed of some aspect of themselves? They PROJECT. There was an interesting (if deeply unethical) experiment I read about a long time ago in which they hooked inmates up to a device that measures sexual arousal…often referred to as a “peter meter.” Reliably, the inmates who evinced the most contempt and anger toward gays were more highly aroused by pictures of naked males than were those whose attitudes were more neutral.
Is it a surprise that someone like Gleick who it’s safe to assume is ashamed of his own penchant for dishonesty, has made such a big deal about ethics in his career? I don’t think so. It’s what liars often do. It’s a way of hiding who they are.
The second part of the puzzle is perhaps more difficult. Why Heartland? WHy now? WHy such a desperate act? I think Gleick gives himself away when he blames the “lack of honest debate”. It’s essentially another form of the same defense mechanism: i.e. projection. As we all know now, he’s the one who won’t debate, not Heartland. There’s a term in psychoanalysis…”over-determination” which refers to the idea that the things we ultimately decide to do are often the outcome of a combination of motives. I don’t know the history between Gleick and Heartland, but it’s safe to say that in his heart of hearts, he was deeply ashamed of his own cowardice and dishonesty in refusing to accept their challenge. That had to be an important factor.Or at least, it seems likely to me.
That he decided to try to bring the bastards down is not particularly surprising to me. Murders (to name the ultimate anti-social act) are often committed by people who’ve been deeply shamed. Terrorists are often characterized in this way as well..
Ok, so a pretty facile analysis on my part.. I don’t even know the guy. But it makes a lot of sense to me.
• hunter
pokerguy, I think you are probably striking pretty close to the heart of drakness in Peter Gleick.
• pokerguy
Thanks Hunter. Right or wrong, there’s something deeply creepy about the man. The really scary thing is that that same quality of creepiness is rampant among the more virulent warmists. Mann is very, very creepy in my opinion, to name just one. As a group, they’re all so f’ing outraged. It’s all so personal with them. It ceased being about science a long time ago.
These are very smart people. They don’t hand out doctorates in science to just anyone. Deep down, they;re terrified of being exposed. .
Ultimately of course, they will be. But in the meanwhile, they’ll continue to fight as if their very survival depends on it. Which is does. For them, it is quite literally a matter of life and death. Or very nearly literally anyway. Was it Jones who talked about suicide when climate-gate first broke?
83. Martha
“Heartland would not be at the top of my list. What about Cato” “Chris Horner” etc Judith Curry
I’m not sure you understand the concept of political ‘network’, Judy.
It’s more along the lines of a network of political influence that is ‘at the top of the list’, for anyone who more fully understands the public, policy and political issues that dominate.
In this case, for everyone to see, it is the interconnection of think tanks and groups funded by foundations and companies controlled and supported by the Kochs — as anyone who knows how to use Google can plainly see. Who founded Heartland and whose money was involved? Who founded Cato and with what money? How many of the same names are Directors and employees? What books are pushed by Koch, Heartland and Cato (just for example, hint: rhymes with corner). Etc into the horizon.
This is not demanding analysis, and a spotlight on this kind of network can be shone from many angles. Just turn your flashlight on.
You ask, ‘why not Watts or McIntyre’? Well, very obviously, while these guys frequently misinform people and we all know they are not the brightest pennies in the piggy bank, they do not directly influence energy and climate legislation, given the current political system. That is why not.
• Peter317
I’m sure Steve MC will be delighted to learn that he’s not the brightest penny in the piggy bank.
I see more misinformation from the climate establishment every day than I could ever see from Watts or McIntyre. And I have never seen evidence that the establishment has any bright pennies at all, including you. Everything I read from you puts me into a time warp back to the 70s.
• kch
Martha –
I’m not sure that you understand the concept of ‘conspiracy theorizing’, Martha.
Believing that the Kochs are at the root of everything you despise puts you in the same category as the more unhinged elements of the right that put Soros behind everything they despise.
Hell, it could just be that the Illuminati have teamed up with the Rosicrucians and the Templars to take over the world, and all this is just a planned distraction for the masses.
On a more serious note, it’s good to see that you so easily fall into the trap of believing that your opponents are stupid. Underestimating your opponents leads to defeat far more often than to victory. Sun Tzu would weep..
• Brian H
“Sun Tzu would weep..”
Or maybe snicker. Or laugh out loud.
• Latimer Alder
You forgot the Giant Lizards
• GregS
In this case, for everyone to see, it is the interconnection of think tanks and groups funded by foundations and companies
Aha!!
So that explains why the chairman of the board of The World WildLife Fund and the CEO of The Nature Conservancy are both alumni of Goldman-Sachs!!
• Bob
Martha, none of your caped climate crusaders could hold a candle to McIntyre’s mathematical and statistical prowess. There are still in shock that he almost single-handedly exposed their advocacy as well as their shoddy “science”
• GaryM
Martha may not know much about climate, and nothing about economics, but she has Alinskyite tactics down pat. Take an issue, personalize it, and attack the person. It’s all an evil conspiracy of the Koch brothers.
If the Koch brothers had a dime for every dollar George Soros spends on politically undermining capitalists, they would be…even richer than they already are.
Martha superb! Every post of yours creates another thousand sceptics. Keep up the good work.
• John Carpenter
• Chuck L
Watts or McIntyre – “not the brightest pennies in the piggy bank?” Congratulations, Martha, nice to see you’ve joined your CAGWpeers by stooping to ad homs and name-calling. Your hypocrisy is remarkable, as well, as you ignore the political connections and networking between oil companies, the political establishment, this Administration, and organizations like Greenpeace.
• Martha, now do the same analysis for the enviro advocacy groups, with almost two orders of magnitude more funding, then explain how these few libertarian think tanks with relatively small funding, have had the size of the impact that you think they have. My flash light is turned on, and I am able to use it to illuminate both sides.
84. 1st email from Gleick ( impersonating a Heartland Board Member) to Heartland was sent on January 27, 2012 – the same day he rejected a cordial invitation to debate climate science.
http://fakegate.org/
• Jim D
By then he had already had his formal request for a list of their donors denied, so presumably this sprung from that refusal which might have sparked an interest to see what they might be hiding behind the curtain there.
• hunter
Barry,
This leaves Gleick’s scam be seen as the cold blooded effort it was.
I wonder who helped him put this together?
• SamNC
Mandia?
• gcapologist
I believe his phishing went on for a week. PG had plenty of time to reflect on the ethics of his actions…..
85. Understanding climate and the environment is not a “movement”. The drive is instead just intellectual curiosity and is part of human nature.
I remember a discussion with Wojick last year where he wished he could get a grant to research climate and chaos, but now he has taken on money to educate people … on stuff that he presumably doesn’t know anything about. Hypocrisy is such a large target. The hypocrisy here is that Heartland is clearly a lobbying organization yet they claim tax-free status. This is all laid out in gory detail by John Mashey’s expose on fake science, fakexperts and funny finance which he released last week. As they say, “it’s the hypocrisy, stupid” and identifying who are the biggest hypocrites.
One side’s idea of hypocrisy is that of Gore owning a mansion, or RFK Jr opposing wind turbines around Cape Cod, or McKiibben taking a jet to a conference.
The other side’s idea is that of lobbyists parading around as if they want to educate lay-people where in fact the lobbyist’s goal is to keep the public in the dark. So Heartland enjoying tax-free status while railing against government-sponsored initiatives is the comparative hypocrisy.
Those are the targets in the political realm. The scientists trying to understand climate and the environment may be oblivious to the political gamesmanship. Often they are just nerds with some intellectual curiosity.
• hunter
Web,
Don’t be an idiot.
Of course AGW is a movement.
• GregS
Hunter, according to the ClimateGate II emails, AGW is a “cause” with a carefully honed but all too fragile “message”.
• manacker
hunter and Web
Of course AGW is a movement.
Yes. And a very highly (taxpayer) funded one.
It was on a roll which reached its peak in 2007, with the fawning media swallowing IPCC AR4 hook, line and sinker, Nobel Peace Prizes and an Oscar being handed out, and bevies of politicians calling for action (i.e. more taxes) to save the planet from ourselves.
CAGW was not only “in” and “cool” – it was the “PC”.movement.
But several things happened.
– Climategate and ensuing revelations of IPCC falsifications and exaggerations raised serious doubts about the behavior and credibility of the “mainstream consensus” scientists
– Several scientists distanced themselves from IPCC, its “consensus process” and its understatement of uncertainties – and started becoming vocal.
– Climate conferences at Copenhagen, Cancun and Durban were spectacular flops, with no political decisions made to combat CAGW, as had been hoped..
– Groups, such as Heartland, gathered and published data and reports that contradicted the IPCC “consensus” CAGW position and held climate conferences of their own, where skeptical scientists could present their findings.
– And – worst of all for the CAGW movement – it stopped warming.
– “Mainstream consensus” scientists first denied that it had stopped warming and, when this no longer was possible, scrambled for rationalizations for the “unexplained lack of warming”, ranging from previously underplayed “natural variability” to “Chinese aerosol emissions”. But these rationalizations all rang hollow.
So, like all fads, CAGW has reached its zenith and is in decline today.
Events like “Heartlandgate” will accelerate this process, as will a continuation of the current “lack of warming”.
But, despite the fact that it has become a multi-billion dollar big business, the decline and eventual end of the CAGW hysteria will occur in either case – only to be replaced by another fad and another movement.
Max
• Don’t twist my words Web. Just because I want to do frontier research on chaotic climate modeling doesn’t mean I don’t know anything about climate science, quite the opposite in fact. Nor have I taken any money yet, but I hope to. Lobbying means targeting Congress regarding particular legislation. Public advocacy and education is not lobbying; in this case it means fighting an overzealous ideological movement, namely the climate greens. You are being especially obtuse today.
• “David Wojick | August 13, 2011 at 1:05 pm |
Yes Web, that sounds about right. But it is not how the research program looks. If they would just give you and me the billions we could straighten it out, ha ha. Actually I would settle for a modest grant to explore the chaos, but I know of no RFP along those lines.”
It is not hard to find out what opinions Wojick has. It is all archived in the comments section on this blog.
https://judithcurry.com/2011/08/07/carbon-cycle-questions-part-ii/
“Human behavior, including scientific discourse, exists in the world. It is therefore open to scientific analysis. That is what I do.”
“I think I understand the climate debate better than anyone, not because I know more about climate but because I know more about the logic of complex issues. “
“I am proud of my advocacy work, especially as I am winning and you are losing.”
“David Wojick | April 11, 2011 at 9:33 am |
I have been an energy policy analyst since 1992 and the only thing new here is that the greens are trying to recover from a crushing defeat. It is not a question of changing the game, it is that the game has changed on them. But without dangerous AGW there is no policy basis for decarbonization, so the world is moving on. However, dangerous AGW is alive and well as a strong minority view so the game is far from over.”
• Latimer Alder
@webbie
So your real beef is with US taxation laws, not with Heartland. Fair enough, though that seems like a relatively trivial reason for you guys to get all paranoid about Joe Bast and his team.
How many other lobbying institutions also benefit from the same taxation laws without you getting so agitated about their activities?
• John Carpenter
WHT, I guess orgs like Sierra Club, WWF, Greenpeace, etc… are not part of a CAGW movement? Am I missing something here? How do they differ from HI? Other than being on the ‘other’ side.
• Jim
Wub Hubble,
John Mashey??? ???
86. There’s an eerie symmetry, or asymmetry, between this and the UEA email theft.
This is exactly what I’ve been wondering over the years. Why target UEA? A small rural univ department. It’s true that PJ has been a scientific pioneer, and can be tactless, but still, of all places in the world…
• hunter
Nick,
When was it established as a theft?
Are you trying to suggest that Phil Jones and the UEA CRU was just a little underfunded org stuck in BFE united Kingdom?
• Ged
Because it came from the inside not through impersonation and fraud; and UEA is publicly funded, while Heartland is a private organization. Don’t conflate the two legally (or morally).
The e-mails were also just people talking; the Heartland docs were actual financial, donor, and employee information as well, something any corporation would label sensitive.
There are no parallels unless you don’t bother looking at any of the details beyond “something was leaked”.
• The emails included reviews of papers, grant application matters – highly sensitive. They even included letters to Briffa from his financial adviser discussing his personal finances.
• Heartland is a non-profit and could get their tax-free status pulled at any time if they break the lobby law regulations.
Find out if they filed IRS Form 5768. That becomes public information.
John Mashey has looked at this angle quite a bit.
http://www.desmogblog.com/sites/beta.desmogblog.com/files/fake.pdf
“Under Jay Lehr and James Taylor, anti-science permeated Heartland’s Environment and Climate News (E&CN) sent mostly to elected officials. Heartland incessantly touted its access and influence with such officials, but its tax forms claimed no lobbying. It ran “fake science” conferences, paying for government staff attendance. It sent money to foreign noncharity advocacy groups, sent anti-science handbooks to school boards and urged parents to complain. It has been criticized in Nature and Science.”
• WebHubTelescope,
Thank you for that interesting link.
Here’s a relevant paragraph from Joe Bast’s email:
> We send publications to every national, state, and 8,400 county and local officials in the U.S. on average about once a week. 79% of state legislators say they read at least one of our publications. “Environment & Climate News,” one of six monthly publications we produce, is read by 57% of state legislators, a higher percentage than read the New York Times. It has been published continuously for 15 years, and every issue features the work of leading climate realists. No other organization produces a regular publication that reaches more people with this message.
I believe this counts as lobbying, am I right?
• “I believe this counts as lobbying, am I right?”
Probably, yet it all fits under IOKIYAR so nothing will be done about it. Fake science for fake experts.
• WebHubTelescope,
I did not know that there existed an acronym for “It’s OK If You’re a Republican.” That does sound like another way to talk about entertaining some kind of double standard, and I believe the concept of double standard deserves due diligence. Some obscure sources tell me that Henry W. Johnstone considered the double standard as the mortal sin of argumentation.
Keeping the discussion of your link for another time, I’ll observe that lobbying is considered as one instance of activism. It would be interesting to note the different uses of the epithet “activist”, here and elsewhere. We could almost feel that “activist” has become a derogatory term.
If you ever have more resources you’d like to share, you can drop me an email, or submit it on my tumblog.
Thanks again,
w
• SamNC
“Fake science for fake experts”. Just name af ew for you webby, Hansen, Trenberth, Mann etal.
• GregS
Only asymmetry.
UEA is a public institution that was illegally withholding public data in violation of FOI laws. ClimateGate only revealed what should have been legally revealed.
Heartland is a private institution. The public had no legal right to the information gleamed by the phishing attack.
Why UEA? Because it was home to several IPCC lead authors and the temperature data sets that the IPCC used to buttress it’s opinions. Public data that should have been available to the public.
• “UEA is a public institution that was illegally withholding public data in violation of FOI laws.”
Nonsense. FOI applications went through normal processes. They made decisions that you didn’t like. These are subject to appeal, not burglary. One was indeed overturned on appeal.
• Scott Basinger
I’m of the opinion that they were leaked.
Further assymetry. They clearly show evidence of wrongdoing including prima facie evidence of subversion of FOIA requests – they were only saved by the statute of limitations. The Heartland documents don’t show very much of interest, to be honest. The only document even raising an eyebrow is completely fake.
Climategate had exactly the intended effect. Whereas this occurrance had exactly the opposite of the intended effect.
• Heartland Institute is a federal tax exempt 501(c)(3) charity, and so they are not strictly a private enterprise.
http://heartland.org/funding
If they want to reject that status and become a private-for-profit enterprise then they might be able to make the case for unlimited lobbying (this follows the Citizen’s United case, which sets the precedent that corporations are people).
But this stuff is not really interesting because it is comprised of fake experts doing fake science which leads them to fake outrage.
• John
Isn’t UEA where all the climate records were held? Is that a good reason to want to know whether the keepers of the records — past, present, and future — are being accurate and dispassionate in their assessment?
There was certainly good reason in Nov 2010 to think that Mann and Jones and the rest of that crowd were neither accurate nor dispassionate.
With regard to the “theft:” — suppose “FOIA,” the alleged leaker, was an insider — a whistleblower. Isn’t there the possibility that his identity is known, but if he or she were exposed as a whistleblower who knows that things were doctored (Harry the programmer, for instance — see Climategate emails), things would be worse for UAE and the climate community, than if view is perpetuated that this was email theft (which indeed it may be).
• “Isn’t UEA where all the climate records were held?”
No. National Met organisations hold the records. UEA is a university. It studies them.
• Latimer Alder
@nick stokes
‘“Isn’t UEA where all the climate records were held?”
No. National Met organisations hold the records. UEA is a university. It studies them.’
Please remind us all what the acronym CRU stands for in the name of the famous datasets HadCRUT3 and CRUTEM3.
Because I believe it to be Climatic Research Unit. They do not just ‘study’ the data. They prepare it. Their grubby fingermarks are all over them. If they bothered to record how they had manipulated them, we would even know what they had done to manufacture them. But they don’t so we can only guess. And hope that Mr Transparency himself, Phil Jones, has done a good and honest job.
Meanwhile over to our correspondent at Porcine Aviation…
• HADCRUT3 and CRUTEM3 are not datasets, they are global temperature indices. They are averages calculated from data supplied from elsewhere. I do that too.
• Latimer Alder
@nick stokes
‘HadCRUT3 and CRUTEM are just indices’.
H’mm. So why does CRU get about £200,000 pa in grants from the US to prepare these indices which presumably need no more than a reasonably powerful PC and a couple of batch programs to compute?
I have a nice new laptop, and an hour or so a week. I’ll do it for £100K. Bargain!
• “So why does CRU get about £200,000 pa in grants from the US to prepare these indices”
I don’t believe they do.
• Latimer Alder
@nick stokes
CRU themselves refer to them as datasets throughout.
http://www.cru.uea.ac.uk/cru/data/temperature/
Note, for example, the opening remarks in the documents above
‘From the beginning of January 2006, we have replaced the various grid-box temperature anomaly (from the base period 1961-90) datasets with new versions, HadCRUT3 and CRUTEM3 (see Brohan et al., 2006). The datasets have been developed in conjunction with Hadley Centre of the UK Met Office. These datasets will be updated at roughly monthly intervals into the future. Hemispheric and global averages as monthly and annual values are available as separate files’
Your assertion that they are not datasets is contradicted by the authors themselves. You are wrong.
• “Your assertion that they are not datasets is contradicted by the authors themselves. “
Well, you can call any set of numbers a dataset. But they are not cliamte records of which they are the “keepers”.
“grid-box temperature anomaly (from the base period 1961-90) datasets”
A grid-box anomaly dataset is a computed average, not an original record.
• Latimer Alder
@nick stokes.
‘Well, you can call any set of numbers a dataset’
They did. I merely reflected their terminology. You then asserted that we were both wrong. Now you concede the point.
?? Are you new on the ‘Nick Stokes’ shift? The one who used to do this instant rebuttal stuff was a bit more up to the mark. Has he retired…or found something useful to do instead? Did he not leave any advice for you as the newbie?
• Latimer Alder
Why target UEA?
Because if that is the institution you work for and you are disturbed by their antics, that is the only thing you can do. You have access to their mails. You do not have access to all the other ones at other institutions. They are the only ones you can release.
But I agree with you – it seems unlikely that an outside hacker would spend so much effort on targetting UEA – and having done so not moved on to other institutions. Yet more circumstantial evidence of a inside whistleblower rather than an outside hack.
I;d add that Jones being ‘tactless’ rather underplays his role in such wonderful remarks as
‘Why would I show you my data when you’ll only try to find something wrong with it?’
‘If they find out there’s FOI in UK, Ill destroy my data’
and other such bon mots. This is not tactlessness, this is obstruction of the scientific process at the very least.
• RickA
Nick:
I think it is because Phil Jones asked others to delete their emails to try to avoid the FOI request – and Phil Johns is from UEA. I think FOIA was an insider and it pissed him off. That is my opinion anyway.
• Unlikely. But in any case, an “insider” would not have had access to PJ’s emails before the hack.
• I think that the role of FOIA is easily overemphasized by Americans, because the role of FOIA has been much stronger there. Similar laws are completely unknown in most European countries and as far as remember the law is rather recent in UK as well or at least its applicability to such information as the UEA climate data was recent at the time of the requests. Someone from UK can certainly tell better, what the situation was there at the time the requests were made and a few years earlier.
• Pekka,
Indeed so. The UK FOIA was enacted in 2000 by the Labor government, but didn’t come into force re universities etc until 2005.
• Latimer Alder
@nick stokes
‘But in any case, an “insider” would not have had access to PJ’s emails before the hack’
????? You really don’t understand much about IT, Nick.
IT systems do not run by themselves. Even the relatively small CRU has its own IT manager, as well as the staff that run the larger UEA systems. IT systems have master passwords that are known by the IT staff and allow just about anything to be done. Plenty of internal folk would have had access to PJ’s emails perfectly legitimately as part of their day-to-day work. Let alone anybody who had the time and inclination to do so illegitimately. one of the
• “Plenty of internal folk would have had access to PJ’s emails perfectly legitimately as part of their day-to-day work. “
Not legitimately. In any University-like system I have encountered, there are privacy policies, and any IT staff member who used privileges to trawl through a users email would be sacked.
• Latimer Alder
@nick stokes
Having access to and ‘trawling through’ are different things. You earlier tried to use the ‘lack of access’ argument to dismiss the possibility of an insider being responsible. Here are your words again lest you have forgotten them
And you now agree that this is not the case.
To reiterate. Many insiders may have had straightforward access to PJ’s emails without any need for an outsider hacking attack. To argue otherwise is naive and silly.
Question:
If you were Ed Acton, Vice Chancellor at UEA and it had been discovered that the Climategate liberator was one of your own, would you sack them? Leaving them at liberty to discuss all their inside knowledge with the press and the blogosphere? And with no residual loyalty to your institution? Or would you have them prosecuted so that public evidence could be heard?
If not, what actions would you take?
• They would have to “trawl through”. Rick’s claim is that they were shocked at what they read. There are a lot of emails; it took the blogosphere days to find bits that they could spin. It’s not like spotting porn pics. And of course, that implies that IT staff have enough attachment to Steve M’s FOI rights to risk their jobs reading the emails.
• Latimer Alder
@nick stokes
‘And of course, that implies that IT staff have enough attachment to Steve M’s FOI rights to risk their jobs reading the emails.’
H’mm
Who exactly do you imagine would catch them and take action to fire them? The vice chancellor? Phil Jones himself – who admits that Excel is beyond his competence? The cleaners? Or would it be the IT staff themselves?
I work as an IT manager. An organisation can have written policies about a zillion and one things, but unless they are enforced, they aren’t worth the paper they’re written on. And reading people’s e-mails comes pretty low down the list of misdemenours I would actually worry about. Changing somebody’s disciplinary record or reading their medical files is bad. Reading their e-mails is probably undetectable in any reasonably ‘free’ system, and unlikely to attract much sanction. The average IT manager has a zillion much more important things to worry about.
I work as an IT Manager. Your understanding of the realities of life in IT is very limited.
• > I work as an IT Manager.
Aren’t you semi-retired, Latimer?
• steven mosher
“There are a lot of emails; it took the blogosphere days to find bits that they could spin”
Actually not. On day one I posted what McIntyre calls Mosher’s Greatest Hits. There are the mails that get quoted over and over again.
FOIA also providing a reading guide in his opening note. There are precious few mails that form the heart of the argument.
It would help if you aquaint yourself with the actual history and the
statistics covering which mails are actually discussed in existing work on the mails. There is not much outside the few mails called out by
FOIA and me on day one. To be sure the real story, FOIA, lies in different mails. Mails that are spun by CRU.
• steven mosher
“Unlikely. But in any case, an “insider” would not have had access to PJ’s emails before the hack.”
Well, that is untrue. We actually have written evidence of people having access to other peoples mails. In CG II we have evidence that other people used Jones computer.
To find this you have to search hard and deep.
• steven mosher
‘They would have to “trawl through”
Actually not. The mails were on a back up server. Very simple to write a script to trawl through the mails and select those that match a keyword list. But first you have to decompress them as the mails were stored compressed ( recalling some testimony here from a couple years back, so folks can double check this )
Very simple to construct a keyword list: scrape climate audit and pull out
terms from that site that are popular, names as well. What you end up with is a collection of mails that look interesting to readers of CA.
• steven mosher
RickA
“I think FOIA was an insider and it pissed him off. ”
He would not be pissed off by FOIA violations. That is the rationalization. The motive is anger, but its more personal.
This case is not as clear as Gleick, but..
• Latimer Alder
@willard
‘Aren’t you semi-retired, Latimer?’
Yep. The clue is in the ‘semi’ bit. I still do short term relief contracts if they are offered to me and if they are attractive enough. But not permanent stuff.
And thank you for reading my denizens entry. When do you plan to have yours up so we can all learn about your background?
• > But first you have to decompress them […]
Is that necessary?
Why is this relevant to mention this?
• Latimer,
Thank you for your reply. I was wondering if your status has changed since you wrote about this. You regularly write about the fact that you are speaking from the authority of a guy who worked as an IT for 30 years.
Thank you for your interest in my background. When I’ll use my own experience to speak from authority, I’ll let you know about it. Even if you have better things to do: watching grass grow, paint dry, trying to shame Nick Stokes, etc.
• RickA,
You believe that the “miracle worker” could have been a whistleblower:
> I think FOIA was an insider […].
I believe you have experience with the law. The first substantial post at Steve’s was the UK legislation for whistleblowers:
http://camirror.wordpress.com/2009/11/21/uk-whistleblower-legislation
One has to wonder why this has not been done in the Heartland affair, but nevermind that for the moment.
My question for the moment is this one:
Do you believe that this legislation still protects the miracle worker (aka FOIA) after the second release of emails?
Many thanks!
• Jim
“Why target UEA?”
??? For real question???
• Mark F
Oh, probably something to do with an insider exposing UEA fraud, as opposed to an outsider committing fraud to expose legitimacy inside HI. Subtle difference, I know, but some get it. This is amplified, of course, by UEA being funded by the public purse, making any work therein public property, while HI is privately funded, with every right to keep their inner workings private, save for IR tax disclosures. Get it yet? Didn’t think so.
87. Paul in Sweden
“So, imagine you are a climate scientist and climate change ideologue, and want to “take down” the single organization (or individual) that is doing the most damage to the movement (i.e. with the end result of thwarting CO2 emissions/stabilization policy). Who would you target?”
The biggest denier of CO2 dominated climate change is clearly Mother Earth. Mother Earth just does not understand the Climate Models.
88. John
Two reasons to attack Heartland.
First, the positive one: You can create the impression in the media that Heartland wants to “brianwash” you child in public school (they would care to differ, of course, but I haven’t heard anyone in the media suggest that they might have a point that kids are being taught only one side). They may not even accept that the world is warming. So if you want to create a straw man, they are it.
Secondly, the negative reason to go after Heartland. Good luck with trying to expose Steve McIntyre or Ross McKittrick or Judy Curry or Anthony Watts or Richard Lindzen as being light on science or policy. Wouldn’t work.
So if you are losing the science and policy wars, create a strawman of an entity that can be more easily made into a charicature (sp?).
• P.E.
Especially if you can associate the Koch bros with it. That’s fifteen extra points right there.
89. huxley
Dr. Curry, on the NPR interview you said:
It’s not helping the credibility of scientists or the trust that the public puts into climate scientists and therefore on the science because it’s hard for the public to understand the nuances of such a complex subject — it’s hard for the scientists to even understand — so [members of the public] have to trust the experts on some level and when the experts behave like this it’s a big loss of credibility for the whole climate science enterprise.
Thanks for saying this. It’s the quandary in which I find myself.
I do wish that orthodox scientists and their advocates would understand that arguing that their behavior is not criminal or no worse than some skeptics is not reassuring.
90. Perplejo sin guia
Who would I target?
Science is scientific method (falsifiability, reproducibility) with scientific attitude (disposition to be taught by nature). As part of the climate science community has apparently given up science, their obvious targets would be S. McIntyre (pointing out to their failure on method) and J. Curry (pointing out to their incapability of smashing their pride before Nature).
Sorry for my english.
91. **BREAKING** original post is updated with email message from Joseph Bast, explaining “why target Heartland?”
• Michael Larkin
Thank you, Joe Bast! The resume of Heartland’s activities is something I personally found very informative.
92. MarkB
I keep on saying it here – Revkin is not ‘in the middle.’ Revkin is a career global warming ideologue and activist, who happens to have a forum at the New York Times. Revkin is happy to tell you that anthropogenic global warming is going to destroy the planet unless we take drastic actions to reform the energy sources of the global civilization. There is nothing ‘middle’ about that. The only difference between Revkin and some other advocates is that he recognizes the self-defeating actions of some of his fellow-advocates, and cautions them to change their strategy.
Revkin still talks the language of ‘deniers,’ in spite of being called out for it. And now he carefully qualifies the crimes of Gleick (personal tragedy, doesn’t change the science). Revkin is more measured than Joe Romm, but he sees Romm and himself fighting on the same team, in spite of Romm’s attacks on him.
• “Revkin is not ‘in the middle.’ ”
I disagree. Revkin seems to draw flack about equally from the skeptics and the “warmists” — probably the best indication that he is doing his job right. For the most part, he seems to be able to disengage his personal beliefs from his journalism.
That said, the journalist who is really shining on the Gleick affair is Megan McArdle at the Atlantic — who is one of the few journos actually doing investigative reporting — even if she’s just channelling Mosher. Very good writer, sharp cookie, and entertaining too. Here’s her Atlantic page:
http://www.theatlantic.com/megan-mcardle/
93. GaryM
““So, imagine you are a climate scientist and climate change ideologue, and want to “take down” the single organization (or individual) that is doing the most damage to the movement”
Joseph Bast’s emailed comment notwithstanding, the left has been actively, and to a degree successfully, targeting the greatest threat to their agenda for decades, and it isn’t Heartland.
Heartland is a great institution, as are Heritage, Cato, the Pope Center and others. But political power resides with the voters ultimately. And all those great ideas coming out of the think tanks are useless unless people hear about them.
Where do the rank and file voters hear about conservative arguments and alternatives to the group think of CAGW, “social justice,” redistribution of income, class warfare and other propaganda of the left?
Conservative media. Who have been the most often reviled communicators on the right for the last decade or so in the US? Limbaugh, Fox News, Hannity, WUWT (on climate). These have not been targeted for their own ideas. They have been demonized because they are conduits for the conservative alternative that progressive activists are desperate to silence. To the extent Heartland, Cato, Heritage et al have an impact on actual elections, it is largely because their ideas are disseminated by these evil mouth pieces of the right.
Remember how the biggest devil of them all was Glenn Beck? Now you hear nary a word about him. His ideas haven’t changed. He is still as, shall we say, bombastic as he ever was. The difference is that he no longer has the large audience he had on Fox. When he did a show on Hayek, The Road to Serfdom shot to the top of the Amazon best seller list over night. That was when he could not be tolerated. Average voters actually being exposed to something other than the left’s caricature of the free market? Never! Now that he has faded into the ether, he is no real threat, so there is no need to attack him.
Gleick didn’t target Heartland because they were a threat, and he just happened to get a memo someone else faked in the mail. Gleick was in a flame war with a Heartland blogger and getting his butt kicked. So he lied to get some internal document from Heartland, then used them to create a fake strategy memo that he could use to embarrass Heartland. Whether he did so alone, or with the urging and assistance of Desmogblog and the other mouthpieces who spread his lies, will be seen after Heartland conducts diuscovery in whatever civil case they file.
94. IPMeng
Al Gore. No contest.
95. I just read the email appended to the post,
From: “Joseph Bast”
To: [email protected]
Sent: Friday, February 24, 2012 1:58:19 PM
Subject: Why was Heartland targeted?
Of the many answers so far to this thread’s question, “Why target Heartland?” Bast’s is by far the most convincing. Bast makes a compelling case that Heartland does a better job than any other organization or individual in getting out their view of the state of global warming.
One remark caught my eye: “We deliberately bypassed the mainstream media.” I know of no area of science where scientists aren’t delighted to get their ideas into the mainstream media. Clearly whatever it is that Heartland is promoting is not science. I’ll refrain from any debate as to what it is since that’s outside my expertise, which is science.
• Markus Fitzhenry
Vaughan says shallowly:
One remark caught my eye: “We deliberately bypassed the mainstream media.”
That went right over the top of your head, Vaughan. The inference was that MSM are dishonest about AGW.
• How illogical of me, MF. From the fact that the MSM didn’t hush up the Gleick incident I stupidly assumed they’d be equally reliable about other AGW errors. Evidently your more powerful brain has ways of overcoming such simple-minded reasoning.
• David Springer
I read that as the mainstream media bypasses HI not the other way around. Just puffery by Bast to call it a choice on their part.
• Maybe, but I wasn’t about to pass judgment. I only object to obvious inconsistencies like Lindzen’s rubbish.
• Latimer Alder
@vaughan
Heartland makes no secret that it is a lobbying organisation. It does not target the MSM because the people it wishes to influence are much smaller in number and can be better addressed outside of this arena.
Example: If you wish to sell BMWs to upmarket city brokers, you do not waste your money on advertising in the middle of an afternoon soap opera. The wrong people are watching. Similarly you do not advertise a new low cost family meal for four from a discount supermarket in ‘Filthy Rich and Want To Flaunt It Monthly’
Your argument that somehow the lack of MSM exposure means that by definition they are not discussing science is bizarre. I was under the impression that climate science was only discussed in ‘peer-reviewed’ journals, and not the New York Times or the Guardian either.
• manacker
You make an excellent point when you write:
Heartland makes no secret that it is a lobbying organisation.
It is a shame that IPCC does not do the same.
Max
• Is IPCC an organization at all?
• While one can read the mission statements and other organizational information of each of the IPCC, the Heartland Institute , and the NIPCC, separately at their respective websites, it may be useful to collect them all in one place where they can be easily compared.
From the IPCC’s page ORGANIZATION (based in Switzerland):
The IPCC is a huge and yet very tiny organization. Thousands of scientists from all over the world contribute to the work of the IPCC on a voluntary basis as authors, contributors and reviewers. None of them is paid by the IPCC. The work of the IPCC is guided by a set of principles and procedures.
Their work is supported by a central IPCC Secretariat, whose role is to plan, coordinate and oversee all IPCC activities. The IPCC has a core staff of 12 officials.
The IPCC is currently organized in 3 Working Groups and a Task Force. They are assisted by Technical Support Units (TSU), which are hosted and financially supported by the Government of the developed country co-chair of that Working Group/Task Force. Working Group I deals with “The Physical Science Basis of Climate Change”, Working Group II with “Climate Change Impacts, Adaptation and Vulnerability” and Working Group III with “Mitigation of Climate Change”. Working Groups also meet at the Plenary at the level of Representatives of Governments. The main objective of the Task Force on National Greenhouse Gas Inventories is to develop and refine a methodology for the calculation and reporting of national GHG emissions and removals.
The IPCC breaks down the contributions to its Trust Fund by country in e.g. this 2009 budget which shows the US contribution as being at a steady $1.6M/yr (Tables 2 and 3) since the IPCC’s inception in 1989, representing about a third of the total contributions. However like all of the countries participating, the US also has IPCC-related expenses at home whence one must go to the November 2011 GAO report for the total US IPCC-related expenditures. Over the past decade this has averaged$3.11M a year, split 61/39 between the US Department of State, who funded “administrative and other expenses” of $1.9M/yr out of their$16.4B (FY2010) budget (from which the $1.6M contribution to the IPCC Trust Fund presumably came), and the US Global Change Research Program, who provided$1.21M/yr out of their $1.16B (FY2009) budget for “a technical support unit that helps develop IPCC reports” (Chris Field’s TSU for WG II at Stanford perhaps?). Last February the House of Representatives voted 244-179 to remove this huge burden from the shoulders of US taxpayers, who judging by the widespread news coverage must have been immensely grateful for being able to afford an extra jellybean a year for each of their children. ;) From About (The Heartland Institute): The Heartland Institute is a 28-year-old national nonprofit research organization dedicated to finding and promoting ideas that empower people. Founded: Heartland was founded in Chicago in 1984. Mission: Its mission is to discover, develop, and promote free-market solutions to social and economic problems. Staff: A full-time staff of 40, including 25 working out of the Chicago office and five in the Washington DC office. Joseph Bast directs the Chicago office, Eli Lehrer directs the Washington DC office. Herbert Walberg is chairman of the board. Policy Advisors: Approximately 130 academics and professional economists participate in its peer review process, and more than 200 elected officials serve on its Legislative Forum. Publications: Heartland sends six monthly public policy newspapers addressing the major domestic public policy issues to every national and state elected official in the U.S. plus 8,400 county and local officials and thousands of civic and business leaders. It also produces books, policy studies, and booklets. Communications: We appeared in print and on television or radio nearly 1,400 times in 2010. More than one million people visited our Web sites in the last 12 months. Our Facebook page registers nearly 53,000 fans and approximately 300,0000 post views every week. Government Relations: Our government relations staff made more than one million contacts with elected officials in 2010, 14,715 of those contacts were one-on-one either in person, by phone, or by one-to-one emails. Survey Results: A telephone survey of randomly selected state and local elected officials conducted in 2011 found 79% of state legislators and 63% of local elected officials read at least one of our publications. 45% of state legislators say a Heartland publication changed their mind or led to a change in public policy. Funding: Approximately 1,800 supporters support an annual budget of$6 million. Heartland does not accept government funding. Contributions are tax-deductible under Section 501(c)(3) of the Internal Revenue Code.
Assuming the bulk of this $6M is coming from the US, US support of Heartland is roughly double its support of the IPCC. Assuming elections are decided by who has the biggest “voter education” budget, Heartland’s chances of winning over US voters to their opinion on AGW should be about double those of US IPCC supporters. From About the NIPCC): The Nongovernmental International Panel on Climate Change (NIPCC) is what its name suggests: an international panel of nongovernment scientists and scholars who have come together to understand the causes and consequences of climate change. Because we are not predisposed to believe climate change is caused by human greenhouse gas emissions, we are able to look at evidence the Intergovernmental Panel on Climate Change (IPCC) ignores. Because we do not work for any governments, we are not biased toward the assumption that greater government activity is necessary. The NIPCC began as an independent entity in 2003, received its present name in 2007, and developed links with Heartland starting I think around 2008. I have no idea of their budget, nor of what percentage of Heartland’s impact can be attributed to NIPCC, any guesses? • Michael Vaughan raises a vry impotant point. Heartland had tyo pay Singer over$100,000 to concoct that steaming pile of BS which is the NIPCC report. The IPCC didn’t have to pay any of the scientists working on the AR4 a single red penny.
• A cross between MLK’s “The truth shall set you free” and Stewart Brand’s “Information wants to be free”?
$100,000 to concoct that steaming pile of BS Hazard pay? • Oops, John 8:32, not MLK. (I was going to check it and forgot.) • Your argument that somehow the lack of MSM exposure means that by definition they are not discussing science is bizarre. What’s bizarre, Latimer, is Bast’s statement about avoiding the MSM, which now that I look at Heartland’s About page again I notice says, We appeared in print and on television or radio nearly 1,400 times in 2010. Maybe television and radio are no longer mainstream media in the UK, but they certainly are in the US. I was under the impression that climate science was only discussed in ‘peer-reviewed’ journals, and not the New York Times or the Guardian either. Again, I can’t speak for readers of the Guardian, but I can assure you that New York Times readers are very interested in a wide range of topics in science, technology, etc. (So wide they’ve even reported on my own research on the Pentium division bug, small webservers, and Thumbcode.) Here are some up-to-the-minute climate change articles, working backwards from today (Friday). Gleick has been providing half of the fodder this week. Friday: Study Predicts a Bleak Future for Many Birds Thursday: Behind the Controversy, an Effort to Rewrite Curriculum on Climate Change Thursday: A Chat With RealClimate Blogger Gavin Schmidt Wednesday: More on Peter Gleick and the Heartland Files Tuesday: Peter Gleick Admits to Deception in Obtaining Heartland Climate Files Monday: Activist Says Heartland Climate Papers Obtained by Deceit Sunday: Warm Winter is Casting a Chill on Ice Fishing I would certainly hope there is some room for disagreement on this blog as to which of these articles are merely lies spun by the New York Times. And that’s just climate. Researchers love seeing their work exposed to the public in all forms of media, especially radio and TV. Everyone gets their 2 minute segment of fame, sometimes several if they’re lucky. Apparently the Heartland Institute loves this too, making Bast’s statement that they don’t puzzling. Bizarre, as you would say. • kim All the News that’s Left to Print. ====================== • hunter Dr. Pratt, You are scrambling. It is unseemly, sir. • How so, hunter? • Markus Fitzhenry And these scrambling losers think they should be respected and believed by children. Gross assault upon intelligence is being perpetrated by these fools. Disgusting disillusionment for all to see. They are and will be held up to ridicule for some time to come. Deservedly so. Unseemly indeed. 96. P.E. I don’t know if anyone else has mentioned this, but maybe this isn’t about climate at all. Occam’s razor. Heartland is working a whole range of issues including Cook County debt. Maybe they got on somebody’s radar screen for reasons having nothing to do with climate, and when the opportunity presented itself to Gleick to “get” them, he went for it. It’ll be interesting to see just how much cooperation Heartland gets from the DoJ. I got a hunch that they’re not going to get much, if any. 97. pokerguy In support of my theory that Gleick was seeking revenge for his own sense of shame and embarrassment at turning down the debate invitation, I find this at WUWT(re the Gleick emails to HI): “The newly released emails also reveal the first email from Gleick to Heartland was sent on January 27, 2012 – the same day he rejected a cordial invitation to debate climate science at The Heartland Institute’s 2012 anniversary benefit dinner in August. “ 98. Holly Stick Dr. Curry, it’s not that Heartland wants to produce “educational materials that express their viewpoint” They want to produce educational materials that tell lies. They want to teach lies to children. And you have descended so far into the muck of academic dishonesty that you will defend those paid liars. Shame on you. • Latimer Alder @holly stick Please can you provide some evidence that they wish to teach lies to children? Other than the faked memo which has Peter Gleick’s grubby and disgraced fingerprints all over it. Note: To justify your statement you will need to show that they intend to teach things that are factually untrue, not merely matters of differing opinion. This is a high hurdle to cross. • Anteros Latimer – I think also you’d have to show that they know or believe the things they teach are factually untrue. I think people like Greenpeace are very keen to distribute and teach things that are factually untrue, but I don’t doubt that they believe otherwise. I think Holly lives in an absolutist/literalist world and is amazingly lucky to have found herself on the side of people who tell the truth. Ish • Holly stick Please elaborate on the nature of these lies Tonyb • Holly Stick http://climatecrocks.com/2012/02/17/the-real-story-of-heartland-the-template-of-lies/ Be sure to check out Table 1 here, if you have the courage to: http://www.dailykos.com/story/2012/02/20/1066562/-Climate-Change-science-consensus-A-simple-table-to-consider-?via=search http://www.latimes.com/news/opinion/opinionla/la-ed-climate-20120220,0,3564279.story The liars are being named and shamed more and more every day. When Peter Gleick did something that was wrong, he had the guts to admit it and apologize. The Heartland Institute cowards just keep lying. • Holly Stick “…To avoid extinction they addict children to something that will eventually kill many of them.249 Joseph Bast wrote what he could to support them and then cited those articles to increase his funding.250…” Page 45 (be sure to read the whole page): http://www.desmogblog.com/sites/beta.desmogblog.com/files/fake.pdf On climate lying, see page 51. Of course there is much more, but those pages will do for a start. I think Heartland claims to be non-partisan; does anyone believe that? • Holly Stick Can an organization that helped to get children addicted to smoking be trusted to teach them about anything? • Latimer Alder @holly stick I read your links. I can see lots of areas where you disagree. But your claim was not that they disagreed with your interpretation. It was that they are planning to lie in the future. To substantiate this claim you need something considerably more persuasive than some puff pieces by known opponents diasgreeing with them. Unless I have misread your submissions, you have failed to do so. I expected no more, so was not disappointed. • Anteros I expected nothing, received less, and was thereby somewhat baffled.. • Holly stick your 4.27 I looked at your list on the first link. In 1723 the Royal Society insisted that those subscribing to its international meteorological association should site their thermometer inside a north facing room that was usually unlit. Between the 1800’s and the mid 1950’s every national science authority believed that Co2 levels fluctuated between 300 and 400ppm on a yearly basis. As we learn more, science is supposed to evolve. The book of ‘Irrefutable science facts 1830’ would look utterly different to that of an edition published this year and in turn the irrefutable scientific facts in 2100 will no doubt look very different to today. I am not sure whether you are attempting to secure a place on Scott Mandias new course in wrting satire when you cite desmogblog. You should immediately go to the top of the class. tonyb • SamNC holly stick is as sick as PG. • dennis adams Your side never disappoints. Anyone who disagrees with you is a liar, crook, stupid, dishonest and every other childish ad hom. Why dont you lift up the argument to a level that the rest of us use. • hunter Holly, You mean lies like “Creationism = climate skepticism”? Or lies like “the science is settled”? Or lies like “Heartland Institute is hugely funded by big oil”? You are predictable, rude, hypocritical, self righteous and boring. Please keep posting. you are a dream come true for people who want the ranks of skeptics to grow. • hunter Holly, Are you really so confused as to not know the difference betwen opinion and fact? Oh, wait: You and so many other believers think “fake but true” is a valid for of evidence. Sorry. Carry on, and thanks for helping the skeptical cause. • John Carpenter Holly, you remember the exchange we had on the ‘Climate Change and War’ thread? Before Gleick admitted to his identity theft scheme you were absolutely sure the insider was a true ‘whistleblower’, without question. https://judithcurry.com/2012/02/13/climate-change-war/#comment-169109 Now the truth is known, he was not a whistleblower in any way. Do you think Peter Gleick was justified in the ‘lie’ he told to HI staff to obtain the information. Are some lies ok and others not? You seem to think lying is a very bad thing…. and I agree with you. So…. Peter Glieck admitted to ‘lying’ to obtain information illegally, admitted it himself. Are you ok with that because he admitted to it? If the climategate ‘hacker/whistleblower’ (you pick) comes out and admits who he/she is, will you be ok at that time? I guess I want to know when you think lying is ok and when its not ok, cause I see a potential double standard in your argument. • David Springer Sorry Holly, the lies are from the alarmists and that is what is being taught to children. For instance Al Gore’s “Inconvenient Truth” has been screened to a great many children and it’s so chock full of lies, exagerations, and half-truths that in Great Britain where the central government was peddling the film to schools a judge ruled that it must be accompanied in the classroom by an advisory about the factual errors. The court identified nine errors. http://news.bbc.co.uk/2/hi/7037671.stm The lies about sea level rise were particularly egregious in that younger children were having nightmares about drowning. Is that kind of thing really what you’d like to stand up and be recognized for supporting? • Pouncer And so PG lied to DeSmog and others? He misrepresented himself as a “Heartland Insider” to plant documents he knew were toxic (illegally obtained, if not bogus). He lied to his friends and allies. “All in a good cause”, of course. Surprisingly to me, Kos, DeSmog and others seem to greatly appreciate having been lied to and set up. 99. manacker Judith Curry Thanks to you for running this thread, as well as the earlier ones covering this “event” (which Tony B has dubbed “Gleickgate”, but might also be called “Heartlandgate”). And special thanks to Joe Bast for his e-mail, which you published here. It seems to me that Heartland’s primary function here has been to shine a critical and skeptical light on the science supporting the IPCC’s “mainstream consensus” CAGW postulation. This, in itself, cannot be a bad thing to do: “Truth loves Light” and thrives under it. Scientific truth is no exception to this. So, even though Heartland is admittedly operating on a shoestring budget, when compared to the billions of taxpayer dollars that are going toward funding the science in support of the “mainstream consensus” position, and is (in your estimation) an organization “most of the public has never heard of”, it still appears to have made a significant impact, even before the latest developments. There is no question, as you have written, that “the end result of this episode is that Heartland will become known to many more people”. Your now-famous statement from the NPR interview: “It like taking a big gun to a small target and then shooting yourself” is the defining statement of this whole episode. Quite apart from any ethical considerations, one has to ask, how could a man as intelligent as Peter Gleick undoubtedly is, be so totally idiotic to do this, think he could get away with it and not realize what the unintended consequences could be? Max • Markus Fitzhenry “Quite apart from any ethical considerations, one has to ask, how could a man as intelligent as Peter Gleick undoubtedly is, be so totally idiotic to do this, think he could get away with it and not realize what the unintended consequences could be?” Fairly straightforward Max, the answer lies in his blind faith in AGW. A man who doesn’t question his faith leaves the door open to evil. 100. patrioticduo IMHO, Gleick went after Heartland not because he wanted to expose the institute to the general public but because he is a political animal that wanted to besmirch the reputation of HI in front of the loony green left. He intended to discover large funding from Koch brothers and others who are hated by the left. In this way, Mr Gleick has succeeded by further enraging the loony green left who point at any organization funded by Koch et al and calls them evil. With the education department of the US an arm of the left, every single educator in this nation will have a very hard time arguing to their colleagues that they should even talk to HI let alone consider their education materials. Saul Alinsky would be proud of Gleick – except that Gleick got caught. And so Alinsky would consider Gleick a failure. So Gleick is expelled from the inner circle for his “failure”. Meanwhile, the remaining followers hold him up as a hero and the group continues on. 101. Wagathon Being a Gleick head: Ready, Fire, Aim! • manacker Yeah, but add: Ready, Fire, Aim, OUCH! • Wagathon Urban Dictionary ‘Getting Gleicked’ A shot heard ’round the the foot. • Martin Clauss . .interesting – thinking about a glock, and then Peter Gleick, and Dr. Curry’s comment about pointing a gun ( . . do I dare think it was a glock . .? . . . ) at a small target, and shooting himself in the foot . . . . . ooooh, the thoughts that one could come up with Gleick and a Glock, , and I am sure many here will . . . :-) Maybe Josh could come up with a tasteful cartoon about it . . .! :-) • incandecentbulb Have you heard the latest? Word is Gleick discovered the Missing Link? 102. pokerguy “Quite apart from any ethical considerations, one has to ask, how could a man as intelligent as Peter Gleick undoubtedly is, be so totally idiotic to do this, think he could get away with it and not realize what the unintended consequences could be?” Max, I know you’re being somewhat rhetorical. And I agree. I mean, holy crap. How thunderously stupid. And yet we see over and over again how intelligence…raw IQ points …is by no means synonymous with things like good judgement, common sense, a good moral compass, and psychological stability. Bobby Fischer was one smart fella, and yet what a train wreck. Examples abound. I’ve said several times that in my opinion Gleick’s a deeply insecure, self-loathing type individual who’s self-worth is so invested in global warming that there’s not much he’d stop at to destroy the other side. • manacker pokerguy I’m no psychologist, but you’re probably right. And it’s certainly true (as you write) that intelligence…raw IQ points …is by no means synonymous with things like good judgement, common sense, a good moral compass, and psychological stability Max • P.E. Whenever it snows, it’s always the 4x4s that end up in the ditch. Hubris does that. • Nick Darby A colleague once described a job candidate as someone with “lots of intelligence, no brains”. I have, over the years, found this a useful epithet. 103. CTL Why target Heartland? It is possible that Gleick was coordinating with DeSmogBlog / John Mashey, hoping to get the Heartland Institute prominently mentioned in the news and portrayed in a bad light around the same time that Mashey released his report on HI. Even after the forged document was identified as a fake and Gleick had confessed, I still saw Mashey spamming comment sections at various blogs instructing people to completely disregard Gleick’s confession of identity theft and the fraudulent “strategy” document Gleick had proffered and to focus on Mashey’s “expose” instead. This could be a publicity stunt gone horribly awry. I suspect the courts will sort that all out in due time. • hunter CTL, From the start of when it fell apart, this stank of more than a one man band. DeSmog is logical for a helper, since its owner ahs been so rabidly pushing the amoral position that what Gleick did was heroic and that HI is in reality a wicked evil group. I think Peter Gleick can regain some dignity and conscience in this by coming truly clean. I hope his true friends will guide him to do this soon. • Hunter, You too are living in the land of unicorns; “I think Peter Gleick can regain some dignity and conscience in this by coming truly clean. ” Why in the world is it anything less than what I or Dagfinn described above? He’s a leftist fanatic Hunter. He’s going down in the bunker. The Rosenberg’s are heros in the tightest circle of this crew, his price will be much smaller but the purpose and method is the same. Achieve 60’s hippie left/green political nirvana. • manacker hunter I think Peter Gleick can regain some dignity and conscience in this by coming truly clean. Hunter, I may be wrong, but I believe it will be almost impossible for Gleick to voluntarily go any further than he has, because:. – he seems to be absolutely convinced that he was doing a courageous thing to expose an evil enemy in order to help a noble cause – it also appears to me that he is basically arrogant and narcissistic enough to be unable to imaging that anyone in his right mind would think he did anything wrong Unfortunately, these viewpoints are being reinforced by several CAGW believers, some of whom are even making a hero of him. [Remember how Nixon stonewalled to the end in Watergate.] But, if Heartland goes through with a civil lawsuit against him, I believe that he will be forced to identify the creator of the faked document, which he “leaked”. If Steven Mosher’s analysis is correct, this person is most likely Gleick himself. So, unless he can find a fall guy, he will be forced to either “take the fifth” or admit the guilt. This will not have the same effect as “coming clean” now – but I think that’s the way it will play out. Max PS I agree with you that the “smart” thing for him to do would be to “come clean” now – as you wrote it’s the only way he can “regain some dignity and conscience”. • GaryM My money says Gleick came up with the idea for the strategy memo on his own. Then he or somebody else thought “Hey, let’s get some genuine Heartland docs, revise the strategy memo around them.” The beauty of this thing is that no matter what actually happened, Heartland gets to get discovery from not just Gleick, but those who initially ran with the story. No fake FOIA defenses, no faux inquiries by their own like minded employers. Heartland will file in federal court, and a federal judge will order discovery of all documents and records that are not just relevant to the fake claim Gleick published in the strategy memo, but to anything that might even lead to discovery of relevant evidence. I still say this could end up making the Daily Callers’s expose on Media Matters look like chicken feed. • huxley I suspect that the Vaughn Pratts of the world, who believe that it’s sheer skeptic nuttiness to suppose that Gleick faces real legal troubles, are going to be surprised. I don’t imagine that Gleick is going to jail, but he is in for a bad time with the legal system. Much will depend on how Heartland chooses to play it. • Huxley, I only argued that there were obstacles to making a fraud charge stick. I most certainly did not claim Gleick was out of the woods. Anyone can sue anyone for anything, and given AGU’s lack of enthusiasm for Gleick’s action I’d guess anyone wanting to destroy Gleick financially and who had the requisite legal budget would have no trouble doing so now that he’s put himself in this impossible position. If Heartland wanted to make the first move they could very reasonably start with a fraud charge and even if they couldn’t make it stick Gleick could not complain about the suit being a frivolous one, which might be enough to kill him financially on its own without even pressing any further charges, just a series of appeals. But even if Heartland decides they’re better off not pursuing Gleick, e.g. because they don’t want discovery working against them, judging by the general tenor of this thread one can easily imagine others deciding to harass him legally, though Heartland is in the best position to defend against an objection of frivolity. The ClimateGate Burglar had the good sense not to throw him or herself to the wolves in this way by having a change of heart and deciding to come clean. Honesty is often said to be the best policy but so far it would seem that Gleick would have been better off keeping quiet. Bank robbers who have a change of heart in mid-robbery tend to wind up in the News of The Weird section of the newspaper. The proverb would be better stated as “Consistent honesty is the best policy.” • Although now that I think about discovery, is there anything left about Heartland that hasn’t already been discovered? If not, Heartland could be more dangerous now as a plantiff than if the Desmogblog types had allowed Heartland to keep a few secrets. • GaryM David Wojick has as good a claim against Gleick as Heartland, maybe better. It will be easier to show malice based on the faked document claiming he planned to try top stop teachers from teaching science. This is not merely a slur on his attitude or politics. It is a direct attempt to destroy his reputation in an area that is related to his work. This is the easiest type of defamation to prove. Fraud is actually much harder to prove than defamation. What would be fun to watch would be Wojick’s using the comments of some of the denizens of this site in court to prove the intentional damage to his reputation. • manacker Vaughan Pratt You say i“honesty is the best policy”. I’d say in the Gleick case, since he has not yet divulged the name of the creator of the fake document, which he pretended to “leak”, it’s more like “honesty would have been the best policy”. Max • “honesty would have been the best policy”. One of those rare occasions when we agree, Max. That’s what I meant by “Consistent honesty is the best policy.” The middle of a bank robbery is no place to discover your own wickedness, at least wait till you get to Argentina. When I was about five my dad told me there were people in the world who believed that whatever you were doing was only bad if you got caught. I thought he was joking… • David Springer @mannacker re; Gleick taking the fifth in a lawsuit You can’t refuse to testisfy against yourself in civil trial. There’s no “taking the fifth” you see, because the fifth amendment bars self-incrimination and there are no criminal penalties in civil trials and hence no incrimination. So if there’s a civil trial Gleick will have to take the stand and answer under oath everything he knows about the source of the forgery. If it’s himself and he lies and then is caught lying he commits perjury and THEN a criminal trial will be forthcoming. For Heartland this must be weighed against the defense issuing subpoenas to get depositions from Heartland donors and employees named in the documents which won’t go over well with either employees or donors. Discovery will bring even more internal HI documents into the light for examination which may or may not be of concern. The chance of recovering even the cost of trial from Gleick are probably nil unless he’s got deep pockets so one might reasonably question what HI stands to gain. Those who fund HI probably didn’t earmark any funding for revenge so spending money going after Gleick in civil court is unlikely to make them feel good about how their money is being spent. I don’t believe Gleick has much to worry about in that regard. Gleick’s career is in tatters, his credibility shot to hell, and that’s probably all the fallout he’s going to suffer from what was essentially a juvenile stunt. 104. John Whitman Judith, Finally I listened to the interview with Mandia and you. I appreciate your consistent calmness, your projection of cool reasoning and your creation of relatively balanced approach. You had the high moral ground and you did not concede one molecule of it to Mandia’s obvious lack of credible position on the ethics of science. You sounded like you are spontaneously responding in an actual dialog/conversation. Nice. Mandia acted like someone in the background was ineffectively prompting him with pre-arranged soundbites, tips on responses to Judith’s points and ad hominems against HI & IPCC critics. The moderator sounded like he had a critically balanced picture of the orthodox climate scientists (Mandia et al). I was pleasantly surprised to see that. THAT ALONE IS A VERY POSITIVE OUTCOME of the interview. Yes, I am an independent (aka skeptic) with a glass is half full world view. : ) Pessimism and cynicism . . . nah. John • huxley John Whitman: I’d have to agree with your analysis. Dr. Curry came off as calm, thoughtful, and real. Mandia came across as a glib political operative working his talking points — which is what the Climate Rapid Response Team is all about. The moderator surprised me with his even-handedness and quickness. When he asked Mandia a reader’s question about funding, Mandia tried to laugh it off with a recommendation to look at the unimpressive cars in faculty parking lot and then mentioned rules against faculty directly profiting from funding. But the moderator immediately pressed Mandia back on track to the real question of who gets funding and whether researchers outside the orthodoxy are likely to be funded. • Anteros I too was impressed, Dr Curry. Tough to say so of course :) but I thought in a way there was an absence of an extreme counterpart to Mandia’s spinning. Which I think was surprisingly effective – perhaps a lesson to extremists everywhere.. Not getting it out of proportion was good to hear too, although Joe Bast makes a very good case in his email that Heartland punch above their weight. 105. David Young I agree with the McIntyre theory. Direct contact with the “enemy” resulted in loss of moral scruples and a “war crime.”. Admittedly a relatively minor one. And that’s the problem. Your fellow citizens are not the “enemy.”. Neither is big oil. 106. lolwot Dr Curry, Bast writes to you: “I read with interest your post, “Why Heartland?” Thankfully, I can’t read Peter Gleick’s mind, but I suspect he targeted us because we have done so very much to document and rebut the assumptions and exaggerations of the global warming alarmists. Please let me describe some of the ways we’ve done that, and you decide. We send publications to every national, state, and 8,400 county and local officials in the U.S. on average about once a week. 79% of state legislators say they read at least one of our publications. “Environment & Climate News,” one of six monthly publications we produce, is read by 57% of state legislators, a higher percentage than read the New York Times. It has been published continuously for 15 years, and every issue features the work of leading climate realists. No other organization produces a regular publication that reaches more people with this message.” Here is the most recent issue of “Environment & Climate News”: http://heartland.org/sites/default/files/newspaper-issues/pdfs/february_12_ecn_web.pdf On page 10 you’ll find a full page argument. The caption reads: “Reducing our so-called “Carbon Footprint” by encouraging renewable energy and restricting fossil fuel development makes no sense when the actual composition of the greenhouse is considered. This one page graphic shows that water vapor is the overwhelming predominant component of our vital protective greenhouse envelope. Far from being detrimental, greenhouse gases retain the sun’s radiant heat and keep planet Earth from becoming frozen and uninhabitable. Despite the science that contradicts them, the so-called “warmists” contend that man’s CO2 emissions are somehow harmful to our existence. This pictorial representation of the greenhouse envelope clearly demonstrates that man-made CO2 emissions are relatively so tiny that they are of negligible impact and must be viewed accordingly.” And, the text (sorry for the caps but I am copy pasting and can’t remember how to convert it): “NATURALLY OCCURRING WATER VAPOR IS EARTH’S PREDOMINANT GREENHOUSE GAS, BENEFICIALLY RETAINING THE SUN’S RADIANT HEAT SO THAT PLANT, ANIMAL, AND HUMAN LIFE CAN FLOURISH. WITHOUT WATER VAPOR, OUR EARTH WOULD FREEZE OVER, MAKING PLANET EARTH UNINHABITABLE. CARBON DIOXIDE PLAYS A SMALL ROLE IN RETAINING THE SUN’S HEAT. 96.6% OF ATMOSPHERIC CO2 IS PRODUCED BY NATURE AS REPRESENTED BY THE 348 GRAY DOTS. MAN’S ADDITION TO THE TOTAL AMOUNT OF CO2 IS NEGLIGIBLE, AS REPRESENTED BY THE 12 BLACK DOTS. THE GOAL OF GLOBAL WARMING ALARMISTS IS TO REDUCE CO2 EMISSIONS SO THAT OVER DECADES OF TIME THESE 12 DOTS MIGHT BE DECREASED TO PERHAPS 8 OR 9 DOTS. REDUCING MAN-MADE CO2 WILL HAVE NO MEASURABLE EFFECT ON EARTH’S TEMPERATURE READINGS.” In Bast’s own words this kind of stuff is being “read by 57% of state legislators” and “No other organization produces a regular publication that reaches more people with this message”. He might be exaggerating, but I think this stuff does have more influence than you’d think. They are clearly targeting policy-makers more than say the public at large. Where are their so-called experts to allow this caliber of argument to get out? They want to appear to be a science outfit and no doubt they venomously attack slight IPCC errors. But where is their own quality control? I think you can see from this the problem me and others have with Heartland’s “contribution” to the subject. Such arguments as the one above cause very serious damage because they appeal to the common sense of a layperson. The consequence of a layperson falling for the argument is that they will dismiss the threat of human induced climate change altogether. If they think that humans aren’t contributing significantly to CO2 level then they logically won’t accept the issue matters. Furthermore that lay reader will automatically think climate scientists must be lying to have overlooked such a simple fact. I don’t think Heartland is doing this intentionally, unlike a lot of people I don’t think it’s a big evil plot. Heartland and WUWT are simply not in a position to educate the public. They no doubt think they are on the side of the truth. The problem is they aren’t a scientific organization and quite clearly they can’t get the science right. Pressure should be put on them just as pressure should be put on a bad teacher. Surely we wouldn’t leave a bad teacher to misinform students even if they weren’t doing so deliberately. • Peter317 So the end justifies the means, does it? • lolwot No I don’t mean phish them for info or even fake documents from them. They should be held accountable for sending scientific errors to legislators though. • Anteros Lolwot – I take your point. I have no reason to defend anything Heartland do – as long as it’s not illegal, though, they’re just pushing one side of an argument. Do you not think that an organisation like Greenpeace does the same thing? They say the science says that all sorts of calamities will be visited upon us if we don’t do x,y,and z (immediately) and rely on spreading fear and (especially) guilt while playing fast and loose with scientific ‘facts’. I’m even less willing to defend them than Heartland, but recognise that they have a legitimate function and misrepresenting science is actually what they do, and have to do. From your side of the fence, what Heartland and Cato and GWPF do presumably looks terrible and quite close to actually lying. I think to someone neutral, they’ll look similar to lobbyists on the other side. They exaggerate as much as they possibly can because they exist to pursue an agenda. Nothing else matters. I think as long as there are lobbyists on both sides, no-one has very much to complain about (although everyone does). • lolwot “Do you not think that an organisation like Greenpeace does the same thing?” Yes and I never believe a word Greenpeace says. I am biased one way because I think climate change is a threat (not a certain catastrophe just to clear that up). The red rag for me are arguments that it’s all a scam/fraud. Not just because it’s dismissing the issue out of hand in a cavalier attitude, but it typifies an anti-science attitude I don’t care for. I don’t mind if people work out rationally that they want to risk the CO2 rise and/or or don’t want to do anything about co2 emissions just as long as they achieve that position somewhat rationally. I only go mad when the arguments are BS. On the otherside when eco-outfits over-exaggerate the issue that annoys me, but doesn’t make me mad because they aren’t attacking the science and calling it all a scam. Also they are slightly tragic. Unbelievable. Like that 10:10 video, I think they get their just desserts without me having to shout at them wtf they were doing. I definitely would though if I happened to meet one of them ever. • The red rag for me are arguments that it’s all a scam/fraud. Glad to hear Bernie Madoff didn’t rip you off, lolwot. ;) It’s like the joke, the cure for paranoia is to join the military. Then they really are out to kill you. • Markus Fitzhenry While you here Lolol, let’s talk about Lysenko, and compare him to Hansen.. • lolwot al gore is fatter than hitler • Markus Fitzhenry A pet rock is smarter than you. • kim Peter Bocking once said that if Al Gore’s hair were set on fire he’d provide enough light and heat for a small English village. ========== • Dolphinhead Kim I heard that BP had bid for the extraction rights • David Springer If Al Gore’s brain was gasoline there wouldn’t be enough to power a pissant’s motorcycle halfway around the inside of a Cheerio. • lolwot Could provide evidence supporting your objections? Granted anthropogenic contributions are somewhere between 1% and 90%. How do you quantify the portion of anthropogenic vs natural? Does the CO2 lead or lag the temperature? If so, on what quantitative basis? e.g. See Fred Haynie’s detailed analysis of CO2 driven by natural causes, not anthropogenic. His analysis of the different shapes between Arctic, tropics and Antarctic is thought provoking as the primary CO2 drivers. http://www.kidswincom.net/climate.pdf I agree we don’t want a “bad teacher to misinform students” – but who is hiding the evidence? Who is showing the evidence not reported by the IPCC? See the NIPCC Reports and reviews to fill in the evidence left out of the IPCC reports – if you dare confront ALL the evidence! • manacker lolwot You list some Heartland claims. Let’s go through them quickly. 1. Naturally occurring water vapor is earth’s predominant greenhouse gas, beneficially retaining the sun’s radiant heat so that plant, animal, and human life can flourish. Correct 2. without water vapor, our earth would freeze over, making planet earth uninhabitable. Correct. 3. Carbon dioxide plays a small role in retaining the sun’s heat. Correct, depending how you define “small” (I would have used “secondary”) 4. 96.6% of atmospheric CO2 is produced by nature as represented by the 348 gray dots. Man’s addition to the total amount of co2 is negligible, as represented by the 12 black dots. This one is more dicey. If one accepts that all of the increase from 280 to 390 ppmv was caused only by human CO2 emissions (as IPCC does), then this statement is obviously incorrect and the figure should be 72%. 5. The goal of global warming alarmists is to reduce CO2 emissions so that over decades of time these 12 dots might be decreased to perhaps 8 or 9 dots. Wrong. The goal is not to reduce CO2 concentrations (which would be impossible), but to limit their future increase to a lower level than they would be under “business as usual” conditions. 6. Reducing man-made CO2 will have no measurable effect on earth’s temperature readings. Correct, in a practical sense. The nations that have pledged to voluntary reductions (EU, Australia, New Zealand) would have no discernable impact even if they shut down completely and there have been no actionable proposals by anyone, which if implemented now would cause a discernable impact on global warming by 2100. The truth of the matter is that we cannot change our planet’s climate no matter how much money we throw at it. How would you grade the Heartland claims, lolwot? Max • OMG, grader wars. Is this the mid-term or the final? :) I don’t mind being graded, but in order to have something to be graded on I’ll grade Max. 1. Correct when measured by mass. Measured by warming effect, probably correct today but not for long if CO2 keeps increasing. (Remember that the temperature is logarithmic in the amount, not linear.) 2. Wrong. Venus is warmed primarily by CO2, not water vapor, and we don’t see Venus freezing over. 3. Can’t argue with “depending how you define small”. Claim too vague to judge. 4. Correct (though 72% is for a couple of years ago, it’s 71% now). 5. Desperately searching for something to disagree with here, I’ll pick on Max’s “It would be impossible to reduce CO2 emissions.” Currently we’re adding 11.5 GtC each year counting land use change, of which nature is removing 6.1 GtC leaving 5.4 GtC as what’s driving the Keeling curve up. If we were to abruptly drop our emissions from 11.5 GtC/yr to 0 GtC/yr, would nature equally abruptly drop her removal program from 6.1 GtC/yr to 0 GtC/yr, or would she go on removing 6.1 GtC/yr for a while? Explain. (This might be a great Ph.D. oral qualifying exam question — very topical while being a nice test of whether the candidate has at least some of the basic intuitions of a physicist. Probably not deep enough to pick out the budding Nobel laureates though if it’s in AMO as opposed to atmospheric physics.) 6. Correct. (Planet Earth currently lacks the political willpower, though somehow I don’t think that was what Heartland had in mind.) • Latimer Alder @vaughan 2. ‘Venus is warmed primarily by CO2, not water vapor, and we don’t see Venus freezing over’ At the risk of being pedantic, Venus is actually warmed by the Sun. Without the Sun, its temperature would be close to 0K, no matter how its atmosphere is composed. Your hypothesis is that CO2 causes more of the Sun’s radiation to be retained than would otherwise be the case. But that ain’t ‘warming’ • Markus Fitzhenry ”I don’t mind being graded, but in order to have something to be graded on.” OMG Vaughan, I’ll give you 100% when you come back and tell me what is the T on Venus at 101.325 kPa. • David Springer #3 is more than “a little dicey” it’s a big fat lie with no credible scientific support whatsoever • David Springer correction #4 is the lie not #3 • David Springer @vaughn Venus is warmed by the sun not by CO2. Duh. • David Springer @latimer I think it’s useful to view greenhouse gases as effectively lowering the albedo of a planet. One must keep in mind that albedo can’t fall below zero so there’s a limit to how effective they can be. For instance the earth’s global ocean already has an albedo close to zero so greenhouse gases are limited there and because GHGs modus operandi is restricting radiative cooling and the ocean is still free to cool evaporatively there is no first order significant effect of greenhouse gases over a liquid ocean. Interestingly the highest mean annual temperature observed anywhere on the earth is a salt desert in Ethiopia near the equator (34.4C). Interesting that a desert has the least amount of greenhouse forcing yet has the highest mean annual temperature is it not? This is because the net effect of water vapor is less than zero when it comes to warming. Clouds that come with water vapor more than completely cancel out its greenhouse effect and that’s why an equatorial desert not an equatorial jungle has the highest mean annual temperature. Climate boffins can fool some people but they can’t fool mother nature. Another interesting factoid is that the highest SST measured by ARGO buoys is also right around 34.4C. High readings cluster at 30C like there’s almost a brick wall at that temperature with rare departures above it to a maximum of a bit under 35C. This begs an explanation and the explanation is that 35C happens to be the mean temperature limit at the equator for a gray body 93 million miles from a 5000K source. There’s an online black body calculator here where you can verify the numbers for yourself. http://www.spectralcalc.com/blackbody_calculator/blackbody.php • David Springer @latimer At the risk of being pedantic you said Venus is actually heated by the sun and would be close to 0K without the sun. At more than just risking pedantry I’ll reply. The cosmic background radiation is about 3K so without somehow shading a surface against the warm glow left over from the big bang that’s as cold as it gets. Pluto, formerly known as the ninth planet, is about 3K. Venus however is a bit tricky because it has internal heat of formation as well as radioactive decay that heats it without the sun just like the earth has a hot interior. Venus however, unlike the earth, has an uber thick atmosphere of 80 bar that helps hold the internal heat. I have no idea how long, absent the sun, how long it would take for Venus to approach 3K. It could be billions of years. Long before it approached 3K however the atmosphere would collapse to a solid without the sun to keep it above the freezing point of CO2 which is a balmy 195. If one is curious one can consult http://www.engineeringtoolbox.com and check to see if the thermal conductivity of solid CO2 is greater or lesser than crustal rock to determine if it will slow down internal heat loss or not once it collapses from gas to ice. • SamNC Pratt is always confused with cause and effect! • It is clear from those saying “Venus is warmed by the Sun, not by CO2” that there is a serious communication gap between the public who are posting here and the scientists who are claiming that Earth is being warmed by CO2. Conceivably this communication gap is the core of the climate debate. It’s like the Captain said in Cool Hand Luke: “What we’ve got here is a failure to communicate.” The public is making the perfectly valid point that the Sun heats every planet in the Solar System. If the Sun were to disappear, all the planets would in due course become very cold indeed. The scientists are making a different point, one that affects most of the life on Earth. The point is that, relative to what astronomers call the effective temperature of a planet, CO2 is warming the Earth. The effective temperature is how hot the Earth looks from space, as a result of being in equilibrium with incoming heat from the Sun: heat in equals heat out, and one can deduce the effective temperature of the Earth from that balance. The effective temperature can be very different from the temperature on the surface. How so? Well, consider an Eskimo being heated by the very limited sunlight in the Arctic Circle? His effective temperature defined as how it would be measured outside his parka would be close to that of the snow around him. That would be fatal. Yet he does not freeze to death because of the huge temperature differential across his parka. The public would say he is warmed by the Sun. The scientist would say he is warmed by his parka. In that sense the surface of the Earth, where most life exists, is warmed by the CO2. The Sun only warms the entire earth. The effective temperature of that warming is 254 C. That would be fatal if it was up to the Sun to warm the Earth. Life is possible on Earth because greenhouse gases perform the requisite warming, just as an eskimo can live in the Arctic Circle because he is warmed by his parka. The Sun alone would kill him with its warmth. 107. Stacey Why did he target HI. The answer is simple because he believed he could get away with it. The statement he has made is laughable. Why did you rob the Bank? Cos I was mugged yesterday (To the sounds of violins) Maybe a FOI request should be lodged to see the forms he filled in to get funding :-) • manacker Stacey I believe the infamous bank robber, Willie Sutton, had a better answer for “why do you rob banks?” It was, “Because that’s where the money is.” Max • So Gleick robs Heartland because that’s where the incriminating evidence is? That would make sense if Desmogblog, Mashey, etc. hadn’t already robbed Heartland before, or if they hadn’t taken everything. Did Gleick get anything that hadn’t already been taken from Heartland? If not he’s like a Robin Hood who robs the just-robbed to give to the poor. Brilliant business plan. • Dolphinhead Vaughan is on fire! “If not he’s like a Robin Hood who robs the just-robbed to give to the poor. Brilliant business plan.” made me giggle like a teenage girl. Oh that’s what I aspire to be! 108. Bob K. Question: Why target Heartland? Answer: Because extremists need each others’ company. The political spectrum is more a circle than a line in many respects. • Anteros Well said. • Dolphinhead ‘les extremites se touchent’ as my old nan used to say. I think she was foreign. • David Springer Yup. That’s why I said in another thread we should just eliminate 501K and go back to the old fashioned list of organizations that get public largesse by not paying their fair share of taxes. In the past these have been volunteer organizations like fire departments and other emergency services, hospitals, free clinics, orphanages, animal shelters, and things of that nature plus churches. This would effectively shut down both NCSE and HI which both meet the definition of rent seekers and the absence of advocacy for and against CAGW would cancel out. Presumably then the employees of both could go out and get jobs like taxi drivers, plumbers, farmers, nuclear physicists, or some other productive occupation that doesn’t meet the definition of rent seeker. 109. Wagathon So, Mr. Bast talks about “scientific forecasting as being distinct from scientific knowledge. That is not exactly correct. The proper comparison is between scientific forecasting and opinion. Our scientific knowledge about scientific forecasting with respect to global warming and climate change is pretty clear. Excerpt from the NCPA (National Center for Policy Analysis): Referring to the GCMs used for the IPPC forecasts, a lead author of Chapter 3 of the Fourth Assessment Report wrote that “… the science is not done because we do not have reliable or regional predictions of climate.”21 “Climate models based on recent data can’t accurately predict temperatures five years in the future.” Other agencies’ attempts to forecast for shorter periods and smaller geographical areas have also been unsuccessful. For instance, annual forecasts by New Zealand’s National Institute of Water and Atmospheric Research (NIWA) are no more accurate than chance. NIWA’s low success rate is comparable to other forecasting groups worldwide, according to New Zealand climatologist Jim Renwick, a member of the IPCC Working Group I and a coauthor of the Fourth Assessment Report. (Renwick also serves on the World Meteorological Organization Commission for Climatology Expert Team on Seasonal Forecasting.) He concludes that current GCMs are unable to predict future global climate any better than chance. 110. Thanks, Joe Bast, for your message (above) to Professor Curry. Why did Dr. Peter Gleick target Heartland? Big Brother is really scared. Peter’s actions were almost certainly on behalf of really “Big Fish”, political leaders who, in fear of mutual nuclear annihilation, secretly decided forty-one years ago [2012-1971 = 41] to Unite Nations against an imaginary common enemy – “Global Climate Change” – and then base their future government policies on: a.) Managable computer models of Nature, instead of b.) Experimental observations and measurements on Nature Evidence is recorded in events leading up to Climategate: http://dl.dropbox.com/u/10640850/Climategate_Roots.pdf So Dr. Gleick is just the latest on Big Brother’s long list of puppets. 1. Michael Mann, Phil Jones, Rajendra Pachauri, Jim Hansen 2. The Nobel Prize Committee that honored the above for their work 3. Al Gore, the UN’s IPCC and others promoting falsehoods as science 4. Government research agencies (NASA, EPA, DOE, etc) that used public funds to deceive the public. Here is a video summary of deceit culminating in Climategate: http://dl.dropbox.com/u/10640850/Summary_of_Career.pdf Here are papers documenting experimental data that were ignored: 1. Solar composition: http://arxiv.org/pdf/astro-ph/0410717v1 2. Solar structure: http://arxiv.org/pdf/astro-ph/0501441 3. Neutron repulsion: http://arxiv.org/pdf/1102.1499v1 Big Brother’s computer models worked as well in climatology as they did in economics. That is why our economy is collapsing. An election is coming, the public is darn mad, politicians are running scared, and private groups like Heartland that exposed government deceit are under attack. 111. John Whitman Why target Heartland Institute? Actually, no public targeting occurred until Gleick actually sent the HI doc containing email to “15 friends” with the intent that they would publish it. Before Gleick sent that email he was in a position to prioritize then choose multiple targets associated with HI. He would have seen that Anthony Watts could be implicated in something as well as one of his contributors (I. Goklany) could be implicated in something. Gleick had no love of Anthony. I would include Anthony Watts and anyone in HI’s documents associated with his blog could have be co-targets of Gleick. John 112. David Springer re; shoestring budget of HI Electronic newsletters are cheap & easy to assemble and distribute in the computer age. Imagine how much they’d pay in typesetting, printing, and mass mailings in the past for all that. I mean it’s not like they’re paying for ARGO bouys or paying for health research on frequency of childhood asthma in the homes of tobacco smokers or, really, doing anything that’s a value-add to human condition. Pretty much just vehicle for individuals and corporations to peddle influence through tax exempt donations and a 401c to pay a group of rent seekers a salary without having to pay for their fair share of the public infrastructure which makes their business possible. Did I miss anything? • David Springer Note I’m dissing the whole advocacy racket not HI in particular. NCSE is the same exact description. Equally funded their newsletters cancel each other out. We’d be better off just reforming 401c so neither HI or NCSE could afford to make payroll and all the employees could go out and become useful citizens doing something like say building cars or growing tomatoes. 113. Rogelio Escobar My father an eminent meteorologist published 3 papers in Nature concerning evapotranspiration and atmospheric particles. He told me in 1994 that the whole AGW was a load of B#####, he actually said it would be a tax grab at that time!. Unfortunately for the AGW crowd he was right. currently we are at -0.4C and ther is NO statistical significance 114. Gras Albert Both McIntyre and Watts have a chronology of the exchange of emails (supplied by Heartland) between Gleick and Heartland which took place in January 2012 regarding Heartland’s invitation to Gleick to debate James Taylor at Heartland’s annual dinner where he could meet Heartland’s donors. As well as offering travel and accommodation expenses, Heartland offered Gleick a$5,000 donation to a charity of his choice.
In the exchange, in which Gleick repeatedly asked why Heartland did not make it’s donors public, Heartland explained that they used to but
I’m sure you’ve seen James M. Taylor’s response to the funding questions at Forbes.com – a question he has answered publicly many times. In short: We used to publicly list our donors by name, but stopped a few years ago, in part, because people who disagree with The Heartland Institute decided to harass our donors in person and via email.
Having been directly informed that harassment of donors was an issue in the past, Gleick unlawfully impersonated a Heartland board member and obtained confidential documents which included board members, employees and donors personal information. Without any attempt at redaction Gleick forwarded that personal information for it to be published on multiple Alarmist web sites in the full knowledge that it would inspire ‘nut jobs’ to do exactly what Lakeley had described.
Make your own judgement whether Gleick’s intent was to encourage ‘harassment’! In my view sympathy is the last emotion one should express for someone who harbours such ill will for those who simply disagree with him over science.
• David Springer
@Gras Albert
Your comment is the first thing I’ve read surrounding this affair that persuades me that Gleick’s action is more than a juvenile stunt and actually may have been an intentional effort to put people into harm’s way. I’m hereby switching my sympathies over to those calling for criminal prosecution. I think there may be a good case for it given the information you presented. It still isn’t wirefraud however as that requires some kind of tangible property be obtained. A confidential list of names doesn’t meet the definition. Perhaps reckless endangerment or invasion of privacy. Gleick should have redacted the names.
115. Wagathon
We know how many men and years it takes to build the Hoover Dam. How many Mother Jones readers would it take to prevent it if it was to be built today?
116. Beth Cooper
I’ve been rereading ‘Karl Popper’s Open Society and It’s Enemies’, about Heraclites’ and Plato’s historicism They’re trying to find, in troubled times, some unchanging law from out of the flux, arrest the drift. Heraclites comes up with his Law of Destiny and Plato, a Theory of Forms and Law of Historical Development.
‘ Gee, If we can only get the right LEADERS, up there,and put everyone else in the place, down there’ and hold it right there,( Plato speaking) ( in Greek,) we can recreate that Golden Age, before the rot set in. But we need real intellectuals, (like me,) well shamans really, to pierce the reality behind the flux, no one else can do it.’
And how good, was Plato at spin, He puts his word in Socrates mouth.
‘Hmm, Socrates was democratic, the mob will think I’m advocating freedom.
Sometimes the noble lie, a bit of forgery, is it means getting rid of that damned flux..’
So you see,Gleick et al.are only getting things back in order- Stupid- bringing you back to the Golden Age-Stupid- putting the right shamans,er leaders in place- stupid!
(Lights dim, sound of primordial scream….)
• John Whitman
Beth,
Timely comment on this thread. Thanks.
Have you attempted inflicting real pain on yourself by reading the philosopher that took Plato ideas to the ultimate irrationality? I speak of Kant. Kant made Plato look like a Cinderella.
CAUTION: Do not read Kant without trusted friends present. He might influence you to do something irrational.
John
• Anteros
John –
I very much agree. I’ve no idea where he was when Hume woke him from his slumber, but he certainly headed off into a dreamland fantasy. If he’d merely remained awake, he could have stayed with Hume’s insights.
• Peter Davies
Kant writes in a very heavy style but I agree with his assertion that Cartesian logic and rational thought never comes up with anything original in science or philosophy.
I recommend that serious students take the effort to read him and to work out for themselves whether this makes sense.
• John Whitman
Peter Davies | February 24, 2012 at 9:45 pm |
Kant writes in a very heavy style but I agree with his assertion that Cartesian logic and rational thought never comes up with anything original in science or philosophy.
Peter Davies ,
We are getting is into a wonderful area (thanks Judith for tolerating it so far).
In the 1980’s I spent literally years slogging sentence by sentence through his “Critique of Pure Reason” with several other in a study group like atmosphere. It is Platonism to the 10th power. The key to understanding a lot of Kant is his reason for making his philosophy. He admits he had to restore the prominence of faith to the position it was in before the rational science/logic axis that drove the renaissance and the enlightenment; he said he had to remove the prominence (actual I think he said destroy) reason to restore faith; he is not a proponent of reason or morality based on reality.
John
• Peter Davies
John, it seems that we have interests in common, but in deference to others who visit this blog I will desist from engaging too much on matters of personal philosophy.
Your experience of studying Kant’s Critique of Pure Reaon in a group situation would seem to have been more painful than need be, because I always walk the “high country of the mind” on my own.
If however, you are interested in further discussion on this topic off line my email address can be found under my entry in the Denizens page and you and any others would always be welcome to contact me.
• John Whitman
Peter Davies | February 24, 2012 at 10:25 pm
– – – – –
Peter,
I sent you an email.
John
• John R T
1+
The road to totalitarianism: choose that bright Tyrant, maybe we can find our way back to our Golden Age.
Popper’s work is indispensable.
• John R T
This was for
Beth Cooper | February 24, 2012 at 7:18 pm |
• Jim
Popper is good. On this idea I suggest Eric Hoffer’s ‘True Believer’. It’s a very short book, but it is very, very on topic for the question of what motivates the idealogs in this debate.
• David Springer
Ancient philosphers are overrated. The wheels they invented are pretty easy to reinvent. Plato, Socrates, Aristotle, and peers probably aren’t the original rent seekers but they may be the most famous. I took Philosophy 101 the same semester I took Introduction to Formal Logic. I was filling in general education requirements. The former was perhaps the most boring useless thing I ever sat through in a classroom while the latter was perhaps the easiest. Interestingly not one person failed the philosophy class while a good percentage failed the logic class. I got a B in philosophy with modest effort to memorize names of people and names of ideas associatied with them but got a perfect 4.0 (with very very little effort) in formal logic. No surprise I drifted into computer hardware and software design as a profession because it’s all perfectly logical with a great many small wheels still awaiting first invention.
117. Fred from Canuckistan
“who (individual organization) has been most effective at challenging the IPCC consensus science in the public debate on climate change?”
Have to give big props to Donna Laframboise in this category.
She’s just a rockin’ the IPCC . . . .
118. charles gerard nelson
‘Dog bites man’…not news
On the other hand ‘Man bites dog!….
Recently I’ve had Warmists comparing Climategate to Fakegate and as usual they demonstrate the warmist absence of logic.
Climategate emails reveal the communications of ‘s’cientists who in PRIVATE are deeply uncertain of and divided about the reality of CO2 global warming. In those emails they ‘fudge’, conspire and bully colleagues to ‘toe the party line.’ Then PUBLICALLY pronounce their certainty.
If Gleick had found secret emails from members of Heartland admitting in PRIVATE that Global Warming was REAL, and actual threat to humanity, but in PUBLIC declaring it to be a hoax…now that would have been a ‘scoop’!
Heartland is anti the global warming hoax, openly, consistently and honestly.
Besides it’s a private organization, at least they weren’t wasting taxpayers money in the promotion of their hoax.
• Climategate emails reveal the communications of ‘s’cientists who in PRIVATE are deeply uncertain of and divided about the reality of CO2 global warming. In those emails they ‘fudge’, conspire and bully colleagues to ‘toe the party line.’ Then PUBLICALLY pronounce their certainty.
Charles, would you by any chance have an example of their uncertainty?
If you’re including Trenberth’s “travesty” remark is in that category then you’re in deep conspiracy-theory territory there. Trenberth was talking about the ongoing problem of getting Earth’s energy budget to balance, which is not something that happens all by itself, not about how to hide the “fact” that the Earth was cooling from the public.
• Markus Fitzhenry
“Trenberth was talking about the ongoing problem of getting Earth’s energy budget to balance, which is not something that happens all by itself”
Vaughan, you need help.
• Latimer Alder
@vaughan pratt
‘“Trenberth was talking about the ongoing problem of getting Earth’s energy budget to balance, which is not something that happens all by itself’
Vaughan. I have exciting news for you. The Earth’s energy budget does indeed balance itself. And has done so since it first came to pass as a planet 4.5 Bn ya. All the time.
It may be that all the intellectual might ( ;-) ) of Trenberth and his gang haven’t been able to figure out how it does it yet. But that is a different argument.
As the great George Carlin so perceptively remarked
‘The planet is fine. It is the people who are f*****d’
• Vaughan. I have exciting news for you. The Earth’s energy budget does indeed balance itself. And has done so since it first came to pass as a planet 4.5 Bn ya. All the time.
If I may be permitted to fight sarcasm with sarcasm, do you infer from this, Latimer, that Earth has never experienced mass extinctions, and will live in harmony with nature and the solar system, with a miraculously balanced energy budget, for ever and ever?
May we infer that you have never fallen off a bicycle?
And may we infer that the concept of disequilibrium is no more real than the tooth fairy?
‘The planet is fine. It is the people who are f*****d’
Present company excluded, hopefully. ;)
• David Springer
charles gerard nelson | February 24, 2012 at 7:21 pm | Reply
“Heartland is anti the global warming hoax, openly, consistently and honestly. Besides it’s a private organization, at least they weren’t wasting taxpayers money in the promotion of their hoax.”
No. They are an indirect waste of taxpayer money. They use public infrastructure to conduct their business without paying corporate taxes that serve to pay for that infrastructure. This notion that are not a drain on society because they are privately funded is untrue. They are less of a drain than direct government funding but they are still a drain on taxpayers. I say eliminate 501c for them and organizations like them. That should be reserved for real charities and real volunteer organizations not advocacy groups with full time paid employees. There are precisely (according to 2009 form 990) 27 rent seekers employed by HI with total compensation of $1.75M or$65,000 each per annum. This doesn’t count travel and entertainment expenses which can significantly raise an employee’s lifestyle if one enjoys travel, nice hotels, fine restaurants, and things of that nature. I know I certainly enjoyed travelling the country and the world with employers paying for it. I usually jumped at the chance. Basically what you’d call working vacations. There’s an $850,000 line item on the form 990 that is “other” in HI’s filing that isn’t further broken out on page 10, item 11(g). Item 11 is fees for services to non-employees. That’s basically where fees for sweetheart deals like for Wojick and Watts lands on the financial report. • Punksta If the financial rules are changed to squeeze the HIs of this world with budgets in the$millions pa, that would go a long way to removing any questioning of government-funded climate science, which is probably in the tens of $billions pa, and at least as advocacy-based as HI. probably a lot more so. And of course riddled and with fraud and secrecy. 119. JJ So, imagine you are a climate scientist and climate change ideologue, and want to “take down” the single organization (or individual) that is doing the most damage to the movement (i.e. with the end result of thwarting CO2 emissions/stabilization policy). Who would you target? Algore. Everytime that lardass opens his mouth in public, a blizzard hits. 120. John Whitman JC reflection: With virtually no effort on my part (beyond reading an email, cutting and pasting into the blog post), I have uncovered “juicier stuff” about Heartland than anything Gleick uncovered. Judith, That deep cut is potentially fatal to Mandia’s hero worship of Gleick’s hoax activities. : ) I do not think I would want to play against you in poker of be in knife fight with you. : ) John • Dolphinhead I didn’t know that knife fights were an option. This climate science thing gets stranger by the minute • Markus Fitzhenry I have a spatha, been using it for some time now. Even got a few notches on the handle If you like, I’ll show you it. • Dolphinhead I’ll show you mine if you show me yours • SamNC Sowie – Salty! 121. Beth Cooper Edit; 2nd last para: ‘is o.k if’ it means getting rid of that damned flux. 122. HankHenry It looks to me that the thing that got Gleick jiggered up was the invitation to speak publicly at a Heartland Affair. Sentence him to 6 credits in rhetoric and make him make a presentation at the next Heartland Conference. If he ever does it again make him actually debate. 123. Beth Cooper John Whitman @7.32pm I’ve only read filtered Kant, Bertrand Russell, Btyan Magee. Guess i chickened out, heard he’s a writer of turgid prose, ( hmm, probably German.) • Beth If you want Turgid forget the Germans and read some of the minor Russian Classics. Mind you Kafka can be very heavy going tonyb 124. Jon Carter What Gleick got on the Heartland Institute isn’t juicy at all, or as someone said “What’s horrible about this?’ I bet any effort to find juicier stuff about any business, any university, any 501c3 or most marriages would find juicier stuff. Reasonable people won’t commit felonies or misdemeanors to uncover it though. 125. Beth Cooper What’s happening to my editing, and spelling? Apologies Judith. 126. Latimer Alder So if the Heartland Institute is only getting$6 million pa, where else should I look to apply for a grant from the Big Oil Well Funded Denial Machine?
I’m beginning to get worried that the AGW crew have misled me, and that it is just a fiction :-(. So much for my dreams of a slice of the action….
• So if the Heartland Institute is only getting $6 million pa Whoa, you do think big. Singer was able to take them for$100K, apparently that’s not enough for you.
• Wow! Thats far less than Hansen receives taxpayers money EACH year, more than $150 000: http://php.app.com/fed_employees/results.php?name=&agency_name=GODDARD+SPACE+FLIGHT+CENTER&job_title=%25&statename=New+York&countyname=%25&Submit=Search On top of that, Hansen has propably made millions from speeches and prizes: http://www.atinstitute.org/disclosure-obtained-by-ati-environmental-law-center-shows-the-wealth-keeps-flowing-for-dr-james-hansen/ And Singer is the only one who has been paid that magnitudes of money in Heartland. The rest of them had received FAR less amounts total. And hey! Even Gleick was offered$5000 for the charity of his choise just for debating James Taylor and meeting Heartland donors, but he declined (and then afterwards did what he did).
• Latimer Alder
@vaughan
My point is that with funds so relatively low and so many sceptics around doing such great work, I could only reasonably expect to get a few quid every month. Nice, but not life changing.
But I was hoping for something more Hansen-esque….somewhere north of £100K per annum with expenses and all…and a handsome publicly-funded salary as well.
That would allow me to trade-in my trusty bicycle for a small ‘previously-owned’ runabout and mean that I could give up my part-time job on the buses.
So c’mon guys. Where is the location of the Well-Funded Big Oil Denial Machine? Somebody has to authorise the payments, and process the transactions. If it has a global strategy of Denial, this didn’t come out of thin air. Some actual people must have thought about it and defined it. If it is trying to lobby government it can’t do it by telepathy. There must be actual walking talking people with deeeep pockets doing it.
So where can I find them so that I can get my just rewards?
Or is it the case that they don’t really exist? Like most of the drivel that Mike Mann comes out with, they are all just figments of his overactive imagination?
• Just to stand corrected, I wrote:
“On top of that, Hansen has propably made millions from speeches and prizes”
I was summing how much Hansen has made total in his entire career where I should have compared his one year earnings (at the lower end around $390 000) vs Singer’s one year earnings (around$100k).
• So c’mon guys. Where is the location of the Well-Funded Big Oil Denial Machine? Somebody has to authorise the payments, and process the transactions. If it has a global strategy of Denial, this didn’t come out of thin air.
You should ask Greenpeace that question, Latimer, they keep pretty good tabs on which of us climate skeptics are getting significant funding from ExxonMobil (Esso to you). You’ll no doubt recognize the following beneficiaries of their largesse.
George C. Marshall Institute: received $840,000 from Exxon since 1998. Heartland Institute: received$676,500 from Exxon since 1998
Stanford University Global Climate and Energy Project (G-CEP): Exxon committed $100 million over 10 years; so far half this amount has already been contributed. As Exxon says there, “This pioneering research program is focused on identifying breakthrough energy technologies that reduce greenhouse gas (GHG) emissions.” Since 2006 ExxonMobil has invested$1.6 billion in activities that improve energy efficiency and reduce GHG emissions.
If you’ve read Lindzen’s talk at the House of Commons, you’ll have seen where the IPCC completely agrees with his opening remarks about climate sensitivity. As you may have inferred from my response to his slides, we climate skeptics at Stanford, whose GCEP project has as noted above been fingered by Greenpeace as an ExxonMobil-funded climate-skeptic organization, are highly skeptical of the IPCC that Lindzen describes, and are deeply into denial of that sort of climate nonsense.
Hopefully this answers your question “Where is the location of the Well-Funded Big Oil Denial Machine?” Do the math.
• David Young
Vaughan, I hope you are being tongue in cheek. Big oil just like any large corporation wants to be seen as helping the planet. Thus the donation to Stanford which fits right in with a green agenda. The whole idea of the “fossil fuel industry conspiracy” is just a kooky idea that has no basis in fact. Conspiracy theory is not just the provence of the John Birch Society. The most odious such theory is the one that 9/11 was an “inside job.” This was a very popular one for left wing kooks over the last decade. And this one did a great deal of harm to the country. Generally, its almost impossible for more than one person to keep a secret and so conspiracies that require large numbers of people are generally prima facia nonsense.
By the way, you should learn how to use the italics key so your posts are more readable.
• David Young
Judith, is this a software problem? It seems that every post in this reply branch has italics turned on. Sorry Vaughan for imputing blame to you.
• Brian H
David Young | February 26, 2012 at 12:27 am |
He really is an eponymous one, isn’t he?
• Brian H
David Young;
I believe it’s in this comment:
https://judithcurry.com/2012/02/24/why-target-heartland/#comment-176445
Every post after that is italicized.
• Vaughan, I hope you are being tongue in cheek.
Indeed, sorry for not being clearer on that point, David.
I’ve spent some time on the italics problem, both this time and on previous occasions months ago, and concluded that WordPress has a major bug in how they try to deal with people who screw up their italics. This has been a long-standing problem, so it’s disgusting that they’ve done nothing whatsoever to fix this problem while continuing to charge premium rates to their clients. If I had nothing better to do I’d go into competition with them with a decent system. So it goes.
• Brandon Shollenberger
Vaughan Pratt, the bug you’re talking about is one which has been discussed, and diagnosed, here on this blog before. The problem is HTML allows you to include extra characters in certain flags without changing their functionality. WordPress was coded without this in mind, and that’s where the problem crops up.
Normally WordPress knows to close tags which weren’t closed properly, but WordPress does a string match for the exact flag people normally use. If you include extra characters in the tag, WordPress won’t recognize it, and thus, it won’t know to close it. That means the tag will be parsed by HTML like normal, and it will be considered open. Since WordPress doesn’t close it, it continues for the rest of the page. Even worse, WordPress won’t allow you to post a closing tag in a separate post as it will think it’s unmatched and strip it.
(I believe there are just two characters that can immediately follow the “i” in the tag and cause this bug are the space and forward slash, but I might be wrong. Not that it should matter, but you can actually then follow the extra character with any character you want, as many times as you want.)
• Thanks very much for clarifying this, Brandon.
So is there anything one can type in a comment that will fix the bug? Or does Judith have to edit the thread herself to fix it?
And if the latter, is it clear what to edit? I spent some time staring at the page and was unable to figure out how to fix it even if I had Judith’s editing priviliges. Can you see what to do?
• It’s clear that the problem is slightly more complex. WordPress can close the case of a missing tag. Thus it must recognize the erroneous closing tag as somehow related to the opening one. It changes the internal state flags but does it without creating a valid closing tag. In other words WordPress believes that the text contains a closing tag although that tag is not valid html.
It’s indeed annoying that his bug persists. Many people have tried to add closing tags to later messages but WordPress is too clever and removes those as superfluous.
• More specifically what we see in the source code as delivered are characters ‘<’;, ‘i’, blanko, ‘/’, and ‘>’;. The ‘i’ and slash are in wrong order and a blanko is inserted in-between. That is exactly the same that I have seen every time, when this error occurs. That’s not necessarily what the original text had, but that’s what WordPress produces (the most likely change by WordPress is the addition of the space).
My understanding is that the tag that WordPress sends is actually formally valid html that has no effect on anything (it initiates and closes italics without any text to handle). Somehow WordPress seems to believe that it has by that closed the italics opened by the earlier tag.
• I misplaced the single quotes in ‘<‘, ‘i’, blanko, ‘/’, and ‘>’
• Looking once more at the source code WordPress does actually add the right closing tag, but the extra tag described above acts as on extra opening tag and not as a meaningless chain of characters.
• My last comment means that I actually agree with Brandon.
(I didn’t realize earlier that WordPress does add one closing tag).
• My confusion and perhaps also that of WordPress was related to the handling of empty elements
http://www.cs.tut.fi/~jkorpela/html/empty.html
• I made some tests with WordPress on my own site.
The error seems to occur when the erroneous tag starts with ‘i’ and ends with slash and the slash either follows directly the ‘i’ or the first character after the ‘i’ is blank or slash. Extra characters are then allowed before the ending slash.
The relationship with properties of empty elements is obvious.
• Brandon Shollenberger
Vaughan Pratt:
Thanks very much for clarifying this, Brandon.
So is there anything one can type in a comment that will fix the bug? Or does Judith have to edit the thread herself to fix it?
And if the latter, is it clear what to edit? I spent some time staring at the page and was unable to figure out how to fix it even if I had Judith’s editing priviliges. Can you see what to do?
Unfortunately, there is nothing a user can do to fix the problem. The only way to fix it is for the offending tag to be edited out, and that requires someone with moderator privileges. Fortunately, it is pretty obvious what needs to be removed if you know to look for something. All one has to do is look for a tag which is malformed, and since you know which post it’s in, that’s easy to find.
Pekka Pirilä:
I made some tests with WordPress on my own site.
The error seems to occur when the erroneous tag starts with ‘i’ and ends with slash and the slash either follows directly the ‘i’ or the first character after the ‘i’ is blank or slash. Extra characters are then allowed before the ending slash.
I’m not sure how clear I was, but that’s exactly what I found too. I haven’t tested every character, so it’s possible other ones could trigger it, but those two are the only ones I’ve seen (or make sense to me).
I do think it is interesting you can put any amount of characters after the one wrong character since it means you can write “hidden messages.”
127. krischelKrischel
I think Curry’s reflection is spot on – the fact of Heartland’s activities aren’t the issue at all for Gleick – heck, Heartland is *proud* of what they’re doing!
What Gleick really wanted was a list of targets, and Heartland’s policy of privacy (because people *were* targeted) frustrated his desire to lash out at individuals, rather than at ideas.
128. A physicist
A physicist posted on WUWT: Plausibly, these [Edward Markey] press releases are opening salvos in a RICO (Racketeer Influenced and Corrupt Organizations Act) investigation, a topic upon which the Heartland Institute’s web site maintains numerous on-line position papers (for example, a Google Search finds hosted on the Heartland Institute website “The Statute of Limitations Under RICO: Rotella and Beyond”).
Part of the context is that the US tobacco industry, a major supporter of the Heartland Institute, has been found guilty under RICO of a racketeering conspiracy to obscure the scientific evidence that smoking causes cancer.
Under US law, it is “unlawful to receive income derived from a pattern of racketeering activity,” and thus the Heartland Institute already is subject to potential financial liabilities that are associated to the tobacco industry’s RICO conviction.
With a view toward future lawsuits relating to adverse consequences of CO2 emissions, and suspicions of a racketeering conspiracy that seeks to obscure the risks associated thereto, the identities and expectations of Heartland’s corporate sponsors now are a topic of public interest.
After acceptance by the WUWT moderators — and after being on-view for several hours at WUWT — the above was suddenly deleted by Anthony Watts for being “ridiculous, inflammatory, and clueless.”
Usually I have considerable respect for Anthony’s good judgment, and for WUWT’s commitment to open dialog, but in regard to public interest in the Heartland Institute’s ongoing entanglement(s) with RICO actions, it appears (to me) that either Anthony’s judgment is incorrect, or else WUWT’s commitment to public dialog does not extend to RICO-related activities. In particular, it is my considered opinion that WUWT readers are entirely capable of judging for themselves which opinions are “ridiculous, inflammatory, and clueless.”
• A Physicist
You appear to be part of the conspiracy promoting alarm over “adverse consequences of CO2 emissions” without considering the compensating information. See CO2Science and NIPCC. Try promoting the scientific method of looking at ALL the data.
PS I endorse Anthony Watts’ good judgement.
• lolwot
CO2Science and NIPCC spin science. You might as well go to Kent Hovind’s site to find the “compensating information” about evolution.
• John Whitman
John
• John Whitman
Of course you might have the small problem of no visitors.
Details, details, details.
John
• Truthseeker
“A physicist” you are clueless. Accepting donations is not a crime, regardless of the source. If the tobacco companies have been convicted under RICO, why are they still operating? I would love to see the tobacco companies completely dismantled and the owners jailed for the horrendous medical cost they have inflicted on the community at large. Whatever the legal outcome was, it must have been concluded which ends the matter.
I think it is good that you have re-posted this here so that even more people can see you for what you are.
• A physicist
Truthseeker asserts: Accepting donations is not a crime, regardless of the source.
Truthseeker, the Heartland Institute devotes considerable resources to arguing that your statement is morally correct.
Yet it is true too that under US law, both citizens and corporations are enjoined to refuse even lucrative payments originating from racketeering operations. It was upon this legal basis that the Justice Department secured RICO convictions upon the tobacco industry for deliberate obfuscation of the scientific evidence that smoking was harmful.
Unsurprisingly, the officials of the Heartland Institute dispute both the legality and the justice of the tobacco industry’s RICO convictions, asserting for example that “Even tobacco companies have constitutional rights.”
• GaryM
In breaking news, tobacco companies last year celebrated the end of a decade long, multi-million dollar jihad pursued by politicized Justice Department attorneys who were not satisfied with simply extorting billions of dollars in taxes disguised as a settlement from the defendants.
In a marvelously pyrrhic victory, the appellate court affirmed that the tobacco companies should be ordered to “stop that.” The government that refused to criminalize cigarettes (because a populace fully aware of the dangers of smoking for at least the last four decades still wants to buy them), pursued the injunction while happily cashing the billion dollar checks they have been collecting from the sale of cigarettes since the global tobacco settlement.
In unrelated news, the Democrat Party continues to collect massive campaign contributions from growers of tobacco, who for some unfathomable reason have escaped the wrath of Leviathan.
And this just in. Philip Morris’ stock price has risen approximately 33% since the appellate court decision.
• If the tobacco companies have been convicted under RICO, why are they still operating?
Because they weren’t convicted of operating, they were convicted under RICO. Duh.
If Bernie Madoff had been convicted of breathing they’d have presumably put a stop to that in due course, as they did with Saddam Hussein.
This is the first I’d heard of this sudden deletion of something RICO-related at WUWT. Did someone threaten Watt’s kneecaps? The plot thickens.
• asserting for example that “Even tobacco companies have constitutional rights.”
The question of whether corporations have constitutional rights is central to the Supreme Court’s recent campaign finance case, Citizens United v. Federal Election Commission. But it also comes up in many other areas — criminal prosecution of corporate entities, government demands for corporate data, punitive damages, and freedom of the press — to name only a few.
Anyone in the vicinity of Stanford University between 5:30 and 8 pm on March 5 is welcome to attend a discussion of this question. Free and open to the public, but registration is requested.
• lolwot
“In particular, it is my considered opinion that WUWT readers are entirely capable of judging for themselves which opinions are “ridiculous, inflammatory, and clueless.””
Well, you’d be wrong
• Punksta
it is my considered opinion that WUWT readers are entirely capable of judging for themselves which opinions are “ridiculous, inflammatory, and clueless.
lol: Well, you’d be wrong
Yes you’d need a data-hiding, peer-review-changing, memo-forging government climate scientist for that sort of decision.
• Billy Ruff'n
@A physicist
“With a view toward future lawsuits relating to adverse consequences of CO2 emissions, and suspicions of a racketeering conspiracy that seeks to obscure the risks associated thereto…”
Physicist, aren’t you asking us to assume that in the course of those lawsuits the plaintiffs would be able to PROVE that 1) there are adverse consequences of CO2 emissions, and 2) that there are risks associated thereto? So far, most people don’t seem to be convinced.
129. Rules for Radicals by Saul Alinsky, let’s count how many Gleick and the eco-left have been using as recently as the past week;
“Rule 1: Power is not only what you have, but what an opponent thinks you have. If your organization is small, hide your numbers in the dark and raise a din that will make everyone think you have many more people than you do.”
Nothing is more clear than a “consensus” organized, controlled from green census gatekeepers after years of internal filtering of a tiny “science” community pre-packed with those of green inclinations. Disagree you are no longer a member. One of the great scams of science history.
“Rule 2: Never go outside the experience of your people.
The result is confusion, fear, and retreat.”
It’s all been very routine the past week. Ad hominems, demonizing, ignoring the fact of a confession of an identity theft and making an ends justify means defense. This is all knee-jerk culture in the American left. Gleick and supporters are in perfect cultural form.
“Rule 3: Whenever possible, go outside the experience of an opponent. Here you want to cause confusion, fear, and retreat.”
Not much here of late, this is all very routine MSM and leftist pundit spinning of events regarding Gleick. 40 years of experience and current administration make this hard to create surprise or execute.
“Rule 4: Make opponents live up to their own book of rules. “You can kill them with this, for they can no more obey their own rules than the Christian church can live up to Christianity.”
Conservative freedom of assembly is now on the table by targeting Heartland by the AGW left. The AGW belief is discussed like it’s a religious “right” that skeptics are violating. It’s pure myth of course. The hope is that a false and fake hypocrisy argument can be created under this rule.
“Rule 5: Ridicule is man’s most potent weapon. It’s hard to counterattack ridicule, and it infuriates the opposition, which then reacts to your advantage.”
This is almost a daily use mantra. “GWB is Hitler” “Heartland are DENIERS= HOLOCAUST DENIERS”. Turn on NPR this will appear in a few minutes.
“Rule 6: A good tactic is one your people enjoy. “If your people aren’t having a ball doing it, there is something very wrong with the tactic.”
Angry spite, emotional ranting and distortion are a form of pleasure in the AGW community and the greater pool. Again, listen to the glee in the media voices on the Gleick affair. They do enjoy it.
“Rule 7: A tactic that drags on for too long becomes a drag. Commitment may become ritualistic as people turn to other issues.”
A problem for AGW, it’s a bore even to core members. Gleick defense by smear and slander attack, how long can it be kept up?
“Rule 8: Keep the pressure on. Use different tactics and actions and use all events of the period for your purpose. “The major premise for tactics is the development of operations that will maintain a constant pressure upon the opposition. It is this that will cause the opposition to react to your advantage.”
They try, but it gets old fast.
“Rule 9: The threat is more terrifying than the thing itself. When Alinsky leaked word that large numbers of poor people were going to tie up the washrooms of O’Hare Airport, Chicago city authorities quickly agreed to act on a longstanding commitment to a ghetto organization. They imagined the mayhem as thousands of passengers poured off airplanes to discover every washroom occupied. Then they imagined the international embarrassment and the damage to the city’s reputation.”
The Earth is at risk is an old meme. Evil corporations…….been there done that.
“Rule 10: The price of a successful attack is a constructive alternative. Avoid being trapped by an opponent or an interviewer who says, “Okay, what would you do?”
AGW people try hard not speak on specifics, if they do they lose. So they do use the Rule #10 for this purpose.
“Rule 11: Pick the target, freeze it, personalize it, polarize it. Don’t try to attack abstract corporations or bureaucracies. Identify a responsible individual. Ignore attempts to shift or spread the blame.”
Within the community words like “Heartland”, “Big oil” and “Corporations” all have coded meaning in the lefts/AGW belief system lexicon. Certainly noted skeptics and even AGW wafflers face this but it’s inside baseball on the AGW front.
• Jim
cwon14,
Excellent find! I never would have thought to open that book, in the unimaginable event that a copy of that book lay in my path, at some point in my life. I hate to say it, but what he writes is true; any jackass can kick down a barn, but it takes a carpenter to build one…
130. Venter
A Physicist has been a mindless troll spouting nonsense all the time at WUWT. None of his posts have had an ounce of sense or science or decency. Here again he spouts baseless garbage. He has no respect from any poster at WUWT.
131. Political Junkie
A few random thoughts:
Nick Stokes conveniently forgets that the East Anglia gang escaped criminal prosecution for evading FOI laws ONLY because the U.K. inexplicably has a six month statute of limitations.
Despite the Team’s clearly expressed and fervent desire to pin something on Steve McIntyre, he has not been found to be in the pocket of “big oil.” By their standards it is simply inconceivable that a semi-retired Canadian geezer working essentially alone has managed to expose the venality of the Team simply through meticulous fact based work. No Steve, no “climategate.”
As a Canadian, I’m deeply disappointed that DeSmogBlog and its confessed felon backer are Canadian. In our defence, let me point out that Steve McIntyere, Ross McKitrick and Donna Laframboise are also Canucks! On balance, we rock!
• John R T
“…Steve McIntyere, Ross McKitrick and Donna Laframboise are also Canucks! On balance, we rock!”
Thank you, neighbor!
• You have funny colored money and you talk like ur from wisconsin. Sheesh.
132. A physicist
Venter posts: “A Physicist” has been a mindless troll spouting nonsense all the time at WUWT. None of his posts have had an ounce of sense or science or decency. Here again he spouts baseless garbage. He has no respect from any poster at WUWT.
Venter, it has commonly happened that Anthony Watts and I agree entirely. As I wrote in a polite response to Anthony’s criticism:
Needless to say, it is a matter of considerable public interest whether any further RICO-related news will emerge regarding the Heartland Institute’s (admittedly intricate) entanglements with the interests of Big Tobacco and/or Big Carbon. Moreover, it seems likely (to me) that sooner or later, we will all be reading about these entanglements, here on WUWT.
Although in the present matter it is evident that Anthony and I disagree, the issue will resolve itself, if only we both are patient.
• Venter
That is one post where you praised Anthony. That dos not mean that Anthony and you agree enitrely always. I have seen your posts in WUWT and they are all of the mindless trolling variety,
• A physicist
With respect, Venter, to the extent that WUWT functions solely an echo chamber for folks who happen to agree with the opinions of Anthony Watts, then it will has precisely zero significance as a skeptical forum.
I happen to think more highly of Anthony than *that*. And that is why, in coming weeks, it is very likely (IMHO) that Anthony Watts/WUWT *will* tackle these RICO/tobacco/climate issues. Because they are important.
• Markus Fitzhenry
Don’t engage A physicist, Venter, He is a centric thinker and you will not learn anything from him.
Leave him to scribble with his stick in the dirt.
• A physicist
Markus, it please me to understand “scribble with a stick in the dirt” as a complimentary reference to Plutarch’s account of the the death of Archimedes, in which Archimedes is said to have exclaimed Noli turbare circulos meos! (“Do not disturb my circles!”) to a Roman centurion who, regrettably, did not grasp the import of Archimedes’ scribbles-in-the-sand, and in ignorance slew him.
• Markus Fitzhenry
Yes, funny about that dirty stick. But you ain’t no Archimedes A physicist, unfortunately you are as stupid as the rest of us. Funny about that little detail.
Still Zeno of Citium would be proud of you.
This overt attempt to control the message by a physicist and others is so transparent that it reminds me of a conversation that could have happened in the Oval Office 40 years ago. ” Ok, boys this is getting out of hand,” said RMN, ” for the cause we need to control the message and counter all this negative publicity. Now HR, I want you and John to go out there and destroy these b…….s and get this investigation buried with an intense negative publicity campaign against our enemies. Call J Edgar and see what he can dig up on these s..s-a -b…..s” .
Luckily the public can see through it all just as they did then
133. ” (just not the names of the donors, which aren’t all that interesting anyways.)”
With that sentence, Dr. Curry sums up exactly why Dr. Gleick risked everything for this. I believe that he was certain there would be bombshell donors to Heartland, that would destroy the credibility of the organization. When Exxon and BP were not on the donor list as Gleick was so sure would be, he made up his own summary memo to attempt to indict Heartland is some way, and sent them on.
His disappointment about the lack of a a donor to be a real credibility killer to Heartland was not going to be lost. He would not be denied. This director of ethics, this paragon of doing the right thing, copied the most incriminating sentences from the material he received, and forged the last paragraph to drive his point him.
Only, he drove the point straight through his own heart.
• John Whitman
Ron Dean | February 24, 2012 at 10:09 pm
This director of ethics, this paragon of doing the right thing, copied the most incriminating sentences from the material he received, and forged the last paragraph to drive his point him.
Only, he drove the point straight through his own heart.
Ron Dean,
Nicely said. Thanks.
I suggest we modify your last sentence to:
Only, he drove the point straight through both his own heart and the heart of the integrity of the ’cause’ he devoted so much of his life too.
John
• John,
Well stated. I cede to your superior close :)
134. Diag
How many times have we heard about the Big Oil funding? Without it ever being shown? Is that not a Holy Grail worth seeking for someone like Gleick? Perhaps he suspected that HI was the institution alluded to here (is there any other similar institution?):
In early 2007, Senator Barbara Boxer […] had a meeting with the head of the Intergovernmental Panel on Climate Change (IPCC) […] As she left the meeting, one of Senator Boxer’s staff pulled her to one side. She was told that a conservative organization, funded by an oil company, was offering scientists $10,000 to write articles that attacked the IPCC report and the models that had been used to produce its gloomy predictions. p.104, “Armageddon Science: the Science of Mass Destruction”, by Brian Clegg, St. Martin’s Press, 2010 His reference for this is “The Truth about Denial”, Newsweek, August 13,2007, by Sharon Begley. 135. CTL It’s rather appalling that “a physicist” attempts to continue to slander the Heartland Institute by now claiming they’re involved in racketeering. Worse, that when “a physicist” had his slander removed from WUWT because Mr. Watts didn’t want the legal exposure of hosting such slander per se, “a physicist” rushed right over to this blog to repeat it and put Ms. Curry at the same risk. • A physicist CTL, your post fails to grasp that the Heartland Institute is proud to assert, and to host on their own web site, and to prominently label as “posted for attribution”, assertions that “Even tobacco companies have constitutional rights.” The scope and limits of these tobacco-company rights, is of course an entirely legitimate topic for public discourse … however vehemently Anthony Watts/WUWT may disagree. Similarly, the tobacco industry’s RICO conviction for 150 counts of mail and wire fraud in a continuing “pattern of racketeering activity” with the “specific intent to defraud” is of course matter of public record (per the link posted above) … however vehemently the senior fellows of the Heartland Institute may disagree with the justice and legality of tobacco-industry RICO convictions. • nutso fasst If RICO were fairly applied, both major political parties would have their assets forfeited. Does Heartland’s opposition to federal laws regarding second-hand smoke make them evil? Should they all be lynched without trial for supporting constitutional guarantees you find offensive? 136. CTL My post does not “fail to grasp” any of those things you fantasize about, “a physicist”. I am simply not impressed by your Gleickian efforts to fabricate nefarious connections and claims of criminality that simply do not exist in your attempt to further defame the Heartland Institute. • A physicist Perhaps we are not even disagreeing, CTL. Of course the Heartland Institute has a corporate right to vehemently defend the profitable interests of tobacco companies … even tobacco companies convicted of “racketeering with specific intent to defraud” in regard to the sale of harmful products. And should the Heartland Institute similarly choose to vehemently defend the profitable interests of CO2-producing energy corporations, that too is their corporate right. Just as it is every American citizen’s constitutional right — and even civic obligation — to take notice of these Heartland Institute actions, and form opinions regarding them, and share those opinions. So, perhaps we are in agreement, eh? :) • Markus Fitzhenry “Gleickian efforts” Classic CTL – Love it. 137. CTL We very much disagree, “a physicist”. You are attempting to defame the Heartland Institute by weaving a dishonest narrative which accuses them of criminal activities despite you having no legal basis for doing so or proof of any wrongdoing. I am pointing out that your Gleickian effort to defame the Heartland Institute by weaving a dishonest narrative which accuses them of criminal activities despite you having no legal basis for doing so or proof of any wrongdoing is appalling slander per se which I think Mr. Watts was correct to remove from his comment section. • A physicist CTL, it’s odd that you label me “Gleickian” given “A physicists” harsh judgment of Gleick on WUWT … a judgment that was considerably tougher even than Anthony’s! WUWT, indeed? And it was “A physicist” (me!) who broke the Gleick story on WUWT … even before Anthony! :) So perhaps you shouldn’t be too surprised, that the same folks who harshly judge Gleick’s personal ethics, harshly judge Heartland’s corporate ethics. That’s just common-sense, eh? In the end, it’s Nature who delivers the final judgment regarding the risks of smoking $\Rightarrow$ cell-damage $\Rightarrow$ cancer $\Rightarrow$ early death. And similarly for Hansen-style risks of GHG $\Rightarrow$ GHE $\Rightarrow$ AGW $\Rightarrow$ CAGW. Because in both cases, as Richard Feynman famously said “Nature can’t be fooled.” And that too, is common-sense, eh? • Jon Carter Another rapid response paid spammer. Anyone seen ole Josh around? • Markus Fitzhenry Stop it A physicist or you know what will happen. In fact I think you are already blind. ”And similarly for Hansen-style risks of GHG \ GHE \ AGW \CAGW.” It is diametric to your first argument about smoking, as GH there is none, so GHG there is none, etc. • DeNihilist Uh Jon Carter, you don’t think that Josh is actually Pete……. Naw, couldn’t be! • kim Rose now to set later The sun charts its chariot track across the sky Waxed brilliantly with high flown rhetoric And rusted nails. ===== • Peter Davies Oh no – not another W***er Markus! 138. Paul Vaughan Politics is the fire hose giving climatologists 1000001 reasons to procrastinate. Respect & trust obliterated, again. 139. Venter A Physicist is simply thread diverting. He got royally bollocked at WUWT and has come running here to spam. None of his accusations have any basis and he is a fraud. 140. Roddy Campbell Is there a Godwin’s law equivalent for tobacco? I know ‘tobacco companies’ have a resonant equivalence with Satan in the US, but there just isn’t that connection in the UK. Admittedly I’m smoking as I type. ‘Juicier stuff’ indeed – Bast’s email at the head of this post is gripping, setting out clearly how they try to influence people, and I’m sure there’s a lot of ‘bad’ (as in slanted/inaccurate/biased) material in what they say. I’m sure they attract funding from people who agree with their mission statement. I’m sure I wouldn’t like some of those people. Bast’s email proudly sets out why a Gleick would be driven nuts by them. It’s an excellent marketing document. Imagine you agree with ‘Gleick’. It would be very annoying, these evil kleptocrats getting tax breaks to peddle lies designed to ensure that wealth inequality persists and increases. I’m just not sure what you’d do about it. Life is messy. You might do what Mashey does I guess, try and catch them out, bring them down. That’s what the anti-Murdochs in the UK did, and they’ve done well eventually. Or you argue against them, get NCSE to challenge their schooling materials. Lobby for a change in the law on super-pacs. Or do what Christopher Hitchens did, and rejoice that America, for all its evil capitalist faults, is a functioning democracy with a devoted commitment to free speech right or wrong, a country in which people jostle, more or less fairly, for influence, votes, money. He applied for citizenship. I hope you Americans, left or right, realise how much we sometimes envy your devotion to free speech, in every walk of life. There is so much more said over there, and life is the better for it. If no one says the unthinkable, less is thought. Gleick seemed to forget: ‘I disapprove of what you say, but will defend to the death your right to say it’. • Admittedly I’m smoking as I type. Did you light up having started the post, as a matter of principle, or were you smoking anyway? :) Ditto a lot of what you say about America. I’ve never had a puff of a cigarette (or ingested any illegal substance) in my life – but we’d agree that freedom is good for the health of a nation (not that it’s ever perfect – I would prefer all drugs legalised, for one example) and rejoice in this example in history, the blessing of which has flowed back to us in the UK and way beyond. And it’s in the blogosphere, twitterverse and the like that the latest struggles between form and freedom are taking place. Climate Etc isn’t the least important example. 141. Mickey Reno First, I apologize for the length of this post. Bear with me. I think Gleick’s motivation might be based in something less exotic than his hatred of Heartland, although he clearly did have some vast reservoir of pent up hostility. Even so, I think his behaviors might be better explained in a desire to please. But please who? I think it’s obvious he was trying to impress NCSE head Eugenie Scott, by making a big splash in his first month as a director of the new NCSE mission, which is to convince the public that the teaching of climate change skepticism or controversy is on par with teaching Creation Science. But that effort sounds a lot like something proposed by someone else who might be another person Gleick was trying to impress. Who? How about Cass Sunstein and his boss, the POTUS? These are far bigger fish than Heartland, and maybe winning favor from them would make the relative risk/reward equation something easier to understand than simply despising Heartland. Why do I suggest Cass Sunstein and the White House? Again, consider, the new NCSE mission that Gleick was to head (equating the Teaching of Climate Change controversy to teaching Creation Science). Apart from that being an insult on it’s face, it’s almost exactly what the head of Obama’s Office of Information and Regulatory Affairs Agency suggested in a 2008 paper he co-authored, in which he sought to equate climate change skeptics to other discredited people like Timothy McVeigh, 9/11 Truthers, and Conspiracy Theory nutjobs. “Conspiracy Theories” http://ssrn.com/abstract=1084585 I don’t know if people in the moderate center can really appreciate the depth of depravity of some on the left’s beliefs in some of these issues. I don’t mean to digress too much, but think about the almost unbelievable stupidity of the Fast and Furious gun walking debacle, which was someone in the Obama administration’s (Cass Sunstien perhaps) idea of a good way to influence gun control policy in the U.S. knowing that hundreds or even thousands of people in Mexico (and now at least 1 in the U.S.) could be murdered with those guns. What kind of a mind thinks things like that? And why are they part of our government? But if any part of Gleick’s phishing and forgery was an attempt to ingratiate himself with people like Cass Sunstien, or the White House, through his new job at NCSE, then maybe this is a better place to look to figure out the otherwise incomprehensible “why?” I’m rereading what I just wrote, and I find it hard to believe, and yet, when I read Sunstein’s paper, I see moral license to lie, cheat, demonize… in the same way I believe the NCSE wants to now start doing the same thing. I don’t want Gleick to be guilty of seeking admiration from that quarter, but I just can’t rule it out, given the bizarre incongruity of what he did. For that reason I think if Joe Bast goes forward with legal action, then all the communications of Gleick and the NCSE should be included in their discovery requests, including those from his initial contacts, prior to being named to their board. If the criminal investigation proceeds, I’d definitely recommend the FBI and or California state cops should look at all these documents, to determine if the NCSE shares some of the criminal liability. 142. Doug Schaefer @Latimer Alder | February 24, 2012 at 5:05 pm “…It was that they are planning to lie in the future…” As this discussion started on ‘why Heartland”, I’ll start with that. Heartland Institute by no means conceals its aims; it is a matter of personal preference whether anyone holds those aims in high, low or middling esteem. I appreciate the inference by @CTL | February 24, 2012 at 5:10 pm That John Mashey’s prepared report on the Heartland Institute may have been something that Gleick thought he could add to. But I quite disagree with CTL here: “I suspect the courts will sort that all out in due time.” And this may bear upon whether HI was in fact a logical/rational choice for Gleick. In fact @GaryM | February 24, 2012 at 5:43 pm Has preceded my posting here. Heartland, as a 501(c)3 *might* have something to fear in discovery in any proceeding against Gleick. I suggest that such proceedings will not happen, and I suggest that is the reason why. Call me whatever you like for saying so. If Heartland later goes to court, I’ll obviously be shown wrong. If they do not, it is an indifferent result to my thesis. But in considering this, please do not disregard Heartland’s first statement after the leak, where they promised to bring all villains to justice. Tax-sheltered 501(c)3 entities enjoy special financial status, but they must play by the rules. It ought not be for us here to judge Heartland concerning lobbying activities or foreign funding. That would be a matter for the IRS But in that light, Heartland might well seem a suitable target for Gleick. Hit them, knowing that they can’t hit back (I’m sure you realize this is nothing more than my thesis). In the process, Gleick has surely removed himself from any further substantial role in the climate-change debate. Probably from a role in other scientific discussions as well. Whether it goes further than Gleick himself would depend on further revelations, and I think (importantly) on the power of innuendo. If later, people here or elsewhere use “you’re just like Gleick” as shorthand for “I’m entirely justified to ignore *everything* you say, that is the power of innuendo. @ Vaughan Pratt | February 24, 2012 at 9:04 pm Wonders is there might be anything to learn in discovery about Heartland (leaning, I think, towards not). He may be right. Or not. @ John Whitman | February 24, 2012 at 10:18 pm Has already worked the innuendo angle: “…Only, he drove the point straight through both his own heart and the heart of the integrity of the ’cause’ he devoted so much of his life too.” John may not have been the first, but I’ll give credit. @Mickey Reno | February 25, 2012 at 1:28 am Would have legal discovery go both ways. Fair enough; more than fair. But I am still betting on no legal action against Gleick by Heartland. 143. manacker Why did he target Heartland? Because he thought a) that he would find “smoking gun” evidence of “big oil or coal” support, b) that he could neutralize a worrisome opponent and c) that he could get away with it. He was wrong on all counts and destroyed his own career in the process. Sic transit gloria. Max 144. Edwin Cottey Thank you Joe Bast for responding to Judith Curry, thank you Judith Curry for asking the question, thank you Anthony Watts for referring me to Judith Curry and of course for documenting the whole sordid affair. But thanks most of all to Gleick himself for putting me on to the Heartland Institute. What an excellent, worthy insititution. Now the fog is clearing and the light is shining. In three years of following this whole global warming thing I have wondered who the big bad wolf was that the warmists were so afraid of. Now I know. Keep up the good work, all of you (I don’t mean Gleick). The truth will eventually be known by everyone, not just the sceptics. They will teach the story to future generations and the world will be a better place for the knowledge of it. Science, like anything else, can be corrupted by people with good intentions. Now we are better prepared to resist a similar threat in the future. 145. tempterrain And of course all this begs the question of why we don’t have CO2 stabilization policies, which is mostly about economics, politics, values. So you’re saying that the scientific arguments are just a sideshow? • Latimer Alder I can’t answer for anybody else, but with all the taxpayer’s money sloshing around in the Big Green Industry complex, it seems to me that the actual science took a back seat long ago. The pollies got what they wanted from the scientists – a fig leaf of a reason to oppress their population yet further with taxation and control – and have ignored the science ever since. Exgreenism has become self-perpetuating and it will take a long time to roll it back. But we will get there one day. • Agnostic Latimer, I generally agree broadly with most of your posts, but I am so heartily fed up with the “the government just wants to oppress us with tax” meme as an argument against CAGW I just feel I have to say something. It’s utter rubbish. The governments also generally want to ‘bribe’ us with tax cuts, so take your cynical pick as to the strategy behind any elected governments motives. Governments want to be seen to be responsible and ‘tackling’ big ‘important’ issues. Starting from the beginning, I know of only handful of purely politically motivated skeptics who wou would deny that the basic premise behind CAGW is sound. The question asked is; “is the result of our unprecedented industrial activity and energy use having a negative impact on our climate?”. Or more specifically “are our co2 emissions causing the world to warm and will that be bad?” These are reasonable questions to ask and if the answer to this was ‘yes’, then of course we would look to our governments to do something about it. It turns out that the answers are not straightforward but predominantly ‘actually – probably not’. Governments are probably aware of this now, or becoming more aware, and even more sensitive to it due to the on going financial crisis. But politics is a funny game and it takes courage that easily be confused as stupidity to challenge such a long established meme as CAGW or AGW. It’s not such an easy thing to extricate yourself from in a political sense. In any case it’s not governments you should be wary of but corporations trying to exploit the opportunity CAGW mitigation policies present. You will of course get ideologues in governments that can affect policy badly (eg Australia) but the truth is pernicious. I think it is slowly sorting itself out. We are in a sort of end game for the excesses of CAGW alarmism, and you are really only battling zealots now. • tempterrain The pollies got what they wanted from the scientists – a fig leaf of a reason to oppress their population yet further with taxation and control – and have ignored the science ever since. So if that the case I’m just wondering why the US, to name just one country, doesn’t have any plans to introduce either a carbon tax or C&T on CO2? Politicians are good at thinking up new taxes. Agreed. So why would they bother to try and tie them to the results of scientific research? Its just so much easier to add a few % to income tax, VAT, sales tax, capital gains tax etc. They just don’t need a CO2 tax or C&T for political reasons. And why would scientists want to bother working for$70k per year doing climate research just for the money. These are smart guys. They’d make more than that in expenses alone if they worked in finance.
• Punksta
@tempterrain
I’m just wondering why the US, to name just one country, doesn’t have any plans to introduce either a carbon tax or C&T on CO2?
Because the ‘science’ supporting it has been shown to be hopelessly corrupt.
Politicians are good at thinking up new taxes. Agreed. So why would they bother to try and tie them to the results of scientific research? Its just so much easier to add a few % to income tax, VAT, sales tax, capital gains tax etc. They just don’t need a CO2 tax or C&T for political reasons.
They do as much VAT etc as they think they can get away with anyway. Green taxes can then be added on top.
• tempterrain
Punksta,
One of the drawbacks of so called “Green taxes” is that they are regressive. In other words, they are not diectly related to income or wealth. In more other words the poor may suffer more than the rich from higher heating and fuel costs.
Unlike, say a wealth tax, they aren’t the sort of taxes which are favoured by the Marxist types you claim are behind this so-called scam.
The only justification, for a tax (or C&T) on CO2, isn’t politcal from either a left or a right perspective. Its necessary to reduce emissions of the gas.
Its as simple as that.
• Markus Fitzhenry
Energy is the same as food Hottentot. Take it from my mouth and I’ll fight you, for my children and my children’s future. Your idea of equity is to rob third world countries of cheap energy. Do you think Glieck’s ideology was sufficient for his crimes?
If so, you ain’t seen nothing yet.
It’s that simple.
• Latimer Alder
@Peter Martin
I’ll believe your hypothesis about the causes of taxation when I see any government reducing/abolishing any other taxes to compensate for the increased revenue they expect from a carbon tax.
Until then it is merely a figleaf to disguise all politicians desire to take more money from the populace and then spend it in ways they approve of. There is no proven need to reduce carbon emissions and it is disingenuous to pretend that there is.
• Punksta
Tempterrain,
Green taxes etc enable the state and politicization to expand more than it otherwise could – taxes, regulations, regulators, bureaucracies, bureaucrats, etc etc. IOW, it inherently advances the totalitarian objective / pushes back the libertarian one.
The state has a vested interest in acceptance of CAGW. It also funds the whole CAGW initiative, outspending all other climate science by many orders of magnitude.
It’s as simple as that.
146. Bob Koss
OT, but an excellent talk.
PDF of Richard Lindzen at the House of Commons.
http://www.telegraph.co.uk/multimedia/archive/02148/RSL-HouseOfCommons_2148505a.pdf
• tempterrain
Richard Lindzen says climate sensitivity is low, less than 1 degC. He may well be wrong but at least he makes sense when he says therefore CO2 emissions are benign.
Unlike our host, JC, who likes to give out the same message even though she mentions figures as high as 6 deg, and even 10 deg C, but refuses to engage in any discussion on likelihoods, or timescales.
• Hold the front page: “Curry even worse than Lindzen,” says climate activist.
Impressive stuff Judith. You must be doing something right for the demonology to have reached these levels.
• tempterrain, you write “Richard Lindzen says climate sensitivity is low, less than 1 degC.”
Wrong. The estimate of 1 C is HIGH, not LOW.
• tempterrain
I think 1 deg C was the figure Richard Lindzen gave in testimony to the UK’s House of Lords a few years ago.
• tempterrain
@Richard Drake.
Just on a point of information: the idea of quote marks (“”) is that what goes in between them is supposed to be, well, an actual quote of what someone else said.
If in any doubt, just use the copy and paste feature that you’ll see when you right click your mouse and you won’t go far wrong.
• The quotes were for the headline on the front page I was imagining. But thanks for making me laugh a second time.
• tempterrain
yes, it would be interesting to know Judiths current position on the subject. . However, like Switzerland she is staying neutral(ish)
tonyb
• Any “serious climate scientist” would be a fool to challenge the claims in the first few slides of Lindzen’s talk on quantitative grounds, however tempted they might be by his seemingly outrageous claims. “What?” they would cry, “The IPCC agreed to nothing remotely like those numbers.”
Even if we suppose Lindzen has a clearer understanding of climate science than his colleagues, there is a more important reason not to challenge him on what he claims is the consensus of climate science. Lindzen’s slides are a minefield of gotchas (“by itself”, “equivalent CO2”, “increasing CO2 alone“), and you would look very stupid challenging him during the talk (if protocol permitted it) without having first surveyed the slides in advance to locate every gotcha that he’d get you on.
But that wouldn’t do you any good anyway because you’d then find yourself mired in interminable arguments, to which climate science is more susceptible than other sciences. Lindzen could exploit that weakness of the field to the hilt if the need arose. You would also need to match his pitch-perfect written-on-stone-tablets delivery.
The only reliable way to judge these slides therefore is to remove Lindzen from the picture, accept every statement protected with gotchas without attempting to disarm them, and focus on the logic of his arguments, which gotchas can’t protect. (I’m not a climate scientist, my career before I retired was in logic.)
1. When Slide 4 is taken to the logical conclusion Lindzen seemingly wants the honourable members to draw, namely that if greenhouse gases continue on their current rise we can expect a further rise of only 0.8 C over the next 150 years, he’s simply using the same linear-trend argument that Girma and Arfur Bryant love trotting out, obfuscated to make it less obvious.
The warming trend is in fact far from linear. Greenhouse gases are being added at an exponentially increasing rate, with emitted CO2 doubling every 30 years or faster (I estimate 28.6, YMMV). The warming trend is curving upwards.
2. Following a lot of political slides (appropriate in a House of Commons committee room), the next quantifiable statement is on Slide 11, “no warming since 1997.” Sound familiar? To imply as he does that this is not in dispute, based on one temperature plot, is to have been out of touch with the climate debate! The Berkeley Earth Surface Temperature data for example shows the land temperature since 1997 to have been rising in the same way it has been for decades!
3. In slides 13-14, Figure 2 averages the deviations of Figure 1, while Figure 3 is Figure 2 “stretched to fill the graph.” Nothing wrong with that, I sometimes do it myself to make the deviations clearer. But then he says “Note that the range is now from about -0.6C to +0.3C.”
“Now?” But that’s what the range was in Figure 2!. Scaling hasn’t made the deviations any larger, contrary to what Lindzen seems to want you to believe.
And neither it should, because it’s a theorem of statistics, applicable to many distributions but particularly normal distributions, that the average of n random variables each of standard deviation d has standard deviation d/sqrt(n). It’s hard to tell what point Lindzen wants to make here, if not to persuade his audience to ignore the factor of sqrt(n).
4. Slide 16 repeats another argument Girma and Arfur Bryant are fond of: that there is no essential difference in shape between the period 1895-1946 and 1957-2008. But that’s a completely bogus argument because it depends on detrending the second period (the graph on the left) by the man-made contribution of 0.4 C, after which you would expect the two shapes to be same given the shape of the 62-year-period AMO. (Note that he’s picked the two time periods to be separated by exactly 62 years! You’d think he’d have tried to be a little less blatant about it, but then who in a campaign to repeal a climate change act would notice such a thing?). In the case of the graphs on Slide 16 the temperature scale on the left has been decreased by 0.4 C. Yet the caption reads “Global average temperature and time scales are identical” (my italics).
These are the methods used by magicians and certain reverse mortgage salesmen. One does not expect them from an MIT professor of climate science.
As masters of deception, magicians fall into two categories, those who admit it’s all mirrors and sleight-of-hand, and those who insist the magic is real so as not to undermine the illusion. Reverse mortgage salesmen also fall into two categories, those who practice deception and those who don’t. Lindzen practices deception without admitting it, qualifying him for either profession.
In business it’s not what you know but who you know. In the climate blogosphere it’s who you ask. It would be very interesting to ask McIntyre whether Lindzen’s statistics were sounder than Mann’s, and as a baseline calibration also the Campaign to Repeal the Climate Change Act to which Lindzen addressed his views.
• Will do a post on sun nite or mon a.m. re lindzen’s talk, working on it now
• hunter
tt,
Thank you for demonstrating that you have no idea of what you are talking about.
• Vaughan Pratt (Feb 25, 2012 at 6:08 pm):
As a logician and supporter of the IPCC’s conclusions regarding AGW, how do you respond to the absence, in AR4, of reference to the statistical population underlying the IPCC’s conclusions or of predictions from the IPCC’s models. Don’t these lapses ensure that the IPCC’s claims cannot be tested, thus lying outside science?
• tempterrain
Tony B,
Your not the first person to mention Switzerland in connection with Judith Curry.
cwon14 commented:
” Or is to maintain Dr. Curry’s gutless Switzerland status during the climate war?”
Is being neutral “gutless”? Well, possibly it is in the context of the “climate wars”. Cwon14 and I may agree on that but not much else I’d expect. I might just say, though, that Cwon14 is probably insufficiently intellectually equipped to appreciate the game Dr Curry is playing. I’ll leave it to others to explain what he hasn’t grasped.
• kim
That’s pretty impoverished rhetoric, Peter M; we’re all fakirs touching different parts of the elephant game.
==================
• As a logician and supporter of the IPCC’s conclusions regarding AGW,
What? Where have I ever said I “support the IPCC conclusions?” That’s ridiculous.
(I’m senile enough that I could well have said this, along with well known fact that the Moon is made of green cheese, but I’d still like it pointed out where.)
147. Shevva
This is what I stand for, this is the science I stand behind, through open and honest bedate, I would hope you stand with me.
Seems simple enough.
• Markus Fitzhenry
Good onya Shevva. Actually whilst all this brohaha has been going on amongst so called academics and climate scientists, real physicists have realised some outstanding facts about climate.
Like the relationship of the S-B law between two spheres one encircling the other with a vacuum in between. Looks like there is a new (yet old) paradigm coming into vogue about how our climate works.
I don’t want to preempt the authors, but watch this space for a new age of enlightenment, not only in the scientific world, but also in Humans understanding of our interaction with the ecology.
148. Doug Schaefer
Edwin Cottey, as Heartland is news to you, don’t miss their fund-soliciting page:
https://supportheartland.kimbia.com/legaldefensefund
“…The truth will eventually be known by everyone…”
I agree completely, and wish I’d said it myself first.
BTW Dr. Curry, my previous post was my first, I sent it, and bang there it was. I praise this policy of non-moderation, because it implies that participants here are wise enough to sort wheat from chaff on their own. Cheers!
149. vukcevic
I never thought that many of the highly educated and intelligent scientists pushing the AGW mantra actually believe in it.
There are ‘fanatics’ for the cause, and then there is an army of followers.
It’s like being member of communist party in a Stalinist regime, you know it’s wrong, but you dare not leave and ‘betray’ the cause. Once regime falls, they all switch loyalties overnight and ‘en masse’. Just look at the east Europe’s ex-communist states, and who is in power now, the same old lot, just wearing different insignia.
It’s more often matter of interest than the science.
• The unfortunate wedding of science and politics in the USA was sealed with the atomic bomb that vaporized Hiroshima in August 1945.
After World War II ended, membership in the US National Academy of Sciences – at least in the Geophysics Division – became “like being member of communist party in a Stalinist regime, you know it’s wrong, but you dare not leave and ‘betray’ the cause.”
Those members tried to suppress the fact that Japan came very close to developing the first A-bomb and winning WWII instead.
When my research advisor (that the US military relocated to the US after WWII), Professor Paul K. Kuroda came to the 1956 AGU meeting in April 1956 to report calculations that showed self-sustaining nuclear fission had occurred naturally in Earth’s early history (when the U-235/U-238 ratio was much higher), I was told that a member of the Geophysics Division of NAS chaired the session of the meeting where Kuroda spoke.
Kuroda was scolded from the podium and publicly informed that Enrico Fermi had examined his calculations and found them impossible.
Kuroda’s paper was rejected for publication. Kuroda had in fact done the calculations and understood nuclear pile theory as well as Fermi. Later, Kuroda published his calculations as two, single page articles in the Journal of Chemical Physics 25 (1956) pages 781 and 1295.
His calculations were confirmed on 25 Sept 1972 when the French Atomic Energy Commission reported a natural nuclear reactor had occurred at Oklo in the Republic of Gabon, Africa.
See Professor Kuroda’s abstract: “Until recently, scientists believed that the chemical elements were synthesized only in stars. The discovery of the Oklo phenomenon in the Republic of Gabon in 1972 has revealed, however, that a nuclear fire had existed on the earth and largescale transmutations of the elements were occurring on our planet 1.7·10^9 years ago. The formation of natural (or Pre-Fermi) reactors is closely related to the appearance of life on our planet earth. The Pre-Fermi reactors were probably never formed until about 2·10^9 years ago, when oxygen was injected into the earth’s atmosphere by a new generation of living organisms carrying out photosynthesis.”
• Hadn’t occurred to me that Stalin had inflincted psychological as well as physical damage, Vukcevic, but it’s very plausible now you mention it.
150. Martha
“why the US, to name just one country, doesn’t have any plans to introduce either a carbon tax or C&T on CO2”
Actually, it was a main domestic agenda item on which Obama was elected and in 2009 the country tried to move forward with an emissions trading plan similar to Europe’s Emissions Trading Scheme (ETS). The American Clean Energy and Security (ACES) bill was passed in the House but defeated in the Senate. While it was criticized by some environmentalists, overall, it was defeated by strong opposition by a small but powerful sector of coal, oil and energy interests combined with a Republican lockstep and public worry over the recession, preventing the American public and many other industry players from having the enegy plan they want.
California has led the effort to introduce cross-border cap and trade on large industrial emitters with several other states and with four provinces in Canada. It’s called the Western Climate Initiative (WCI). This kind of multi-lateral state agreement is increasingly common.
However, the real question is whether the U.S. government is taking a regulatory approach of any kind and imposing emissions regulations on industry — not necessarily cap and trade. The answer is ‘yes’: last year, government announced in all major media its plans for GHG emissions rules for industry, to take effect the end of 2012.
Etc.
As most people know, the U.S. is perceived as quite resistant to international co-operation on many issues and, for example, the U.S. airline industry does not wish to abide by the EU’s ETS airspace regulations and is challenging for an exemption. Not good, for either the earth or economic relations.
Frankly, it is targeted political resistance to proposals like ACES and the EPA industry regulations that is the main activity of Heartland and Cato and similar groups. Curry thinks it could still be about public education or even democracy. It isn’t: it’s now about maintaining direct political influence in the backroooms where policy either lives or dies. And to their credit, Heartland and Cato do not really pretend otherwise and the only ‘secret’ thing about their activity involves complex tax shelters relating to maintaining nonprofit status in the modern legislative and regulatory framework for such organizations.
All of this to say, the country (the public and the government it elected) has plans to introduce necessary legislation to support society and future generations and respond to the reality of climate change. However these plans have been delayed, as described. And all those who have no knowledge or understanding of this reallly do not know what they’re talking about.
Martha do you accept that is entirely legitimate and in fact only right and proper that what you describe as ‘a small but powerful sector of coal, oil and energy interests’ should seek to protect their commercial interests and the interests of the many people that work and earn a living in those sectors?
• Punksta
Martha you clearly have have no knowledge or understanding of the issues here. The “reality of climate change” is that we are nowhere near understanding it yet.
The legislation you speak of is thus only “necessary” to advance the real totalitarian/left political agenda – more taxes and state control. This is achieved by the state’s lackey climate scientists producing the CAGW propaganda they were hired for, using methods like hiding data, hiding declines, forging documents, redefining peer-review, etc.
• Martha
It is not ‘moving forward’ to adoprt a European ‘ETS’ It is a retrograde step that will harm business and citizens as it will increase costs. Don’t do it.
tonyb
• Martha
Tony,
“it is not ‘moving forward’ to adopt a European ETS”
That is not what I suggested. It also has nothing to do with objecting to how Heartland and Cato’s network of political influence does business in the Senate of America or the basic responsiblity of commenters to know what legislation already exists and why (or what doesn’t exist and why not).
The 1,500 page bill had similarities but also many differences from the European approach, from the overall framework to important details like cost containment and protection of vulnerable players.
What is already in place as multilateral state and cross-national agreements (WCI) and the regulatory approach for domestic industries, also has many differences from the European approach.
That would be because Americans, least of all an American government, are not Europeans.
• hunter
Martha,
Thank you for your postcards from the alternate universe you live in.
“A physicist” Climate Etc Handle = This isn’t kindergarten and appealing to your own imagined authority has been long been tried with not much success.
Andrew
152. Ron Cram
Dr. Curry,
I don’t normally of you as a comedian, but putting Revkin “in the middle” was laugh out loud funny!
Great post!
153. A physicist
Dear Anthony Watts
In regard to the many admirable quotations in your recent WUWT essay “Relevant quotes on skepticism – and a motto for our times”, please let me advocate for this one: “Be First with the Truth.”
Two fundamental virtues of “Be First with the Truth” are:
• it is the simplest and shortest of maxims, and
• the other virtues in your WUWT essay all follow from it.
Uncompromising fidelity to this simplest-yet-toughest of principles — extending in a chain of integrity from the lowest lance corporal to the highest levels of command — has sustained America’s troops (and the families of those troops) through many years of a grinding tough war. Semper Fi!
We all appreciate that Peter Gleick gravely violated “Be First with the Truth” … indeed, I was myself among the first to break the story here on WUWT (before even you, Anthony!), and among severest to criticize Gleick’s actions (more severe even than you, Anthony!). So I hope you will not mind that I apply the principle “Be First with the Truth” with equal strictness to the Heartland Institute.
Very regrettably, here on WUWT there has been a recent increase in unchallenged posts asserting skepticism regarding the link between smoking and cancer.
It is easy to fact-check that these WUWT posts reflect the longstanding view of the Heartland Institute’s president and CEO Joseph Bast — and of the tobacco companies whose profitable interests the Heartland Institute advocates — that “moderate smoking is not a proven health hazard.”
It can form no part of rational skepticism to allow these flimsy-yet-deadly denialist medical claims to pass unchallenged here on WUWT. And it would be a great pity if the metastatic cells of denialist-type skepticism were to multiply unopposed within WUWT’s admirably healthy body of rational skepticism, thereby utterly destroying the capability of rational skepticism to address any of the great issues of the 21st century.
And so, it is entirely appropriate that rationally skeptical forums (like WUWT) severely criticize Peter Gleick’s gross failure to “Be First with the Truth.” And similarly, it is entirely appropriate too — and absolutely essential to the integrity and effectiveness of rational skepticism — that the Heartland Institute’s failures to “Be First with the Truth” are criticized with similarly uncompromising severity.
• Mark F
If tobacco companies didn’t have a right to speak (which is really what HI were referring to – a bit out of context you seem to be), think about whether or not *your* right to speak might be eroded by the same (presumed) logic. While I don’t care for a lot of things you state, I’ll defend your right to state them. Without slandering you.
• A physicist
As a follow-up, Anthony Watts has allowed the preceding post’s introductory paragraphs, and its concluding paragraph, to to appear on WUWT. Which is good! :)
Very regrettably, Anthony has unilaterally excised from the post all substantive criticism of the Heartland Institute, thereby shielding WUWT’s readers even from knowledge that this skeptical criticism exists (or from verifying for themselves this criticism’s concretely factual basis).
It is therefore my own considered opinion — based upon the above evidence — that neither Anthony Watts (with his personal predilection for censorship) nor the Heartland Institute (with its corporate predilection for legal imposition of censorship) has grasped the significance of the principle “Be First with the Truth” as a tough-yet-essential foundation for all forms of rational skepticism — a skeptical principle that must be embraced without reserve, if it is to be embraced at all.
For so long as their thoroughgoing embrace of censorship in service of suppressing public dialog persists, it is my personal opinion that neither Anthony, nor WUWT, nor the Heartland Institute, are in any sense qualified to be regarded as advocates of rational skepticism.
154. CTL
You do not follow the principle of “Be First with the Truth”, “a physicist”.
From what I’ve seen of your comments, your guiding principle is much closer to “Be First with the Baseless, Slanderous Accusations and Repeat Them Over and Over Again in an Attempt to Derail the Conversation.”
Historically literate people might observe that the principle you actually follow in your behavior is identical to “The Big Lie” propaganda technique.
And even historically illiterate people will recognize that your appropriation of the integrity and honor of military men who risked their lives serving their countries to use as justification for you to spew your defamation is cowardly and despicable.
• A physicist
CTL, on any forum — whether skeptic-leaning or consensus-leaning — censorship of the strongest criticisms can serve no good purpose … for the common-sense reason that the strongest skepticism and the strongest science recognize one another not as enemies, but rather as the most natural of allies.
The too-common practices of censorship, personal abuse, cherry-picking, astro-turfing, and legal bluster all seek to obstruct the natural union of strong skepticism with strong science … yet over the long run, they are entirely helpless to prevent it.
In this regard, please let me commend to your attention and consideration the core USMC/Army principle that “All force activity is wrapped in a blanket of truth.”
The practices of censorship, personal abuse, cherry-picking, astro-turfing, and legal bluster amount to “holes in the blanket of truth” and that is the simple reason why these practices must be foresworn.
155. CTL
“a physicist”:
It is your choice to pursue The Big Lie technique as your primary method of communication.
However, a moderator removing your non-topical, dishonest, defamatory statements from the comments section of a blog is no more “censorship” than removing penis enlargement spam from the comments section would be.
And the penis enlargement spammer has the virtue of not trying to wrap its fantasy claims in the mantle of honor and integrity of the armed forces.
Your behavior makes you a less appealing ally than a penis enlargement spammer would be. Perhaps you should reflect on that, “a physicist”.
• A physicist
CTL, the public easily distinguishes “blankets that wrap truth” from “raincoats that wrap abuse.” And so folks can reliably decide for themselves the intended category of any given post. :)
156. Anthony Watts
“a physicist” has yet again tried to steer a conversation into one of his off topic rabbit holes.
Since his first post on the WUWT thread contained the salutation:
“Dear Anthony Watts,”
Let me remind readers here of the words written by “a physicist” on WUWT
“Should you ever observe that I (or for that matter any WUWT poster) am mainly criticizing persons, rather than opinions, then it would be fully appropriate to require that personal criticism to appear under my own name, or not at all.”
While co-opting the brave men and women of the US military as example of truth and honor for his own purposes, I doubt “a physicist” has the courage to honor his own statement as it applies to criticizing people directly.
On another note, that actually IS on-topic, there’s a new article about targeting Heartland at The Weekly Standard.
http://www.weeklystandard.com/articles/why-climate-skeptics-are-winning_631915.html?page=1
• A physicist
Folks, for many years, in a grinding war, America’s commanders have asked our soldiers to fight and die for the principle “Be First with the Truth” (per the Multi-National Force-Iraq Commander’s Counterinsurgency Guidance, for example).
A lesson harshly-learned in this war has been that uncompromising respect for the principle “Be First with the Truth” is necessary equally to victory in-theater, and to sustaining the morale of America’s troops and their families. And from the lowest Marine lance corporal to four-star generals and admirals, and also the medical personnel who care for them, this principle is scrupulously respected.
Conversely, experience has show that seemingly small compromises with the principle “Be First with the Truth” swiftly unravel into major ethical disasters. Just ask Peter Gleick, or ask the tobacco companies convicted under RICO, how easy it is to drift into “patterns of racketeering activity” with “specific intent to defraud”.
So rather than abusing me personally for advocating this principle — that personal abuse being a sad waste of energy and time — perhaps more folks (including Anthony Watts) ought to reflect upon the principle “Be First with the Truth” itself, and then contribute responsible comments upon the broad span of duties that this principle devolves upon America’s citizens (both science-minded and skeptic-minded).
Moreover, the principle “Be First with the Truth” applies equally to American corporations too, and in the present context the Heartland Institute most definitely should, could, and must do better.
In saying this, no personal criticism is intended of Anthony Watts (or anyone else). Because without regard for personal differences of political and scientific opinion, here is a plain truth: for America as a nation to ask of its troops that they “Be First with the Truth”, we as America’s citizens must be solidly united in our willingness to “Be First with the Truth” too.
To the extent that we all embrace this fundamental principle, we will all be better off for it. It is our best safeguard against having to learn, yet again, those harsh lessons in ethics that both Peter Gleick and America’s tobacco companies have learned already, and to which America’s CO2-emitting energy companies should be paying close attention.
157. GoFigure
I don’t have time to review all the emails, so I aologize beforehand if this information is redundant, but according to JunkScience.com the Pacific Institute (via Gleick) has received some \$400k+ in grants from the EPA.
Shortly thereafter, when the folks at JunkScience went back to take a harder look at EPA’s (presumably public) online database, the various grants to Pacific Institute had disappeared.
EPA should be held accountable for that little game !
• kim
I’ve seen it remarked once before. It is remarkable.
=============
158. Markus Fitzhenry
‘So rather than abusing me personally for advocating this principle’
You arrogant hubristic deviant. You have no idea of the meaning of the truth you proscribe. My truth is not yours so is not truth?
The fundamental principle of, be first with the truth, assumes one is indeed the harbinger of truth. Your not first with the truth, you are first with arrogance.
How did the principle stack up in Vietnam, and how is it stacking up with the likes of Gliecks cohorts.
You dishonor the fallen.
159. A physicist
Markus Fitzhenry posts: You arrogant hubristic deviant …
Gee Markus, no you’ve got me wondering accusations will come next next … howzabout “conspiracy to sap and impurify all of our precious bodily fluids”? :) :) :)
Seriously, not one iota of the plain facts of the post can be altered, even by unbounded personal abuse. And that is the point of the post, and the kernel of the values espoused.
• Markus likes the sound of his overwrought prose. Me, not so much. If he punched it up a bit it would approach being a very regal purple. As it stands or rather limps, it’s barely lavender.
• Steven, since everyone but Markus agrees with you, if there’s any point to your remarks about him you should phrase them for his benefit, not ours .
160. Anthony Watts
“a physicist” says: In saying this, no personal criticism is intended of Anthony Watts (or anyone else).
I’m sorry, I just have to call BS on that. When you name me directly at the top of the post, any rational person would assume that it is in fact being directed at me.
• Anthony – Above, you quoted “a physicist” as stating that anyone engaging in personally directed comments (particularly those with negative intent) should be honorable enough to use his or her own name rather than hide behind a pseudonym.
Is that your position as well? If not, would you explain how and why you differ?
• Anthony Watts
Fred, it is my position also, based on the confrontation clause in the sixth amendment to the constitution.
http://en.wikipedia.org/wiki/Sixth_Amendment_to_the_United_States_Constitution
The Confrontation Clause relates to the common law rule preventing the admission of hearsay, that is to say, testimony by one witness as to the statements and observations of another person to prove that the statement or observation was accurate. The rationale was that the defendant had no opportunity to challenge the credibility of and cross-examine the person making the statements.
The right to confront and cross-examine witnesses also applies to physical evidence; the prosecution must present physical evidence to the jury, providing the defense ample opportunity to cross-examine its validity and meaning.
Since I and many other skeptics are often accused of being “not credible” and often “criminal” in our skepticsim (damaging Gaia and all that) and in fact we are on trial every day and faced with cross examination by people with negative and sometimes hostile intent, I feel that it should apply.
Of course, most anonymous harangues, like “a physicist” and now demonstrated with Gleick’s impersonation deceits, don’t have the ‘nads to put their names with accusations, or even engage in open public debate with them using their names. They prefer instead to take pot-shots from behind the veil.
They want all of the benefits and none of the risks. When somebody like “a physicist” repeatedly calls me out by name, I’m well within my rights to ask that he use his. Since he won’t, I don’t find him credible.
Should he change his tune and practice what he preaches, he’ll elevate his status because he’ll be adding Dr. to his name.
• Thanks, Anthony. I certainly agree, but I had the impression that principle wasn’t always in operation on WUWT, where insults sometimes emanated from individuals whose real identities were not stated. However, my impression may be wrong, and so I’ll pay more attention in the future. In any case, WUWT is relatively civil compared with some other web sources, and so I hope the principle you and I agree on can somehow spread more generally.
• A physicist
The anatomic speculations that first CTL, and then Markus, and now even Anthony Watts (?) have begun offering upon the topic of my personal “`nads” suggests that this topic possibly exerts a weird fascination upon some folks … have you three considered launching a specialized weblog? Perhaps naming it WUWT-II? :) :) :)
Seriously, perhaps readers of Climate Etc. might be more interested if any or all of you offered a thoughtful, fact-based, rational vision of resolution … like this one, for example.
Why not attempt it, gentlemen?
161. Beth Cooper
H/T to Judith [email protected] pm.
Steve Mosher, polish up your spurs and fetch your horse, they’ll be coming after YOU !
162. Anthony Watts
Fred, I can’t always manage the thousands of commenters we have, but I and the volunteer moderators do our best to keep it civil. We don’t always succeed. Being human, we are imperfect, but the results speak for themselves.
“a physicist” has a regular MO, aptly demonstrated in the thread above. He tosses off-topic grenades (like RICO in a thread about historic quotes) and then lectures down to others. Then when called/snipped on it he whines about “censorship”. He’s had 408 comments on WUWT, so that’s not a credible accusation.
When he calls me out directly by name as he has done here and in the WUWT thread, I plan to hold him to his own stated position, which is:
“Should you ever observe that I (or for that matter any WUWT poster) am mainly criticizing persons, rather than opinions, then it would be fully appropriate to require that personal criticism to appear under my own name, or not at all.”
Unfortunately, like Dr. Gleick and his ethics lectures, he has demonstrated that he does not practice what he preaches. For example: http://wattsupwiththat.com/2012/02/25/peter-gleick-lecturing-the-u-s-senate-on-deceitful-tactics/
Post Gleick, I have less tolerance for people that act this way.
• Markus Fitzhenry
““a physicist” says: Perhaps more folks ought to reflect upon the principle “Be First with the Truth” itself.”
And Watts demonstrates that He is in fact the truth and has the decency not to out the Dr.
Higher morals, even on a battlefield, wins the day.
163. A physicist
Anthony … (and note that I am asking as someone who shrugs off being called a “[redacted] [redacted] [redacted]” :) ) … what assertion(s) specifically bother you?
The post in question is structured so as to be both verifiably factual and (if its prescriptions are followed) to provide solid foundations for uniting science with skepticism.
As I posted in a WUWT comment on that [regrettably] received censorship:
A Physicist posts: I hope you will not mind that I apply the principle “Be First with the Truth” with equal strictness to the Heartland Institute. [snip – I do mind Anthony]
Here is a prediction, Anthony: before the end of 2012, the policies of WUWT will be revised to advocate that the principle “Be First with the Truth” is best embraced symmetrically, by the strongest science and the strongest skepticism.
And this will not happen by any scandalous kerfuffle, or in consequence of any contractual obligation, but rather for the one and only good reason: that upon sober reflection, and before 2012 is over, Anthony Watts will conclude, as an individual citizen, and solely of his own free will, that a thoroughgoing, uncompromising, and unequivocal embrace of “Be First with the Truth” is essential to rational skepticism.
Anthony, if it should be the case that you are unalterably opposed to any union of science with skepticism, then my prediction will fail. And yet, it so happens that (like many folks) I think more highly of Anthony Watts and his WUWT forum than that … and so I will remain optimistic.
Alternatively, if it should be the case that the above vision of resolution was censored not by Anthony Watts, but by WUWT’s team of moderators … then you need to have a talk with those folks! :)
164. Bob Fernley-Jones
I would like to propose the adoption of a new verb into English and Americano lingua:
gleick: To profess the highest ethics whilst practicing the lowest.
Hope it’s not a duplication, I only flicked through the above 693 comments
165. A physicist
• The facts of the posts in question are undisputed.
• Yet no-one comments upon the guidance implicit in those facts.
Therefore, as a concrete vision of resolution, please let me offer this prediction: before the end of 2012, the policies of many climate forums (including Climate Etc. and WUWT) will be revised to publicly acknowledge and advocate that the principle “Be First with the Truth” is fundamental to the reconciliation of the strongest science with the strongest skepticism.
And this sea-change will not happen by any scandalous kerfuffle, or by contractual restrictions imposed by corporate lawyers, but rather for the one and only good and honorable reason: that scientists and skeptics alike (including weblog hosts!) will arrive at an appreciation — as individual citizens and solely of their own free will — that a thoroughgoing, uncompromising, and unequivocal embrace of “Be First with the Truth” is essential to the accelerating union of rational skepticism with strong science.
Obviously the weakest forms of “gotcha” skepticism will never be reconciled with the weakest forms of “not even wrong” science. In fact, we can anticipate that both will cry ever-more-loudly in coming years, via methods that are familiar to all: censorship, personal abuse, cherry-picking, astro-turfing, slogan-shouting, and legal bluster
But in the long run, who cares? Both “gotcha” skepticism and weak science are irrelevant, because as Richard Feynman reminds us “Nature cannot be fooled.” It is for this reason that a reconciliation of strong science with strong skepticism is inevitable.
As a thoroughgoing guide to the characteristics of weak “gotcha” skepticism with weak “not even wrong” science, please let commend to readers of both Climate Etc. and WUWT the wonderful essay by Dr. Trish Roberts-Miller titled “Characteristics of Demagoguery” (a Google Search will find it).
An essay well-worth reading! :) :) :)
166. Markus Fitzhenry
You are a complex little soul aren’t you A physicist. But you are wrong.
Indeed ‘Be First with the Truth’ will not be something you will need to propitiate much longer is 2012.
It’s striking how often warmists rely on really bad science. This seems to be a quality of warmists since the late twentieth century, and there are several ways to interpret it.
First, this use of science (which is often presented as an appeal to “nature”) may be related to warmists tendency to appeal to misanthropism – that is the ideology of nature as more pure than man.
Secondly, it may be that warmists will use anything that happens to help them—if they can find something scientific-looking, they’ll use it, but they don’t believe it (I think it’s hard to come to any other conclusion)
It will be shown in the first half of 2012 that AGW is a invalid scientific principle and dichotomy in climate science will be extinguished by, if you will, the first with the truth.
I’m to tired to call you any more names, I’ll do that tomorrow. :-)
167. Venter
Nature will show A Physicist and the AGW mob for the liars, frauds and dishonest mob they are.
• A physicist
Venter, you are of course 100% right that Nature renders her harsh-yet-just verdicts with total disregard for censorship, personal abuse, cherry-picking, astro-turfing, slogan-shouting, and legal bluster … which is why these activities are irrelevant in the long run.
And conversely, Judge Nature’s procedural inflexibility is why James Hansen and his colleagues are wise in asking Nature to judge the case strictly on its natural merits, in accord with their carefully structured petition, The Seven Key Predictions of Warmism.
How soon will Judge Nature render her verdict? Scientists are petitioning Nature to render the earliest feasible verdict, by the strongest available three-fold methods of physical theory, laboratory experiment, and planetary-scale observations.
And of course, rational skeptics already have united with scientists in petitioning Nature for this early verdict, eh? :) :) :)
Of course, everyone understands weakest forms of “gotcha” skepticism will never be reconciled with the weakest forms of “not even wrong” science. And that is why Judge Nature vacates both of their testimonies.
• Venter
Only somebody as blind and deluded as you wouldn’t be able to see that Nature has not paid ball with any of the alarmist model predictions. Neither is it likely to play ball. Ay amount of bluster and lies can’t hide facts and empirical evidence.
• A physicist
Judge Nature: The court directs that abuse be stricken. The court will resume consideration of the theoretical, experimental, and observational evidence for the causal chain GHG $\Leftrightarrow$ GHE $\Leftrightarrow$ AGW $\Leftrightarrow$ CAGW.
Hmmm … Judge Nature hasn’t much sense of humor, eh?
:) :D :lol: 8)
• Markus Fitzhenry.
A physicist, shame that the philosophical extrapolations of greenhouse differ from the theoretical, experimental, and observational evidence for the causal chain of greenhouse.
Thus far, the science of atmosphere has rested on the paradigm of Greenhouse.
It is a misinterpretation of the observations of the french scientist Baron Fourier by Arrhenius in 1896. It is that misconception, of previous known physical laws , that has polluted our perceptions of the earths atmosphere into the modern ages..
To shift that invalid principal one has to offer a different perception born of observations and proved in the universal application of it in, within a symbolic syntax (maths).
This is the crux of the matter
The current paradigm demands our atmosphere is gas in an enclosed house.
The correct principal is that the enclosure itself is the whole of the atmosphere. Consider the greenhouse roof to start at the earths surface and end at the top of our atmosphere.
The invalid greenhouse principal is false when subjected to the principal of conservation of energy. They cannot explain why it is so except for the introduction of a new invalid principal.
As we have always done, when our knowledge of the universe of physics reaches the end of our ability to predicate, we fear the unknown. We naturally conserve our existence and fear is a mechanism of this conservation.
It must be so, that earth, water, air, are different forms of the manifestation of energy in mass. The perception of a greenhouse allows a supposition that the energy equation of the equilibrium of mass can be different in its different forms of manifestation.
Baron Fourier would be aghast.
168. A physicist
Markus, we have learned quite a bit about thermodynamics and transport since 1896.
We’ve learned enough for (most of) humanity to be rationally aware that the probability of catastrophic global warming $P_{\text{CAGW}}$ associated with the Hansen-style physics chain GHG $\Leftrightarrow$ GHE $\Leftrightarrow$ AGW $\Leftrightarrow$ CAGW is plausibly in the range
$20\% \lesssim P_{\text{CAGW}} \lesssim 80\%$
There are of course extremist advocates — among both scientists and skeptics — who passionately affirm that $P_{\text{CAGW}}$ surely is outside this range. But given the undoubted complexity of climate physics, these extremist affirmations — no matter how sincerely and passionately espoused — can scarcely be regarded as rational, eh? :)
• Markus Fitzhenry.
Climate physics isn’t complex.
It’s rather simple once you get the correct principle.
Gas laws explain our atmosphere very well, moreover, physics cannot model a greenhouse when it’s hotter at TOA. The attempts thus far have failed.
Climate scientists were not true to themselves, end of story. Hansen’s back radiation is bunk. I wrote the following on the 23/1/12.
——
By the knowing that I know, a proclamation is made.
Arrhenioushensonous has been slain, by the hand of a man
Rejoice for the fear of climate is no more
The most powerful force in the universe is the reasoning of a man.
——
Sweetheart, it’s His grace that you need to take up the plausibility of Hansens nonsense with. He cannot be denied. His love, His children
, His planet. Look what has happened since his involved on the 23/1/12. I had little to do with this BS, before that.
The force of pressure encloses our atmosphere, no matter what extreme radiation affirmations dopes like you make.
Now no more talkies to you, you’re dumbing me down. Oh, BTW you are a loser.
• A physicist
Markus, surely prophecy-and-poetry can reside safely in your stewardship! As for math-and-physics, maybe not so much. :)
169. I wonder how had the balancing act is to make the right people think you are very influential and others think you are not really all that big a deal.
170. Who would you target?
…In the U.S. anyways, who (individual organization) has been most effective at challenging the IPCC consensus science in the public debate on climate change?
Peter Gleick seems to think it is Heartland Institute. Even among the libertarian think tank/advocacy groups, Heartland would not be at the top of my list…
…What about bloggers such as Anthony Watts and Steve McIntyre?
What about skeptical scientists such as Richard Lindzen and Roy Spencer?
And what of the people in the (relative) middle, e.g. Revkin, Curry, Pielkes, Randy Olson?
Now THIS is an “I told ya so.” From the moment I heard of the fraud, before anyone knew it was Gleick, I am on record as saying that all this doesn’t mean a damned thing, because Heartland wasn’t in the top 20 of effective skeptical forces of nature. I asked “What the heck was anyone going after Heartland for? If they were going to go after someone, the most effective were Anthony Watts and Steve McIntyre.
I find it very enlightening hat the one person involved who would ask the same question is the president at Heartland. HE could see that Heartland’s piffling dollars were not a factor, and that Heartland’s efforts simply weren’t doing anything measurable to injure the warmist cause.
But I know exactly why Gleick did it: The warmists in feeding off each other, long ago came to the conclusion that “big industry and its think tanks” were funding skeptics right and left. That meme has been around for a decade or more – without one shred of evidence. The warmist idiots never got around to producing any evidence, but they nevertheless never let go of the idea.
Gleick as Don Quixote
So, here came Gleick, all frustrated at the demise of the warmist’s monopoly on the climate soap box, carrying the absolute wrong concept, and out to destroy the “windmills” – his (and the common) delusions of what they imagined was the funnel of skeptical activity.
It simply doesn’t occur to any of them that they are up against two bloggers who are doing it gratis.
But even Watts and McIntyre take a back seat to Climategate and the Hockey Team with their ultimate foot-in-mouth “Mike’s Nature trick to hide the decline”. Till Climategate, all Watts and McIntyre were doing was slingshots from the barrricades; none of it made inroads. Not directly. It was ony by being PESTS that their efforts paid off. Even while 100% ruling the roost in the world of the IPCC, climatology, and funding, The Hockey Team began to freak out.
But Gleick can’t undo Climategate. He can’t go back in time and tell Phil Jones to not write that email. But Glieck doesn’t know that, even to this day. To him it is the industrial bottomless money that killed the warmist mojo. And THAT he could do something about.
Except: The money from industry was all a warmist delusion, and he bought into it, hook line and Sing Sing.
I imagine more persons than just Gleick thought about doing just what he did. He was just the only one stupid enough to do it.
Steve Garcia
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https://link.springer.com/article/10.1007/s10958-015-2488-0?error=cookies_not_supported&code=2b430087-fd20-4886-9be4-e04e3205878e
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# Functions from Sobolev and Besov Spaces with Maximal Hausdorff Dimension of the Exceptional Lebesgue Set
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## Abstract
We prove that for p > 1 and 0 < α < n/p there exists a function from the Bessel potentials class J α (L p(ℝn)) such that the Hausdorff dimension of its exceptional Lebesgue set is n − αp. We also show that such a function may be taken from the Besov class B α p,q (L p(ℝn)) with any q > 0.
This is a preview of subscription content, access via your institution.
## References
1. 1.
D. R. Adams and L. I. Hedberg, Function Spaces and Potential Theory, Springer, Berlin (1996).
2. 2.
T. Bagby and C. Ziemer, “Pointwise differentiability and absolute continuity,” Trans. Am. Math. Soc., 191, 129–148 (1974).
3. 3.
A. P. Calderón, “Lebesgue spaces of differentiable functions and distributions,” in: Proc. Symp. Pure Math., Vol. 4, Amer. Math. Soc., Providence (1961), pp. 33–49.
4. 4.
C. P. Calderon, E. B. Fabes, and N. M. Riviere, “Maximal smoothing operators,” Indiana Univ. Math. J., 232, No. 10, 889–898 (1974).
5. 5.
K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, Wiley, Chichester (1990).
6. 6.
H. Federer, Geometric Measure Theory, Springer, Berlin (1969).
7. 7.
H. Federer and C. Ziemer, “The Lebesgue sets of a function whose distribution derivatives are pth power summable,” Indiana Univ. Math. J., 22, No. 2, 139–158 (1972).
8. 8.
V. G. Krotov, “Maximal functions measuring smoothness,” in: Recent Advances in Harmonic Analysis and Applications in Honor of Konstantin Oskolkov, Springer Proc. Math. Stat., Vol. 25, Springer, Berlin (2013), pp. 197–223.
9. 9.
V. G. Krotov and M. A. Prokhorovich, “Estimates for the exceptional Lebesgue sets of functions from Sobolev classes,” in: Recent Advances in Harmonic Analysis and Applications in Honor of Konstantin Oskolkov, Springer Proc. Math. Stat., Vol. 25, Springer, Berlin (2013), pp. 225–234.
10. 10.
N. G. Meyers, “Taylor expansion of Bessel potentials,” Indiana Univ. Math. J., 23, No. 11, 1043–1049 (1974).
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E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton (1970).
12. 12.
H. Triebel, Theory of Function Spaces, Birkhäuser, Basel (1983).
13. 13.
H. Triebel, Theory of Function Spaces. II, Birkhäuser, Basel (1992).
## Author information
Authors
### Corresponding author
Correspondence to V. G. Krotov.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 5, pp. 145–153, 2013.
## Rights and permissions
Reprints and Permissions
Krotov, V.G., Prokhorovich, M.A. Functions from Sobolev and Besov Spaces with Maximal Hausdorff Dimension of the Exceptional Lebesgue Set. J Math Sci 209, 108–114 (2015). https://doi.org/10.1007/s10958-015-2488-0
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http://crypto.stackexchange.com/users/4082/tylo?tab=activity&sort=all&page=2
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# tylo
less info
reputation
213
bio website location age member for 1 year, 10 months seen 2 days ago profile views 38
# 428 Actions
Jul1 comment Exactly two of the four roots must be greater than N/2 It is correct for all primes greater than 2. There are (at least) 4 square roots if $\phi(N)$ is a multiple of 4. And for every uneven $p,q$, that's the case. Jun30 comment How to prove NIZK proof of knowledge? The problem is, there is no $s$. Of course you can base $st_i$ on some value $s$ and reuse this. But you can not prove that to anyone. The protocol would have the very same statistical distribution as if you chose $st_i$ at random in every round. Assume e.g. the cyclic group $\mathbb{Z}_3^*=\{1,2\}$. Assume $s$ is from that group, too, but fixed, and $s'$ the other element (also fixed). Now it doesn't matter if I give you $t_i$, $s\cdot t_i$ or (s' \cdot t_i). In either case, if $t_i$ is chosen uniform, those 3 choices are uniform, too. But you can not prove that you used a fixed $s$ either. Jun30 comment Functions that are only second-preimage resistant? I don't think that there is such a function. Noncryptographic hash functions are neither designed for nor examined w.r.t. preimage resistance. Either you care for cryptographic aspects and then you need to do it properly, or you don't. I don't think there is a middle ground. Jun26 comment RSA example-calculation: Public Key = Private Key (e = d) Have a look here, that's the same problem with different numbers ($e=d=5, N=15,\phi(N)=12$) Jun24 revised Choose a random number that is different from a bunch of other secret numbers revised my statement Jun24 comment Choose a random number that is different from a bunch of other secret numbers Hm, you're right about that, there is a ZK proof. But even thinking about it makes my head hurt... I'll change my answer accordingly, and add how to go about it. Jun23 comment What algorithm would give the shortest ciphertext for very short plaintexts? Ah, you're right about counter mode offering no integrity any more. But it does avoid the weakness of ECB that the same plaintext is always transformed into the same ciphertext. But I guess, counter mode is after all a bad idea. Jun23 comment What algorithm would give the shortest ciphertext for very short plaintexts? Alternatively, AES in counter mode also hides the ECB weakness. If you have some part of the message as verification means (something like 3 bytes zero at the end), it doesn't even matter if packages arrive slightly out of order, because multiple counter increments can be tested. Jun23 comment What algorithm would give the shortest ciphertext for very short plaintexts? Do not do this. Especially if you have a very small plaintext space, ECB performs poorly. Imagine using AES in ECB mode on messages with length 1 bit. Every message would be an encryption of $0$ or $1$. Finding out what is $E(0)$ and $E(1)$ is not that much guesswork any more. Especially with short messages, it is very important to have some form of randomization to hide the fact that the same message has been encrypted. Jun23 answered Choose a random number that is different from a bunch of other secret numbers Jun23 comment Functions that are only second-preimage resistant? The definition of collision resistance means "find two values, which result in the same hash". If such a value is already baked in the definition of the function, collision resistance is broken. Additionally, the (small) difference between first and second preimage resistance becomes clear when you look for the $a\neq b$ statement, although in real functions are considered pretty much the same. But for example the identity function is collision resistant and second preimage resistant but not first preimage resistant. Jun23 comment Functions that are only second-preimage resistant? Dingo, you might want to state what your actual goal is. Avoiding to use a "normal" cryptographic hash function? Or do you actually want to have something that is not collision resistant? As practical example of such a function, you can use MD5, which is broken for collision resistance but preimage resistance is still considered okay-ish. Jun23 comment In public key cryptography, how many keys are required for secure communication between n parties? You're welcome. But tbh, most of this discussion still should be deleted. This isn't a discussion forum. Next time you have a question try asking the real question instead of providing the answer and asking "Am I right?". If you focus on what is actually unclear to you, you will get more helpful answers. And I suggest keeping an open mind instead of insisting on your own thought process. Jun23 comment In public key cryptography, how many keys are required for secure communication between n parties? I'm voting for closing this thread now, because it started to become a discussion. Besides being pretty much "below homework level", this question isn't beneficial for anyone else, because the basic understanding of the question is just wrong. Jun23 comment In public key cryptography, how many keys are required for secure communication between n parties? I have absolutely no clue what that diagram shows, but your thought process is totally wrong, yes. The assumption in your question is "there are public keys". and that means "they are secure". Questioning the assumption of the question is plain wrong. Jun23 revised In public key cryptography, how many keys are required for secure communication between n parties? removed "cryptanalysis" tag Jun23 comment In public key cryptography, how many keys are required for secure communication between n parties? As mikeazo said, the answer is $2n$: each user has one private key and one public key. That's it. But because public keys are public, everyone has all $n$ public keys (including his own). Since people don't need their own public key, it's enough to know the own private key and all $n-1$ public keys of the other users. Jun23 comment Is email an example of public-key cryptography? The lockbox analogy is usually used for symmetric encryption or commitments, and it is a little off for public key encryption (everynoe can create the lock, but only the owner has the key to unlock it). However, I think email is an even worse example, since it provides a false sense of confidentiality or is based on wrong assumptions about email. There is no confidentiality for transmission of emails. There is no proof that an email actually came from a certain email address or that the email wasn't tempered with. Email doesn't fulfill any security definition on its own. Jun23 reviewed Reviewed In public key cryptography, how many keys are required for secure communication between n parties? Jun23 comment In public key cryptography, how many keys are required for secure communication between n parties? Why would every party have one public key and $n$ private keys? That would mean there are $n$ public keys and $n^2-n$ private keys in the total system. Usually there is one public key for every private key, so the answer you proposed in the question is wrong. It is correct, that each user will have a total of $n$ keys, but the distribution of public and private keys will be different, and there are duplicates over all users (the questions states how many keys are required, not how many keys are in the system).
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http://mathcentral.uregina.ca/QQ/database/QQ.09.07/h/hilary1.html
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SEARCH HOME
Math Central Quandaries & Queries
Question from Hilary, a student: 10g/100ml=?g/?l 52g/100ml=?g/?l 65g/100ml=?g/?l 100g/100ml=?g/?l 137g/100ml=?g/?l 0.15g/100ml=?g/?l
Hi Hillary,
If you have something with density say 75g/100ml then 100 ml weighs 75 grams. That means 1000 ml will weigh 750 grams. But 1000 ml is one litre so the density is 750ml/l.
Penny
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
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https://arxiv.org/abs/1510.05539
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astro-ph.GA
(what is this?)
# Title: Variable stars in the field of the Hydra II ultra-faint dwarf galaxy
Abstract: We report the discovery of one RR Lyrae star in the ultra--faint satellite galaxy Hydra II based on time series photometry in the g, r and i bands obtained with the Dark Energy Camera at Cerro Tololo Interamerican Observatory, Chile. The RR Lyrae star has a mean magnitude of $i = 21.30\pm 0.04$ which translates to a heliocentric distance of $151\pm 8$ kpc for Hydra II; this value is $\sim 13\%$ larger than the estimate from the discovery paper based on the average magnitude of several blue horizontal branch star candidates. The new distance implies a slightly larger half-light radius of $76^{+12}_{-10}$ pc and a brighter absolute magnitude of $M_V = -5.1 \pm 0.3$, which keeps this object within the realm of the dwarf galaxies. The pulsational properties of the RR Lyrae star ($P=0.645$ d, $\Delta g = 0.68$ mag) suggest Hydra II may be a member of the intermediate Oosterhoff or Oosterhoff II group. A comparison with other RR Lyrae stars in ultra--faint systems indicates similar pulsational properties among them, which are different to those found among halo field stars and those in the largest of the Milky Way satellites. We also report the discovery of 31 additional short period variables in the field of view (RR Lyrae, SX Phe, eclipsing binaries, and a likely anomalous cepheid). However, given their magnitudes and large angular separation from Hydra II, they must be field stars not related to Hydra II.
Comments: Revised version after comments from the referee. Accepted for publication in AJ Subjects: Astrophysics of Galaxies (astro-ph.GA) DOI: 10.3847/0004-6256/151/5/118 Cite as: arXiv:1510.05539 [astro-ph.GA] (or arXiv:1510.05539v2 [astro-ph.GA] for this version)
## Submission history
From: A. Katherina Vivas [view email]
[v1] Mon, 19 Oct 2015 15:45:21 GMT (1256kb)
[v2] Wed, 24 Feb 2016 02:41:10 GMT (1257kb)
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http://cs.oberlin.edu/~cs150/lab-8/part-1/
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# SoundWave
soundwave.py: 22 points
Our main goal for this lab is to write a sound generator capable of playing any combination of notes, or tones, we desire. We can think of these tones as objects with their own attributes and methods. For example, a tone can have a duration attribute and a method for combining itself with other tones to create a song!
In this part of the lab, we’ll get started by creating a SoundWave class that will represent a sampled sound wave. Your SoundWave class should be written in a separate soundwave.py file, and it should follow the specifications below. Remember to refer back to the Warmup for details on how to generate and sample the sine waves needed to create your tones.
### SoundWave Constructor
The constructor for your SoundWave class will begin with an __init__() function for instantiating new SoundWave objects. We’ll start by designing our constructor to accept four parameters specifying a single note:
1. halftones - the number of halftones above or below middle C of the note
2. duration - the length of the note in seconds
3. amp - the amplitude of the note (i.e., it’s volume or loudness)
4. sample_rate - the interval at which the sine wave is sampled
These four parameters define everything we need to generate the sine wave for a given half tone. Recall, however, that the sine wave equation requires a frequency. We can compute the frequency as outlined in the Warmup using:
freq = 220*(2**((halftones+3)/12))
Now that the sine wave parameters have been determined, we need to sample the waveform and store those sampled values. Your constructor should create an instance variable called self.samples, and define self.samples to be the list of sampled values. You should populate this list such that it has a length of duration * sample_rate (truncated to an integer), where entry i in this list is created as follows:
s = amp * math.sin(2 * math.pi * freq * i/sample_rate)
Say you’ve computed a new sample s that you plan on appending to your list samples. A natural way to do this is with the instruction:
self.samples.append(s)
#### Default Values
For the purposes of this lab, we’ll always be using a sample rate of 44100, or 44.1 kHz (this value is dictated by the WAV audio format we’ll be using to save our music). To make our programs cleaner, we’ll want our SoundWave constructor to assign default values when parameters are left unspecified. The default values for halftones, duration, amp, and sample_rate should be 0 (middle C), 0.0 (zero seconds), 1.0 (max volume), and 44100, respectively.
Setting Default Values
We can set the default value of a function parameter by doing an assignment within the function definition. For example,
def my_function(param1, param2=10):
# do something
sets a default value of 10 to param2 and no default value for param1. By setting the default value of param2, we can call the function with
my_function(param1)
and Python will automatically set param2 to 10. Note that default values work the same for methods.
By having these default values (and the parameters in this order), we allow users of this object to invoke the constructor as:
note = soundwave.SoundWave(6,3,.5)
to get an F-sharp with length 3 seconds at volume 0.5,
note = soundwave.SoundWave(2,1)
to generate a D with length 1 second at volume 1.0, or
note = soundwave.SoundWave()
to generate an empty SoundWave object.
### Checking Your Samples
Before moving on, you should test out your SoundWave class, even though you can’t play the full tone just yet!
Below your class definition, write a function called test_samples() which, when called, creates a SoundWave instance s and prints out the first 10 samples of that instance (e.g., s.samples[0:10]). You should look at the output and check that the values seem to be changing in a sensical way as you adjust the parameters passed to the constructor (i.e., getting bigger but less than amp). Your function should also print out the total number of samples in s to confirm you are generating what you intended (i.e., duration * sample_rate, truncated to an int).
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http://math.stackexchange.com/questions/109747/unit-of-measure-for-t-in-exponential-growth-formula
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Unit of measure for $t$ in Exponential Growth Formula
In the exponential growth formula, $N = N(0)e^{kt}$, I know that $t$ is for time, but what is the unit of measure? Years? Months? Days? Hours?
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Depends on the problem, but generally $t$ is dimensionless in the general formula: $N = N_0e^{kt}$. – William Feb 15 '12 at 20:49
Inside the exponential, that should be dimensionless. So if you want $t$ to be in sec, then $k$ should be in 1/sec. – GEdgar Feb 15 '12 at 21:07
$$\frac{dN}{dt} = kN$$ That is, the rate of the growth of the population is directly proportional to the number at that instant.
When solved for N, $$\frac{dN}{N} = k.dt$$ $$\int_{N_0}^N\frac{dN}{N} = \int_0^t k.dt$$ $$\ln \frac{N}{N_0} = kt$$ $$N = N_0.e^{kt}$$
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https://istopdeath.com/evaluate-integral-of-2-natural-log-of-x-with-respect-to-x/
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# Evaluate integral of 2 natural log of x with respect to x
Since is constant with respect to , move out of the integral.
Integrate by parts using the formula , where and .
Simplify.
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Since is constant with respect to , move out of the integral.
Simplify.
Evaluate integral of 2 natural log of x with respect to x
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http://mathhelpforum.com/statistics/22062-2-q-needs-2-ans-print.html
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# 2 Q. needs 2 ANS.
• November 5th 2007, 12:19 PM
compufatwa
2 Q. needs 2 ANS.
22. in a city ,25% of the cars emit pollutions to the air of the city .if a car failed to pass the emission of air pollutants with probability 0.99 and if a car that is not emitting air pollutants also fails the test with probability 0.17 .what is the probability that a car that fails the test actually emits air pollution ?
23.the number of employees working in factories A,B and C are , respectively 50,75 and 100 . suppose that of those employees ,50% ,60 % and 70%,respectively ,are women .assuming that the probability of resignation is the same for men and women and that woman resigned ,what is the probability that she is from factory c ?
• November 5th 2007, 02:20 PM
Soroban
Hello, compufatwa!
I'll do the second one . . .
These are Conditional Probability problems.
You're expected to be familiar with the formula: . $P(A|B) \:=\:\frac{P(A \wedge B)}{P(B)}$
Quote:
23. The number of employees at factories A,B and C are , respectively 50, 75 and 100.
Suppose that of those employees, 50%, 60% and 70%, respectively, are women.
Assuming that the probability of resignation is the same for men and women
and that woman resigned, what is the probability that she is from factory C?
I tabulated the data . . .
$\begin{array}{cccccccc}
& |& \text{Women} &|& \text{Men} &|& \text{Total} & | \\ \hline
A &|& 25 &|& 25 &|&50 &| \\
B &|& 45 &|& 30 &|&75 &| \\
C &|& 70 &|& 30 &|& 100 &| \\ \hline
\text{Total} &|& 140 &|& 85 &|& 225 &| \end{array}$
Formula: . $P(\text{from C }|\text{ Woman}) \;=\;\frac{P(\text{from C }\wedge\text{ Woman})}{P(\text{Woman})}$
From the chart, we have: . $\begin{Bmatrix}P(\text{from C }\wedge\text{ Woman}) &=& \frac{70}{225} \\
P(\text{Woman}) & = & \frac{140}{225} \end{Bmatrix}$
Therefore: . $P(\text{from C }|\text{ Woman}) \;=\;\frac{\frac{70}{225}}{\frac{140}{225}} \;=\;\frac{1}{2}$
But check my reasoning and work . . . please!
.
• November 7th 2007, 12:30 AM
compufatwa
Soroban thanks alot for the answer
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http://mathhelpforum.com/differential-equations/212209-differential-eqn-generation-print.html
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# differential eqn generation
• January 29th 2013, 03:58 AM
prasum
differential eqn generation
y=(x^100)*(e^x)
what will be the differential equation if the above is one of its solution
• January 29th 2013, 05:14 AM
Prove It
Re: differential eqn generation
Why not differentiate the function you have been given? That would be appropriate since a differential equation is an equation that has derivatives in it...
• January 29th 2013, 07:30 AM
prasum
Re: differential eqn generation
how to find the derivatives of this
• January 29th 2013, 09:05 AM
HallsofIvy
Re: differential eqn generation
Take a Calculus course! Then you will learn that the derivative of $e^x$ is simply $e^x$, that the derivative of $x^n$ is $nx^{n-1}$ for all n except n= 1, and the "product rule": the derivative of f(x)g(x) is the derivative of f(x) times g(x) plus f(x) times the derivative of g(x)- (fg)'= f'g+ fg'.
• January 29th 2013, 10:22 AM
Hartlw
Re: differential eqn generation
y= f(x) satisfies the DE y'=f'(x). For ex, if y=x^2, the DE is dy/dx = 2x.
That's the crux of the question. The actual differentiatin should be trivial.
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http://mathoverflow.net/questions/86000/non-bimeromorphic-compactifications/86009
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# Non-bimeromorphic compactifications
Let $X$ be a (smooth, non-compact) complex space. By a compactification of $X$ we mean a compact complex space $\overline X$ which contains a dense open subset biholomorphic to $X$ (we shall identify this subset with $X$) and such that $\overline X\setminus X$ is a proper analytic subset (with no conditions on its codimension).
In particular, given two (different) compactifications of $X$, they always contain biholomorphic dense open subsets.
My question is: given two compactifications of $X$, are they necessarily bimeromorphic?
More precisely, does the biholomorphism between the two dense open subsets always extend to a global bimeromorphic map?
I guess the answer is no, but after a moment of reflection I cannot find any counterexample. Perhaps, it would suffice to look at compactifications of $\mathbb C^2$...
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This seems related: mathoverflow.net/questions/68421/… – M P Jan 18 '12 at 16:36
I think that the tag ag.algebraic-geometry could be also appropriate here. I added it – Francesco Polizzi Jan 18 '12 at 17:51
As you wish! The power of points... :) – diverietti Jan 18 '12 at 18:13
As you guessed, the answer is no.
The following counterexample in dimension $2$ can be found in Vo Van Tan's paper On the compactification of strongly pseudoconvex surfaces III, Mathematische Zeitschrift 195 (1987), 259-267.
The Stein surface $\mathbb{C}^* \times \mathbb{C}^*$ admits two algebraic compactifications $M_1$ and $M_2$ which are not bimeromorphic. In fact, $M_1=\mathbb{P}^1 \times \mathbb{P}^1$ is a rational surface whereas $M_2$ is a $\mathbb{P}^1$-bundle over an elliptic curve.
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Another example, different but diffeomorphic to Polizzi's, is given by
$E \times \mathbb C$, where $E$ is a fixed elliptic curve say $\mathbb C^* / \lbrace z \mapsto 2z \rbrace$. It can be compactified as the projective surface $E \times \mathbb P^1$ or as the (non-Kähler) Hopf surface $\mathbb C^2-\{0\} / \lbrace (z,w) \mapsto (2z,2w) \rbrace$.
Notice that the two compactifications have fields of meromorphic functions of different transcendence degree over $\mathbb C$, i.e., they have different algebraic dimensions.
-
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https://image.hanspub.org/Html/2-1270449_30200.htm
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Applied Physics
Vol. 09 No. 05 ( 2019 ), Article ID: 30200 , 7 pages
10.12677/APP.2019.95027
Theoretical Study of the Probabilities for the Reaction H + DBr (v = 0, j = 0) on the 12A' Potential Energy Surface
Yuliang Wang*, Hui Li, Dezhi Su, Mingyu Zhou
School of Basic Sciences for Aviation, Naval Aviation University, Yantai Shandong
Received: Apr. 25th, 2019; accepted: May 7th, 2019; published: May 14th, 2019
ABSTRACT
Quasi-classical trajectory calculations were carried out for H + DBr (v = 0, j = 0) over the collision energy range 0 - 2.0 eV on the 12A' potential energy surface. The probabilities for both the exchange and abstraction channels of the reaction at total angular momentum J = 0, 10, 20, 30, 40 are predicted in this work. The attack angle dependent probabilities of H + DBr at J = 0 are calculated. It was found that the influence of attack angle on the distribution of probabilities for both two channels is significant because of the different effective potential barrier heights at different attack angles.
Keywords:H + DBr Reaction, Attack Angle, Reaction Probability, Reaction Dynamics
Copyright © 2019 by author(s) and Hans Publishers Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/
1. 引言
2. 计算理论
Figure 1. The definition figure of the attack angle
3. 结果与讨论
Figure 2. Minimum energy pathways of abstraction for the collinear configuration
Figure 3. Comparison of integral cross section for abstraction between present work and other theoretical results in the text
Figure 4. The reaction probabilities for exchange channel at different J values
Figure 5. The reaction probabilities for abstraction channel at different J values
Figure 6. The attack angle dependent probability of exchange channel
Figure 7. The attack angle dependent probability of abstraction channel
4. 结论
Theoretical Study of the Probabilities for the Reaction H + DBr (v = 0, j = 0) on the 12A' Potential Energy[J]. 应用物理, 2019, 09(05): 226-232. https://doi.org/10.12677/APP.2019.95027
1. 1. Aker, P.M., Germann, G.J. and Valentini, J.J. (1989) State-to-State Dynamics of H+HX Collisions. I. The H+HX→H2+X (X=Cl, Br, I) Abstraction Reactions at 1.6 eV Collision Energy. Journal of Chemical Physics, 90, 4795-4808. https://doi.org/10.1063/1.456574
2. 2. Pomerantz, A.E., Camden, J.P., Chiou, A.S., Ausfelder, F., Chawla, N., Hase, W.L. and Zare, R.N. (2005) Reaction Products with Internal Energy beyond the Kinematic Limit Result from Trajectories Far from the Minimum Energy Path: An Example from H+HBrH2 + Br. Journal of American Society, 127, 16368-16369. https://doi.org/10.1021/ja055440a
3. 3. Zhang, J.Y., Jankunas, J., Bartlett, N.C.M., Goldberg, N.T. and Zare, R.N. (2010) Search for Br Production in the D + DBr Reaction. Journal of Chemical Physics, 132, 084301. https://doi.org/10.1063/1.3319717
4. 4. Lynch, G.C., Truhlar, D.G., Brown, F.B. and Zhao, J.G. (1995) A New Potential Energy Surface for H2Br and Its Use to Calculate Branching Ratios and Kinetic Isotope Effects for the H + HBr Reaction. Journal of Chemical Physics, 99, 207-225. https://doi.org/10.1021/j100001a034
5. 5. Mielke, S.L., Tawa, G.J., Truhlar, D.G. and Schwenke, D.W. (1995) Quantum Photochemistry. Accurate Quantum Scattering Calculations for an Electronically Nonadiabatic Reaction. Chemical Physics Letters, 234, 57-63. https://doi.org/10.1016/0009-2614(94)01515-w
6. 6. Kurosaki, Y. and Takayanagi, T. (2003) Global ab initio Potential Energy Surfaces for the Lowest Three Doublet States (12A′, 22A′, and 12A′′) of the BrH2 System. Journal of Chemical Physics, 119, 7838-7856. https://doi.org/10.1063/1.1609398
7. 7. Kurosaki, Y. and Takayanagi, T. (2005) A Modified Version of the Ana-lytical Potential Function for the Global ab initio Ground-State Potential Energy Surface of the BrH2 System. Chemical Physics Letters, 406, 121-125. https://doi.org/10.1016/j.cplett.2005.02.106
8. 8. Jiang, B., Xie, C.J. and Xie, D.Q. (2011) New ab initio Potential Energy Surface for BrH2 and Rate Constants for the H + HBrH2 + Br Abstraction Reaction. Journal of Chemical Physics, 134, Article ID: 114301. https://doi.org/10.1063/1.3563750
9. 9. Quan, W.L., Song, Q. and Tang, B.Y. (2007) The Effects of the Rotational Excitation on the Br+H2 Reaction and Its Dependence on the Potential Energy Surfaces. Chemical Physics Letters, 442, 228-232. https://doi.org/10.1016/j.cplett.2007.05.105
10. 10. Zhang, W.Q., Cong, S.L., Zhang, C.H., Xu, X.S. and Chen, M.D. (2009) Theoretical Study of Dynamics for the Abstraction Reaction H′ + HBr (v=0, j=0)H′H + Br. The Journal of Physical Chemistry A, 113, 4192-4197. https://doi.org/10.1021/jp8105716
11. 11. Fu, B.N. and Zhang, D.H. (2007) A Time-Dependent Quantum Dynamical Study of the H + HBr Reaction. The Journal of Physical Chemistry A, 111, 9516-9521. https://doi.org/10.1021/jp073811z
12. 12. Xie, C.J., Jiang, B. and Xie, D.Q. (2011) State-to-State Quantum Dynamics of the H + HBr Reaction: Competition between the Abstraction and Exchange Reactions, Journal of Chemical Physics, 134, Article ID: 184303. https://doi.org/10.1063/1.3589407
13. 13. Zhang, A.J., Zhang, P.Y., Chu, T.S., Han, K.L. and He, G.Z. (2012) Quantum Dynamical Study of the Electronic Nonadiabaticity in the D + DBr→Br(Br*) + D2 Reaction on New Diabatic Potential Energy Surfaces. Journal of Chemical Physics, 137, Article ID: 194305. https://doi.org/10.1063/1.4766355
NOTES
*通讯作者。
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http://arresto-sala.pl/misirlou-lyrics-wegvqil/0e096c-dividing-mixed-numbers-practice
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Dividing Mixed Numbers. Step 1: Write the mixed numbers as improper fractions. Answers. Dividing Fractions and Mixed Numbers DRAFT. So, how do we divide mixed numbers? 0. end. Grades: 6 th, 7 th. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. The only way is to convert the mixed numbers to improper fractions and multiply or divide as usual. Then, switch to a multiplication problem by multiply by the reciprocal of the divisor. Let's try some in context. Next Scatter Graphs Practice Questions. Practice dividing fractions, get the answer right and see if you can make the shot. Similar: Dividing fractions Mixed division practice. Multiplying and dividing fractions and mixed numbers homework sheet with answers. Here are the steps followed when dividing mixed numbers: Begin by converting each mixed fraction to an improper. Step 1: Write the mixed numbers as improper fractions. Description: This packet helps students practice solving division problems with mixed numbers. Practice Problem 2 : If each cake requires $2\frac 13$ cups of sugar. Click here for Answers . Finish Editing. Types: Activities, Games, Math Centers. How can you do that? Simplify and convert the More fractions worksheets. The first is like a simple fraction a/b and then there are mixed numbers of the form C a/b. 6th grade . Dividing fractions. Besides, you’ll equally find here well exemplified, fun and motivational dividing fractions exercises with answers that will encourage an immediate understanding of dividing fractions concept. When understanding the concept of fractions, we come across two different types. Dividing-mixed-fraction-by-a-whole-number; 5. Proper fractions are a case where the numerator is smaller than the denominator. When the product of two numbers is equal to 1, we can say that the numbers are _____? Dividing Mixed Numbers. Delete Quiz. A. > Fractions Worksheet: Dividing Mixed Numbers. More Dividing Mixed Numbers Worksheets . The answer key 5th Grade. So to divide mixed numbers you should change the fractions to improper fraction and the convert the problem to a multiplication question. Learn how to divide mixed numbers. is below. 2 8/9 4. Khan Academy is a 501(c)(3) nonprofit organization. Worksheets > Math > Grade 6 > Fractions: multiply/divide > Mixed numbers by fractions. Then you will be ready to solve. CCSS.Math: 6.NS.A.1. 4. Example 2: Divide Analysis: First convert each mixed number to an improper fraction.Then divide. Answers are on the 2nd page of the PDF. 20 problems that review all skills within the unit. Multiplication of numerators and denominators are done separately. Each page also has a speed and accuracy guide to help students see how fast and how accurately they should be doing these problems. Convert all mixed numbers to improper fractions. Save. This Math quiz is called 'Fractions (Dividing with Mixed Numbers)' and it has been written by teachers to help you if you are studying the subject at middle school. Further Maths; Practice Papers; Conundrums; Class Quizzes; … How many pieces of strings will she be able to cut? Convert the result back to a mixed number if it is an improper fraction. Here’s how to multiply or divide mixed numbers. Step 3: Use KCF. These two fractions are improper fractions that will be used for division. Multiply dividend by reciprocal of divisor. If you're seeing this message, it means we're having trouble loading external resources on our website. Search form. A … 7. Similar: Numbers in these problems may be positive or negative. Al builds 32 models in a day; Sal can do the same in 3 days. To divide mixed fractions, you could first convert each to an improper fraction. Description: This packet helps students practice solving division problems with mixed numbers.Each page has a set of 6 problems. All of the numbers you use should be mixed numbers or fractions. Here are the steps followed when dividing mixed numbers: Begin by converting each mixed fraction to an improper. 12 ÷ 4/5; Dividing Fractions e.g. This is a digital version of my Multiply & Divide Fractions & Mixed Numbers Scavenger Hunt Activity created for use in Google Drive™. Answers for both lessons and both practice sheets. Lesson 4-3 Dividing Mixed Numbers Practice and Problem Solving: A/B Find the reciprocal. My Tweets. Login Time. Convert the mixed numbers to improper fractions. Practice dividing by mixed numbers and fractions. How many cakes can be made from $8\frac 17$ cups of sugar? Fractions and Mixed Number Games There are two ways of writing an improper fraction. Homework. Dividing two mixed numbers: Convert each mixed number to an improper fraction. 4. Multiply the numerators and multiply the denominators. is by their actions. 2 3 3 4 14 3 7 4 Write the mixed numbers as improper fractions. Scroll down the page for more examples and solutions of dividing mixed numbers. A mixed number is a number that consists of a fraction and a whole number. 10 1/2 2. If they work together, how long will it take them to build 32 models? One payment, lifetime access. Step 2: Rewrite the division problem using the improper fractions. Simplify. Keep change flip. Math worksheets: Dividing mixed numbers by mixed numbers. In an improper fraction, the numerator is greater than the denominator. Play this game to review Pre-algebra. Here we have enlisted a step-wise approach for dividing the mixed number. Dividing Fractions and Mixed Numbers COURSE 2 LESSON 4-5 2 3 3 4 Find 4 ÷ 1 . Multiply the two denominators together. Print PDF worksheet below. Show that the product of the mixed number and its reciprocal is 1. Convert the result back to a mixed number if it is an improper fraction. Write each answer in simplest form. Google Classroom Facebook Twitter. Applying arithmetic operations on simple fractions is simple, but students may freak out when they have to apply these operations on mixed numbers. Demonstrates the division of mixed numbers. a c b = a + c b = ab + c b a c b = a + c b = a b + c b. Divide fractions and simplify if necessary. Mixed numbers consist of an integer followed by a fraction. Lifetime Membership Offer. The easiest way to do this is to convert the mixed number into an improper fraction: 2 1/4 equals 9/4. … Players try to hold on to their strips and not get ZAPPED. Multiplying and Dividing Mixed Numbers 1) 98 15 2) 11 3 8 3) 12 3 5 1 4) 3 1 18 3 5) 9 2 7 19 6) 20 4 9 13 7) 86 19 36 21 8) 13 3 7 1 9) 14 1 25 57 10) 14 5 21 11) 1 2 12) 1 2 13) 6 10 14) 28 15) 1 20 16) 26 17) 1 11 2 18) 58 19) 3 31 48 20) 1 19 56 21) 1 5 12 22) 11 16 23) 3 3 35 24) 2 1 16 25) 3 1 8 26) 5 8 After doing all 12 problems, students should be more comfortable doing these problems and have a clear understanding of how to … First, we need to multiply the denominator with the whole and add it with the numerator. Fun maths practice! Practice Problem 1 : Divide $1\frac 47\div 3\frac 25$ and write the result in the simplest form. Scroll down the page for more examples and solutions of dividing mixed numbers. 5th and 6th grade math worksheets. Each page also has a speed and accuracy guide to help students see how fast and how accurately they should be doing these problems. Our answer will be, 2 8/9. When you divide 10 by 2, you are working out how many 2s there are in 10. Share practice link. The easiest way to do this is to convert the mixed number into an improper fraction: 2 1/4 equals 9/4. Divide mixed numbers by fractions, whole numbers, and mixed numbers. Play. The obtained fraction will be 13/2 and 9/4. Math worksheets: Dividing mixed numbers by fractions (whole number quotients) Below are six versions of our grade 6 math worksheet on dividing mixed numbers by fractions. Exploring Two-Step Problems CE 2015 Math 7 A Unit 5: Equations and Inequalities practice 1.D 2.A 3.B 4.B 5.D 6.A 7.B 8.A 9.C 10.B . Mixed Review Games that Have it All. Procedure: To divide mixed numbers, first convert each mixed number to an improper fraction, then divide the first fraction by the second.Simplify your result, if necessary. These bump games are perfect for small groups and centers, or can even be used as an informal assessment tool. Then do the division: since we're dividing by a whole number, just divide the numerator by the whole number, and leave the denominator alone: 9/4 ÷ 3 = 3/4, your final answer. CHALLENGE Without dividing, explain whether 5 — — is greater than or less than 5— : Sample answer: 8—+3 OPEN ENDED Find two mixed numbers with a quotient of 2— peed — — distance -7 260 by gboughton. D. Russell. So to divide mixed numbers you should change the fractions to improper fraction and the convert the problem to a multiplication question. The answer key GCSE Revision Cards. Edit. Read this lesson on dividing mixed numbers if you need help on how to divide mixed numbers. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. 3. 6 3/7 3. Division means multiplying by the inverse of the divisor. CHALLENGE Without dividing, explain whether 5 — — is greater than or less than 5— : Sample answer: 8—+3 OPEN ENDED Find two mixed numbers with a quotient of 2— peed — — distance -7 260 The sum will look like, 13/2 x 4/9. Dividing Fractions Basketball. the least common multiple of Improper Fractions, Mixed Numbers Practice Questions Click here for Questions . Write the improper fraction in mixed form. We're going to leave the party behind and talk about flowers. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. simplify. How to Use this Worksheet. The only way I can distinguish proper from improper fractions The answers can be found Since How to Divide Mixed Numbers Refresher. 3. Dividing Mixed Numbers Don't Get ZAPPED contains: 20 cards with dividing mixed numbers 4 You've been Z. Email. works 3 times as fast, so he would be building 24 models; Sal does 8. These worksheets are pdf files.. Share practice link. Sheet includes practice, AQA multiple choice question, problem solving and feedback sheet. Worksheets > Math > Grade 5 > Fractions: multiply & divide > Dividing practice. Multiply the two numerators together. For example, if we have 6 1/2 and 2 1/4 , you will multiply 6 x 2 + 1 = 13 and 2 x 4 +1 = 9. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14. For example, suppose you want to multiply 1-3/5 by 2-1/3. Improve your skills with free problems in 'Divide fractions and mixed numbers: word problems' and thousands of other practice lessons. 6/7 ÷ 3/4; Mixed. 5th and 6th Grades. Corbettmaths Videos, worksheets, 5-a-day and much more. fraction to a mixed number. Simplify the answer, if possible. 2. Dividing two mixed numbers: Convert each mixed number to an improper fraction. Practice Dividing Mixed Numbers. the denominators. 12 problems to reinforce the lessons and practice pages. Explore all of our fractions worksheets, from dividing shapes into "equal parts" … To play this quiz, please finish editing it. Division of mixed numbers is very similar to the multiplication of the mixed numbers. Solo Practice. Step 1: Step 2: The following is the procedure for dividing mixed numbers. If you're seeing this message, it means we're having trouble loading external resources on our website. Multiplying and Dividing Decimals by Powers of Ten Quick Check Lesson is skipped. Convert mixed numbers into rational numbers. 18 problems that review all skills within the unit. The Corbettmaths Practice Questions on Improper (top-heavy) Fractions and Mixed Numbers. Step 5: Simplify. Practice. Available in our outstanding 6th grade math dividing fractions worksheets are quickest techniques for easy dividing fractions. Invert the improper fraction that is the divisor. 3. Try a workout of 10 problems. Delete Quiz. Al Search . 2 / 1 6/7 AAA Math Dividing Mixed Numbers. Start by converting a mixed number into a fraction. Then you will be ready to solve. Cry because it is so difficult! If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Below are six versions of our grade 5 math worksheet on dividing fractions and mixed numbers practice. As improper fractions and check your work as you go so you if... Problems ' and thousands of other math skills explains the process of dividing mixed numbers, we say! By their actions into an improper fraction practice lessons with the numerator will become denominator! Below are six versions of our grade 5 math worksheet on dividing fractions mixed... Numerator and the convert the mixed number to improper fractions that will be 13/2 ÷ 9/4 six of. Fractions, you could first convert the problem to a multiplication problem by multiply by the of... So he would be building 24 models ; Sal does 8 are?... Digital Activity contains 10 different games to help students see how fast and how accurately they should doing! 3 4 14 3 7 4 Write the mixed numbers the steps followed when dividing mixed:! Are _____ look at the preview carefully and ask me any questions you have before you buy.kastatic.org *! Your math knowledge with free problems in 'Divide fractions and mixed numbers, need. Fractions are a case where the numerator have two improper fractions that is the second form are improper... Practice, AQA multiple choice question, problem solving: a/b find the number tinier! Practice multiplying dividing mixed numbers practice dividing fractions, mixed numbers: Begin by converting each mixed number to improper fractions like fractions! Fractions and mixed numbers as improper fractions multiplication, and mixed numbers by other mixed numbers of... But students may freak out when they have to first convert the fraction. A raised flower bed out of some scrap lumber on the 2nd of. This fifth grade level math lesson for dividing the mixed numbers in the simplest form a... We come across two different types come across two different types practice ) now we will take the and... On dividing mixed numbers, and the convert the mixed number to an improper.. Numbers homework sheet with answers works 3 times as fast, so there mixed! The following diagram shows examples of dividing mixed numbers practice and problem solving feedback.: step dividing mixed numbers practice: the following pairs of numbers contains like fractions & mixed.... Corbettmaths Videos, worksheets, 5-a-day and much more change each mixed number and! Problem by multiply by the reciprocal, the answer right and see if 're. Each exercise below your skills with free problems in 'Divide fractions and mixed numbers or fractions you want to the... First convert each mixed fraction to a mixed number if it is an fraction! 3\Frac 25 $and Write the result in the preview carefully and ask me any questions have... 6 > fractions: multiply/divide > mixed numbers: Begin by converting a mixed number in days. 2S in 10 following diagram shows examples of dividing mixed numbers in the time! Lessons as shown in the simplest form back to a mixed number to an improper fraction that is modeled multiplying... This lesson on dividing mixed numbers you should change the fractions to improper fractions improper fractions packet helps practice. And feedback sheet first convert the mixed numbers, we can say that the numbers you use be! Strings will she be able to cut arithmetic operations on mixed numbers, we have first. Of sugar multiplying and dividing fractions and mixed numbers by whole numbers, we will take the reciprocal of numerator! Means multiplying by the reciprocal, the answer with 2, we first need to multiply 1-3/5 2-1/3!, AQA multiple choice question, problem solving: a/b find the reciprocal and simplify where can! Numbers by fractions, you could first convert the result back to a mixed number to an improper.! Be positive or negative she be able to cut Further Maths ; 5-a-day GCSE a * -G ; 5-a-day 1. ' and thousands of other math skills 2, we first need to convert the result in the sum will... Could first convert each mixed fraction to an improper fraction, the division sign into multiplication, the... Cakes can be made dividing mixed numbers practice$ 8\frac 17 \$ cups of sugar some lumber! There ’ s how to divide mixed numbers practice with your class today this on. And Write the mixed numbers you use should be doing these problems may be positive or negative number into fraction. The fractions to improper fractions following diagram shows examples of dividing mixed numbers, we come two! Explore all of the following is the divisor ; multiply the denominator with the whole and add it with whole... And the denominator with the whole and add it with the numerator will become the numerator will become denominator! 24 models ; Sal does 8 we have enlisted a step-wise approach for the. Not get ZAPPED simple, but students may freak out when they to. Al works 3 times as fast, so there are two ways of writing an fraction. Then divide them like other fractions the same in each exercise below to log in and use the! The unit Independent practice ) now we will get will be 13/2 ÷.! This fifth grade level math lesson for dividing the mixed number if it is improper with this self-checking... Accuracy guide to help students practice dividing fractions and mixed numbers, we can say that product! Numerators, 13 x 4 = 52 and the denominator, and this result... Ways of writing an improper fraction, enter 4, a space, and this will in... Can Do the same 're building a raised flower bed out of some scrap lumber they have to apply operations. All the features of Khan Academy, please make sure that the domains *.kastatic.org and *.kasandbox.org are.! > grade 6 math worksheet on dividing mixed numbers Hunt Activity created for in. 2 = 5, so there are two ways of writing an.... Writing an improper fraction and a whole number can divide fractions & numbers... Help students practice solving division problems with mixed numbers.Each page has a speed and accuracy guide to help students solving! > math > grade 6 math worksheet on dividing fractions and mixed numbers into fractions. Knowledge with free problems in 'Divide mixed numbers, we have enlisted a step-wise approach for mixed. The PDF ; Delete ; Host a game practice questions Click here for questions the necessary in...: multiply & divide > dividing practice 4, a space, and mixed numbers example:! Academy is a 501 ( c ) ( 3 ) nonprofit organization out of some scrap lumber ways of an... Numbers or fractions ÷ 9/4 ) ( 3 ) nonprofit organization which one of the denominators diagram... A 501 ( c ) ( 3 ) nonprofit organization number that consists of a.. And mixed numbers you should change the fractions to improper fractions building 24 ;. Enter 4, a space, and mixed numbers practice questions Click for...... What is the procedure for dividing the mixed numbers *.kastatic.org *! Math practice website in the sum being reciprocated and *.kasandbox.org are.. Consists of a fraction please make sure that the numbers you use be. The PDF: convert each mixed number to an improper fraction there ’ how. Of two numbers is very similar to the multiplication of the numbers you use should be doing these.... Divide them like other fractions I know it is improper a free, world-class education to anyone, anywhere following!, enter 4, a space, and then multiply the denominator math lesson for dividing numbers! Editing it 2s in 10 help on how to multiply the two fractions or mixed numbers in the position the! Way is to convert them into an improper fraction, the numerator how to divide mixed numbers 4 've. Say you 're behind a web filter, please enable JavaScript in your.... Digital version of my multiply & divide fractions and mixed numbers by whole '... Six versions of our fractions worksheets, from dividing shapes into equal parts '' … by! From improper fractions and then there are two ways of writing an improper that. Fractions is by their actions by a fraction and the convert the result back to multiplication! Number of tinier pieces, we first need to practice correct or not than. And how accurately they should be mixed numbers apply these operations on mixed numbers race to see who divide! Look at the preview in each exercise below now we will get, 26/9 and... Academy, please finish editing it at the preview carefully and ask me any questions you have you. Include detailed scripted lesson plans—only the short and simple lessons as shown in the sum will like! With free problems in 'Divide fractions and mixed numbers practice questions Click here for questions Write the mixed numbers improper. 2, we will get will be used as an informal assessment tool right and see you! One of the mixed number into a mixed number to an improper and. Fractions: multiply/divide > mixed numbers then divide them like other fractions 501 ( c ) ( 3 ) organization... Our example, the numerator she be able to cut whole numbers, we first convert each mixed four! In between multiply the two fractions or mixed numbers: Begin by converting mixed. 2/3 into the form 2 = 5, so he would be building 24 models ; Sal can Do same. Different games to help students see how fast and how accurately they should doing! ) now we will have a race to see who can divide fractions & mixed numbers answer with,. And solutions of dividing mixed numbers of the mixed number if it is an improper fraction as usual you....
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https://mathoverflow.net/questions/98229/is-the-4-line-of-the-e-2-term-of-the-classical-adams-spectral-sequence-known
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# Is the 4-line of the E_2 term of the classical Adams spectral sequence known?
In other words:
What is $\mathrm{Ext}_{\mathcal{A}}^{4,t}(\mathbb{Z}/2,\mathbb{Z}/2)$?
If the 4-line is not known, how much is known about it?
Here, $\mathcal{A}$ is the 2-primary Steenrod algebra, $4$ is the homological degree corresponding to the Adams filtration, and $t$ is the internal grading degree. Those $\mathrm{Ext}$ groups make up the fourth row of the classical Adams spectral sequence $E_2 = \mathrm{Ext}_{\mathcal{A}}^{s,t}(\mathbb{Z}/2,\mathbb{Z}/2)$ converging to the 2-adic completion of the $(t-s)^{\mathrm{th}}$ stable homotopy group of the sphere.
For context,
• the 1-line is generated by the classes $h_i$, $i \geq 0$, ($\mathrm{deg}\: h_i = (1,2^i)$),
• the 2-line is generated by the product classes $h_i h_j$, subject to the relations $h_i h_{i+1} = 0$ and $h_i h_j = h_j h_i$,
• the 3-line is generated by two sets of classes,
1. the product classes $h_i h_j h_k$, subject to the relations implied by $h_i h_{i+2}^2 = 0$, $h_{i+1}^3 = h_i^2 h_{i+2}$, $h_i h_{i+1} = 0$, and $h_i h_j = h_j h_i$,
2. the Massey products $\langle h_{i+1},h_i,h_{i+2}^2 \rangle$.
The 4-line is determined by Wen-Hsiung Lin in "$Ext_A^{4,*}({\bf Z}/2,{\bf Z}/2)$ and $Ext_A^{5,*}({\bf Z}/2,{\bf Z}/2)$", Topology and its Applications (2008) vol 155 no.5 pp 459-496.
He gives a basis for the indecomposable elements in $Ext_A^{4,*}$ and generators and relations for the quotient of $Ext_A^{s,*}$ for $s \le 4$ by the indecomposables of \$Ext_A^{4,*}
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http://math.stackexchange.com/questions/22246/covering-space-of-circle
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# Covering Space of Circle
It is easy to see that
$p:\mathbb{R} \rightarrow S^1: p(t)=(\cos t, \sin t)$ is a covering map of $S^1$
(Indeed take a point $x_0$ in $S^1$, take $U=S^1\setminus \{-x_0\}$ as an open neighborhood and then $p^{-1}(U)=\cup_{n \in Z} J_n$ where $J_n=\{t\in\mathbb{R} : t_0-n-1/2<t<t+0+n+1/2\}$. $p$ then maps $J_n$ homeomorphically onto $U$.)
I can't see why we can't take a similar $p:(a,b) \to S^1$. For example, Massey states that if we take the open interval $(0,10)$ onto the circle, then some points in $S^1$ fail to have an elementary neighborhood.
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Think about what the preimage of a neighborhood of p(a) looks like. – Qiaochu Yuan Feb 15 '11 at 23:36
You appear to be confusing covering maps with local homeomorphisms. They are not the same. en.wikipedia.org/wiki/Local_homeomorphism – George Lowther Feb 15 '11 at 23:42
@George: this is exactly what Massey is showing - that they are not the same – Juan S Feb 15 '11 at 23:43
Does Massey really say "a similar map" or rather "the same map"? – a.r. Feb 16 '11 at 5:53
@Agusti - Neither - that was all me – Juan S Feb 16 '11 at 10:19
Look at a preimage of a small neighborhood $U$ of $p(10)$. It will have one component which doesn't map homeomorphically onto $U$.
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http://tex.stackexchange.com/questions/14580/luaotfload-cant-find-font-cmu-sans-serif-demi-condensed
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# luaotfload can't find font “CMU Sans Serif Demi Condensed”
Luaotfload has problems finding a font that is installed in my texmf tree. The source:
``````\input luaotfload.sty
\font\myfont={CMU Sans Serif Demi Condensed} at 10pt
\myfont
foo
\bye
``````
The font is in `texmf-dist/fonts/opentype/public/cm-unicode/cmunssdc.otf` and kpsewhich finds it. What can I do now?
Edit: a sister font `{CMU Sans Serif Bold Extended Oblique}` works fine. Same directory...
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Try searching for this font in the font database (a plain text file named `otfl-names.lua`, in the directory `\luatex-cache\generic\names` in one of your `texmf` trees). Maybe it has a slightly different name there, so it isn't found by your specification. – diabonas Mar 30 '11 at 14:44
The name is from the database itself. So somehow `mkluatexfontdb` finds the font in the tree but luaotfload can't load it. It is taken from the `names.fullname` entry. – topskip Mar 30 '11 at 14:50
Not a solution, but to say that I see the same behaviour on the Mac and on Windows, both with TL 2010. `CMU Sans Serif Bold Extended Oblique` is found, but `CMU Sans Serif Demi Condensed` is not. I wonder therefore about the font file: it does seem to be that one that is an issue. – Joseph Wright Mar 30 '11 at 15:29
Well at first look in otfl-names.lua if the font is there and if you are using the correct name.
If the font is not there, the folder is not cached. Why and what to do about it depends on your system. `mkluatexfontdb --help` says:
``````Fonts are searched in directories on Windows or Linux that have been
searched with fontconfig.
On Mac OS X, only fonts located in the following standard font locations are
included in the font database:
~/Library/Fonts /Library/Fonts
/System/Library/Fonts /Network/Library/Fonts
In particular, fonts installed in other locations with "Font Book" will not
be available.
``````
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The font is in the database. Also fonts included in the texmf tree are included in the database (on all systems I guess, I am on OS X). – topskip Mar 30 '11 at 14:57
Why didn't you say directly that you already checked the database? Well the above message says that in OS X fonts in texmf trees are not available. I don't know why it is nevertheless in the database and I can't make tests as I have windows. – Ulrike Fischer Mar 30 '11 at 15:04
Of course I should have mentioned that directly. Didn't think about it. Sorry – topskip Mar 30 '11 at 15:09
@Urlike, no texmf tree is searched in all systems, the above message is misleading, I'll try to fix it when I've time (I'm half sleeping now). – Khaled Hosny Mar 31 '11 at 0:40
I have no explanation for the strange behaviour of `luaotfload` at all, but for me (TeX Live 2010, Windows), the font is loaded when using exactly the same font name as `fc-list` does, which is `CMU Sans Serif Demi Condensed:style=DemiCondensed`:
``````\input luaotfload.sty
\font\myfont={CMU Sans Serif Demi Condensed:style=DemiCondensed} at 10pt
\myfont
foo
\bye
``````
works fine for me.
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Also works for me on the Mac, even though it's not listed by `fc-list`! – Joseph Wright Mar 30 '11 at 16:09
@joseph: we don't use FontConfig on mac at all (on linux, we may read its configuration files if present), fonts in texmf tree are located using kpse. – Khaled Hosny Mar 31 '11 at 0:44
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http://forums.penny-arcade.com/discussion/124608/newbie-xna-game-programming-thread-one-spritebatch-per-customer-please/p2
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Our new Indie Games subforum is now open for business in G&T. Go and check it out, you might land a code for a free game. If you're developing an indie game and want to post about it, follow these directions. If you don't, he'll break your legs! Hahaha! Seriously though.
Our rules have been updated and given their own forum. Go and look at them! They are nice, and there may be new ones that you didn't know about! Hooray for rules! Hooray for The System! Hooray for Conforming!
2»
## Posts
• Registered User regular
edited July 2010
Michael H wrote: »
Oh that's not your fault, I'm just surprised that they don't have XNA capable of working with either environment.
You can get it working. 1s let me find the article I was looking at.
[ed] Oh, crap. It won't even install. Hmmmmm. That might be more of an issue.
This was the article I was thinking of. It's from a google cache, 'cause the guy's changed his site since he posted the article.
iTunesIsEvil on
• Registered User
edited July 2010
Cool, thanks... I might have to give that a shot.
Michael H on
• Registered User regular
edited August 2010
So right now my bullet emitter will shoot exactly at the player, but miss the player if the player is moving. I want to lead the target reliably. If you can't possibly hit the player then don't shoot, otherwise fire at where the player will be.
I said to myself "I'll use math, and I'll cheat." I constructed a scenario.
Bullet emitter at (ex,ey), target at (tx,ty). Not shown is the intercept point for the fired bullet, (ix,iy). Coordinate system uses screen coordinates, so the top left is 0,0 and positive Y goes down instead of up. For a given angle of movement theta, the X deflection is cosine(theta) and the Y deflection is sine(theta), with theta 0 pointing to the right.
So I tried to get Mathematica to do all the work.
LogicalExpand[
FullSimplify[
Reduce[
Eliminate[
{ix == ex + T * Cos[theta],
ix == tx + T * tv * Cos[ta],
iy == ey + T * Sin[theta],
iy == ty + T * tv * Sin[ta]},
{T}],
{theta, ix, iy},
GeneratedParameters -> (Subscript[k, #] &)]
]
]
I ended up with output in disjunctive normal form -- a bunch of either-or situations. Problem is, I got 28 different scenarios, many of them special cases where the target is not moving or is moving directly toward or away from the emitter.
The plan is to interpret these as code for a branching tree of execution: some conditions will be tested to tell the difference between special cases, and some conditions will be go/no-go and will tell me if a firing solution even exists.
mspencer on
MEMBER OF THE PARANOIA GM GUILD
XBL Michael Spencer || Wii 6007 6812 1605 7315 || PSN MichaelSpencerJr || Steam Michael_Spencer || Ham NOØK
QRZ || My last known GPS coordinates: FindU or APRS.fi (Car antenna feed line busted -- no ham radio for me X__X )
• Registered User regular
edited August 2010
Can I reasonably expect that if I write a 2D platformer in this, it'll run on my antique low-end-for-2005 laptop? Or is that entirely dependent on how good I am at writing efficient code?
MKR on
• Building Planet Busters Tasting FruitRegistered User regular
edited August 2010
That seems excessively complicated. Given points T and E with object T moving at known velocity and bullets fired from E moving at a constant speed in a variable direction, you end up looking for theta such that the integrals meet.
However, it's a lot simpler than that, it forms a triangle TEI where the ratio of sides EI and TI are the ratio of the speeds of the bullet target respectively (since there is no acceleration) and angle ETI is known (as the direction of travel is known and fixed.
Now, to calculate the optimal intercept point, you require minimal deflection from a straight shot at your target so we will be calculating the minimum internal angle TEI which is given by the smallest possible length of side TI
Distance of any point k along line TI from E is given by the law of cosines: EI² = k² + ET² - 2k*ET*cos(ETI)
You are looking for the smallest k where: sqrt(k² + ET² - 2k*ET*cos(ETI)) == k * ratio
Where ratio is speed of bullet / speed of ship
k² + ET² - 2k*ET*cos(ETI) == k² * ratio²
k²(1 - ratio²) -2k*ET*cos(ETI) + ET²
k = (2*ET*cos(ETI) +- sqrt(4*ET²*cos²(ETI) - 4ET² + 4ET²*ratio²)) / (2-2ratio²)
There are some restrictions on the result. k should be chosen as the smallest positive result. Only negative k indicates that there was a solution in the past but none in the future. Imaginary k indicates no solution.
The angle is trival to calculate given the intercept point.
Example
E is at 0,0
T is at 0,5
T is moving horizontally at 5 units/s therefore ETI = 90 degrees
Bullets move at 10 units/s
k²(1 - ratio²) -2k*ET*cos(ETI) + ET²
k²(1 - 4) -2k*5*0 + 25
-3k² + 25
Ratio is 2
k = 2.8867
We would expect the length of EI to be double that or 5.7735
Since it's a right triangle, 5² + 2.8867² = 5.7735²
edit: I suppose there's also the case where E, T and I are collinear and so don't actually form a triangle, however the in that case you always shoot directly at them if bullet speed + closing velocity is positive
Phyphor on
Magic Box
Academician Prokhor "Phyphor" Zakharov, Chief Scientist of China, Provost of the University of Planet - SE++ Megagame
• I have been shown the end of my world Round Rock, TXRegistered User regular
edited August 2010
Awesome OP. Almost makes me want to give XNA another try.
I messed with it a couple of years ago trying to make a single-player Wurm clone, but my head exploded when I started trying to learn about drawing a 3D landscape, specifically one that used square tiles and was deformable. Are there any good resources for doing that kind of stuff, preferably specifically for XNA? Or hell, some sort of library that does that stuff for me?
Sir Carcass on
• Hunkrat Primed and ReadyRegistered User regular
edited August 2010
I could not have found this thread at a better time, having just deemed Unity3d unsuitable for my plans, and decided that the extra work involved in XNA is more than worthwhile considering the extra control/flexibility.
Starting tonight: a tile-based map editor! oooooooooooooooexciting.
Fearghaill on
• Registered User regular
edited August 2010
Awesome OP. Almost makes me want to give XNA another try.
I messed with it a couple of years ago trying to make a single-player Wurm clone, but my head exploded when I started trying to learn about drawing a 3D landscape, specifically one that used square tiles and was deformable. Are there any good resources for doing that kind of stuff, preferably specifically for XNA? Or hell, some sort of library that does that stuff for me?
I have a book XNA 3.0 Game Programming Recipes: A Problem-Solution Approach by Riemer Grootjans with a chapter about something like that. This book assumes you already understand the basics and essentially discusses individual problems to solve and how you solve them. I don't think it covers deformation, but you could try modifying the terrain heightmap array dynamically and see if anything breaks. The author's web site is here: http://www.riemers.net/
Specifically two sections seem applicable to 3D terrain rendering:
2-10: Use a Quadtree to Hide Parts of a Grid That Are Not In Sight
2-11: Create a Real-Time Camera-Dependent Optimally Adapting Mesh (ROAM) Terrain
At the end of 2-10 the author talks about terrain being such a large subject he could fill an entire book with it.
mspencer on
MEMBER OF THE PARANOIA GM GUILD
XBL Michael Spencer || Wii 6007 6812 1605 7315 || PSN MichaelSpencerJr || Steam Michael_Spencer || Ham NOØK
QRZ || My last known GPS coordinates: FindU or APRS.fi (Car antenna feed line busted -- no ham radio for me X__X )
• I have been shown the end of my world Round Rock, TXRegistered User regular
edited August 2010
mspencer wrote: »
At the end of 2-10 the author talks about terrain being such a large subject he could fill an entire book with it.
Yeah, that's kinda the impression I got when I was doing my research. I'll look around some more.
Edit: Looking at his website, I actually remember following those tutorials. They were pretty awesome.
Sir Carcass on
• Registered User regular
edited August 2010
Phyphor wrote: »
That seems excessively complicated. Given points T and E with object T moving at known velocity and bullets fired from E moving at a constant speed in a variable direction, you end up looking for theta such that the integrals meet.
However, it's a lot simpler than that, it forms a triangle TEI where the ratio of sides EI and TI are the ratio of the speeds of the bullet target respectively (since there is no acceleration) and angle ETI is known (as the direction of travel is known and fixed.
Now, to calculate the optimal intercept point, you require minimal deflection from a straight shot at your target so we will be calculating the minimum internal angle TEI which is given by the smallest possible length of side TI
Distance of any point k along line TI from E is given by the law of cosines: EI² = k² + ET² - 2k*ET*cos(ETI)
You are looking for the smallest k where: sqrt(k² + ET² - 2k*ET*cos(ETI)) == k * ratio
Where ratio is speed of bullet / speed of ship
k² + ET² - 2k*ET*cos(ETI) == k² * ratio²
k²(1 - ratio²) -2k*ET*cos(ETI) + ET²
k = (2*ET*cos(ETI) +- sqrt(4*ET²*cos²(ETI) - 4ET² + 4ET²*ratio²)) / (2-2ratio²)
There are some restrictions on the result. k should be chosen as the smallest positive result. Only negative k indicates that there was a solution in the past but none in the future. Imaginary k indicates no solution.
The angle is trival to calculate given the intercept point.
Example
E is at 0,0
T is at 0,5
T is moving horizontally at 5 units/s therefore ETI = 90 degrees
Bullets move at 10 units/s
k²(1 - ratio²) -2k*ET*cos(ETI) + ET²
k²(1 - 4) -2k*5*0 + 25
-3k² + 25
Ratio is 2
k = 2.8867
We would expect the length of EI to be double that or 5.7735
Since it's a right triangle, 5² + 2.8867² = 5.7735²
edit: I suppose there's also the case where E, T and I are collinear and so don't actually form a triangle, however the in that case you always shoot directly at them if bullet speed + closing velocity is positive
Law of cosines! I don't know if I ever learned that in school, but if I did I've since forgotten it.
I did initially try using geometry and trig, but all I could remember required use of right triangles. I had this construction where I took a tangent line to the target's movement vector and constructed a right triangle there. I used the ratio of the triangle's legs as the ratio of the speeds, but I couldn't figure out how to handle the case where the target is behind or in front of the 90-degree part of the right triangle. I ended up having to add or subtract the offset, and the offset didn't scale with the speeds.
It's so much easier when the triangle doesn't have to be a right triangle!
Thank you kindly. I'm still working through and absorbing what you wrote, charting it out with paper and pen.
mspencer on
MEMBER OF THE PARANOIA GM GUILD
XBL Michael Spencer || Wii 6007 6812 1605 7315 || PSN MichaelSpencerJr || Steam Michael_Spencer || Ham NOØK
QRZ || My last known GPS coordinates: FindU or APRS.fi (Car antenna feed line busted -- no ham radio for me X__X )
• Registered User regular
edited August 2010
I learned me some C# a while back and have always wanted to make a game. Now I just need to find some inspiration.
Also, I learned C# from the "Head First C#" book, which was really nice because the end project is to build a Space Invaders clone (they provide the sprites).
phekno on
• Building Planet Busters Tasting FruitRegistered User regular
edited August 2010
No problem. The law of cosines is the Pythagorean theorem generalized to all triangles, it's usually covered in school but most people forget it I find. That and the law of sines tend to be really useful for general geometry stuff (although I still had to look up the exact formula)
Phyphor on
Magic Box
Academician Prokhor "Phyphor" Zakharov, Chief Scientist of China, Provost of the University of Planet - SE++ Megagame
• beso el culo shitlord in residenceRegistered User regular
edited August 2010
Fearghaill wrote: »
I could not have found this thread at a better time, having just deemed Unity3d unsuitable for my plans, and decided that the extra work involved in XNA is more than worthwhile considering the extra control/flexibility.
Starting tonight: a tile-based map editor! oooooooooooooooexciting.
Yeah I sat down with XNA last night and I was amazed at how simple it was to make a guy move around the screen.
Back in the day it took me a half a week to write something that good, but I did it in about 2 minutes.
bowen on
Warning: I am a programmer/sysop. Do not take my word as law in any other fields, it is not professional advice.
• Registered User regular
edited August 2010
XNA is amazing. I have been playing around with it for awhile now, though I don't really have anything REAL to show. I'm still pretty much a novice to the whole thing, but I probably have some limited information for the real newbies if there are any questions. I intend to learn a lot from this topic as well.
Kyanilis on
• Registered User regular
edited August 2010
I think I'm finally getting somewhere. Sorry Phyphor but I went back to trying to do it with straight trig and Mathematica. I feel like I'm closer. http://mspencer.net/PA_XNA/TargetLeading3.pdf
The second page of that document is in disjunctive normal form (like: A-and-B, or A-and-C-and-D, or A-and-C-and-E, or . . .) and it lists only nine scenarios. I've been studying them and so far they make sense.
The beginning of the expression (tx=0) is the first scenario, and then each time you see OR (huge letter V like symbol) c1 subset of Z (set of integers), that's a new scenario.
Scenario 1: if the target is on top of the cannon, fire in any direction except to the left. (Probably caused a divide by zero somewhere.)
Scenario 2: if the target is on the X axis (ty == 0) and is not moving, fire directly at it.
Scenario 3: if the target is on top of the cannon, fire to the left. (Weird duplicate of scenario 1.)
Scenarios 4 and 5: these cover most non-special-case scenarios and will be explained later. (once I figure out how they work and what each expression means.)
Scenario 6: if the target is headed toward the x-axis, timed just right so a bullet fired along the x-axis will reach the target, go ahead and fire directly along the x-axis. Must be a special case that avoids making another formula divide by zero.
Scenario 7: if the target is on the X axis and is not moving, fire directly at it. (Opposite of Scenario 2.)
Scenario 8: if the target is on the Y axis and is heading toward the X axis at just the right angle that the horizontal component of motion exactly matches a bullet's speed, fire directly along the X axis.
Scenario 9: if the target is on a collision course with the origin (flying directly at the emitter) then fire directly at the target. (Edit: on closer examination, I don't think this does what I think it does. theta is 2*arctan. Something is weird.)
I think I might be able to resume coding on that bullet hell game pretty soon!
mspencer on
MEMBER OF THE PARANOIA GM GUILD
XBL Michael Spencer || Wii 6007 6812 1605 7315 || PSN MichaelSpencerJr || Steam Michael_Spencer || Ham NOØK
QRZ || My last known GPS coordinates: FindU or APRS.fi (Car antenna feed line busted -- no ham radio for me X__X )
• beso el culo shitlord in residenceRegistered User regular
edited August 2010
I hate game math, just throwing that out there.
bowen on
Warning: I am a programmer/sysop. Do not take my word as law in any other fields, it is not professional advice.
• Building Planet Busters Tasting FruitRegistered User regular
edited August 2010
Just, to check, this is basically what you're looking for, right? (C++ on windows, ignore the poor coding, I only spent 15 minutes on it)
Phyphor on
Magic Box
Academician Prokhor "Phyphor" Zakharov, Chief Scientist of China, Provost of the University of Planet - SE++ Megagame
• Registered User regular
edited August 2010
I think so, but while reinventing the wheel is usually a bad thing, this time I'd like the experience of building code from Mathematica output. Thanks though -- I'll be sure and compare our code once I'm done.
mspencer on
MEMBER OF THE PARANOIA GM GUILD
XBL Michael Spencer || Wii 6007 6812 1605 7315 || PSN MichaelSpencerJr || Steam Michael_Spencer || Ham NOØK
QRZ || My last known GPS coordinates: FindU or APRS.fi (Car antenna feed line busted -- no ham radio for me X__X )
• Registered User regular
edited August 2010
So, I have the need to find if something is in line of sight in a 2D grid based system (the grid is basically passable terrain or unpassable). My initial thought for doing this was to find the equation of the line between the 2 points then checking it for every x and y value between the points, first checking x values, then y (but skipping any that have already been checked). Is this a silly way of doing things? Is there a better way?
Scroffus on
• beso el culo shitlord in residenceRegistered User regular
edited August 2010
Scroffus wrote: »
So, I have the need to find if something is in line of sight in a 2D grid based system (the grid is basically passable terrain or unpassable). My initial thought for doing this was to find the equation of the line between the 2 points then checking it for every x and y value between the points, first checking x values, then y (but skipping any that have already been checked). Is this a silly way of doing things? Is there a better way?
That's probably how I'd do it. That's also how you'd probably do it in terms of 3d space too.
http://cs.fit.edu/~wds/classes/cse5255/thesis/lineEqn/lineEqn.html
Use those.
bowen on
Warning: I am a programmer/sysop. Do not take my word as law in any other fields, it is not professional advice.
• Registered User regular
edited August 2010
bowen wrote: »
Scroffus wrote: »
So, I have the need to find if something is in line of sight in a 2D grid based system (the grid is basically passable terrain or unpassable). My initial thought for doing this was to find the equation of the line between the 2 points then checking it for every x and y value between the points, first checking x values, then y (but skipping any that have already been checked). Is this a silly way of doing things? Is there a better way?
That's probably how I'd do it. That's also how you'd probably do it in terms of 3d space too.
http://cs.fit.edu/~wds/classes/cse5255/thesis/lineEqn/lineEqn.html
Use those.
Yeah, that's what I figured. I'm so glad my high school math is useful. Screw those other kids who said I'd never use it, now who's laughing!
Scroffus on
• beso el culo shitlord in residenceRegistered User regular
edited August 2010
You because those kids are flipping burgers for us. Delicious isn't it?
bowen on
Warning: I am a programmer/sysop. Do not take my word as law in any other fields, it is not professional advice.
• Registered User regular
edited August 2010
They still probably have better jobs than me, but at least I have a use for high school math. It's a hollow victory, but I'll take it.
Scroffus on
• Registered User regular
edited August 2010
There's a slightly better way to do that in XNA: Ray.Intersects()
mspencer on
MEMBER OF THE PARANOIA GM GUILD
XBL Michael Spencer || Wii 6007 6812 1605 7315 || PSN MichaelSpencerJr || Steam Michael_Spencer || Ham NOØK
QRZ || My last known GPS coordinates: FindU or APRS.fi (Car antenna feed line busted -- no ham radio for me X__X )
• beso el culo shitlord in residenceRegistered User regular
edited August 2010
XNA why do you want me to love you so much?
bowen on
Warning: I am a programmer/sysop. Do not take my word as law in any other fields, it is not professional advice.
• Dr EdinburghRegistered User regular
edited August 2010
bowen wrote: »
XNA why do you want me to love you so much?
Don't worry, soon you will do something with the content pipeline that's not loading a texture and then the true horror will begin.
Alistair Hutton on
I made a game, it has penguins in it. It's pay what you like on Gumroad.
Currently Ebaying Nothing at all but I might do in the future.
• beso el culo shitlord in residenceRegistered User regular
edited August 2010
Well, it'll certainly beat doing it from scratch.
bowen on
Warning: I am a programmer/sysop. Do not take my word as law in any other fields, it is not professional advice.
• Dr EdinburghRegistered User regular
edited August 2010
bowen wrote: »
Well, it'll certainly beat doing it from scratch.
Having been laoding information as both ContentPipeline serialised XML and my own free form effort parsed with LINQ I would say the LINQ method did not cause me to tweet offensive message at Shawn Hargreaves.
(Overall the ContentPipeline method is better but the fucking invisible hoops you have to jump through first!)
Alistair Hutton on
I made a game, it has penguins in it. It's pay what you like on Gumroad.
Currently Ebaying Nothing at all but I might do in the future.
• beso el culo shitlord in residenceRegistered User regular
edited August 2010
Oh, well, I meant trying to use DX in C or C++.
bowen on
Warning: I am a programmer/sysop. Do not take my word as law in any other fields, it is not professional advice.
• Registered User regular
edited August 2010
I think you have to go pretty far beyond "newbie XNA" before you run into Alistair Hutton's problems though. Please don't be discouraged from using XNA.
mspencer on
MEMBER OF THE PARANOIA GM GUILD
XBL Michael Spencer || Wii 6007 6812 1605 7315 || PSN MichaelSpencerJr || Steam Michael_Spencer || Ham NOØK
QRZ || My last known GPS coordinates: FindU or APRS.fi (Car antenna feed line busted -- no ham radio for me X__X )
2»
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https://experts.umn.edu/en/publications/the-distributed-feedback-of-counter-propagating-waves-in-a-period
|
# The distributed feedback of counter-propagating waves in a periodically modulated medium with relaxing cubic nonlinearity
A. A. Afanas’ev, B. A. Samson, E. G. Tolkacheva
Research output: Contribution to journalArticle
8 Scopus citations
### Abstract
An interaction of two counter-propagating waves in a periodically modulated medium with relaxing cubic nonlinearity is considered. On the basis of analytical solutions of the equations under the weak distributed feedback (DFB) approximation, we show that an increase in the reflectivity of ‘nonlinear’ DFB-structures takes place due to phase mismatching between the radiation and the light-induced grating. We carry out a numerical simulation of the obtained equations for arbitrary values of the coupling coefficient, Bragg detuning and incident pulse intensity. We also analysed the dynamics of the regular temporal modulation of initially continuous wave radiation caused by the ‘nonlinear’ grating.
Original language English (US) 2285-2294 10 Journal of Modern Optics 42 11 https://doi.org/10.1080/09500349514551981 Published - Jan 1 1995
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http://www.gamedev.net/index.php?app=forums&module=extras§ion=postHistory&pid=5080527
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• Create Account
### #Actualdr4cula
Posted 29 July 2013 - 10:15 AM
Okay, so I decided to use FBOs instead since that problem seems to have been indeed me rendering onto the back framebuffer immediately. And having switched to FBOs I can actually see the shadowmap when I map it onto a quad (it's faint but it's visible at least). However, my problems don't end there: now the entire scene is black (except for the textured quad and brownish glClearColor() defined background). I'm guessing my texture coordinate generation is wrong but not sure. Any help would be greatly appreciated!
new init:
glGenTextures(1, &shadowmap_);
glTexImage2D(GL_TEXTURE_2D, 0, GL_DEPTH_COMPONENT, 512, 512, 0, GL_DEPTH_COMPONENT, GL_UNSIGNED_BYTE, NULL);
//glGenRenderbuffers(1, &renderbuffer_);
//glBindRenderbuffer(GL_RENDERBUFFER, renderbuffer_);
//glRenderbufferStorage(GL_RENDERBUFFER, GL_DEPTH_COMPONENT, 512, 512);
glGenFramebuffers(1, &framebuffer_);
glBindFramebuffer(GL_FRAMEBUFFER, framebuffer_);
//glFramebufferRenderbuffer(GL_FRAMEBUFFER, GL_DEPTH_ATTACHMENT, GL_RENDERBUFFER, renderbuffer_);
glFramebufferTexture2D(GL_FRAMEBUFFER, GL_DEPTH_ATTACHMENT, GL_TEXTURE_2D, shadowmap_, 0);
new render:
glBindFramebuffer(GL_FRAMEBUFFER, framebuffer_);
//glDrawBuffer(GL_NONE);
glClearColor(0.5, 0.2, 0.1, 1.0f);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
// position the light
glLightfv(GL_LIGHT0, GL_POSITION, lightPos_);
// set up the projection parameters from the light's POV
glMatrixMode(GL_PROJECTION);
glPushMatrix();
gluPerspective(lightFOV_, lightAspect_, lightNear_, lightFar_);
glMatrixMode(GL_MODELVIEW);
glPushMatrix();
// translate to the light's position
gluLookAt(lightPos_[0], lightPos_[1], lightPos_[2], -1.0f, 0.0f, 5.0f, 0.0f, 1.0f, 0.0f);
// render the scene to get the depth information
renderSceneElements();
glPopMatrix();
// end the projection modification
glMatrixMode(GL_PROJECTION);
glPopMatrix();
glMatrixMode(GL_MODELVIEW);
glBindFramebuffer(GL_FRAMEBUFFER, 0);
// copy over the depth information
//glCopyTexSubImage2D(GL_TEXTURE_2D, 0, 0, 0, 0, 0, 512, 512);
// matrix defining the planes for S, Q, R, T components for texture generation
float planeMatrix[16];
glPushMatrix();
// compensate for the eye-coordinate to texture coordinate conversion: [-1,1] to [0,1]
glTranslatef(0.5f, 0.5f, 0.0f);
glScalef(0.5f, 0.5f, 1.0f);
// do the perspective projection and translate to the light's position
gluPerspective(lightFOV_, lightAspect_, lightNear_, lightFar_);
gluLookAt(lightPos_[0], lightPos_[1], lightPos_[2], -1.0f, 0.0f, 5.0f, 0.0f, 1.0f, 0.0f);
glGetFloatv(GL_MODELVIEW_MATRIX, planeMatrix);
glPopMatrix();
// go from OpenGL's column-major to row-major matrix form
transposeMatrix16(planeMatrix);
// set up the type for texture generation
glTexGeni(GL_S, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
glTexGeni(GL_T, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
glTexGeni(GL_R, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
glTexGeni(GL_Q, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
// data for texture generation
glTexGenfv(GL_S, GL_OBJECT_PLANE, &planeMatrix[0]);
glTexGenfv(GL_T, GL_OBJECT_PLANE, &planeMatrix[4]);
glTexGenfv(GL_R, GL_OBJECT_PLANE, &planeMatrix[8]);
glTexGenfv(GL_Q, GL_OBJECT_PLANE, &planeMatrix[12]);
glEnable(GL_TEXTURE_GEN_S);
glEnable(GL_TEXTURE_GEN_T);
glEnable(GL_TEXTURE_GEN_R);
glEnable(GL_TEXTURE_GEN_Q);
glEnable(GL_TEXTURE_2D);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_FUNC, GL_LEQUAL);
glTexParameteri(GL_TEXTURE_2D, GL_DEPTH_TEXTURE_MODE, GL_LUMINANCE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_MODE, GL_COMPARE_R_TO_TEXTURE);
glEnable(GL_LIGHTING);
glEnable(GL_LIGHT0);
renderSceneElements();
glDisable(GL_LIGHTING);
glDisable(GL_LIGHT0);
glDisable(GL_TEXTURE_2D);
glDisable(GL_TEXTURE_GEN_Q);
glDisable(GL_TEXTURE_GEN_R);
glDisable(GL_TEXTURE_GEN_T);
glDisable(GL_TEXTURE_GEN_S);
glPushMatrix();
glEnable(GL_TEXTURE_2D);
glTexParameteri(GL_TEXTURE_2D, GL_DEPTH_TEXTURE_MODE, GL_NONE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_MODE, GL_NONE);
glTranslatef(3.0f, 2.0f, 5.0f);
glTexCoord2f(0.0f, 0.0f);
glVertex3f(0.0f, 0.0f, 0.0f);
glTexCoord2f(1.0f, 0.0f);
glVertex3f(3.0f, 0.0f, 0.0f);
glTexCoord2f(1.0f, 1.0f);
glVertex3f(3.0f, 3.0f, 0.0f);
glTexCoord2f(0.0f, 1.0f);
glVertex3f(0.0f, 3.0f, 0.0f);
glEnd();
glDisable(GL_TEXTURE_2D);
glPopMatrix();
Note that I had to explicitly bind the texture - I thought it would be automatically related to the framebuffer and hence enabling texturing would have caused that texture to be used? If I don't have that binding there, OpenGL selects my previously used texture.
EDIT: After searching on Google for the millionth time, I ran into someone's post stating that glTexGen works only with specific objects, ie OpenGL wouldn't generate proper coordinates for quads/cubes. Now I knew that before but for whatever reason hadn't considered it until now. The OpenGL Red Book doesn't clarify it either and the given code there is really awkward. I've matched most of my code with the stuff in the book but I'm not really sure about the glTexGen stuff... If I have the shadowmap then how do I map it onto the scene?
EDIT2: Found someone on the official OpenGL forums who helped me wrap my head around this. Nothing more frustrating than running into a forum post and finding someone had a similar problem and had fixed it and not posted the solution so here you go: http://www.opengl.org/discussion_boards/showthread.php/182327-Reading-the-depth-buffer-into-texture-memory
### #4dr4cula
Posted 25 July 2013 - 02:27 PM
Okay, so I decided to use FBOs instead since that problem seems to have been indeed me rendering onto the back framebuffer immediately. And having switched to FBOs I can actually see the shadowmap when I map it onto a quad (it's faint but it's visible at least). However, my problems don't end there: now the entire scene is black (except for the textured quad and brownish glClearColor() defined background). I'm guessing my texture coordinate generation is wrong but not sure. Any help would be greatly appreciated!
new init:
glGenTextures(1, &shadowmap_);
glTexImage2D(GL_TEXTURE_2D, 0, GL_DEPTH_COMPONENT, 512, 512, 0, GL_DEPTH_COMPONENT, GL_UNSIGNED_BYTE, NULL);
//glGenRenderbuffers(1, &renderbuffer_);
//glBindRenderbuffer(GL_RENDERBUFFER, renderbuffer_);
//glRenderbufferStorage(GL_RENDERBUFFER, GL_DEPTH_COMPONENT, 512, 512);
glGenFramebuffers(1, &framebuffer_);
glBindFramebuffer(GL_FRAMEBUFFER, framebuffer_);
//glFramebufferRenderbuffer(GL_FRAMEBUFFER, GL_DEPTH_ATTACHMENT, GL_RENDERBUFFER, renderbuffer_);
glFramebufferTexture2D(GL_FRAMEBUFFER, GL_DEPTH_ATTACHMENT, GL_TEXTURE_2D, shadowmap_, 0);
new render:
glBindFramebuffer(GL_FRAMEBUFFER, framebuffer_);
//glDrawBuffer(GL_NONE);
glClearColor(0.5, 0.2, 0.1, 1.0f);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
// position the light
glLightfv(GL_LIGHT0, GL_POSITION, lightPos_);
// set up the projection parameters from the light's POV
glMatrixMode(GL_PROJECTION);
glPushMatrix();
gluPerspective(lightFOV_, lightAspect_, lightNear_, lightFar_);
glMatrixMode(GL_MODELVIEW);
glPushMatrix();
// translate to the light's position
gluLookAt(lightPos_[0], lightPos_[1], lightPos_[2], -1.0f, 0.0f, 5.0f, 0.0f, 1.0f, 0.0f);
// render the scene to get the depth information
renderSceneElements();
glPopMatrix();
// end the projection modification
glMatrixMode(GL_PROJECTION);
glPopMatrix();
glMatrixMode(GL_MODELVIEW);
glBindFramebuffer(GL_FRAMEBUFFER, 0);
// copy over the depth information
//glCopyTexSubImage2D(GL_TEXTURE_2D, 0, 0, 0, 0, 0, 512, 512);
// matrix defining the planes for S, Q, R, T components for texture generation
float planeMatrix[16];
glPushMatrix();
// compensate for the eye-coordinate to texture coordinate conversion: [-1,1] to [0,1]
glTranslatef(0.5f, 0.5f, 0.0f);
glScalef(0.5f, 0.5f, 1.0f);
// do the perspective projection and translate to the light's position
gluPerspective(lightFOV_, lightAspect_, lightNear_, lightFar_);
gluLookAt(lightPos_[0], lightPos_[1], lightPos_[2], -1.0f, 0.0f, 5.0f, 0.0f, 1.0f, 0.0f);
glGetFloatv(GL_MODELVIEW_MATRIX, planeMatrix);
glPopMatrix();
// go from OpenGL's column-major to row-major matrix form
transposeMatrix16(planeMatrix);
// set up the type for texture generation
glTexGeni(GL_S, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
glTexGeni(GL_T, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
glTexGeni(GL_R, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
glTexGeni(GL_Q, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
// data for texture generation
glTexGenfv(GL_S, GL_OBJECT_PLANE, &planeMatrix[0]);
glTexGenfv(GL_T, GL_OBJECT_PLANE, &planeMatrix[4]);
glTexGenfv(GL_R, GL_OBJECT_PLANE, &planeMatrix[8]);
glTexGenfv(GL_Q, GL_OBJECT_PLANE, &planeMatrix[12]);
glEnable(GL_TEXTURE_GEN_S);
glEnable(GL_TEXTURE_GEN_T);
glEnable(GL_TEXTURE_GEN_R);
glEnable(GL_TEXTURE_GEN_Q);
glEnable(GL_TEXTURE_2D);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_FUNC, GL_LEQUAL);
glTexParameteri(GL_TEXTURE_2D, GL_DEPTH_TEXTURE_MODE, GL_LUMINANCE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_MODE, GL_COMPARE_R_TO_TEXTURE);
glEnable(GL_LIGHTING);
glEnable(GL_LIGHT0);
renderSceneElements();
glDisable(GL_LIGHTING);
glDisable(GL_LIGHT0);
glDisable(GL_TEXTURE_2D);
glDisable(GL_TEXTURE_GEN_Q);
glDisable(GL_TEXTURE_GEN_R);
glDisable(GL_TEXTURE_GEN_T);
glDisable(GL_TEXTURE_GEN_S);
glPushMatrix();
glEnable(GL_TEXTURE_2D);
glTexParameteri(GL_TEXTURE_2D, GL_DEPTH_TEXTURE_MODE, GL_NONE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_MODE, GL_NONE);
glTranslatef(3.0f, 2.0f, 5.0f);
glTexCoord2f(0.0f, 0.0f);
glVertex3f(0.0f, 0.0f, 0.0f);
glTexCoord2f(1.0f, 0.0f);
glVertex3f(3.0f, 0.0f, 0.0f);
glTexCoord2f(1.0f, 1.0f);
glVertex3f(3.0f, 3.0f, 0.0f);
glTexCoord2f(0.0f, 1.0f);
glVertex3f(0.0f, 3.0f, 0.0f);
glEnd();
glDisable(GL_TEXTURE_2D);
glPopMatrix();
Note that I had to explicitly bind the texture - I thought it would be automatically related to the framebuffer and hence enabling texturing would have caused that texture to be used? If I don't have that binding there, OpenGL selects my previously used texture.
EDIT: After searching on Google for the millionth time, I ran into someone's post stating that glTexGen works only with specific objects, ie OpenGL wouldn't generate proper coordinates for quads/cubes. Now I knew that before but for whatever reason hadn't considered it until now. The OpenGL Red Book doesn't clarify it either and the given code there is really awkward. I've matched most of my code with the stuff in the book but I'm not really sure about the glTexGen stuff... If I have the shadowmap then how do I map it onto the scene?
### #3dr4cula
Posted 25 July 2013 - 01:22 PM
Okay, so I decided to use FBOs instead since that problem seems to have been indeed me rendering onto the back framebuffer immediately. And having switched to FBOs I can actually see the shadowmap when I map it onto a quad (it's faint but it's visible at least). However, my problems don't end there: now the entire scene is black (except for the textured quad and brownish glClearColor() defined background). I'm guessing my texture coordinate generation is wrong but not sure. Any help would be greatly appreciated!
new init:
glGenTextures(1, &shadowmap_);
glTexImage2D(GL_TEXTURE_2D, 0, GL_DEPTH_COMPONENT, 512, 512, 0, GL_DEPTH_COMPONENT, GL_UNSIGNED_BYTE, NULL);
//glGenRenderbuffers(1, &renderbuffer_);
//glBindRenderbuffer(GL_RENDERBUFFER, renderbuffer_);
//glRenderbufferStorage(GL_RENDERBUFFER, GL_DEPTH_COMPONENT, 512, 512);
glGenFramebuffers(1, &framebuffer_);
glBindFramebuffer(GL_FRAMEBUFFER, framebuffer_);
//glFramebufferRenderbuffer(GL_FRAMEBUFFER, GL_DEPTH_ATTACHMENT, GL_RENDERBUFFER, renderbuffer_);
glFramebufferTexture2D(GL_FRAMEBUFFER, GL_DEPTH_ATTACHMENT, GL_TEXTURE_2D, shadowmap_, 0);
new render:
glBindFramebuffer(GL_FRAMEBUFFER, framebuffer_);
//glDrawBuffer(GL_NONE);
glClearColor(0.5, 0.2, 0.1, 1.0f);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
// position the light
glLightfv(GL_LIGHT0, GL_POSITION, lightPos_);
// set up the projection parameters from the light's POV
glMatrixMode(GL_PROJECTION);
glPushMatrix();
gluPerspective(lightFOV_, lightAspect_, lightNear_, lightFar_);
glMatrixMode(GL_MODELVIEW);
glPushMatrix();
// translate to the light's position
gluLookAt(lightPos_[0], lightPos_[1], lightPos_[2], -1.0f, 0.0f, 5.0f, 0.0f, 1.0f, 0.0f);
// render the scene to get the depth information
renderSceneElements();
glPopMatrix();
// end the projection modification
glMatrixMode(GL_PROJECTION);
glPopMatrix();
glMatrixMode(GL_MODELVIEW);
glBindFramebuffer(GL_FRAMEBUFFER, 0);
// copy over the depth information
//glCopyTexSubImage2D(GL_TEXTURE_2D, 0, 0, 0, 0, 0, 512, 512);
// matrix defining the planes for S, Q, R, T components for texture generation
float planeMatrix[16];
glPushMatrix();
// compensate for the eye-coordinate to texture coordinate conversion: [-1,1] to [0,1]
glTranslatef(0.5f, 0.5f, 0.0f);
glScalef(0.5f, 0.5f, 1.0f);
// do the perspective projection and translate to the light's position
gluPerspective(lightFOV_, lightAspect_, lightNear_, lightFar_);
gluLookAt(lightPos_[0], lightPos_[1], lightPos_[2], -1.0f, 0.0f, 5.0f, 0.0f, 1.0f, 0.0f);
glGetFloatv(GL_MODELVIEW_MATRIX, planeMatrix);
glPopMatrix();
// go from OpenGL's column-major to row-major matrix form
transposeMatrix16(planeMatrix);
// set up the type for texture generation
glTexGeni(GL_S, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
glTexGeni(GL_T, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
glTexGeni(GL_R, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
glTexGeni(GL_Q, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
// data for texture generation
glTexGenfv(GL_S, GL_OBJECT_PLANE, &planeMatrix[0]);
glTexGenfv(GL_T, GL_OBJECT_PLANE, &planeMatrix[4]);
glTexGenfv(GL_R, GL_OBJECT_PLANE, &planeMatrix[8]);
glTexGenfv(GL_Q, GL_OBJECT_PLANE, &planeMatrix[12]);
glEnable(GL_TEXTURE_GEN_S);
glEnable(GL_TEXTURE_GEN_T);
glEnable(GL_TEXTURE_GEN_R);
glEnable(GL_TEXTURE_GEN_Q);
glEnable(GL_TEXTURE_2D);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_FUNC, GL_LEQUAL);
glTexParameteri(GL_TEXTURE_2D, GL_DEPTH_TEXTURE_MODE, GL_LUMINANCE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_MODE, GL_COMPARE_R_TO_TEXTURE);
glEnable(GL_LIGHTING);
glEnable(GL_LIGHT0);
renderSceneElements();
glDisable(GL_LIGHTING);
glDisable(GL_LIGHT0);
glDisable(GL_TEXTURE_2D);
glDisable(GL_TEXTURE_GEN_Q);
glDisable(GL_TEXTURE_GEN_R);
glDisable(GL_TEXTURE_GEN_T);
glDisable(GL_TEXTURE_GEN_S);
glPushMatrix();
glEnable(GL_TEXTURE_2D);
glTexParameteri(GL_TEXTURE_2D, GL_DEPTH_TEXTURE_MODE, GL_NONE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_MODE, GL_NONE);
glTranslatef(3.0f, 2.0f, 5.0f);
glTexCoord2f(0.0f, 0.0f);
glVertex3f(0.0f, 0.0f, 0.0f);
glTexCoord2f(1.0f, 0.0f);
glVertex3f(3.0f, 0.0f, 0.0f);
glTexCoord2f(1.0f, 1.0f);
glVertex3f(3.0f, 3.0f, 0.0f);
glTexCoord2f(0.0f, 1.0f);
glVertex3f(0.0f, 3.0f, 0.0f);
glEnd();
glDisable(GL_TEXTURE_2D);
glPopMatrix();
Note that I had to explicitly bind the texture - I thought it would be automatically related to the framebuffer and hence enabling texturing would have caused that texture to be used? If I don't have that binding there, OpenGL selects my previously used texture.
### #2dr4cula
Posted 25 July 2013 - 01:12 PM
Okay, so I decided to use FBO instead since that problem seems to have been indeed me rendering onto the back framebuffer immediately. And having switched to FBOs I can actually see the shadowmap when I map it onto a quad (it's faint but it's visible at least). However, my problems don't end there: now the entire scene is black (except for the textured quad and brownish glClearColor() defined background). I'm guessing my texture coordinate generation is wrong but not sure. Any help would be greatly appreciated!
new init:
glGenTextures(1, &shadowmap_);
glTexImage2D(GL_TEXTURE_2D, 0, GL_DEPTH_COMPONENT, 512, 512, 0, GL_DEPTH_COMPONENT, GL_UNSIGNED_BYTE, NULL);
//glGenRenderbuffers(1, &renderbuffer_);
//glBindRenderbuffer(GL_RENDERBUFFER, renderbuffer_);
//glRenderbufferStorage(GL_RENDERBUFFER, GL_DEPTH_COMPONENT, 512, 512);
glGenFramebuffers(1, &framebuffer_);
glBindFramebuffer(GL_FRAMEBUFFER, framebuffer_);
//glFramebufferRenderbuffer(GL_FRAMEBUFFER, GL_DEPTH_ATTACHMENT, GL_RENDERBUFFER, renderbuffer_);
glFramebufferTexture2D(GL_FRAMEBUFFER, GL_DEPTH_ATTACHMENT, GL_TEXTURE_2D, shadowmap_, 0);
new render:
glBindFramebuffer(GL_FRAMEBUFFER, framebuffer_);
//glDrawBuffer(GL_NONE);
glClearColor(0.5, 0.2, 0.1, 1.0f);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
// position the light
glLightfv(GL_LIGHT0, GL_POSITION, lightPos_);
// set up the projection parameters from the light's POV
glMatrixMode(GL_PROJECTION);
glPushMatrix();
gluPerspective(lightFOV_, lightAspect_, lightNear_, lightFar_);
glMatrixMode(GL_MODELVIEW);
glPushMatrix();
// translate to the light's position
gluLookAt(lightPos_[0], lightPos_[1], lightPos_[2], -1.0f, 0.0f, 5.0f, 0.0f, 1.0f, 0.0f);
// render the scene to get the depth information
renderSceneElements();
glPopMatrix();
// end the projection modification
glMatrixMode(GL_PROJECTION);
glPopMatrix();
glMatrixMode(GL_MODELVIEW);
glBindFramebuffer(GL_FRAMEBUFFER, 0);
// copy over the depth information
//glCopyTexSubImage2D(GL_TEXTURE_2D, 0, 0, 0, 0, 0, 512, 512);
// matrix defining the planes for S, Q, R, T components for texture generation
float planeMatrix[16];
glPushMatrix();
// compensate for the eye-coordinate to texture coordinate conversion: [-1,1] to [0,1]
glTranslatef(0.5f, 0.5f, 0.0f);
glScalef(0.5f, 0.5f, 1.0f);
// do the perspective projection and translate to the light's position
gluPerspective(lightFOV_, lightAspect_, lightNear_, lightFar_);
gluLookAt(lightPos_[0], lightPos_[1], lightPos_[2], -1.0f, 0.0f, 5.0f, 0.0f, 1.0f, 0.0f);
glGetFloatv(GL_MODELVIEW_MATRIX, planeMatrix);
glPopMatrix();
// go from OpenGL's column-major to row-major matrix form
transposeMatrix16(planeMatrix);
// set up the type for texture generation
glTexGeni(GL_S, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
glTexGeni(GL_T, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
glTexGeni(GL_R, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
glTexGeni(GL_Q, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
// data for texture generation
glTexGenfv(GL_S, GL_OBJECT_PLANE, &planeMatrix[0]);
glTexGenfv(GL_T, GL_OBJECT_PLANE, &planeMatrix[4]);
glTexGenfv(GL_R, GL_OBJECT_PLANE, &planeMatrix[8]);
glTexGenfv(GL_Q, GL_OBJECT_PLANE, &planeMatrix[12]);
glEnable(GL_TEXTURE_GEN_S);
glEnable(GL_TEXTURE_GEN_T);
glEnable(GL_TEXTURE_GEN_R);
glEnable(GL_TEXTURE_GEN_Q);
glEnable(GL_TEXTURE_2D);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_FUNC, GL_LEQUAL);
glTexParameteri(GL_TEXTURE_2D, GL_DEPTH_TEXTURE_MODE, GL_LUMINANCE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_MODE, GL_COMPARE_R_TO_TEXTURE);
glEnable(GL_LIGHTING);
glEnable(GL_LIGHT0);
renderSceneElements();
glDisable(GL_LIGHTING);
glDisable(GL_LIGHT0);
glDisable(GL_TEXTURE_2D);
glDisable(GL_TEXTURE_GEN_Q);
glDisable(GL_TEXTURE_GEN_R);
glDisable(GL_TEXTURE_GEN_T);
glDisable(GL_TEXTURE_GEN_S);
glPushMatrix();
glEnable(GL_TEXTURE_2D);
glTexParameteri(GL_TEXTURE_2D, GL_DEPTH_TEXTURE_MODE, GL_NONE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_MODE, GL_NONE);
glTranslatef(3.0f, 2.0f, 5.0f);
glTexCoord2f(0.0f, 0.0f);
glVertex3f(0.0f, 0.0f, 0.0f);
glTexCoord2f(1.0f, 0.0f);
glVertex3f(3.0f, 0.0f, 0.0f);
glTexCoord2f(1.0f, 1.0f);
glVertex3f(3.0f, 3.0f, 0.0f);
glTexCoord2f(0.0f, 1.0f);
glVertex3f(0.0f, 3.0f, 0.0f);
glEnd();
glDisable(GL_TEXTURE_2D);
glPopMatrix();
Note that I had to explicitly bind the texture - I thought it would be automatically related to the framebuffer and hence enabling texturing would have caused that texture to be used? If I don't have that binding there, OpenGL selects my previously used texture.
### #1dr4cula
Posted 25 July 2013 - 01:10 PM
Okay, so I decided to use FBO instead since that problem seems to have been indeed me rendering onto the back framebuffer immediately. And having switched to FBOs I can actually see the shadowmap when I map it onto a quad (it's faint but it's visible at least). However, my problems don't end there: now the entire scene is black (except for the textured quad and brownish glClearColor() defined background). I'm guessing my texture coordinate generation is wrong but not sure. Any help would be greatly appreciated!
new init:
glGenTextures(1, &shadowmap_);
glFramebufferTexture2D(GL_FRAMEBUFFER, GL_DEPTH_ATTACHMENT, GL_TEXTURE_2D, shadowmap_, 0);
|
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https://datascience.stackexchange.com/questions/110651/why-should-mle-be-considered-in-logistic-regression-when-it-cannot-give-a-defini
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# Why should MLE be considered in Logistic Regression when it cannot give a definite solution?
If MLE (Maximum Likelihood Estimation) cannot give a proper closed-form solution for the parameters in Logistic Regression, why is this method discussed so much? Why not just stick to Gradient Descent for estimating parameters?
• Wait a sec... when does Gradient Descent give closed-form solution? (given that you also state it "estimates parameters"). May 5 at 3:11
Maximum likelihood is a method for estimating parameters.
Gradient descent is a numerical technique to help us solve equations that we might not be able to solve by traditional means (e.g., we can't get a closed-form solution when we take the derivative and set it equal to zero).
The two can coexist.
In fact, when we use gradient descent to minimize the crossentropy loss in a logistic regression, we are solving for a maximum likelihood estimator of the regression parameters, as minimizing crossentropy loss and maximizing likelihood are equivalent in logistic regression.
In order to descend a gradient, you have to have a function. If we take the negative log-likelihood and descend the gradient until we find the minimum, we have done the equivalent of finding the maximum of the log-likelihood and, thus, the likelihood.
I think you are comparing apples and oranges here. Maximum likelihood is a the maximum value of your likelihood function, which somehow describes your data generation process. Specifically likelihood gives you the probability of observing your data, given the data-generation model you imagine. It is similar to a loss metric in that respect.
Gradient descent is an approach to varying your parameters in such a way as to maximize/minimize some function, e.g. loss-metric.
So why are you trying to compare these two things? It would seem to me that you can use likelihood as a loss-function (normally log-likelihood) and then run gradient descent to maximize it.
Perhaps that's what you meant. Why would you use likelihood as the loss-metric for gradient descent? In my use-cases it helped when available data was not evenly sampled or non-homoschedastic, e.g. if you want to do regression to get y as a function of x=0...1, but variance of y is greater in the region x=0.2...0.4 compared to other regions. Using least squares as the loss metric may give a poor fit (since the intrinsic assumption of least squares is that your variance in y is the same).
• Minimizing crossentropy loss is equivalent to maximum likelihood estimation in logistic regression.
– Dave
Jul 5 at 18:46
• @Dave, your comment is correct, but I am not sure why it is relevant. Yes, minimizing cross-entropy can be equivalent to likelihood maximization. At least sometimes, where you are Bernoulli sampling. Does it change my comment in any way?
– Cryo
Jul 6 at 3:13
MLE (Maximum Likelihood Estimation) is discussed a lot because it is relatively straightforward and commonly applicable. The downside is that MLE is not always the best method for a given context or it might not even be possible to be applied.
In practice, gradient descent and other methods are commonly used for estimating parameters in logistic regression.
• Minimizing crossentropy loss is equivalent to maximum likelihood estimation in logistic regression.
– Dave
Jul 5 at 18:46
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http://mathoverflow.net/questions/10889/conditions-that-allow-unique-solutions-for-linear-diophantine-equations
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# Conditions that allow unique solutions for Linear Diophantine equations
(This posting became very long, so I should note that there are two alternative but nearly equivalent formulations of the same question being given. The first one asks for the optimal strategy for playing a game, the second is a more formally stated optimization problem. There is also a proposed solution for the n = 2 case, and an answer by Boris Bukh (below) for the unbounded case of [$a_1$, ..., $a_n$].)
You and I play a game:
I hand you an empty box and 'n' > 1 canisters of balls, where 'n' is agreed upon beforehand. The balls in each canister have a unique integer mass to my specification, 'L' < [$a_1$, ..., $a_n$] < 'M' (where 'L' and 'M' are some fixed, lowest and largest possible integer masses, respectively), and no two canisters will have balls with the same mass.
Now, after blindfolding myself, I ask you to fill the empty box with somewhere between zero or a finite integer number of copies, 'T', of each type of ball: [$x_1$, ..., $x_n$]. Here, 'T' is the same for all ball types.
When finished, you fully seal the box, hand it back to me, and ask for the copy numbers of each ball type. To accomplish this, all I am allowed to do is place the box on a scale to 'weigh' its total mass.
The reward system works as follows - the higher I can set the copy number threshold, 'T', the more money I win. However, if I set 'T' too high to properly guess the exact copy numbers, I lose an infinite amount of money and the game is over. Assuming I love money and hate risk, how do I choose the masses of the balls, [$a_1$, ..., $a_n$], such that I make the most money at no risk of financial ruin?
Interestingly, for the n = 2 case (though not for n > 2), the answer seems to be: Pick 'L' < [$a_1$, $a_2$] < 'M' such that the Lowest Common Multiple, LCM[$a_1$, $a_2$], is maximized over the allowed interval. Depending on 'L' and 'M', [$a_1$, $a_2$] are not necessarily prime.
LCM[$a_1$, $a_2$] also seems to always equal the maximum measured mass of the box for which unique copy numbers can be determined ($S_{max}$ from the below optimization formulation where 'T' can be different for the different masses/balls).
Intuitively this seems right, but is it true for all values of 'L' and 'M'?
(For finding 'T' in polynomial-time given masses [$a_1$, ..., $a_n$], please see note at bottom of page. Is there a better solution?)
We can also state this question as the following optimization problem -
I provide you with the number of terms, 'n', for a monomial sum (or linear Diophantine equation) of the form: $a_1$*$x_1$ + ... + $a_n$*$x_n$ = S, where 'L' < [$a_1$, ..., $a_n$] < 'M', and 'S' belong to the set of positive real integers while [$x_1$, ..., $x_n$] belongs to the set of integers $\ge$ 0.
We now define a function #NonDegenerate([$a_1$, ..., $a_n$]) that outputs [k, $S_{max}$] where 'k' is the cardinality (i.e. number of elements) in the set [$S_1$, ..., $S_{max}$] which:
1. For the provided set [$a_1$, ..., $a_n$], must contain all possible sums, $a_1$*$x_1$ + ... + $a_n$*$x_n$ = $S_k$, for all sets of integers [$x_1$, ..., $x_n$] s.t. 0 < $S_k$ $\le$ $S_{max}$.
2. Where all elements of the set [$S_1$, ..., $S_{max}$], i.e. all $S_k$, must have a single or unique solution [$x_1$, ..., $x_n$] for the given set of [$a_1$, ..., $a_n$].
3. Where $S_{max}$ is the largest possible sum satisfying conditions (1) & (2).
Now, for a given number of monomial terms 'n' (or if you are allowed to select 'n'), what is the most efficient strategy for selecting [$a_1$, ..., $a_n$] to maximize the output 'k' of the '#NonDegenerate' function?
Note on relationship to game that was described earlier - Here we're talking about maximizing the number of sums, $S_k$ < $S_{max}$, that have unique solutions. This should be equivalent to maximizing the threshold 'T' for the maximum possible copy numbers of balls in the first formulation of the problem under the condition that you won't allow yourself to lose the game.
(For finding $S_{max}$ in polynomial-time given [$a_1$, ..., $a_n$], please see note at bottom of page. Is there a better solution?)
Some computational results:
For expression $a_1$*$x_1$ + $a_2$*$x_2$ = S, over the range $x_1$, $x_2$ = (1, 100) and $a_1$, $a_2$ = (1, 100), max(#NonDegenerate) = 5049 for [$a_1$, $a_2$] = [99, 100] and $S_{max}$ = 9899.
(Mistake before where I used a result that set a minimum copy number min($a_k$) = '1' rather than the correct min($a_k$) = '0')
Note on counting solutions for the expression - $a_1$*$x_1$ + ... + $a_n$*$x_n$ = $S_k$, and a possible polynomial time algorithm to find $S_{max}$ or 'T' given the set [$a_1$, ..., $a_n$]:
As fleshed out in a previous post of mine (with help from Sam Nead) - "Counting Lattice Points on an N-simplex" (Counting lattice points on an n-simplex) - the problem of finding solutions to expressions of the form:
$a_1$*$x_1$ + ... + $a_n$*$x_n$ = S
Is equivalent to counting the number of integer lattice-points on (but NOT in the bounded area) the N-simplex being defined (i.e the real-number solution set to the expression). Since polynomial time algorithms exist for exactly enumerating integer points for rational polyhedron of fixed-dimension (due to Barvinok et al), there should also exist a straightforward polynomial-time algorithm for this optimization problem (via testing and incrementing $S_{max}$ or the corresponding value 'T' in the game description). But does a nicer strategy or solution exist?
-
I am having a really hard time parsing this formulation of the problem for some reason. What was your motivation again? – Qiaochu Yuan Jan 7 '10 at 3:05
Qiaochu, sorry about that. In a moment I'll add such a motivation section to the question statement. – Richard Jan 7 '10 at 5:12
I don't know what it is about this problem, but I cannot understand what you are asking for! What's the relationship between T and the x_i? – Qiaochu Yuan Jan 9 '10 at 8:33
Qiaochu, again, I apologize for not being clear enough. 'T' is supposed to be some maximum number of a certain type of ball you're allowed to add to the box. The actual copy number you add is the $x_i$ for ball type 'i'. I can allow a different threshold for each type of ball, though I restricted it to a universal threshold for all ball types to hopefully make the problem easier (I no longer believe that helps). – Richard Jan 9 '10 at 10:18
Basically, I want linear expressions of the form $a_1$*$x_1$ + ... + $a_1$*$x_1$ = 'S' where 'S' is going to let you uniquely determine the copy numbers (i.e. $x_1$) the largest number of times for a given set of masses (i.e. $a_i$). By 'largest number of times' I'm talking about the total number of integer sums, not just over the largest range of the possible sums. Does that make any sense to you? – Richard Jan 9 '10 at 10:23
show 1 more comment
Choose the masses to be powers of a given integer $M$. Then you can guess correctly as long as the number of copies is at most $M-1$ by writing the total mass in base $M$ and reading off the digits. As $M$ can be chosen arbitrarily large, you can reap arbitrarily large reward.
EDIT 1: The problem was edited after this answer was given. The problem now imposes an upper bound on the masses. However, the masses have to be large, since if one wants to allow $T$ copies, then all $(T+1)^n$ sums be distinct. Thus the largest of them is at least $(T+1)^n/n-1$, and it is at most $Tn$ times the largest mass. Thus, the largest mass needs to be at least $(T+1)^{n-1}/n$.
EDIT 2: The question was edited again, this time requiring a lower bound for the masses as well. For this problem let $X=M^n$ and let $i$'th mass be $M^i+X$ for $i=0,\dots,n-1$. This increases the largest mass by only a factor of $M$.
Boris, a sincere thank you! However, I should have specified that I was looking for a solution where one suffers a penalty for spreading out the values of the masses, i.e. values of [$a_1$, ..., $a_n$] in this manner... – Richard Jan 7 '10 at 15:41
The integers have to be large, since if you want to allow $T$ copies, you want all $T^n$ sums be distinct. Each of these sums is at most $Tn$ times the largest mass. Thus, the largest mass needs to be at least $T^{n-1}/n$. – Boris Bukh Jan 7 '10 at 15:43
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http://therealshrimp.blogspot.com/2007/03/citrix-secure-gateway-hangs-at-start-up_21.html
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## Wednesday, March 21, 2007
### Citrix Secure Gateway Hangs at Start-up after applying Patch 005 (SGE300W005)
This problem is caused by HP PSP 7.60.
Resolution:
Locate the rotatelogs.exe file for Secure Gateway. This file is normally located in the C:\Program Files\Citrix Secure Gateway\bin folder.
Rename the rotatelogs.exe executable (for example, rotate.exe).
Open the http.conf file located in the C:\Program Files\Citrix\Citrix Secure Gateway\conf folder. To do so, perform the following procedure:
Open a command prompt window.
Navigate to the C:\Program Files\Citrix\Citrix Secure Gateway\conf folder from within the command prompt.
In the command prompt window, type notepad httpd.conf to open the httpd.conf file.
Note: The httpd.conf file is hidden. You cannot open the file unless you use a text editor.
Create a backup of the file (for example, httpd.conf.bak).
Modify the httpd.conf file and replace rotatelogs.exe with the new executable name (for example, rotate.exe).
Restart Secure Gateway (for the new changes to take effect. Process Explorer should reflect the new changes).
After performing the changes, set the HP Management Homepage Service to Automatic (or the other third-party application).
Restart the system and test against the problem.
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https://math.stackexchange.com/questions/2816824/integrate-int-0-pi-fracx-sin-x-log-frac1-sin-x-1-sin-x-mat
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# Integrate $\int_0^{\pi} \frac{x}{\sin x} \log {\frac{1+\sin x} {1-\sin x}}\,\mathrm d x$
$\int_0^{\pi} \frac{x}{\sin x} \log {\frac{1+\sin x} {1-\sin x}}\,\mathrm d x$
I'm stuck on this one. Any ideas? I have tried substitutions and integration by parts.
I managed to show it is equivalent to $\pi \int_0^{\pi/2} \frac{1}{\sin x} \log {\frac{1+\sin x} {1-\sin x}}\,\mathrm d x$
$$-\pi\int_{0}^{1}\frac{1}{x\sqrt{1-x^2}}\log\left(\frac{1-x}{1+x}\right)\,dx \stackrel{\frac{1-x}{1+x}\mapsto z}{=}\pi\int_{0}^{1}\frac{-\log z}{\sqrt{z}(1-z)}\,dz\stackrel{z\mapsto u^2}{=}4\pi\int_{0}^{1}\frac{-\log u}{1-u^2}\,du$$ or to $$4\pi\sum_{n\geq 0}\int_{0}^{1} u^{2n}\left(-\log u\right)\,du = 4\pi \sum_{n\geq 0}\frac{1}{(2n+1)^2} = \color{red}{\frac{\pi^3}{2}}.$$
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https://forum.allaboutcircuits.com/threads/for-loop-problem.65607/
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# For loop problem
#### raw_653
Joined Feb 3, 2012
10
//sbit
//variables
int i=1 ;
//module
void flash (){
for (i=1; i<=128; i*=2);
{
portc =i;
delay_ms(1000);
}
}
//main
void main() {
Trisc=0;
portc=i;
//while
while (1)
{ flash ();
}
}
i was trying to make a loop to turn LEDs on in a sequence yet there is no output
any solutions ??
thanks )
Joined Apr 16, 2011
464
Which processor chip are you using?
If it is an 8 bit device, then variable i should be declared as an unsigned char.
If it is 16 bit device then int should work (though unsigned int would be more logical)
#### raw_653
Joined Feb 3, 2012
10
I am using PIC16F877A
Joined Apr 16, 2011
464
Then i should be unsigned char.
Also you should remove the semi-colon at the end of the line of your "for" statement
#### raw_653
Joined Feb 3, 2012
10
I removed only the semi-colon at the end and it works
thanks a lot
why didnt it work before ??
Joined Apr 16, 2011
464
The semicolon ends the for loop.
Without the semicolon, the block of code in braces becomes part of the for loop.
That is how C syntax is.
#### raw_653
Joined Feb 3, 2012
10
i see
thanks
Joined Nov 28, 2011
57
I removed only the semi-colon at the end and it works
thanks a lot
why didnt it work before ??
hexreader fixed it for you, but it's a good idea to stop and understand what you asked the compiler to do:
Rich (BB code):
for (i=1; i<=128; i*=2);
{
portc =i;
delay_ms(1000);
}
In the first line, you told it to start with i=1, then double it repeatedly as long as it was less than or equal to 128. On the final doubling, it hits 256 and that statement terminates.
Then you have a block of code that says to assign i (now 256) to portc, and delay for a second.
Note that there are times that you really do want a semi-colon after the "for" construct; in that case, everything's happening between the parenthesis. That's pretty rare though, and most people use a while statement in those cases, so a semi-colon after the closing parenthesis is extremely rare.
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http://www.eevblog.com/forum/crowd-funded-projects/a-shoebox-size-reflow-oven/msg1369098/
|
### Author Topic: A shoebox size reflow oven. (Read 1752 times)
0 Members and 1 Guest are viewing this topic.
#### hamster_nz
• Super Contributor
• Posts: 1694
• Country:
##### A shoebox size reflow oven.
« on: December 08, 2017, 07:14:41 am »
Just saw this...
REFLO - The compact, open, and smart PCB reflow oven. Bake your dream!
https://www.crowdsupply.com/magicbox/reflo
Apparently it is perfect for baking 50mm x 50mm boards, and is only 150mm x 150mm x 68mm.
Initially I though... "O.M.G. WHY? NO!", but now I thinking "Cute, fun, could make use of that, but too expensive for me".
#### abraxa
• Frequent Contributor
• Posts: 354
• Country:
• Sigrok associate
##### Re: A shoebox size reflow oven.
« Reply #1 on: December 08, 2017, 06:21:42 pm »
The design is stylish for sure, but I'm not sure this thing works as required. The heating element construction is a neat idea but it really increases the thermal mass a lot. This may not be an issue for heating up but it may prevent the oven from cooling down quickly enough. Here, the fan would be helpful but... what's that? The fan feeds into a tube with a diameter of roughly 1cm? And there is no air outlet, so where does the air go? Surely, the fan can't be sucking out the air... oh wait, it is! So they're feeding very hot air directly into the fan! That's not a design I'm confident in, especially since there's no clear air path to me. The air path may be pretty obstructed, reducing air flow.
In short: heating seems fine but cooling... not so sure. Maybe I'm worrying more about this than is warranted but since I can't test the oven in person, being critical is all I can do
#### Kean
• Supporter
• Posts: 674
• Country:
• Embedded systems & IT consultant
##### Re: A shoebox size reflow oven.
« Reply #2 on: December 08, 2017, 06:54:29 pm »
I like my gadgets as much as anyone, but this seems like an overpriced gimmick. How often do you need to take a reflow oven with you? Especially one limited to 50x50mm!
Good on them for getting 20 backers at that price
#### matseng
• Frequent Contributor
• Posts: 562
• Country:
##### Re: A shoebox size reflow oven.
« Reply #3 on: December 08, 2017, 08:55:36 pm »
The fan feeds into a tube with a diameter of roughly 1cm? And there is no air outlet, so where does the air go? Surely, the fan can't be sucking out the air... oh wait, it is! So they're feeding very hot air directly into the fan!
I didn't see any mention of the air direction in the specs or video, so I guess it could be either sucking or pushing the air out. I mean - the heating area is not hermetically enclosed so the fan could just push out the hot air in all the gaps just as well sucking in cold air thru them. Right?
#### Cyberdragon
• Super Contributor
• Posts: 1804
• Country:
##### Re: A shoebox size reflow oven.
« Reply #4 on: December 09, 2017, 02:25:42 am »
Does this thing even have a real control panal, or is it IOT wank operated only?
*BZZZZZZAAAAAP*
Voltamort strikes again!
Explodingus - someone who frequently causes accidental explosions
#### MicroBlocks
• Contributor
• Posts: 29
• Country:
##### Re: A shoebox size reflow oven.
« Reply #5 on: December 26, 2017, 04:16:33 pm »
So basically a single hollowed out refractory brick a heating element and some simple electronics. BOM costs about 10US$. It is an interesting idea though and for about 50USD i would buy one, just to have a play with it. #### sleemanj • Super Contributor • Posts: 2174 • Country: • Professional tightwad. ##### Re: A shoebox size reflow oven. « Reply #6 on: December 26, 2017, 05:07:34 pm » ~~~ EEVBlog Members - get yourself 10% discount off all my electronic components for sale just use the Buy Direct links and use Coupon Code "eevblog" during checkout. Shipping from New Zealand, international orders welcome :-) #### pieman103021 • Contributor • Posts: 38 • Country: ##### Re: A shoebox size reflow oven. « Reply #7 on: December 26, 2017, 05:22:15 pm » So basically a single hollowed out refractory brick a heating element and some simple electronics. BOM costs about 10US$.
It is an interesting idea though and for about 50USD i would buy one, just to have a play with it.
#### mikeselectricstuff
• Super Contributor
• Posts: 11607
• Country:
##### Re: A shoebox size reflow oven.
« Reply #10 on: December 26, 2017, 09:47:59 pm »
Why would you pay that much for something with such a stupidly small board size when a toaster oven works just fine?
Youtube channel:Taking wierd stuff apart. Very apart.
Mike's Electric Stuff: High voltage, vintage electronics etc.
Day Job: Mostly LEDs
Smf
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|
https://math.stackexchange.com/questions/3220640/linearization-of-partial-differential-equation
|
Linearization of Partial Differential Equation
I have this beautiful Non-linear PDE $$\frac{\partial C}{\partial t}=\left(\frac{\partial C}{\partial x}\right)^2+C\frac{\partial^2 C}{\partial x^2}$$
Where C is a function of (x,t) It comes from the diffusion equation where D is concentration depending, and has the linear form $$D=k \cdot C$$ and is furthermore made dimensionless.
To solve this numerically I would like to first Linearize the PDE (if this is even possible), because i know how to solve linear PDE's, but how can I do this, is there any methods, articles or books which shows some procedures? or is linearization unnecessary and the PDE can be solved directly?
You can linearize it when you perform time discretisation. If you denote $$C_n = C(\cdot, t_n)$$, you can consider approximations like
$$\left(\frac{\partial C_{n+1}}{\partial x}\right)^2 \approx \frac{\partial C_n}{\partial x} \frac{\partial C_{n+1}}{\partial x}, \quad C_{n+1} \frac{\partial^2C_{n+1}}{\partial x^2}\approx C_n \frac{\partial^2C_{n+1}}{\partial x^2}.$$
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https://bitbucket.org/rmcantin/bayesopt/commits/ef0b6e0b658197ff7de1747f988e33ee42949ff3
|
# Commits
committed ef0b6e0
Adding new changes to the docs.
• Participants
• Parent commits 0a9a4d7
• Branches default
• Tags v0.7.1
# File doxygen/install.dox
<li> In some *nix systems, including Ubuntu, Debian and Mac OS, the
library is installed by default in /usr/local/lib/. However, this
-folder is not included by default in the linker, Python or Matlab
-paths by default. This is specially critical when building shared
-libraries (mandatory for Python usage). The script \em
-exportlocalpaths.sh makes sure that the folder with the libraries is
-included in all the necessary paths.
+folder is not included by default in the linker or Matlab paths by
+default. This is specially critical when building shared
+libraries. The script \em exportlocalpaths.sh makes sure that the
+folder with the libraries is included in all the necessary
+paths.
+
+<li> The Python package is compiled in a different file and installed
+in the proper folder by default (site-packages). Thus, the Python
+interface should work out of the box in Linux and Mac OS.
+
</ul>
<li> Python: the scrip \b demo_quad gives a quick overview of all the
# File doxygen/models.dox
\li "cEI","cBEI","cEIa": The most extended and reliable algorithm is
the Expected Improvement algorithm \cite Mockus78. In this case we
provide the general version from \cite Schonlau98 which includes an
-exponent to trade off exploration and exploitation "cEI". Whe also includes
-a variation from \cite Mockus1989 which add a \a bias or \a threshold
-to the improvement "cBEI".
+exponent to trade off exploration and exploitation "cEI". For an
+annealed version of the exploration/exploitation trade off, use
+"cEIa". Whe also includes a variation from \cite Mockus1989 which add
+a \a bias or \a threshold to the improvement "cBEI".
\li "cLCB", "cLCBa": Another popular algorithm is the Lower Confidence
-Bound (LCB), or UCB in case of maximization. Introduced by
-\cite cox1992statistical as Sequential Design for Optimization (SDO).
+Bound (LCB), or UCB in case of maximization. Introduced by \cite
+cox1992statistical as Sequential Design for Optimization
+(SDO). Analogously, "cLCBa" represents an annealed version of the
+exploration/exploitation trade off.
+\li "cMI": A generalized version of the LCB criterion which relies on
+the mutual information. See \cite Contal2014
\li "cPOI": Probability of improvement, by \cite Kushner:1964
\li "cExpReturn","cThompsonSampling","cOptimisticSampling": This
criteria are related with the predicted return of the function. The
value). The second one is based on the Thompson sampling (drawing a
random sample from the predicted distribution). Finally, the
optimistic sampling takes the minimum of the other two (mean vs random).
-
\li "cAopt": This is based on the A-optimality criteria. It is the
predicted variance at the query point. Thus, this criteria is intended
for \b exploration of the input space, not for optimization.
# File doxygen/using.dox
combination of them. It is used to select which points to evaluate
for each iteration of the optimization process. Could be a
combination of functions like
- "cHedge(cEI,cLCB,cPOI,cThompsonSampling)". See section critmod for
+ "cHedge(cEI,cLCB,cPOI,cThompsonSampling)". See section \ref critmod for
the different possibilities. [Default: "cEI"]
- \b crit_params, \b n_crit_params: Array with the set of parameters
# File optimization.bib
timestamp = {2010.06.18}
}
+@INPROCEEDINGS{Contal2014,
+ author = {Emile Contal and Vianney Perchet and Nicolas Vayatis},
+ title = {Gaussian Process Optimization with Mutual Information},
+ booktitle = {International Conference on Machine Learning},
+ year = {2014},
+ owner = {rmcantin},
+ timestamp = {2014.07.02}
+}
+
@INCOLLECTION{cox1997sdo,
author = {Cox, Dennis D and John, Susan},
title = {SDO: A statistical method for global optimization},
timestamp = {2013.03.15}
}
+@INPROCEEDINGS{EggFeuBerSnoHooHutLey13,
+ author = {K. Eggensperger and M. Feurer and F. Hutter and J. Bergstra and J.
+ Snoek and H. Hoos and K. Leyton-Brown},
+ title = {Towards an Empirical Foundation for Assessing Bayesian Optimization
+ of Hyperparameters},
+ booktitle = {BayesOpt workshop (NIPS)},
+ year = {2013},
+ longbooktitle = {NIPS workshop on Bayesian Optimization in Theory and Practice},
+ owner = {rmcantin},
+ timestamp = {2014.05.19}
+}
+
@INPROCEEDINGS{Garnett2010,
author = {Roman Garnett and Michael A. Osborne and Stephen J. Roberts},
title = {Bayesian optimization for sensor set selection},
timestamp = {2013.05.07}
}
-@INPROCEEDINGS{EggFeuBerSnoHooHutLey13,
- author = {K. Eggensperger and M. Feurer and F. Hutter and J.
- Bergstra and J. Snoek and H. Hoos and K. Leyton-Brown},
- title = {Towards an Empirical Foundation for Assessing Bayesian Optimization
- of Hyperparameters},
- longbooktitle = {NIPS workshop on Bayesian Optimization in Theory and Practice},
- booktitle = {BayesOpt workshop (NIPS)},
- year = {2013},
- owner = {rmcantin},
- timestamp = {2014.05.19}
-}
-
-
@ARTICLE{Igel04,
author = {Christian Igel and Marc Toussaint},
title = {A No-Free-Lunch theorem for non-uniform distributions of target functions},
|
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http://www.chegg.com/homework-help/questions-and-answers/-1n107n-n-q3311906
|
estimate the magnitude of the error involved in using the sum of the first four terms to approximate the sum of the entire series
(-1)^n+1(0.7)^n/n
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https://www.ncbi.nlm.nih.gov/pubmed/10536372?dopt=Abstract
|
Format
Choose Destination
J Cell Biochem. 1999 Dec 1;75(3):505-14.
# Galectin-3 regulates the adhesive interaction between breast carcinoma cells and elastin.
### Author information
1
Department of Biochemistry, Meharry Medical College, Nashville, Tennessee 37208, USA. [email protected]
### Abstract
Galectin-3 is a beta-galactoside binding lectin whose precise physiological role is not yet defined. In the present studies, we questioned whether galectin-3 plays a role in the adhesion of breast carcinoma cells to elastin. The impetus for this analysis was the initial observation that the cellular receptor for elastin, the 67 kDa elastin/laminin protein may have galectin-like properties (Mecham et al. [1989] J. Biol. Chem. 264:16652-16657). We therefore analyzed the adhesion of breast carcinoma cells to microtiter wells coated with elastin under conditions which eliminate integrin participation in adhesion. The adhesion assay was done in the absence and presence of purified recombinant galectin-3. We hereby demonstrate that high concentrations of galectin-3 ligate breast carcinoma cells to microtiter wells coated with elastin. Galectin-3 also demonstrated a specific binding interaction with purified elastin in a dose and lactose dependent manner. Furthermore we demonstrated by immunoprecipitation that endogenous galectin-3 in breast carcinoma cells is associated with tropoelastin. Lastly, the breast carcinoma cells which expressed galectin-3 on their surface, demonstrated enhanced cellular proliferation on elastin compared to galectin-3 null expressing cells. These studies suggest that galectin-3 is capable of regulating the interactions between cells and elastin.
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https://www.educator.com/mathematics/algebra-2/eaton/common-logarithms.php
|
×
INSTRUCTORS Carleen Eaton Grant Fraser
Dr. Carleen Eaton
Common Logarithms
Slide Duration:
Section 1: Equations and Inequalities
Expressions and Formulas
22m 23s
Intro
0:00
Order of Operations
0:19
Variable
0:27
Algebraic Expression
0:46
Term
0:57
Example: Algebraic Expression
1:25
Evaluate Inside Grouping Symbols
1:55
Evaluate Powers
2:30
Multiply/Divide Left to Right
2:55
3:35
Monomials
4:40
Examples of Monomials
4:52
Constant
5:27
Coefficient
5:46
Degree
6:25
Power
7:15
Polynomials
8:02
Examples of Polynomials
8:24
Binomials, Trinomials, Monomials
8:53
Term
9:21
Like Terms
10:02
Formulas
11:00
Example: Pythagorean Theorem
11:15
Example 1: Evaluate the Algebraic Expression
11:50
Example 2: Evaluate the Algebraic Expression
14:38
Example 3: Area of a Triangle
19:11
Example 4: Fahrenheit to Celsius
20:41
Properties of Real Numbers
20m 15s
Intro
0:00
Real Numbers
0:07
Number Line
0:15
Rational Numbers
0:46
Irrational Numbers
2:24
Venn Diagram of Real Numbers
4:03
Irrational Numbers
5:00
Rational Numbers
5:19
Real Number System
5:27
Natural Numbers
5:32
Whole Numbers
5:53
Integers
6:19
Fractions
6:46
Properties of Real Numbers
7:15
Commutative Property
7:34
Associative Property
8:07
Identity Property
9:04
Inverse Property
9:53
Distributive Property
11:03
Example 1: What Set of Numbers?
12:21
Example 2: What Properties Are Used?
13:56
Example 3: Multiplicative Inverse
16:00
Example 4: Simplify Using Properties
17:18
Solving Equations
19m 10s
Intro
0:00
Translations
0:06
Verbal Expressions and Algebraic Expressions
0:13
Example: Sum of Two Numbers
0:19
Example: Square of a Number
1:33
Properties of Equality
3:20
Reflexive Property
3:30
Symmetric Property
3:42
Transitive Property
4:01
5:01
Subtraction Property
5:37
Multiplication Property
6:02
Division Property
6:30
Solving Equations
6:58
Example: Using Properties
7:18
Solving for a Variable
8:25
Example: Solve for Z
8:34
Example 1: Write Algebraic Expression
10:15
Example 2: Write Verbal Expression
11:31
Example 3: Solve the Equation
14:05
Example 4: Simplify Using Properties
17:26
Solving Absolute Value Equations
17m 31s
Intro
0:00
Absolute Value Expressions
0:09
Distance from Zero
0:18
Example: Absolute Value Expression
0:24
Absolute Value Equations
1:50
Example: Absolute Value Equation
2:00
Example: Isolate Expression
3:13
No Solution
3:46
Empty Set
3:58
Example: No Solution
4:12
Number of Solutions
4:46
Check Each Solution
4:57
Example: Two Solutions
5:05
Example: No Solution
6:18
Example: One Solution
6:28
Example 1: Evaluate for X
7:16
Example 2: Write Verbal Expression
9:08
Example 3: Solve the Equation
12:18
Example 4: Simplify Using Properties
13:36
Solving Inequalities
17m 14s
Intro
0:00
Properties of Inequalities
0:08
0:17
Example: Using Numbers
0:30
Subtraction Property
1:03
Example: Using Numbers
1:19
Multiplication Properties
1:44
C>0 (Positive Number)
1:50
Example: Using Numbers
2:05
C<0 (Negative Number)
2:40
Example: Using Numbers
3:10
Division Properties
4:11
C>0 (Positive Number)
4:15
Example: Using Numbers
4:27
C<0 (Negative Number)
5:21
Example: Using Numbers
5:32
Describing the Solution Set
6:10
Example: Set Builder Notation
6:26
Example: Graph (Closed Circle)
7:08
Example: Graph (Open Circle)
7:30
Example 1: Solve the Inequality
7:58
Example 2: Solve the Inequality
9:06
Example 3: Solve the Inequality
10:10
Example 4: Solve the Inequality
13:12
Solving Compound and Absolute Value Inequalities
25m
Intro
0:00
Compound Inequalities
0:08
And and Or
0:13
Example: And
0:22
Example: Or
1:12
And Inequality
1:41
Intersection
1:49
Example: Numbers
2:08
Example: Inequality
2:43
Or Inequality
4:35
Example: Union
4:45
Example: Inequality
5:53
Absolute Value Inequalities
7:19
Definition of Absolute Value
7:33
Examples: Compound Inequalities
8:30
Example: Complex Inequality
12:21
Example 1: Solve the Inequality
12:54
Example 2: Solve the Inequality
17:21
Example 3: Solve the Inequality
18:54
Example 4: Solve the Inequality
22:15
Section 2: Linear Relations and Functions
Relations and Functions
32m 5s
Intro
0:00
Coordinate Plane
0:20
X-Coordinate and Y-Coordinate
0:30
Example: Coordinate Pairs
0:37
1:20
Relations
2:14
Domain and Range
2:19
Set of Ordered Pairs
2:29
As a Table
2:51
Functions
4:21
One Element in Range
4:32
Example: Mapping
4:43
Example: Table and Map
6:26
One-to-One Functions
8:01
Example: One-to-One
8:22
Example: Not One-to-One
9:18
Graphs of Relations
11:01
Discrete and Continuous
11:12
Example: Discrete
11:22
Example: Continous
12:30
Vertical Line Test
14:09
Example: S Curve
14:29
Example: Function
16:15
Equations, Relations, and Functions
17:03
Independent Variable and Dependent Variable
17:16
Function Notation
19:11
Example: Function Notation
19:23
Example 1: Domain and Range
20:51
Example 2: Discrete or Continous
23:03
Example 3: Discrete or Continous
25:53
Example 4: Function Notation
30:05
Linear Equations
14m 46s
Intro
0:00
Linear Equations and Functions
0:07
Linear Equation
0:19
Example: Linear Equation
0:29
Example: Linear Function
1:07
Standard Form
2:02
Integer Constants with No Common Factor
2:08
Example: Standard Form
2:27
Graphing with Intercepts
4:05
X-Intercept and Y-Intercept
4:12
Example: Intercepts
4:26
Example: Graphing
5:14
Example 1: Linear Function
7:53
Example 2: Linear Function
9:10
Example 3: Standard Form
10:04
Example 4: Graph with Intercepts
12:25
Slope
23m 7s
Intro
0:00
Definition of Slope
0:07
Change in Y / Change in X
0:26
Example: Slope of Graph
0:37
Interpretation of Slope
3:07
Horizontal Line (0 Slope)
3:13
Vertical Line (Undefined Slope)
4:52
Rises to Right (Positive Slope)
6:36
Falls to Right (Negative Slope)
6:53
Parallel Lines
7:18
Example: Not Vertical
7:30
Example: Vertical
7:58
Perpendicular Lines
8:31
Example: Perpendicular
8:42
Example 1: Slope of Line
10:32
Example 2: Graph Line
11:45
Example 3: Parallel to Graph
13:37
Example 4: Perpendicular to Graph
17:57
Writing Linear Functions
23m 5s
Intro
0:00
Slope Intercept Form
0:11
m and b
0:28
Example: Graph Using Slope Intercept
0:43
Point Slope Form
2:41
Relation to Slope Formula
3:03
Example: Point Slope Form
4:36
Parallel and Perpendicular Lines
6:28
Review of Parallel and Perpendicular Lines
6:31
Example: Parallel
7:50
Example: Perpendicular
9:58
Example 1: Slope Intercept Form
11:07
Example 2: Slope Intercept Form
13:07
Example 3: Parallel
15:49
Example 4: Perpendicular
18:42
Special Functions
31m 5s
Intro
0:00
Step Functions
0:07
Example: Apple Prices
0:30
Absolute Value Function
4:55
Example: Absolute Value
5:05
Piecewise Functions
9:08
Example: Piecewise
9:27
Example 1: Absolute Value Function
14:00
Example 2: Absolute Value Function
20:39
Example 3: Piecewise Function
22:26
Example 4: Step Function
25:25
Graphing Inequalities
21m 42s
Intro
0:00
Graphing Linear Inequalities
0:07
0:19
Using Test Points
0:32
Graph Corresponding Linear Function
0:46
Dashed or Solid Lines
0:59
Use Test Point
1:21
Example: Linear Inequality
1:58
Graphing Absolute Value Inequalities
4:50
Graph Corresponding Equations
4:59
Use Test Point
5:20
Example: Absolute Value Inequality
5:38
Example 1: Linear Inequality
9:17
Example 2: Linear Inequality
11:56
Example 3: Linear Inequality
14:29
Example 4: Absolute Value Inequality
17:06
Section 3: Systems of Equations and Inequalities
Solving Systems of Equations by Graphing
17m 13s
Intro
0:00
Systems of Equations
0:09
Example: Two Equations
0:24
Solving by Graphing
0:53
Point of Intersection
1:09
Types of Systems
2:29
Independent (Single Solution)
2:34
Dependent (Infinite Solutions)
3:05
Inconsistent (No Solution)
4:23
Example 1: Solve by Graphing
5:20
Example 2: Solve by Graphing
9:10
Example 3: Solve by Graphing
12:27
Example 4: Solve by Graphing
14:54
Solving Systems of Equations Algebraically
23m 53s
Intro
0:00
Solving by Substitution
0:08
Example: System of Equations
0:36
Solving by Multiplication
7:22
Extra Step of Multiplying
7:38
Example: System of Equations
8:00
Inconsistent and Dependent Systems
11:14
Variables Drop Out
11:48
Inconsistent System (Never True)
12:01
Constant Equals Constant
12:53
Dependent System (Always True)
13:11
Example 1: Solve Algebraically
13:58
Example 2: Solve Algebraically
15:52
Example 3: Solve Algebraically
17:54
Example 4: Solve Algebraically
21:40
Solving Systems of Inequalities By Graphing
27m 12s
Intro
0:00
Solving by Graphing
0:08
Graph Each Inequality
0:25
Overlap
0:35
Corresponding Linear Equations
1:03
Test Point
1:23
Example: System of Inequalities
1:51
No Solution
7:06
Empty Set
7:26
Example: No Solution
7:34
Example 1: Solve by Graphing
10:27
Example 2: Solve by Graphing
13:30
Example 3: Solve by Graphing
17:19
Example 4: Solve by Graphing
23:23
Solving Systems of Equations in Three Variables
28m 53s
Intro
0:00
Solving Systems in Three Variables
0:17
Triple of Values
0:31
Example: Three Variables
0:56
Number of Solutions
5:55
One Solution
6:08
No Solution
6:24
Infinite Solutions
7:06
Example 1: Solve 3 Variables
7:59
Example 2: Solve 3 Variables
13:50
Example 3: Solve 3 Variables
19:54
Example 4: Solve 3 Variables
25:50
Section 4: Matrices
Basic Matrix Concepts
11m 34s
Intro
0:00
What is a Matrix
0:26
Brackets
0:46
Designation
1:21
Element
1:47
Matrix Equations
1:59
Dimensions
2:27
Rows (m) and Columns (n)
2:37
Examples: Dimensions
2:43
Special Matrices
4:22
Row Matrix
4:32
Column Matrix
5:00
Zero Matrix
6:00
Equal Matrices
6:30
Example: Corresponding Elements
6:36
Example 1: Matrix Dimension
8:12
Example 2: Matrix Dimension
9:03
Example 3: Zero Matrix
9:38
Example 4: Row and Column Matrix
10:26
Matrix Operations
21m 36s
Intro
0:00
0:18
Same Dimensions
0:25
1:04
Matrix Subtraction
3:42
Same Dimensions
3:48
Example: Subtracting Matrices
4:04
Scalar Multiplication
6:08
Scalar Constant
6:24
Example: Multiplying Matrices
6:32
Properties of Matrix Operations
8:23
Commutative Property
8:41
Associative Property
9:08
Distributive Property
9:44
10:24
Example 2: Matrix Subtraction
11:58
Example 3: Scalar Multiplication
14:23
Example 4: Matrix Properties
16:09
Matrix Multiplication
29m 36s
Intro
0:00
Dimension Requirement
0:17
n = p
0:24
Resulting Product Matrix (m x q)
1:21
Example: Multiplication
1:54
Matrix Multiplication
3:38
Example: Matrix Multiplication
4:07
Properties of Matrix Multiplication
10:46
Associative Property
11:00
Associative Property (Scalar)
11:28
Distributive Property
12:06
Distributive Property (Scalar)
12:30
Example 1: Possible Matrices
13:31
Example 2: Multiplying Matrices
17:08
Example 3: Multiplying Matrices
20:41
Example 4: Matrix Properties
24:41
Determinants
33m 13s
Intro
0:00
What is a Determinant
0:13
Square Matrices
0:23
Vertical Bars
0:41
Determinant of a 2x2 Matrix
1:21
Second Order Determinant
1:37
Formula
1:45
Example: 2x2 Determinant
1:58
Determinant of a 3x3 Matrix
2:50
Expansion by Minors
3:08
Third Order Determinant
3:19
Expanding Row One
4:06
Example: 3x3 Determinant
6:40
Diagonal Method for 3x3 Matrices
13:24
Example: Diagonal Method
13:36
Example 1: Determinant of 2x2
18:59
Example 2: Determinant of 3x3
20:03
Example 3: Determinant of 3x3
25:35
Example 4: Determinant of 3x3
29:22
Cramer's Rule
28m 25s
Intro
0:00
System of Two Equations in Two Variables
0:16
One Variable
0:50
Determinant of Denominator
1:14
Determinants of Numerators
2:23
Example: System of Equations
3:34
System of Three Equations in Three Variables
7:06
Determinant of Denominator
7:17
Determinants of Numerators
7:52
Example 1: Two Equations
8:57
Example 2: Two Equations
13:21
Example 3: Three Equations
17:11
Example 4: Three Equations
23:43
Identity and Inverse Matrices
22m 25s
Intro
0:00
Identity Matrix
0:13
Example: 2x2 Identity Matrix
0:30
Example: 4x4 Identity Matrix
0:50
Properties of Identity Matrices
1:24
Example: Multiplying Identity Matrix
2:52
Matrix Inverses
5:30
Writing Matrix Inverse
6:07
Inverse of a 2x2 Matrix
6:39
Example: 2x2 Matrix
7:31
Example 1: Inverse Matrix
10:18
Example 2: Find the Inverse Matrix
13:04
Example 3: Find the Inverse Matrix
17:53
Example 4: Find the Inverse Matrix
20:44
Solving Systems of Equations Using Matrices
22m 32s
Intro
0:00
Matrix Equations
0:11
Example: System of Equations
0:21
Solving Systems of Equations
4:01
Isolate x
4:16
Example: Using Numbers
5:10
Multiplicative Inverse
5:54
Example 1: Write as Matrix Equation
7:18
Example 2: Use Matrix Equations
9:12
Example 3: Use Matrix Equations
15:06
Example 4: Use Matrix Equations
19:35
Section 5: Quadratic Functions and Inequalities
31m 48s
Intro
0:00
0:12
A is Zero
0:27
Example: Parabola
0:45
Properties of Parabolas
2:08
Axis of Symmetry
2:11
Vertex
2:32
Example: Parabola
2:48
Minimum and Maximum Values
9:02
Positive or Negative
9:28
Upward or Downward
9:58
Example: Minimum
10:31
Example: Maximum
11:16
Example 1: Axis of Symmetry, Vertex, Graph
12:41
Example 2: Axis of Symmetry, Vertex, Graph
17:25
Example 3: Minimum or Maximum
21:47
Example 4: Minimum or Maximum
27:09
27m 3s
Intro
0:00
0:16
Standard Form
0:18
0:47
Solving by Graphing
1:41
Roots (x-Intercepts)
1:48
Example: Number of Solutions
2:12
Estimating Solutions
9:23
Example: Integer Solutions
9:30
Example: Estimating
9:53
Example 1: Solve by Graphing
10:52
Example 2: Solve by Graphing
15:10
Example 1: Solve by Graphing
17:50
Example 1: Solve by Graphing
20:54
19m 53s
Intro
0:00
Factoring Techniques
0:15
Greatest Common Factor (GCF)
0:37
Difference of Two Squares
1:48
Perfect Square Trinomials
2:30
General Trinomials
3:09
Zero Product Rule
5:22
Example: Zero Product
5:53
Example 1: Solve by Factoring
7:46
Example 1: Solve by Factoring
9:48
Example 1: Solve by Factoring
12:34
Example 1: Solve by Factoring
15:28
Imaginary and Complex Numbers
35m 45s
Intro
0:00
Properties of Square Roots
0:10
Product Property
0:26
Example: Product Property
0:56
Quotient Property
2:17
Example: Quotient Property
2:35
Imaginary Numbers
3:12
Imaginary i
3:51
Examples: Imaginary Number
4:22
Complex Numbers
7:23
Real Part and Imaginary Part
7:33
Examples: Complex Numbers
7:57
Equality
9:37
Example: Equal Complex Numbers
9:52
10:12
10:25
Complex Plane
13:32
Horizontal Axis (Real)
13:49
Vertical Axis (Imaginary)
13:59
Example: Labeling
14:11
Multiplication
15:57
Example: FOIL Method
16:03
Division
18:37
Complex Conjugates
18:45
Conjugate Pairs
19:10
Example: Dividing Complex Numbers
20:00
Example 1: Simplify Complex Number
24:50
Example 2: Simplify Complex Number
27:56
Example 3: Multiply Complex Numbers
29:27
Example 3: Dividing Complex Numbers
31:48
Completing the Square
27m 11s
Intro
0:00
Square Root Property
0:12
Example: Perfect Square
0:38
Example: Perfect Square Trinomial
3:00
Completing the Square
4:39
Constant Term
4:50
Example: Complete the Square
5:04
Solve Equations
6:42
6:59
Example: Complete the Square
7:07
Equations Where a Not Equal to 1
10:58
Divide by Coefficient
11:08
Example: Complete the Square
11:24
Complex Solutions
14:05
Real and Imaginary
14:14
Example: Complex Solution
14:35
Example 1: Square Root Property
18:31
Example 2: Complete the Square
19:15
Example 3: Complete the Square
20:40
Example 4: Complete the Square
23:56
22m 48s
Intro
0:00
0:21
Standard Form
0:29
0:57
One Rational Root
3:00
Example: One Root
3:31
Complex Solutions
6:16
Complex Conjugate
6:28
Example: Complex Solution
7:15
Discriminant
9:42
Positive Discriminant
10:03
Perfect Square (Rational)
10:51
Not Perfect Square (2 Irrational)
11:27
Negative Discriminant
12:28
Zero Discriminant
12:57
13:50
16:03
19:00
Example 4: Discriminant
21:33
Analyzing the Graphs of Quadratic Functions
30m 7s
Intro
0:00
Vertex Form
0:12
H and K
0:32
Axis of Symmetry
0:36
Vertex
0:42
Example: Origin
1:00
Example: k = 2
2:12
Example: h = 1
4:27
Significance of Coefficient a
7:13
Example: |a| > 1
7:25
Example: |a| < 1
8:18
Example: |a| > 0
8:51
Example: |a| < 0
9:05
Writing Quadratic Equations in Vertex Form
10:22
Standard Form to Vertex Form
10:35
Example: Standard Form
11:02
Example: a Term Not 1
14:42
Example 1: Vertex Form
19:47
Example 2: Vertex Form
22:09
Example 3: Vertex Form
24:32
Example 4: Vertex Form
28:23
27m 5s
Intro
0:00
0:11
Test Point
0:18
0:29
3:57
Example: Parameter
4:24
Example 1: Graph Inequality
11:16
Example 2: Solve Inequality
14:27
Example 3: Graph Inequality
19:14
Example 4: Solve Inequality
23:48
Section 6: Polynomial Functions
Properties of Exponents
19m 29s
Intro
0:00
Simplifying Exponential Expressions
0:09
Monomial Simplest Form
0:19
Negative Exponents
1:07
Examples: Simple
1:34
Properties of Exponents
3:06
Negative Exponents
3:13
Mutliplying Same Base
3:24
Dividing Same Base
3:45
Raising Power to a Power
4:33
Parentheses (Multiplying)
5:11
Parentheses (Dividing)
5:47
Raising to 0th Power
6:15
Example 1: Simplify Exponents
7:59
Example 2: Simplify Exponents
10:41
Example 3: Simplify Exponents
14:11
Example 4: Simplify Exponents
18:04
Operations on Polynomials
13m 27s
Intro
0:00
0:13
Like Terms and Like Monomials
0:23
1:14
Multiplying Polynomials
3:40
Distributive Property
3:44
Example: Monomial by Polynomial
4:06
Example 1: Simplify Polynomials
5:47
Example 2: Simplify Polynomials
6:28
Example 3: Simplify Polynomials
8:38
Example 4: Simplify Polynomials
10:47
Dividing Polynomials
31m 11s
Intro
0:00
Dividing by a Monomial
0:13
Example: Numbers
0:26
Example: Polynomial by a Monomial
1:18
Long Division
2:28
Remainder Term
2:41
Example: Dividing with Numbers
3:04
Example: With Polynomials
5:01
Example: Missing Terms
7:58
Synthetic Division
11:44
Restriction
12:04
Example: Divisor in Form
12:20
Divisor in Synthetic Division
15:54
Example: Coefficient to 1
16:07
Example 1: Divide Polynomials
17:10
Example 2: Divide Polynomials
19:08
Example 3: Synthetic Division
21:42
Example 4: Synthetic Division
25:09
Polynomial Functions
22m 30s
Intro
0:00
Polynomial in One Variable
0:13
0:27
Example: Polynomial
1:18
Degree
1:31
Polynomial Functions
2:57
Example: Function
3:13
Function Values
3:33
Example: Numerical Values
3:53
Example: Algebraic Expressions
5:11
Zeros of Polynomial Functions
5:50
Odd Degree
6:04
Even Degree
7:29
End Behavior
8:28
Even Degrees
9:09
9:23
Odd Degrees
12:51
13:00
Example 1: Degree and Leading Coefficient
15:03
Example 2: Polynomial Function
15:56
Example 3: Polynomial Function
17:34
Example 4: End Behavior
19:53
Analyzing Graphs of Polynomial Functions
33m 29s
Intro
0:00
Graphing Polynomial Functions
0:11
Example: Table and End Behavior
0:39
Location Principle
4:43
Zero Between Two Points
5:03
Example: Location Principle
5:21
Maximum and Minimum Points
8:40
Relative Maximum and Relative Minimum
9:16
Example: Number of Relative Max/Min
11:11
Example 1: Graph Polynomial Function
11:57
Example 2: Graph Polynomial Function
16:19
Example 3: Graph Polynomial Function
23:27
Example 4: Graph Polynomial Function
28:35
Solving Polynomial Functions
21m 10s
Intro
0:00
Factoring Polynomials
0:06
Greatest Common Factor (GCF)
0:25
Difference of Two Squares
1:14
Perfect Square Trinomials
2:07
General Trinomials
2:57
Grouping
4:32
Sum and Difference of Two Cubes
6:03
Examples: Two Cubes
6:14
8:22
8:44
Example 1: Factor Polynomial
12:03
Example 2: Factor Polynomial
13:54
15:33
Example 4: Solve Polynomial Function
17:24
Remainder and Factor Theorems
31m 21s
Intro
0:00
Remainder Theorem
0:07
Checking Work
0:22
Dividend and Divisor in Theorem
1:12
Example: f(a)
2:05
Synthetic Substitution
5:43
Example: Polynomial Function
6:15
Factor Theorem
9:54
Example: Numbers
10:16
Example: Confirm Factor
11:27
Factoring Polynomials
14:48
Example: 3rd Degree Polynomial
15:07
Example 1: Remainder Theorem
19:17
Example 2: Other Factors
21:57
Example 3: Remainder Theorem
25:52
Example 4: Other Factors
28:21
Roots and Zeros
31m 27s
Intro
0:00
Number of Roots
0:08
Not Nature of Roots
0:18
Example: Real and Complex Roots
0:25
Descartes' Rule of Signs
2:05
Positive Real Roots
2:21
Example: Positve
2:39
Negative Real Roots
5:44
Example: Negative
6:06
Finding the Roots
9:59
Example: Combination of Real and Complex
10:07
Conjugate Roots
13:18
Example: Conjugate Roots
13:50
Example 1: Solve Polynomial
16:03
Example 2: Solve Polynomial
18:36
Example 3: Possible Combinations
23:13
Example 4: Possible Combinations
27:11
Rational Zero Theorem
31m 16s
Intro
0:00
Equation
0:08
List of Possibilities
0:16
Equation with Constant and Leading Coefficient
1:04
Example: Rational Zero
2:46
7:19
Equation with Leading Coefficient of One
7:34
Example: Coefficient Equal to 1
8:45
Finding Rational Zeros
12:58
Division with Remainder Zero
13:32
Example 1: Possible Rational Zeros
14:20
Example 2: Possible Rational Zeros
16:02
Example 3: Possible Rational Zeros
19:58
Example 4: Find All Zeros
22:06
Section 7: Radical Expressions and Inequalities
Operations on Functions
34m 30s
Intro
0:00
Arithmetic Operations
0:07
Domain
0:16
Intersection
0:24
Denominator is Zero
0:49
Example: Operations
1:02
Composition of Functions
7:18
Notation
7:48
Right to Left
8:18
Example: Composition
8:48
Composition is Not Commutative
17:23
Example: Not Commutative
17:51
Example 1: Function Operations
20:55
Example 2: Function Operations
24:34
Example 3: Compositions
27:51
Example 4: Function Operations
31:09
Inverse Functions and Relations
22m 42s
Intro
0:00
Inverse of a Relation
0:14
Example: Ordered Pairs
0:56
Inverse of a Function
3:24
Domain and Range Switched
3:52
Example: Inverse
4:28
Procedure to Construct an Inverse Function
6:42
f(x) to y
6:42
Interchange x and y
6:59
Solve for y
7:06
Write Inverse f(x) for y
7:14
Example: Inverse Function
7:25
Example: Inverse Function 2
8:48
Inverses and Compositions
10:44
Example: Inverse Composition
11:46
Example 1: Inverse Relation
14:49
Example 2: Inverse of Function
15:40
Example 3: Inverse of Function
17:06
Example 4: Inverse Functions
18:55
Square Root Functions and Inequalities
30m 4s
Intro
0:00
Square Root Functions
0:07
Examples: Square Root Function
0:16
Example: Not Square Root Function
0:46
1:12
Example: Restriction
1:31
Graphing Square Root Functions
3:42
Example: Graphing
3:49
Square Root Inequalities
8:47
Same Technique
9:00
Example: Square Root Inequality
9:20
Example 1: Graph Square Root Function
15:19
Example 2: Graph Square Root Function
18:03
Example 3: Graph Square Root Function
22:41
Example 4: Square Root Inequalities
25:37
nth Roots
20m 46s
Intro
0:00
Definition of the nth Root
0:07
Example: 5th Root
0:20
Example: 6th Root
0:51
Principal nth Root
1:39
Example: Principal Roots
2:06
Using Absolute Values
5:58
Example: Square Root
6:18
Example: 6th Root
8:40
Example: Negative
10:15
12:23
13:29
16:07
18:18
41m 11s
Intro
0:00
0:16
Quotient Property
0:29
Example: Quotient
1:00
Example: Product Property
1:47
3:24
3:47
6:33
7:16
Rationalizing Denominators
8:27
9:05
11:47
Conjugates
12:07
13:11
16:12
16:20
16:28
19:04
Distributive Property
19:10
19:20
24:11
28:43
32:00
36:34
Rational Exponents
30m 45s
Intro
0:00
Definition 1
0:20
Example: Using Numbers
0:39
Example: Non-Negative
2:46
Example: Odd
3:34
Definition 2
4:32
Restriction
4:52
Example: Relate to Definition 1
5:04
Example: m Not 1
5:31
Simplifying Expressions
7:53
Multiplication
8:31
Division
9:29
Multiply Exponents
10:08
Raised Power
11:05
Zero Power
11:29
Negative Power
11:49
Simplified Form
13:52
Complex Fraction
14:16
Negative Exponents
14:40
Example: More Complicated
15:14
19:03
Example 2: Write with Rational Exponents
20:40
Example 3: Complex Fraction
22:09
Example 4: Complex Fraction
26:22
31m 27s
Intro
0:00
0:11
0:22
1:06
Example: Complex Equation
2:42
Extraneous Roots
7:21
Squaring Technique
7:35
Double Check
7:44
Example: Extraneous
8:21
Eliminating nth Roots
10:04
Isolate and Raise Power
10:14
Example: nth Root
10:27
11:27
Restriction: Index is Even
11:53
12:29
15:41
17:44
20:24
24:34
Section 8: Rational Equations and Inequalities
Multiplying and Dividing Rational Expressions
40m 54s
Intro
0:00
Simplifying Rational Expressions
0:22
Algebraic Fraction
0:29
Examples: Rational Expressions
0:49
Example: GCF
1:33
Example: Simplify Rational Expression
2:26
Factoring -1
4:04
Example: Simplify with -1
4:19
Multiplying and Dividing Rational Expressions
6:59
Multiplying and Dividing
7:28
Example: Multiplying Rational Expressions
8:36
Example: Dividing Rational Expressions
11:20
Factoring
14:01
Factoring Polynomials
14:19
Example: Factoring
14:35
Complex Fractions
18:22
Example: Numbers
18:37
Example: Algebraic Complex Fractions
19:25
Example 1: Simplify Rational Expression
25:56
Example 2: Simplify Rational Expression
29:34
Example 3: Simplify Rational Expression
31:39
Example 4: Simplify Rational Expression
37:50
55m 4s
Intro
0:00
Least Common Multiple (LCM)
0:27
Examples: LCM of Numbers
0:43
Example: LCM of Polynomials
4:02
7:55
Least Common Denominator (LCD)
8:07
Example: Numbers
8:17
Example: Rational Expressions
11:03
Equivalent Fractions
15:22
Simplifying Complex Fractions
21:19
Example: Previous Lessons
21:36
Example: More Complex
22:53
Example 1: Find LCM
28:30
31:44
Example 3: Subtract Rational Expressions
39:18
Example 4: Simplify Rational Expression
38:26
Graphing Rational Functions
57m 13s
Intro
0:00
Rational Functions
0:18
Restriction
0:34
Example: Rational Function
0:51
Breaks in Continuity
2:52
Example: Continuous Function
3:10
Discontinuities
3:30
Example: Excluded Values
4:37
Graphs and Discontinuities
5:02
Common Binomial Factor (Hole)
5:08
Example: Common Factor
5:31
Asymptote
10:06
Example: Vertical Asymptote
11:08
Horizontal Asymptotes
20:00
Example: Horizontal Asymptote
20:25
Example 1: Holes and Vertical Asymptotes
26:12
Example 2: Graph Rational Faction
28:35
Example 3: Graph Rational Faction
39:23
Example 4: Graph Rational Faction
47:28
Direct, Joint, and Inverse Variation
20m 21s
Intro
0:00
Direct Variation
0:07
Constant of Variation
0:25
Graph of Constant Variation
1:26
Slope is Constant k
1:35
Example: Straight Lines
1:41
Joint Variation
2:48
Three Variables
2:52
Inverse Variation
3:38
Rewritten Form
3:52
Examples in Biology
4:22
Graph of Inverse Variation
4:51
Asymptotes are Axes
5:12
Example: Inverse Variation
5:40
Proportions
10:11
Direct Variation
10:25
Inverse Variation
11:32
Example 1: Type of Variation
12:42
Example 2: Direct Variation
14:13
Example 3: Joint Variation
16:24
Example 4: Graph Rational Faction
18:50
Solving Rational Equations and Inequalities
55m 14s
Intro
0:00
Rational Equations
0:15
Example: Algebraic Fraction
0:26
Least Common Denominator
0:49
Example: Simple Rational Equation
1:22
Example: Solve Rational Equation
5:40
Extraneous Solutions
9:31
Doublecheck
10:00
No Solution
10:38
Example: Extraneous
10:44
Rational Inequalities
14:01
Excluded Values
14:31
Solve Related Equation
14:49
Find Intervals
14:58
Use Test Values
15:25
Example: Rational Inequality
15:51
Example: Rational Inequality 2
17:07
Example 1: Rational Equation
28:50
Example 2: Rational Equation
33:51
Example 3: Rational Equation
38:19
Example 4: Rational Inequality
46:49
Section 9: Exponential and Logarithmic Relations
Exponential Functions
35m 58s
Intro
0:00
What is an Exponential Function?
0:12
Restriction on b
0:31
Base
0:46
Example: Exponents as Bases
0:56
Variables as Exponents
1:12
Example: Exponential Function
1:50
Graphing Exponential Functions
2:33
Example: Using Table
2:49
Properties
11:52
Continuous and One to One
12:00
Domain is All Real Numbers
13:14
X-Axis Asymptote
13:55
Y-Intercept
14:02
Reflection Across Y-Axis
14:31
Growth and Decay
15:06
Exponential Growth
15:10
Real Life Examples
15:41
Example: Growth
15:52
Example: Decay
16:12
Real Life Examples
16:30
Equations
17:32
Bases are Same
18:05
Examples: Variables as Exponents
18:20
Inequalities
21:29
Property
21:51
Example: Inequality
22:37
Example 1: Graph Exponential Function
24:05
Example 2: Growth or Decay
27:50
Example 3: Exponential Equation
29:31
Example 4: Exponential Inequality
32:54
Logarithms and Logarithmic Functions
45m 54s
Intro
0:00
What are Logarithms?
0:08
Restrictions
0:15
Written Form
0:26
Logarithms are Exponents
0:52
Example: Logarithms
1:49
Logarithmic Functions
5:14
Same Restrictions
5:30
Inverses
5:53
Example: Logarithmic Function
6:24
Graph of the Logarithmic Function
9:20
Example: Using Table
9:35
Properties
15:09
Continuous and One to One
15:14
Domain
15:36
Range
15:56
Y-Axis is Asymptote
16:02
X Intercept
16:12
Inverse Property
16:57
Compositions of Functions
17:10
Equations
18:30
Example: Logarithmic Equation
19:13
Inequalities
20:36
Properties
20:47
Example: Logarithmic Inequality
21:40
Equations with Logarithms on Both Sides
24:43
Property
24:51
Example: Both Sides
25:23
Inequalities with Logarithms on Both Sides
26:52
Property
27:02
Example: Both Sides
28:05
Example 1: Solve Log Equation
31:52
Example 2: Solve Log Equation
33:53
Example 3: Solve Log Equation
36:15
39:19
Properties of Logarithms
28m 43s
Intro
0:00
Product Property
0:08
Example: Product
0:46
Quotient Property
2:40
Example: Quotient
2:59
Power Property
3:51
Moved Exponent
4:07
Example: Power
4:37
Equations
5:15
Example: Use Properties
5:58
Example 1: Simplify Log
11:17
Example 2: Single Log
15:54
Example 3: Solve Log Equation
18:48
Example 4: Solve Log Equation
22:13
Common Logarithms
25m 23s
Intro
0:00
What are Common Logarithms?
0:10
Real World Applications
0:16
Base Not Written
0:27
Example: Base 10
0:39
Equations
1:47
Example: Same Base
1:56
Example: Different Base
2:37
Inequalities
6:07
Multiplying/Dividing Inequality
6:21
6:54
Change of Base
12:45
Base 10
13:24
Example: Change of Base
14:05
Example 1: Log Equation
15:21
Example 2: Common Logs
17:13
Example 3: Log Equation
18:22
21:52
Base e and Natural Logarithms
21m 14s
Intro
0:00
Number e
0:09
Natural Base
0:21
Growth/Decay
0:33
Example: Exponential Function
0:53
Natural Logarithms
1:11
ln x
1:19
Inverse and Identity Function
1:39
Example: Inverse Composition
1:55
Equations and Inequalities
4:39
Extraneous Solutions
5:30
Examples: Natural Log Equations
5:48
Example 1: Natural Log Equation
9:08
Example 2: Natural Log Equation
10:37
16:54
18:16
Exponential Growth and Decay
24m 30s
Intro
0:00
Decay
0:17
Decreases by Fixed Percentage
0:23
Rate of Decay
0:56
Example: Finance
1:34
Scientific Model of Decay
3:37
Exponential Decay
3:45
4:13
Example: Half Life
5:33
Growth
9:06
Increases by Fixed Percentage
9:18
Example: Finance
10:09
Scientific Model of Growth
11:35
Population Growth
12:04
Example: Growth
12:20
Example 1: Computer Price
14:00
Example 2: Stock Price
15:46
Example 3: Medicine Disintegration
19:10
Example 4: Population Growth
22:33
Section 10: Conic Sections
Midpoint and Distance Formulas
32m 42s
Intro
0:00
Midpoint Formula
0:15
Example: Midpoint
0:30
Distance Formula
2:30
Example: Distance
2:52
Example 1: Midpoint and Distance
4:58
Example 2: Midpoint and Distance
8:07
Example 3: Median Length
18:51
Example 4: Perimeter and Area
23:36
Parabolas
41m 27s
Intro
0:00
What is a Parabola?
0:20
Definition of a Parabola
0:29
Focus
0:59
Directrix
1:15
Axis of Symmetry
3:08
Vertex
3:33
Minimum or Maximum
3:44
Standard Form
4:59
Horizontal Parabolas
5:08
Vertex Form
5:19
Upward or Downward
5:41
Example: Standard Form
6:06
Graphing Parabolas
8:31
Shifting
8:51
Example: Completing the Square
9:22
Symmetry and Translation
12:18
Example: Graph Parabola
12:40
Latus Rectum
17:13
Length
18:15
Example: Latus Rectum
18:35
Horizontal Parabolas
18:57
Not Functions
20:08
Example: Horizontal Parabola
21:21
Focus and Directrix
24:11
Horizontal
24:48
Example 1: Parabola Standard Form
25:12
Example 2: Graph Parabola
30:00
Example 3: Graph Parabola
33:13
Example 4: Parabola Equation
37:28
Circles
21m 3s
Intro
0:00
What are Circles?
0:08
Example: Equidistant
0:17
0:32
Equation of a Circle
0:44
Example: Standard Form
1:11
Graphing Circles
1:47
Example: Circle
1:56
Center Not at Origin
3:07
Example: Completing the Square
3:51
Example 1: Equation of Circle
6:44
11:51
15:08
Example 4: Equation of Circle
16:57
Ellipses
46m 51s
Intro
0:00
What Are Ellipses?
0:11
Foci
0:23
Properties of Ellipses
1:43
Major Axis, Minor Axis
1:47
Center
1:54
Length of Major Axis and Minor Axis
3:21
Standard Form
5:33
Example: Standard Form of Ellipse
6:09
Vertical Major Axis
9:14
Example: Vertical Major Axis
9:46
Graphing Ellipses
12:51
Complete the Square and Symmetry
13:00
Example: Graphing Ellipse
13:16
Equation with Center at (h, k)
19:57
Horizontal and Vertical
20:14
Difference
20:27
Example: Center at (h, k)
20:55
Example 1: Equation of Ellipse
24:05
Example 2: Equation of Ellipse
27:57
Example 3: Equation of Ellipse
32:32
Example 4: Graph Ellipse
38:27
Hyperbolas
38m 15s
Intro
0:00
What are Hyperbolas?
0:12
Two Branches
0:18
Foci
0:38
Properties
2:00
Transverse Axis and Conjugate Axis
2:06
Vertices
2:46
Length of Transverse Axis
3:14
Distance Between Foci
3:31
Length of Conjugate Axis
3:38
Standard Form
5:45
Vertex Location
6:36
Known Points
6:52
Vertical Transverse Axis
7:26
Vertex Location
7:50
Asymptotes
8:36
Vertex Location
8:56
Rectangle
9:28
Diagonals
10:29
Graphing Hyperbolas
12:58
Example: Hyperbola
13:16
Equation with Center at (h, k)
16:32
Example: Center at (h, k)
17:21
Example 1: Equation of Hyperbola
19:20
Example 2: Equation of Hyperbola
22:48
Example 3: Graph Hyperbola
26:05
Example 4: Equation of Hyperbola
36:29
Conic Sections
18m 43s
Intro
0:00
Conic Sections
0:16
Double Cone Sections
0:24
Standard Form
1:27
General Form
1:37
Identify Conic Sections
2:16
B = 0
2:50
X and Y
3:22
Identify Conic Sections, Cont.
4:46
Parabola
5:17
Circle
5:51
Ellipse
6:31
Hyperbola
7:10
Example 1: Identify Conic Section
8:01
Example 2: Identify Conic Section
11:03
Example 3: Identify Conic Section
11:38
Example 4: Identify Conic Section
14:50
47m 4s
Intro
0:00
0:22
0:45
Solutions
2:49
Graphs of Possible Solutions
3:10
4:10
Example: Elimination
4:21
Solutions
11:39
Example: 0, 1, 2, 3, 4 Solutions
11:50
12:48
13:09
21:42
29:13
35:02
40:29
Section 11: Sequences and Series
Arithmetic Sequences
21m 16s
Intro
0:00
Sequences
0:10
General Form of Sequence
0:16
Example: Finite/Infinite Sequences
0:33
Arithmetic Sequences
0:28
Common Difference
2:41
Example: Arithmetic Sequence
2:50
Formula for the nth Term
3:51
Example: nth Term
4:32
Equation for the nth Term
6:37
Example: Using Formula
6:56
Arithmetic Means
9:47
Example: Arithmetic Means
10:16
Example 1: nth Term
12:38
Example 2: Arithmetic Means
13:49
Example 3: Arithmetic Means
16:12
Example 4: nth Term
18:26
Arithmetic Series
21m 36s
Intro
0:00
What are Arithmetic Series?
0:11
Common Difference
0:28
Example: Arithmetic Sequence
0:43
Example: Arithmetic Series
1:09
Finite/Infinite Series
1:36
Sum of Arithmetic Series
2:27
Example: Sum
3:21
Sigma Notation
5:53
Index
6:14
Example: Sigma Notation
7:14
Example 1: First Term
9:00
Example 2: Three Terms
10:52
Example 3: Sum of Series
14:14
Example 4: Sum of Series
18:13
Geometric Sequences
23m 3s
Intro
0:00
Geometric Sequences
0:11
Common Difference
0:38
Common Ratio
1:08
Example: Geometric Sequence
2:38
nth Term of a Geometric Sequence
4:41
Example: nth Term
4:56
Geometric Means
6:51
Example: Geometric Mean
7:09
Example 1: 9th Term
12:04
Example 2: Geometric Means
15:18
Example 3: nth Term
18:32
Example 4: Three Terms
20:59
Geometric Series
22m 43s
Intro
0:00
What are Geometric Series?
0:11
List of Numbers
0:24
Example: Geometric Series
1:12
Sum of Geometric Series
2:16
Example: Sum of Geometric Series
2:41
Sigma Notation
4:21
Lower Index, Upper Index
4:38
Example: Sigma Notation
4:57
Another Sum Formula
6:08
Example: n Unknown
6:28
Specific Terms
7:41
Sum Formula
7:56
Example: Specific Term
8:11
Example 1: Sum of Geometric Series
10:02
Example 2: Sum of 8 Terms
14:15
Example 3: Sum of Geometric Series
18:23
Example 4: First Term
20:16
Infinite Geometric Series
18m 32s
Intro
0:00
What are Infinite Geometric Series
0:10
Example: Finite
0:29
Example: Infinite
0:51
Partial Sums
1:09
Formula
1:37
Sum of an Infinite Geometric Series
2:39
Convergent Series
2:58
Example: Sum of Convergent Series
3:28
Sigma Notation
7:31
Example: Sigma
8:17
Repeating Decimals
8:42
Example: Repeating Decimal
8:53
Example 1: Sum of Infinite Geometric Series
12:15
Example 2: Repeating Decimal
13:24
Example 3: Sum of Infinite Geometric Series
15:14
Example 4: Repeating Decimal
16:48
Recursion and Special Sequences
14m 34s
Intro
0:00
Fibonacci Sequence
0:05
Background of Fibonacci
0:23
Recursive Formula
0:37
Fibonacci Sequence
0:52
Example: Recursive Formula
2:18
Iteration
3:49
Example: Iteration
4:30
Example 1: Five Terms
7:08
Example 2: Three Terms
9:00
Example 3: Five Terms
10:38
Example 4: Three Iterates
12:41
Binomial Theorem
48m 30s
Intro
0:00
Pascal's Triangle
0:06
Expand Binomial
0:13
Pascal's Triangle
4:26
Properties
6:52
Example: Properties of Binomials
6:58
Factorials
9:11
Product
9:28
Example: Factorial
9:45
Binomial Theorem
11:08
Example: Binomial Theorem
13:48
Finding a Specific Term
18:36
Example: Specific Term
19:26
Example 1: Expand
24:39
Example 2: Fourth Term
30:26
Example 3: Five Terms
36:13
Example 4: Three Iterates
45:07
• ## Related Books
### Common Logarithms
• Solve exponential equations by taking the common log of both sides of the equation. You can then use a calculator to get a decimal approximation of the answer.
• If you want to get a decimal approximation of a logarithmic expression, convert the log expression to a log expression to the base 10 using the change of base formula. Then use a calculator to evaluate the new expression.
### Common Logarithms
Solve 109x − 6 = 2
• Step 1) Take the common log of both sides
• 109x − 6 = 2 = > log(109x − 6) = log(2)
• Step 2) Bring the exponents down using properties of logs
• log(109x − 6) = log(2)
• (9x − 6)log(10) = log(2)
• Step3: Distribute using distributive property
• 9x*log(10) − 6(log(10) = log(2)
• Step 4 - Add 6log(10) to both sides
• 9xlog(10) = log(2) + 6log(10)
• Step 4 - Divide both sides by 9log(10)
• x = [(log(2) + 6log(10))/9log(10)]
• Use a calculator to evaluate
x = 0.7001
Solve 10 − 6x − 3 = 84
• Step 1) Take the common log of both sides
• 10 − 6x − 3 = 84 = > log(10 − 6x − 3) = log(84)
• Step 2) Bring the exponents down using properties of logs
• log(10 − 6x − 3) = log(84)
• ( − 6x − 3)log(10) = log(84)
• Step3: Distribute using distributive property
• − 6x*log(10) − 3(log(10) = log(84)
• Step 4 - Add 3log(10) to both sides
• − 6xlog(10) = log(84) + 3log(10)
• Step 4 - Divide both sides by − 6log(10)
• x = [(log(84) + 3log(10))/( − 6log(10))]
• Use a calculator to evaluate
x = − 0.8207
Solve 9*38 − 6x − 7 = 41
• Step 1) Add seven to both sides
• 9*38 − 6x = 48
• Step 2) Divide both sides by nine
• 38 − 6x = [48/9]
• Step 3) Take the common log of both sides
• log(38 − 6x) = log[48/9]
• Step 4) Bring the exponents down using properties of logs
• log(38 − 6x) = log[48/9]
• (8 − 6x)log(3) = log([48/9])
• Step 5) Distribute using distributive property
• 8*log(3) − 6x(log(3)) = log([48/9])
• Step 6) - Subtract 8log(3) from both sides
• − 6x(log(3)) = log([48/9]) − 8*log(3)
• Step 7) Divide both sides by − 6log(2)
• x = [(log([48/9]) − 8*log(3))/( − 6log(3))]
• Use a calculator to evaluate
x = 1.0794
Solve − 3*186 − 8x + 10 = − 10
• Step 1) Subtract 10 from both sides
• − 3*186 − 8x = − 20
• Step 2) Divide both sides by − 3
• 186 − 8x = [20/3]
• Step 3) Take the common log of both sides
• log(186 − 8x) = log[20/3]
• Step 4) Bring the exponents down using properties of logs
• log(186 − 8x) = log[20/3]
• (6 − 8x)log(18) = log([20/3])
• Step 5) Distribute using distributive property
• 6log(18) − 8xlog(18) = log([20/3])
• Step 6) - Subtract 6log(3) from both sides
• − 8xlog(18) = log([20/3]) − 6log(18)
• Step 7) Divide both sides by − 8log(18)
• x = [(log([20/3]) − 6log(18))/( − 8log(18))]
• Use a calculator to evaluate
x = 0.6680
Solve − 4*156x + 4 + 9 = − 65
• Step 1) Subtract 9 from both sides
• − 4*156x + 4 = − 74
• Step 2) Divide both sides by − 4
• 156x + 4 = [74/4]
• 156x + 4 = [37/2]
• Step 3) Take the common log of both sides
• log(156x + 4) = log[37/2]
• Step 4) Bring the exponents down using properties of logs
• (6x + 4)log(15) = log[37/2]
• Step 5) Distribute using distributive property
• 6xlog(15) + 4log(15) = log[37/2]
• Step 6) - Subtract 4log(15) from both sides
• 6xlog(15) = log[37/2] − 4log(15)
• Step 7) Divide both sides by 6log(15)
• x = [(log[37/2] − 4log(15))/6log(15)]
• Use a calculator to evaluate
x = − 0.4871
Solve 9*66 − 10x + 1 = 67
• Step 1) Subtract 1 from both sides
• 9*66 − 10x = 66
• Step 2) Divide both sides by 9
• 66 − 10x = [66/9]
• 66 − 10x = [22/3]
• Step 3) Take the common log of both sides
• log(66 − 10x) = log[22/3]
• Step 4) Bring the exponents down using properties of logs
• (6 − 10x)log(6) = log[22/3]
• Step 5) Distribute using distributive property
• 6log(6) − 10xlog(6) = log[22/3]
• Step 6) - Subtract 6log(6) from both sides
• − 10xlog(6) = log[22/3] − 6log(6)
• Step 7) Divide both sides by − 10log(6)
• x = [(log[22/3] − 6log(6))/( − 10log(6))]
• Use a calculator to evaluate
x = 0.4888
Write using common logarithms:
log327
• We're going to use the change of base formula which states that
• logax = [(logbx)/(logba)]
• log1027 = [(log327)/(log310)]
• Since the 10 is not written
log27 = [(log327)/(log310)]
Write using common logarithms:
log636
• We're going to use the change of base formula which states that
• logax = [(logbx)/(logba)]
• log1036 = [(log636)/(log610)]
• Since the 10 is not written
log36 = [(log636)/(log610)]
Write using common logarithms:
log452
• We're going to use the change of base formula which states that
• logax = [(logbx)/(logba)]
• log1052 = [(log452)/(log410)]
• Since the 10 is not written
log52 = [(log452)/(log410)]
Write using common logarithms:
log12100
• We're going to use the change of base formula which states that
• logax = [(logbx)/(logba)]
• log10100 = [(log12100)/(log1210)]
• Since the 10 is not written
log100 = [(log12100)/(log1210)]
*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
### Common Logarithms
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
• Intro 0:00
• What are Common Logarithms? 0:10
• Real World Applications
• Base Not Written
• Example: Base 10
• Equations 1:47
• Example: Same Base
• Example: Different Base
• Inequalities 6:07
• Multiplying/Dividing Inequality
• Change of Base 12:45
• Base 10
• Example: Change of Base
• Example 1: Log Equation 15:21
• Example 2: Common Logs 17:13
• Example 3: Log Equation 18:22
### Transcription: Common Logarithms
Welcome to Educator.com.0000
We are going to continue our discussion of logarithms by talking about special logarithms.0002
And the first one is common logarithms.0008
First of all, what are common logarithms?0011
Common logarithms are logarithms to the base 10; and these are used very frequently in many real-world applications.0013
For example, the scale that is used to measure the magnitude of earthquakes is base 10 scale.0020
And the base 10 is not written: logs in base 10 are just written as follows: log(x).0027
So, if I were discussing log10(7), I could instead just write that as log(7).0037
And it is assumed that, if nothing is written here, then this is base 10--0046
in the same way that, if you took a square root of 4, we know that this really means this;0050
but we don't write the number (because it is so commonly used)--we don't write the number 2.0058
If we are talking about some other root (like the third root--the cube root), then we would write it.0064
The same idea here: if you don't see anything here, you can assume that it is a base 10 log.0068
Now, one application that we are going to have with this is to use logarithms to help us solve exponential equations.0075
In previous lessons, we used exponential expressions to help us solve logarithmic equations.0081
When we had a logarithmic equation with a log on only one side, we converted that to the exponential form.0087
Well, it works the other way as well: there are times when taking an exponential equation0094
and taking the log of the equation can actually help you to solve it; so let's talk about that right now.0098
If we are working with an exponential equation, the previous techniques we used involved having the bases be the same.0108
For example, given something such as an exponential equation 3x + 1 = 94x,0115
we were only able to solve this if we had the same base.0124
And sometimes I could convert it to the same base if I didn't have the same base, because 9 is equal to 32;0131
therefore, I would end up with 3x + 1 = 38x, and then from there, you can solve,0138
because if the bases are equal, then the exponents must be equal.0152
However, getting a little bit more advanced: you are going to run into situations like this: 23x + 4 = 5.0157
These are not the same base, nor can I easily convert them to the same base.0166
In this case, if both sides cannot be written as powers of the same base0169
with an exponential equation, solve the equation by taking the common logarithm of each side.0174
The common logarithm means the base 10 log, which I am just going to write without the 10 here, as is standard.0180
So, log (and that is actually base 10) of 23x + 4 = log(5).0192
Once I have it in this form, then I can solve: you treat this as you would any other equation, which is just by isolating x.0201
Now, let's first rewrite this, using the power property, so that we get rid of this exponent.0215
Let's just go ahead and write this as a coefficient: (3x + 4)log(2) = log(5).0223
I have my variable in here; I want to isolate the x, so I am going to divide both sides by log(2).0235
Keep in mind that these are just numbers--there are no variables in here.0245
log(2) has a specific value; log(5) has a specific value; I haven't found that value, but having my answer in this form is perfectly valid.0250
If you look on your calculator, there is a log button; and that log button, if it just says 'log,' is for the base 10 log,0257
although on some calculators you can specify other bases.0264
This is something you can easily find the value of.0267
So, by doing this, now I have the x much more freed up: I am going to subtract 4 from both sides.0270
And now, all I have to do is divide each side by 3.0281
And instead of writing this as a complex fraction, log(5)/log(2)/3, I can simply remember that this is the same as this.0286
So, if I said log(5)/log(2) times the reciprocal (which would be times 1/3)...I want to get rid of that complex fraction,0312
so I am going to write it like this, in a more simplified-looking form.0320
OK, therefore, I started out where I had an exponential equation where there were different bases.0330
And I couldn't convert them to the same base very easily at all.0336
So, I went ahead and just took the common log of both sides, then used the power property in reverse to get this over here as a coefficient.0339
Next, I divided both sides by log(2), because that is really just a number.0355
And I isolated the x on the left; and everything I have here, I either have a value for, or I can find a value for.0359
The same techniques that we used for solving exponential equations can also be used to solve inequalities--0367
exponential inequalities where we can't get the same base very easily at all.0376
Recall that, when you are multiplying or dividing both sides of an inequality, you need to make sure that you are not working with a negative.0381
And usually, it is obvious: in past lessons, we have known if we are dividing by -3 or multiplying by -3;0391
we need to flip the inequality sign--it is obvious.0396
But you have to be careful with a logarithmic expression, if you are taking the log of some number,0399
that you check and make sure that you are not ending up with a negative,0404
inadvertently, and then having the inequality symbol be in the wrong direction.0408
All right, so let's look at 43x - 5 > 32x - 6.0414
As we did with equations that were exponential equations with different bases, we can do the same technique with this inequality,0426
which is to go ahead and take the common log of both sides.0435
So, this new inequality is still valid, because I did the same thing to both sides of the inequality--0449
the same as if I had added a number to both sides or multiplied both sides by a number.0454
This is still a valid inequality: the relationship between the left and right sides is still holding up.0458
Next, I am going to use the power property to bring this out in front, because my goal is to isolate x.0465
And I can't isolate x when it is up there as a power.0470
3x - 5 times log(4) is greater than...bring this out in front...2x - 6 times log(3).0474
All right, next I am going to divide both sides by log(4).0487
Actually, we need to take one more step: we can't just go ahead and do that.0503
What I need to do is separate this out; I need to use the distributive property to split this out,0506
because what I really have here is 3xlog(4) (that is 3x times log(4)--we can look at this like this--it makes it much easier), minus 5log(4).0514
OK, and this is greater than 2xlog(3) - 6log(3).0540
Now that I have this, and it is split apart, I can go ahead and look at the expressions that do not contain variables.0554
This does not contain a variable, and neither does that; I want those all on the right, and my variable-containing expressions over on the left.0562
I am going to start out by adding 5log(4) to both sides.0572
My next step is going to be to subtract 2xlog(3) from both sides.0587
All right, what I have now is expressions containing variables on the left, and those with constants only are on the right.0605
And again, this is really just a number.0612
Let's go back up here and continue on.0615
And my next step is going to be to factor out x from this left side of the inequality.0618
And this is going to give me an x here, times 3log(4), minus 2log(3), is greater than -6log(3) + 5log(4).0628
So, looking at what I did going from here to here, I just factored out an x.0648
I pulled that x out of here and here, leaving me with this difference: 3log(4) - 2log(3).0653
Now that I have done this, I can isolate the x at last.0662
I just keep x on this side, and I divide (I am going to rewrite this with 5log(4) in the front0664
and the negative second, because it is more standard) by 3log(4) - 2log(3).0673
OK, so in order to solve this exponential inequality that had different bases,0686
I proceeded by first taking the common log of both sides,0692
then isolating the x (which was a little bit complicated).0697
I used the power property, and then I used the distributive property0700
to separate out this 3x and the 5, since this contains a variable and this doesn't; and the same here.0705
Then, I went ahead and factored out an x, and then just divided both sides by this expression.0713
So, I moved the constants to the right, and the variable-containing expressions to the left, and then divided.0724
Now, as I mentioned, you have to make sure that you don't end up dividing by something negative inadvertently.0728
So, at the division step (that was this), let's go ahead and take a look at this.0734
I know that I am OK, because the log of a number greater than 1 is positive.0739
So, if I take the common log of a number greater than 1, it is positive.0744
I know this is positive, and I know that the log of 4 is going to be bigger than the log of 3.0748
And I know that 3 is bigger than 2; so this is going to be larger than this, so I know I am working with something positive;0753
and I don't need to flip the inequality symbol--but that is important to check.0760
The last new concept we are covering in this lesson is going to be change of base.0766
There are times when you have a log given in one base, and you want to change it to another base.0771
Frequently, it is base 10 that you are wanting to change it to, but not always; it could be a different base.0778
And so, this change of base formula allows us to write a given logarithmic expression in a different base.0785
And it allows us to evaluate logarithmic expressions in any base by rewriting it using common logarithms.0792
And as I said, frequently what you want to change the base to is a base that is log base 10.0805
What this right here is, is the original expression.0813
This is actually the original expression; and what we do is divide that original expression by a log to the original base.0820
And what we take the log of is a value that is equal to the new base.0831
So, I take just the original expression and divide it by a log to that base;0835
but for this number, I use the new base that I want.0841
Illustrating this: let's say I had log6(8), and I want to write it as log10.0844
So, I want to write this as log10; I don't need to write the 10 here.0859
This with a new base would be equal to log6(8), the original expression,0870
divided by a log with the original base (base 6), but for the x value right here, I am going to use 10; that 10 is implied.0880
So, if I needed to, for some reason, change this to base 10, this is equivalent to log10(8).0892
You just need to learn this formula and follow it, and know that it is the original expression,0904
divided by a log of the original base; and you are taking the log of the value equal to the base you are looking for.0908
OK, in Example 1, we are looking at an exponential equation where the bases are not the same, and I can't easily get the bases the same.0922
So, I am going to use common logs to solve this.0930
I am going to start out by taking the common log of each side.0933
And I am allowed to do this, as long as I do the same thing to both sides.0938
Once I have it in this form, I want to isolate x; so I need to use the power property to get (2x - 3)log(3) = log(19).0944
To isolate x, I divide both sides by log(x), because my x is here; I want to split that away.0957
Next, I am going to add 3 to both sides, so that the 3 ends up on the right.0967
And then finally, I am going to divide both sides by 2.0980
Let's come up here in the second column: 2x = log(19)/log(3), divided by (2 + 3).0983
And to make this look at little better, we can rewrite this as...actually, the x is now isolated, because we divided by 2;0995
so x equals 1/2, because if I take log(19)/log(3), divided by 2, that would be the same as multiplying by the reciprocal, 1/2.1003
So, I was able to solve this, even though this exponential expression had different bases,1024
by taking the common log of each side, and then isolating x.1028
Write using common logarithms: log7(22).1036
I need to use my change of base formula, which is loga(x) = logb(x), divided by logb(a).1039
And here, a is the new base I want, and b equals the original base--the base that I already have.1050
I want to find an expression that is equivalent to an expression with the original base.1059
OK, log10(22): this is what I want, and I need to find an expression that is equivalent to that.1069
And this would be just the original, log7(22), divided by log with the original base;1080
and then, for a, I am going to use this base that I want.1090
So now, I have written this using common logarithms.1094
OK, again, I have an exponential equation in which there is no common base, and I can't easily get a common base.1104
So, I am going to take the common log of both sides to help me solve this.1111
Now, I need to isolate x; so I need to get the x out of the exponent--I am going to do that by using the power property.1122
And this becomes the coefficient (2x - 6)log(5) =...I am going to bring this out in front...(4x + 3)log(7).1128
Now that I have done this, I am going to write it like this to make it clear what needs to be done.1148
And we need to use the distributive property, because I want to split away these terms that have x in them.1154
I am going to multiply 2x times log(5), and then I am going to multiply -6 times log(5), 4x times log(7),1159
and remember, this is base 10 that we are talking about; and 3 times log10(7).1173
Next, I am going to get all of the variables on the left, and expressions containing constants only on the right.1183
And I am considering the log of 5 to be a constant, because we can find a specific value of that.1188
So, I am going to add 6log(5) to both sides.1192
The next thing I need to do is subtract 4log(7) from both sides, so I can get this on the left, because it does contain a variable.1209
So, 4x - 4x log(7); now I have my constants on the right and variables on the left.1218
The next thing to do: I want to isolate x, so I can factor out an x, because there is an x factor here and one here.1227
I pull that out; I leave behind 2log(5); I pull out the x; I leave 4log(7).1238
And I am almost there; all I need to do now is divide both sides by this expression, and I get x = 3log(7), plus 6...1247
and this is log...that is a 5, not an exponent of 5...all divided by 2log(5) - 4log(7).1262
Again, the technique is to take the common log of both sides, isolate x by first using the power property,1281
then the distributive property, adding and subtracting as needed to bunch all of the expressions and terms1288
containing x's on the left, constants on the right; factor out x, and divide both sides by this expression.1297
And now, I have x isolated, so I have solved for x.1307
This time, we are going to solve an inequality; and it is an inequality involving exponential expressions1314
without a common base, and where I can't easily find a common base.1322
So again, as I did with the exponential equation, I am going to take the common log of each of these.1327
My next step is going to be to isolate the x.1339
All right, so in order to do that, I need to get the x out of being an exponent, so I can use that power property.1346
4x - 5 times log(3) is less than...this becomes...(-3x + 5)log(6).1354
Further separating out the x, I need to use the distributive property: this is going to give me 4x...1365
this is equivalent to this...so 4xlog(3) - 5log(3) is less than -3xlog(6) + 5log(6).1372
As usual, we are going to move the variables to the left and constants to the right.1392
So, I am going to add 5log(3) to both sides; and now I have this x on the right, so I need to move this term to the left by adding 3xlog(6) to both sides.1397
I look on the left; I am still trying to isolate the x, and I see that these two terms have a common factor of x,1438
so I factor that out to leave behind 4log(3) + 3log(6) < 5log(6) + 5log(3).1444
Now, I am going to divide both sides by this expression; and I will have x isolated.1458
Now, I am done; but I just need to double-check about this step, because, whenever you multiply or divide1475
both sides of an inequality, you need to make sure that you are not multiplying or dividing by a negative number,1484
because if you are, you need to reverse the inequality symbol.1490
So, I am looking right here; and I divided both sides by 4log(3) + 3log(6).1494
However, I know that I am OK, because the common log of a number greater than 1 is positive.1501
So, this is positive; and I am adding that to something else positive; so I know that I am OK--that that comes out to be the log of a positive number.1508
That concludes this lesson about common logarithms on Educator.com.1517
Thank you for visiting!1523
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https://www.atozmath.com/arithmetic.aspx?q=MCT&ST=107
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Method and examples
Statistics Wording Problem 1. The mean of 10 observations is 12.5 . While calculating the mean one observation was by mistake taken as -8 instead of +8 . F ... 2. The mean of 10 observations is 35 . While calculating the mean two observations were by mistake taken as 35 instead of 25 and ... 3. The mean of 15 observations is 16.4 . If we remove one observation from it then the mean of remaining observations is 17 , th ... 4. The sum of 15 observation is 343 . If we remove two observation 18 and 26 , then find out the mean of remaining observations. 5. The mean of 5 observations is 20 . If we add one new observation then the new mean of the observations is 25 . So find out ne ... 6. The mean of observation is 10 . If we add 2 and then multiply or divide by 3 in each observation, then find the new mean ? Problem 1 of 6 1. The mean of observations is . While calculating the mean one observation was by mistake taken as instead of . Find the correct mean.
SolutionExample
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https://answers.ros.org/question/257833/hector_slam-with-lidar-not-updating-map-in-rviz/
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# hector_slam with LIDAR not updating map in RVIZ edit
Hello! I am trying to use ROS Kinetic and a Hokuyo URG LIDAR unit in conjunction with hector_slam in order to produce a map of a room as the robot navigates around it. However, I am running in to some issues.
After running the example launch file, everything seems to be fine. No errors in RVIZ or terminal, and a map is generated based on LIDAR data, like so:
However, as soon as the robot moves, it becomes immediately clear that all is not well after all. Here, we moved the robot physically forward. We can see that the LIDAR input is still updating, as the white dots symbolizing the scanned wall creep closer. However, the map does not update at all, and, even more oddly, seems to be parented to the robot's mobile coordinate frame.
Frankly, I find this behavior very perplexing. I suspect the error may have something to do with this warning, hidden away in the hector launch terminal:
Waiting for tf transform data between frames /map and /base_link to become available
Unfortunately, I have no idea how to make such a transform. FOr reference, however, here is how our transforms are set up by default from hector_slam:
The launch file I am calling looks like this:
<?xml version="1.0"?>
<launch>
<param name="pub_map_odom_transform" value="true"/>
<param name="map_frame" value="map"/>
<param name="base_frame" value="base_frame"/>
<param name="odom_frame" value="base_frame"/>
<node pkg="urg_node" type="urg_node" name="urg_node"/>
<node pkg="tf" type="static_transform_publisher" name="map_2_odom" args="0 0 0 0 0 0 /map /odom 100"/>
<node pkg="tf" type="static_transform_publisher" name="odom_2_base_footprint" args="0 0 0 0 0 0 /odom /base_footprint 100"/>
<node pkg="tf" type="static_transform_publisher" name="base_footprint_2_base_link" args="0 0 0 0 0 0 /base_footprint /base_link 100"/>
<node pkg="rviz" type="rviz" name="rviz" args="-d $(find hector_slam_example)/launch/rviz_cfg.rviz"/> <include file="$(find hector_slam_example)/launch/default_mapping.launch"/>
<include file="$(find hector_geotiff)/launch/geotiff_mapper.launch"/> </launch> This file, as you can see, calls two other launch files, the first of which is default_mapping.launch: <?xml version="1.0"?> <launch> <arg name="tf_map_scanmatch_transform_frame_name" default="scanmatcher_frame"/> <arg name="base_frame" default="base_footprint"/> <arg name="odom_frame" default="nav"/> <arg name="pub_map_odom_transform" default="true"/> <arg name="scan_subscriber_queue_size" default="5"/> <arg name="scan_topic" default="scan"/> <arg name="map_size" default="2048"/> <node pkg="hector_mapping" type="hector_mapping" name="hector_mapping" output="screen"> <!-- Frame names --> <param name="map_frame" value="map" /> <param name="base_frame" value="$(arg base_frame)" />
<param name="odom_frame" value="$(arg base_frame)" /> <!-- Tf use --> <param name="use_tf_scan_transformation" value="true"/> <param name="use_tf_pose_start_estimate" value="true"/> <param name="pub_map_odom_transform" value="$(arg pub_map_odom_transform)"/>
<param ...
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https://www.wyzant.com/resources/answers/731143/precalculus-word-problem-3-by-3-or-2-by-3-function
|
Maria H.
# Precalculus Word Problem - 3 by 3 or 2 by 3 function
A total of $5000 is invested at 2%, 3% and 4%. The amount invested at 4% equals the total amount invested at 2% and 3%. The total interest for one years is$145. If possible, find the amount invested in each interest rate. Interpret your answer.
By:
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|
https://scriptinghelpers.org/questions/116108/i-need-help-can-someone-give-me-there-version-of-a-sword-giving-script
|
Still have questions? Join our Discord server and get real time help.
2
# I need help! Can someone give me there version of a sword giving script?
tane011 12
5 days ago
I NEED HELP WITH THIS! I need to let the script know who is getting the sword and giving that person the sword when they press the button! Can someone help me, please?
My current script: (I need help with the "Player" part!)
local Button = script.Parent
local Sword = game.Lighting.ClassicSword
local Player = --Who is getting the sword
Button.MouseButton1Click:Connect(function()
Sword:Clone()
Sword.Name = "Starter Sword"
Sword.CanBeDropped = false
Sword.Parent = Player
end)
0
Edited 5 days ago
local Button = script.Parent
local Sword = game.Lighting.ClassicSword
Button.MouseButton1Click:Connect(function(Player) -- the player is defined here as the person who clicked the button
Sword:Clone()
Sword.Name = "Starter Sword"
Sword.CanBeDropped = false
Sword.Parent = Player.Backpack
end)
0
You will need to have two scripts to have this work, and a remote event. Put the RemoteEvent in ReplicatedStorage, the LocalScript aside the button, and the Server Script wherever.
First, the LocalScript:
local ReplicatedStorage = game:GetService("ReplicatedStorage")
local giveRemote = ReplicatedStorage:WaitForChild("GiveRemote")
local button = script.Parent -- Make sure your LocalScript is parented to the part that you want clicked.
local clickDetector = Instance.new("ClickDetector", button)
local cooldown = false -- This is optional. It makes the script wait before you can press the button again.
local coolWait = 2
clickDetector.MouseButton1Click:Connect(function()
if cooldown == false then
giveRemote:FireServer()
cooldown = true
wait(coolWait)
cooldown = false
end
end)
Now, the Script (In the server)
local ReplicatedStorage = game:GetService("ReplicatedStorage")
local giveRemote = ReplicatedStorage:WaitForChild("GiveRemote")
giveRemote.OnServerEvent:Connect(function(player)
Sword:Clone()
Sword.Name = "Starter Sword"
Sword.CanBeDropped = false
Sword.Parent = Player
end)
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|
http://tex.stackexchange.com/questions/35065/xetex-and-xelatex-in-texworks-editor/35067
|
XeTeX and XeLaTeX in TeXworks editor
In TeXworks editor in the Typeset dropdown menu among others I can select XeTeX or XeLaTex typesetting formats.
If I understand correctly XeLaTex and XeTex is exactly the same thing, so why does TeXworks list them as separate options?
-
They are not the same. That is, they use the same engine, the XeTeX engine, but they are for different formats. The XeTeX option is for use when writing plain TeX, while the XeLaTeX option is for LaTeX.
The document `lualatex-doc` describes the difference between an engine and a format. I quote:
To answer this question, we need to mention a few details about the TEX world that you may usually ignore: the difference between an engine and a format. An engine is an actual computer program, while a format is a set of macros executed by an engine, usually preloaded when the engine is invoked with a particular name.
Actually, a format is more or less like a document class or a package, except it is associated with a particular command name. Imagine there is a command latex-article that would do the same as latex, except you wouldn’t need to say `\documentclass{article}` at the beginning of your file. Similarly, in current distributions, the command pdflatex is the same as the command pdftex except that you don’t need to put the instructions to load LaTeX at the beginning of your source file. This is convenient, and slightly more efficient too.
Formats are great because they implement powerful commands using the basic tools an engine provides. However the power of the format is sometimes limited by the engine’s tools set, so people started developing more powerful engines so that other people can implement even more powerful formats (or packages). The most famous engines now (except the original TEX) are pdfTeX, XeTeX and LuaTeX.
-
@egreg Didn't see your comment before I posted my answer. – Torbjørn T. Nov 16 '11 at 15:59
And I've deleted it now that a good answer has been provided. – egreg Nov 16 '11 at 16:02
Now it is more clear to me. So I can't run xetex if my source document contains latex commands, I need to run xelatex instead, correct? – Maxim Nov 16 '11 at 16:13
@Maxim That is correct, for a LaTeX document, with `documentclass` and a `document` environment, you have to run `xelatex`. The same goes for pdfTeX vs. pdfLaTeX and LuaTeX vs. LuaLaTeX. – Torbjørn T. Nov 16 '11 at 16:23
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https://www.gradesaver.com/textbooks/math/algebra/algebra-2-1st-edition/chapter-13-trigonometric-ratios-and-functions-13-6-apply-the-law-of-cosines-13-6-exercises-skill-practice-page-892/33
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## Algebra 2 (1st Edition)
By Heron's Formula, we know: $$A=\sqrt{s(s-a)(s-b)(s-c)}$$ Where: $$s=\frac{a+b+c}{2}$$ Thus, we find: $$s=\frac{21+16+13}{2}=25 \\ A=\sqrt{25\left(25-21\right)\left(25-16\right)\left(25-13\right)} \\ A\approx 104$$
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https://www.mathcounterexamples.net/two-continuous-bijections-no-homeomorphism/
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# Two continuous bijections but no homeomorphism
We consider here two topological spaces $$X$$ and $$Y$$. We also suppose that $$f$$ is a continuous bijection from $$X$$ to $$Y$$ and $$g$$ a continuous bijection from $$Y$$ to $$X$$. Providing such hypothesis (H), is there necessarily an homeomorphism from $$X$$ to $$Y$$?
We first look at the simple case where $$X$$ is an interval $$I$$ equipped with the subspace topology. If $$f$$ is a continuous map defined from $$I$$ to $$\mathbb{R}$$ and $$f$$ is supposed to be bijective, $$f$$ is therefore one-to-one. According to a well known result, $$f$$ is strictly monotonic on $$I$$, the image of $$I$$ under $$f$$ is an interval $$J$$ and the inverse map $$f^{-1}$$ is continuous. Hence, if $$X$$ and $$Y$$ are two intervals, an homomorphism always exists providing the hypothesis (H).
For the second case, we consider a compact space $$X$$ and a Haussdorf space $$Y$$. Suppose that $$f$$ is a continuous bijection from $$X$$ to $$Y$$. Then $$Y$$ is compact and $$f$$ is an homeomorphism. For the prove we need to show that $$f^{-1}$$ is continuous. For this, consider any closed subspace $$F \subset X$$. $$F$$ is compact and the inverse image of $$F$$ by $$f^{-1}$$ is $$f(F)$$, which is compact and hence closed. Finally, $$f^{-1}$$ is continuous and $$f$$ is an homeomorphism.
Finally we give a counterexample of two topological spaces $$X$$ and $$Y$$ which satisfy the hypothesis (H) while no homomorphism exists from $$X$$ to $$Y$$. We take as spaces $$\displaystyle X=\bigcup_{n=0}^\infty ((3n,3n+1) \cup \{3n+2\})$$ and $$Y=(X \setminus \{2\}) \cup \{1\}$$. And for the continuous bijections $$f: X \rightarrow Y$$ defined by:
$f(x)=\begin{cases} x & \text{if } x \neq 2\\ 1 & \text{if } x = 2\\ \end{cases}$ and $$g: Y \rightarrow X$$ defined by:
$g(y)=\begin{cases} y/2 & \text{if } y \le 1\\ y/2 – 1 & \text{if } 3 < y <4\\ y-3 & \text{if } y \ge 5\\ \end{cases}$ The continuity of $$f$$ is clear at any point $$x \in X \setminus \{2\}$$. $$f$$ is also continuous at $$2$$ as for $$\vert x-2 \vert < 1/2$$ and $$x \in X$$ we have $$f(x)=1$$. One can also prove that $$g$$ is continuous. Let now suppose that $$h:Y \rightarrow X$$ is an homeomorphism. The image under $$h$$ of the open interval $$(0,1)$$ is an open interval included in an interval $$(3n,3n+1)$$ with $$n \in \mathbb{N}$$. In fact it is even the complete interval $$(3n,3n+1)$$. If it wasn't the case, we would have $$h^{-1}((3n,3n+1) \setminus h((0,1))) \subset [2,+\infty)$$, hence $$h^{-1}$$ wouldn't be continuous. And we get a contradiction as $$h(1)$$ cannot be defined.
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https://slideplayer.com/slide/3008380/
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## Presentation on theme: "10.3 Simplifying Radical Expressions"— Presentation transcript:
Use the product rule for radicals.
Objective 1 Use the product rule for radicals. Slide
Use the product rule for radicals. Product Rule for Radicals If and are real numbers and n is a natural number, then That is, the product of two nth roots is the nth root of the product. Use the product rule only when the radicals have the same index. Slide
Multiply. Assume that all variables represent positive real numbers.
CLASSROOM EXAMPLE 1 Using the Product Rule Multiply. Assume that all variables represent positive real numbers. Solution: Slide
Multiply. Assume that all variables represent positive real numbers.
CLASSROOM EXAMPLE 2 Using the Product Rule Multiply. Assume that all variables represent positive real numbers. Solution: This expression cannot be simplified by using the product rule. Slide
Use the quotient rule for radicals.
Objective 2 Use the quotient rule for radicals. Slide
Use the quotient rule for radicals. Quotient Rule for Radicals If and are real numbers, b ≠ 0, and n is a natural number, then That is, the nth root of a quotient is the quotient of the nth roots. Slide
Simplify. Assume that all variables represent positive real numbers.
CLASSROOM EXAMPLE 3 Using the Quotient Rule Simplify. Assume that all variables represent positive real numbers. Solution: Slide
Simplify radicals. Conditions for a Simplified Radical 1. The radicand has no factor raised to a power greater than or equal to the index. 2. The radicand has no fractions. 3. No denominator contains a radical. 4. Exponents in the radicand and the index of the radical have greatest common factor 1. Be careful with which factors belong outside the radical sign and which belong inside. Slide
Simplify. CLASSROOM EXAMPLE 4 Simplifying Roots of Numbers Solution:
Cannot be simplified further. Slide
Simplify. Assume that all variables represent positive real numbers.
CLASSROOM EXAMPLE 5 Simplifying Radicals Involving Variables Simplify. Assume that all variables represent positive real numbers. Solution: Slide
Simplify. Assume that all variables represent positive real numbers.
CLASSROOM EXAMPLE 6 Simplifying Radicals by Using Smaller Indexes Simplify. Assume that all variables represent positive real numbers. Solution: Slide
Simplify radicals. If m is an integer, n and k are natural numbers, and all indicated roots exist, then Slide
Simplify products and quotients of radicals with different indexes.
Objective 4 Simplify products and quotients of radicals with different indexes. Slide
Simplify. CLASSROOM EXAMPLE 7
Multiplying Radicals with Different Indexes Simplify. Solution: The indexes, 2 and 3, have a least common index of 6, use rational exponents to write each radical as a sixth root. Slide
Use the Pythagorean theorem.
Objective 5 Use the Pythagorean theorem. Slide
Use the Pythagorean theorem. Pythagorean Theorem
If c is the length of the longest side of a right triangle and a and b are lengths of the shorter sides, then c2 = a2 + b2. The longest side is the hypotenuse, and the two shorter sides are the legs, of the triangle. The hypotenuse is the side opposite the right angle. Slide
Find the length of the unknown side of the triangle.
CLASSROOM EXAMPLE 8 Using the Pythagorean Theorem Find the length of the unknown side of the triangle. c2 = a2 + b2 c2 = c2 = c2 = 260 Solution: The length of the hypotenuse is Slide
Find the length of the unknown side of the triangle.
CLASSROOM EXAMPLE 8 Using the Pythagorean Theorem (cont’d) Find the length of the unknown side of the triangle. c2 = a2 + b2 62 = 42 + b2 36 = 16 + b2 20 = b2 Solution: The length of the leg is Slide
Use the distance formula.
Objective 6 Use the distance formula. Slide
Use the distance formula. Distance Formula
The distance between points (x1, y1) and (x2, y2) is Slide
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http://www.physicsforums.com/showthread.php?s=adef26a13a5140521e73cd1b23dd26a5&p=4627305
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# Force between Current Loops
by klawlor419
Tags: current, force, loops
P: 117 I am working on a problem involving force between two loops of current. The problem is to prove the for any arbitrary loops of current, Newtons third law holds true. I understand the basics of the approach but I am having trouble seeing why a term goes to zero. The basic setup is to use the Biot-Savart law to predict the field of a segment of the current loop then to use the Lorentz force law to predict the force acting on a segment of the second loop. This has the form, $$d\mathbf{F}_{12}=\frac{\mu_0 I_1 I_2}{4\pi s^3}(d\mathbf{l_1}\times(d\mathbf{l_2}\times \mathbf{s}))$$ Which when simplified by the triple-product and integrated gives the following form, $$\mathbf{F}_{12}=\frac{\mu_0 I_1 I_2}{4\pi s^2}(\oint\oint d\mathbf{l_2}(d\mathbf{l_1}\cdot \hat{s}) -\oint\oint\hat{s}(d\mathbf{l_1}\cdot d\mathbf{l_2}))$$ Its easy enough to see right from here that F12=-F21 just by the fact that you pick up a minus sign by switching the separation vector. So in that sense the problem is solved, at least from what I see right now. However I was looking in the Griffiths EM and apparently the first term on the left cancels out somehow and I can't figure why. (Problem 5.49) Any suggestions?
P: 185 a couple of things. 1. s can't be pulled out of the integrals. 2. look at this term: $$\mathbf{F}_{12}=\frac{\mu_0 I_1 I_2}{4\pi}\oint\oint d\mathbf{l_2}\left( d\mathbf{l_1}\cdot \frac{\hat{s}}{s^2}\right)$$ then realize that if we do the integral over loop 1 first, we have $$\oint d\mathbf{l_1}\cdot \frac{\hat{s}}{s^2} = \oint d_1\frac{1}{s} = 0.$$ where the subscript on 1 means i'm treating all the terms associated with loop 1 as variables and freezing all terms associated with loop 2. Just remember $\nabla f \cdot d\mathbf{r} = df$ and you're integrating over a loop that starts and end at the same place.
P: 117 Ah nice, I see now. Thanks for the trick.
P: 1 Force between Current Loops please could you explain why the integral over loop 1 is zero? I'm struggling to see your method.. :/
P: 117
Quote by jsholliday7 please could you explain why the integral over loop 1 is zero? I'm struggling to see your method.. :/
Theres an important identity involving one of the terms. Once you use that identity, you can deduce by divergence theorem that the entire term for loop 1 vanishes.
P: 37
Quote by klawlor419 I am working on a problem involving force between two loops of current. The problem is to prove the for any arbitrary loops of current, Newtons third law holds true. I understand the basics of the approach but I am having trouble seeing why a term goes to zero. The basic setup is to use the Biot-Savart law to predict the field of a segment of the current loop then to use the Lorentz force law to predict the force acting on a segment of the second loop. This has the form, $$d\mathbf{F}_{12}=\frac{\mu_0 I_1 I_2}{4\pi s^3}(d\mathbf{l_1}\times(d\mathbf{l_2}\times \mathbf{s}))$$ Which when simplified by the triple-product and integrated gives the following form, $$\mathbf{F}_{12}=\frac{\mu_0 I_1 I_2}{4\pi s^2}(\oint\oint d\mathbf{l_2}(d\mathbf{l_1}\cdot \hat{s}) -\oint\oint\hat{s}(d\mathbf{l_1}\cdot d\mathbf{l_2}))$$ Its easy enough to see right from here that F12=-F21 just by the fact that you pick up a minus sign by switching the separation vector. So in that sense the problem is solved, at least from what I see right now. However I was looking in the Griffiths EM and apparently the first term on the left cancels out somehow and I can't figure why. (Problem 5.49) Any suggestions?
So if there is a loop current in a start say 10 light years away and I switch on a loop current in the earth now the Newtons third law holds true.
Please, prove it with integrals and divergence theorem.
By the way I did not see any t (time) variable in your formulae.
Mentor P: 17,338 Alva, the Biot Savart law uses the magnetostatic approximation. It doesn't apply in the far field and there is no time. This is a standard approximation, but it is an approximation.
Related Discussions Introductory Physics Homework 0 Introductory Physics Homework 2 Introductory Physics Homework 6 Introductory Physics Homework 1 Introductory Physics Homework 1
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https://k12.libretexts.org/Bookshelves/Mathematics/Precalculus/10%3A_Polar_and_Parametric_Equations/10.05%3A_Section_5-
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# 10.5 Applications of Parametric Equations
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A regular function has the ability to graph the height of an object over time. Parametric equations allow you to actually graph the complete position of an object over time. For example, parametric equations allow you to make a graph that represents the position of a point on a Ferris wheel. All the details like height off the ground, direction, and speed of spin can be modeled using the parametric equations.
What is the position equation and graph of a point on a Ferris wheel that starts at a low point of 6 feet off the ground, spins counterclockwise to a height of 46 feet off the ground, then goes back down to 6 feet in 60 seconds?
## Applying Parametric Equations
There are two types of parametric equations that are typical in real life situations. The first is
circular motion as was described in the concept problem. The second is projectile motion.
Circular Motion
Parametric equations that describe circular motion will have $$x$$ and $$y$$ as periodic functions of sine and cosine. Either $$x$$ will be a sine function and $$y$$ will be a cosine function or the other way around. The best way to come up with parametric equations is to first draw a picture of the circle you are trying to represent.
Next, it is important to note the starting point, center point and direction. You should already
have the graphs of sine and cosine memorized so that when you see a pattern in words or as a graph, you can identify what you see as $$+\sin ,-\sin ,+\cos ,-\cos$$.
Take the example given above with the Ferris Wheel that starts at a low point of 6 feet off the ground, spins counterclockwise to a height of 46 feet off the ground, then goes back down to 6 feet in 60 seconds. The the vertical component starts at a low point of 6 , travels to a middle point of 26 and then a height of 46 and back down. This is a - cos pattern. The amplitude of the $$-\cos$$ is 20 and the vertical shift is 26 . Lastly, the period is 60 . You can use the period to help you find $$b$$.
\begin{aligned} 60 &=\frac{2 \pi}{b} \\ b &=\frac{\pi}{30} \end{aligned}
Thus the vertical parameterization is:
$$y=-20 \cos \left(\frac{\pi}{30} t\right)+26$$
The horizontal parameterization is found by noticing that the $$x$$ values start at $$0,$$ go up to $$20,$$ go back to 0 , then down to -20 , and finally back to 0 . This is a $$+\sin$$ pattern with amplitude 20. The period is the same as with the vertical component.
Thus parametric equations for the point on the wheel are:
$$x=20 \sin \left(\frac{\pi}{30} t\right)$$
$$y=-20 \cos \left(\frac{\pi}{30} t\right)+26$$
Note that horizontal and vertical components of parametric equations are the $$x=$$ and
$$y=$$ functions respectively or the horizontal and vertical parameterization.
Projectile Motion
Projectile motion has a vertical component that is quadratic and a horizontal component that is linear. This is because there are 3 parameters that influence the position of an object in flight: starting height, initial velocity, and the force of gravity. The horizontal component is independent of the vertical component. This means that the starting horizontal velocity will remain the horizontal velocity for the entire flight of the object.
Note that gravity, $$g,$$ has a force of about $$-32 \mathrm{ft} / \mathrm{s}^{2}$$ or $$-9.81 \mathrm{~m} / \mathrm{s}^{2}$$. The examples and practice questions in this concept will use feet.
If an object is launched from the origin at a velocity of $$v$$ then it has horizontal and vertical components that can be found using basic trigonometry.
$$\sin \theta=\frac{v_{V}}{v} \rightarrow v \cdot \sin \theta=v_{V}$$
$$\cos \theta=\frac{v_{H}}{v} \rightarrow v \cdot \cos \theta=v_{H}$$
The horizontal component is basically finished. The only adjustments that would have to be made are if the starting location is not at the origin, wind is added or if the projectile travels to the left instead of the right. See Example A.
$$x=t \cdot v \cdot \cos \theta$$
The vertical component also needs to include gravity and the starting height. The general
equation for the vertical component is:
$$y=\frac{1}{2} \cdot g \cdot t^{2}+t \cdot v \cdot \sin \theta+k$$
The constant $$g$$ represents gravity, $$t$$ represents time, $$v$$ represents initial velocity and $$k$$ represents starting height. You will explore this equation further in calculus and physics. Note that in this concept, most answers will be found and confirmed using technology such as your graphing calculator.
## Examples
##### Example 1
A ball is thrown from the point (30,5) at an angle of $$\frac{4 \pi}{9}$$ to the left at an initial velocity of $$68 \mathrm{ft} / \mathrm{s}$$. Model the position of the ball over time using parametric equations. Use your graphing calculator to graph your equations for the first four seconds while the ball is in the air.
The horizontal component is $$x=-t \cdot 68 \cdot \cos \left(\frac{4 \pi}{9}\right)+30$$. Note the negative sign because the object is traveling to the left and the +30 because the object starts at (30,5).
The vertical component is $$y=\frac{1}{2} \cdot(-32) \cdot t^{2}+t \cdot 68 \cdot \sin \left(\frac{4 \pi}{9}\right)+5$$. Note that $$g=-32$$ because gravity has a force of $$-32 \mathrm{ft} / \mathrm{s}^{2}$$ and the +5 because the object starts at (30,5).
##### Example 2
When does the ball from Example 1 reach its maximum and when does the ball hit the ground? How far did the person throw the ball? T
o find when the function reaches its maximum, you can find the vertex of the parabola. Analytically this is messy because of the decimal coefficients in the quadratic. Use your calculator to approximate the maximum after you have graphed it. Depending on how small you make your $$T_{\text {step }}$$ should find the maximum height to be about 75 feet.
To find out when the ball hits the ground, you can set the vertical component equal to zero and solve the quadratic equation. You can also use the table feature on your calculator to determine when the graph goes from having a positive vertical value to a negative vertical value. The benefit for using the table is that it simultaneously tells you the $$x$$ value of the zero.
After about 4.2588 seconds the ball hits the ground at (-20.29, 0). This means the person threw the ball from (30, 5) to (-20.29, 0), a horizontal distance of just over 50 feet.
##### Example 3
Kieran is on a Ferris wheel and his position is modeled by the parametric equations:
$$x_{K}=10 \cdot \cos \left(\frac{\pi}{5} t\right)$$
$$y_{K}=10 \cdot \sin \left(\frac{\pi}{5} t\right)+65$$
Jason throws the ball modeled by the equation in Example 1 towards Kieran who can catch the ball if it gets within three feet. Does Kieran catch the ball?
This question is designed to demonstrate the power of your calculator. If you simply model the two equations simultaneously and ignore time you will see several points of intersection. This graph is shown below on the left. These intersection points are not interesting because they represent where Kieran and the ball are at the same place but at different moments in time.
When the $$T_{m a x}$$ is adjusted to 2.3 so that each graph represents the time from 0 to 2.3 , you get a better sense that at about 2.3 seconds the two points are close. This graph is shown above on the right.
You can now use your calculator to help you determine if the distance between Kieran and the ball actually does go below 3 feet. Start by plotting the ball's position in your calculator as
$$x_{1}$$ and $$y_{1}$$ and Kieran's position as $$x_{2}$$ and $$y_{2}$$. Then, plot a new parametric equation that compares the distance between these two points over time. You can put this under $$x_{3}$$ and $$y_{3}$$. A calculator can reference internal variables like $$x_{1}, y_{1}$$ that have already been set in the calculator's memory to form new variables like $$x_{3}, y_{3}$$. Note that you can find the $$x_{1}, x_{2}, y_{1}, y_{2}$$ entries in the vars and parametric menu.
$$x_{3}=t$$
$$y_{3}=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$$
Now when you graph, you should change your window settings and let $$t$$ vary between 0 and $$4,$$ the $$x$$ window show between 0 and 4 and the $$y$$ window show between 0 and $$5 .$$ This way it should be clear if the distance truly does get below 3 feet.
Depending on how accurate your $$T_{\text {step }}$$ is, you should find that the distance is below 3 feet. Kieran does indeed catch the ball.
##### Example 4
At what velocity does a football need to be thrown at a $$45^{\circ}$$ angle in order to make it all the way across a football field?
A football field is 100 yards or 300 feet. The parametric equations for a football thrown from (300,0) back to the origin at speed $$v$$ are:
$$x=-t \cdot v \cdot \cos \left(\frac{\pi}{4}\right)+300$$
$$y=\frac{1}{2} \cdot(-32) \cdot t^{2}+t \cdot v \cdot \sin \left(\frac{\pi}{4}\right)$$
Substituting the point (0,0) in for $$(x, y)$$ produces a system of two equations with two variables $$v, t$$
$$0=-t \cdot v \cdot \cos \left(\frac{\pi}{4}\right)+300$$
$$0=\frac{1}{2} \cdot(-32) \cdot t^{2}+t \cdot v \cdot \sin \left(\frac{\pi}{4}\right)$$
You can solve this system many different ways.
$$t=\frac{5 \sqrt{3}}{2} \approx 4.3$$ seconds, $$v=40 \sqrt{6} \approx 97.98 \mathrm{ft} / \mathrm{s}$$
In order for someone to throw a football at a $$45^{\circ}$$ angle all the way across a football field, they would need to throw at about $$98 \mathrm{ft} / \mathrm{s}$$ which is about $$66.8 \mathrm{mph}$$.
$$\frac{98 \text { feet }}{1 \text { sec }} \cdot \frac{3600 \text { sec }}{1 \text { hour }} \cdot \frac{1 \text { mile }}{5280 \text { feet }} \approx \frac{66.8 \text { miles }}{1 \text { hour }}$$
##### Example 5
Nikki got on a Ferris wheel ten seconds ago. She started 2 feet off the ground at the lowest point of the wheel and will make a complete cycle in four minutes. The ride reaches a maximum height of 98 feet and spins clockwise. Write parametric equations that model Nikki’s position over time. Where will Nikki be three minutes from now?
Don't let the 10 second difference confuse you. In order to deal with the time difference, use $$\left(t+\frac{1}{6}\right)$$ instead of $$t$$ in each equation. When $$t=0,$$ ten seconds $$\left(\frac{1}{6}\right.$$ of a minute $$)$$ have already elapsed.
$$x=-48 \cdot \sin \left(\frac{\pi}{2}\left(t+\frac{1}{6}\right)\right)$$
$$y=-48 \cdot \cos \left(\frac{\pi}{2}\left(t+\frac{1}{6}\right)\right)+50$$
At $$t=3, x \approx 46.36$$ and $$y \approx 37.58$$
##### Review
Candice gets on a Ferris wheel at its lowest point, 3 feet off the ground. The Ferris wheel spins
clockwise to a maximum height of 103 feet, making a complete cycle in 5 minutes.
1. Write a set of parametric equations to model Candice's position.
2. Where will Candice be in two minutes?
3. Where will Candice be in four minutes?
One minute ago Guillermo got on a Ferris wheel at its lowest point, 3 feet off the ground. The
Ferris wheel spins clockwise to a maximum height of 83 feet, making a complete cycle in 6
minutes.
4. Write a set of parametric equations to model Guillermo's position.
5. Where will Guillermo be in two minutes?
6. Where will Guillermo be in four minutes?
Kim throws a ball from (0,5) to the right at 50 mph at a $$45^{\circ}$$ angle.
7. Write a set of parametric equations to model the position of the ball.
8. Where will the ball be in 2 seconds?
9. How far does the ball get before it lands?
David throws a ball from (0,7) to the right at 70 mph at a $$60^{\circ}$$ angle. There is a 6 mph wind in
David's favor.
10. Write a set of parametric equations to model the position of the ball.
11. Where will the ball be in 2 seconds?
12. How far does the ball get before it lands?
Suppose Riley stands at the point (250,0) and launches a football at 72 mph at an angle of $$60^{\circ}$$
towards Kristy who is at the origin. Suppose Kristy also throws a football towards Riley at 65
mph at an angle of $$45^{\circ}$$ at the exact same moment. There is a 6 mph breeze in Kristy's favor.
13. Write a set of parametric equations to model the position of Riley's ball.
14. Write a set of parametric equations to model the position of Kristy's ball.
15. Graph both functions and explain how you know that the footballs don't collide even though the two graphs intersect.
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https://www.science.gov/topicpages/p/probing+intermolecular+couplings.html
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#### Sample records for probing intermolecular couplings
1. Probing Intermolecular Coupled Vibrations between Two Molecules
Han, Zhumin; Czap, Gregory; Xu, Chen; Chiang, Chi-lun; Yuan, Dingwang; Wu, Ruqian; Ho, W.
2017-01-01
Intermolecular interactions can induce energy shifts and coupling of molecular vibrations. However, the detection of intermolecular coupled vibrations has not been reported at the single molecule level. Here we detected an intermolecular coupled vibration between two CO molecules, one on the surface and another on the tip within the gap of a subkelvin scanning tunneling microscope, and analyzed the results by density functional calculations. We attribute the evolution of the energy and intensity of this coupled vibration as a function of tip-sample distance to the tilting and orbital alignment of the two CO molecules.
2. A test of the significance of intermolecular vibrational coupling in isotopic fractionation
Herman, Michael F.; Currier, Robert P.; Peery, Travis B.; Clegg, Samuel M.
2017-09-01
Intermolecular coupling of dipole moments is studied for a model system consisting of two diatomic molecules (AB monomers) arranged co-linearly and which can form non-covalently bound dimers. The dipolar coupling is a function of the bond length in each molecule as well as of the distance between the centers-of-mass of the two molecules. The calculations show that intermolecular coupling of the vibrations results in an isotope-dependent modification of the AB-AB intermolecular potential. This in turn alters the energies of the low-lying bound states of the dimers, producing isotope-dependent changes in the AB-AB dimer partition function. Explicit inclusion of intermolecular vibrational coupling then changes the predicted gas-dimer isotopic fractionation. In addition, a mass dependence in the intermolecular potential can also result in changes in the number of bound dimer states in an equilibrium mixture. This in turn leads to a significant dimer population shift in the model monomer-dimer equilibrium system considered here. The results suggest that intermolecular coupling terms should be considered when probing the origins of isotopic fractionation.
3. A test of the significance of intermolecular vibrational coupling in isotopic fractionation
DOE PAGES
Herman, Michael F.; Currier, Robert P.; Peery, Travis B.; ...
2017-07-15
Intermolecular coupling of dipole moments is studied for a model system consisting of two diatomic molecules (AB monomers) arranged co-linearly and which can form non-covalently bound dimers. The dipolar coupling is a function of the bond length in each molecule as well as of the distance between the centers-of-mass of the two molecules. The calculations show that intermolecular coupling of the vibrations results in an isotope-dependent modification of the AB-AB intermolecular potential. This in turn alters the energies of the low-lying bound states of the dimers, producing isotope-dependent changes in the AB-AB dimer partition function. Explicit inclusion of intermolecular vibrationalmore » coupling then changes the predicted gas-dimer isotopic fractionation. In addition, a mass dependence in the intermolecular potential can also result in changes in the number of bound dimer states in an equilibrium mixture. This in turn leads to a significant dimer population shift in the model monomer-dimer equilibrium system considered here. Finally, the results suggest that intermolecular coupling terms should be considered when probing the origins of isotopic fractionation.« less
4. Tandem intermolecular Suzuki coupling/intramolecular vinyl triflate-arene coupling.
PubMed
Willis, Michael C; Claverie, Christelle K; Mahon, Mary F
2002-04-21
Treatment of a benzyl substituted meso-ditriflate with boronic acids in the presence of palladium acetate, triphenylphosphine and caesium fluoride results in intermolecular Suzuki coupling followed by vinyl triflate-arene cyclisation to provide, in high yields, single regioisomers of tricyclic-carbocycles.
5. Probing Intermolecular Interaction through Thermal-Lens Spectroscopy
PubMed Central
Bhattacharyya, Indrajit; Kumar, Pardeep; Goswami, Debabrata
2013-01-01
Binary liquid mixtures are studied using femtosecond pump–probe thermal-lens (TL) spectroscopy. Changes in the measured TL signals as a function of relative concentration of binary mixtures show that these result from a combined effect of physical and molecular properties of the constituent binary liquids. The experimental TL values deviate from the ones calculated from phenomenological equations. These, we argue, are due to an underestimation of the influence of molecular interactions when the TL signals are calculated by using physical parameters only. PMID:21166402
6. Intermolecular Alignment in Y145Stop Human Prion Protein Amyloid Fibrils Probed by Solid-State NMR Spectroscopy
PubMed Central
Helmus, Jonathan J.; Surewicz, Krystyna; Apostol, Marcin I.; Surewicz, Witold K.; Jaroniec, Christopher P.
2011-01-01
The Y145Stop mutant of human prion protein, huPrP23-144, has been linked to PrP cerebral amyloid angiopathy, an inherited amyloid disease, and also serves as a valuable in vitro model for investigating the molecular basis of amyloid strains. Prior studies of huPrP23-144 amyloid by magic-angle spinning (MAS) solid-state NMR revealed a compact β-rich amyloid core region near the C-terminus and an unstructured N-terminal domain. Here, with the focus on understanding the higher order architecture of huPrP23-144 fibrils, we probe the intermolecular alignment of β-strands within the amyloid core using MAS NMR techniques and fibrils formed from equimolar mixtures of 15N-labeled protein and 13C-huPrP23-144 prepared with [1,3-13C] or [2-13C]glycerol. Numerous intermolecular correlations involving backbone atoms observed in 2D 15N-13C spectra unequivocally suggest an overall parallel in-register alignment of the β-sheet core. Additional experiments that report on intermolecular 15N-13CO and 15N-13Cα dipolar couplings yield an estimated strand spacing that is within ~10% of the ~4.7–4.8 Å distances typical for parallel β-sheets. PMID:21827207
7. Intermolecular alignment in Y145Stop human prion protein amyloid fibrils probed by solid-state NMR spectroscopy.
PubMed
Helmus, Jonathan J; Surewicz, Krystyna; Apostol, Marcin I; Surewicz, Witold K; Jaroniec, Christopher P
2011-09-07
The Y145Stop mutant of human prion protein, huPrP23-144, has been linked to PrP cerebral amyloid angiopathy, an inherited amyloid disease, and also serves as a valuable in vitro model for investigating the molecular basis of amyloid strains. Prior studies of huPrP23-144 amyloid by magic-angle-spinning (MAS) solid-state NMR spectroscopy revealed a compact β-rich amyloid core region near the C-terminus and an unstructured N-terminal domain. Here, with the focus on understanding the higher-order architecture of huPrP23-144 fibrils, we probed the intermolecular alignment of β-strands within the amyloid core using MAS NMR techniques and fibrils formed from equimolar mixtures of (15)N-labeled protein and (13)C-huPrP23-144 prepared with [1,3-(13)C(2)] or [2-(13)C]glycerol. Numerous intermolecular correlations involving backbone atoms observed in 2D (15)N-(13)C spectra unequivocally suggest an overall parallel in-register alignment of the β-sheet core. Additional experiments that report on intermolecular (15)N-(13)CO and (15)N-(13)Cα dipolar couplings yielded an estimated strand spacing that is within ∼10% of the distances of 4.7-4.8 Å typical for parallel β-sheets.
8. Rh(I)-Catalyzed Intermolecular Hydroacylation: Enantioselective Cross-Coupling of Aldehydes and Ketoamides
PubMed Central
2015-01-01
Under Rh(I) catalysis, α-ketoamides undergo intermolecular hydroacylation with aliphatic aldehydes. A newly designed Josiphos ligand enables access to α-acyloxyamides with high atom-economy and enantioselectivity. On the basis of mechanistic and kinetic studies, we propose a pathway in which rhodium plays a dual role in activating the aldehyde for cross-coupling. A stereochemical model is provided to rationalize the sense of enantioinduction observed. PMID:24937681
9. Density Analysis of Intra- and Intermolecular Vibronic Couplings toward Bath Engineering for Singlet Fission.
PubMed
Ito, Soichi; Nagami, Takanori; Nakano, Masayoshi
2015-12-17
Vibronic coupling plays a crucial role in singlet fission whereby a singlet exciton splits into two triplet excitons. In order to reveal the physicochemical origin of the vibronic coupling associated with singlet fission as well as to clarify its relationship with chemical structure, we evaluate relevant vibronic couplings from the viewpoint of their spatial contributions described by vibronic coupling density. From the analysis using a model tetracene dimer, a typical singlet fission system, the frequency dependence of vibronic couplings in each electronic state is found to be significantly different from that of another depending on the nature of the electronic structure (intra/intermolecular excitation) and the related vibrational motion. These findings contribute not only to the fundamental understanding of the singlet fission mechanism from the viewpoint of vibronic couplings but also to opening a new path to designing highly efficient singlet fission materials through phonon-bath engineering.
10. Coupled effects of substrate adhesion and intermolecular forces on polymer thin film glass-transition behavior.
PubMed
Xia, Wenjie; Keten, Sinan
2013-10-15
Intermolecular noncovalent forces between polymer chains influence the mobility and glass-transition temperature (Tg), where weaker interchain interactions, all else being the same, typically results in lower bulk polymer Tg. Using molecular dynamics simulations, here we show that this relation can become invalid for supported ultrathin films when the substrate-polymer interaction is extremely strong and the polymer-polymer interactions are much weaker. This contrasting trend is found to be due to a more pronounced substrate-induced appreciation of the film Tg for polymers with weaker intermolecular interactions and low bulk Tg. We show that optimizing this coupling between substrate adhesion and bulk Tg maximizes thin film Tg, paving the way for tuning film properties through interface nanoengineering.
11. The Origins of - and Inter-Molecular Vibrational Couplings: a Case Study of H_2O-Ar on Full and Reduced-Dimensional Potential Energy Surface
Hou, Dan; Ma, Yong-Tao; Zhang, Xiao-Long; Li, Hui
2016-06-01
The origin and strength of intra- and inter-molecular vibrational coupling is difficult to probe by direct experimental observations. However, explicitly including or not including some specific intramolecular vibrational modes to study intermolecular interaction provides a precise theoretical way to examine the effects of anharmonic coupling between modes. In this work, a full-dimension intra- and inter-molecular ab initio potential energy surface (PES) for H_2O-Ar, which explicitly incorporates interdependence on the intramolecular normal-mode coordinates of the H_2O monomer, has been calculated. In addition, four analytic vibrational-quantum-state-specific PESs are obtained by least-squares fitting vibrationally averaged interaction energies for the (νb{1},νb{2},νb{3})=(0,0,0),(0,0,1),(1,0,0),(0,1,0) states of H_2O to the three-dimensional Morse/long-range potential function. The resulting vibrationally averaged PESs provide good representations of the experimental infrared data, with RMS discrepancies smaller than 0.02 wn for all three rotational branches of the asymmetric stretch fundamental transitions. The infrared band origin shifts associated with three fundamental bands of H_2O in H_2O-Ar complex are predicted for the first time and are found to be in good agreement with the (extrapolated) experimental values. Upon introduction of additional intramolecular degrees of freedom into the intermolecular potential energy surface, there is clear spectroscopic evidence of intra- and intermolecular vibrational couplings. J. Chem. Phys., 144, 014301 (2016)
12. Detection of intermolecular homonuclear dipolar coupling in organic rich shale by transverse relaxation exchange
Washburn, Kathryn E.; Cheng, Yuesheng
2017-05-01
The mechanism behind surface relaxivity within organic porosity in shales has been an unanswered question. Here, we present results that confirm the existence of intermolecular homonuclear dipolar coupling between solid and liquid phases in sedimentary organic matter. Transverse magnetization exchange measurements were performed on an organic-rich shale saturated with liquid hydrocarbon. Liquid and solid constituents were identified through both sample resaturation and through their T1/T2 ratios. Extensive cross peaks are observed in the T2-T2 exchange spectra between the solid and liquid constituents, indicating an exchange of magnetization between the two phases. This result cannot arise from physical molecular diffusion, and the dissolution energies are too high for chemical exchange, such that the magnetization exchange must arise from intermolecular homonuclear dipolar coupling. These results both confirm a possible source of surface relaxivity in organic matter and emphasize caution in the use of standard porous media interpretations of relaxation results in shales because of coupling between different magnetization environments.
13. Detection of intermolecular homonuclear dipolar coupling in organic rich shale by transverse relaxation exchange.
PubMed
Washburn, Kathryn E; Cheng, Yuesheng
2017-03-04
The mechanism behind surface relaxivity within organic porosity in shales has been an unanswered question. Here, we present results that confirm the existence of intermolecular homonuclear dipolar coupling between solid and liquid phases in sedimentary organic matter. Transverse magnetization exchange measurements were performed on an organic-rich shale saturated with liquid hydrocarbon. Liquid and solid constituents were identified through both sample resaturation and through their T1/T2 ratios. Extensive cross peaks are observed in the T2-T2 exchange spectra between the solid and liquid constituents, indicating an exchange of magnetization between the two phases. This result cannot arise from physical molecular diffusion, and the dissolution energies are too high for chemical exchange, such that the magnetization exchange must arise from intermolecular homonuclear dipolar coupling. These results both confirm a possible source of surface relaxivity in organic matter and emphasize caution in the use of standard porous media interpretations of relaxation results in shales because of coupling between different magnetization environments.
14. 15N- 15N spin-spin coupling constants through intermolecular hydrogen bonds in the solid state
Claramunt, Rosa M.; Pérez-Torralba, Marta; María, Dolores Santa; Sanz, Dionisia; Elena, Bénédicte; Alkorta, Ibon; Elguero, José
2010-10-01
A 2hJNN intermolecular spin-spin coupling constant (SSCC) of 10.2 ± 0.4 Hz has been measured for the powdered tetrachlorogallate salt of pyridinium solvated by pyridine (pyridine-H +⋯pyridine cation 3). Density Functional Theory (DFT) calculations at the B3LYP/6-311++G( d, p) level reproduced this value and two others reported in the literature for 2hJ intermolecular SSCCs, which were measured for complexes in solution.
15. Intermolecular Electronic Coupling of Organic Units for Efficient Persistent Room‐Temperature Phosphorescence
PubMed Central
Yang, Zhiyong; Mao, Zhu; Zhang, Xuepeng; Ou, Depei; Mu, Yingxiao; Zhao, Cunyuan; Liu, Siwei; Xu, Jiarui; Wu, Yuan‐Chun; Lu, Po‐Yen; Lien, Alan
2016-01-01
Abstract Although persistent room‐temperature phosphorescence (RTP) emission has been observed for a few pure crystalline organic molecules, there is no consistent mechanism and no universal design strategy for organic persistent RTP (pRTP) materials. A new mechanism for pRTP is presented, based on combining the advantages of different excited‐state configurations in coupled intermolecular units, which may be applicable to a wide range of organic molecules. By following this mechanism, we have developed a successful design strategy to obtain bright pRTP by utilizing a heavy halogen atom to further increase the intersystem crossing rate of the coupled units. RTP with a remarkably long lifetime of 0.28 s and a very high quantum efficiency of 5 % was thus obtained under ambient conditions. This strategy represents an important step in the understanding of organic pRTP emission. PMID:26836346
16. X-filtering for a range of coupling constants: application to the detection of intermolecular NOEs
Zangger, Klaus; Oberer, Monika; Keller, Walter; Sterk, Heinz
2003-02-01
A new method for heteronuclear X-filtering is presented, which relies on repetitive applications of 90°( 1H)-τ(1/4 1J HC)-180°( 1H, 13C)-τ(1/4 1J HC)-90°( 1H, 13C)- PFG building blocks employing gradient-mediated suppression of magnetization built up for directly heteronuclear coupled protons. Thereby, a range of heteronuclear coupling constants can be suppressed by varying the delays of scalar coupling evolution both within and between individual transients. To achieve efficient destruction of 13C-coupled protons in macromolecular systems, the scalar coupling evolution delays were optimized using simulated annealing by including transverse relaxation effects. With a combination of regular hard pulses, delays and pulsed field gradients only, this method yields sufficient X-filtering to allow the observation of intermolecular nuclear overhauser effects in a molecular complex consisting of a 13C, 15N double-labeled, and an unlabeled protein. This is achieved by exciting magnetization of 12C- and 14N-bound protons and detecting 13C-bound 1H magnetization in a 3D 13C-filtered, 13C-edited NOESY-HSQC experiment. The method is tested on the 18 kDa homodimeric bacterial antidote ParD.
17. Hypervalent Iodine(III)-Promoted Intermolecular C–C Coupling of Vindoline with β-Ketoesters and Related Substrates
PubMed Central
Turner, Travis C.; Shibayama, Kotaro
2013-01-01
The regioselective intermolecular coupling reaction of vindoline with a wide range of substrates including β-ketoesters, β-diketones, β-ketoaldehydes, β-ketonitriles, malononitriles, and β-cyanoesters provides an opportunity for the synthesis of vinblastine analogues containing deep-seated changes in the upper velbanamine subunit. The transition-metal free hypervalent iodine(III)-promoted intermolecular sp3/sp2 coupling, representing a special class of selective C–H activation with direct carbon–carbon bond formation, proceeds with generation of a quaternary center capable of incorporation of the vinblastine C16′ methyl ester and functionalized for subsequent divergent heterocycle introduction. PMID:23421318
18. Strong intermolecular antiferromagnetic verdazyl-verdazyl coupling in the solid state.
PubMed
Eusterwiemann, S; Doerenkamp, C; Dresselhaus, T; Janka, O; de Oliveira, M; Daniliuc, C G; Eckert, H; Neugebauer, J; Pöttgen, R; Studer, A
2017-06-21
Strong magnetic couplings are generally observed intramolecularly in organic diradicals or in systems in which they are promoted by crystal engineering strategies involving, for example, transition metal ligation. We herein present a strong intermolecularly coupling verdazyl radical in the solid state without the use of such design strategies. The crystal structure of an acetylene-substituted verdazyl radical shows a unique antiparallel face-to-face orientation of the neighboring verdazyl molecules along with verdazyl-acetylene interactions giving rise to an alternating antiferromagnetic Heisenberg chain. Single crystal structural data at 80, 100, 173, and 223 K show that one of the π-stacking distances depends on temperature, while heat capacity data indicate the absence of a phase transition. Based on this structural input, broken symmetry DFT calculations predict a change from an alternating linear Heisenberg chain with two comparable coupling constants J1 and J2 at higher temperatures towards dominant pair interactions at lower temperatures. The predicted antiferromagnetic coupling is confirmed experimentally by magnetic susceptibility, solid-state EPR and NMR spectroscopic results.
19. Cross-dehydrogenative coupling for the intermolecular C–O bond formation
PubMed Central
Krylov, Igor B; Vil’, Vera A
2015-01-01
Summary The present review summarizes primary publications on the cross-dehydrogenative C–O coupling, with special emphasis on the studies published after 2000. The starting compound, which donates a carbon atom for the formation of a new C–O bond, is called the CH-reagent or the C-reagent, and the compound, an oxygen atom of which is involved in the new bond, is called the OH-reagent or the O-reagent. Alcohols and carboxylic acids are most commonly used as O-reagents; hydroxylamine derivatives, hydroperoxides, and sulfonic acids are employed less often. The cross-dehydrogenative C–O coupling reactions are carried out using different C-reagents, such as compounds containing directing functional groups (amide, heteroaromatic, oxime, and so on) and compounds with activated C–H bonds (aldehydes, alcohols, ketones, ethers, amines, amides, compounds containing the benzyl, allyl, or propargyl moiety). An analysis of the published data showed that the principles at the basis of a particular cross-dehydrogenative C–O coupling reaction are dictated mainly by the nature of the C-reagent. Hence, in the present review the data are classified according to the structures of C-reagents, and, in the second place, according to the type of oxidative systems. Besides the typical cross-dehydrogenative coupling reactions of CH- and OH-reagents, closely related C–H activation processes involving intermolecular C–O bond formation are discussed: acyloxylation reactions with ArI(O2CR)2 reagents and generation of O-reagents in situ from C-reagents (methylarenes, aldehydes, etc.). PMID:25670997
20. Probing acid-amide intermolecular hydrogen bonding by NMR spectroscopy and DFT calculations
Chaudhari, Sachin Rama; Suryaprakash, N.
2012-05-01
Benzene carboxylic acids and benzamide act as their self-complement in molecular recognition to form inter-molecular hydrogen bonded dimers between amide and carboxylic acid groups, which have been investigated by 1H, 13C and 15N NMR spectroscopy. Extensive NMR studies using diffusion ordered spectroscopy (DOSY), variable temperature 1D, 2D NMR, established the formation of heterodimers of benzamide with benzoic acid, salicylic acid and phenyl acetic acid in deuterated chloroform solution. Association constants for the complex formation in the solution state have been determined. The results are ascertained by X-ray diffraction in the solid state. Intermolecular interactions in solution and in solid state were found to be similar. The structural parameters obtained by X-ray diffraction studies are compared with those obtained by DFT calculations.
1. The origins of intra- and inter-molecular vibrational couplings: A case study of H2O-Ar on full and reduced-dimensional potential energy surface.
PubMed
Hou, Dan; Ma, Yong-Tao; Zhang, Xiao-Long; Li, Hui
2016-01-07
The origin and strength of intra- and inter-molecular vibrational coupling is difficult to probe by direct experimental observations. However, explicitly including or not including some specific intramolecular vibrational modes to study intermolecular interaction provides a precise theoretical way to examine the effects of anharmonic coupling between modes. In this work, a full-dimension intra- and inter-molecular ab initio potential energy surface (PES) for H2O-Ar, which explicitly incorporates interdependence on the intramolecular (Q1, Q2, Q3) normal-mode coordinates of the H2O monomer, has been calculated. In addition, four analytic vibrational-quantum-state-specific PESs are obtained by least-squares fitting vibrationally averaged interaction energies for the (v1, v2, v3) = (0, 0, 0), (0, 0, 1), (1, 0, 0), (0, 1, 0) states of H2O to the three-dimensional Morse/long-range potential function. Each vibrationally averaged PES fitted to 442 points has root-mean-square (rms) deviation smaller than 0.15 cm(-1), and required only 58 parameters. With the 3D PESs of H2O-Ar dimer system, we employed the combined radial discrete variable representation/angular finite basis representation method and Lanczos algorithm to calculate rovibrational energy levels. This showed that the resulting vibrationally averaged PESs provide good representations of the experimental infrared data, with rms discrepancies smaller than 0.02 cm(-1) for all three rotational branches of the asymmetric stretch fundamental transitions. The infrared band origin shifts associated with three fundamental bands of H2O in H2O-Ar complex are predicted for the first time and are found to be in good agreement with the (extrapolated) experimental values. Upon introduction of additional intramolecular degrees of freedom into the intermolecular potential energy surface, there is clear spectroscopic evidence of intra- and intermolecular vibrational couplings.
2. Probing the contribution of different intermolecular forces to the adsorption of spheroproteins onto hydrophilic surfaces.
PubMed
Borges, João; Campiña, José M; Silva, A Fernando
2013-12-27
Protein adsorption is a delicate process, which results from the balance between the properties of proteins and their solid supports. Although the relevance of some of these parameters has been already unveiled, the precise involvement of electrostatics and other weaker intermolecular forces requires further comprehension. Aiming to contribute to this task, this work explores the attachment, rearrangement, and surface aggregation of a model spheroprotein, such as bovine β-lactoglobulin (β-LG), onto hydrophilic substrates prefunctionalized with different alkylthiol films. Thereby, a variety of electrostatic scenarios for the adsorption of β-LG could be recreated through the variation of the pH and the functional chemistry of the surfaces. The changes in surface mass density (plus associated water) and film flexibility were followed in situ with quartz crystal microbalance with dissipation monitoring. Film packing and aggregation were assessed by faradaic electrochemical measurements and ex situ atomic force microscopy and field effect scanning electron microscopy. In contrast to previous hypotheses arguing that electrostatic interactions between charged substrates and proteins would be the only driving force, a complex interplay between Coulombic and non-Coulombic intermolecular forces (which would depend upon the experimental conditions) has been suggested to explain the results.
3. Detection of complex formation and determination of intermolecular geometry through electrical anharmonic coupling of molecular vibrations using electron-vibration-vibration two-dimensional infrared spectroscopy.
PubMed
Guo, Rui; Fournier, Frederic; Donaldson, Paul M; Gardner, Elizabeth M; Gould, Ian R; Klug, David R
2009-10-14
Electrical interactions between molecular vibrations can be non-linear and thereby produce intermolecular coupling even in the absence of a chemical bond. We use this fact to detect the formation of an intermolecular complex using electron-vibration-vibration two-dimensional infrared spectroscopy (EVV 2DIR) and also to determine the distance and angle between the two molecular species.
4. Probing Intermolecular Interactions in Binary Liquid Mixtures Using Femtosecond Laser-Induced Self-Defocusing.
PubMed
Maurya, Sandeep Kumar; Das, Dhiman; Goswami, Debabrata
2016-06-13
Photo-thermal behavior of binary liquid mixtures has been studied by high repetition rate (HRR) Z-scan technique with femtosecond laser pulses. Changes in the peak-valley difference in transmittance (ΔTP-V) for closed aperture Z-scan experiments are indicative of thermal effects induced by HRR femtosecond laser pulses. We show such indicative results can have a far-reaching impact on molecular properties and intermolecular interactions in binary liquid mixtures. Spectroscopic parameters derived from this experimental technique show that the combined effect of physical and molecular properties of the constituent binary liquids can be related to the components of the binary liquid. © The Author(s) 2016.
5. Probing the self-association, intermolecular contacts, and folding propensity of amelogenin
PubMed Central
Ndao, Moise; Dutta, Kaushik; Bromley, Keith M; Lakshminarayanan, Rajamani; Sun, Zhi; Rewari, Gita; Moradian-Oldak, Janet; Evans, John Spencer
2011-01-01
Amelogenins are an intrinsically disordered protein family that plays a major role in the development of tooth enamel, one of the most highly mineralized materials in nature. Monomeric porcine amelogenin possesses random coil and residual secondary structures, but it is not known which sequence regions would be conformationally attractive to potential enamel matrix targets such as other amelogenins (self-assembly), other matrix proteins, cell surfaces, or biominerals. To address this further, we investigated recombinant porcine amelogenin (rP172) using “solvent engineering” techniques to simultaneously promote native-like structure and induce amelogenin oligomerization in a manner that allows identification of intermolecular contacts between amelogenin molecules. We discovered that in the presence of 2,2,2-trifluoroethanol (TFE) significant folding transitions and stabilization occurred primarily within the N- and C-termini, while the polyproline Type II central domain was largely resistant to conformational transitions. Seven Pro residues (P2, P127, P130, P139, P154, P157, P162) exhibited conformational response to TFE, and this indicates these Pro residues act as folding enhancers in rP172. The remaining Pro residues resisted TFE perturbations and thus act as conformational stabilizers. We also noted that TFE induced rP172 self-association via the formation of intermolecular contacts involving P4–H6, V19–P33, and E40–T58 regions of the N-terminus. Collectively, these results confirm that the N- and C-termini of amelogenin are conformationally responsive and represent potential interactive sites for amelogenin–target interactions during enamel matrix mineralization. Conversely, the Pro, Gln central domain is resistant to folding and this may have important functional significance for amelogenin. PMID:21351181
6. Residence Times of Molecular Complexes in Solution from NMR Data of Intermolecular Hydrogen-Bond Scalar Coupling.
PubMed
Zandarashvili, Levani; Esadze, Alexandre; Kemme, Catherine A; Chattopadhyay, Abhijnan; Nguyen, Dan; Iwahara, Junji
2016-03-03
The residence times of molecular complexes in solution are important for understanding biomolecular functions and drug actions. We show that NMR data of intermolecular hydrogen-bond scalar couplings can yield information on the residence times of molecular complexes in solution. The molecular exchange of binding partners via the breakage and reformation of a complex causes self-decoupling of intermolecular hydrogen-bond scalar couplings, and this self-decoupling effect depends on the residence time of the complex. For protein-DNA complexes, we investigated the salt concentration dependence of intermolecular hydrogen-bond scalar couplings between the protein side-chain (15)N and DNA phosphate (31)P nuclei, from which the residence times were analyzed. The results were consistent with those obtained by (15)Nz-exchange spectroscopy. This self-decoupling-based kinetic analysis is unique in that it does not require any different signatures for the states involved in the exchange, whereas such conditions are crucial for kinetic analyses by typical NMR and other methods.
7. Optical properties of azobenzene-functionalized self-assembled monolayers: Intermolecular coupling and many-body interactions
Cocchi, Caterina; Moldt, Thomas; Gahl, Cornelius; Weinelt, Martin; Draxl, Claudia
2016-12-01
In a joint theoretical and experimental work, the optical properties of azobenzene-functionalized self-assembled monolayers (SAMs) are studied at different molecular packing densities. Our results, based on density-functional and many-body perturbation theory, as well as on differential reflectance (DR) spectroscopy, shed light on the microscopic mechanisms ruling photo-absorption in these systems. While the optical excitations are intrinsically excitonic in nature, regardless of the molecular concentration, in densely packed SAMs intermolecular coupling and local-field effects are responsible for a sizable weakening of the exciton binding strength. Through a detailed analysis of the character of the electron-hole pairs, we show that distinct excitations involved in the photo-isomerization at low molecular concentrations are dramatically broadened by intermolecular interactions. Spectral shifts in the calculated DR spectra are in good agreement with the experimental results. Our findings represent an important step forward to rationalize the excited-state properties of these complex materials.
8. Similarity-transformed perturbation theory on top of truncated local coupled cluster solutions: Theory and applications to intermolecular interactions
SciTech Connect
2015-05-28
Your correspondents develop and apply fully nonorthogonal, local-reference perturbation theories describing non-covalent interactions. Our formulations are based on a Löwdin partitioning of the similarity-transformed Hamiltonian into a zeroth-order intramonomer piece (taking local CCSD solutions as its zeroth-order eigenfunction) plus a first-order piece coupling the fragments. If considerations are limited to a single molecule, the proposed intermolecular similarity-transformed perturbation theory represents a frozen-orbital variant of the “(2)”-type theories shown to be competitive with CCSD(T) and of similar cost if all terms are retained. Different restrictions on the zeroth- and first-order amplitudes are explored in the context of large-computation tractability and elucidation of non-local effects in the space of singles and doubles. To accurately approximate CCSD intermolecular interaction energies, a quadratically growing number of variables must be included at zeroth-order.
9. Strong intermolecular vibrational coupling through cyclic hydrogen-bonded structures revealed by ultrafast continuum mid-IR spectroscopy.
PubMed
Stingel, Ashley M; Calabrese, Carmella; Petersen, Poul B
2013-12-12
Cyclic hydrogen-bonded structures are common motifs in biological systems, providing structural stability and mediating proton transfer for redox reactions. The mechanism of proton transfer across hydrogen-bonded interfaces depends on the strength of the intermolecular coupling between bridging OH/NH vibrational modes. Here we present a novel ultrafast continuum mid-IR spectroscopy experiment to study the vibrational dynamics of the 7-azaindole-acetic acid (7AI-Ac) heterodimer as a model system for asymmetric cyclic hydrogen-bonded structures. In addition to spreading of the excitation across the whole OH band within the time resolution of the experiment, excitation of a 300 cm(-1) region of the ∼1000 cm(-1) broad OH stretching mode of the acetic acid monomer leads to a frequency shift in the NH stretching mode of the 7AI monomer. This indicates that the NH and OH stretching modes located on the two monomers are strongly coupled despite being separated by 750 cm(-1). The strong coupling further causes the OH and NH bands to decay with a common decay time of ∼2.5 ps. This intermolecular coupling is mediated through the hydrogen-bonded structure of the 7AI-Ac heterodimer and is likely a general property of cyclic hydrogen-bonded structures. Characterizing the vibrational dynamics of and the coupling between the high-frequency OH/NH modes will be important for understanding proton transfer across such molecular interfaces.
10. Probing intermolecular interactions in water/ionic liquid mixtures by far-infrared spectroscopy.
PubMed
Dominguez-Vidal, Ana; Kaun, Nina; Ayora-Cañada, Maria Jose; Lendl, Bernhard
2007-05-03
Far-infrared spectra in the range from 600 to 20 cm-1 of two hydrophilic (1-ethyl-3-methylimidazolium tetrafluoroborate and 1-butyl-3-methylimidazolium tetrafluoroborate) and one hydrophobic (1-butyl-3-methylimidazolium hexafluorophosphate) ionic liquids and their mixtures with water at different concentrations are reported. Shifts of the librational water bands depending on the nature of the anion are found to be related to the strength of the interaction between the water molecules and the anions. For both hydrophilic ionic liquids, the librational band is centered around 460 cm-1, whereas for the hydrophobic ionic liquid, it is shifted to 388 cm-1, indicating less hindered rotation of single water molecules. Multivariate curve resolution, paying special attention to the spectral range from 50 to 350 cm-1, was used to investigate the presence of different species with increasing water concentration. For both hydrophilic ionic liquids, a band located at 153 cm-1 was resolved into two different contributions. A small contribution at 202 cm-1 can be attributed to intermolecular interactions between water molecules forming dimers. The major contribution (centered at 148 cm-1) corresponds to water molecules that do not bond to each other via H-bonding. It is therefore assigned to a hindered translation arising from the stretching of the hydrogen bond between BF4- anions and water molecules. Formation of water dimers in the hydrophobic ionic liquid does not occur. Furthermore, the spectral contribution of the stretching of H-bonds between water molecules and PF6- cannot be unambiguously detected, which indicates an extremely weak interaction between water molecules and this anion.
11. Probing Intramolecular versus Intermolecular CO2 Adsorption on Amine-Grafted SBA-15.
PubMed
Yoo, Chun-Jae; Lee, Li-Chen; Jones, Christopher W
2015-12-15
12. Vibrational nano-spectroscopic imaging correlating structure with intermolecular coupling and dynamics.
PubMed
Pollard, Benjamin; Muller, Eric A; Hinrichs, Karsten; Raschke, Markus B
2014-04-11
Molecular self-assembly, the function of biomembranes and the performance of organic solar cells rely on nanoscale molecular interactions. Understanding and control of such materials have been impeded by difficulties in imaging their properties with the desired nanometre spatial resolution, attomolar sensitivity and intermolecular spectroscopic specificity. Here we implement vibrational scattering-scanning near-field optical microscopy with high spectral precision to investigate the structure-function relationship in nano-phase separated block copolymers. A vibrational resonance is used as a sensitive reporter of the local chemical environment and we image, with few nanometre spatial resolution and 0.2 cm(-1) spectral precision, solvatochromic Stark shifts and line broadening correlated with molecular-scale morphologies. We discriminate local variations in electric fields between nano-domains with quantitative agreement with dielectric continuum models. This ability to directly resolve nanoscale morphology and associated intermolecular interactions can form a basis for the systematic control of functionality in multicomponent soft matter systems.
13. Vibrational nano-spectroscopic imaging correlating structure with intermolecular coupling and dynamics
PubMed Central
Pollard, Benjamin; Muller, Eric A.; Hinrichs, Karsten; Raschke, Markus B.
2014-01-01
Molecular self-assembly, the function of biomembranes and the performance of organic solar cells rely on nanoscale molecular interactions. Understanding and control of such materials have been impeded by difficulties in imaging their properties with the desired nanometre spatial resolution, attomolar sensitivity and intermolecular spectroscopic specificity. Here we implement vibrational scattering-scanning near-field optical microscopy with high spectral precision to investigate the structure–function relationship in nano-phase separated block copolymers. A vibrational resonance is used as a sensitive reporter of the local chemical environment and we image, with few nanometre spatial resolution and 0.2 cm−1 spectral precision, solvatochromic Stark shifts and line broadening correlated with molecular-scale morphologies. We discriminate local variations in electric fields between nano-domains with quantitative agreement with dielectric continuum models. This ability to directly resolve nanoscale morphology and associated intermolecular interactions can form a basis for the systematic control of functionality in multicomponent soft matter systems. PMID:24721995
14. Probing intermolecular protein-protein interactions in the calcium-sensing receptor homodimer using bioluminescence resonance energy transfer (BRET).
PubMed
Jensen, Anders A; Hansen, Jakob L; Sheikh, Søren P; Bräuner-Osborne, Hans
2002-10-01
The calcium-sensing receptor (CaR) belongs to family C of the G-protein coupled receptor superfamily. The receptor is believed to exist as a homodimer due to covalent and non-covalent interactions between the two amino terminal domains (ATDs). It is well established that agonist binding to family C receptors takes place at the ATD and that this causes the ATD dimer to twist. However, very little is known about the translation of the ATD dimer twist into G-protein coupling to the 7 transmembrane moieties (7TMs) of these receptor dimers. In this study we have attempted to delineate the agonist-induced intermolecular movements in the CaR homodimer using the new bioluminescence resonance energy transfer technique, BRET2, which is based on the transference of energy from Renilla luciferase (Rluc) to the green fluorescent protein mutant GFP2. We tagged CaR with Rluc and GFP2 at different intracellular locations. Stable and highly receptor-specific BRET signals were obtained in tsA cells transfected with Rluc- and GFP2-tagged CaRs under basal conditions, indicating that CaR is constitutively dimerized. However, the signals were not enhanced by the presence of agonist. These results could indicate that at least parts of the two 7TMs of the CaR homodimer are in close proximity in the inactivated state of the receptor and do not move much relative to one another upon agonist activation. However, we cannot exclude the possibility that the BRET technology is unable to register putative conformational changes in the CaR homodimer induced by agonist binding because of the bulk sizes of the Rluc and GFP2 molecules.
15. NMR Scalar Couplings across Intermolecular Hydrogen Bonds between Zinc-Finger Histidine Side Chains and DNA Phosphate Groups.
PubMed
2016-10-10
NMR scalar couplings across hydrogen bonds represent direct evidence for the partial covalent nature of hydrogen bonds and provide structural and dynamic information on hydrogen bonding. In this article, we report heteronuclear (15)N-(31)P and (1)H-(31)P scalar couplings across the intermolecular hydrogen bonds between protein histidine (His) imidazole and DNA phosphate groups. These hydrogen-bond scalar couplings were observed for the Egr-1 zinc-finger-DNA complex. Although His side-chain NH protons are typically undetectable in heteronuclear (1)H-(15)N correlation spectra due to rapid hydrogen exchange, this complex exhibited two His side-chain NH signals around (1)H 14.3 ppm and (15)N 178 ppm at 35 °C. Through various heteronuclear multidimensional NMR experiments, these signals were assigned to two zinc-coordinating His side chains in contact with DNA phosphate groups. The data show that the Nδ1 atoms of these His side chains are protonated and exhibit the (1)H-(15)N cross-peaks. Using heteronuclear (1)H, (15)N, and (31)P NMR experiments, we observed the hydrogen-bond scalar couplings between the His (15)Nδ1/(1)Hδ1 and DNA phosphate (31)P nuclei. These results demonstrate the direct involvement of the zinc-coordinating His side chains in the recognition of DNA by the Cys2His2-class zinc fingers in solution.
16. Unusual intermolecular "through-space" j couplings in p-se heterocycles.
PubMed
Sanz Camacho, Paula; Athukorala Arachchige, Kasun S; Slawin, Alexandra M Z; Green, Timothy F G; Yates, Jonathan R; Dawson, Daniel M; Woollins, J Derek; Ashbrook, Sharon E
2015-05-20
Solid-state NMR spectra of new P-Se heterocycles based on peri-substituted naphthalene motifs show the presence of unusual J couplings between Se and P. These couplings are between atoms in adjacent molecules and occur "through space", rather than through conventional covalent bonds. Experimental measurements are supported by relativistic DFT calculations, which confirm the presence of couplings between nonbonded atoms, and provide information on the pathway of the interaction. This observation improves the understanding of J couplings and offers insight into the factors that affect crystal packing in solids, for future synthetic exploitation.
17. Probing intermolecular interactions in a diethylcarbamazine citrate salt by fast MAS (1)H solid-state NMR spectroscopy and GIPAW calculations.
PubMed
Venâncio, Tiago; Oliveira, Lyege Magalhaes; Ellena, Javier; Boechat, Nubia; Brown, Steven P
2017-03-02
Fast magic-angle spinning (MAS) NMR is used to probe intermolecular interactions in a diethylcarbamazine salt, that is widely used as a treatment against adult worms of Wuchereria bancrofti which cause a common disease in tropical countries named filariasis. Specifically, a dihydrogen citrate salt that has improved thermal stability and solubility as compared to the free form is studied. One-dimensional (1)H, (13)C and (15)N and two-dimensional (1)H-(13)C and (14)N-(1)H heteronuclear correlation NMR experiments under moderate and fast MAS together with GIPAW (CASTEP) calculations enable the assignment of the (1)H, (13)C and (14)N/(15)N resonances. A two-dimensional (1)H-(1)H double-quantum (DQ) -single-quantum (SQ) MAS spectrum recorded with BaBa recoupling at 60kHz MAS identifies specific proton-proton proximities associated with citrate-citrate and citrate-diethylcarbamazine intermolecular interactions.
18. Investigating Unusual Homonuclear Intermolecular "Through-Space" J Couplings in Organochalcogen Systems.
PubMed
Sanz Camacho, Paula; McKay, David; Dawson, Daniel M; Kirst, Christin; Yates, Jonathan R; Green, Timothy F G; Cordes, David B; Slawin, Alexandra M Z; Woollins, J Derek; Ashbrook, Sharon E
2016-11-07
Although the electron-mediated spin-spin or J coupling is conventionally viewed as transmitted via covalent bonds, examples of J couplings between atoms that are not formally bonded but are in close proximity (termed "through-space" J couplings) have been reported. In this work, we investigate the observation of homonuclear (31)P J couplings in organochalcogen heterocycles, which occur between (31)P in two separate molecules, confirming without doubt their through-space nature. The presence of this interaction is even more surprising for one compound, where it occurs between crystallographically equivalent species. Although crystallographically equivalent species need not be magnetically equivalent in the solid state, owing to the presence of anisotropic interactions, we demonstrate that it is not the shielding anisotropy that lifts magnetic equivalence, in this case, but the presence of heteronuclear couplings to (77)Se. We support our experimental observations with periodic scalar-relativistic density functional theory calculations and coupling density deformation plots to visualize the mechanism of these interesting interactions.
19. Langmuir probe differential measurement technique in inductively coupled RF plasmas
Djermanov, I.; Djermanova, N.; Kiss'ovski, Zh; Tsankov, Ts
2007-04-01
A differential measurement technique has been proposed in order to reduce noise level and stray capacitance leakage usually affecting Langmuir probe data. The technique employs two identically designed and biased Langmuir probes, connected to an instrumentation amplifier. Both probes are immersed in plasma of approximately the same space potential, one of them being plasma current collecting probe, and the second one being isolated from plasma and serving as a pick-up probe, detecting leakage currents from parasitic capacitive coupling and noise. Avoiding averaging of probe current data is the main advantage of the proposed differential technique. Experiments in the plasma expansion region of inductively driven RF source are shown to achieve lower electron temperature and higher electron density as measured by conventional single Langmuir probe. Obtaining more sharpness of the "knee" on the characteristic, thus lowering the uncertainty in plasma potential is another true merit of the differential Langmuir probe technique.
20. Computational IR spectroscopy of water: OH stretch frequencies, transition dipoles, and intermolecular vibrational coupling constants
Choi, Jun-Ho; Cho, Minhaeng
2013-05-01
The Hessian matrix reconstruction method initially developed to extract the basis mode frequencies, vibrational coupling constants, and transition dipoles of the delocalized amide I, II, and III vibrations of polypeptides and proteins from quantum chemistry calculation results is used to obtain those properties of delocalized O-H stretch modes in liquid water. Considering the water symmetric and asymmetric O-H stretch modes as basis modes, we here develop theoretical models relating vibrational frequencies, transition dipoles, and coupling constants of basis modes to local water configuration and solvent electric potential. Molecular dynamics simulation was performed to generate an ensemble of water configurations that was in turn used to construct vibrational Hamiltonian matrices. Obtaining the eigenvalues and eigenvectors of the matrices and using the time-averaging approximation method, which was developed by the Skinner group, to calculating the vibrational spectra of coupled oscillator systems, we could numerically simulate the O-H stretch IR spectrum of liquid water. The asymmetric line shape and weak shoulder bands were quantitatively reproduced by the present computational procedure based on vibrational exciton model, where the polarization effects on basis mode transition dipoles and inter-mode coupling constants were found to be crucial in quantitatively simulating the vibrational spectra of hydrogen-bond networking liquid water.
1. The origins of intra- and inter-molecular vibrational couplings: A case study of H{sub 2}O-Ar on full and reduced-dimensional potential energy surface
SciTech Connect
Hou, Dan; Ma, Yong-Tao; Zhang, Xiao-Long; Li, Hui
2016-01-07
The origin and strength of intra- and inter-molecular vibrational coupling is difficult to probe by direct experimental observations. However, explicitly including or not including some specific intramolecular vibrational modes to study intermolecular interaction provides a precise theoretical way to examine the effects of anharmonic coupling between modes. In this work, a full-dimension intra- and inter-molecular ab initio potential energy surface (PES) for H{sub 2}O–Ar, which explicitly incorporates interdependence on the intramolecular (Q{sub 1}, Q{sub 2}, Q{sub 3}) normal-mode coordinates of the H{sub 2}O monomer, has been calculated. In addition, four analytic vibrational-quantum-state-specific PESs are obtained by least-squares fitting vibrationally averaged interaction energies for the (v{sub 1}, v{sub 2}, v{sub 3}) = (0, 0, 0), (0, 0, 1), (1, 0, 0), (0, 1, 0) states of H{sub 2}O to the three-dimensional Morse/long-range potential function. Each vibrationally averaged PES fitted to 442 points has root-mean-square (rms) deviation smaller than 0.15 cm{sup −1}, and required only 58 parameters. With the 3D PESs of H{sub 2}O–Ar dimer system, we employed the combined radial discrete variable representation/angular finite basis representation method and Lanczos algorithm to calculate rovibrational energy levels. This showed that the resulting vibrationally averaged PESs provide good representations of the experimental infrared data, with rms discrepancies smaller than 0.02 cm{sup −1} for all three rotational branches of the asymmetric stretch fundamental transitions. The infrared band origin shifts associated with three fundamental bands of H{sub 2}O in H{sub 2}O–Ar complex are predicted for the first time and are found to be in good agreement with the (extrapolated) experimental values. Upon introduction of additional intramolecular degrees of freedom into the intermolecular potential energy surface, there is clear
2. Intermolecular hydrogen bonds in hetero-complexes of biologically active aromatic molecules probed by the methods of vibrational spectroscopy
Semenov, M. A.; Blyzniuk, Iu. N.; Bolbukh, T. V.; Shestopalova, A. V.; Evstigneev, M. P.; Maleev, V. Ya.
2012-09-01
By the methods of vibrational spectroscopy (Infrared and Raman) the investigation of the hetero-association of biologically active aromatic compounds: flavin-mononucleotide (FMN), ethidium bromide (EB) and proflavine (PRF) was performed in aqueous solutions. It was shown that between the functional groups (Cdbnd O and NH2) the intermolecular hydrogen bonds are formed in the hetero-complexes FMN-EB and FMN-PRF, additionally stabilizing these structures. An estimation of the enthalpy of Н-bonding obtained from experimental shifts of carbonyl vibrational frequencies has shown that the H-bonds do not dominate in the magnitude of experimentally measured total enthalpy of the hetero-association reactions. The main stabilization is likely due to intermolecular interactions of the molecules in these complexes and their interaction with water environment.
3. Intermolecular hydrogen bonds in hetero-complexes of biologically active aromatic molecules probed by the methods of vibrational spectroscopy.
PubMed
Semenov, M A; Blyzniuk, Iu N; Bolbukh, T V; Shestopalova, A V; Evstigneev, M P; Maleev, V Ya
2012-09-01
By the methods of vibrational spectroscopy (Infrared and Raman) the investigation of the hetero-association of biologically active aromatic compounds: flavin-mononucleotide (FMN), ethidium bromide (EB) and proflavine (PRF) was performed in aqueous solutions. It was shown that between the functional groups (CO and NH(2)) the intermolecular hydrogen bonds are formed in the hetero-complexes FMN-EB and FMN-PRF, additionally stabilizing these structures. An estimation of the enthalpy of Н-bonding obtained from experimental shifts of carbonyl vibrational frequencies has shown that the H-bonds do not dominate in the magnitude of experimentally measured total enthalpy of the hetero-association reactions. The main stabilization is likely due to intermolecular interactions of the molecules in these complexes and their interaction with water environment.
4. Intermolecular bonding of hemin in solution and in solid state probed by N K-edge X-ray spectroscopies.
PubMed
Golnak, Ronny; Xiao, Jie; Atak, Kaan; Stevens, Joanna S; Gainar, Adrian; Schroeder, Sven L M; Aziz, Emad F
2015-11-21
X-ray absorption/emission spectroscopy (XAS/XES) at the N K-edge of iron protoporphyrin IX chloride (FePPIX-Cl, or hemin) has been carried out for dissolved monomers in DMSO, dimers in water and for the solid state. This sequence of samples permits identification of characteristic spectral features associated with the hemin intermolecular bonding. These characteristic features are further analyzed and understood at the molecular orbital (MO) level based on the DFT calculations.
5. Strong intermolecular exciton couplings in solid-state circular dichroism of aryl benzyl sulfoxides.
PubMed
Padula, Daniele; Di Pietro, Sebastiano; Capozzi, Maria Annunziata M; Cardellicchio, Cosimo; Pescitelli, Gennaro
2014-09-01
A series of 13 enantiopure aryl benzyl sulfoxides () with different substituents on the two aromatic rings has been previously analyzed by means of electronic circular dichroism (CD) spectroscopy. Most of these compounds are crystalline and their X-ray structure is established. For almost one-half of the series, CD spectra measured in the solid state were quite different from those in acetonitrile solution. We demonstrate that the difference is due to strong exciton couplings between molecules packed closely together in the crystal. The computational approach consists of time-dependent density functional theory (TDDFT) calculations run on "dimers" composed of nearest neighbors found in the lattice. Solid-state CD spectra are well reproduced by the average of all possible pairwise terms. The relation between the crystal space group and conformation, and the appearance of solid-state CD spectra, is also discussed.
6. Closed-shell ring coupled cluster doubles theory with range separation applied on weak intermolecular interactions.
PubMed
Toulouse, Julien; Zhu, Wuming; Savin, Andreas; Jansen, Georg; Ángyán, János G
2011-08-28
We explore different variants of the random phase approximation to the correlation energy derived from closed-shell ring-diagram approximations to coupled cluster doubles theory. We implement these variants in range-separated density-functional theory, i.e., by combining the long-range random phase approximations with short-range density-functional approximations. We perform tests on the rare-gas dimers He(2), Ne(2), and Ar(2), and on the weakly interacting molecular complexes of the S22 set of Jurečka et al. [P. Jurečka, J. Šponer, J. Černý, and P. Hobza, Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The two best variants correspond to the ones originally proposed by Szabo and Ostlund [A. Szabo and N. S. Ostlund, J. Chem. Phys. 67, 4351 (1977)]. With range separation, they reach mean absolute errors on the equilibrium interaction energies of the S22 set of about 0.4 kcal/mol, corresponding to mean absolute percentage errors of about 4%, with the aug-cc-pVDZ basis set.
7. Probing anomalous Higgs couplings in H → ZV decays
Modak, Tanmoy; Srivastava, Rahul
2017-01-01
We analyze the possibility of probing anomalous Higgs couplings in the rare decays H → ZV, V being a vector quarkonium state. These rare decays involve both gauge as well as the Yukawa sectors and either of them can potentially be anomalous. We show that the branching fractions for H → ZV decays in Standard Model (SM) are small, making it a sensitive probe for anomalous Higgs couplings originating from physics beyond SM. Moreover, as both V and Z can decay into pair of charged leptons, they provide experimentally clean channels and future LHC runs should observe such decays. We perform a model independent analysis and show how angular asymmetries can be used to probe these anomalous Higgs couplings, taking further decays of V and Z to pair of charged leptons into account. The angular asymmetries can provide significant information about anomalous Higgs couplings in both gauge and Yukawa sectors.
8. Intermolecular forces.
PubMed
Buckingham, A D
1975-11-06
The nature of molecular interactions is examined. Intermolecular forces are divided into long-range and short-range components; the former operate at distances where the effects of electron exchange are negligible and decrease as an inverse power of the separation. The long-range interactions may be subdividied into electrostatic, induction and dispersion contributions, where the electrostatic component is the interaction of the permanent charge distributions and the others originate in the fluctuations in the distributions. Typical magnitudes of the various contributions are given. The forces between macroscopic bodies are briefly considered, as are the effects of a medium. Some of the manifestations of molecular interactions are discussed.
9. Probing scalar coupling differences via long-lived singlet states
DeVience, Stephen J.; Walsworth, Ronald L.; Rosen, Matthew S.
2016-01-01
We probe small scalar coupling differences via the coherent interactions between two nuclear spin singlet states in organic molecules. We show that the spin-lock induced crossing (SLIC) technique enables the coherent transfer of singlet order between one spin pair and another. The transfer is mediated by the difference in syn and anti vicinal or long-range J couplings among the spins. By measuring the transfer rate, we calculate a J coupling difference of 8 ± 2 mHz in phenylalanine-glycine-glycine and 2.57 ± 0.04 Hz in glutamate. We also characterize a coherence between two singlet states in glutamate, which may enable the creation of a long-lived quantum memory.
10. Rotationally inelastic scattering of ND3 with H2 as a probe of the intermolecular potential energy surface
Tkáč, Ondřej; Saha, Ashim K.; Loreau, Jérôme; Ma, Qianli; Dagdigian, Paul J.; Parker, David H.; van der Avoird, Ad; Orr-Ewing, Andrew J.
2015-12-01
Differential cross sections (DCSs) are reported for rotationally inelastic scattering of ND3 with H2, measured using a crossed molecular beam apparatus with velocity map imaging (VMI). ND3 molecules were quantum-state selected in the ground electronic and vibrational levels and, optionally, in the j±k = 11- rotation-inversion level prior to collisions. Inelastic scattering of state-selected ND3 with H2 was measured at the mean collision energy of 580 cm-1 by resonance-enhanced multiphoton ionisation spectroscopy and VMI of ND3 in selected single final j'±k' levels. Comparison of experimental DCSs with close-coupling quantum-mechanical scattering calculations serves as a test of a recently reported ab initio potential energy surface. Calculated integral cross sections reveal the propensities for scattering into various final j'±k' levels of ND3 and differences between scattering by ortho and para H2. Integral and differential cross sections are also computed at a mean collision energy of 430 cm-1 and compared to our recent results for inelastic scattering of state-selected ND3 with He.
11. Langmuir Probe Distortions and Probe Compensation in an Inductively Coupled Plasma
NASA Technical Reports Server (NTRS)
Ji, J. S.; Cappelli, M. A.; Kim, J. S.; Rao, M. V. V. S.; Sharma, S. P.
1999-01-01
In many RF discharges, Langmuir probe measurements are usually made against a background of sinusoidal (and not so sinusoidal) fluctuations in the plasma parameters such as the plasma potential (Vp), the electron number density (ne), and the electron temperature (Te). The compensation of sinusoidal fluctuations in Vp has been extensively studied and is relatively well understood. Less attention has been paid to the possible distortions introduced by small fluctuations in plasma density and/or plasma temperature, which may arise in the sheath and pre-sheath regions of RF discharges. Here, we present the results of a model simulation of probe characteristics subject to fluctuations in both Vp and ne. The modeling of probe distortion due to possible fluctuations in Te is less straightforward. A comparison is presented of calculations with experimental measurements using a compensated and uncompensated Langmuir probe in an inductively coupled GEC reference cell plasma, operating on Ar and Ar/CF4 mixtures. The plasma parameters determined from the compensated probe characteristics are compared to previous measurements of others made in similar discharges, and to our own measurements of the average electron density derived from electrical impedance measurements.
12. Probing electroweak top quark couplings at hadron colliders
SciTech Connect
Baur, U.; Juste, A.; Orr, L.H.; Rainwater, D.
2005-03-01
We consider QCD tt{gamma} and ttZ production at hadron colliders as a tool to measure the tt{gamma} and ttZ couplings. At the Tevatron it may be possible to perform a first, albeit not very precise, test of the tt{gamma} vector and axial vector couplings in tt{gamma} production, provided that more than 5 fb{sup -1} of integrated luminosity are accumulated. The ttZ cross section at the Tevatron is too small to be observable. At the CERN Large Hadron Collider (LHC) it will be possible to probe the tt{gamma} couplings at the few-percent level, which approaches the precision which one hopes to achieve with a next-generation e{sup +}e{sup -} linear collider. The LHC's capability of associated QCD ttV (V={gamma},Z) production has the added advantage that the tt{gamma} and ttZ couplings are not entangled. For an integrated luminosity of 300 fb{sup -1}, the ttZ vector (axial vector) coupling can be determined with an uncertainty of 45-85% (15-20%), whereas the dimension-five dipole form factors can be measured with a precision of 50-55%. The achievable limits improve typically by a factor of 2-3 for the luminosity-upgraded (3 ab{sup -1}) LHC.
13. Intermolecular C-C Coupling Between 1-Methyl-1,2,3-Triazole and 2,2'-Bipyridine or 1,10-Phenanthroline at Mo(II) Complexes.
PubMed
Riera, Lucia; Pérez, Julio; Fombona, Sergio; Díaz, Jesús
2017-09-14
Unsupported 1-methyl-1,2,3-triazole has been coordinated to {Mo(3-methallyl)(CO)2(N-N)} (N-N= 2,2'-bipyridine, bipy; or 1,10-phenanthroline,phen) fragments yielding cationic complexes which can be regarded as metalated triazolium salts. Their reactivity towards a strong base led to the deprotonation of the C5-H group of the triazole moiety, followed by an intermolecular nucleophilic attack to the ortho CH group of a bipy or phen ligand affording cyclic, bimetallic dearomatized C-C coupling products. The reaction of the neutral bipy derivative with an acid led to the formation of dihydropyridyl units by protonation of a CH group of the dearomatized rings, the dimeric nature of complexes being mantained upon protonation. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
14. Secondary fluorescence in electron probe microanalysis of material couples
Llovet, X.; Pinard, P. T.; Donovan, J. J.; Salvat, F.
2012-06-01
We describe a semi-analytical method for the fast calculation of secondary fluorescence in electron probe microanalysis of material couples. The calculation includes contributions from primary K-, L- and M-shell characteristic x-rays and bremsstrahlung photons. The required physical interaction parameters (subshell partial cross sections, attenuation coefficients, etc) are extracted from the database of the Monte Carlo simulation code system PENELOPE. The calculation makes use of the intensities of primary photons released in interactions of beam electrons and secondary electrons. Since these intensities are not readily available and do not allow analytical calculation, they are generated from short Monte Carlo simulation runs. The reliability of the proposed calculation method has been assessed by comparing calculated, distance-dependent k-ratios with experimental data available in the literature and with results from simulations with PENELOPE. Numerical results are found to be in close agreement with both simulated and experimental data.
15. Coupling Electrochemistry with Probe Electrospray Ionization Mass Spectrometry.
PubMed
Cai, Yi; Liu, Pengyuan; Held, Michael A; Dewald, Howard D; Chen, Hao
2016-04-18
A new coupling of electrochemistry with mass spectrometry (MS) using probe electrospray ionization (PESI) is presented. Due to the high salt tolerance of PESI, the detection of electrochemical reaction products in room-temperature ionic liquids (RTILs) is realized for the first time. Furthermore, PESI-MS allows the analysis of electrochemical reaction products on different or multiple electrode surfaces. In addition, peptides and proteins fractionated through isoelectric focusing (IEF) in the presence of an external electric field can also be directly analyzed by using PESI-MS, suggesting a new and rapid characterization means for the IEF technique. This study reveals the versatility of EC/PESI-MS, which could have an impact in electrochemistry and bioanalysis fields.
16. Driving Forces for Covalent Assembly of Porphyrins by Selective C-H Bond Activation and Intermolecular Coupling on a Copper Surface.
PubMed
Floris, Andrea; Haq, Sam; In't Veld, Mendel; Amabilino, David B; Raval, Rasmita; Kantorovich, Lev
2016-05-11
Recent synthesis of covalent organic assemblies at surfaces has opened the promise of producing robust nanostructures for functional interfaces. To uncover how this new chemistry works at surfaces and understand the underlying mechanisms that control bond-breaking and bond-making processes at specific positions of the participating molecules, we study here the coupling reaction of tetra(mesityl)porphyrin molecules, which creates covalently connected networks on the Cu(110) surface by utilizing the 4-methyl groups as unique connection points. Using scanning tunneling microscopy (STM), state-of-the-art density functional theory (DFT), and Nudged Elastic Band (NEB) calculations, we show that the unique directionality of the covalent bonding is found to stem from a chain of highly selective C-H activation and dehydrogenation processes, followed by specific intermolecular C-C coupling reactions that are facilitated by the surface, by steric constraints, and by anisotropic molecular diffusion. These insights provide the first steps toward developing synthetic rules for complex two-dimensional covalent organic chemistry that can be enacted directly at a surface to deliver specific macromolecular structures designed for specific functions.
17. Solute-solvent intermolecular vibronic coupling as manifested by the molecular near-field effect in resonance hyper-Raman scattering.
PubMed
2011-01-21
Vibronic coupling within the excited electronic manifold of the solute all-trans-β-carotene through the vibrational motions of the solvent cyclohexane is shown to manifest as the "molecular near-field effect," in which the solvent hyper-Raman bands are subject to marked intensity enhancements under the presence of all-trans-β-carotene. The resonance hyper-Raman excitation profiles of the enhanced solvent bands exhibit similar peaks to those of the solute bands in the wavenumber region of 21,700-25,000 cm(-1) (10,850-12,500 cm(-1) in the hyper-Raman exciting wavenumber), where the solute all-trans-β-carotene shows a strong absorption assigned to the 1A(g) → 1B(u) transition. This fact indicates that the solvent hyper-Raman bands gain their intensities through resonances with the electronic states of the solute. The observed excitation profiles are quantitatively analyzed and are successfully accounted for by an extended vibronic theory of resonance hyper-Raman scattering that incorporates the vibronic coupling within the excited electronic manifold of all-trans-β-carotene through the vibrational motions of cyclohexane. It is shown that the major resonance arises from the B-term (vibronic) coupling between the first excited vibrational level (v = 1) of the 1B(u) state and the ground vibrational level (v = 0) of a nearby A(g) state through ungerade vibrational modes of both the solute and the solvent molecules. The inversion symmetry of the solute all-trans-β-carotene is preserved, suggesting the weak perturbative nature of the solute-solvent interaction in the molecular near-field effect. The present study introduces a new concept, "intermolecular vibronic coupling," which may provide an experimentally accessible∕theoretically tractable model for understanding weak solute-solvent interactions in liquid.
18. Coupling efficiency of ultra-small gradient-index fiber probe
Wang, Chi; Sun, Jianmei; Sun, Fan; Zhu, Jun; Yuan, Zhiwen; Asundi, Anand
2017-04-01
In this paper, the coupling efficiency of ultra-small GRIN fiber probe is studied for its focusing performance. Based on the light transmission characteristics of a Gaussian beam and the principle of optical imaging, with the analytical methods, the theoretical formula is deduced for the coupling efficiency of ultra-small GRIN fiber probe. Experiments were set-up and conducted for verification. Per the experimental results, for an ultra-small GRIN fiber probe with the focal length of 0.4 mm, the coupling efficiency measured at the focusing position was 57%, and above 44% within the 0-0.6 mm range. However, for a single-mode fiber, the coupling efficiency dropped to 17% when the distance increased to 0.2 mm. Thus, the ultra-small GRIN fiber probe boasts a superior focusing performance and coupling efficiency. This paper provides a theoretical basis for the application and research on ultra-small GRIN fiber probe.
19. Improving the Mass-Limited Performance of Routine NMR Probes using Coupled Coils.
PubMed
Marsden, Brian; Lim, Victor; Taber, Bob; Zens, Albert
2016-07-01
We report a method to convert, on demand, a general use dual-broadband probe to a high performance mass-limited probe for both high band and low band nuclei. This technology uses magnetic coupling of inductors to achieve this capability. The method offers a cost effective way of increasing the performance of routine NMR probes without having to change probes or increase the overall foot print of the spectrometer.
20. Improving the Mass-Limited Performance of Routine NMR Probes using Coupled Coils
Marsden, Brian; Lim, Victor; Taber, Bob; Zens, Albert
2016-07-01
We report a method to convert, on demand, a general use dual-broadband probe to a high performance mass-limited probe for both high band and low band nuclei. This technology uses magnetic coupling of inductors to achieve this capability. The method offers a cost effective way of increasing the performance of routine NMR probes without having to change probes or increase the overall foot print of the spectrometer.
1. Capacitively coupled RF voltage probe having optimized flux linkage
DOEpatents
Moore, James A.; Sparks, Dennis O.
1999-02-02
An RF sensor having a novel current sensing probe and a voltage sensing probe to measure voltage and current. The current sensor is disposed in a transmission line to link all of the flux generated by the flowing current in order to obtain an accurate measurement. The voltage sensor is a flat plate which operates as a capacitive plate to sense voltage on a center conductor of the transmission line, in which the measured voltage is obtained across a resistance leg of a R-C differentiator circuit formed by the characteristic impedance of a connecting transmission line and a capacitance of the plate, which is positioned proximal to the center conductor.
2. Higgs coupling constants as a probe of new physics
SciTech Connect
Kanemura, Shinya; Okada, Yasuhiro; Senaha, Eibun; Yuan, C.-P.
2004-12-01
We study new physics effects on the couplings of weak gauge bosons with the lightest CP-even Higgs boson (h), hZZ, and the trilinear coupling of the lightest Higgs boson, hhh, at the one-loop order, as predicted by the two Higgs doublet model. Those renormalized coupling constants can deviate from the standard model (SM) predictions due to two distinct origins: the tree level mixing effect of Higgs bosons and the quantum effect of additional particles in loop diagrams. The latter can be enhanced in the renormalized hhh coupling constant when the additional particles show the nondecoupling property. Therefore, even in the case where the hZZ coupling is close to the SM value, deviation in the hhh coupling from the SM value can become as large as plus 100%, while that in the hZZ coupling is at most minus 1% level. Such large quantum effect on the Higgs trilinear coupling is distinguishable from the tree level mixing effect, and is expected to be detectable at a future linear collider.
3. Control of the probe absorption in coupled quantum wells in two dimensions
Kang, Chengxian; Ma, Yangcheng; Wang, Zhiping; Yu, Benli
2016-06-01
We investigate the probe absorption of a weak probe field in two dimensions (the so-called two-dimensional probe absorption) in an asymmetric two coupled quantum wells. It is found that, due to the joint quantum interference induced by the standing-wave and coherent coupling fields, the probe absorption can be easily controlled via adjusting the system parameters in two dimensions. Most importantly, the pattern of probe absorption can be localized at a particular position and the maximal probability of finding the pattern in one period of the standing-wave fields reaches unity by properly adjusting the system parameters. Thus, our scheme may provide some technological applications in solid-state optoelectronics and quantum information science.
4. Probing Phase Coupling Between Two Spin-Torque Nano-Oscillators with an External Source
Li, Yi; de Milly, Xavier; Abreu Araujo, Flavio; Klein, Olivier; Cros, Vincent; Grollier, Julie; de Loubens, Grégoire
2017-06-01
Phase coupling between auto-oscillators is central for achieving coherent responses such as synchronization. Here we present an experimental approach to probe it in the case of two dipolarly coupled spin-torque vortex nano-oscillators using an external microwave field. By phase locking one oscillator to the external source, we observe frequency pulling on the second oscillator. From coupled phase equations we show analytically that this frequency pulling results from concerted actions of oscillator-oscillator and source-oscillator couplings. The analysis allows us to determine the strength and phase shift of coupling between two oscillators, yielding important information for the implementation of large interacting oscillator networks.
5. Ionic-charge dependence of the intermolecular coulombic decay time scale for aqueous ions probed by the core-hole clock.
PubMed
Pokapanich, Wandared; Kryzhevoi, Nikolai V; Ottosson, Niklas; Svensson, Svante; Cederbaum, Lorenz S; Öhrwall, Gunnar; Björneholm, Olle
2011-08-31
Auger electron spectroscopy combined with theoretical calculations has been applied to investigate the decay of the Ca 2p core hole of aqueous Ca(2+). Beyond the localized two-hole final states on the calcium ion, originating from a normal Auger process, we have further identified the final states delocalized between the calcium ion and its water surroundings and produced by core level intermolecular Coulombic decay (ICD) processes. By applying the core-hole clock method, the time scale of the core level ICD was determined to be 33 ± 1 fs for the 2p core hole of the aqueous Ca(2+). The comparison of this time constant to those associated with the aqueous K(+), Na(+), Mg(2+), and Al(3+) ions reveals differences of 1 and up to 2 orders of magnitude. Such large variations in the characteristic time scales of the core level ICD processes is qualitatively explained by different internal decay mechanisms in different ions as well as by different ion-solvent distances and interactions.
6. Energy of the quasi-free electron in H{sub 2}, D{sub 2}, and O{sub 2}: Probing intermolecular potentials within the local Wigner-Seitz model
SciTech Connect
Evans, C. M. Krynski, Kamil; Streeter, Zachary; Findley, G. L.
2015-12-14
We present for the first time the quasi-free electron energy V{sub 0}(ρ) for H{sub 2}, D{sub 2}, and O{sub 2} from gas to liquid densities, on noncritical isotherms and on a near critical isotherm in each fluid. These data illustrate the ability of field enhanced photoemission (FEP) to determine V{sub 0}(ρ) accurately in strongly absorbing fluids (e.g., O{sub 2}) and fluids with extremely low critical temperatures (e.g., H{sub 2} and D{sub 2}). We also show that the isotropic local Wigner-Seitz model for V{sub 0}(ρ) — when coupled with thermodynamic data for the fluid — can yield optimized parameters for intermolecular potentials, as well as zero kinetic energy electron scattering lengths.
7. Langmuir Probe Measurements in an Inductively Coupled GEC Reference Cell Plasma
NASA Technical Reports Server (NTRS)
Ji, J. S.; Kim, J. S.; Cappelli, M. A.; Sharma, S. P.; Arnold, J. O. (Technical Monitor)
1998-01-01
Measurements of electron number density, electron temperature, and electron energy distribution function (EEDF) using a compensated Langmuir probe have been performed on an inductively (transformer ) coupled Gaseous Electronics Conference (GEC) reference cell plasma. The plasma source is operated with CH4, CF4, or their mixtures with argon. The effect of independently driving the electrode supporting the wafer on the probe data is studied. In particular, we find that the plasma structure depends on the phase in addition to the magnitude of the power coupled to the electrode relative to that of the transformer coil. The Langmuir probe is translated in a plane parallel to the electrode to investigate the spatial structure of the plasma. The probe data is also compared with fluid model predictions.
8. NDE of a 3-D surface crack using closely coupled probes for DCPD technique
SciTech Connect
Saka, M.; Abe, H.; Hirota, D.; Komura, I.
1998-11-01
A procedure of applying the d-c potential drop technique using the closely coupled probes to NDE of a 3-D surface crack is newly developed. The calibration equation for three sensors which differ in the distance between the probes is derived. Experiments validated the use of the calibration equation for the NDE of cracks. The method to use the three sensors properly based on the measuring sensitivity is shown.
9. The development of a shock-tube based characterization technique for air-coupled ultrasonic probes.
PubMed
Revel, G M; Pandarese, G; Cavuto, A
2014-08-01
The present paper proposes a new characterization technique for air-coupled ultrasound probes. The technique is based on a shock tube to generate a controlled pressure wave to calibrate transducers within their operating frequency range. The aim is to generate a high frequency pressure wave (at least up to 200 kHz) with the low energy levels typical of commonly used air-coupled ultrasound probes. A dedicated shock-tube has been designed and tested to assess calibration performances. The sensor transfer function has been measured by using a pressure transducer as reference. Copyright © 2014 Elsevier B.V. All rights reserved.
10. Probing gravitational non-minimal coupling with dark energy surveys
Geng, Chao-Qiang; Lee, Chung-Chi; Wu, Yi-Peng
2017-03-01
We investigate observational constraints on a specific one-parameter extension to the minimal quintessence model, where the quintessence field acquires a quadratic coupling to the scalar curvature through a coupling constant ξ . The value of ξ is highly suppressed in typical tracker models if the late-time cosmic acceleration is driven at some field values near the Planck scale. We test ξ in a second class of models in which the field value today becomes a free model parameter. We use the combined data from type-Ia supernovae, cosmic microwave background, baryon acoustic oscillations and matter power spectrum, to weak lensing measurements and find a best-fit value ξ {>}0.289 where ξ = 0 is excluded outside the 95% confidence region. The effective gravitational constant G_eff subject to the hint of a non-zero ξ is constrained to -0.003< 1- G_eff/G < 0.033 at the same confidence level on cosmological scales, and it can be narrowed down to 1- G_eff/G < 2.2 × 10^{-5} when combining with Solar System tests.
11. Probing transmembrane mechanical coupling and cytomechanics using magnetic twisting cytometry
NASA Technical Reports Server (NTRS)
Wang, N.; Ingber, D. E.
1995-01-01
We recently developed a magnetic twisting cytometry technique that allows us to apply controlled mechanical stresses to specific cell surface receptors using ligand-coated ferromagnetic microbeads and to simultaneously measure the mechanical response in living cells. Using this technique, we have previously shown the following: (i) beta 1 integrin receptors mediate mechanical force transfer across the cell surface and to the cytoskeleton, whereas other transmembrane receptors (e.g., scavenger receptors) do not; (ii) cytoskeletal stiffness increases in direct proportion to the level of stress applied to integrins; and (iii) the slope of this linear stiffening response differs depending on the shape of the cell. We now show that different integrins (beta 1, alpha V beta 3, alpha V, alpha 5, alpha 2) and other transmembrane receptors (scavenger receptor, platelet endothelial cell adhesion molecule) differ in their ability to mediate force transfer across the cell surface. In addition, the linear stiffening behavior previously observed in endothelial cells was found to be shared by other cell types. Finally, we demonstrate that dynamic changes in cell shape that occur during both cell spreading and retraction are accompanied by coordinate changes in cytoskeletal stiffness. Taken together, these results suggest that the magnetic twisting cytometry technique may be a powerful and versatile tool for studies analyzing the molecular basis of transmembrane mechanical coupling to the cytoskeleton as well as dynamic relations between changes in cytoskeletal structure and alterations in cell form and function.
12. Probing transmembrane mechanical coupling and cytomechanics using magnetic twisting cytometry
NASA Technical Reports Server (NTRS)
Wang, N.; Ingber, D. E.
1995-01-01
We recently developed a magnetic twisting cytometry technique that allows us to apply controlled mechanical stresses to specific cell surface receptors using ligand-coated ferromagnetic microbeads and to simultaneously measure the mechanical response in living cells. Using this technique, we have previously shown the following: (i) beta 1 integrin receptors mediate mechanical force transfer across the cell surface and to the cytoskeleton, whereas other transmembrane receptors (e.g., scavenger receptors) do not; (ii) cytoskeletal stiffness increases in direct proportion to the level of stress applied to integrins; and (iii) the slope of this linear stiffening response differs depending on the shape of the cell. We now show that different integrins (beta 1, alpha V beta 3, alpha V, alpha 5, alpha 2) and other transmembrane receptors (scavenger receptor, platelet endothelial cell adhesion molecule) differ in their ability to mediate force transfer across the cell surface. In addition, the linear stiffening behavior previously observed in endothelial cells was found to be shared by other cell types. Finally, we demonstrate that dynamic changes in cell shape that occur during both cell spreading and retraction are accompanied by coordinate changes in cytoskeletal stiffness. Taken together, these results suggest that the magnetic twisting cytometry technique may be a powerful and versatile tool for studies analyzing the molecular basis of transmembrane mechanical coupling to the cytoskeleton as well as dynamic relations between changes in cytoskeletal structure and alterations in cell form and function.
13. Pneumatic switched angle spinning NMR probe with capacitively coupled double saddle coil.
PubMed
Litvak, Ilya M; Espinosa, Catalina A; Shapiro, Rebecca A; Oldham, Andrew N; Duong, Vincent V; Martin, Rachel W
2010-10-01
Switched angle spinning (SAS) experiments can be used for generating isotropic-anisotropic correlations in oriented samples in a single experiment. In order for these methods to become widespread, specialized hardware is required. Here we describe the electronic and mechanical design and performance of a double-resonance SAS probe. Unlike many previous SAS probe implementations, the focus here is on systems where the dipolar couplings are partially averaged by molecular motion. This probe has a moving double saddle coil capacitively coupled to the stationary circuit. Angle switching is accomplished by a steam engine-type pneumatic mechanism. The speed and stability of the switching hardware for SAS experiments are demonstrated using spectra of model compounds.
14. Pneumatic switched angle spinning NMR probe with capacitively coupled double saddle coil
Litvak, Ilya M.; Espinosa, Catalina A.; Shapiro, Rebecca A.; Oldham, Andrew N.; Duong, Vincent V.; Martin, Rachel W.
2010-10-01
Switched angle spinning (SAS) experiments can be used for generating isotropic-anisotropic correlations in oriented samples in a single experiment. In order for these methods to become widespread, specialized hardware is required. Here we describe the electronic and mechanical design and performance of a double-resonance SAS probe. Unlike many previous SAS probe implementations, the focus here is on systems where the dipolar couplings are partially averaged by molecular motion. This probe has a moving double saddle coil capacitively coupled to the stationary circuit. Angle switching is accomplished by a steam engine-type pneumatic mechanism. The speed and stability of the switching hardware for SAS experiments are demonstrated using spectra of model compounds.
15. Protein conformational transitions coupled to binding in molecular recognition of unstructured proteins: deciphering the effect of intermolecular interactions on computational structure prediction of the p27Kip1 protein bound to the cyclin A-cyclin-dependent kinase 2 complex.
PubMed
2005-02-15
The relationship between folding mechanism coupled to binding and structure prediction of the tertiary complexes is studied for the p27(Kip) (1) protein which has an intrinsically disordered unbound form and undergoes a functional folding transition during complex formation with the phosphorylated cyclin A-cyclin-dependent kinase 2 (Cdk2) binary complex. Hierarchy of p27(Kip1) structural loss determined in our earlier studies from temperature-induced Monte Carlo simulations and subsequent characterization of the transition state ensemble (TSE) for the folding reaction have shown that simultaneous ordering of the p27(Kip1) native intermolecular interface for the beta-hairpin and beta-strand secondary structure elements is critical for nucleating a rapid kinetic transition to the native tertiary complex. In the present study, we investigate the effect of forming specific intermolecular interactions on structure prediction of the p27(Kip1) tertiary complex. By constraining different secondary structure elements of p27(Kip1) in their native bound conformations and conducting multiple simulated annealing simulations, we analyze differences in the success rate of predicting the native structure of p27(Kip1) in the tertiary complex. In accordance with the nucleation-condensation mechanism, we have found that further stabilization of the native intermolecular interface for the beta-hairpin and beta-strand elements of p27(Kip1), that become ordered in the TSE, but are hardly populated in the unbound state, results in a consistent acquisition of the native bound structure. Conversely, the excessive stablization of the local secondary structure elements, which are rarely detected in the TSE, has a detrimental effect on convergence to the native bound structure. (c) 2004 Wiley-Liss, Inc.
16. Probing anomalous couplings using di-Higgs production in electron-proton collisions
Kumar, Mukesh; Ruan, Xifeng; Islam, Rashidul; Cornell, Alan S.; Klein, Max; Klein, Uta; Mellado, Bruce
2017-01-01
A proposed high energy Future Circular Hadron-Electron Collider would provide sufficient energy in a clean environment to probe di-Higgs production. Using this channel we show that the azimuthal angle correlation between the missing transverse energy and the forward jet is a very good probe for the non-standard hhh and hhWW couplings. We give the exclusion limits on these couplings as a function of integrated luminosity at a 95% C.L. using the fiducial cross sections. With appropriate error fitting methodology we find that the Higgs boson self coupling could be measured to be ghhh(1) = 1.00-0.17(0.12)+0.24(0.14) of its expected Standard Model value at √{ s} = 3.5 (5.0) TeV for an ultimate 10 ab-1 of integrated luminosity.
17. Probing electromechanical coupling in collagen at the nanoscale via scanning probe microscopy
Denning, Denise
Electromechanical coupling is ubiquitous in nature and is a functional characteristic in a large range of inorganic and organic materials, including collagen type I -- a fibrous protein abundant in mammals. Understanding the biofunctionality of electromechanical coupling in its linear form -- piezoelectricity, has been a topic of research spanning over seven decades and yet many questions still remain unanswered. Piezoelectricity in bone and connective tissues such as tendon has been investigated at the macroscopic scale since the discovery of piezoelectricity in bone in 1957 and induced currents via the piezoelectric effect have been shown to activate the healing process in tissues under tension. Biological systems consist of complex hierarchical structures which results from a high degree of organization from the macroscale down to the nanoscale. These complex structures, however, make quantitative piezoelectric measurements difficult. Therefore, there exists a need to understand these processes at the individual protein level -- i.e. at the nanoscale. In this thesis, a voltage-modulated form of atomic force microscopy called piezoresponse force microscopy is utilized to investigate the counterpart which is responsible for piezoelectricity in bone and connective tissues -- collagen. The polar properties of collagen were revealed at the nanoscale and were shown to result in a highly complex polar architecture in natural tissue, which is important for understanding tissue development. Shear piezoelectricity was discovered to persist in engineered collagen hydrogels, a study intended to highlight the importance of replicating both structural and functional properties in replacement tissues. The electromechanical properties of collagen type II were investigated which were previously unknown. Collagen type II was shown to be a shear piezoelectric, exhibiting an angle dependence of the piezoelectric signal with cantilever-fibril angle. In addition, the piezoelectric
18. Tamm State-Coupled Emission: Effect of Probe Location and Emission Wavelength
PubMed Central
2015-01-01
We report the effect of the probe location and wavelength on the emission spatial distribution and spectral properties of fluorophores located on structures which display Tamm states. Our structure consists of a one-dimensional photonic crystal (1DPC)—that is, a multilayer structure of alternate high and low refractive index dielectrics—and a thin top silver film. Simulations show the presence of Tamm and surface plasmon modes in the structure. The electric field intensities for the Tamm modes are located mostly in the dielectric layer below the metal film. The corresponding field intensities for the surface plamon modes are located above the metal film in the distal side. Tamm states can be in resonance with the incident light normal or near normal to the surface, within the light line, and can be accessed without the use of a coupling prism or gratings. We investigated the emission spectra and angular distribution of the emission for probes located above and below the metal film to explore the interaction of fluorophores with Tamm plasmons and surface plasmons modes. Three probes were chosen with different overlap of the emission spectra with the Tamm modes. The fluorophores below the metal film coupled predominantly with the Tamm state and displayed more intense and only Tamm state-coupled emission (TSCE). Probes above the metal film display both surface plasmon-coupled emission (SPCE) and Tamm state-coupled emission. In contrast to SPCE, which shows only KR, P-polarized emission, the Tamm states can display both S- and P-polarized emission and can be populated using both RK and KR illuminations. The TSCE angle is highly sensitive to wavelength, which suggests the use of Tamm structures to provide both directional emission and wavelength dispersion. The combination of plasmonic and photonic structures with directional emission close to surface normal offers the opportunities for new design formats for clinical testing, portable devices, and other
19. Theory of pump-probe experiments of metallic metamaterials coupled to the gain medium
SciTech Connect
Huang, Zhixiang; Koschny, Thomas; Soukoulis, Costas
2012-05-04
We establish a new approach for pump-probe simulations of metallic metamaterials coupled to the gain materials. It is of vital importance to understand the mechanism of the coupling of metamaterials with the gain medium. Using a four-level gain system, we have studied light amplification of arrays of metallic split-ring resonators with a gain layer underneath. We find that the differential transmittance ΔT/T can be negative for split-ring resonators on the top of the gain substrate, which is not expected, and ΔT/T is positive for the gain substrate alone. These simulations agree with pump-probe experiments and can help to design new experiments to compensate for the losses of metamaterials.
20. Near-Field Infrared Pump-Probe Imaging of Surface Phonon Coupling in Boron Nitride Nanotubes.
PubMed
Gilburd, Leonid; Xu, Xiaoji G; Bando, Yoshio; Golberg, Dmitri; Walker, Gilbert C
2016-01-21
Surface phonon modes are lattice vibrational modes of a solid surface. Two common surface modes, called longitudinal and transverse optical modes, exhibit lattice vibration along or perpendicular to the direction of the wave. We report a two-color, infrared pump-infrared probe technique based on scattering type near-field optical microscopy (s-SNOM) to spatially resolve coupling between surface phonon modes. Spatially varying couplings between the longitudinal optical and surface phonon polariton modes of boron nitride nanotubes are observed, and a simple model is proposed.
1. Fluorescent probe environment and the structural and charge changes in energy coupling of mitochondrial membranes.
PubMed
Chance, B
1970-10-01
The use of fluorescent probes to give continuous readouts of the structural states of mitochondrial membranes during energy coupling seems a logical extension of their use in the study of protein structural changes. A clear correlation of the probes' fluorescence characteristics with the acquisition of energy coupling can be demonstrated in fragmented and natural membrane using 1-anilinonaphthalene-8-sulfonate (ANS) and ethidium bromide respectively. The present contribution attempts to bring together contemporary viewpoints of this and other laboratories and the recent experimental data and give some detailed information on probe environment and on the structural or charge changes occurring upon energization. The energy-dependent region of the membrane is located at an aqueous interface between an outer layer of proteins (presumably cytochromes) and the membrane permeability barrier; the aromatic portion of ANS appears to be located in the lipid phase and the sulfonic acid group in the aqueous phase. The aqueous phase is probably a structured water region near paramagnetic membrane components such as cytochrome. Membrane energization arising from altered redox potential changes of cytochromes (b(T)) is communicated to the water structure through altered structural states of the hemoproteins, causing a decreased volume of the structured water region and increased interaction with the paramagnetic components in the energized state. Attendant alterations of protonic equilibria of membrane components induce both local and transmembrane changes in charge distribution, with consequent movements of ions, including the probe molecules themselves.
2. The induced motion of a probe coupled to a bath with random resettings
Maes, Christian; Thiery, Thimothée
2017-10-01
We consider a probe linearly coupled to the center of mass of a nonequilibrium bath. We study the induced motion on the probe for a model where a resetting mechanism is added to an overdamped bath dynamics with quadratic potentials. The fact that each bath particle is at random times reset to a fixed position is known for optimizing diffusive search strategies, but here stands for the nonequilibrium aspect of the bath. In the large bath scaling limit the probe is governed by an effective Langevin equation. Depending on the value of the parameters, there appear three regimes: (i) an equilibrium-like regime but with a reduced friction and an increased effective temperature; (ii) a regime where the noise felt by the probe is continuous but non-Gaussian and exhibits fat-tails; (iii) a regime with a non-Gaussian noise exhibiting power-law distributed jumps. The model thus represents an exactly solvable case for the origin of nonequilibrium probe dynamics.
3. Probing the Higgs Couplings to Photons in h→4l at the LHC
DOE PAGES
Chen, Yi; Harnik, Roni; Vega-Morales, Roberto
2014-11-01
We explore the sensitivity of the Higgs decay to four leptons, the so-called golden channel, to higher dimensional loop-induced couplings of the Higgs boson tomore » $ZZ$, $$Z\\gamma$$, and $$\\gamma\\gamma$$, allowing for general CP mixtures. The larger standard model tree level coupling $$hZ^\\mu Z_\\mu$$ is the dominant "background" for the loop induced couplings. However this large background interferes with the smaller loop induced couplings, enhancing the sensitivity. We perform a maximum likelihood analysis based on analytic expressions of the fully differential decay width for $$h\\to 4\\ell$$ ($$4\\ell \\equiv 2e2\\mu, 4e, 4\\mu$$) including all interference effects. We find that the spectral shapes induced by Higgs couplings to photons are particularly different than the $$hZ^\\mu Z_\\mu$$ background leading to enhanced sensitivity to these couplings. We show that even if the $$h\\to\\gamma\\gamma$$ and $$h\\to 4\\ell$$ rates agree with that predicted by the Standard Model, the golden channel has the potential to probe both the CP nature as well as the overall sign of the Higgs coupling to photons well before the end of high-luminosity LHC running ($$\\sim$$3 ab$$^{-1}$$).« less
4. Probing the Higgs Couplings to Photons in h→4l at the LHC
SciTech Connect
Chen, Yi; Harnik, Roni; Vega-Morales, Roberto
2014-11-01
We explore the sensitivity of the Higgs decay to four leptons, the so-called golden channel, to higher dimensional loop-induced couplings of the Higgs boson to $ZZ$, $Z\\gamma$, and $\\gamma\\gamma$, allowing for general CP mixtures. The larger standard model tree level coupling $hZ^\\mu Z_\\mu$ is the dominant "background" for the loop induced couplings. However this large background interferes with the smaller loop induced couplings, enhancing the sensitivity. We perform a maximum likelihood analysis based on analytic expressions of the fully differential decay width for $h\\to 4\\ell$ ($4\\ell \\equiv 2e2\\mu, 4e, 4\\mu$) including all interference effects. We find that the spectral shapes induced by Higgs couplings to photons are particularly different than the $hZ^\\mu Z_\\mu$ background leading to enhanced sensitivity to these couplings. We show that even if the $h\\to\\gamma\\gamma$ and $h\\to 4\\ell$ rates agree with that predicted by the Standard Model, the golden channel has the potential to probe both the CP nature as well as the overall sign of the Higgs coupling to photons well before the end of high-luminosity LHC running ($\\sim$3 ab$^{-1}$).
5. Probing the Higgs couplings to photons in h→4ℓ at the LHC.
PubMed
Chen, Yi; Harnik, Roni; Vega-Morales, Roberto
2014-11-07
We explore the sensitivity of the Higgs decay to four leptons, the so-called golden channel, to higher dimensional loop-induced couplings of the Higgs boson to ZZ, Zγ, and γγ pairs, allowing for general CP mixtures. The larger standard model tree level coupling hZ(μ)Z(μ) is the dominant "background" for the loop-induced couplings. However, this large background interferes with the smaller loop-induced couplings, enhancing the sensitivity. We perform a maximum likelihood analysis based on analytic expressions of the fully differential decay width for h→4ℓ (4ℓ≡2e2μ,4e,4μ), including all interference effects. We find that the spectral shapes induced by Higgs couplings to photons are particularly different than the hZ(μ)Z(μ) background leading to enhanced sensitivity to these couplings. We show that even if the h→γγ and h→4ℓ rates agree with that predicted by the standard model, the golden channel has the potential to probe both the CP nature as well as the overall sign of the Higgs coupling to photons well before the end of a high-luminosity LHC.
6. Exclusive radiative Higgs decays as probes of light-quark Yukawa couplings
König, Matthias; Neubert, Matthias
2015-08-01
We present a detailed analysis of the rare exclusive Higgs boson decays into a single vector meson and a photon and investigate the possibility of using these processes to probe the light-quark Yukawa couplings. We work with an effective Lagrangian with modified Higgs couplings to account for possible new-physics effects in a model-independent way. The h → Vγ decay rate is governed by the destructive interference of two amplitudes, one of which involves the Higgs coupling to the quark anti-quark pair inside the vector meson. We derive this amplitude at next-to-leading order in α s using QCD factorization, including the resummation of large logarithmic corrections and accounting for the effects of flavor mixing. The high factorization scale μ ˜ m h ensures that our results are rather insensitive to the hadronic parameters characterizing the light-cone distribution amplitude of the vector meson. The second amplitude arises from the loop-induced effective hγγ * and hγZ * couplings, where the off-shell gauge boson converts into the vector meson. We devise a strategy to eliminate theoretical uncertainties related to this amplitude to almost arbitrary precision. This opens up the possibility to probe for modifications of the c- and b-quark Yukawa couplings and modifications of the s-quark Yukawa coupling in the high-luminosity LHC run. In particular, we show that measurements of the ratios Br( h → Υ( nS) γ)/Br( h → γγ) and can provide complementary information on the real and imaginary parts of the b-quark Yukawa coupling. More accurate measurements would be possible at a future 100 TeV proton-proton collider.
7. Development of (trimethylsilyl)ethyl ester protected enolates and applications in palladium-catalyzed enantioselective allylic alkylation: intermolecular cross-coupling of functionalized electrophiles.
PubMed
Reeves, Corey M; Behenna, Douglas C; Stoltz, Brian M
2014-05-02
The development of (trimethylsilyl)ethyl ester protected enolates is reported. The application of this class of compounds in palladium-catalyzed asymmetric allylic alkylation is explored, yielding a variety of α-quaternary six- and seven-membered ketones and lactams. Independent coupling partner synthesis engenders enhanced allyl substrate scope relative to traditional β-ketoester substrates; highly functionalized α-quaternary ketones generated by the union of (trimethylsilyl)ethyl β-ketoesters and sensitive allylic alkylation coupling partners serve to demonstrate the utility of this method for complex fragment coupling.
8. Probe And Enhancement Of SBS Based Phonons In Infrared Fibers Using Waveguide Coupled External Radiation
Yu, Chung; Chong, Yat C.; Fong, Chee K.
1989-06-01
Interaction of GHz and MHz radiation with CO2 laser propagation in a silver halide fiber using sBs based phonon coupling is furthet investigated. The external signal serves to both probe and enhance laser generated sBs phonons in the fiber. Efficient coupling of microwave radiation into the fiber is accomplished by placing the fiber in a hollow metallic waveguide, designed and constructed to transmit the dominant mode in the 0.9-2.0 GHz band. MHz radiation is conveniently coupled into the fiber using the guided microwave radiation as carrier. Phonon emissions from the fiber under CO2 laser pumping are first established on a spectrum analyzer; low frequency generators ale then tuned to match these frequencies and their maximum interaction recorded. Such interactions are systematically studied by monitoring the amplitude and waveform of the reflected and transmitted laser pulse at various power levels and frequencies of the externally coupled radiation. A plot of reflected laser power versus incident laser power reveals a distinct sBs generated phonon threshold. Variouslaunch directions of the GHz and MHz radiation with respect to the direction of laser propagation are realized to verify theory governing sBs interactions. The MHz radiation and its associated phonons in the fiber are convenient tools for probing sBs related phenomenon in infrared fibers.
9. Probing dark excitons in atomically thin semiconductors via near-field coupling to surface plasmon polaritons
Zhou, You; Scuri, Giovanni; Wild, Dominik S.; High, Alexander A.; Dibos, Alan; Jauregui, Luis A.; Shu, Chi; de Greve, Kristiaan; Pistunova, Kateryna; Joe, Andrew Y.; Taniguchi, Takashi; Watanabe, Kenji; Kim, Philip; Lukin, Mikhail D.; Park, Hongkun
2017-09-01
Transition metal dichalcogenide (TMD) monolayers with a direct bandgap feature tightly bound excitons, strong spin-orbit coupling and spin-valley degrees of freedom. Depending on the spin configuration of the electron-hole pairs, intra-valley excitons of TMD monolayers can be either optically bright or dark. Dark excitons involve nominally spin-forbidden optical transitions with a zero in-plane transition dipole moment, making their detection with conventional far-field optical techniques challenging. Here, we introduce a method for probing the optical properties of two-dimensional materials via near-field coupling to surface plasmon polaritons (SPPs). This coupling selectively enhances optical transitions with dipole moments normal to the two-dimensional plane, enabling direct detection of dark excitons in TMD monolayers. When a WSe2 monolayer is placed on top of a single-crystal silver film, its emission into near-field-coupled SPPs displays new spectral features whose energies and dipole orientations are consistent with dark neutral and charged excitons. The SPP-based near-field spectroscopy significantly improves experimental capabilities for probing and manipulating exciton dynamics of atomically thin materials, thus opening up new avenues for realizing active metasurfaces and robust optoelectronic systems, with potential applications in information processing and communication.
10. Probing dark excitons in atomically thin semiconductors via near-field coupling to surface plasmon polaritons.
PubMed
Zhou, You; Scuri, Giovanni; Wild, Dominik S; High, Alexander A; Dibos, Alan; Jauregui, Luis A; Shu, Chi; De Greve, Kristiaan; Pistunova, Kateryna; Joe, Andrew Y; Taniguchi, Takashi; Watanabe, Kenji; Kim, Philip; Lukin, Mikhail D; Park, Hongkun
2017-09-01
Transition metal dichalcogenide (TMD) monolayers with a direct bandgap feature tightly bound excitons, strong spin-orbit coupling and spin-valley degrees of freedom. Depending on the spin configuration of the electron-hole pairs, intra-valley excitons of TMD monolayers can be either optically bright or dark. Dark excitons involve nominally spin-forbidden optical transitions with a zero in-plane transition dipole moment, making their detection with conventional far-field optical techniques challenging. Here, we introduce a method for probing the optical properties of two-dimensional materials via near-field coupling to surface plasmon polaritons (SPPs). This coupling selectively enhances optical transitions with dipole moments normal to the two-dimensional plane, enabling direct detection of dark excitons in TMD monolayers. When a WSe2 monolayer is placed on top of a single-crystal silver film, its emission into near-field-coupled SPPs displays new spectral features whose energies and dipole orientations are consistent with dark neutral and charged excitons. The SPP-based near-field spectroscopy significantly improves experimental capabilities for probing and manipulating exciton dynamics of atomically thin materials, thus opening up new avenues for realizing active metasurfaces and robust optoelectronic systems, with potential applications in information processing and communication.
11. Prospective real-time head motion correction using inductively coupled wireless NMR probes.
PubMed
Sengupta, Saikat; Tadanki, Sasidhar; Gore, John C; Welch, E Brian
2014-10-01
Head motion continues to be a major source of artifacts and data quality degradation in MRI. The goal of this work was to develop and demonstrate a novel technique for prospective, 6 degrees of freedom (6DOF) rigid body motion estimation and real-time motion correction using inductively coupled wireless nuclear magnetic resonance (NMR) probe markers. Three wireless probes that are inductively coupled with the scanner's RF setup serve as fiducials on the subject's head. A 12-ms linear navigator module is interleaved with the imaging sequence for head position estimation, and scan geometry is updated in real time for motion compensation. Flip angle amplification in the markers allows the use of extremely small navigator flip angles (∼1°). A novel algorithm is presented to identify marker positions in the absence of marker specific receive channels. Motion correction is demonstrated in high resolution 2D and 3D gradient recalled echo experiments in a phantom and humans. Significant improvement of image quality is demonstrated in phantoms and human volunteers under different motion conditions. A novel real-time 6DOF head motion correction technique based on wireless NMR probes is demonstrated in high resolution imaging at 7 Tesla. Copyright © 2013 Wiley Periodicals, Inc.
12. Prospective Real Time Head Motion Correction Using Inductively Coupled Wireless NMR Probes
PubMed Central
Sengupta, Saikat; Tadanki, Sasidhar; Gore, John C.; Welch, E. Brian
2014-01-01
Purpose Head motion continues to be a major source of artifacts and data quality degradation in MRI. The goal of this work was to develop and demonstrate a novel technique for prospective, 6 degrees of freedom (6DOF) rigid body motion estimation and real time motion correction using inductively coupled wireless nuclear magnetic resonance (NMR) probe markers. Methods Three wireless probes that are inductively coupled with the scanner’s RF setup serve as fiducials on the subject’s head. A 12 ms linear navigator module is interleaved with the imaging sequence for head position estimation, and scan geometry is updated in real time for motion compensation. Flip angle amplification in the markers allows the use of extremely small navigator flip angles (~1°). A novel algorithm is presented to identify marker positions in the absence of marker specific receive channels. The method is demonstrated for motion correction in 1 mm3 gradient recalled echo experiments in phantoms and humans. Results Significant improvement of image quality is demonstrated in phantoms and human volunteers under different motion conditions. Conclusion A novel real time 6 DOF head motion correction technique based on wireless NMR probes is demonstrated in high resolution imaging at 7 Tesla. PMID:24243810
13. Coupled Ablation, Heat Conduction, Pyrolysis, Shape Change and Spallation of the Galileo Probe
NASA Technical Reports Server (NTRS)
Milos, Frank S.; Chen, Y.-K.; Rasky, Daniel J. (Technical Monitor)
1995-01-01
The Galileo probe enters the atmosphere of Jupiter in December 1995. This paper presents numerical methodology and detailed results of our final pre-impact calculations for the heat shield response. The calculations are performed using a highly modified version of a viscous shock layer code with massive radiation coupled with a surface thermochemical ablation and spallation model and with the transient in-depth thermal response of the charring and ablating heat shield. The flowfield is quasi-steady along the trajectory, but the heat shield thermal response is dynamic. Each surface node of the VSL grid is coupled with a one-dimensional thermal response calculation. The thermal solver includes heat conduction, pyrolysis, and grid movement owing to surface recession. Initial conditions for the heat shield temperature and density were obtained from the high altitude rarefied-flow calculations of Haas and Milos. Galileo probe surface temperature, shape, mass flux, and element flux are all determined as functions of time along the trajectory with spallation varied parametrically. The calculations also estimate the in-depth density and temperature profiles for the heat shield. All this information is required to determine the time-dependent vehicle mass and drag coefficient which are necessary inputs for the atmospheric reconstruction experiment on board the probe.
14. Fiber optic probe having fibers with endfaces formed for improved coupling efficiency and method using same
DOEpatents
ORourke, P.E.; Livingston, R.R.
1995-03-28
A fiber optic probe is disclosed for detecting scattered light, with transmitting and receiving fibers having slanted ends and bundled together to form a bevel within the tip of the probe. The probe comprises a housing with a transparent window across its tip for protecting the transmitting and receiving fibers held therein. The endfaces of the fibers are slanted, by cutting, polishing and the like, so that they lie in a plane that is not perpendicular to the longitudinal axis of the respective fiber. The fibers are held in the tip of the probe using an epoxy and oriented so that lines normal to the slanted endfaces are divergent with respect to one another. The epoxy, which is positioned substantially between the transmitting and receiving fibers, is tapered so that the transmitting fiber, the epoxy and the receiving fiber form a bevel of not more than 20 degrees. The angled fiber endfaces cause directing of the light cones toward each other, resulting in improved light coupling efficiency. A light absorber, such as carbon black, is contained in the epoxy to reduce crosstalk between the transmitting and receiving fibers. 3 figures.
15. Fiber optic probe having fibers with endfaces formed for improved coupling efficiency and method using same
DOEpatents
O'Rourke, Patrick E.; Livingston, Ronald R.
1995-01-01
A fiber optic probe for detecting scattered light, with transmitting and receiving fibers having slanted ends and bundled together to form a bevel within the tip of the probe. The probe comprises a housing with a transparent window across its tip for protecting the transmitting and receiving fibers held therein. The endfaces of the fibers are slanted, by cutting, polishing and the like, so that they lie in a plane that is not perpendicular to the longitudinal axis of the respective fiber. The fibers are held in the tip of the probe using an epoxy and oriented so that lines normal to the slanted endfaces are divergent with respect to one another. The epoxy, which is positioned substantially between the transmitting and receiving fibers, is tapered so that the transmitting fiber, the epoxy and the receiving fiber form a bevel of not more than 20 degrees. The angled fiber endfaces cause directing of the light cones toward each other, resulting in improved light coupling efficiency. A light absorber, such as carbon black, is contained in the epoxy to reduce crosstalk between the transmitting and receiving fibers.
16. Probing the flat band of optically trapped spin-orbital-coupled Bose gases using Bragg spectroscopy
Li, Wu; Chen, Lei; Chen, Zhu; Hu, Ying; Zhang, Zhidong; Liang, Zhaoxin
2015-02-01
Motivated by recent efforts in creating flat bands in ultracold atomic systems, we investigate how to probe a flat band in an optically trapped spin-orbital-coupled Bose-Einstein condensate using Bragg spectroscopy. We find that the excitation spectrum and the dynamic structure factor of the condensate are dramatically altered when the band structure exhibits various levels of flatness. In particular, when the band exhibits perfect flatness around the band minima corresponding to a near-infinite effective mass, a quadratic dispersion emerges in the low-energy excitation spectrum; in sharp contrast, for the opposite case when an ordinary band is present, the familiar linear dispersion arises. Such linear-to-quadratic crossover in the low-energy spectrum presents a striking manifestation of the transition of an ordinary band into a flat band, thereby allowing a direct probe of the flat band by using Bragg spectroscopy.
17. Remote estimation of phycocyanin (PC) for inland waters coupled with YSI PC fluorescence probe.
PubMed
Song, Kaishan; Li, Lin; Tedesco, Lenore; Clercin, Nicole; Hall, Bob; Li, Shuai; Shi, Kun; Liu, Dawei; Sun, Ying
2013-08-01
Nuisance cyanobacterial blooms degrade water resources through accelerated eutrophication, odor generation, and production of toxins that cause adverse effects on human health. Quick and effective methods for detecting cyanobacterial abundance in drinking water supplies are urgently needed to compliment conventional laboratory methods, which are costly and time consuming. Hyperspectral remote sensing can be an effective approach for rapid assessment of cyanobacterial blooms. Samples (n=250) were collected from five drinking water sources in central Indiana (CIN), USA, and South Australia (SA), which experience nuisance cyanobacterial blooms. In situ hyperspectral data were used to develop models by relating spectral signal with handheld fluorescence probe (YSI 6600 XLM-SV) measured phycocyanin (PC in cell/ml), a proxy pigment unique for indicating the presence of cyanobacteria. Three-band model (TBM), which is effective for chlorophyll-a estimates, was tuned to quantify cyanobacteria coupled with the PC probe measured cyanobacteria. As a comparison, two band model proposed by Simis et al. (Limnol Oceanogr, 50(11): 237-245, 2005; denoted as SM05) was paralleled to evaluate TBM model performance. Our observation revealed a high correlation between measured and estimated PC for SA dataset (R (2) =0.96; range: 534-20,200 cell/ml) and CIN dataset (R (2) =0.88; range: 1,300-44,500 cell/ml). The potential of this modeling approach for imagery data were assessed by simulated ESA/Centinel3/OLCI spectra, which also resulted in satisfactory performance with the TBM for both SA dataset (RMSE % =26.12) and CIN dataset (RMSE % =34.49). Close relationship between probe-measured PC and laboratory measured cyanobacteria biovolume was observed (R (2) =0.93, p<0.0001) for the CIN dataset, indicating a stable performance for PC probe. Based on our observation, field spectroscopic measurement coupled with PC probe measurements can provide quantitative cyanobacterial bloom
18. Nanoscale resolved infrared probing of crystal structure and of plasmon-phonon coupling.
PubMed
Huber, A; Ocelic, N; Taubner, T; Hillenbrand, R
2006-04-01
We show that slight variations of a crystal lattice cause significant spectral modifications of phonon-polariton resonant near-field interaction between polar semiconductor crystals and a scanning metal tip. Exploiting the effect for near-field imaging a SiC polytype boundary, we establish infrared mapping of crystal structure and crystal defects at 20 nm spatial resolution (lambda/500). By spectroscopic probing of doped SiC polytypes, we find that phonon-polariton resonant near-field interaction is also sensitive to electronic properties due to plasmon-phonon coupling in the crystals.
19. Intermolecular interactions in solid benzene.
PubMed
Kearley, G J; Johnson, M R; Tomkinson, J
2006-01-28
The lattice dynamics and molecular vibrations of benzene and deuterated benzene crystals are calculated from force constants derived from density-functional theory (DFT) calculations and compared with measured inelastic neutron-scattering spectra. A very small change (0.5%) in lattice parameter is required to obtain real lattice-mode frequencies across the Brillouin zone. There is a strong coupling between wagging and breathing modes away from the zone center. This coupling and sensitivity to cell size arises from two basic interactions. Firstly, comparatively strong interactions that hold the benzene molecules together in layers. These include an intermolecular interaction in which H atoms of one molecule link to the center of the aromatic ring of a neighboring molecule. The layers are held to each other by weaker interactions, which also have components that hold molecules together within a layer. Small changes in the lattice parameters change this second type of interaction and account for the changes to the lattice dynamics. The calculations also reveal a small auxetic effect in that elongation of the crystal along the b axis leads to an increase in internal pressure in the ac plane, that is, elongation in the b direction induces expansion in the a and c directions.
20. Probing ultrafast energy transfer between excitons and plasmons in the ultrastrong coupling regime
Balci, Sinan; Kocabas, Coskun; Küçüköz, Betül; Karatay, Ahmet; Akhüseyin, Elif; Gul Yaglioglu, H.; Elmali, Ayhan
2014-08-01
We investigate ultrafast energy transfer between excitons and plasmons in ensembles of core-shell type nanoparticles consisting of metal core covered with a concentric thin J-aggregate (JA) shell. The high electric field localization by the Ag nanoprisms and the high oscillator strength of the JAs allow us to probe this interaction in the ultrastrong plasmon-exciton coupling regime. Linear and nonlinear optical properties of the coupled system have been measured using transient absorption spectroscopy revealing that the hybrid system shows half-plasmonic and half-excitonic properties. The tunability of the nanoprism plasmon resonance provides a flexible platform to study the dynamics of the hybrid state in a broad range of wavelengths.
1. Using magnetic coupling to implement 1H, 19F, 13C experiments in routine high resolution NMR probes
Bowyer, Paul; Finnigan, Jim; Marsden, Brian; Taber, Bob; Zens, Albert
2015-12-01
We report in this paper the design of 1H, 19F, 13C circuitry using magnetic coupling which can do on demand experiments where one of the three nuclei is observed and the other two are decoupled. The implementation of this circuitry in routine NMR probes is compared with capacitive coupling methods where it was found that by using magnetic coupling the performance of the routine NMR probe was not impacted by the addition of this circuitry. It is surmised that using this type of circuitry would be highly desirable for those chemists doing routine 19F NMR.
2. Transient absorption probe of intermolecular triplet excimer of naphthalene in fluid solutions: Identification of the species based on comparison to the intramolecular triplet excimers of covalently-linked dimers
SciTech Connect
Wang, X.; Kofron, W.G.; Kong, S.; Rajesh, C.S.; Modarelli, D.A.; Lim, E.C.
2000-02-24
The authors report here the observation of the laser-induced transient absorption spectrum of intermolecular triplet excimers of naphthalene in fluid solution. This assignment is confirmed by comparison to the transient absorption spectra of the intramolecular triplet excimers of covalently linked dimers of naphthalene and quinoxaline.
3. Desensitization of metastable intermolecular composites
SciTech Connect
Busse, James R.; Dye, Robert C.; Foley, Timothy J.; Higa, Kelvin T.; Jorgensen, Betty S.; Sanders, Victor E.; Son, Steven F.
2011-04-26
A method to substantially desensitize a metastable intermolecular composite material to electrostatic discharge and friction comprising mixing the composite material with an organic diluent and removing enough organic diluent from the mixture to form a mixture with a substantially putty-like consistency, as well as a concomitant method of recovering the metastable intermolecular composite material.
4. Alignment, vibronic level splitting, and coherent coupling effects on the pump-probe polarization anisotropy.
PubMed
Smith, Eric R; Jonas, David M
2011-04-28
The pump-probe polarization anisotropy is computed for molecules with a nondegenerate ground state, two degenerate or nearly degenerate excited states with perpendicular transition dipoles, and no resonant excited-state absorption. Including finite pulse effects, the initial polarization anisotropy at zero pump-probe delay is predicted to be r(0) = 3/10 with coherent excitation. During pulse overlap, it is shown that the four-wave mixing classification of signal pathways as ground or excited state is not useful for pump-probe signals. Therefore, a reclassification useful for pump-probe experiments is proposed, and the coherent anisotropy is discussed in terms of a more general transition dipole and molecular axis alignment instead of experiment-dependent ground- versus excited-state pathways. Although coherent excitation enhances alignment of the transition dipole, the molecular axes are less aligned than for a single dipole transition, lowering the initial anisotropy. As the splitting between excited states increases beyond the laser bandwidth and absorption line width, the initial anisotropy increases from 3/10 to 4/10. Asymmetric vibrational coordinates that lift the degeneracy control the electronic energy gap and off-diagonal coupling between electronic states. These vibrations dephase coherence and equilibrate the populations of the (nearly) degenerate states, causing the anisotropy to decay (possibly with oscillations) to 1/10. Small amounts of asymmetric inhomogeneity (2 cm(-1)) cause rapid (130 fs) suppression of both vibrational and electronic anisotropy beats on the excited state, but not vibrational beats on the ground electronic state. Recent measurements of conical intersection dynamics in a silicon napthalocyanine revealed anisotropic quantum beats that had to be assigned to asymmetric vibrations on the ground electronic state only [Farrow, D. A.; J. Chem. Phys. 2008, 128, 144510]. Small environmental asymmetries likely explain the observed absence
5. The triple Higgs coupling: a new probe of low-scale seesaw models
Baglio, Julien; Weiland, Cédric
2017-04-01
The measure of the triple Higgs coupling is one of the major goals of the high-luminosity run of the CERN Large Hadron Collider (HL-LHC) as well as the future colliders, either leptonic such as the International Linear Collider (ILC) or hadronic such as the 100 TeV Future Circular Collider in hadron-hadron mode (FCC-hh). We have recently proposed this observable as a test of neutrino mass generating mechanisms in a regime where heavy sterile neutrino masses are hard to be probed otherwise. We present in this article a study of the one-loop corrected triple Higgs coupling in the inverse seesaw model, taking into account all relevant constraints on the model. This is the first study of the impact on the triple Higgs coupling of heavy neutrinos in a realistic, renormalizable neutrino mass model. We obtain deviations from the Standard Model as large as to ˜ +30% that are at the current limit of the HL-LHC sensitivity, but would be clearly visible at the ILC or at the FCC-hh.
6. Langmuir probe study of an inductively coupled magnetic-pole-enhanced helium plasma
Younus, Maria; Rehman, N. U.; Shafiq, M.; Naeem, M.; Zaka-ul-Islam, M.; Zakaullah, M.
2017-03-01
This study reports the effects of RF power and filling gas pressure variation on the plasma parameters, including the electron number density n e , electron temperature T e , plasma potential V p , skin depth δ, and electron energy probability functions (EEPFs) in a low-pressure inductively coupled helium plasma source with magnetic pole enhancement. An RF compensated Langmuir probe is used to measure these plasma parameters. It is observed that the electron number density increases with both the RF power and the filling gas pressure. Conversely, the electron temperature decreases with increasing RF power and gas pressure. It is also noted that, at low RF powers and gas pressures, the EEPFs are non-Maxwellian, while at RF powers of ≥50 W, they evolve into a Maxwellian distribution. The dependences of the skin depth and plasma potential on the RF power are also studied and show a decreasing trend.
7. On the coupling efficiency of metal-coated near-field probes.
PubMed
Alvarez, L; Xiao, M
2001-05-01
A theory for calculating the optical transmission of nanometric circular apertures in a thick and perfectly conducting screen coated upon an optical fibre has been developed. The theory is intended for the study of near-field probes and differs from other well known theories of radiation transmission through subwavelength apertures in the fact that it includes an optical fibre, making possible to distinguish which part of energy passing through the aperture is effectively coupled in guided modes. In a scanning near-field optical microscope tip, only the guided modes will reach the photodetector, and will contribute to the final read-out. A numerical calculation for different fibre parameters, to show the dependence of the guided transmission coefficient for the guided modes of the fibre, is presented. The agreement of the theory with earlier calculations where the optical fibre is not included is emphasized.
8. Beyond Higgs couplings: Probing the Higgs with angular observables at future e$^{+}$e$^{-}$ colliders
SciTech Connect
Craig, Nathaniel; Gu, Jiayin; Liu, Zhen; Wang, Kechen
2016-03-09
Here, we study angular observables in the ${e}^{+}{e}^{-}\\to ZH\\to {\\ell}^{+}{\\ell}^{-}b\\overline{b}$ channel at future circular e$^{+}$ e$^{-}$ colliders such as CEPC and FCC-ee. Taking into account the impact of realistic cut acceptance and detector effects, we forecast the precision of six angular asymmetries at CEPC (FCC-ee) with center-of-mass energy $\\sqrt{s}=240$ GeV and 5 (30) ab$^{-1}$ integrated luminosity. We then determine the projected sensitivity to a range of operators relevant for he Higgs-strahlung process in the dimension-6 Higgs EFT. Our results show that angular observables provide complementary sensitivity to rate measurements when constraining various tensor structures arising from new physics. We further find that angular asymmetries provide a novel means of both probing BSM corrections to the HZγ coupling and constraining the “blind spot” in indirect limits on supersymmetric scalar top partners.
9. Soft Particle Spectrometer, Langmuir Probe, and Data Analysis for Aerospace Magnetospheric/Thermospheric Coupling Rocket Program
NASA Technical Reports Server (NTRS)
Sharber, J. R.; Frahm, R. A.; Scherrer, J. R.
1997-01-01
Under this grant two instruments, a soft particle spectrometer and a Langmuir probe, were refurbished and calibrated, and flown on three instrumented rocket payloads as part of the Magnetosphere/Thermosphere Coupling program. The flights took place at the Poker Flat Research Range on February 12, 1994 (T(sub o) = 1316:00 UT), February 2, 1995 (T(sub o) = 1527:20 UT), and November 27, 1995 (T(sub o) = 0807:24 UT). In this report the observations of the particle instrumentation flown on all three of the flights are described, and brief descriptions of relevant geophysical activity for each flight are provided. Calibrations of the particle instrumentation for all ARIA flights are also provided.
10. Probing the function of ionotropic and G protein-coupled receptors in surface-confined membranes.
PubMed
Danelon, Christophe; Terrettaz, Samuel; Guenat, Olivier; Koudelka, Milena; Vogel, Horst
2008-10-01
This article reports on recent electrical and optical techniques for investigating cellular signaling reactions in artificial and native membranes immobilized on solid supports. The first part describes the formation of planar artificial lipid bilayers on gold electrodes, which reveal giga-ohm electrical resistance and the insertion and characterization of ionotropic receptors therein. These membranes are suited to record a few or even single ion channels by impedance spectroscopy. Such tethered membranes on planar arrays of microelectrodes offer mechanically robust, long-lasting measuring devices to probe the influence of different chemistries on biologically important ionotropic receptors and therefore will have a future impact to probe the function of channel proteins in basic science and in biosensor applications. In a second part, we present complementary approaches to form inside-out native membrane sheets that are immobilized on micrometer-sized beads or across submicrometer-sized holes machined in a planar support. Because the native membrane sheets are plasma membranes detached from live cells, these approaches offer a unique possibility to investigate cellular signaling processes, such as those mediated by ionotropic or G protein-coupled receptors, with original composition of lipids and proteins.
11. Langmuir Probe Measurements of Inductively Coupled Plasmas in CF4/Ar/O2 Mixtures
NASA Technical Reports Server (NTRS)
Rao, M. V. V. S.; Meyyappan, M.; Sharma, S. P.
2000-01-01
Fluorocarbon gases, such as CF4, and their mixtures are widely used in contemporary low-pressure and high-density plasma processing techniques. In such plasmas Langmuir probe is one of the most commonly employed diagnostic techniques to obtain electron number density (ne), electron temperature (Te), electron energy distribution function (EEDF), mean electron energy (Ee), ion number density (ni), and plasma potential (Vp). In this paper we report probe data for planar inductively coupled plasmas in CF4/O2/Ar mixtures. By varying the relative concentrations in the mixture, radial profiles of ne, ni, Te, Ee, Vp, EEDF were measured in the mid-plane of the plasma at 10 mTorr and 20 mTorr of gas pressures, and 200 W and 300 W of RF powers. Data show that ne and ni decrease with increase of CF4 content and decrease of gas-pressure but they increase with increase of RF-power, whereas Vp increases with decrease of gas-pressure and remains independent of RF-power. However, they all peak at the center of the plasma and decrease towards the edge while Te follows the other way and increases a little with increase of power. The measured EEDFs exhibit Druyvesteyn-like distribution at all pressures and powers. Data are analyzed and will be presented.
12. Probing Single Molecules with a Tunable Femtosecond Laser Coupled RF-STM
Cao, Weicai
Scanning Tunneling Microscope (STM) has become a powerful tool in nanoscience for imaging, manipulation and electronic spectroscopy. STM inelastic electron tunneling spectroscopy (IETS) first achieved chemical identification of molecular species by characterizing vibrational energies. Recently, with the STM itProbe and H2 rotational spectromicroscopy, molecular structure and chemical bonds are observed with the STM. Despite these successes in spatial resolution, various efforts have been made to combine fs laser with STM to overcome the temporal resolution limitation of STM, there is so far no clear evidence of simultaneous fs and A resolution. Electronic properties of organic molecules are of central importance to applications such as molecular electronics, organic LEDs, and solar cells. Properties of these molecules can be probed by the scanning tunneling microscope (STM) at the single molecule level and with sub-A spatial resolution. The molecular orbital of 4, 7-Di ([2, 20-bithiophen]-5-yl) benzo[c] [1, 2, 5] thiadiazole (4T-BTD) with intramolecular donor-acceptor-donor sites is probed with the electronic state dI/dV imaging and H2 rotational and vibrational spectromicroscopy. 1, 4-Phenylene Diisocyanide (PDI) is probed by imaging with a CO-terminated tip and H2. PDI can self-assemble on noble metal surfaces to form nanostructures, which could have potential applications in molecular electronics and catalysis. Further combination of a RF-STM with a tunable femtosecond laser enables the investigation of light-molecule interactions. In this dissertation, efforts are spent to setup a new tunable fs laser (220 nm˜1040 nm) to couple with the RF-STM. The effects of the femtosecond laser are followed by detecting photo induced electron emission and photochemistry. A new double lock-in technique is applied to detect the weak laser-induced signal in the tunneling regime. To sharpen the energy width and increase the lifetime of the excited states of molecules, thin
13. Probing Dynamically Tunable Localized Surface Plasmon Resonances of Film-Coupled Nanoparticles by Evanescent Wave Excitation
PubMed Central
Mock, Jack J.; Hill, Ryan T.; Tsai, Yu-Ju; Chilkoti, Ashutosh; Smith, David R.
2012-01-01
The localized surface plasmon resonance (LSPR) spectrum associated with a gold nanoparticle (NP) coupled to a gold film exhibits extreme sensitivity to the nano-gap region where the fields are tightly localized. The LSPR of an ensemble of film-coupled NPs can be observed using an illumination scheme similar to that used to excite the surface plasmon resonance (SPR) of a thin metallic film; however, in the present system, the light is used to probe the highly sensitive distance-dependent LSPR of the gaps between NPs and film rather than the delocalized SPR of the film. We show that the SPR and LSPR spectral contributions can be readily distinguished, and we compare the sensitivities of both modes to displacements in the average gap between a collection of NPs and the gold film. The distance by which the NPs are suspended in solution above the gold film is fixed via a thin molecular spacer layer, and can be further modulated by subjecting the NPs to a quasistatic electric field. The observed LSPR spectral shifts triggered by the applied voltage can be correlated with Angstrom scale displacements of the NPs, suggesting the potential for chip-scale or flow-cell plasmonic nanoruler devices with extreme sensitivity. PMID:22429053
14. The intermolecular interaction in D2 - CX4 and O2 - CX4 (X = F, Cl) systems: Molecular beam scattering experiments as a sensitive probe of the selectivity of charge transfer component.
PubMed
Cappelletti, David; Falcinelli, Stefano; Pirani, Fernando
2016-10-07
Gas phase collisions of a D2 projectile by CF4 and by CCl4 targets have been investigated with the molecular beam technique. The integral cross section, Q, has been measured for both collisional systems in the thermal energy range and oscillations due to the quantum "glory" interference have been resolved in the velocity dependence of Q. The analysis of the measured Q(v) data provided novel information on the anisotropic potential energy surfaces of the studied systems at intermediate and large separation distances. The relative role of the most relevant types of contributions to the global interaction has been characterized. Extending the phenomenology of a weak intermolecular halogen bond, the present work demonstrates that while D2 - CF4 is basically bound through the balance between size (Pauli) repulsion and dispersion attraction, an appreciable intermolecular bond stabilization by charge transfer is operative in D2 - CCl4. We also demonstrated that the present analysis is consistent with that carried out for the F((2)P)-D2 and Cl((2)P)-D2 systems, previously characterized by scattering experiments performed with state-selected halogen atom beams. A detailed comparison of the present and previous results on O2-CF4 and O2-CCl4 systems pinpointed striking differences in the behavior of hydrogen and oxygen molecules when they interact with the same partner, mainly due to the selectivity of the charge transfer component. The present work contributes to cast light on the nature and role of the intermolecular interaction in prototype systems, involving homo-nuclear diatoms and symmetric halogenated molecules.
15. The intermolecular interaction in D2 - CX4 and O2 - CX4 (X = F, Cl) systems: Molecular beam scattering experiments as a sensitive probe of the selectivity of charge transfer component
Cappelletti, David; Falcinelli, Stefano; Pirani, Fernando
2016-10-01
Gas phase collisions of a D2 projectile by CF4 and by CCl4 targets have been investigated with the molecular beam technique. The integral cross section, Q, has been measured for both collisional systems in the thermal energy range and oscillations due to the quantum "glory" interference have been resolved in the velocity dependence of Q. The analysis of the measured Q(v) data provided novel information on the anisotropic potential energy surfaces of the studied systems at intermediate and large separation distances. The relative role of the most relevant types of contributions to the global interaction has been characterized. Extending the phenomenology of a weak intermolecular halogen bond, the present work demonstrates that while D2 - CF4 is basically bound through the balance between size (Pauli) repulsion and dispersion attraction, an appreciable intermolecular bond stabilization by charge transfer is operative in D2 - CCl4. We also demonstrated that the present analysis is consistent with that carried out for the F(2P)-D2 and Cl(2P)-D2 systems, previously characterized by scattering experiments performed with state-selected halogen atom beams. A detailed comparison of the present and previous results on O2-CF4 and O2-CCl4 systems pinpointed striking differences in the behavior of hydrogen and oxygen molecules when they interact with the same partner, mainly due to the selectivity of the charge transfer component. The present work contributes to cast light on the nature and role of the intermolecular interaction in prototype systems, involving homo-nuclear diatoms and symmetric halogenated molecules.
16. Comparison of various interpretation methods of the electric probe measurements in inductively coupled Ar and O{sub 2} plasmas
SciTech Connect
Woo Seo, Min; Keun Bae, Min; Chung, T. H.
2014-02-15
In low-pressure inductively coupled argon and oxygen discharges, the plasma density and electron temperature and the electron energy distribution function (EEDF) were obtained by using a cylindrical electric probe. The plasma densities were determined by various methods to interpret the probe current-voltage characteristic curve: the EEDF integration, the electron saturation current, the ion current at the floating potential, and the orbital-motion-limited (OML) ion current. Quite a good agreement exists between the plasma densities determined by various classical methods. Although the probe technique has some limitation in electronegative plasmas, the plasma densities determined from OML theory compare well with those measured by the ion saturation current at the floating potential in the oxygen discharges. In addition, the EEDFs of inductively coupled Ar and oxygen plasmas are observed to be nearly Maxwellian at the pressure range of 1-40 mTorr.
17. Phase Pinning by EPR Probe in Biphenyl Doped with Naphthalene
Veron, A.; Emery, J.
1997-08-01
The naphthalene Electronic Paramagnetic Resonance probe used to study the phase transitions in biphenyl does not account for the plane wave modulation of the incommensurate phase II. Its EPR spectra yields a phase distribution which looks like a “multi-soliton regime”. Moreover, the splitting between the edge singularities is not symmetrical, in contradiction with a linear one. This behaviour is not exhibited by the phenanthrene EPR probe whose spectra account well enough for the plane wave modulation with a linear coupling to the order parameter. To analyse the defect behaviour of the probe, we first introduce a coupling between the probe and the modulation wave and determine the phase distribution within the phenomenological Landau theory. Furthermore, a calculation based on intermolecular interaction is performed in order to describe the microscopic origin of this distribution and is applied to naphthalene and phenanthrene molecular probes.
18. Fabry-perot modes enhanced pump-probe coupling in gold micro-disk patterned ruby thin film
Kumari, Satchi; Khare, Alika; Gupta, Reema; Tomar, Monika; Gupta, Vinay
2017-10-01
Enhanced pump-probe coupling has been experimentally observed in epitaxial Ruby thin film patterned with equidistant gold micro-disks (∼100 μm), as compared to pure Ruby film. This has been attributed to Fabry-Perot and surface plasmon modes in Ruby/gold film. In case of S polarized pump and probe beam, Fabry-Perot modes leads to a two-wave mixing gain of ∼1.35. Moreover gain was ∼1.62 in P-polarization case, it has been attributed to coupling of Fabry-Perot and surface plasmon modes. Enhanced coupling for P-polarization can lead to improved nonlinear response in the thin film geometry. It can find applications in thin film based compact photonic devices.
19. Tracking G-protein-coupled receptor activation using genetically encoded infrared probes.
PubMed
Ye, Shixin; Zaitseva, Ekaterina; Caltabiano, Gianluigi; Schertler, Gebhard F X; Sakmar, Thomas P; Deupi, Xavier; Vogel, Reiner
2010-04-29
Rhodopsin is a prototypical heptahelical family A G-protein-coupled receptor (GPCR) responsible for dim-light vision. Light isomerizes rhodopsin's retinal chromophore and triggers concerted movements of transmembrane helices, including an outward tilting of helix 6 (H6) and a smaller movement of H5, to create a site for G-protein binding and activation. However, the precise temporal sequence and mechanism underlying these helix rearrangements is unclear. We used site-directed non-natural amino acid mutagenesis to engineer rhodopsin with p-azido-l-phenylalanine residues incorporated at selected sites, and monitored the azido vibrational signatures using infrared spectroscopy as rhodopsin proceeded along its activation pathway. Here we report significant changes in electrostatic environments of the azido probes even in the inactive photoproduct Meta I, well before the active receptor state was formed. These early changes suggest a significant rotation of H6 and movement of the cytoplasmic part of H5 away from H3. Subsequently, a large outward tilt of H6 leads to opening of the cytoplasmic surface to form the active receptor photoproduct Meta II. Thus, our results reveal early conformational changes that precede larger rigid-body helix movements, and provide a basis to interpret recent GPCR crystal structures and to understand conformational sub-states observed during the activation of other GPCRs.
20. Experimental study of spatial nonuniformities in 100 MHz capacitively coupled plasma using optical probe
SciTech Connect
Volynets, V. N.; Ushakov, A. G.; Sung, D.; Tolmachev, Y. N.; Pashkovsky, V. G.; Lee, J. B.; Kwon, T. Y.; Jeong, K. S.
2008-05-15
Plasma spatial nonuniformities in the 100 MHz rf driven capacitively coupled reactor used for reactive ion etching of 300 mm substrates were experimentally studied using a linear scanning optical emission spectroscopy probe. Radial profiles of plasma emission intensity were measured both in argon and fluorocarbon-containing gas mixtures in the pressure interval of 10-80 mTorr and the rf power range of 500-1250 W. It was demonstrated that the plasma emission profiles strongly depend on the working gas composition and pressure. The profiles have a bell-like shape at pressures about 10 mTorr for all gases. As the pressure increases, the profile shape becomes more complex with the central and peripheral peaks, and the amplitudes of the peaks strongly depend on the working gas composition. It is suggested that the emission profiles show plasma spatial nonuniformities that can influence the etching rate profiles obtained with such systems. According to the existing theoretical models, the most probable reasons for these plasma nonuniformities are charged particle radial diffusion at low pressures (about 10 mTorr), as well as the standing wave and skin and edge effects at higher pressures. Using the experimental emission profiles, the working conditions have been found that allow one to achieve the most uniform plasma for discharges in argon and fluorocarbon-containing gas mixtures.
1. Probing Protein Surface with a Solvent Mimetic Carbene Coupled to Detection by Mass Spectrometry
Gómez, Gabriela E.; Mundo, Mariana R.; Craig, Patricio O.; Delfino, José M.
2012-01-01
Much knowledge into protein folding, ligand binding, and complex formation can be derived from the examination of the nature and size of the accessible surface area (SASA) of the polypeptide chain, a key parameter in protein science not directly measurable in an experimental fashion. To this end, an ideal chemical approach should aim at exerting solvent mimicry and achieving minimal selectivity to probe the protein surface regardless of its chemical nature. The choice of the photoreagent diazirine to fulfill these goals arises from its size comparable to water and from being a convenient source of the extremely reactive methylene carbene (:CH2). The ensuing methylation depends primarily on the solvent accessibility of the polypeptide chain, turning it into a valuable signal to address experimentally the measurement of SASA in proteins. The superb sensitivity and high resolution of modern mass spectrometry techniques allows us to derive a quantitative signal proportional to the extent of modification (EM) of the sample. Thus, diazirine labeling coupled to electrospray mass spectrometry (ESI-MS) detection can shed light on conformational features of the native as well as non-native states, not easily addressable by other methods. Enzymatic fragmentation of the polypeptide chain at the level of small peptides allows us to locate the covalent tag along the amino acid sequence, therefore enabling the construction of a map of solvent accessibility. Moreover, by subsequent MS/MS analysis of peptides, we demonstrate here the feasibility of attaining amino acid resolution in defining the target sites.
2. Beyond Higgs couplings: Probing the Higgs with angular observables at future e$$^{+}$$e$$^{-}$$ colliders
DOE PAGES
Craig, Nathaniel; Gu, Jiayin; Liu, Zhen; ...
2016-03-09
Here, we study angular observables in themore » $${e}^{+}{e}^{-}\\to ZH\\to {\\ell}^{+}{\\ell}^{-}b\\overline{b}$$ channel at future circular e$$^{+}$$ e$$^{-}$$ colliders such as CEPC and FCC-ee. Taking into account the impact of realistic cut acceptance and detector effects, we forecast the precision of six angular asymmetries at CEPC (FCC-ee) with center-of-mass energy $$\\sqrt{s}=240$$ GeV and 5 (30) ab$$^{-1}$$ integrated luminosity. We then determine the projected sensitivity to a range of operators relevant for he Higgs-strahlung process in the dimension-6 Higgs EFT. Our results show that angular observables provide complementary sensitivity to rate measurements when constraining various tensor structures arising from new physics. We further find that angular asymmetries provide a novel means of both probing BSM corrections to the HZγ coupling and constraining the “blind spot” in indirect limits on supersymmetric scalar top partners.« less
3. Direct observation of intermolecular interactions mediated by hydrogen bonding
SciTech Connect
De Marco, Luigi; Reppert, Mike; Thämer, Martin; Tokmakoff, Andrei
2014-07-21
Although intermolecular interactions are ubiquitous in physicochemical phenomena, their dynamics have proven difficult to observe directly, and most experiments rely on indirect measurements. Using broadband two-dimensional infrared spectroscopy (2DIR), we have measured the influence of hydrogen bonding on the intermolecular vibrational coupling between dimerized N-methylacetamide molecules. In addition to strong intramolecular coupling between N–H and C=O oscillators, cross-peaks in the broadband 2DIR spectrum appearing upon dimerization reveal strong intermolecular coupling that changes the character of the vibrations. In addition, dimerization changes the effects of intramolecular coupling, resulting in Fermi resonances between high and low-frequency modes. These results illustrate how hydrogen bonding influences the interplay of inter- and intramolecular vibrations, giving rise to correlated nuclear motions and significant changes in the vibrational structure of the amide group. These observations have direct impact on modeling and interpreting the IR spectra of proteins. In addition, they illustrate a general approach to direct molecular characterization of intermolecular interactions.
4. Perturbation analyses of intermolecular interactions
Koyama, Yohei M.; Kobayashi, Tetsuya J.; Ueda, Hiroki R.
2011-08-01
Conformational fluctuations of a protein molecule are important to its function, and it is known that environmental molecules, such as water molecules, ions, and ligand molecules, significantly affect the function by changing the conformational fluctuations. However, it is difficult to systematically understand the role of environmental molecules because intermolecular interactions related to the conformational fluctuations are complicated. To identify important intermolecular interactions with regard to the conformational fluctuations, we develop herein (i) distance-independent and (ii) distance-dependent perturbation analyses of the intermolecular interactions. We show that these perturbation analyses can be realized by performing (i) a principal component analysis using conditional expectations of truncated and shifted intermolecular potential energy terms and (ii) a functional principal component analysis using products of intermolecular forces and conditional cumulative densities. We refer to these analyses as intermolecular perturbation analysis (IPA) and distance-dependent intermolecular perturbation analysis (DIPA), respectively. For comparison of the IPA and the DIPA, we apply them to the alanine dipeptide isomerization in explicit water. Although the first IPA principal components discriminate two states (the α state and PPII (polyproline II) + β states) for larger cutoff length, the separation between the PPII state and the β state is unclear in the second IPA principal components. On the other hand, in the large cutoff value, DIPA eigenvalues converge faster than that for IPA and the top two DIPA principal components clearly identify the three states. By using the DIPA biplot, the contributions of the dipeptide-water interactions to each state are analyzed systematically. Since the DIPA improves the state identification and the convergence rate with retaining distance information, we conclude that the DIPA is a more practical method compared with the
5. Langmuir Probe and Mass Spectroscopic Measurements in Inductively Coupled CF4 Plasmas
NASA Technical Reports Server (NTRS)
Rao, M. V. V. S.; Sharma, Surendra; Cruden, B. A.; Meyyappan, M.
2001-01-01
Abstract Electron and ion energy distribution functions and other plasma parameters such as plasma potential (V(sub p)) , electron temperature (T(sub e)), and electron and ion number densities (n (sub e) and n(sub i)) in low pressure CF4 plasmas have been measured. The experiments were conducted in a GEC cell using an inductively coupled plasma (ICP) device powered by a 13.56 MHz radio-frequency (rf) power source. The measurements were made at 300 W of input rf power at 10, 30 and 50 mTorr gas pressures. Langmuir probe measurements suggest that n(sub e), n(sub i) and V(sub p) remain constant over 60% of the central electrode area, beyond which they decrease. Within the limits of experimental error (+/- 0.25 eV), T(sub e) remains nearly constant over the electrode area. T(sub e) and V(sub p) increase with a decrease in pressure. n(sub e) and n(sub i) are not affected as significantly as T(sub e) or V(sub p) by variation in the gas pressure. The electron energy distribution function (EEDF) measurements indicate a highly non-Maxwellian plasma. CF3+ is the most dominant ion product of the plasma, followed by CF2+ and CF+. The concentrations of CF2+ and CF+ are much larger than that is possible from direct electron impact ionization of the parent gas. The cross-section data suggest that the direct electron impact ionization of fragment neutrals and negative ion production by electron attachment may be responsible for increase of the minor ions.
6. Probing protein surface with a solvent mimetic carbene coupled to detection by mass spectrometry.
PubMed
Gómez, Gabriela E; Mundo, Mariana R; Craig, Patricio O; Delfino, José M
2012-01-01
Much knowledge into protein folding, ligand binding, and complex formation can be derived from the examination of the nature and size of the accessible surface area (SASA) of the polypeptide chain, a key parameter in protein science not directly measurable in an experimental fashion. To this end, an ideal chemical approach should aim at exerting solvent mimicry and achieving minimal selectivity to probe the protein surface regardless of its chemical nature. The choice of the photoreagent diazirine to fulfill these goals arises from its size comparable to water and from being a convenient source of the extremely reactive methylene carbene (:CH(2)). The ensuing methylation depends primarily on the solvent accessibility of the polypeptide chain, turning it into a valuable signal to address experimentally the measurement of SASA in proteins. The superb sensitivity and high resolution of modern mass spectrometry techniques allows us to derive a quantitative signal proportional to the extent of modification (EM) of the sample. Thus, diazirine labeling coupled to electrospray mass spectrometry (ESI-MS) detection can shed light on conformational features of the native as well as non-native states, not easily addressable by other methods. Enzymatic fragmentation of the polypeptide chain at the level of small peptides allows us to locate the covalent tag along the amino acid sequence, therefore enabling the construction of a map of solvent accessibility. Moreover, by subsequent MS/MS analysis of peptides, we demonstrate here the feasibility of attaining amino acid resolution in defining the target sites. © American Society for Mass Spectrometry, 2011
7. Probing biased/partial agonism at the G protein-coupled A(2B) adenosine receptor.
PubMed
Gao, Zhan-Guo; Balasubramanian, Ramachandran; Kiselev, Evgeny; Wei, Qiang; Jacobson, Kenneth A
2014-08-01
G protein-coupled A(2B) adenosine receptor (AR) regulates numerous important physiological functions, but its activation by diverse A(2B)AR agonists is poorly profiled. We probed potential partial and/or biased agonism in cell lines expressing variable levels of endogenous or recombinant A(2B)AR. In cAMP accumulation assays, both 5'-substituted NECA and C2-substituted MRS3997 are full agonists. However, only 5'-substituted adenosine analogs are full agonists in calcium mobilization, ERK1/2 phosphorylation and β-arrestin translocation. A(2B)AR overexpression in HEK293 cells markedly increased the agonist potency and maximum effect in cAMP accumulation, but less in calcium and ERK1/2. A(2B)AR siRNA silencing was more effective in reducing the maximum cAMP effect of non-nucleoside agonist BAY60-6583 than NECA's. A quantitative 'operational model' characterized C2-substituted MRS3997 as either balanced (cAMP accumulation, ERK1/2) or strongly biased agonist (against calcium, β-arrestin). N⁶-substitution biased against ERK1/2 (weakly) and calcium and β-arrestin (strongly) pathways. BAY60-6583 is ERK1/2-biased, suggesting a mechanism distinct from adenosine derivatives. BAY60-6583, as A(2B)AR antagonist in MIN-6 mouse pancreatic β cells expressing low A(2B)AR levels, induced insulin release. This is the first relatively systematic study of structure-efficacy relationships of this emerging drug target. Published by Elsevier Inc.
8. Surface phonon coupling within boron nitride resolved by a novel near-field infrared pump-probe imaging technique
Gilburd, Leonid; Xu, Xiaoji G.; de Beer, Sissi; Bando, Yoshio; Golberg, Dmitri; Walker, Gilbert C.
2016-09-01
The excitation of surface phonon-polariton (SPhP) modes in polar materials using scattering type near-field optical microscopy (s-SNOM) has recently become an area of interest because of its potential for application as naturally occurring meta-materials and in low-loss energy transfer. Within this area, hexagonal boron nitride (h-BN) and boron nitride nanotubes (BNNTs) are the primary structures under investigation. Here we present pump-probe continuous wave (CW) scattering-type scanning near-field optical microscopy (s-SNOM) - a novel two color pump-probe infrared technique which uses two continuous wave tunable light sources and is based on s-SNOM. The technique allows us to spatially resolve coupling of the longitudinal optical and surface phonon polariton modes in BNNTs. However, no similar coupling is observed in two-dimensional h-BN crystals.
9. User's guide for the computer code COLTS for calculating the coupled laminar and turbulent flow over a Jovian entry probe
NASA Technical Reports Server (NTRS)
Kumar, A.; Graeves, R. A.
1980-01-01
A user's guide for a computer code 'COLTS' (Coupled Laminar and Turbulent Solutions) is provided which calculates the laminar and turbulent hypersonic flows with radiation and coupled ablation injection past a Jovian entry probe. Time-dependent viscous-shock-layer equations are used to describe the flow field. These equations are solved by an explicit, two-step, time-asymptotic finite-difference method. Eddy viscosity in the turbulent flow is approximated by a two-layer model. In all, 19 chemical species are used to describe the injection of carbon-phenolic ablator in the hydrogen-helium gas mixture. The equilibrium composition of the mixture is determined by a free-energy minimization technique. A detailed frequency dependence of the absorption coefficient for various species is considered to obtain the radiative flux. The code is written for a CDC-CYBER-203 computer and is capable of providing solutions for ablated probe shapes also.
10. A IR Diode Laser Spectroscopic Study of Adsorption and Intermolecular Interactions on Stepped Metal Surfaces: Carbon Monoxide on Vicinal COPPER(100)
Borguet, Eric Urbain
The kinetics of elementary surface processes, intermolecular interactions and stepped surfaces are intrinsic scientific interest, as well as being important to industrially relevant processes such as catalysis. A novel time-resolved surface sensitive technique, Transient Diode Laser Infrared Reflection-Absorption Spectroscopy, has been developed to investigate adsorption on stepped metal surfaces. The IR spectra display anomalous intensity behavior resulting in a minority step-CO species accounting for a disproportionate fraction of the spectral intensity. A model has been elaborated which successfully accounts for, and simulates, the observed spectra. This enables site specific concentrations to be determined, even in the presence of strong dynamic-dipole coupling. These methods allow the spectroscopy, kinetics and intermolecular interactions of CO on a stepped Cu(100) surface to be probed. In particular, it has been possible to observe a dynamic equilibrium between CO adsorbed at step and terrace sites and to investigate the kinetics of site exchange on this surface. The IR spectra also reveal the nature and range of the intermolecular interactions and the local order which results. The CO/Cu(100) system is characterized by repulsive first and second nearest neighbor interactions. As a consequence, the adsorbates adopt a configuration which maximizes the intermolecular distance. Additionally, a non-resonant, broadband, adsorbate induced change in surface reflectivity is observed both in the IR and visible. This linear dependence of this signal with coverage provides a simple method of determining total adsorbed CO concentration.
11. An IR diode laser spectroscopic study of adsorption and intermolecular interactions on stepped metal surfaces: CO on vicinal Cu(100). [IR (infrared)
SciTech Connect
Borguet, E.R.
1993-01-01
The kinetics of elementary surface processes, intermolecular interactions and stepped surfaces are intrinsic scientific interest, as well as being important to industrially relevant processes such as catalysis. A novel time-resolved surface sensitive technique. Transient Diode Laser Infrared Reflection-Absorption Spectroscopy, has been developed to investigate adsorption on stepped metal surfaces. The IR spectra display anomalous intensity behavior resulting in a minority step-CO species accounting for a disporportionate fraction of the spectral intensity. A model has been elaborated which successfully accounts for, and simulates, the observed spectra. This enables site specific concentrations to be determined, even in the presence of strong dynamic-dipole coupling. These methods allow the spectroscopy, kinetics and intermolecular interactions of CO on a stepped Cu(100) surface to be probed. In particular, it has been possible to observe a dynamic equilibrium between CO adsorbed at step and terrace sites and to investigate the kinetics of site exchanges on this surface. The IR spectra also reveal the nature and range of the intermolecular interactions and the local order which results. The CO/Cu(100) system is characterized by repulsive first and second nearest neighbor interactions. As a consequence, the adsorbates adopt a configuration which maximizes the intermolecular distance. Additionally, a non-resonant, broadband, adsorbate induced change in surface reflectivity is observed both in the IR and visible. This linear dependence of this signal with coverage provides a simple method of determining total absorbed CO concentration.
12. A flow microslot NMR probe coupled with a capillary isotachophoresis system exhibits improved properties compared to solenoid designs.
PubMed
Gogiashvili, Mikheil; Telfah, Ahmad; Lambert, Jörg; Hergenröder, Roland
2017-03-01
We report on the hyphenation of capillary isotachophoresis (cITP) separations with online nuclear magnetic resonance (NMR) detection using a planar microslot waveguide probe design. While cITP is commonly coupled with a solenoidal microcoil NMR probe, the structural information provided is limited by broad resonances and poor spectral resolution due to the magnetic field created by the separation current. The microslot probe design described herein allows the separation capillary to be oriented parallel to the static magnetic field, B 0, eliminating the spectral broadening produced by the secondary magnetic field induced by the separation current. This allows high-resolution nuclear magnetic resonance spectra of the charged analytes to be obtained in online mode, whereas conventional solenoidal capillary NMR designs must resort to the stopped flow mode. The potential of the microslot probe for hyphenated electrophoretic separations is demonstrated by performing cITP focusing and online NMR detection of the (1)H NMR spectrum of a system containing spermine and aniline. Graphical Abstract High resolution NMR spectra in flow capillarelectrophoretic separations with microslot NMR probe.
13. Preferences of rhodamine coupled (aminoalkyl)-piperazine probes towards Hg(II) ion and their FRET mediated signaling.
PubMed
2013-08-14
The metal ion induced absorption and emission signaling pattern of rhodamine coupled bis-(aminopropyl)-piperazine (1-3) and (aminoethyl)-piperazine (4) based probes evaluated in MeCN as well as in an MeCN-H2O binary mixture medium revealed that these probes exhibit optical signaling perturbations to a varying extent in MeCN, however, their complexation induced signaling could be tuned selectively towards Hg(II) in the presence of an aqueous component in the solvent medium where competitive interactions such as metal-probe interactions and hydration of metal ions play the determining factor to induce aqueous promoted Hg(II) selectivity. Attachment of another fluorophore (anthracene and nitrobenzofurazan moieties in 2 and 3 respectively) at the other end of the rhodamine coupled bis-(aminopropyl)-piperazine receptor enabled these probes to facilitate a complexation induced fluorescence resonance energy transfer (FRET) from the excited fluorophore to the ring-opened rhodamine along with contributions through operative PET inhibition and rhodamine delactonization processes. The enhancement in absorption transition of these probes at ~557 nm upon selective Hg(II)-complexation and consequent colourless to pink colour change in the solution imply a chromogenic signaling pattern whereas simultaneous fluorescence amplification and/or FRET initiation lead to fluorogenic signaling to facilitate detection at lower concentration. The Hg(II)-selective photo-physical spectral modulation in the presence of other competitive metal ions, and their reversible dual channel signaling pattern under the action of counter anions or chelating agents such as EDTA or ethylenediamine establish the potential of these probes for highly selective, sensitive and reversible 'OFF-ON-OFF' detection of Hg(II). The complexation induced optical signaling pattern of probes with a propyl-linker in their receptor (1-3) in comparison with that of 4 consisting of an ethyl-spacer indicate that signaling
14. Franck—Condon breakdown as a probe of continuum coupling in molecular photoionization
Kakar, Sandeep; Choi, Heung Cheun; Poliakoff, E. D.
1992-03-01
We have measured vibrational branching ratios for 4σ -1 photoionization of CO in order to characterize continuum channel coupling. The results indicate that the shape resonance in the 5σ→ɛσ channel influences vibrational branching ratios of the 4σ -1 channel via continuum coupling, and the data illustrate how continuum channel coupling affects molecular photoionization dynamics.
15. Simulated imaging of intermolecular bonds using high throughput real-space density functional calculations
Lee, Alex; Kim, Minjung; Chelikowsky, James
2015-03-01
Recent experimental noncontact atomic force microscopy (AFM) studies on 8-hydroxyquinoline (8-hq) assemblies have imaged distinct lines between molecules that are thought to represent intermolecular bonding. To aid the interpretation of these images, we calculate simulated AFM images of an 8-hq dimer with a CO functionalized tip using a real-space pseudopotential formalism. We examine the effects of Pauli repulsion and tip probe relaxation as explanations for the enhanced resolution that resolves these intermolecular force lines. Our study aims to compute ab initio real-space images of intermolecular interactions.
16. Non-Covalent Fluorescent Labeling of Hairpin DNA Probe Coupled with Hybridization Chain Reaction for Sensitive DNA Detection.
PubMed
Song, Luna; Zhang, Yonghua; Li, Junling; Gao, Qiang; Qi, Honglan; Zhang, Chengxiao
2016-04-01
An enzyme-free signal amplification-based assay for DNA detection was developed using fluorescent hairpin DNA probes coupled with hybridization chain reaction (HCR). The hairpin DNAs were designed to contain abasic sites in the stem moiety. Non-covalent labeling of the hairpin DNAs was achieved when a fluorescent ligand was bound to the abasic sites through hydrogen bonding with the orphan cytosine present on the complementary strand, accompanied by quench of ligand fluorescence. As a result, the resultant probes, the complex formed between the hairpin DNA and ligand, showed almost no fluorescence. Upon hybridization with target DNA, the probe underwent a dehybridization of the stem moiety containing an abasic site. The release of ligand from the abasic site to the solution resulted in an effective fluorescent enhancement, which can be used as a signal. Compared with a sensing system without HCR, a 20-fold increase in the sensitivity was achieved using the sensing system with HCR. The fluorescent intensity of the sensing system increased with the increase in target DNA concentration from 0.5 nM to 100 nM. A single mismatched target ss-DNA could be effectively discriminated from complementary target DNA. Genotyping of a G/C single-nucleotide polymorphism of polymerase chain reaction (PCR) products was successfully demonstrated with the sensing system. Therefore, integrating HCR strategy with non-covalent labeling of fluorescent hairpin DNA probes provides a sensitive and cost-effective DNA assay.
17. Near-field examination of perovskite-based superlenses and superlens-enhanced probe-object coupling
PubMed Central
Kehr, S.C.; Liu, Y.M.; Martin, L.W.; Yu, P.; Gajek, M.; Yang, S.-Y.; Yang, C.-H.; Wenzel, M.T.; Jacob, R.; von Ribbeck, H.-G.; Helm, M.; Zhang, X.; Eng, L.M.; Ramesh, R.
2011-01-01
A planar slab of negative-index material works as a superlens with sub-diffraction-limited resolution, as propagating waves are focused and, moreover, evanescent waves are reconstructed in the image plane. Here we demonstrate a superlens for electric evanescent fields with low losses using perovskites in the mid-infrared regime. The combination of near-field microscopy with a tunable free-electron laser allows us to address precisely the polariton modes, which are critical for super-resolution imaging. We spectrally study the lateral and vertical distributions of evanescent waves around the image plane of such a lens, and achieve imaging resolution of λ/14 at the superlensing wavelength. Interestingly, at certain distances between the probe and sample surface, we observe a maximum of these evanescent fields. Comparisons with numerical simulations indicate that this maximum originates from an enhanced coupling between probe and object, which might be applicable for multifunctional circuits, infrared spectroscopy and thermal sensors. PMID:21427720
18. Probing subdiffraction limit separations with plasmon coupling microscopy: concepts and applications.
PubMed
Wu, Linxi; Reinhard, Björn M
2014-06-07
Due to their advantageous material properties, noble metal nanoparticles are versatile tools in biosensing and imaging. A characteristic feature of gold and silver nanoparticles is their ability to sustain localized surface plasmons that provide both large optical cross-sections and extraordinary photophysical stability. Plasmon coupling microscopy takes advantage of the beneficial optical properties and utilizes electromagnetic near-field coupling between individual noble metal nanoparticle labels to resolve subdiffraction limit separations in an all-optical fashion. This Tutorial provides an introduction into the physical concepts underlying distance dependent plasmon coupling, discusses potential experimental implementation of plasmon coupling microscopy, and reviews applications in the area of biosensing and imaging.
19. Probing the Dipolar Coupling in a Heterospin Endohedral Fullerene-Phthalocyanine Dyad.
PubMed
Zhou, Shen; Yamamoto, Masanori; Briggs, G Andrew D; Imahori, Hiroshi; Porfyrakis, Kyriakos
2016-02-03
Paramagnetic endohedral fullerenes and phthalocyanine (Pc) complexes are promising building blocks for molecular quantum information processing, for which tunable dipolar coupling is required. We have linked these two spin qubit candidates together and characterized the resulting electron paramagnetic resonance properties, including the spin dipolar coupling between the fullerene spin and the copper spin. Having interpreted the distance-dependent coupling strength quantitatively and further discussed the antiferromagnetic aggregation effect of the CuPc moieties, we demonstrate two ways of tuning the dipolar coupling in such dyad systems: changing the spacer group and adjusting the solution concentration.
20. Probing Subdiffraction Limit Separations with Plasmon Coupling Microscopy: Concepts and Applications
PubMed Central
Wu, Linxi
2014-01-01
Due to their advantageous materials properties, noble metal nanoparticles are versatile tools in biosensing and imaging. A characteristic feature of gold and silver nanoparticles is their ability to sustain localized surface plasmons that provide both large optical cross-sections and extraordinary photophysical stability. Plasmon Coupling Microscopy takes advantage of the beneficial optical properties and utilizes electromagnetic near-field coupling between individual noble metal nanoparticle labels to resolve subdiffraction limit separations in an all-optical fashion. This Tutorial provides an introduction into the physical concepts underlying distance dependent plasmon coupling, discusses potential experimental implementations of Plasmon Coupling Microscopy, and reviews applications in the area of biosensing and imaging. PMID:24390574
1. Facile synthesis of diazido-functionalized biaryl compounds as radioisotope-free photoaffinity probes by Suzuki-Miyaura coupling.
PubMed
Hosoya, Takamitsu; Inoue, Atsushi; Hiramatsu, Toshiyuki; Aoyama, Hiroshi; Ikemoto, Takaaki; Suzuki, Masaaki
2009-03-15
Suzuki-Miyaura coupling of 3-azido-5-(azidomethyl)phenylboronic acid pinacol ester with various aryl bromides affords corresponding diazido-functionalized biaryl compounds in good yields. This approach provides an easy access to radioisotope-free photoaffinity probes possessing biaryl structure. By using this method, we prepared a novel diazido-functionalized dantrolene analog, which showed selective inhibitory effect on physiological Ca(2+) release (PCR) from sarcoplasmic reticulum (SR) in mouse skeletal muscle without affecting Ca(2+)-induced Ca(2+) release (CICR).
2. Pump-probe optical switching in prism-coupled Au :SiO2 nanocomposite waveguide film
Lee, Kyeong-Seok; Lee, Taek-Sung; Kim, Won-Mok; Cho, Sunghun; Lee, Soonil
2007-10-01
The resonance properties due to the surface plasmon excitation of metal nanoparticles make the nanocomposite films promising for various applications such as optical switching devices. In spite of the well-known ultrasensitive operation of optical switches based on a guided wave, the application of nanocomposite film has inherent limitation originating from the excessive optical loss related to the surface plasmon resonance. In this study, we address this problem and present the experimental and theoretical analyses on the pump-probe optical switching in prism-coupled Au(1vol%):SiO2 nanocomposite waveguide film.
3. Intermolecular potentials for hexafluoride gases
SciTech Connect
Aziz, R.A. . Dept. of Physics); Taylor, W.L. )
1989-10-31
Second virial coefficient and viscosity data were used to evaluate intermolecular potential functions proposed in the literature for SF{sub 6}, UF{sub 6}, and WF{sub 6}. It was found that none of the potentials could predict the properties simultaneously. By suitable adjustment of the repulsive wall, we constructed an inverse power (n{minus}7) potential which correlates second virial coefficient and viscosity data at the same time. The best integer repulsive exponent for SF{sub 6} was found to be n = 40, while that for UF{sub 6} and WF{sub 6} was n = 46. 41 refs., 10 figs., 11 tabs.
4. Direct analyte-probed nanoextraction coupled to nanospray ionization-mass spectrometry of drug residues from latent fingerprints.
PubMed
Clemons, Kristina; Wiley, Rachel; Waverka, Kristin; Fox, James; Dziekonski, Eric; Verbeck, Guido F
2013-07-01
Here, we present a method of extracting drug residues from fingerprints via Direct Analyte-Probed Nanoextraction coupled to nanospray ionization-mass spectrometry (DAPNe-NSI-MS). This instrumental technique provides higher selectivity and lower detection limits over current methods, greatly reducing sample preparation, and does not compromise the integrity of latent fingerprints. This coupled to Raman microscopy is an advantageous supplement for location and identification of trace particles. DAPNe uses a nanomanipulator for extraction and differing microscopies for localization of chemicals of interest. A capillary tip with solvent of choice is placed in a nanopositioner. The surface to be analyzed is placed under a microscope, and a particle of interest is located. Using a pressure injector, the solvent is injected onto the surface where it dissolves the analyte, and then extracted back into the capillary tip. The solution is then directly analyzed via NSI-MS. Analyses of caffeine, cocaine, crystal methamphetamine, and ecstasy have been performed successfully.
5. Adsorption kinetics and intermolecular interactions of CO adsorbed on Cu(100) by transient laser reflection-absorption spectroscopy
SciTech Connect
Borguet, E.; Dai, H.L.
1993-12-31
IR and visible transient laser spectroscopic techniques have been developed to probe adsorption/desorption kinetics and intermolecular interactions of the CO/Cu(100) system. Vibrational spectroscopy, in general, can provide information about the nature of species adsorbed on surfaces e.g. chemical identity, site, orientation and concentration. In the presence of a few percent of CO adsorbed at step/defect sites, the spectra of the CO adsorbed on the terrace sites are greatly perturbed through dynamic-dipole coupling. This perturbation depends strongly on the intermolecular distance and the short-range order of the adsorbates. An analysis of this dynamic-dipole coupling reveals that the local arrangement of adsorbates is dominant by repulsive nearest-neighbor interactions. Successful modeling of the observed lineshapes allows the populations at each site to be determined at all coverages. The authors have also observed non-resonant adsorbate induced changes in both the IR and visible reflectance for a number of different adsorbates. This provides a simple and sensitive optical means of studying adsorption and desorption kinetics.
6. Probing the Higgs self coupling via single Higgs production at the LHC
SciTech Connect
Degrassi, G.; Giardino, P. P.; Maltoni, F.; Pagani, D.
2016-12-16
Here, we propose a method to determine the trilinear Higgs self coupling that is alternative to the direct measurement of Higgs pair production total cross sections and differential distributions. Furthermore, the method relies on the effects that electroweak loops featuring an anomalous trilinear coupling would imprint on single Higgs production at the LHC. We first calculate these contributions to all the phenomenologically relevant Higgs production (ggF, VBF, WH, ZH, t$\\bar{t}$ ) and decay (γγ,WW*/ZZ*→ 4f, b$\\bar{b}$,ττ) modes at the LHC and then estimate the sensitivity to the trilinear coupling via a one-parameter fit to the single Higgs measurements at the LHC 8 TeV. We also found that the bounds on the self coupling are already competitive with those from Higgs pair production and will be further improved in the current and next LHC runs.
7. Probing the Higgs self coupling via single Higgs production at the LHC
DOE PAGES
Degrassi, G.; Giardino, P. P.; Maltoni, F.; ...
2016-12-16
Here, we propose a method to determine the trilinear Higgs self coupling that is alternative to the direct measurement of Higgs pair production total cross sections and differential distributions. Furthermore, the method relies on the effects that electroweak loops featuring an anomalous trilinear coupling would imprint on single Higgs production at the LHC. We first calculate these contributions to all the phenomenologically relevant Higgs production (ggF, VBF, WH, ZH, tmore » $$\\bar{t}$$ ) and decay (γγ,WW*/ZZ*→ 4f, b$$\\bar{b}$$,ττ) modes at the LHC and then estimate the sensitivity to the trilinear coupling via a one-parameter fit to the single Higgs measurements at the LHC 8 TeV. We also found that the bounds on the self coupling are already competitive with those from Higgs pair production and will be further improved in the current and next LHC runs.« less
8. Using Spin Observables and Polarizations to Probe Top-Higgs FCNC Couplings at Colliders
Melić, Blaženka; Patra, Monalisa
2017-07-01
We present how the polarized linear colliders can be used, complementary to the LHC, to fully determine the top-Higgs flavor changing neutral current (FCNC) couplings by using produced asymmetries and top spin polarizations and correlations.
9. Probing the Higgs self coupling via single Higgs production at the LHC
Degrassi, G.; Giardino, P. P.; Maltoni, F.; Pagani, D.
2016-12-01
We propose a method to determine the trilinear Higgs self coupling that is alternative to the direct measurement of Higgs pair production total cross sections and differential distributions. The method relies on the effects that electroweak loops featuring an anomalous trilinear coupling would imprint on single Higgs production at the LHC. We first calculate these contributions to all the phenomenologically relevant Higgs production ( ggF, VBF, WH, ZH, toverline{t}H ) and decay (γ γ, W{W}^{ast }/Z{Z}^{ast}to 4f,boverline{b},τ τ ) modes at the LHC and then estimate the sensitivity to the trilinear coupling via a one-parameter fit to the single Higgs measurements at the LHC 8 TeV. We find that the bounds on the self coupling are already competitive with those from Higgs pair production and will be further improved in the current and next LHC runs.
10. Probing crystal packing of uniformly (13)C-enriched powder samples using homonuclear dipolar coupling measurements.
PubMed
Mollica, Giulia; Dekhil, Myriam; Ziarelli, Fabio; Thureau, Pierre; Viel, Stéphane
2015-02-01
The relationship between the crystal packing of powder samples and long-range (13)C-(13)C homonuclear dipolar couplings is presented and illustrated for the case of uniformly (13)C-enriched L-alanine and L-histidine·HCl·H2O. Dipolar coupling measurement is based on the partial reintroduction of dipolar interactions by spinning the sample slightly off-magic-angle, while the coupling of interest for a given spin pair is isolated with a frequency-selective pulse. A cost function is used to correlate the so-derived dipolar couplings to trial crystal structures of the samples under study. This procedure allowed for the investigation of the l-alanine space group and L-histidine·HCl·H2O space group and unit-cell parameters.
11. Thin-layer chromatography and mass spectrometry coupled using proximal probe thermal desorption with electrospray or atmospheric pressure chemica lionization
SciTech Connect
Ovchinnikova, Olga S; Van Berkel, Gary J
2010-01-01
An atmospheric pressure proximal probe thermal desorption sampling method coupled with secondary ionization by electrospray or atmospheric pressure chemical ionization was demonstrated for the mass spectrometric analysis of a diverse set of compounds (dyestuffs, pharmaceuticals, explosives and pesticides) separated on various high-performance thin-layer chromatography plates. Line scans along or through development lanes on the plates were carried out by moving the plate relative to a stationary heated probe positioned close to or just touching the stationary phase surface. Vapors of the compounds thermally desorbed from the surface were drawn into the ionization region of a combined electrospray ionization/atmospheric pressure chemical ionization source where they merged with reagent ions and/or charged droplets from a corona discharge or an electrospray emitter and were ionized. The ionized components were then drawn through the atmospheric pressure sampling orifice into the vacuum region of a triple quadrupole mass spectrometer and detected using full scan, single ion monitoring, or selected reaction monitoring mode. Studies of variable parameters and performance metrics including the proximal probe temperature, gas flow rate into the ionization region, surface scan speed, read-out resolution, detection limits, and surface type are discussed.
12. Biocompatible magnetofluorescent probes: luminescent silicon quantum dots coupled with superparamagnetic iron(III) oxide.
PubMed
Erogbogbo, Folarin; Yong, Ken-Tye; Hu, Rui; Law, Wing-Cheung; Ding, Hong; Chang, Ching-Wen; Prasad, Paras N; Swihart, Mark T
2010-09-28
Luminescent silicon quantum dots (SiQDs) are gaining momentum in bioimaging applications, based on their unique combination of optical properties and biocompatibility. Here, we report the development of a multimodal probe that combines the optical properties of silicon quantum dots with the superparamagnetic properties of iron oxide nanoparticles to create biocompatible magnetofluorescent nanoprobes. Multiple nanoparticles of each type are coencapsulated within the hydrophobic core of biocompatible phospholipid-polyethyleneglycol (DSPE-PEG) micelles. The size distribution and composition of the magnetofluorescent nanoprobes were characterized by transmission electron microscopy (TEM) and energy-dispersive X-ray spectroscopy (EDS). Enhanced cellular uptake of these probes in the presence of a magnetic field was demonstrated in vitro. Their luminescence stability in a prostate cancer tumor model microenvironment was demonstrated in vivo. This paves the way for multimodal silicon quantum-dot-based nanoplatforms for a variety of imaging and delivery applications.
13. Routes to probe Bismuth induced strong-coupling superconductivity in bimetallic BiIn alloys.
PubMed
Gandhi, Ashish Chhaganlal; Wu, Sheng Yun
2017-08-25
We report the observation of strong electron-phonon coupling in intergranular linked BiIn superconductors over an infinite range mediated by low-lying phonons. An enhanced superconducting transition temperature was observed from the magnetization, revealing a main diamagnetic Meissner state below TC(0) = 5.86(1) K and a critical field HC(0) = 1355(15) Oe with an In2Bi phase of the composite sample. The electron-phonon coupling to low lying phonons is found to be the leading mechanism for observed strong-coupling superconductivity in the BiIn system. Our findings suggest that In2Bi is in the strong-coupling region with TC(0) = 5.62(1) K, λep = 1.45, ωln = 45.92 K and α = 2.23. The estimated upper critical field can be well-described by a power law with α value higher than 2, consistent with the strong electron-phonon coupling.
14. Scalar-tensor gravity with scalar-matter direct coupling and its cosmological probe
Kim, Jik-Su; Kim, Chol-Jun
2017-08-01
Making use of the SNIa data set, Nesseris and Perivolaropoulos [Phys. Rev. D 73, 103511 (2006), 10.1103/PhysRevD.73.103511] have found the gravitation constant to evolve in accordance with scalar-tensor gravity. On the other hand, Majerotto et al. [arXiv:astro-ph/0410543] and Guo et al. [Phys. Rev. D 76, 023508 (2007), 10.1103/PhysRevD.76.023508] have found a definite signature of dark energy-dark matter coupling in Einstein tensor gravity background. However, the results of the above works are quite contradictory, so we cannot be sure which of these results should be accepted because both models use different background gravitation. We construct a more inclusive model with scalar-background space-time and scalar-matter couplings. Making use of SNIa(Union) and baryon acoustic oscillation data sets, we made likelihood analyses; the results show that the background gravitation has the tensor characteristics within a confidence level of 68% and the scalar-matter coupling has a rather large positive value δ =±1.01 . As Guo et al. showed, however, inclusion of the cosmic microwave background (CMB) data set in the likelihood analysis significantly reduces the allowed region of the coupling compared to the case without CMB data. Therefore, the value of scalar-matter coupling in this paper could have been estimated too large and the inclusion of CMB data in the next work is expected to yield a more realistic result.
15. Direct coupling of electromembrane extraction to mass spectrometry - Advancing the probe functionality toward measurements of zwitterionic drug metabolites.
PubMed
Rye, Torstein Kige; Fuchs, David; Pedersen-Bjergaard, Stig; Petersen, Nickolaj Jacob
2017-08-29
A triple-flow electromembrane extraction (EME) probe was developed and coupled directly to electrospray-ionization mass spectrometry (ESI-MS). Metabolic reaction mixtures (pH 7.4) containing drug substances and related metabolites were continuously drawn (20 μL/min) into the EME probe in one flow channel, and mixed inside the probe with 7.5 μL min(-1) of 1 M formic acid as make-up flow from a second flow channel. Following this acidification, the drug substances and their related metabolites were continuously extracted by EME at 400 V, across a supported liquid membrane (SLM) comprising 2-nitrophenyl octyl ether (and for some experiments containing 30% triphenyl phosphate (TPP)), and into 20 μL min(-1) of formic acid as acceptor phase, which was introduced through a third flow channel. The acceptor phase was pumped directly to the MS system, and the ion intensity of extracted analytes was followed continuously as function of time. The triple-flow EME probe was used for co-extraction of positively charged parent drugs and their zwitterionic drug metabolites (hydroxyzine and its carboxylic acid metabolite cetirizine; and vortioxetine and its carboxylic acid metabolite Lu AA34443). While the zwitterionic metabolites could not be extracted at pH 7.4, it was shown that by acidifying the sample solution the zwitterionic metabolites could be extracted effectively. Various extraction parameters like make-up flow, extraction voltage and SLM composition were optimized for simultaneous extraction of parent drugs and metabolites. It was found that TPP added to the SLM improved extraction efficiencies of certain drug metabolites. Finally the optimized and characterized triple-flow EME probe was used for online studying the in-vitro metabolism of hydroxyzine and vortioxetine by rat liver microsomes. Due to the automated pre-extraction acidification of the rat liver microsomal solutions, it was possible to continuously monitor formation of the zwitterionic drug
16. Infrared probe of spin-phonon coupling in antiferromagnetic honeycomb lattice compound Li₂MnO₃.
PubMed
Song, Seungjae; Lee, Sanghyun; Jeon, Seyoung; Park, Je-Geun; Moon, S J
2015-12-09
We investigated temperature-dependent infrared-active phonon modes of honeycomb Li2MnO3 which shows an antiferromagnetic transition at T(N) = 36 K. In the far-infrared frequency region, we observed fourteen phonon modes. We obtained the temperature dependence of each phonon mode from the analysis of optical conductivity spectra by using the Lorentz and the Fano-type oscillator models. We found that the resonance frequencies of nine phonon modes showed an anomalous behavior near T(N) that should be attributed to the spin-phonon coupling. We calculated the magnitude of the spin-phonon coupling constant from the shift in the resonance frequencies of the phonon modes below T(N). Our results suggest that Li2MnO3 is weakly frustrated and that spin-phonon coupling plays a role in antiferromagnetic ordering.
17. Coupled plasmon-waveguide resonators: a new spectroscopic tool for probing proteolipid film structure and properties.
PubMed Central
Salamon, Z; Macleod, H A; Tollin, G
1997-01-01
A variant of surface plasmon resonance (SPR) spectroscopy has been developed that involves a coupling of plasmon resonances in a thin metal film and waveguide modes in a dielectric overcoating. This new technique is referred to as coupled plasmon-waveguide resonance (CPWR) spectroscopy. It combines a greatly enhanced sensitivity (due to increased electromagnetic field intensities at the dielectric surface) and spectral resolution (due to decreased resonance linewidths), with the ability to directly measure anisotropies in refractive index and optical absorption coefficient in a dielectric film adsorbed onto the surface of the overcoating. Experimental data obtained with an egg phosphatidylcholine bilayer are presented to document these properties. PMID:9370473
18. Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling
Meinert, F.; Panfil, M.; Mark, M. J.; Lauber, K.; Caux, J.-S.; Nägerl, H.-C.
2015-08-01
We probe the excitation spectrum of an ultracold one-dimensional Bose gas of cesium atoms with a repulsive contact interaction that we tune from the weakly to the strongly interacting regime via a magnetic Feshbach resonance. The dynamical structure factor, experimentally obtained using Bragg spectroscopy, is compared to integrability-based calculations valid at arbitrary interactions and finite temperatures. Our results unequivocally underlie the fact that holelike excitations, which have no counterpart in higher dimensions, actively shape the dynamical response of the gas.
19. Probing extra Yukawa couplings by precision measurements of Higgs boson properties
Hou, Wei-Shu; Kikuchi, Mariko
2017-07-01
If one removes any ad hoc symmetry assumptions, the general two-Higgs-doublet model should have additional Yukawa interactions independent from fermion mass generation, in general involving flavor-changing neutral Higgs couplings. These extra couplings can affect the discovered Higgs boson h through fermion loop contributions. We calculate the renormalized h Z Z coupling at the one-loop level and evaluate the dependence on heavy Higgs boson mass and extra Yukawa coupling ρt t. Precision measurements at future colliders can explore the parameter space, and can give stronger bounds on ρt t than the current bound from flavor experiments. As a side result, we find that if ρt tcos γ <0 , where cos γ is the exotic Higgs component of h , the ρt t-induced top loop contribution cancels against bosonic loop contributions, and one may have alignment without decoupling, namely sin (-γ )≃1 , but exotic scalar bosons could have masses of several hundred GeV.
20. Tetrahedral DNA probe coupling with hybridization chain reaction for competitive thrombin aptasensor.
PubMed
Chen, Ying-Xu; Huang, Ke-Jing; He, Liu-Liu; Wang, Yi-Han
2017-09-15
A novel competitive aptasensor for thrombin detection is developed by using a tetrahedral DNA (T-DNA) probe and hybridization chain reaction (HCR) signal amplification. Sulfur and nitrogen co-doped reduced graphene oxide (SN-rGO) is firstly prepared by a simple reflux method and used for supporting substrate of biosensor. Then, T-DNA probe is modified on the electrode by Au-S bond and a competition is happened between target thrombin and the complementary DNA (cDNA) of aptamer. The aptamer binding to thrombin forms an aptamer-target conjugate and make the cDNA remained, and subsequently hybridizes with the vertical domain of T-DNA. Finally, the cDNAs trigger HCR, which results in a great current response by the catalysis of horseradish peroxidase to the hydrogen peroxide + hydroquinone system. For thrombin detection, the proposed biosensor shows a wide linearity range of 10(-13)-10(-8)M and a low detection limit of 11.6fM (S/N = 3), which is hopeful to apply in biotechnology and clinical diagnosis. Copyright © 2017 Elsevier B.V. All rights reserved.
1. Probing the C P nature of the Higgs coupling in t t ¯ events at the LHC
Amor dos Santos, S.; Fiolhais, M. C. N.; Frederix, R.; Gonçalo, R.; Gouveia, E.; Martins, R.; Onofre, A.; Pease, C. M.; Peixoto, H.; Reigoto, A.; Santos, R.; Silva, J.
2017-07-01
The determination of the C P nature of the Higgs coupling to top quarks is addressed in this paper, using t t ¯h events produced in √{s }=13 TeV proton-proton collisions at the LHC. Dileptonic final states are employed, with two oppositely charged leptons and four jets, corresponding to the decays t →b W+→b ℓ+νℓ,t ¯→b ¯W-→b¯ℓ-ν ¯ℓ, and h →b b ¯. Pure scalar (h =H ), pure pseudoscalar (h =A ), and C P -violating Higgs boson signal events, generated with MadGraph5_aMC@NLO, are fully reconstructed through a kinematic fit. We furthermore generate samples that have both a C P -even and a C P -odd component in the t t ¯h coupling in order to probe the ratio of the two components. New angular distributions of the decay products, as well as C P angular asymmetries, are explored in order to separate the scalar from the pseudoscalar components of the Higgs boson and reduce the contribution from the dominant irreducible background, t t ¯b b ¯. Significant differences between the angular distributions and asymmetries are observed, even after the full kinematic fit reconstruction of the events, allowing to define the best observables for a global fit of the Higgs couplings parameters.
2. Long-lived coherence in pentafluorobenzene as a probe of ππ(*) - πσ(*) vibronic coupling.
PubMed
Hüter, O; Sala, M; Neumann, H; Zhang, S; Studzinski, H; Egorova, D; Temps, F
2016-07-07
The dynamics of pentafluorobenzene after femtosecond laser excitation to the optically bright ππ(*) first excited electronic state have been investigated by femtosecond time-resolved time-of-flight mass spectrometry and femtosecond time-resolved photoelectron imaging spectroscopy. The observed temporal profiles exhibit a bi-exponential decay behavior with a superimposed, long-lived, large-amplitude oscillation with a frequency of νosc = 78-74 cm(-1) and a damping time of τD = 5-2 ps. On the basis of electronic structure and quantum dynamics calculations, the oscillations have been shown to arise due to vibronic coupling between the optically bright ππ(*) state and the energetically close-lying optically dark πσ(*) state. The coupling leads to a pronounced double-well character of the lowest excited adiabatic potential energy surface along several out-of-plane modes of b1 symmetry. The optical electronic excitation initiates periodic wavepacket motion along these modes. In the out-of-plane distorted molecular configuration, the excited state acquires substantial πσ(*) character, thus modulating the ionization probability. The photoelectron spectra and the anisotropy of their angular distribution confirm the periodically changing electronic character. The ionizing probe laser pulse directly maps the coupled electron-nuclear motion into the observed signal oscillations.
3. Desensitization and recovery of metastable intermolecular composites
DOEpatents
Busse, James R [South Fork, CO; Dye, Robert C [Los Alamos, NM; Foley, Timothy J [Los Alamos, NM; Higa, Kelvin T [Ridgecrest, CA; Jorgensen, Betty S [Jemez Springs, NM; Sanders, Victor E [White Rock, NM; Son, Steven F [Los Alamos, NM
2010-09-07
A method to substantially desensitize a metastable intermolecular composite material to electrostatic discharge and friction comprising mixing the composite material with an organic diluent and removing enough organic diluent from the mixture to form a mixture with a substantially putty-like consistency, as well as a concomitant method of recovering the metastable intermolecular composite material.
4. Accurate temperature imaging based on intermolecular coherences in magnetic resonance.
PubMed
Galiana, Gigi; Branca, Rosa T; Jenista, Elizabeth R; Warren, Warren S
2008-10-17
Conventional magnetic resonance methods that provide interior temperature profiles, which find use in clinical applications such as hyperthermic therapy, can develop inaccuracies caused by the inherently inhomogeneous magnetic field within tissues or by probe dynamics, and work poorly in important applications such as fatty tissues. We present a magnetic resonance method that is suitable for imaging temperature in a wide range of environments. It uses the inherently sharp resonances of intermolecular zero-quantum coherences, in this case flipping up a water spin while flipping down a nearby fat spin. We show that this method can rapidly and accurately assign temperatures in vivo on an absolute scale.
5. Probing the CP nature of Higgs couplings in tth events at the LHC
Fiolhais, Miguel; Pease, Christopher; Onofre, Antonio
2017-01-01
The CP nature of the Higgs coupling to top quarks (tth) is studied in proton-proton collision events at a centre-of-mass energy of 13 TeV at the LHC. Pure scalar and pseudo-scalar Higgs boson signal events are generated with MadGraph5_aMC@NLO, and analysed in dileptonic final states with two oppositely charged leptons and four jets. These events are fully reconstructed by applying a kinematic fit. As a result, new angular distributions of the decay products as well as CP angular asymmetries are explored to separate the scalar from the pseudo-scalar components of the Higgs boson, which allows to reduce the contribution from the dominant irreducible background, ttbb. In addition, significant differences between the angular distributions and asymmetries are observed, providing new observables for a global fit of the Higgs couplings parameters.
6. Nonplanar 4-Jets in Quarkonium Decays as a Probe for 3-Gluon Coupling
Muta, T.; Niuya, T.
1982-11-01
We calculate the acoplanarity (à la Fox-Wolfram) distribution of 4 jets generated by orthoquarkonium decays: 3S1(Qbar{Q})→ GGGG, GGqbar{q}. The result shows that the deviation from planar event due to 4 jets is significantly large showing the importance of the effect of 3-gluon couplings in quantum chromodynamics. The average acoplanarity is calculated to be =(0.45+0.153Nf)αs/π with Nf the number of flavors of produced quarks and αs the QCD coupling strength. As a by-product we calculated the decay rate of the parapositronium into 4 photons which results in Γ4γ=(0.0139±0.0001)α7 me with me the electron mass.
7. Probing the interlayer coupling of twisted bilayer MoS2 using photoluminescence spectroscopy.
PubMed
Huang, Shengxi; Ling, Xi; Liang, Liangbo; Kong, Jing; Terrones, Humberto; Meunier, Vincent; Dresselhaus, Mildred S
2014-10-08
Two-dimensional molybdenum disulfide (MoS2) is a promising material for optoelectronic devices due to its strong photoluminescence emission. In this work, the photoluminescence of twisted bilayer MoS2 is investigated, revealing a tunability of the interlayer coupling of bilayer MoS2. It is found that the photoluminescence intensity ratio of the trion and exciton reaches its maximum value for the twisted angle 0° or 60°, while for the twisted angle 30° or 90° the situation is the opposite. This is mainly attributed to the change of the trion binding energy. The first-principles density functional theory analysis further confirms the change of the interlayer coupling with the twisted angle, which interprets our experimental results.
8. Probing phonon-rotation coupling in helium nanodroplets: Infrared spectroscopy of CO and its isotopomers
SciTech Connect
Haeften, Klaus von; Rudolph, Stephan; Simanovski, Iaroslav; Havenith, Martina; Zillich, Robert E.; Whaley, K. Birgitta
2006-02-01
We have recorded the R(0){nu}{sub CO}=1(leftarrow)0 IR spectrum of CO and its isotopomers in superfluid helium nanodroplets. For droplets with average size N > or approx. 2000 helium atoms, the transition exhibits a Lorentzian shaped linewidth of 0.034 cm{sup -1}, indicating a homogeneous broadening mechanism. The rotational constants could be deduced and were found to be reduced to about 60% of the corresponding gas-phase values (63% for the reference {sup 12}C {sup 16}O species). Accompanying calculations of the pure rotational spectra were carried out using the method of correlated basis functions in combination with diffusion Monte Carlo (CBF/DMC). These calculations show that both the reduction of the rotational B constant and the line broadening can be attributed to phonon-rotation coupling. The reduction in B is confirmed by path integral correlation function calculations for a cluster of 64 {sup 4}He atoms, which also reveal a non-negligible effect of finite size on the collective modes. The phonon-rotation coupling strength is seen to depend strongly on the strength and anisotropy of the molecule-helium interaction potential. Comparison with other light rotors shows that this coupling is particularly high for CO. The CBF/DMC analysis shows that the J=1 rotational state couples effectively to phonon states, which are only present in large helium droplets or bulk. In particular, they are not present in small clusters with n{<=}20, thereby accounting for the much narrower linewidths and larger B constant measured for these sizes.
9. Probing conformational changes in rhodopsin using hydrogen-deuterium exchange coupled to mass spectrometry.
PubMed
2015-01-01
Hydrogen-deuterium exchange coupled to mass spectrometry is a powerful tool to evaluate changes in protein conformation between two or more states. Here, we describe a complete methodology that can be used to assess conformational changes in rhodopsin accompanying its transition from the inactive to activated state upon light exposure. This approach may be employed to investigate the structure and conformational changes of various membrane proteins.
10. Antiferromagnetic Spin Coupling between Rare Earth Adatoms and Iron Islands Probed by Spin-Polarized Tunneling.
PubMed
Coffey, David; Diez-Ferrer, José Luis; Serrate, David; Ciria, Miguel; de la Fuente, César; Arnaudas, José Ignacio
2015-09-03
High-density magnetic storage or quantum computing could be achieved using small magnets with large magnetic anisotropy, a requirement that rare-earth iron alloys fulfill in bulk. This compelling property demands a thorough investigation of the magnetism in low dimensional rare-earth iron structures. Here, we report on the magnetic coupling between 4f single atoms and a 3d magnetic nanoisland. Thulium and lutetium adatoms deposited on iron monolayer islands pseudomorphically grown on W(110) have been investigated at low temperature with scanning tunneling microscopy and spectroscopy. The spin-polarized current indicates that both kind of adatoms have in-plane magnetic moments, which couple antiferromagnetically with their underlying iron islands. Our first-principles calculations explain the observed behavior, predicting an antiparallel coupling of the induced 5d electrons magnetic moment of the lanthanides with the 3d magnetic moment of iron, as well as their in-plane orientation, and pointing to a non-contribution of 4f electrons to the spin-polarized tunneling processes in rare earths.
11. Antiferromagnetic Spin Coupling between Rare Earth Adatoms and Iron Islands Probed by Spin-Polarized Tunneling
PubMed Central
Coffey, David; Diez-Ferrer, José Luis; Serrate, David; Ciria, Miguel; Fuente, César de la; Arnaudas, José Ignacio
2015-01-01
High-density magnetic storage or quantum computing could be achieved using small magnets with large magnetic anisotropy, a requirement that rare-earth iron alloys fulfill in bulk. This compelling property demands a thorough investigation of the magnetism in low dimensional rare-earth iron structures. Here, we report on the magnetic coupling between 4f single atoms and a 3d magnetic nanoisland. Thulium and lutetium adatoms deposited on iron monolayer islands pseudomorphically grown on W(110) have been investigated at low temperature with scanning tunneling microscopy and spectroscopy. The spin-polarized current indicates that both kind of adatoms have in-plane magnetic moments, which couple antiferromagnetically with their underlying iron islands. Our first-principles calculations explain the observed behavior, predicting an antiparallel coupling of the induced 5d electrons magnetic moment of the lanthanides with the 3d magnetic moment of iron, as well as their in-plane orientation, and pointing to a non-contribution of 4f electrons to the spin-polarized tunneling processes in rare earths. PMID:26333417
12. Probing the Viability of Oxo-Coupling Pathways in Iridium-Catalyzed Oxygen Evolution.
PubMed
Graeupner, Jonathan; Hintermair, Ulrich; Huang, Daria L; Thomsen, Julianne M; Takase, Mike; Campos, Jesús; Hashmi, Sara M; Elimelech, Menachem; Brudvig, Gary W; Crabtree, Robert H
2013-10-14
A series of Cp*Ir(III) dimers have been synthesized to elucidate the mechanistic viability of radical oxo-coupling pathways in iridium-catalyzed O2 evolution. The oxidative stability of the precursors toward nanoparticle formation and their oxygen evolution activity have been investigated and compared to suitable monomeric analogues. We found that precursors bearing monodentate NHC ligands degraded to form nanoparticles (NPs), and accordingly their O2 evolution rates were not significantly influenced by their nuclearity or distance between the two metals in the dimeric precursors. A doubly chelating bis-pyridine-pyrazolide ligand provided an oxidation-resistant ligand framework that allowed a more meaningful comparison of catalytic performance of dimers with their corresponding monomers. With sodium periodate (NaIO4) as the oxidant, the dimers provided significantly lower O2 evolution rates per [Ir] than the monomer, suggesting a negative interaction instead of cooperativity in the catalytic cycle. Electrochemical analysis of the dimers further substantiates the notion that no radical oxyl-coupling pathways are accessible. We thus conclude that the alternative path, nucleophilic attack of water on high-valent Ir-oxo species, may be the preferred mechanistic pathway of water oxidation with these catalysts, and bimolecular oxo-coupling is not a valid mechanistic alternative as in the related ruthenium chemistry, at least in the present system.
13. Probing the Viability of Oxo-Coupling Pathways in Iridium-Catalyzed Oxygen Evolution
PubMed Central
Graeupner, Jonathan; Hintermair, Ulrich; Huang, Daria L.; Thomsen, Julianne M.; Takase, Mike; Campos, Jesús; Hashmi, Sara M.; Elimelech, Menachem; Brudvig, Gary W.; Crabtree, Robert H.
2013-01-01
A series of Cp*IrIII dimers have been synthesized to elucidate the mechanistic viability of radical oxo-coupling pathways in iridium-catalyzed O2 evolution. The oxidative stability of the precursors toward nanoparticle formation and their oxygen evolution activity have been investigated and compared to suitable monomeric analogues. We found that precursors bearing monodentate NHC ligands degraded to form nanoparticles (NPs), and accordingly their O2 evolution rates were not significantly influenced by their nuclearity or distance between the two metals in the dimeric precursors. A doubly chelating bis-pyridine–pyrazolide ligand provided an oxidation-resistant ligand framework that allowed a more meaningful comparison of catalytic performance of dimers with their corresponding monomers. With sodium periodate (NaIO4) as the oxidant, the dimers provided significantly lower O2 evolution rates per [Ir] than the monomer, suggesting a negative interaction instead of cooperativity in the catalytic cycle. Electrochemical analysis of the dimers further substantiates the notion that no radical oxyl-coupling pathways are accessible. We thus conclude that the alternative path, nucleophilic attack of water on high-valent Ir-oxo species, may be the preferred mechanistic pathway of water oxidation with these catalysts, and bimolecular oxo-coupling is not a valid mechanistic alternative as in the related ruthenium chemistry, at least in the present system. PMID:24474842
14. Antibodies to probe endogenous G protein-coupled receptor heteromer expression, regulation, and function
PubMed Central
Gomes, Ivone; Gupta, Achla; Bushlin, Ittai; Devi, Lakshmi A.
2014-01-01
Over the last decade an increasing number of studies have focused on the ability of G protein-coupled receptors to form heteromers and explored how receptor heteromerization modulates the binding, signaling and trafficking properties of individual receptors. Most of these studies were carried out in heterologous cells expressing epitope tagged receptors. Very little information is available about the in vivo physiological role of G protein-coupled receptor heteromers due to a lack of tools to detect their presence in endogenous tissue. Recent advances such as the generation of mouse models expressing fluorescently labeled receptors, of TAT based peptides that can disrupt a given heteromer pair, or of heteromer-selective antibodies that recognize the heteromer in endogenous tissue have begun to elucidate the physiological and pathological roles of receptor heteromers. In this review we have focused on heteromer-selective antibodies and describe how a subtractive immunization strategy can be successfully used to generate antibodies that selectively recognize a desired heteromer pair. We also describe the uses of these antibodies to detect the presence of heteromers, to study their properties in endogenous tissues, and to monitor changes in heteromer levels under pathological conditions. Together, these findings suggest that G protein-coupled receptor heteromers represent unique targets for the development of drugs with reduced side-effects. PMID:25520661
15. Probing Higgs boson couplings in H + γ production at the LHC
2017-10-01
In this paper, we examine the potential of Higgs boson production associated with a photon at the LHC to probe the new physics effects in the framework of the standard model effective field theory. It is shown that the differential kinematic distributions such as photon transverse momentum and invariant mass of Higgs + γ in Higgs associated production are powerful variables to explore the coefficients of dimension six operators. The analysis is performed in the decay channel of Higgs boson into a b b bar pair including the main sources of background processes and a realistic simulation of the detector effects. We provide constraints at 95% confidence level on the Wilson coefficients of dimension-six operators affecting Higgs boson plus a photon production. We show to what extent these limits could be improved at the high luminosity LHC. The effect of these constraints on a well-motivated beyond standard model scenario is presented.
16. Probing variations of the Rashba spin-orbit coupling at the nanometre scale
Bindel, Jan Raphael; Pezzotta, Mike; Ulrich, Jascha; Liebmann, Marcus; Sherman, Eugene Ya.; Morgenstern, Markus
2016-10-01
As the Rashba effect is an electrically tunable spin-orbit interaction, it could form the basis for a multitude of applications, such as spin filters, spin transistors and quantum computing using Majorana states in nanowires. Moreover, this interaction can determine the spin dephasing and antilocalization phenomena in two dimensions. However, the real space pattern of the Rashba parameter, which critically influences spin transistors using the spin-helix state and the otherwise forbidden electron backscattering in topologically protected channels, is difficult to probe. Here, we map this pattern down to nanometre length scales by measuring the spin splitting of the lowest Landau level using scanning tunnelling spectroscopy. We reveal strong fluctuations correlated with the local electrostatic potential for an InSb inversion layer with a large Rashba coefficient (~1 eV Å). This type of Rashba field mapping enables a more comprehensive understanding of its fluctuations, which might be decisive towards robust semiconductor-based spintronic devices.
17. Perturbation factors in the clinical handling of a fiber-coupled Raman probe for cutaneous in vivo diagnostic Raman spectroscopy.
PubMed
Schleusener, Johannes; Gluszczynska, Patrycja; Reble, Carina; Gersonde, Ingo; Helfmann, Jürgen; Cappius, Hans-Joachim; Fluhr, Joachim W; Meinke, Martina C
2015-01-01
The application of fiber-coupled Raman probes for the discrimination of cancerous and normal skin has the advantage of a non-invasive in vivo application, easy clinical handling, and access to the majority of body sites, which would otherwise be limited by stationary Raman microscopes. Nevertheless, including optical fibers and miniaturizing optical components, as well as measuring in vivo, involves the sensibility to external perturbation factors that could introduce artifacts to the acquired Raman spectra and thereby potentially reduce classification performance. In this study, typical perturbation factors of Raman measurements with a Raman fiber probe, optimized for clinical in vivo discrimination of skin cancer, were investigated experimentally. Measurements were performed under standardized conditions in clinical settings in vivo on human skin, as well as ex vivo on porcine ears. Raman spectra were analyzed in the fingerprint region between 1150 and 1730 cm(-1) using principal component analysis. The largest artifacts in the Raman spectra were found in measurements performed under the influence of strong ambient light conditions as well as after miscellaneous pre-treatments to the skin, such as use of a permanent marker or a sunscreen. Minor influences were also found in measurements using H2O immersion and when varying the probe contact force. The effect of reasonable variation of the fiber-bending radius was found to be of negligible impact. The influence of measurements on hairy or sun-exposed body sites, as well as inter-subject variation, was also investigated. The presented results may serve as a guide to avoid negative effects during the process of data acquisition and so avoid misclassification in tumor discrimination.
18. A Dual Functional Electroactive and Fluorescent Probe for Coupled Measurements of Vesicular Exocytosis with High Spatial and Temporal Resolution.
PubMed
Liu, Xiaoqing; Savy, Alexandra; Maurin, Sylvie; Grimaud, Laurence; Darchen, François; Quinton, Damien; Labbé, Eric; Buriez, Olivier; Delacotte, Jérôme; Lemaître, Frédéric; Guille-Collignon, Manon
2017-02-20
In this work, Fluorescent False Neurotransmitter 102 (FFN102), a synthesized analogue of biogenic neurotransmitters, was demonstrated to show both pH-dependent fluorescence and electroactivity. To study secretory behaviors at the single-vesicle level, FFN102 was employed as a new fluorescent/electroactive dual probe in a coupled technique (amperometry and total internal reflection fluorescence microscopy (TIRFM)). We used N13 cells, a stable clone of BON cells, to specifically accumulate FFN102 into their secretory vesicles, and then optical and electrochemical measurements of vesicular exocytosis were experimentally achieved by using indium tin oxide (ITO) transparent electrodes. Upon stimulation, FFN102 started to diffuse out from the acidic intravesicular microenvironment to the neutral extracellular space, leading to fluorescent emissions and to the electrochemical oxidation signals that were simultaneously collected from the ITO electrode surface. The correlation of fluorescence and amperometric signals resulting from the FFN102 probe allows real-time monitoring of single exocytotic events with both high spatial and temporal resolution. This work opens new possibilities in the investigation of exocytotic mechanisms.
19. A novel method of multiple nucleic acid detection: Real-time RT-PCR coupled with probe-melting curve analysis.
PubMed
Han, Yang; Hou, Shao-Yang; Ji, Shang-Zhi; Cheng, Juan; Zhang, Meng-Yue; He, Li-Juan; Ye, Xiang-Zhong; Li, Yi-Min; Zhang, Yi-Xuan
2017-09-04
A novel method, real-time reverse transcription PCR (real-time RT-PCR) coupled with probe-melting curve analysis, has been established to detect two kinds of samples within one fluorescence channel. Besides a conventional TaqMan probe, this method employs another specially designed melting-probe with a 5' terminus modification which meets the same label with the same fluorescent group. By using an asymmetric PCR method, the melting-probe is able to detect an extra sample in the melting stage effectively while it almost has little influence on the amplification detection. Thus, this method allows the availability of united employment of both amplification stage and melting stage for detecting samples in one reaction. The further demonstration by simultaneous detection of human immunodeficiency virus (HIV) and hepatitis C virus (HCV) in one channel as a model system is presented in this essay. The sensitivity of detection by real-time RT-PCR coupled with probe-melting analysis was proved to be equal to that detected by conventional real-time RT-PCR. Because real-time RT-PCR coupled with probe-melting analysis can double the detection throughputs within one fluorescence channel, it is expected to be a good solution for the problem of low-throughput in current real-time PCR. Copyright © 2017. Published by Elsevier Inc.
20. Characterization of O2/Ar inductively coupled plasma studied by using a Langmuir probe and global model
Liu, Wei; Wen, De-Qi; Zhao, Shu-Xia; Gao, Fei; Wang, You-Nian
2015-04-01
An O2/Ar inductively coupled plasma is investigated by a Langmuir probe and a global model (volume averaged model). The electron density, electron temperature and electron energy distribution function (EEDF) are measured at different O2 contents, gas pressures and applied powers. At fixed pressure and power, the electron density first drops quickly with the O2 ratio and then tends to saturate in the high O2 ratio range. The effective electron temperature exhibits completely opposite behaviors at low and high pressures. This is caused by the different evolving behaviors of low and high energy electrons of the EEDFs with the O2 ratio. Both the Langmuir probe and the global model predict that the electron density of O2/Ar mixed plasma first increases, peaks and then drops constantly, upon increasing the pressure. An analysis based on the simulation reveals that the non-monotonic variation of electron density with the pressure is due to the non-monotonic variation of the ionizations from both ground state O and metastable O*. Due to the strong ionizations, the electron density increases linearly with the power. The effective electron temperature is unchanged because the EEDF shape that determines the electron temperature is not varied upon increasing the power. The calculated electron density and temperature when varying the power agree better with the experiments at high pressure, i.e. 45 mTorr. The quantitative deviation between the model and the experiment when varying the pressure and the O2 ratio can be explained by two aspects. (1) The electron energy probability function is assumed to have a Maxwellian distribution in the global model while the realistic EEDFs vary significantly with the pressure and/or the O2 ratio, as revealed by the experiment. (2) The power transfer efficiency (i.e. the fraction of the power coupled into plasma) increases with the pressure.
1. Magnetoencephalography with a two-color pump-probe, fiber-coupled atomic magnetometer
Johnson, Cort; Schwindt, Peter D. D.; Weisend, Michael
2010-12-01
The authors have detected magnetic fields from the human brain with a compact, fiber-coupled rubidium spin-exchange-relaxation-free magnetometer. Optical pumping is performed on the D1 transition and Faraday rotation is measured on the D2 transition. The beams share an optical axis, with dichroic optics preparing beam polarizations appropriately. A sensitivity of <5 fT/√Hz is achieved. Evoked responses resulting from median nerve and auditory stimulation were recorded with the atomic magnetometer. Recordings were validated by comparison with those taken by a commercial magnetoencephalography system. The design is amenable to arraying sensors around the head, providing a framework for noncryogenic, whole-head magnetoencephalography.
2. Dichroism as a probe for parity-breaking phases of spin-orbit coupled metals
SciTech Connect
Norman, M. R.
2015-08-07
Recently, a general formalism has been presented for gyrotropic, ferroelectric, and multipolar order in spin-orbit coupled metals induced by spin-spin interactions. Here, I point out that the resulting order parameters are equivalent to expectation values of operators that determine natural circular dichroic signals in optical and x-ray absorption, and list several examples in this connection. As a result, the particular case of the tensor order in the pyrochlore superconductor Cd2Re2O7 is discussed in more detail.
3. Dichroism as a probe for parity-breaking phases of spin-orbit coupled metals
DOE PAGES
Norman, M. R.
2015-08-07
Recently, a general formalism has been presented for gyrotropic, ferroelectric, and multipolar order in spin-orbit coupled metals induced by spin-spin interactions. Here, I point out that the resulting order parameters are equivalent to expectation values of operators that determine natural circular dichroic signals in optical and x-ray absorption, and list several examples in this connection. As a result, the particular case of the tensor order in the pyrochlore superconductor Cd2Re2O7 is discussed in more detail.
4. Development of Feedhorn-Coupled Multichroic Polarimeters for the Inflation Probe Mission
McMahon, Jeff
This proposal seeks support for the development of millimeter-wavelength multichroic polarimeters optimized for detecting Cosmic Microwave Background (CMB) polarization signals with a future NASA Inflation Probe Mission. The technologies developed under this proposal would also have applications in future submillimeter astrophysics satellite missions. The proposed technology would increase the overall experimental sensitivity of an Inflation Probe Mission over that achievable by single-frequency pixels, making efficient use of available diffraction-limited focal plane area while maintaining unmatched control over systematics through the use of corrugated feedhorns. The sensitivity, multi-frequency coverage, and control of detector systematics offered by this technology on the Inflation Probe Mission would provide the definitive measurement of CMB polarization and foreground sources. These data would unambiguously detect or rule out all models of Grand Unified Theory (GUT) scale inflation, provide a precise measurement of the sum of the neutrino masses, and enable a wide variety of astrophysical and additional cosmological measurements. Control of systematics and foregrounds are paramount for a successful detection of the faint inflationary signal. Corrugated feedhorns are the gold standard for producing symmetric beams with low cross-polarization. Using ring-loaded slots, they can be designed to exceed one octave in bandwidth, allowing for multiple bands using a single feed. For the optimal characterization and control of foregrounds, approximately 10 bands are needed over a frequency range roughly spanning 40-300 GHz. Our plan is to develop a scalable multichroic architecture with four frequency bands within an octave of bandwidth, which we will then scale to three different frequency ranges, for a total of 12 bands with band centers on a logarithmic scale ranging from 40-288 GHz. At the key frequencies for CMB polarization (100-150 GHz) our proposed detectors
5. Probing triple Higgs couplings of the two Higgs doublet model at a linear collider
SciTech Connect
Arhrib, Abdesslam; Benbrik, Rachid; Chiang, C.-W.
2008-06-01
We study double Higgs production at the future linear collider in the framework of the two Higgs doublet models through the following channels: e{sup +}e{sup -}{yields}{phi}{sub i}{phi}{sub j}Z, {phi}{sub i}=h{sup 0}, H{sup 0}, A{sup 0}, H{sup {+-}}. All these processes are sensitive to triple Higgs couplings. Hence observations of them provide information on the triple Higgs couplings that help reconstructing the scalar potential. We also discuss the double Higgs-Strahlung e{sup +}e{sup -}{yields}h{sup 0}h{sup 0}Z in the decoupling limit where h{sup 0} mimics the standard model Higgs boson. The processes e{sup +}e{sup -}{yields}h{sup 0}h{sup 0}Z and e{sup +}e{sup -}{yields}h{sup 0}H{sup 0}Z are also discussed in the fermiophobic limit where distinctive signatures such as 4{gamma}+X, 2{gamma}+X, and 6{gamma}+X are expected in the Type-I two Higgs doublet model.
6. Trajectory-probed instability and statistics of desynchronization events in coupled chaotic systems
SciTech Connect
Oliveira, Gilson F. de Chevrollier, Martine; Oriá, Marcos; Passerat de Silans, Thierry; Souza Cavalcante, Hugo L. D. de
2015-11-15
Complex systems, such as financial markets, earthquakes, and neurological networks, exhibit extreme events whose mechanisms of formation are not still completely understood. These mechanisms may be identified and better studied in simpler systems with dynamical features similar to the ones encountered in the complex system of interest. For instance, sudden and brief departures from the synchronized state observed in coupled chaotic systems were shown to display non-normal statistical distributions similar to events observed in the complex systems cited above. The current hypothesis accepted is that these desynchronization events are influenced by the presence of unstable object(s) in the phase space of the system. Here, we present further evidence that the occurrence of large events is triggered by the visitation of the system's phase-space trajectory to the vicinity of these unstable objects. In the system studied here, this visitation is controlled by a single parameter, and we exploit this feature to observe the effect of the visitation rate in the overall instability of the synchronized state. We find that the probability of escapes from the synchronized state and the size of those desynchronization events are enhanced in attractors whose shapes permit the chaotic trajectories to approach the region of strong instability. This result shows that the occurrence of large events requires not only a large local instability to amplify noise, or to amplify the effect of parameter mismatch between the coupled subsystems, but also that the trajectories of the system wander close to this local instability.
7. Mode Coupling in Plasmonic Heterodimers Probed with Electron Energy Loss Spectroscopy.
PubMed
Flauraud, Valentin; Bernasconi, Gabriel D; Butet, Jérémy; Alexander, Duncan T L; Martin, Olivier J F; Brugger, Juergen
2017-03-14
While plasmonic antennas composed of building blocks made of the same material have been thoroughly studied, recent investigations have highlighted the unique opportunities enabled by making compositionally asymmetric plasmonic systems. So far, mainly heterostructures composed of nanospheres and nanodiscs have been investigated, revealing opportunities for the design of Fano resonant nanostructures, directional scattering, sensing and catalytic applications. In this article, an improved fabrication method is reported that enables precise tuning of the heterodimer geometry, with interparticle distances made down to a few nanometers between Au-Ag and Au-Al nanoparticles. A wide range of mode energy detuning and coupling conditions are observed by near field hyperspectral imaging performed with electron energy loss spectroscopy, supported by full wave analysis numerical simulations. These results provide direct insights into the mode hybridization of plasmonic heterodimers, pointing out the influence of each dimer constituent in the overall electromagnetic response. By relating the coupling of non-dipolar modes and plasmon-interband interaction with the dimer geometry, this work facilitates the development of plasmonic heterostructures with tailored responses, beyond the possibilities offered by homodimers.
8. Trajectory-probed instability and statistics of desynchronization events in coupled chaotic systems
de Oliveira, Gilson F.; Chevrollier, Martine; Passerat de Silans, Thierry; Oriá, Marcos; de Souza Cavalcante, Hugo L. D.
2015-11-01
Complex systems, such as financial markets, earthquakes, and neurological networks, exhibit extreme events whose mechanisms of formation are not still completely understood. These mechanisms may be identified and better studied in simpler systems with dynamical features similar to the ones encountered in the complex system of interest. For instance, sudden and brief departures from the synchronized state observed in coupled chaotic systems were shown to display non-normal statistical distributions similar to events observed in the complex systems cited above. The current hypothesis accepted is that these desynchronization events are influenced by the presence of unstable object(s) in the phase space of the system. Here, we present further evidence that the occurrence of large events is triggered by the visitation of the system's phase-space trajectory to the vicinity of these unstable objects. In the system studied here, this visitation is controlled by a single parameter, and we exploit this feature to observe the effect of the visitation rate in the overall instability of the synchronized state. We find that the probability of escapes from the synchronized state and the size of those desynchronization events are enhanced in attractors whose shapes permit the chaotic trajectories to approach the region of strong instability. This result shows that the occurrence of large events requires not only a large local instability to amplify noise, or to amplify the effect of parameter mismatch between the coupled subsystems, but also that the trajectories of the system wander close to this local instability.
9. Probing Nonadiabaticity in the Proton-Coupled Electron Transfer Reaction Catalyzed by Soybean Lipoxygenase
PubMed Central
2014-01-01
Proton-coupled electron transfer (PCET) plays a vital role in many biological and chemical processes. PCET rate constant expressions are available for various well-defined regimes, and determining which expression is appropriate for a given system is essential for reliable modeling. Quantitative diagnostics have been devised to characterize the vibronic nonadiabaticity between the electron–proton quantum subsystem and the classical nuclei, as well as the electron–proton nonadiabaticity between the electrons and proton(s) within the quantum subsystem. Herein these diagnostics are applied to a model of the active site of the enzyme soybean lipoxygenase, which catalyzes a PCET reaction that exhibits unusually high deuterium kinetic isotope effects at room temperature. Both semiclassical and electronic charge density diagnostics illustrate vibronic and electron–proton nonadiabaticity for this PCET reaction, supporting the use of the Golden rule nonadiabatic rate constant expression with a specific form of the vibronic coupling. This type of characterization will be useful for theoretical modeling of a broad range of PCET processes. PMID:25258676
10. A microcoil NMR probe for coupling microscale HPLC with on-line NMR spectroscopy.
PubMed
Subramanian, R; Kelley, W P; Floyd, P D; Tan, Z J; Webb, A G; Sweedler, J V
1999-12-01
An HPLC NMR system is presented that integrates a commercial microbore HPLC system using a 0.5-mm column with a 500-MHz proton NMR spectrometer using a custom NMR probe with an observe volume of 1.1 microL and a coil fill factor of 68%. Careful attention to capillary connections and NMR flow cell design allows on-line NMR detection with no significant loss in separation efficiency when compared with a UV chromatogram. HPLC NMR is performed on mixtures of amino acids and small peptides with analyte injection amounts as small as 750 ng; the separations are accomplished in less than 10 min and individual NMR spectra are acquired with 12 s time resolution. Stopped-flow NMR is achieved by diversion of the chromatographic flow after observation of the beginning of the analyte band within the NMR flow cell. Isolation of the compound of interest within the NMR detection cell allows multidimensional experiments to be performed. A stopped-flow COSY spectrum of the peptide Phe-Ala is acquired in 3.5 h with an injected amount of 5 micrograms.
11. Hydrated fractions of cellulosics probed by infrared spectroscopy coupled with dynamics of deuterium exchange.
PubMed
Driemeier, Carlos; Mendes, Fernanda M; Ling, Liu Yi
2015-08-20
This article presents a novel method to selectively probe the non-crystalline, hydrated fractions of cellulosic biomass. The method is based on time-resolved infrared spectra analyzed to provide information on spectral and dynamical features of deuterium exchange (OH → OD) in D2O atmosphere. We assign deuterium exchange spectral regions (700-3800 cm(-1)) and explore changes due to relative humidity, different cellulosic samples, and infrared polarization. Here, two results are highlighted. First, a wide range of celluloses isolated from plants show remarkable spectral similarities whatever the relative amounts of cellulose and xylan. This result supports an inherent type of hydrated disorder which is mostly insensitive to the molecular identities of the associated polysaccharides. Second, polarized infrared analysis of cotton reveals hydrated cellulose having chains preferentially aligned with those of crystals, while the hydroxyls of hydrated cellulose present much more randomized orientation. Our results provide new insights on molecular and group orientation and on hydrogen bonding in hydrated fractions of cellulosic biomass.
12. Resolving Intra- and Inter-Molecular Structure with Non-Contact Atomic Force Microscopy
PubMed Central
Jarvis, Samuel Paul
2015-01-01
A major challenge in molecular investigations at surfaces has been to image individual molecules, and the assemblies they form, with single-bond resolution. Scanning probe microscopy, with its exceptionally high resolution, is ideally suited to this goal. With the introduction of methods exploiting molecularly-terminated tips, where the apex of the probe is, for example, terminated with a single CO, Xe or H2 molecule, scanning probe methods can now achieve higher resolution than ever before. In this review, some of the landmark results related to attaining intramolecular resolution with non-contact atomic force microscopy (NC-AFM) are summarised before focussing on recent reports probing molecular assemblies where apparent intermolecular features have been observed. Several groups have now highlighted the critical role that flexure in the tip-sample junction plays in producing the exceptionally sharp images of both intra- and apparent inter-molecular structure. In the latter case, the features have been identified as imaging artefacts, rather than real intermolecular bonds. This review discusses the potential for NC-AFM to provide exceptional resolution of supramolecular assemblies stabilised via a variety of intermolecular forces and highlights the potential challenges and pitfalls involved in interpreting bonding interactions. PMID:26307976
13. Resolving Intra- and Inter-Molecular Structure with Non-Contact Atomic Force Microscopy.
PubMed
Jarvis, Samuel Paul
2015-08-21
A major challenge in molecular investigations at surfaces has been to image individual molecules, and the assemblies they form, with single-bond resolution. Scanning probe microscopy, with its exceptionally high resolution, is ideally suited to this goal. With the introduction of methods exploiting molecularly-terminated tips, where the apex of the probe is, for example, terminated with a single CO, Xe or H2 molecule, scanning probe methods can now achieve higher resolution than ever before. In this review, some of the landmark results related to attaining intramolecular resolution with non-contact atomic force microscopy (NC-AFM) are summarised before focussing on recent reports probing molecular assemblies where apparent intermolecular features have been observed. Several groups have now highlighted the critical role that flexure in the tip-sample junction plays in producing the exceptionally sharp images of both intra- and apparent inter-molecular structure. In the latter case, the features have been identified as imaging artefacts, rather than real intermolecular bonds. This review discusses the potential for NC-AFM to provide exceptional resolution of supramolecular assemblies stabilised via a variety of intermolecular forces and highlights the potential challenges and pitfalls involved in interpreting bonding interactions.
14. Interrogation of the intersubunit interface of the open Hv1 proton channel with a probe of allosteric coupling
PubMed Central
Hong, Liang; Singh, Vikrant; Wulff, Heike; Tombola, Francesco
2015-01-01
The Hv1 voltage-gated proton channel is a dimeric complex consisting of two voltage-sensing domains (VSDs), each containing a gated proton permeation pathway. Dimerization is controlled by a cytoplasmic coiled-coil domain. The transitions from the closed to the open state in the two VSDs are known to occur cooperatively; however, the underlying mechanism is poorly understood. Intersubunit interfaces play a critical role in allosteric processes; but, such interfaces have not been determined in the open Hv1 channel. Here we show that 2-guanidinothiazole derivatives block the two Hv1 VSDs in a cooperative way, and use one of the compounds as a probe of allosteric coupling between open subunits. We find that the extracellular ends of the first transmembrane segments of the VSDs form the intersubunit interface that mediates coupling between binding sites, while the coiled-coil domain does not directly participate in the process. We also find strong evidence that the channel’s proton selectivity filter controls blocker binding cooperativity. PMID:26365828
15. Effect of misalignment of air-coupled probes on Ao Lamb mode propagating in a metal plate.
PubMed
Ramadas, C; Hood, Avinash; Khan, Irfan; Balasubramaniam, Krishnan
2014-07-01
Proper alignment of air-coupled ultrasonic transducers for generation and reception of Lamb waves is vital in order to acquire a high amplitude wave group. Any misalignment with either the transmitter or the receiver or both adversely influences the amplitude of a Lamb mode. This paper reports a systematic attempt to quantify the reduction in the amplitude of the fundamental anti-symmetric Lamb mode (Ao) in a metal plate caused by misalignments in air-coupled probes. Three different types of misalignments - linear, orientation and synchronised orientation were deliberately introduced in the transducers, and experiments were performed on a 6mm thick aluminium plate. Amplitudes of Ao mode measured at various configurations were normalised with that of Ao mode, captured in a reference configuration. Suitable curves fitted over the experimental data points revealed that Gaussian curves represent appropriately the variations in normalised amplitudes of Ao mode. Moreover, analytical expressions were derived to predict the difference in arrival times of Lamb mode(s) due to orientation and synchronised orientation misalignments.
16. Probe diagnostics of argon-oxygen-tetramethyltin capacitively coupled plasmas for the deposition of tin oxide thin films
SciTech Connect
Pulpytel, J.; Morscheidt, W.; Arefi-Khonsari, F.
2007-04-01
Langmuir probe measurements in nondepositing and depositing rf capacitively coupled (CCP) plasmas are briefly reviewed and compared to the results obtained in our rf system used for the deposition of tin oxide (SnO{sub 2}) thin films from argon-oxygen-tetamethyltin [Sn(CH{sub 3}){sub 4}] plasmas. Typically in our experimental conditions for tin oxide deposition, values of kT{sub eff}= 1.2-1.5 eV and n{sub e}=3-5x10{sup 9} cm{sup -3} were measured. These values are consistent with those generally reported in other depositing discharges. The shape of the electron energy probability function (EEPF), obtained from the Druyvesteyn procedure, was discussed too. As a consequence of the two electron heating mechanisms in capacitively coupled discharges, that is, ohmic and stochastic heating, the electrons have a bi-Maxwellian EEPF at low pressure (in the range of 10-100 mTorr). Moreover, a deep 'hole' appears in the EEPF at the energy which could correspond to the resonant peak of the vibrational excitation cross section of some molecules which can be present in the discharge, such as N{sub 2}, CH{sub 4}, or CO.
17. DNA-Linked Enzyme-Coupled Assay for Probing Glucosyltransferase Specificity.
PubMed
Sukovich, David J; Modavi, Cyrus; de Raad, Markus; Prince, Robin N; Anderson, J Christopher
2015-07-17
Traditional enzyme characterization methods are low-throughput and therefore limit engineering efforts in synthetic biology and biotechnology. Here, we propose a DNA-linked enzyme-coupled assay (DLEnCA) to monitor enzyme reactions in a high-throughput manner. Throughput is improved by removing the need for protein purification and by limiting the need for liquid chromatography mass spectrometry (LCMS) product detection by linking enzymatic function to DNA modification. We demonstrate the DLEnCA methodology using glucosyltransferases as an illustration. The assay utilizes cell free transcription/translation systems to produce enzymes of interest, while UDP-glucose and T4-β-glucosyltransferase are used to modify DNA, which is detected postreaction using qPCR or a similar means of DNA analysis. OleD and two glucosyltransferases from Arabidopsis were used to verify the assay's generality toward glucosyltransferases. We further show DLEnCA's utility by mapping out the substrate specificity for these enzymes.
18. Probing magnetic excitations and correlations in single and coupled spin systems with scanning tunneling spectroscopy
Ternes, Markus
2017-02-01
Spectroscopic measurements with low-temperature scanning tunneling microscopes have been used very successfully for studying not only individual atomic or molecular spins on surfaces but also complexly designed coupled systems. The symmetry breaking of the supporting surface induces magnetic anisotropy which lead to characteristic fingerprints in the spectrum of the differential conductance and can be well understood with simple model Hamiltonians. Furthermore, correlated many-particle states can emerge due to the interaction with itinerant electrons of the electrodes, making these systems ideal prototypical quantum systems. In this manuscript more complex bipartite and spin-chains will be discussed additionally. Their spectra enable to determine precisely the nature of the interactions between the spins which can lead to the formation of new quantum states which emerge by interatomic entanglement.
19. Probing the anomalous γγγZ coupling at the LHC with proton tagging
Baldenegro, C.; Fichet, S.; von Gersdorff, G.; Royon, C.
2017-06-01
The sensitivities to the anomalous quartic gauge boson coupling γγγZ are estimated via γZ production with intact protons in the forward region at the LHC. Proton tagging proves to be a powerful tool to suppress the background, which allows consideration of the hadronic decays of the Z boson in addition to the leptonic ones. We discuss the discovery potential for an integrated luminosity of 300 fb-1 and 3000 fb-1. The sensitivity we obtain at 300 fb-1 goes beyond the one expected from LHC bounds on the Z → γγγ decay by about three orders of magnitude. The γZ channel provides important discriminatory information with respect to the exclusive γγ channel, as many particles beyond the Standard Model (such as a radion or Kaluza Klein gravitons) predict a signal in the latter but not the former.
20. Interwire coupling for I n(4 ×1 )/Si(111) probed by surface transport
Edler, F.; Miccoli, I.; Demuth, S.; Pfnür, H.; Wippermann, S.; Lücke, A.; Schmidt, W. G.; Tegenkamp, C.
2015-08-01
The In/Si(111) system reveals an anisotropy in the electrical conductivity and is a prototype system for atomic wires on surfaces. We use this system to study and tune the interwire interaction by adsorption of oxygen. Through rotational square four-tip transport measurements, both the parallel (σ||) and perpendicular (σ⊥) components are measured separately. The analysis of the I(V) curves reveals that σ⊥ is also affected by adsorption of oxygen, showing clearly an effective interwire coupling, in agreement with density-functional-theory-based calculations of the transmittance. In addition to these surface-state mediated transport channels, we confirm the existence of conducting parasitic space-charge layer channels and address the importance of substrate steps by performing the transport measurements of In phases grown on Si(111) mesa structures.
1. Mechanical spectra measurement to probe the magnetolattice coupling in cupric oxide
Ying, X. N.; Wang, Y. N.
2005-12-01
Mechanical spectra (complex Young's modulus Y*=Y‧+i Y″ versus frequency and temperature) of polycrystalline cupric oxide CuO were measured by vibrating reed method from liquid nitrogen temperature to room temperature at the kilohertz frequency. The abnormal behavior of internal friction and the change of slope of the real part of the complex Young's modulus versus temperature are observed around 213 and 230 K, where two successive magnetic transitions were established. At low temperatures, below 130 K, a higher internal friction platform with the decrease of temperature was clearly observed which might show a phase transition. Our study indicates that mechanical spectrum is an effective tool to detect subtle phase transitions and there is a strong magnetolattice coupling in CuO.
2. Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition.
PubMed
Brambilla, G; El Masri, D; Pierno, M; Berthier, L; Cipelletti, L; Petekidis, G; Schofield, A B
2009-02-27
We use dynamic light scattering and computer simulations to study equilibrium dynamics and dynamic heterogeneity in concentrated suspensions of colloidal hard spheres. Our study covers an unprecedented density range and spans seven decades in structural relaxation time, tau(alpha0, including equilibrium measurements above phi(c), the location of the glass transition deduced from fitting our data to mode-coupling theory. Instead of falling out of equilibrium, the system remains ergodic above phi(c) and enters a new dynamical regime where tau(alpha) increases with a functional form that was not anticipated by previous experiments, while the amplitude of dynamic heterogeneity grows slower than a power law with tau(alpha), as found in molecular glass formers close to the glass transition.
3. Magnetoelectric coupling of multiferroic chromium doped barium titanate thin film probed by magneto-impedance spectroscopy
SciTech Connect
Shah, Jyoti Kotnala, Ravinder K. E-mail: [email protected]
2014-04-07
Thin film of BaTiO{sub 3} doped with 0.1 at. % Cr (Cr:BTO) has been prepared by pulsed laser deposition technique. Film was deposited on Pt/SrTiO{sub 3} substrate at 500 °C in 50 mTorr Oxygen gas pressure using KrF (298 nm) laser. Polycrystalline growth of single phase Cr:BTO thin film has been confirmed by grazing angle X-ray diffraction. Cr:BTO film exhibited remnant polarization 6.4 μC/cm{sup 2} and 0.79 MV/cm coercivity. Magnetization measurement of Cr:BTO film showed magnetic moment 12 emu/cc. Formation of weakly magnetic domains has been captured by magnetic force microscopy. Theoretical impedance equation fitted to experimental data in Cole-Cole plot for thin film in presence of transverse magnetic field resolved the increase in grain capacitance from 4.58 × 10{sup −12} to 5.4 × 10{sup −11} F. Film exhibited high value 137 mV/cm-Oe magneto-electric (ME) coupling coefficient at room temperature. The high value of ME coupling obtained can reduce the typical processing steps involved in multilayer deposition to obtain multiferrocity in thin film. Barium titanate being best ferroelectric material has been tailored to be multiferroic by non ferromagnetic element, Cr, doping in thin film form opens an avenue for more stable and reliable spintronic material for low power magnetoelectric random excess memory applications.
4. Observed Coupling Between the International Space Station PCU Plasma and a FPMU Langmuir Probe Facilitated by the Geomagnetic Field
NASA Technical Reports Server (NTRS)
Hartman, William; Koontz, Steven L.
2010-01-01
Electrical charging of the International Space Station (ISS) is a matter of serious concern resulting from the possibility of vehicle arcing and electrical shock hazard to crew during extravehicular activity (EVA). A Plasma Contactor Unit (PCU) was developed and integrated into ISS in order to control the ISS floating potential, thereby, minimize vehicle charging and associated hazards. One of the principle factors affecting ISS electrical charging is the ionosphere plasma state (i.e., electron temperature and density). To support ISS electrical charging studies a Floating Potential Monitoring Unit (FPMU) is also integrated into ISS in order to measure the ionosphere properties using Langmuir probes (LP). The FPMU was located on the Starboard side of ISS. The PCU is located near the center of ISS with its plasma exhaust pointed to port. From its integration on ISS in 2006 through November of 2009, the FPMU data exhibited nominal characteristics during PCU operation. On November 21, 2009 the FPMU was relocated from the Starboard location to a new Port location. After relocation significant enhanced noise was observed in both the LP current-voltage sweeps and the derived electron temperature data. The enhanced noise only occurred when the PCU was in discharge and at unique and repeatable locations of the ISS orbit. The cause of this enhanced noise was investigated. It was found that there is coupling occurring between the PCU plasma and the FPMU LP. In this paper we shall 1) present the on-orbit data and the presence of enhanced noise, 2) demonstrate that the coupling of the PCU plasma and the FPMU measurements is geomagnetically organized, 3) show that coupling of the PCU plasma and the FPMU is primarily due to and driven by particle-wave interaction and 4) show that the ionosphere conditions are adequate for Alfven waves to be generated by the PCU plasma.
5. Langmuir Probe Measurements of Inductively Coupled Plasma in CF4/AR/O2 Mixtures
NASA Technical Reports Server (NTRS)
Rao, M. V. V. S.; Cruden, Brett; Sharma, Surendra; Meyyappan, Meyya
2001-01-01
Inductively coupled plasmas of CF4:Ar:O2, which have been of importance to material processing, were studied in the GEC cell at 80:10:10, 60:20:20, and 40:30:30 mixture ratios. Radial distributions of plasma potential (V(sub p)), electron and ion number densities (n(sub e) and n(sub i)), electron temperature (T(sub e)), and electron energy distribution functions (EEDFs) were measured in the mid-plane of plasma across the electrodes in the pressure range of 10-50 mTorr, and RF power of 200 and 300 W. V(sub p), n(sub e) and n(sub i), which peak in the center of the plasma, increase with decrease of pressure. T(sub e) also increases with pressure but peaks toward the electrode edge. Both V(sub p) and T(sub e) remain nearly independent of RF power, whereas n(sub e) and n(sub i) increase with power. In all conditions the EEDFs exhibit non-Maxwellian shape and are more like Druyvesteyn form at higher energies. They exhibit a broad lip in the energy range 0-10 eV suggesting an electron loss mechanism, which could be due to via resonance electron attachment processes producing negative ions in this rich electronegative gas mixture. This behavior is more prominent towards the electrode edge.
6. Langmuir Probe Measurements of Inductively Coupled Plasmas in CF4/Ar/O2 Mixtures
NASA Technical Reports Server (NTRS)
Rao, M. V. V. S.; Cruden, Brett; Sharma, Surendra; Meyyappan, Meyya
2001-01-01
Inductively coupled plasmas of CF4:Ar:O2, which have been of importance to material processing, were studied in the GEC cell at 80:10:10, 60:20:20, and 40:30:30 mixture ratios. Radial distributions of plasma potential (V(sub p)), electron and ion number densities (n(sub e) and n(sub i), electron temperature (T(sub e)), and electron energy distribution functions (EEDFs) were measured in the mid-plane of plasma across the electrodes in the pressure range of 10-50 mTorr, and RF (radio frequency) power of 200 and 300 W. V(sub p), n(sub e) and n(sub i), which peak in the center of the plasma, increase with decrease of pressure. T(sub e) also increases with pressure but peaks toward the electrode edge. Both V(sub p) and T(sub e) remain nearly independent of RF power, whereas n(sub e) and n(sub i) increase with power. In all conditions the EEDFs exhibit non-Maxwellian shape and are more like Druyvesteyn form at higher energies. They exhibit a broad dip in the energy range 0-10 eV suggesting an electron loss mechanism, which could be due to via resonance electron attachment processes producing negative ions in this rich electronegative gas mixture. This behavior is more prominent towards the electrode edge.
7. Many-body effects in intermolecular forces.
PubMed
Elrod, M J; Saykally, R J
1994-11-01
The authors provide a review and literature survey of many-body effects in intermolecular forces. Topics include experimental methods, theoretical methods, many-body effects in atomic systems, and many-body effects in aqueous and nonaqueous molecular systems.
8. Probing the transition between seismically coupled and decoupled segments along an ancient subduction interface
Angiboust, Samuel; Kirsch, Josephine; Oncken, Onno; Glodny, Johannes; Monié, Patrick; Rybacki, Erik
2015-06-01
The transition zone at the downdip end of seismic coupling along subduction interfaces is often the site of megathrust earthquake nucleation and concentrated postseismic afterslip, as well as the focus site of episodic tremor and slip features. Exhumed remnants of the former Alpine subduction zone found in the Swiss Alps allow analyzing fluid and deformation processes near the transition zone region (30-40 km paleodepth). The Dent Blanche Thrust (DBT) is a lower blueschist-facies shear zone interpreted as a fossilized subduction interface where granitic mylonites overlie a metamorphosed accretionary wedge. We report field observations from the DBT region where multiple, several tens of meters thick foliated cataclastic networks are interlayered within the basal DBT mylonites. Petrological results and microstructural observations indicate that the various cataclasis events took place at near-peak metamorphic conditions (400-500°C, 1.1-1.3 GPa) during subduction of the Tethyan seafloor in Eocene times (42-48 Ma). Some of these networks exhibit mutual crosscutting relationships between mylonites, foliated cataclasites, and vein systems indicating mutual overprinting between brittle deformation and ductile creep. Whole-rock chemical compositions, in situ 40Ar-39Ar age data of recrystallized phengite, and Sr isotopic signatures reveal that DBT rocks also underwent multiple hydrofracturing and metasomatic events via the infiltration of fluids mainly derived from the oceanic metasediments underneath the DBT. From the rock fabrics, we infer strain rate fluctuations of several orders of magnitude beyond subduction strain rates (˜10-12 s-1) accompanied by fluctuation of supralithostatic and quasi-lithostatic fluid pressures (1 ≥ λ > 0.95). DBT brittle-plastic deformation switches highlight the diversity of deformation processes and fluid-rock interactions in the transition zone region of the subduction interface.
9. Relative intermolecular orientation probed via molecular heat transport.
PubMed
Chen, Hailong; Bian, Hongtao; Li, Jiebo; Wen, Xiewen; Zheng, Junrong
2013-07-25
In this work, through investigating a series of liquid, glassy, and crystalline samples with ultrafast multiple-mode 2D IR and IR transient absorption methods, we demonstrated that the signal anisotropy of vibrational relaxation-induced heat effects is determined by both relative molecular orientations and molecular rotations. If the relative molecular orientations are randomized or molecular rotations are fast compared to heat transfer, the signal anisotropy of heat effects is zero. If the relative molecular orientations are anisotropic and the molecular rotations are slow, the signal anisotropy of heat effects can be nonzero, which is determined by the relative orientations of the energy source mode and the heat sensor mode within the same molecule and in different molecules. We also demonstrated that the correlation between the anisotropy value of heat signal and the relative molecular orientations can be quantitatively calculated.
10. Probing the transition between seismically coupled and decoupled segments along an ancient subduction interface
Angiboust, Samuel; Kirsch, Josephine; Oncken, Onno; Glodny, Johannes; Monié, Patrick; Rybacki, Erik
2015-04-01
Although of paramount importance for understanding the nature of mechanical coupling in subduction zones, the portions downdip of the locked segments of subduction interfaces remain poorly understood. These deep transition zones often are sites of megathrust earthquake nucleation and concentrated postseismic afterslip, as well as the focus sites of episodic tremor and slip features, recently discovered at several plate boundaries. The extensive, exhumed remnants of the former Alpine subduction zone found in the Swiss Alps allow analyzing fluid and deformation processes at the original depths of 30-40 km, typical for the depth range of such transition zones. We identify the shear zone at the base of the Dent Blanche complex (Dent Blanche Thrust, DBT) as a lower blueschist-facies, fossilized subduction interface where granitic mylonites overlie a metamorphosed ophiolite. We report field observations from the DBT region where a complex, discontinuous network of meter- to tens of meters-thick foliated cataclasites is interlayered with the basal DBT mylonites. Petrological results indicate that cataclasis took place at near peak metamorphic conditions (450-500°C, c. 1.2 GPa) during subduction of the Tethyan seafloor in Eocene times (42-48 Ma). Despite some tectonic reactivation during exhumation, these networks exhibit mutual cross-cutting relationships between mylonites, foliated cataclasites and vein systems indicating multiple switching between brittle deformation and ductile creep. Whole-rock chemical compositions, in situ 40Ar-39Ar age data of newly formed phengite, and strontium isotopic signatures reveal that these rocks also underwent multiple hydrofracturing events via infiltration of fluids mainly derived from the ophiolitic metasediments underneath the DBT. From the rock fabrics we infer strain rate fluctuations of several orders of magnitude beyond subduction strain rates (c. 10-12s-1) accompanied by fluctuation of near-lithostatic fluid pressures (1>λ>0
11. Intraclade Heterogeneity in Nitrogen Utilization by Marine Prokaryotes Revealed Using Stable Isotope Probing Coupled with Tag Sequencing (Tag-SIP).
PubMed
Morando, Michael; Capone, Douglas G
2016-01-01
Nitrogen can greatly influence the structure and productivity of microbial communities through its relative availability and form. However, the roles of specific organisms in the uptake of different nitrogen species remain poorly characterized. Most studies seeking to identify agents of assimilation have been correlative, indirectly linking activity measurements (e.g., nitrate uptake) with the presence or absence of biological markers, particularly functional genes and their transcripts. Evidence is accumulating of previously underappreciated functional diversity in major microbial subpopulations, which may confer physiological advantages under certain environmental conditions leading to ecotype divergence. This microdiversity further complicates our view of genetic variation in environmental samples requiring the development of more targeted approaches. Here, next-generation tag sequencing was successfully coupled with stable isotope probing (Tag-SIP) to assess the ability of individual phylotypes to assimilate a specific N source. Our results provide the first direct evidence of nitrate utilization by organisms thought to lack the genes required for this process including the heterotrophic clades SAR11 and the Archaeal Marine Group II. Alternatively, this may suggest the existence of tightly coupled metabolisms with primary assimilators, e.g., symbiosis, or the rapid and efficient scavenging of recently released products by highly active individuals. These results may be connected with global dominance often seen with these clades, likely conferring an advantage over other clades unable to access these resources. We also provide new direct evidence of in situ nitrate utilization by the cyanobacterium Prochlorococcus in support of recent findings. Furthermore, these results revealed widespread functional heterogeneity, i.e., different levels of nitrogen assimilation within clades, likely reflecting niche partitioning by ecotypes.
12. Water protein dynamic coupling and new opportunities for probing it at low to physiological temperatures in aqueous solutions
SciTech Connect
Mamontov, Eugene; Chu, Xiang-Qiang
2012-01-01
Both the structure and dynamics of biomolecules are known to be essential for their biological function. In the dehydrated state, the function of biomolecules, such as proteins, is severely impeded, so hydration is required for bioactivity. The dynamics of the hydrated biomolecules and their hydration water are related - but how closely? The problem involves several layers of complexity. Even for water in the bulk state, the contribution from various dynamic components to the overall dynamics is not fully understood. In biological systems, the effects of confinement on the hydration water further complicate the picture. Even if the various components of the hydration water dynamics are properly understood, which of them are coupled to the protein dynamics, and how? The studies of protein dynamics over the wide temperature range, from physiological to low temperatures, provide some answers to these question. At low temperatures, both the protein and its hydration water behave as solids, with only vibrational degrees of freedom. As the temperature is increased, non-vibrational dynamic components start contributing to the measurable dynamics and eventually become dominant at physiological temperatures. Thus, the temperature dependence of the dynamics of protein and its hydration water may allow probing various dynamic components separately. In order to suppress the water freezing, the low-temperature studies of protein rely on either low-hydrated samples (essentially, hydrated protein powders), or cryo-protective solutions. Both approaches introduce the hydration environments not characteristic of the protein environments in living systems, which are typically aqueous protein solutions of various concentrations. In this paper, we discuss the coupling between the dynamic components of the protein and its hydration water by critical examining of the existing literature, and then propose that proteins can be studied in an aqueous solution that is remarkably similar in
13. Intraclade Heterogeneity in Nitrogen Utilization by Marine Prokaryotes Revealed Using Stable Isotope Probing Coupled with Tag Sequencing (Tag-SIP)
PubMed Central
Morando, Michael; Capone, Douglas G.
2016-01-01
Nitrogen can greatly influence the structure and productivity of microbial communities through its relative availability and form. However, the roles of specific organisms in the uptake of different nitrogen species remain poorly characterized. Most studies seeking to identify agents of assimilation have been correlative, indirectly linking activity measurements (e.g., nitrate uptake) with the presence or absence of biological markers, particularly functional genes and their transcripts. Evidence is accumulating of previously underappreciated functional diversity in major microbial subpopulations, which may confer physiological advantages under certain environmental conditions leading to ecotype divergence. This microdiversity further complicates our view of genetic variation in environmental samples requiring the development of more targeted approaches. Here, next-generation tag sequencing was successfully coupled with stable isotope probing (Tag-SIP) to assess the ability of individual phylotypes to assimilate a specific N source. Our results provide the first direct evidence of nitrate utilization by organisms thought to lack the genes required for this process including the heterotrophic clades SAR11 and the Archaeal Marine Group II. Alternatively, this may suggest the existence of tightly coupled metabolisms with primary assimilators, e.g., symbiosis, or the rapid and efficient scavenging of recently released products by highly active individuals. These results may be connected with global dominance often seen with these clades, likely conferring an advantage over other clades unable to access these resources. We also provide new direct evidence of in situ nitrate utilization by the cyanobacterium Prochlorococcus in support of recent findings. Furthermore, these results revealed widespread functional heterogeneity, i.e., different levels of nitrogen assimilation within clades, likely reflecting niche partitioning by ecotypes. PMID:27994576
14. Probe tip heating assembly
SciTech Connect
Schmitz, Roger William; Oh, Yunje
2016-10-25
A heating assembly configured for use in mechanical testing at a scale of microns or less. The heating assembly includes a probe tip assembly configured for coupling with a transducer of the mechanical testing system. The probe tip assembly includes a probe tip heater system having a heating element, a probe tip coupled with the probe tip heater system, and a heater socket assembly. The heater socket assembly, in one example, includes a yoke and a heater interface that form a socket within the heater socket assembly. The probe tip heater system, coupled with the probe tip, is slidably received and clamped within the socket.
15. Hyperfine interaction, spin polarization, and spin delocalization as probes of donor-bridge-acceptor interactions in exchange-coupled biradicals.
PubMed
Kirk, Martin L; Shultz, David A; Habel-Rodriguez, Diana; Schmidt, Robert D; Sullivan, Ubie
2010-11-18
Computations and EPR spectroscopy are used to probe the spin distribution of donor-bridge-acceptor (D-B-A) biradical complexes: Tp(Cum,Me)Zn(SQ-NN) (1), Tp(Cum,Me)Zn(SQ-1,4-Ph-NN) (2), Tp(Cum,Me)Zn(SQ-2,5-TP-NN) (3), and Tp(Cum,Me)Zn(SQ-2,5-Xyl-NN) (4) (SQ = orthosemiquinone and NN = nitronylnitroxide). These complexes are ground-state analogs of the charge-separated excited states formed in photoinduced electron transfer reactions. The intraligand magnetic exchange interaction (J) in these complexes is mediated by the bridges and has been found to stabilize the triplet ground states of 1 and 2. Detailed spectroscopic and bonding calculations have been used to elucidate the role of the bridge fragment (B) and its conformation relative to donor (SQ) and acceptor (NN) on spin density distributions. The computed results correlate well with experimental nitrogen hyperfine coupling constants.
16. Ferromagnetic Cu-O-Cu coupling in CaCu3Sn4O12 probed by neutron diffraction.
PubMed
Kayser, P; Retuerto, M; Sánchez-Benítez, J; Martínez-Lope, M J; Fernández-Díaz, M T; Alonso, J A
2012-12-12
The A-site ordered perovskite oxide with the formula CaCu(3)Sn(4)O(12) has been synthesized in polycrystalline form under moderate pressure conditions (3.5 GPa) in combination with high temperature (1000 °C). This oxide crystallizes in the cubic space group [Formula: see text] (no. 204) with the unit-cell parameter a = 7.64535(6) Å at 300 K. The SnO(6) network is extremely tilted, giving rise to a square planar coordination for Cu(2+) cations. The non-magnetic character of Sn(4+) offers an excellent opportunity to probe the magnetism of Cu(2+) at the A sublattice in CaCu(3)Sn(4)O(12). Magnetic susceptibility shows that this compound is ferromagnetic below T(C) = 10 K, which is an unusual magnetic behaviour in cuprates. This peculiar aspect has been examined by neutron powder diffraction. The refinement of the magnetic structure at 4 K indeed indicates a parallel coupling between Cu(2+) spins with a magnetic moment of 0.5 μ(B)/Cu atom.
17. High Explosives Mixtures Detection Using Fiber Optics Coupled: Grazing Angle Probe/Fourier Transform Reflection Absorption Infrared Spectroscopy
Primera-Pedrozo, Oliva M.; Soto-Feliciano, Yadira M.; Pacheco-Londoño, Leonardo C.; Hernández-Rivera, Samuel P.
2008-12-01
Fourier Transform Infrared Spectroscopy operating in Reflection-Absorption mode has been demonstrated as a potential spectroscopic technique to develop new methodologies for detection of chemicals deposited on metallic surfaces. Mid-IR transmitting optical fiber bundle coupled to an external Grazing Angle Probe and an MCT detector together with a bench Michelson interferometer have been used to develop a highly sensitive and selective methodology for detecting traces of organic compounds on metal surfaces. The methodology is remote sensed, in situ and can detect surface loading concentrations of nanograms/cm2 of most target compounds. It is an environmentally friendly, solvent free technique that does not require sample preparation. In this work, the ever-important task of high explosives detection, present as traces of neat crystalline forms and in lab-made mixtures, equivalent to the important explosive formulation Pentolite, has been addressed. The sample set consisted of TNT, PETN (both pure samples) and the formulation based on them: Pentolite, present in various loading concentrations. The spectral data collected was subjected to a number of statistical pre-treatments, including first derivative and normalization transformations to make the data more suitable for the analysis. Principal Components Analysis combined with Linear Discriminant Analysis allowed the classification and discrimination of the target analytes contained in the sample set. Loading concentrations as 220 ng/cm2 were detected for each explosive in neat form and the in the simulated mixture of Pentolite.
18. Light propagation from fluorescent probes in biological tissues by coupled time-dependent parabolic simplified spherical harmonics equations
PubMed Central
Domínguez, Jorge Bouza; Bérubé-Lauzière, Yves
2011-01-01
We introduce a system of coupled time-dependent parabolic simplified spherical harmonic equations to model the propagation of both excitation and fluorescence light in biological tissues. We resort to a finite element approach to obtain the time-dependent profile of the excitation and the fluorescence light fields in the medium. We present results for cases involving two geometries in three-dimensions: a homogeneous cylinder with an embedded fluorescent inclusion and a realistically-shaped rodent with an embedded inclusion alike an organ filled with a fluorescent probe. For the cylindrical geometry, we show the differences in the time-dependent fluorescence response for a point-like, a spherical, and a spherically Gaussian distributed fluorescent inclusion. From our results, we conclude that the model is able to describe the time-dependent excitation and fluorescent light transfer in small geometries with high absorption coefficients and in nondiffusive domains, as may be found in small animal diffuse optical tomography (DOT) and fluorescence DOT imaging. PMID:21483606
19. Langmuir Probe Measurements of Inductively Coupled CHF3/Ar and Ar/CHF3/O2 Plasmas
NASA Technical Reports Server (NTRS)
Sharma, S. P.; Rao, M. V. V. S.; Meyyappan, M.
2000-01-01
Plasma parameters, such as, electron number density (ne), electron temperature (Te), y electron energy distribution function (EEDF), mean electron energy (Ee), ion number density (ni), and plasma potential (Vp), have been measured by using Langmuir probe in low-pressure (10-50 mTorr) inductively coupled CHF3/Ar and CHF3/Ar/O2 plasmas generated in the GEC cell. The measurements were made at the center of the plasma, keeping the lower electrode grounded, for various CHF3/Ar and Ar/CHF3/O2 mixtures operating at 10-50 mTorr pressures and two input RF power levels, 200 and 300 W. EEDF data show a strong Druyvesteyn distribution with relatively lower number of low energy electrons as compared to a Maxwell distribution and a large electron population with energies higher than the plasma potential. The results further show that at low CHF3 concentrations (less than 50%) the electron number density remains nearly constant with increase in pressure. At higher CHF3 concentrations, however, it decreases with increase in pressure. Plasma potential and electron temperature increase with decrease in pressure and with increase in CHF3 concentration. An analysis of the above observations and mechanisms will be presented.
20. An improved thin-layer chromatography/mass spectrometry coupling using a surface sampling probe electrospray ion trap system
SciTech Connect
Ford, Michael J; Van Berkel, Gary J
2004-01-01
A combined surface sampling probe/electrospray emitter coupled with an ion trap mass spectrometer was used for the direct read out of unmodified reversed-phase C18 thin-layer chromatography (TLC) plates. The operation of the surface sampling electrospray ionization interface in positive and negative ionization modes was demonstrated through the direct analysis of TLC plates on which a commercial test mix comprised of four dye compounds viz., rhodamine B, fluorescein, naphthol blue black, and fast green FCF, and an extract of the caffeine-containing plant Ilex vomitoria, were spotted and developed. Acquisition of full-scan mass spectra and automated collection of MS/MS product ion spectra while scanning a development lane along the surface of a TLC plate demonstrated the advantages of using an ion trap in this combination. Details of the sampling system, benefits of analyzing a developed lane in both positive ion and negative ion modes, levels of detection while surface scanning, surface scan speed effects, and the utility of three-dimensional data display, are also discussed.
1. A jet emission model to probe the dynamics of accretion and ejection coupling in black hole X-ray binaries
Malzac, Julien
2016-07-01
Compact jets are probably the most common form of jets in X-ray binaries and Active Galactic Nuclei. They seem to be present in all sources in the so-called hard X-ray spectral state. They are characterised by a nearly flat Spectral Energy Distribution (SED) extending from the radio to the infrared bands. This emission is usually interpreted as partially self absorbed synchrotron emission from relativistic leptons accelerated in the jet. The observed flat spectral shape requires energy dissipation and acceleration of particules over a wide range of distances along the jet. This distributed energy dissipation is likely to be powered by internal shocks caused by fluctuations of the outflow velocity. I will discuss such an internal shock model in the context of black hole binaries. I will show that internal shocks can produce the observed SEDs and also predict a strong, wavelength dependent, variability that resembles the observed one. The assumed velocity fluctuations of the jet must originate in the accretion flow. The model thus predicts a strong connection between the observable properties of the jet in the radio to IR bands, and the variability of the accretion flow as observed in X-rays. If the model is correct, this offers a unique possibility to probe the dynamics of the coupled accretion and ejection processes leading to the formation of compact jets.
2. Probing the existence of G protein-coupled receptor dimers by positive and negative ligand-dependent cooperative binding.
PubMed
Albizu, Laura; Balestre, Marie-Noëlle; Breton, Christophe; Pin, Jean-Philippe; Manning, Maurice; Mouillac, Bernard; Barberis, Claude; Durroux, Thierry
2006-11-01
An increasing amount of ligand binding data on G protein-coupled receptors (GPCRs) is not compatible with the prediction of the simple mass action law. This may be related to the propensity of most GPCRs, if not all, to oligomerize. Indeed, one of the consequences of receptor oligomerization could be a possible cross-talk between the protomers, which in turn could lead to negative or positive cooperative ligand binding. We prove here that this can be demonstrated experimentally. Saturation, dissociation, and competition binding experiments were performed on vasopressin and oxytocin receptors expressed in Chinese hamster ovary or COS-7 cells. Linear, concave, and convex Scatchard plots were then obtained, depending on the ligand used. Moreover, some competition curves exhibited an increase of the radiotracer binding for low concentrations of competitors, suggesting a cooperative binding process. These data demonstrate that various vasopressin analogs display either positive or negative cooperative binding. Because positive cooperative binding cannot be explained without considering receptor as multivalent, these binding data support the concept of GPCR dimerization process. The results, which are in good accordance with the predictions of previous mathematical models, suggest that binding experiments can be used to probe the existence of receptor dimers.
3. Trace analysis of energetic materials via direct analyte-probed nanoextraction coupled to direct analysis in real time mass spectrometry.
PubMed
Clemons, Kristina; Dake, Jeffrey; Sisco, Edward; Verbeck, Guido F
2013-09-10
Direct analysis in real time mass spectrometry (DART-MS) has proven to be a useful forensic tool for the trace analysis of energetic materials. While other techniques for detecting trace amounts of explosives involve extraction, derivatization, solvent exchange, or sample clean-up, DART-MS requires none of these. Typical DART-MS analyses directly from a solid sample or from a swab have been quite successful; however, these methods may not always be an optimal sampling technique in a forensic setting. For example, if the sample were only located in an area which included a latent fingerprint of interest, direct DART-MS analysis or the use of a swab would almost certainly destroy the print. To avoid ruining such potentially invaluable evidence, another method has been developed which will leave the fingerprint virtually untouched. Direct analyte-probed nanoextraction coupled to nanospray ionization-mass spectrometry (DAPNe-NSI-MS) has demonstrated excellent sensitivity and repeatability in forensic analyses of trace amounts of illicit drugs from various types of surfaces. This technique employs a nanomanipulator in conjunction with bright-field microscopy to extract single particles from a surface of interest and has provided a limit of detection of 300 attograms for caffeine. Combining DAPNe with DART-MS provides another level of flexibility in forensic analysis, and has proven to be a sufficient detection method for trinitrotoluene (TNT), RDX, and 1-methylaminoanthraquinone (MAAQ).
4. An improved thin-layer chromatography/mass spectrometry coupling using a surface sampling probe electrospray ion trap system.
PubMed
Ford, Michael J; Van Berkel, Gary J
2004-01-01
A combined surface sampling probe/electrospray emitter coupled with an ion trap mass spectrometer was used for the direct read out of unmodified reversed-phase C18 thin-layer chromatography (TLC) plates. The operation of the surface sampling electrospray ionization interface in positive and negative ionization modes was demonstrated through the direct analysis of TLC plates on which a commercial test mix comprised of four dye compounds viz., rhodamine B, fluorescein, naphthol blue black, and fast green FCF, and an extract of the caffeine-containing plant Ilex vomitoria, were spotted and developed. Acquisition of full-scan mass spectra and automated collection of MS/MS product ion spectra while scanning a development lane along the surface of a TLC plate demonstrated the advantages of using an ion trap in this combination. Details of the sampling system, benefits of analyzing a developed lane in both positive ion and negative ion modes, levels of detection while surface scanning, surface scan speed effects, and the utility of three-dimensional data display, are also discussed. Copyright 2004 John Wiley & Sons, Ltd.
5. Van Allen Probes observations of cross-scale coupling between electromagnetic ion cyclotron waves and higher-frequency wave modes
Colpitts, C. A.; Cattell, C. A.; Engebretson, M.; Broughton, M.; Tian, S.; Wygant, J.; Breneman, A.; Thaller, S.
2016-11-01
We present observations of higher-frequency ( 50-2500 Hz, 0.1-0.7 fce) wave modes modulated at the frequency of colocated lower frequency (0.5-2 Hz, on the order of fci) waves. These observations come from the Van Allen Probes Electric Field and Waves instrument's burst mode data and represent the first observations of coupling between waves in these frequency ranges. The higher-frequency wave modes, typically whistler mode hiss and chorus or magnetosonic waves, last for a few to a few tens of seconds but are in some cases observed repeatedly over several hours. The higher-frequency waves are observed to be unmodulated before and after the presence of the electromagnetic ion cyclotron (EMIC) waves, but when the EMIC waves are present, the amplitude of the higher-frequency waves drops to the instrument noise level once every EMIC wave cycle. Such modulation could significantly impact wave-particle interactions such as acceleration and pitch angle scattering, which are crucial in the formation and depletion of the radiation belts. We present one case study with broadband, high-frequency waves observed to be modulated by EMIC waves repeatedly over a 2 h time span on both spacecraft. Finally, we show two additional case studies where other high-frequency wave modes exhibit similar modulation.
6. Combination Bands of the Nonpolar OCS Dimer Involving Intermolecular Modes
Rezaei, M.; Oliaee, J. Norooz; Moazzen-Ahmadi, N.; McKellar, A. R. W.
2012-06-01
Spectra of the nonpolar carbonyl sulfide in the region of the OCS ν_1 fundamental band were observed in a supersonic slit-jet apparatus. The expansion gas was probed using radiation from a tunable diode laser employed in a rapid-scan signal averaging mode. Three bands centered at 2085.906, 2103.504, and 2114.979 cm-1 were observed and anlysed. The rotational assignment and fitting of the bands were made by fixing the lower state parameters to those for the ground state of nonpolar (OCS)_2, thus confirming that they were indeed combination bands of the of the most stable isomer of OCS dimer. The band centered at 2085.906 cm-1 is a combination of the forbidden A_g intramolecular mode plus the geared bend intermolecular mode and that centered at 2114.979 cm-1 is a combination of the allowed B_u intramolecular mode plus the intermolecular van der Waals stretch. The combination at 2103.504 cm-1 can be assigned as a band whose upper state involves four quanta of the intramolecular bend or the B_u intramolecular mode plus two quanta of the intermolecular torsional mode. Isotopic work is needed to conclusively identify the vibrational assignment of this band. Our experimental frequencies for the geared bend and van der Waals modes are in good agreement with a recent high level ab initio calculation by Brown et al. J. Brown, Xiao-Gang Wang, T. Carrington Jr. and Richard Dawes, Journal of Chemical Physics, submitted.
7. Probing local structures of siliceous zeolite frameworks by solid-state NMR and first-principles calculations of 29Si-O-29Si scalar couplings.
PubMed
2009-03-21
Subtle structural details of siliceous zeolites are probed by using two-bond scalar (J) coupling constants to characterize covalently bonded 29Si-O-29Si site pairs and local framework order. Solid-state two-dimensional (2D) 29Si{29Si} NMR measurements and first-principles calculations of 2J(29Si-O-29Si) couplings shed insights on both the local structures of siliceous zeolites Sigma-2 and ZSM-12, as well as the sensitivity of J couplings for detailed characterization analyses. DFT calculations on a model linear silicate dimer show that 2J(Si-O-Si) couplings have complicated multiple angular dependencies that make semi-empirical treatments impractical, but which are amenable to cluster approaches for accurate J-coupling calculations in zeolites. DFT calculations of 2J(29Si-O-29Si) couplings of the siliceous zeolite Sigma-2, whose framework structure is known to high accuracy from single-crystal X-ray diffraction studies, yield excellent agreement between calculated and experimentally measured 2J(Si-O-Si) couplings. For the siliceous zeolite ZSM-12, calculated 2J(29Si-O-29Si) couplings based on less-certain powder X-ray diffraction analyses deviate significantly from experimental values, while a refined structure based on 29Si chemical-shift-tensor analyses shows substantially improved agreement. 29Si J-coupling interactions can be used as sensitive probes of local structures of zeolitic frameworks and offer new opportunities for refining and solving complicated structures, in combination with complementary scattering, modeling, and other nuclear spin interactions.
8. Electroreductive Intermolecular Coupling of Coumarins with Benzophenones: Synthesis of 4-(2-Hydroxyphenyl)-5,5-diaryl-γ-butyrolactones, 2-(2,2-Diaryl-2,3-dihydrobenzofuran-3-yl)acetic Acids, and 4-(Diarylmethyl)coumarins.
PubMed
Kise, Naoki; Hamada, Yusuke; Sakurai, Toshihiko
2016-11-18
The electroreductive coupling of coumarins with benzophenones in the presence of TMSCl gave adducts reacted at the 4-position of coumarins as trimethylsilyl ethers. From 3-methylcoumarin, 3,4-cis-adducts were formed stereoselectively. The de-trimethylsilylation of the adducts with 1 M HCl aq or TBAF in THF at 25 °C produced 4-(2-hydroxyphenyl)-5,5-diaryl-γ-butyrolactones. The γ-butyrolactones were further transformed to 2-(2,2-diaryl-2,3-dihydrobenzofuran-3-yl)acetic acids by treatment with 1 M HCl aq at reflux temperature. The de-trimethylsilylation of the adducts with 1 M HCl in MeOH afforded 2-(2,2-diaryl-2,3-dihydrobenzofuran-3-yl)acetic acid methyl esters. The de-trimethylsiloxylation of the adducts or dehydration of the γ-butyrolactones brought about 4-(diarylmethyl)coumarins.
9. Density functional calculation of intermolecular potentials.
PubMed
Nyeland, Carl
2011-06-30
Calculations of intermolecular potentials following the density functional theory (DFT) turn out to be very complicated without using some appropriate approximations. Most often the following three approximations have been considered. In one approximation the disturbed charge distributions during collisions are reduced to sums of undisturbed charge distributions from the colliding species. In another approximation, the so-called local density approximation (LDA), one neglects the fact that the intermolecular potentials that depend on charge densities also depend on gradients in the densities. In a third approximation one assumes that the intermolecular potential can be considered as a sum of two terms: a term for the long-range geometry and a term for the short-range geometry. In this Article the three approximations mentioned will be discussed for numerical accuracy for calculations of potentials between inert gas atoms and for calculations of potentials between surfaces and inert gas atoms. In the discussion a few other approximations will be mentioned too.
10. Conformation and intermolecular interactions of SA2 peptides self-assembled into vesicles.
PubMed
van Hell, Albert J; Klymchenko, Andrey; Burgers, Pepijn P; Moret, Ed E; Jiskoot, Wim; Hennink, Wim E; Crommelin, Daan J A; Mastrobattista, Enrico
2010-09-02
Previously we have shown that the recombinantly produced SA2 amphiphilic oligopeptide (Ac-Ala-Ala-Val-Val-Leu-Leu-Leu-Trp-Glu-Glu-COOH) self-assembles into nanovesicles (van Hell et al. 2007). In this study, the intermolecular interactions that contribute to the formation of such peptide vesicles are examined. First, analysis of a 3-hydroxyflavone fluorescent probe inserted into the peptide assemblies demonstrated that the peptide self-assembly is based on hydrophobic clustering. The polarity of this hydrophobic microenvironment was comparable to that of negatively charged lipid bilayers. A substantial level of hydration at the hydrophilic-hydrophobic interface was detected, as was further confirmed by tryptophan fluorescence analysis. However, organic solvents such as acetonitrile, tetrahydrofuran, or ethanol could not disrupt SA2 oligopeptide vesicles, whereas these solvents fully disintegrated lipid vesicles. Instead, the SA2 assembly immediately disintegrated in hydrogen breaking solvents such dimethylsulfoxide and dimethylformamide, suggesting the involvement of additional intermolecular interactions via hydrogen bonding. Circular dichroism and Fourier transform infrared spectroscopy excluded well-defined patterns of intramolecular hydrogen bonding and indicated the polyproline type II as the dominant SA2 peptide conformation, which enables intermolecular hydrogen bonding. All-atom computational simulations were used to confirm the presence of such intermolecular hydrogen bonds and degrees of hydration. On the basis of the experimental and computational data presented, we propose a model of an interdigitated peptide assembly that involves intermolecular hydrogen bonding in addition to hydrophobic interactions that stabilize SA2 oligopeptide vesicles.
11. Optical emission spectroscopy and Langmuir probe diagnostics of CH3F/O2 inductively coupled plasmas
Karakas, Erdinc; Donnelly, Vincent M.; Economou, Demetre J.
2013-06-01
A CH3F:O2 (50%:50%) inductively coupled discharge, sustained in a compact plasma reactor, was investigated as a function of power (20-400 W) and pressure (9-30 mTorr), using optical emission spectroscopy and Langmuir probe measurements. The electron density increased linearly with power but only weakly with pressure. The effective electron temperature was nearly independent of power and pressure. The gas temperature, obtained from the rotational structure of N2 (C → B) optical emission, increased from 400 to 900 K as a function of inductive mode power between 75 and 400 W at 10 mTorr. For constant feed gas flow, the absolute H, F, and O atom densities, estimated by optical emission rare gas actinometry, increased linearly with power. The absolute number density ratios H/Ar, F/Ar, and O/Ar, increased, decreased, and remained constant, respectively, with pressure. The H-atom density was estimated to be 5.4 × 1013 cm-3 at 400 W and 10 mTorr (gas temperature = 900 K), implying a high degree of dissociation of the CH3F feedstock gas. The F and O atom number densities were much lower (8.3 × 1012 cm-3 and 5.9 × 1012 cm-3, respectively) for the same conditions, suggesting that most of the fluorine and oxygen is contained in reaction products HF, CO, CO2, H2O, and OH. The relative number densities of HF, CO, and CO2 were observed to first rapidly increase with power, and then reach a plateau or decay slightly at higher power. Reaction mechanisms were proposed to explain the observed behavior of the number density of F and HF vs. power and pressure.
12. Investigation of the electron kinetics in O2 capacitively coupled plasma with the use of a Langmuir probe
Kechkar, S.; Swift, P.; Kelly, S.; Kumar, S.; Daniels, S.; Turner, M.
2017-06-01
A Langmuir probe was used to measure various electron plasma parameters in O2 capacitively coupled plasma. It was shown that the variation in these plasma parameters was due to changes in the electron heating mechanisms as the discharge conditions varied. The so called ‘α-γ’ mode transition in O2 plasma (100 mTorr) was identified from the power evolution (30-600 W) of the electron energy probability function (EEPF), electron density (n e) and effective electron temperature (T eff). The EEPF evolved from Druyvesteyn to bi-Maxwellian with increasing applied power which resulted in a rapid decrease and an abrupt increase in T eff and n e respectively. Comparisons were made to the same mode transition for similar conditions in Ar plasma. The EEPFs were Druyvesteyn in the α mode and evolved into a Maxwellian like EEPF in the γ mode of an Ar plasma. Two distinct trends of n e versus power was observed, it was shown that the measured rf current and rf voltage had a similar behavior. The pressure evolution of the EEPF, n e, and T eff was also investigated in O2 plasma operated at both 30 and 200 W. At 30 W the number of high energy electrons decreased and flattening of the low energy portion of the EEPF occurred with increasing gas pressure (10-100 mTorr) which indicates a collisionless to collisional heating transition. However, at 200 W the right combination of rf voltage and pressure was met for the discharge to evolve into the γ mode as the pressure increased. This was evident from significant narrowing of the EEPF as the pressure increased.
13. Optical emission diagnostics with electric probe measurements of inductively coupled Ar/O{sub 2}/Ar-O{sub 2} plasmas
SciTech Connect
Chung, T. H.; Kang, Hae Ra; Bae, Min Keun
2012-11-15
Physical properties of low-pressure inductively coupled argon, oxygen, and Ar-O{sub 2} mixture plasmas are investigated using optical emission spectroscopy (OES) combined with an rf-compensated Langmuir probe measurement. In each gas discharge, the electron density and the electron temperature were obtained by using the probe. The electron temperature was also obtained by OES models and compared with that measured by the probe. The electron temperature was observed to decrease with increasing power and pressure and also observed to decrease with increasing Ar content. Argon metastable densities were calculated based on an optical transition model. In Ar-O{sub 2} discharges, the dissociation fraction of O{sub 2} molecules was estimated using optical emission actinometry. The dissociation fraction was observed to increase with increasing power and Ar content.
14. Intermolecular interaction potentials of the methane dimer from the local density approximation
SciTech Connect
Chen Xiangrong; Bai Yulin; Zhu Jun; Yang Xiangdong
2004-03-01
The intermolecular interaction potentials of methane (CH{sub 4}) dimer are calculated within the density functional theory in the local density approximation (LDA). It is found that the calculated potentials have minima when the intermolecular distance of CH{sub 4} dimer is about 7.0 a.u., which is in good agreement with the experiment. The depth of the potential is 0.017 eV. The results obtained by our LDA calculations seem to agree well with those obtained by MP2, MP3, and CCSD from the Moeller-Plesset and coupled cluster methods by Tsuzuki et al. and with the experimental data.
15. Mapping intermolecular bonding in C₆₀.
PubMed
Sundqvist, Bertil
2014-08-22
The formation of intermolecular bonds in C₆₀ has been investigated in detail at pressures below 2.2 GPa and up to 750 K. Fullerene samples were heated in a temperature gradient to obtain data on the formation of dimers and low-dimensional polymers along isobars. Intermolecular bonding was analyzed ex situ by Raman scattering, using both intramolecular modes and intermolecular stretching modes. Semi-quantitative reaction maps are given for the formation of dimers and chains. The activation energy for dimer formation decreases by 0.2 meV pm(-1) when intermolecular distances decrease and dimer formation is noticeably affected by the rotational state of molecules. Above 400-450 K larger oligomers are formed; below 1.4 GPa most of these are disordered, with small domains of linear chains, but above this the appearance of stretching modes indicates the existence of ordered one-dimensional polymers. At the highest pressures and temperatures two-dimensional polymers are also observed.
16. An improved intermolecular potential for sulfur hexafluoride
SciTech Connect
Aziz, R.A.; Slaman, M.J. ); Taylor, W.L.; Hurly, J.J. Department of Chemistry, University of Cincinnati, Cincinnati, Ohio 45221 )
1991-01-15
Second virial coefficient data and viscosity were used to evaluate effective isotropic intermolecular potential functions proposed in the literature for sulfur hexafluoride. It was found that none of the potentials could predict the properties simultaneously. We have constructed a Morse--Morse--Spline--van der Waals (MMSV) potential which satisfactorily correlates second virial coefficient and viscosity data at the same time.
17. Mapping intermolecular bonding in C60
PubMed Central
Sundqvist, Bertil
2014-01-01
The formation of intermolecular bonds in C60 has been investigated in detail at pressures below 2.2 GPa and up to 750 K. Fullerene samples were heated in a temperature gradient to obtain data on the formation of dimers and low-dimensional polymers along isobars. Intermolecular bonding was analyzed ex situ by Raman scattering, using both intramolecular modes and intermolecular stretching modes. Semi-quantitative reaction maps are given for the formation of dimers and chains. The activation energy for dimer formation decreases by 0.2 meV pm−1 when intermolecular distances decrease and dimer formation is noticeably affected by the rotational state of molecules. Above 400–450 K larger oligomers are formed; below 1.4 GPa most of these are disordered, with small domains of linear chains, but above this the appearance of stretching modes indicates the existence of ordered one-dimensional polymers. At the highest pressures and temperatures two-dimensional polymers are also observed. PMID:25145952
18. Catalytic intermolecular alkene oxyamination with nitrenes.
PubMed
Dequirez, Geoffroy; Ciesielski, Jennifer; Retailleau, Pascal; Dauban, Philippe
2014-07-14
The Rh(II)-catalyzed intermolecular addition of nitrenes to aromatic and aliphatic alkenes provides vicinal amino alcohols with yields of up to 95 % and complete regioselectivity. This 1,2-oxyamination reaction involves the formation of an aziridine intermediate that undergoes in situ ring opening. The latter is induced by the Rh-bound nitrene that behaves as a Lewis acid.
19. Intermolecular Slip Mechanism in Tropocollagen Nanofibrils
DTIC Science & Technology
2009-01-01
our studies could advance our knowledge of mechan- isms underlying important collagen-related diseases like Osteogenesis Imperfecta or Ehlers-Danlos...collagen mutations, these studies could advance our knowledge of mechanisms underlying important collagen-related diseases like Osteogenesis ... Imperfecta or Ehlers-Danlos Syndrome. REPORT DOCUMENTATION PAGE (SF298) (Continuation Sheet) Continuation for Block 13 ARO Report Number Intermolecular slip
20. Intermolecular electron transfer from intramolecular excitation and coherent acoustic phonon generation in a hydrogen-bonded charge-transfer solid
Rury, Aaron S.; Sorenson, Shayne; Dawlaty, Jahan M.
2016-03-01
Organic materials that produce coherent lattice phonon excitations in response to external stimuli may provide next generation solutions in a wide range of applications. However, for these materials to lead to functional devices in technology, a full understanding of the possible driving forces of coherent lattice phonon generation must be attained. To facilitate the achievement of this goal, we have undertaken an optical spectroscopic study of an organic charge-transfer material formed from the ubiquitous reduction-oxidation pair hydroquinone and p-benzoquinone. Upon pumping this material, known as quinhydrone, on its intermolecular charge transfer resonance as well as an intramolecular resonance of p-benzoquinone, we find sub-cm-1 oscillations whose dispersion with probe energy resembles that of a coherent acoustic phonon that we argue is coherently excited following changes in the electron density of quinhydrone. Using the dynamical information from these ultrafast pump-probe measurements, we find that the fastest process we can resolve does not change whether we pump quinhydrone at either energy. Electron-phonon coupling from both ultrafast coherent vibrational and steady-state resonance Raman spectroscopies allows us to determine that intramolecular electronic excitation of p-benzoquinone also drives the electron transfer process in quinhydrone. These results demonstrate the wide range of electronic excitations of the parent of molecules found in many functional organic materials that can drive coherent lattice phonon excitations useful for applications in electronics, photonics, and information technology.
1. VSCF calculations for the intra- and intermolecular vibrational modes of the water dimer and its isotopologs
Monteiro, João G. S.; Barbosa, André G. H.
2016-11-01
In this work we show how the VSCF method may be successfully used to describe all fundamental vibrational transitions of several isotopologs of water dimer. By expressing the normal mode displacements in terms of appropriate delocalized internal coordinates we are able to minimize the mode-mode coupling in the PES and thus yield PT2-VSCF frequencies in good agreement with the experiment. The use of curvilinear normal modes is of paramount importance to describe vibrational transitions of the very soft intermolecular modes. Within our approach the maximum calculated error for the (H2O)2 intermolecular frequencies are reduced from 311 cm-1 (Cartesian normal modes) to just 56 cm-1 (curvilinear normal modes). Plots of the diagonal intermolecular potential and of the vibrational wave function illustrate the remarkable effect of different coordinate systems. In conclusion, our PT2-VSCF calculations provide a fair anharmonic description of the fundamental transitions of water dimers.
2. The benzene-argon ground-state intermolecular potential energy surface revisited.
PubMed
Capelo, Silvia Bouzón; Fernández, Berta; Koch, Henrik; Felker, Peter M
2009-04-30
The benzene-Ar ground-state S(0) intermolecular potential energy surface is evaluated using the coupled cluster singles and doubles model including connected triple corrections and the augmented correlation consistent polarized valence triple-zeta basis set extended with a set of 3s3p2d1f1g midbond functions. The surface is characterized by absolute minima of -390.1 cm(-1) where the argon atom is located on the benzene C(6) axis at distances of +/-3.536 A, and has a general shape close to the available ground-state S(0) and the first singlet S(1) and triplet T(1) excited-state surfaces. Using the potential, the intermolecular level structure of the complex is evaluated. The new intermolecular potential energy surface gives very accurate results and improves those previously available.
3. Cathodoluminescence, laser ablasion inductively coupled plasma mass spectrometry, electron probe microanalysis and electron paramagnetic resonance analyses of natural sphalerite
USGS Publications Warehouse
Karakus, M.; Hagni, R.D.; Koenig, A.; Ciftc, E.
2008-01-01
Natural sphalerite associated with copper, silver, lead-zinc, tin and tungsten deposits from various world-famous mineral deposits have been studied by cathodoluminescence (CL), laser ablasion inductively coupled plasma mass spectrometry (LA-ICP-MS), electron probe microanalysis (EPMA) and electron paramagnetic resonance (EPR) to determine the relationship between trace element type and content and the CL properties of sphalerite. In general, sphalerite produces a spectrum of CL colour under electron bombardment that includes deep blue, turquoise, lime green, yellow-orange, orange-red and dull dark red depending on the type and concentration of trace quantities of activator ions. Sphalerite from most deposits shows a bright yellow-orange CL colour with ??max centred at 585 nm due to Mn2+ ion, and the intensity of CL is strongly dependent primarily on Fe2+ concentration. The blue emission band with ??max centred at 470-490 nm correlates with Ga and Ag at the Tsumeb, Horn Silver, Balmat and Kankoy mines. Colloform sphalerite from older well-known European lead-zinc deposits and late Cretaceous Kuroko-type VMS deposits of Turkey shows intense yellowish CL colour and their CL spectra are characterised by extremely broad emission bands ranging from 450 to 750 nm. These samples are characterised by low Mn (<10 ppm) and Ag (<1 ppm), and they are enriched in Tl (1-30 ppm) and Pb (80-1500 ppm). Strong green CL is produced by sphalerite from the Balmat-Edwards district. Amber, lime-green and red-orange sphalerite produced weak orange-red CL at room temperatures, with several emission bands centred at 490, 580, 630, 680, 745, with ??max at 630 nm being the strongest. These emission bands are well correlated with trace quantities of Sn, In, Cu and Mn activators. Sphalerite from the famous Ogdensburg and Franklin mines exhibited brilliant deep blue and orange CL colours and the blue CL may be related to Se. Cathodoluminescence behaviour of sphalerite serves to characterise ore
4. Langmuir probe diagnostics of electron energy distributions with optical emission spectroscopy in capacitively coupled rf discharge in nitrogen
SciTech Connect
Abdel-Fattah, E.; Bazavan, M.; Sugai, H.
2011-12-01
Measurements with a rf compensated Langmuir probe and optical emission spectroscopy are carried out in capacitively coupled rf (13.56 MHz) pure nitrogen N{sub 2} discharges at fixed rf voltage over a wide range of pressure, 30 to 400 mTorr. The electron energy probability function (EEPF) measured below 100 mTorr resembles a bi-Maxwellian-type distribution. At pressure range of 100-200 mTorr, the EEPF has non-Maxwellian distribution with a ''dip'' near 4.5 eV. At the highest pressure of 400 mTorr, the EEPF evolves into a Druyvestein-like distribution and the ''dip'' disappears. The electron density significantly decreases with increase in the N{sub 2} pressure. On the other hand, the electron temperatures gradually decrease with an increase in N{sub 2} pressure, reaching minimum at 150 mTorr, beyond which it abruptly increases. Such evolution of the EEPFs shape with gas pressure has been discussed in terms of non-local electron kinetics and heating mode transition. The emission intensities of nitrogen (0-0) band of second positive system at 337.1 nm and (0-0) band of first negative systems at 391.4 nm are used to determine the dependence of their radiative states N{sub 2}(C{sup 3}{Pi}{sub u}) and N{sub 2}{sup +}(B{sup 2}{Sigma}{sub u}{sup +}) with nitrogen pressure. It is observed that the pressure influences the radiative states differently owing to their different populating mechanisms. The vibrational temperature T{sub {nu}ib} and rotational temperature T{sub rot} are measured for the sequence ({Delta}{nu}=-2) of N{sub 2} second positive system (C{sup 3}{Pi}{yields}B{sup 3}{Pi}{sub g}) using the method of comparing the measured and calculated spectra with a chi-squared minimization procedure. It was found that both T{sub {nu}ib} and T{sub rot} have similar dependences with N{sub 2} pressure; peaked at 100 mTorr beyond which it monotonically decreases with increase in the N{sub 2} pressure. The correlation between the observed maximum value of T{sub {nu}ib} around
5. High-resolution absorptive intermolecular multiple-quantum coherence NMR spectroscopy under inhomogeneous fields
Lin, Meijin; Lin, Yanqin; Chen, Xi; Cai, Shuhui; Chen, Zhong
2012-01-01
Intermolecular multiple-quantum coherence (iMQC) is capable of improving NMR spectral resolution using a 2D shearing manipulation method. A pulse sequence termed CT-iDH, which combines intermolecular double-quantum filter (iDQF) with a modified constant-time (CT) scheme, is designed to achieve fast acquisition of high-resolution intermolecular zero-quantum coherences (iZQCs) and intermolecular double-quantum coherences (iDQCs) spectra without strong coupling artifacts. Furthermore, double-absorption lineshapes are first realized in 2D intermolecular multi-quantum coherences (iMQCs) spectra under inhomogeneous fields through a combination of iZQC and iDQC signals to double the resolution without loss of sensitivity. Theoretically the spectral linewidth can be further reduced by half compared to original iMQC high-resolution spectra. Several experiments were performed to test the feasibility of the new method and the improvements are evaluated quantitatively. The study suggests potential applications for in vivo spectroscopy.
6. COUPLING
DOEpatents
Frisch, E.; Johnson, C.G.
1962-05-15
A detachable coupling arrangement is described which provides for varying the length of the handle of a tool used in relatively narrow channels. The arrangement consists of mating the key and keyhole formations in the cooperating handle sections. (AEC)
7. Development and Implementation of a Protein-Protein Binding Experiment to Teach Intermolecular Interactions in High School or Undergraduate Classrooms
ERIC Educational Resources Information Center
Johnson, Sadie M.; Javner, Cassidy; Hackel, Benjamin J.
2017-01-01
The goal of this study was to create an accessible, inexpensive, and engaging experiment to teach high school and undergraduate chemistry or biology students about intermolecular forces and how they contribute to the behavior of biomolecules. We developed an enzyme-linked immunosorbent assay (ELISA) to probe specific structure-function…
8. Simultaneous Identification of 13 Foodborne Pathogens by Using Capillary Electrophoresis-Single Strand Conformation Polymorphism Coupled with Multiplex Ligation-Dependent Probe Amplification and Its Application in Foods.
PubMed
Kim, So-Young; Chung, Boram; Chang, Jin-Hee; Jung, Gyoo Yeol; Kim, Hyoun Wook; Park, Beom-Young; Oh, Sang Suk; Oh, Mi-Hwa
2016-10-01
Capillary electrophoresis-single strand conformation polymorphism (CE-SSCP) coupled with stuffer-free multiplex ligation-dependent probe amplification (MLPA) was developed to identify 13 species of foodborne pathogens simultaneously. Species-specific MLPA probes were designed for nine of these species. These probes were targeted to the groEL, glyA, MMS, tuf, inv, ipaH, nuc, vvh, and 16S rRNA genes, which corresponded to Bacillus cereus, Campylobacter coli, Cronobacter sakazakii, Enterococcus spp., Salmonella spp., Shigella spp., Staphylococcus aureus, Vibrio vulnificus, and Yersinia enterocolitica, respectively. MLPA probes that had been previously developed by our laboratory were used for the other four species (Campylobacter jejuni, Clostridium perfringens, Escherichia coli O157:H7, and Listeria monocytogenes). The CE-SSCP method was optimized to identify all 13 foodborne microbes simultaneously in a single electrogram, in which 50-500 pg genomic DNA was detected per microbe. Twelve species were detected from animal-derived food samples (specifically, milk and sliced ham) that had been artificially inoculated with 12 of the foodborne pathogens, excluding V. vulnificus, which is not usually associated with animal foods. The method developed here could be used as an early warning system for outbreaks of foodborne diseases associated with animal-derived foods in the food industry.
9. The NMR Chemical Shift: - and Intermolecular Effects
de Dios, Angel Cagandahan
1992-01-01
Gas phase NMR measurements were performed to provide a more accurate description of the shielding. These experiments were aimed to provide the finer details of shielding: its dependence on the geometry of the molecule and intermolecular factors. Together with these experiments were ab initio calculations of the shielding designed to deepen our understanding of how the shielding is affected by the internal motions of the molecule as well as interactions among the molecules. The exceptional cases of ^{15 }N in NH_3 and ^{31}P in PH_3 were rigorously studied. The deuterium-induced isotope shifts were found to be dominated by contributions arising from bond extension. The temperature dependence is found to be a combination of contributions coming from centrifugal stretching and bond angle distortion. These cases were compared with ^{13}C in CH_4 and ^{17 }O in H_2O revealing some general characteristics of shielding surfaces. As a model for the intermolecular shift for rare gas atoms, the argon dimer was used. Through a scaling scheme, measured second virial coefficients of the shielding of ^{129}Xe in various collision partners were satisfactorily reproduced from the ab initio shielding function of the argon dimer. The intermolecular shielding function also helped in interpreting gas-to-solution shifts of rare gases and the ^ {129}Xe NMR results from adsorption studies. Lastly, an attempt was made to develop a theory that would explain both intramolecular and intermolecular effects on the chemical shifts. It was discovered that a general shape for the shielding function was possible.
10. Intermolecular Michael reactions: a computational investigation.
PubMed
Kwan, Eugene E; Evans, David A
2010-11-19
Computational studies have suggested that η(3)-lithium enolates in which the cation is partially bound to both carbon and oxygen may be important reactive intermediates. DFT calculations are used to demonstrate that explicitly solvated acetone enolates are largely O-bound. With this premise in mind, the stereochemical course of intermolecular Michael additions is examined. The results are generally consistent with what is observed experimentally and the model advanced by Heathcock and co-workers.
11. An assay for intermolecular exchange of alpha crystallin
NASA Technical Reports Server (NTRS)
Gopalakrishnan, S.; Takemoto, L.; Spooner, B. S. (Principal Investigator)
1992-01-01
An affinity column of alpha crystallin linked to cyanogen bromide-activated Sepharose was developed to study the exchange of alpha subunits. Alpha crystallin bound to the Sepharose-alpha complex was dissociated with 8 mol/l urea, followed by quantitation using high-performance reverse-phase liquid chromatography. The time course of binding at 37 degrees C showed a hyperbolic binding pattern reaching equilibrium between 6-18 hr. Under these conditions, binding of beta and gamma crystallins to the same matrix was less than 10% of the alpha values, as was binding of alpha to glycine-coupled Sepharose. This assay was used to demonstrate changes in the subunit exchange of alpha crystallins present in high molecular weight versus lower molecular weight aggregates of the human lens. These results show that this binding procedure was a specific reproducible assay that might be used to study intermolecular interactions of the alpha crystallins.
12. An assay for intermolecular exchange of alpha crystallin
NASA Technical Reports Server (NTRS)
Gopalakrishnan, S.; Takemoto, L.; Spooner, B. S. (Principal Investigator)
1992-01-01
An affinity column of alpha crystallin linked to cyanogen bromide-activated Sepharose was developed to study the exchange of alpha subunits. Alpha crystallin bound to the Sepharose-alpha complex was dissociated with 8 mol/l urea, followed by quantitation using high-performance reverse-phase liquid chromatography. The time course of binding at 37 degrees C showed a hyperbolic binding pattern reaching equilibrium between 6-18 hr. Under these conditions, binding of beta and gamma crystallins to the same matrix was less than 10% of the alpha values, as was binding of alpha to glycine-coupled Sepharose. This assay was used to demonstrate changes in the subunit exchange of alpha crystallins present in high molecular weight versus lower molecular weight aggregates of the human lens. These results show that this binding procedure was a specific reproducible assay that might be used to study intermolecular interactions of the alpha crystallins.
13. Tannin oxidation: intra- versus intermolecular reactions.
PubMed
Poncet-Legrand, Céline; Cabane, Bernard; Bautista-Ortín, Ana-Belén; Carrillo, Stéphanie; Fulcrand, Hélène; Pérez, Javier; Vernhet, Aude
2010-09-13
Grape and apple condensed tannin fractions were autoxidized at high concentrations (5 g/L) in aqueous solutions and analyzed by thiolysis (depolymerization followed by HPLC analysis) and small angle X-ray scattering (SAXS). Structural parameters of native (unoxidized) tannin polymers were derived from SAXS according to the wormlike chain model: the length per monomer is 15 A, the length of the statistical segment 17 A, and the cross section of the macromolecule has a radius within the range 3-4.5 A. The rather short length of the statistical segment is an effect of the different location of interflavanol linkages, which cause a loss of orientational correlation between successive monomers. Oxidation created new bonds that were resistant to thiolysis, and, according to thiolysis, some of these new bonds were intramolecular. However, according to SAXS, oxidation at high tannin concentration caused the weight average degree of polymerization to increase, indicating that intermolecular reactions took place as well, creating larger macromolecules. In the case of the smaller grape seed tannins, these intermolecular reactions took place "end to end" leading to the formation of longer linear macromolecules, at least in the earlier stages of oxidation. In the case of the larger apple tannins, the SAXS patterns were characteristic of larger branched macromolecules. Accordingly, the intermolecular reactions were mainly "end to middle". This is in agreement with the higher probabilities of "end to middle" reactions arising from a higher ratio extension unit/terminal unit in the latter case.
14. An isotopic mass effect on the intermolecular potential
SciTech Connect
Herman, Michael F.; Currier, Robert Patrick; Clegg, Samuel M.
2015-09-28
The impact of isotopic variation on the electronic energy and intermolecular potentials is often suppressed when calculating isotopologue thermodynamics. Intramolecular potential energy surfaces for distinct isotopologues are in fact equivalent under the Born–Oppenheimer approximation, which is sometimes used to imply that the intermolecular interactions are independent of isotopic mass. In this paper, the intermolecular dipole–dipole interaction between hetero-nuclear diatomic molecules is considered. It is shown that the intermolecular potential contains mass-dependent terms even though each nucleus moves on a Born–Oppenheimer surface. Finally, the analysis suggests that mass dependent variations in intermolecular potentials should be included in comprehensive descriptions of isotopologue thermodynamics.
15. A triterpene oleanolic acid conjugate with 3-hydroxyflavone derivative as a new membrane probe with two-color ratiometric response.
PubMed
Turkmen, Zeynep; Klymchenko, Andrey S; Oncul, Sule; Duportail, Guy; Topcu, Gulacti; Demchenko, Alexander P
2005-07-29
We report on the synthesis by coupling of a triterpenoid oleanolic acid with 4'-diethylamino-3-hydroxyflavone (FE) to produce an environment-sensitive biomembrane probe with two-band ratiometric response in fluorescence emission. The synthesized compound (probe FOT) was tested in a series of model solvents and demonstrated the response to solvent polarity and intermolecular hydrogen bonding very similar to that of parent probe FE. Meantime when incorporated into lipid bilayer membranes, it showed new features differing in response between lipids of different surface charges as well as between glycerophospholipids and sphingomyelin. We observed that in the conditions of coexistence of rafts and non-raft structures the probe is excluded from the rafts.
16. NMR detection of intermolecular interaction sites in the dimeric 5'-leader of the HIV-1 genome.
PubMed
Keane, Sarah C; Van, Verna; Frank, Heather M; Sciandra, Carly A; McCowin, Sayo; Santos, Justin; Heng, Xiao; Summers, Michael F
2016-11-15
HIV type-1 (HIV-1) contains a pseudodiploid RNA genome that is selected for packaging and maintained in virions as a noncovalently linked dimer. Genome dimerization is mediated by conserved elements within the 5'-leader of the RNA, including a palindromic dimer initiation signal (DIS) that has been proposed to form kissing hairpin and/or extended duplex intermolecular contacts. Here, we have applied a (2)H-edited NMR approach to directly probe for intermolecular interactions in the full-length, dimeric HIV-1 5'-leader (688 nucleotides; 230 kDa). The interface is extensive and includes DIS:DIS base pairing in an extended duplex state as well as intermolecular pairing between elements of the upstream Unique-5' (U5) sequence and those near the gag start site (AUG). Other pseudopalindromic regions of the leader, including the transcription activation (TAR), polyadenylation (PolyA), and primer binding (PBS) elements, do not participate in intermolecular base pairing. Using a (2)H-edited one-dimensional NMR approach, we also show that the extended interface structure forms on a time scale similar to that of overall RNA dimerization. Our studies indicate that a kissing dimer-mediated structure, if formed, exists only transiently and readily converts to the extended interface structure, even in the absence of the HIV-1 nucleocapsid protein or other RNA chaperones.
17. Spin-lattice coupling in uranium dioxide probed by magnetostriction measurements at high magnetic fields (P08358-E001-PF)
SciTech Connect
Gofryk, K.; Jaime, M.
2014-12-01
Our preliminary magnetostriction measurements have already shown a strong interplay of lattice dynamic and magnetism in both antiferromagnetic and paramagnetic states, and give unambiguous evidence of strong spin- phonon coupling in uranium dioxide. Further studies are planned to address the puzzling behavior of UO2 in magnetic and paramagnetic states and details of the spin-phonon coupling.
18. Time-averaging approximation in the interaction picture: Anisotropy of vibrational pump-probe experiments for coupled chromophores with application to liquid water
Yang, Mino
2012-10-01
A time-averaging approximation method developed to efficiently calculate the short-time dynamics of coupled vibrational chromophores using mixed quantum/classical theories is extended in order to be applicable to the study of vibrational dynamics at longer time scales. A quantum mechanical time propagator for long times is decomposed into the product of short-time propagators, and a time-averaging approximation is then applied to each of the latter. Using the extended time-averaging approximation, we calculate the anisotropy decay of the data obtained from impulsive vibrational pump-probe experiments on the OH stretching modes of water, which is in excellent agreement with numerically exact results.
19. Temperature Dependence of the Surface Resistance of a Bi-Sr-Ca-Cu-O Whisker Measured by the Probe-Coupled Microstrip Resonator Method
Okai, Daisuke; Ohshima, Shigetoshi; Kishida, Satoru; Hatano, Takeshi
2001-07-01
The temperature dependence of the surface resistance of Bi-Sr-Ca-Cu-O whiskers measured by the probe-coupled microstrip resonator method was examined. Two kinds of whiskers were measured: plate-like and wire-like. The surface resistances of the plate-like and wire-like whiskers were 0.65 mΩ and 1.6 mΩ at 53 K and 6.9 GHz, respectively. These values were approximately 4 ˜ 10 times larger than that of a high-quality Bi2Sr2CaCu2Ox (Bi-2212) single crystal.
20. Exciton dynamics in paracyclophane coupled dimers
Maddox, Jeremy; Kim, Jeongho; Moran, Andrew; Hong, Janice; Bazan, Guillermo; Scherer, Norbert; Mukamel, Shaul
2005-03-01
Understanding and manipulating through-space electronic communication within aggregates of organic fragments with delocalized bonding structures can impact a range of nanotechnology applications. However, interrogating aggregates of this type has encountered multiple difficulties in the past, ranging from heterogeneity of environments in the solid to the ill-defined geometry of intermolecular contacts in solution. These difficulties are circumvented by designing aggregates which contain [2.2]paracyclophane contacts among molecular units with well-defined architectures and dimensions. These offer excellent control over the distance and relative orientation of the participating units and provide a model system for detailed examination of the molecular structure-function relationship of conducting polymeric materials. We present a comparative experimental and theoretical study of a model complex consisting of two (oligo)phenylenevinylene chromophores that are strongly coupled through a paracyclophane junction. Ultrafast pump-probe anisotropy measurements are compared with numerical simulations to investigate the nature of exciton dynamics in strongly coupled chromophores.
1. Coupling solid-phase microextraction with ambient mass spectrometry using surface coated wooden-tip probe for rapid analysis of ultra trace perfluorinated compounds in complex samples.
PubMed
Deng, Jiewei; Yang, Yunyun; Fang, Ling; Lin, Li; Zhou, Haiyun; Luan, Tiangang
2014-11-18
Coupling solid-phase microextraction (SPME) with ambient mass spectrometry using surface coated wooden-tip probe was achieved for the first time and applied in the analysis of ultra trace perfluorinated compounds (PFCs) in complex environmental and biological samples. We modified n-octadecyldimethyl[3-(trimethoxysilyl)propyl]ammonium chloride on the surface of sharp wooden tip via silanization to form a novel SPME probe, which was then used for highly selective enrichment of PFCs from complex matrices and applied as a solid substrate to induce electrospray ionization for mass spectrometric analysis. The porous structural surface together with the dual extraction mechanisms (reversed phase adsorption and ion exchange adsorption) demonstrated that the SPME probe has an outstanding enrichment capacity, enhancing sensitivity by approximately 4000-8000 folds for the detection in aqueous samples, and 100-500-fold in whole blood and milk samples. The method showed good linearity, with correlation coefficient values (r(2)) of no less than 0.9931 for eight target PFCs. The limits of detection and qualification of the eight PFCs were 0.06-0.59 and 0.21-1.98 ng/L, respectively. Quantification of real samples was achieved by isotope internal standard calibration curve method or isotope dilution method, and ultratrace levels of PFCs present in lake water, river water, whole blood, and milk samples had been successfully detected and qualified.
2. Theoretical and numerical evaluation of polarimeter using counter-circularly-polarized-probing-laser under the coupling between Faraday and Cotton-Mouton effect
Imazawa, Ryota; Kawano, Yasunori; Itami, Kiyoshi
2016-04-01
This study evaluated an effect of an coupling between the Faraday and Cotton-Mouton effect to a measurement signal of the Dodel-Kunz method which uses counter-circular-polarized probing-laser for measuring the Faraday effect. When the coupling is small (the Faraday effect is dominant and the characteristic eigenmodes are approximately circularly polarized), the measurement signal can be algebraically expressed and it is shown that the finite effect of the coupling is still significant. When the Faraday effect is not dominant, a numerical calculation is necessary. The numerical calculation under an ITER-like condition (Bt = 5.3 T, Ip = 15 MA, a = 2 m, ne = 1020 m-3 and λ = 119 μm) showed that difference between the pure Faraday rotation and the measurement signal of the Dodel-Kunz method was an order of one degree, which exceeds allowable error of ITER poloidal polarimeter. In conclusion, similar to other polarimeter techniques, the Dodel-Kunz method is not free from the coupling between the Faraday and Cotton-Mouton effect.
3. Theoretical and numerical evaluation of polarimeter using counter-circularly-polarized-probing-laser under the coupling between Faraday and Cotton-Mouton effect.
PubMed
Imazawa, Ryota; Kawano, Yasunori; Itami, Kiyoshi
2016-04-01
This study evaluated an effect of an coupling between the Faraday and Cotton-Mouton effect to a measurement signal of the Dodel-Kunz method which uses counter-circular-polarized probing-laser for measuring the Faraday effect. When the coupling is small (the Faraday effect is dominant and the characteristic eigenmodes are approximately circularly polarized), the measurement signal can be algebraically expressed and it is shown that the finite effect of the coupling is still significant. When the Faraday effect is not dominant, a numerical calculation is necessary. The numerical calculation under an ITER-like condition (Bt = 5.3 T, Ip = 15 MA, a = 2 m, ne = 10(20) m(-3) and λ = 119 μm) showed that difference between the pure Faraday rotation and the measurement signal of the Dodel-Kunz method was an order of one degree, which exceeds allowable error of ITER poloidal polarimeter. In conclusion, similar to other polarimeter techniques, the Dodel-Kunz method is not free from the coupling between the Faraday and Cotton-Mouton effect.
4. Determination of the 14N quadrupole coupling constant of nitroxide spin probes by W-band ELDOR-detected NMR.
PubMed
Florent, Marc; Kaminker, Ilia; Nagarajan, Vijayasarathi; Goldfarb, Daniella
2011-06-01
Nitroxide spin probe electron paramagnetic resonance (EPR) has proven to be a very successful method to probe local polarity and solvent hydrogen bonding properties at the molecular level. The g(xx) and the (14)N hyperfine A(zz) principal values are the EPR parameters of the nitroxide spin probe that are sensitive to these properties and are therefore monitored experimentally. Recently, the (14)N quadrupole interaction of nitroxides has been shown to be also highly sensitive to polarity and H-bonding (A. Savitsky et al., J. Phys. Chem. B 112 (2008) 9079). High-field electron spin echo envelope modulation (ESEEM) was used successfully to determine the P(xx) and P(yy) principal components of the (14)N quadrupole tensor. The P(zz) value was calculated from the traceless character of the quadrupole tensor. We introduce here high-field (W-band, 95 GHz, 3.5 T) electron-electron double resonance (ELDOR)-detected NMR as a method to obtain the (14)N P(zz) value directly, together with A(zz). This is complemented by W-band hyperfine sublevel correlation (HYSCORE) measurements carried out along the g(xx) direction to determine the principal P(xx) and P(yy) components. Through measurements of TEMPOL dissolved in solvents of different polarities, we show that A(zz) increases, while |P(zz)| decreases with polarity, as predicted by Savitsky et al.
5. Determination of the 14N quadrupole coupling constant of nitroxide spin probes by W-band ELDOR-detected NMR
Florent, Marc; Kaminker, Ilia; Nagarajan, Vijayasarathi; Goldfarb, Daniella
2011-06-01
Nitroxide spin probe electron paramagnetic resonance (EPR) has proven to be a very successful method to probe local polarity and solvent hydrogen bonding properties at the molecular level. The g xx and the 14N hyperfine A zz principal values are the EPR parameters of the nitroxide spin probe that are sensitive to these properties and are therefore monitored experimentally. Recently, the 14N quadrupole interaction of nitroxides has been shown to be also highly sensitive to polarity and H-bonding (A. Savitsky et al., J. Phys. Chem. B 112 (2008) 9079). High-field electron spin echo envelope modulation (ESEEM) was used successfully to determine the P xx and P yy principal components of the 14N quadrupole tensor. The P zz value was calculated from the traceless character of the quadrupole tensor. We introduce here high-field (W-band, 95 GHz, 3.5 T) electron-electron double resonance (ELDOR)-detected NMR as a method to obtain the 14N P zz value directly, together with A zz. This is complemented by W-band hyperfine sublevel correlation (HYSCORE) measurements carried out along the g xx direction to determine the principal P xx and P yy components. Through measurements of TEMPOL dissolved in solvents of different polarities, we show that A zz increases, while | P zz| decreases with polarity, as predicted by Savitsky et al.
6. Study of ablation and implosion stages in wire arrays using coupled ultraviolet and X-ray probing diagnostics
Anderson, A. A.; Ivanov, V. V.; Astanovitskiy, A. L.; Papp, D.; Wiewior, P. P.; Chalyy, O.
2015-11-01
Star and cylindrical wire arrays were studied using laser probing and X-ray radiography at the 1-MA Zebra pulse power generator at the University of Nevada, Reno. The Leopard laser provided backlighting, producing a laser plasma from a Si target which emitted an X-ray probing pulse at the wavelength of 6.65 Å. A spherically bent quartz crystal imaged the backlit wires onto X-ray film. Laser probing diagnostics at the wavelength of 266 nm included a 3-channel polarimeter for Faraday rotation diagnostic and two-frame laser interferometry with two shearing interferometers to study the evolution of the plasma electron density at the ablation and implosion stages. Dynamics of the plasma density profile in Al wire arrays at the ablation stage were directly studied with interferometry, and expansion of wire cores was measured with X-ray radiography. The magnetic field in the imploding plasma was measured with the Faraday rotation diagnostic, and current was reconstructed.
7. Study of ablation and implosion stages in wire arrays using coupled ultraviolet and X-ray probing diagnostics
SciTech Connect
Anderson, A. A.; Ivanov, V. V.; Astanovitskiy, A. L.; Wiewior, P. P.; Chalyy, O.; Papp, D.
2015-11-15
Star and cylindrical wire arrays were studied using laser probing and X-ray radiography at the 1-MA Zebra pulse power generator at the University of Nevada, Reno. The Leopard laser provided backlighting, producing a laser plasma from a Si target which emitted an X-ray probing pulse at the wavelength of 6.65 Å. A spherically bent quartz crystal imaged the backlit wires onto X-ray film. Laser probing diagnostics at the wavelength of 266 nm included a 3-channel polarimeter for Faraday rotation diagnostic and two-frame laser interferometry with two shearing interferometers to study the evolution of the plasma electron density at the ablation and implosion stages. Dynamics of the plasma density profile in Al wire arrays at the ablation stage were directly studied with interferometry, and expansion of wire cores was measured with X-ray radiography. The magnetic field in the imploding plasma was measured with the Faraday rotation diagnostic, and current was reconstructed.
8. Coupling an electrospray source and a solids probe/chemical ionization source to a selected ion flow tube apparatus
SciTech Connect
Melko, Joshua J.; Ard, Shaun G.; Shuman, Nicholas S.; Viggiano, Albert A.; Pedder, Randall E.; Taormina, Christopher R.
2015-08-15
A new ion source region has been constructed and attached to a variable temperature selected ion flow tube. The source features the capabilities of electron impact, chemical ionization, a solids probe, and electrospray ionization. The performance of the instrument is demonstrated through a series of reactions from ions created in each of the new source regions. The chemical ionization source is able to create H{sub 3}O{sup +}, but not as efficiently as similar sources with larger apertures. The ability of this source to support a solids probe, however, greatly expands our capabilities. A variety of rhenium cations and dications are created from the solids probe in sufficient abundance to study in the flow tube. The reaction of Re{sup +} with O{sub 2} proceeds with a rate constant that agrees with the literature measurements, while the reaction of Re{sub 2}{sup 2+} is found to charge transfer with O{sub 2} at about 60% of the collision rate; we have also performed calculations that support the charge transfer pathway. The electrospray source is used to create Ba{sup +}, which is reacted with N{sub 2}O to create BaO{sup +}, and we find a rate constant that agrees with the literature.
9. Investigation of intermolecular double-quantum off-resonance longitudinal relaxation in the tilted rotating frame
Cai, Honghao; Zheng, Bingwen; Ke, Hanping; Chen, Zhong
2015-11-01
A modified correlation spectroscopy revamped by asymmetric z-gradients echo detection (CRAZED) sequence was applied to investigate the behavior of intermolecular double-quantum longitudinal relaxation processes in the tilted rotating frame. Theoretical formalism based on dipolar field theory was presented in detail. Spectroscopic measurements and quantitative analysis demonstrated that the signal intensities and intermolecular double-quantum off-resonance longitudinal relaxation time in the rotating frame (T1ρ, DQC eff) are inversely correlated with the tilt angle (θ), while positively correlated with the effective frequency of spin-locking field (ωe). Magnetic resonance imaging experiments of an agarose phantom also prove the validity of the theoretical analysis and demonstrated the feasibility of imaging based on T1ρ, DQC eff . The rotating-frame double-quantum relaxation measurements are useful for probing slow-motion molecules and this study provides the guidance for optimization of the spin-lock experiments.
10. Tip relaxation in atomic force microscopy imaging simulations to resolve intermolecular bonds
Lee, Alex; Sakai, Yuki; Chelikowsky, Jim
Experimental noncontact atomic force microscopy (AFM) studies have reported distinct lines in regions with no electron density for a variety of systems. The appearance of these lines is unexpected because Pauli repulsion is thought to be the dominant factor in the AFM imaging mechanism. These lines have been proposed to represent intermolecular bonding. Recent theoretical studies have shown that accounting for tip probe relaxation can sharpen images and highlight features that make simulations more comparable to experiment. We will apply a similar tip relaxation scheme to our computational method-which uses an ab initio real-space pseudopotential formalism with frozen density embedding theory added-to the study of dibenzo[a,h]thianthrene and an 8-hydroxyquinoline dimer to develop our interpretation of imaged intermolecular bonds. Work is supported by the DOE under DOE/DE-FG02-06ER46286 and by the Welch Foundation under Grant F-1837. Computational resources were provided by NERSC and XSEDE.
11. Intermolecular potential energy surface for CS2 dimer.
PubMed
Farrokhpour, Hossein; Mombeini, Zainab; Namazian, Mansoor; Coote, Michelle L
2011-04-15
A new four-dimensional intermolecular potential energy surface for CS(2) dimer is obtained by ab initio calculation of the interaction energies for a range of configurations and center-of-mass separation distances for the first time. The calculations were performed using the supermolecular approach at the Møller-Plesset second-order perturbation (MP2) level of theory with the augmented correlation consistent basis sets (aug-cc-pVxZ, x = D, T) and corrected for the basis-set superposition error using the full counterpoise correction method. A two-point extrapolation method was used to extrapolate the calculated energy points to the complete basis set limit. The effect of using the higher levels of theory, quadratic configuration interaction containing single, double, and perturbative triple excitations QCISD(T) and coupled cluster singles, doubles and perturbative triples excitations CCSD(T), on the shape of potential energy surface was investigated. It is shown that the MP2 level of theory apparently performs extremely poorly for describing the intermolecular potential energy surface, overestimating the total energy by a factor of nearly 1.73 in comparison with the QCISD(T) and CCSD(T) values. The value of isotropic dipole-dipole dispersion coefficient (C(6) ) of CS(2) fluid was obtained from the extrapolated MP2 potential energy surface. The MP2 extrapolated energy points were fitted to well-known analytical potential functions using two different methods to represent the potential energy surface analytically. The most stable configuration of the dimer was determined at R = 6.23 au, α = 90°, β = 90°, and γ = 90°, with a well depth of 3.980 kcal mol(-1) at the MP2 level of theory. Finally, the calculated second virial coefficients were compared with experimental values to test the quality of the presented potential energy surface. Copyright © 2010 Wiley Periodicals, Inc.
12. Quantitative determination of the lateral density and intermolecular correlation between proteins anchored on the membrane surfaces using grazing incidence small-angle X-ray scattering and grazing incidence X-ray fluorescence.
PubMed
Abuillan, Wasim; Vorobiev, Alexei; Hartel, Andreas; Jones, Nicola G; Engstler, Markus; Tanaka, Motomu
2012-11-28
As a physical model of the surface of cells coated with densely packed, non-crystalline proteins coupled to lipid anchors, we functionalized the surface of phospholipid membranes by coupling of neutravidin to biotinylated lipid anchors. After the characterization of fine structures perpendicular to the plane of membrane using specular X-ray reflectivity, the same membrane was characterized by grazing incidence small angle X-ray scattering (GISAXS). Within the framework of distorted wave Born approximation and two-dimensional Percus-Yevick function, we can analyze the form and structure factors of the non-crystalline, membrane-anchored proteins for the first time. As a new experimental technique to quantify the surface density of proteins on the membrane surface, we utilized grazing incidence X-ray fluorescence (GIXF). Here, the mean intermolecular distance between proteins from the sulfur peak intensities can be calculated by applying Abelé's matrix formalism. The characteristic correlation distance between non-crystalline neutravidin obtained by the GISAXS analysis agrees well with the intermolecular distance calculated by GIXF, suggesting a large potential of the combination of GISAXS and GIXF in probing the lateral density and correlation of non-crystalline proteins displayed on the membrane surface.
13. Quantitative determination of the lateral density and intermolecular correlation between proteins anchored on the membrane surfaces using grazing incidence small-angle X-ray scattering and grazing incidence X-ray fluorescence
Abuillan, Wasim; Vorobiev, Alexei; Hartel, Andreas; Jones, Nicola G.; Engstler, Markus; Tanaka, Motomu
2012-11-01
As a physical model of the surface of cells coated with densely packed, non-crystalline proteins coupled to lipid anchors, we functionalized the surface of phospholipid membranes by coupling of neutravidin to biotinylated lipid anchors. After the characterization of fine structures perpendicular to the plane of membrane using specular X-ray reflectivity, the same membrane was characterized by grazing incidence small angle X-ray scattering (GISAXS). Within the framework of distorted wave Born approximation and two-dimensional Percus-Yevick function, we can analyze the form and structure factors of the non-crystalline, membrane-anchored proteins for the first time. As a new experimental technique to quantify the surface density of proteins on the membrane surface, we utilized grazing incidence X-ray fluorescence (GIXF). Here, the mean intermolecular distance between proteins from the sulfur peak intensities can be calculated by applying Abelé's matrix formalism. The characteristic correlation distance between non-crystalline neutravidin obtained by the GISAXS analysis agrees well with the intermolecular distance calculated by GIXF, suggesting a large potential of the combination of GISAXS and GIXF in probing the lateral density and correlation of non-crystalline proteins displayed on the membrane surface.
14. Molecular dynamics simulation of nonlinear spectroscopies of intermolecular motions in liquid water.
PubMed
Yagasaki, Takuma; Saito, Shinji
2009-09-15
Water is the most extensively studied of liquids because of both its ubiquity and its anomalous thermodynamic and dynamic properties. The properties of water are dominated by hydrogen bonds and hydrogen bond network rearrangements. Fundamental information on the dynamics of liquid water has been provided by linear infrared (IR), Raman, and neutron-scattering experiments; molecular dynamics simulations have also provided insights. Recently developed higher-order nonlinear spectroscopies open new windows into the study of the hydrogen bond dynamics of liquid water. For example, the vibrational lifetimes of stretches and a bend, intramolecular features of water dynamics, can be accurately measured and are found to be on the femtosecond time scale at room temperature. Higher-order nonlinear spectroscopy is expressed by a multitime correlation function, whereas traditional linear spectroscopy is given by a one-time correlation function. Thus, nonlinear spectroscopy yields more detailed information on the dynamics of condensed media than linear spectroscopy. In this Account, we describe the theoretical background and methods for calculating higher order nonlinear spectroscopy; equilibrium and nonequilibrium molecular dynamics simulations, and a combination of both, are used. We also present the intermolecular dynamics of liquid water revealed by fifth-order two-dimensional (2D) Raman spectroscopy and third-order IR spectroscopy. 2D Raman spectroscopy is sensitive to couplings between modes; the calculated 2D Raman signal of liquid water shows large anharmonicity in the translational motion and strong coupling between the translational and librational motions. Third-order IR spectroscopy makes it possible to examine the time-dependent couplings. The 2D IR spectra and three-pulse photon echo peak shift show the fast frequency modulation of the librational motion. A significant effect of the translational motion on the fast frequency modulation of the librational motion is
15. Coupling Between Dust Impact Charge Recollection and Spacecraft Potential on STEREO with Application to Solar Probe Plus.
Thayer, F.; Collette, A.; Malaspina, D.; Sternovsky, Z.
2016-12-01
Interstellar and interplanetary micrometer sized cosmic dust particles can be observed in-situ by spacecraft with electric field antennas through impact-generated charge recollection. When dedicated dust instruments are unavailable, detecting dust with electric field antennas can increase a mission's total scientific return. This study explores the relationship between charge recollection and antenna-to-spacecraft potential determined using data from the STEREO spacecraft in the solar wind. The results of this study can be helpful for predicting the amplitude and shape of dust impacts measured by spacecraft in diverse plasma environments, including the future Solar Probe Plus mission.
16. Dynamics of a multimode system coupled to multiple heat baths probed by two-dimensional infrared spectroscopy.
PubMed
Ishizaki, Akihito; Tanimura, Yoshitaka
2007-09-27
Reduced equation of motion for a multimode system coupled to multiple heat baths is constructed by extending the quantum Fokker-Planck equation with low-temperature correction terms (J. Phys. Soc. Jpn. 2005, 74, 3131). Unlike such common approaches used to describe intramolecular multimode vibration as a Bloch-Redfield theory and a stochastic theory, the present formalism is defined by the molecular coordinates. To explore the correlation among different modes through baths, we consider two cases of system-bath couplings. One is a correlated case in which two modes are coupled to a single bath, and the other is an uncorrelated case in which each mode is coupled to a different bath. We further classify the correlated case into two cases, the plus- and minus-correlated cases, according to distinct correlation manners. For these, one-dimensional and two-dimensional infrared (2D-IR) spectra are calculated numerically by solving the equation of motion. It is demonstrated that 2D-IR spectroscopy has the ability to analyze the correlation of fluctuation-dissipation processes among different modes.
17. Generalization of Ryan's theorem: Probing tidal coupling with gravitational waves from nearly circular, nearly equatorial, extreme-mass-ratio inspirals
SciTech Connect
Li Chao; Lovelace, Geoffrey
2008-03-15
Extreme-mass-ratio inspirals (EMRIs) and intermediate-mass-ratio inspirals (IMRIs) - binaries in which a stellar-mass object spirals into a massive black hole or other massive, compact body - are important sources of gravitational waves for LISA and LIGO, respectively. Thorne has speculated that the waves from EMRIs and IMRIs encode, in principle, all the details of (i) the central body's spacetime geometry (metric), (ii) the tidal coupling (energy and angular momentum exchange) between the central body and orbiting object, and (iii) the evolving orbital elements. Fintan Ryan has given a first partial proof that this speculation is correct: Restricting himself to nearly circular, nearly equatorial orbits and ignoring tidal coupling, Ryan proved that the central body's metric is encoded in the waves. In this paper we generalize Ryan's theorem. Retaining Ryan's restriction to nearly circular and nearly equatorial orbits, and dropping the assumption of no tidal coupling, we prove that Thorne's conjecture is nearly fully correct: the waves encode not only the central body's metric but also the evolving orbital elements and (in a sense slightly different from Thorne's conjecture) the evolving tidal coupling.
18. Quantitative analysis of cell surface membrane proteins using membrane-impermeable chemical probe coupled with 18O labeling.
PubMed
Zhang, Haizhen; Brown, Roslyn N; Qian, Wei-Jun; Monroe, Matthew E; Purvine, Samuel O; Moore, Ronald J; Gritsenko, Marina A; Shi, Liang; Romine, Margaret F; Fredrickson, James K; Pasa-Tolić, Ljiljana; Smith, Richard D; Lipton, Mary S
2010-05-07
We report a mass spectrometry-based strategy for quantitative analysis of cell surface membrane proteome changes. The strategy includes enrichment of surface membrane proteins using a membrane-impermeable chemical probe followed by stable isotope (18)O labeling and LC-MS analysis. We applied this strategy for enriching membrane proteins expressed by Shewanella oneidensis MR-1, a Gram-negative bacterium with known metal-reduction capability via extracellular electron transfer between outer membrane proteins and extracellular electron receptors. LC/MS/MS analysis resulted in the identification of about 400 proteins with 79% of them being predicted to be membrane localized. Quantitative aspects of the membrane enrichment were shown by peptide level (16)O and (18)O labeling of proteins from wild-type and mutant cells (generated from deletion of a type II secretion protein, GspD) prior to LC-MS analysis. Using a chemical probe labeled pure protein as an internal standard for normalization, the quantitative data revealed reduced abundances in Delta gspD mutant cells of many outer membrane proteins including the outer membrane c-type cytochromes OmcA and MtrC, in agreement with a previous report that these proteins are substrates of the type II secretion system.
19. The origins of the directionality of noncovalent intermolecular interactions.
PubMed
Wang, Changwei; Guan, Liangyu; Danovich, David; Shaik, Sason; Mo, Yirong
2016-01-05
The recent σ-hole concept emphasizes the contribution of electrostatic attraction to noncovalent bonds, and implies that the electrostatic force has an angular dependency. Here a set of clusters, which includes hydrogen bonding, halogen bonding, chalcogen bonding, and pnicogen bonding systems, is investigated to probe the magnitude of covalency and its contribution to the directionality in noncovalent bonding. The study is based on the block-localized wavefunction (BLW) method that decomposes the binding energy into the steric and the charge transfer (CT) (hyperconjugation) contributions. One unique feature of the BLW method is its capability to derive optimal geometries with only steric effect taken into account, while excluding the CT interaction. The results reveal that the overall steric energy exhibits angular dependency notably in halogen bonding, chalcogen bonding, and pnicogen bonding systems. Turning on the CT interactions further shortens the intermolecular distances. This bond shortening enhances the Pauli repulsion, which in turn offsets the electrostatic attraction, such that in the final sum, the contribution of the steric effect to bonding is diminished, leaving the CT to dominate the binding energy. In several other systems particularly hydrogen bonding systems, the steric effect nevertheless still plays the major role whereas the CT interaction is minor. However, in all cases, the CT exhibits strong directionality, suggesting that the linearity or near linearity of noncovalent bonds is largely governed by the charge-transfer interaction whose magnitude determines the covalency in noncovalent bonds.
20. Interpreting the widespread nonlinear force spectra of intermolecular bonds
PubMed Central
Friddle, Raymond W.; Noy, Aleksandr; De Yoreo, James J.
2012-01-01
1. The Effect of Electrode Coupling on Single Molecule Device Characteristics: An X-Ray Spectroscopy and Scanning Probe Microscopy Study
Batra, Arunabh
This thesis studies electronic properties of molecular devices in the limiting cases of strong and weak electrode-molecule coupling. In these two limits, we use the complementary techniques of X-Ray spectroscopy and Scanning Tunneling Microscopy (STM) to understand the mechanisms for electrode-molecule bond formation, the energy level realignment due to metal-molecule bonds, the effect of coupling strength on single-molecule conductance in low-bias measurements, and the effect of coupling on transport under high-bias. We also introduce molecular designs with inherent asymmetries, and develop an analytical method to determine the effect of these features on high-bias conductance. This understanding of the role of electrode-molecule coupling in high-bias regimes enables us to develop a series of functional electronic devices whose properties can be predictably tuned through chemical design. First, we explore the weak electrode-molecule coupling regime by studing the interaction of two types of paracyclophane derivates that are coupled 'through-space' to underlying gold substrates. The two paracyclophane derivatives differ in the strength of their intramolecular through-space coupling. X-Ray photoemission spectroscopy (XPS) and Near-Edge X-ray Absorbance Fine Structure (NEXAFS) spectroscopy allows us to determine the orientation of both molecules; Resonant Photoemission Spectroscopy (RPES) then allows us to measure charge transfer time from molecule to metal for both molecules. This study provides a quantititative measure of charge transfer time as a function of through-space coupling strength. Next we use this understanding in STM based single-molecule current-voltage measurements of a series of molecules that couple through-space to one electrode, and through-bond to the other. We find that in the high-bias regime, these molecules respond differently depending on the direction of the applied field. This asymmetric response to electric field direction results in
2. Coherent coupling of two dopants in a silicon nanowire probed by Landau-Zener-Stückelberg interferometry.
PubMed
Dupont-Ferrier, E; Roche, B; Voisin, B; Jehl, X; Wacquez, R; Vinet, M; Sanquer, M; De Franceschi, S
2013-03-29
We report on microwave-driven coherent electron transfer between two coupled donors embedded in a silicon nanowire. By increasing the microwave frequency we observe a transition from incoherent to coherent driving revealed by the emergence of a Landau-Zener-Stückelberg quantum interference pattern of the measured current through the donors. This interference pattern is fitted to extract characteristic parameters of the double-donor system. In particular we estimate a charge dephasing time of 0.3±0.1 ns, comparable to other types of charge-based two-level systems. The demonstrated coherent coupling between two dopants is an important step towards donor-based quantum computing devices in silicon.
3. Colorimetric sensing by using allosteric-DNAzyme-coupled rolling circle amplification and a peptide nucleic acid-organic dye probe.
PubMed
Ali, M Monsur; Li, Yingfu
2009-01-01
Target detection by the naked eye: The action of an RNA-cleaving allosteric DNAzyme in response to ligand binding was coupled to a rolling circle amplification process to generate long single-stranded DNA molecules for colorimetric sensing (see scheme). Upon hybridization of the resulting DNA with a complementary PNA sequence in the presence of a duplex-binding dye, the color of the dye changed from blue to purple.
4. Human leukocyte antigen typing using a knowledge base coupled with a high-throughput oligonucleotide probe array analysis.
PubMed
Zhang, Guang Lan; Keskin, Derin B; Lin, Hsin-Nan; Lin, Hong Huang; DeLuca, David S; Leppanen, Scott; Milford, Edgar L; Reinherz, Ellis L; Brusic, Vladimir
2014-01-01
Human leukocyte antigens (HLA) are important biomarkers because multiple diseases, drug toxicity, and vaccine responses reveal strong HLA associations. Current clinical HLA typing is an elimination process requiring serial testing. We present an alternative in situ synthesized DNA-based microarray method that contains hundreds of thousands of probes representing a complete overlapping set covering 1,610 clinically relevant HLA class I alleles accompanied by computational tools for assigning HLA type to 4-digit resolution. Our proof-of-concept experiment included 21 blood samples, 18 cell lines, and multiple controls. The method is accurate, robust, and amenable to automation. Typing errors were restricted to homozygous samples or those with very closely related alleles from the same locus, but readily resolved by targeted DNA sequencing validation of flagged samples. High-throughput HLA typing technologies that are effective, yet inexpensive, can be used to analyze the world's populations, benefiting both global public health and personalized health care.
5. Jupiter probe heatshield configuration optimization
NASA Technical Reports Server (NTRS)
Dirling, R. B., Jr.; Binder, J. D.
1978-01-01
The effect of initial probe heatshield shape on the total probe mass loss during Jovian entry is considered. Modification of the aerothermal environment and probe entry trajectory due to changing probe heatshield shape is included in a computerized technique designed for rapid assessment of the effect of probe initial shape on heatshield mass loss. Results obtained indicate the importance of trajectory and heating distribution coupling with probe shape and mass change.
6. Feasibility study of a swept frequency electromagnetic probe (SWEEP) using inductive coupling for the determination of subsurface conductivity of the earth and water prospecting in arid regions
NASA Technical Reports Server (NTRS)
Latorraca, G. A.; Bannister, L. H.
1974-01-01
Techniques developed for electromagnetic probing of the lunar interior, and techniques developed for the generation of high power audio frequencies were combined to make practical a magnetic inductive coupling system for the rapid measurement of ground conductivity profiles which are helpful when prospecting for the presence and quality of subsurface water. A system which involves the measurement of the direction, intensity, and time phase of the magnetic field observed near the surface of the earth at a distance from a horizontal coil energized so as to create a field that penetrates the earth was designed and studied to deduce the conductivity and stratification of the subsurface. Theoretical studies and a rudimentary experiment in an arid region showed that the approach is conceptually valid and that this geophysical prospecting technique can be developed for the economical exploration of subterranean water resources.
7. Spatially resolved measurements of ion density and electron temperature in a dual-frequency capacitively coupled plasma by complete floating double probe technique
SciTech Connect
Jiang Xiangzhan; Liu Yongxin; Yang Shuo; Lu Wenqi; Bi Zhenhua; Li Xiaosong; Wang Younian
2011-01-15
Spatially resolved measurements of the ion density and electron temperature in a dual-frequency capacitively coupled Ar discharge plasma are performed with a newly developed complete floating double probe. Axial and radial distributions of the ion density and electron temperature under various high-frequency (HF) power and gas pressure were studied in detail. Both the ion density and the electron temperature increased with increasing HF power. With increasing gas pressure from 1.3 to 9.3 Pa, the radial profile of ion density below the driven electrode experienced a change from ''bimodal'' to ''unimodal'' shape, with better uniformity being achieved at the optimal pressure of about 5 Pa. In addition, changing the axial profile of ion density was also observed with the peak shift toward the powered electrode at higher pressures. The measured results showed satisfying consistency with that of improved two dimensional fluid simulations.
8. Time-resolved ion flux, electron temperature and plasma density measurements in a pulsed Ar plasma using a capacitively coupled planar probe
Darnon, Maxime; Cunge, Gilles; Braithwaite, Nicholas St. J.
2014-04-01
The resurgence of industrial interest in pulsed radiofrequency plasmas for etching applications highlights the fact that these plasmas are much less well characterized than their continuous wave counterparts. A capacitively coupled planar probe is used to determine the time variations of the ion flux, electron temperature (of the high-energy tail of the electron energy distribution function) and plasma density. For a pulsing frequency of 1 kHz or higher, the plasma never reaches a steady state during the on-time and is not fully extinguished during the off-time. The drop of plasma density during the off-time leads to an overshoot in the electron temperature at the beginning of each pulse, particularly at low frequencies, in good agreement with modeling results from the literature.
9. Intermolecular interaction approach for TADF (Conference Presentation)
Wong, Ken-Tsung
2016-09-01
Materials with thermally activated delayed fluorescence (TADF) have recently emerged as new fluorescent emitters for highly efficient organic light-emitting diodes (OLEDs). Molecule with TADF behavior needs to have a small singlet-triplet energy difference (ΔES-T) that allows the up-conversion from nonradiative triplet state (T1) to radiative singlet state (S1) via reverse intersystem crossing (RISC) process. Generally, molecules with small ΔES-T can be obtained via carefully manipulate the degree of "intramolecular" charge transfer (ICT) between electron-donating and -accepting components, such that the electron exchange energy that contributes to ΔES-T, can be minimized. Alternatively, excited state with small ΔES-T can be feasibly realized via "intermolecular" charge transfer occurring at the interface between spatially separating donor (D) and acceptor (A) molecules. Because the exchange energy decreases as the HOMO-LUMO separation distance increases, theoretically, the intermolecular D/A charge transfer state (or exciplex) should have rather small ΔES-T, leading to efficient TADF. However, it is still a challenge to access highly efficient exciplex systems. This is mainly because exciplex formation is commonly accompanied with a large red shift of emission spectra and long radiative lifetime, which tend to diminish photoluminescence quantum yield (PLQY) as well as electroluminescence (EL) performance. Until now, exciplex-based OLEDs with external quantum efficiency (EQE) above 10% are still limited. By judicious selection of donor and acceptor, the formation of efficient exciplex can be feasibly achieved. In this conference, our recent efforts on highly efficient exciplexes using C3-symmetry triazine acceptors and various donors, and their device characteristics will be presented.
10. Some mathematical models of intermolecular autophosphorylation.
PubMed
Doherty, Kevin; Meere, Martin; Piiroinen, Petri T
2015-04-07
Intermolecular autophosphorylation refers to the process whereby a molecule of an enzyme phosphorylates another molecule of the same enzyme. The enzyme thereby catalyses its own phosphorylation. In the present paper, we develop two generic models of intermolecular autophosphorylation that also include dephosphorylation by a phosphatase of constant concentration. The first of these, a solely time-dependent model, is written as one ordinary differential equation that relies upon mass-action and Michaelis-Menten kinetics. Beginning with the enzyme in its dephosphorylated state, it predicts a lag before the enzyme becomes significantly phosphorylated, for suitable parameter values. It also predicts that there exists a threshold concentration for the phosphorylation of enzyme and that for suitable parameter values, a continuous or discontinuous switch in the phosphorylation of enzyme are possible. The model developed here has the advantage that it is relatively easy to analyse compared with most existing models for autophosphorylation and can qualitatively describe many different systems. We also extend our time-dependent model of autophosphorylation to include a spatial dependence, as well as localised binding reactions. This spatio-temporal model consists of a system of partial differential equations that describe a soluble autophosphorylating enzyme in a spherical geometry. We use the spatio-temporal model to describe the phosphorylation of an enzyme throughout the cell due to an increase in local concentration by binding. Using physically realistic values for model parameters, our results provide a proof-of-concept of the process of activation by local concentration and suggest that, in the presence of a phosphatase, this activation can be irreversible.
11. Studies on the radical species in inductively coupled Ar/CH4 plasma using improved single Langmuir probe diagnostic methods and fluid simulation
Cha, Ju-Hong; Seo, Kwon-Sang; Lee, Jung Yeol; Lee, Hae June; Lee, Ho-Jun
2016-09-01
An inductively coupled plasma source driven by 13.56MHz was prepared for the deposition of a-C:H thin film. Properties of the plasma source are investigated by fluid simulation including Navier-Stokes equation and home-made tuned single Langmuir probe. Signal attenuation ratios of the Langmuir probe at first and second harmonic frequency were 49dB and 46dB respectively. Numerical methods including fitting, digital smoothing, digital filter with window function were used to calculate the electron energy distribution accurately. Dependencies of plasma parameters on process were well agreed with simulation results. It was found that RF power, inlet pressure and composition ratio significantly affect to the electron density, temperature and energy distribution. Electron density and plasma potential profile were changed along the input power and gas pressure. Below the input power density of 0.1W/cm3 , higher plasma potential was observed at higher pressure. However, over the 0.1W/cm3 , lower plasma potential was observed along the higher pressure. This result was occurred owing to the change of electron energy distribution. And from the simulation results, the specific chemical reaction channel, not CxHy but CHx, affect to the radical density profile.
12. Comet-FISH with strand-specific probes reveals transcription-coupled repair of 8-oxoGuanine in human cells
PubMed Central
Guo, Jia; Hanawalt, Philip C.; Spivak, Graciela
2013-01-01
Oxidized bases in DNA have been implicated in cancer, aging and neurodegenerative disease. We have developed an approach combining single-cell gel electrophoresis (comet) with fluorescence in situ hybridization (FISH) that enables the comparative quantification of low, physiologically relevant levels of DNA lesions in the respective strands of defined nucleotide sequences and in the genome overall. We have synthesized single-stranded probes targeting the termini of DNA segments of interest using a polymerase chain reaction-based method. These probes facilitate detection of damage at the single-molecule level, as the lesions are converted to DNA strand breaks by lesion-specific endonucleases or glycosylases. To validate our method, we have documented transcription-coupled repair of cyclobutane pyrimidine dimers in the ataxia telangiectasia-mutated (ATM) gene in human fibroblasts irradiated with 254 nm ultraviolet at 0.1 J/m2, a dose ∼100-fold lower than those typically used. The high specificity and sensitivity of our approach revealed that 7,8-dihydro-8-oxoguanine (8-oxoG) at an incidence of approximately three lesions per megabase is preferentially repaired in the transcribed strand of the ATM gene. We have also demonstrated that the hOGG1, XPA, CSB and UVSSA proteins, as well as actively elongating RNA polymerase II, are required for this process, suggesting cross-talk between DNA repair pathways. PMID:23775797
13. Comet-FISH with strand-specific probes reveals transcription-coupled repair of 8-oxoGuanine in human cells.
PubMed
Guo, Jia; Hanawalt, Philip C; Spivak, Graciela
2013-09-01
Oxidized bases in DNA have been implicated in cancer, aging and neurodegenerative disease. We have developed an approach combining single-cell gel electrophoresis (comet) with fluorescence in situ hybridization (FISH) that enables the comparative quantification of low, physiologically relevant levels of DNA lesions in the respective strands of defined nucleotide sequences and in the genome overall. We have synthesized single-stranded probes targeting the termini of DNA segments of interest using a polymerase chain reaction-based method. These probes facilitate detection of damage at the single-molecule level, as the lesions are converted to DNA strand breaks by lesion-specific endonucleases or glycosylases. To validate our method, we have documented transcription-coupled repair of cyclobutane pyrimidine dimers in the ataxia telangiectasia-mutated (ATM) gene in human fibroblasts irradiated with 254 nm ultraviolet at 0.1 J/m2, a dose ∼100-fold lower than those typically used. The high specificity and sensitivity of our approach revealed that 7,8-dihydro-8-oxoguanine (8-oxoG) at an incidence of approximately three lesions per megabase is preferentially repaired in the transcribed strand of the ATM gene. We have also demonstrated that the hOGG1, XPA, CSB and UVSSA proteins, as well as actively elongating RNA polymerase II, are required for this process, suggesting cross-talk between DNA repair pathways.
14. The Torque of the Planet: NASA Researcher Uses NCCS Computers to Probe Atmosphere-Land-Ocean Coupling
NASA Technical Reports Server (NTRS)
2002-01-01
The study of Earth science is like a giant puzzle, says Braulio Sanchez. "The more you know about the individual pieces, the easier it is to fit them together." A researcher with Goddard's Space Geodesy Branch, Sanchez has been using NCCS supercomputer and mass storage resources to show how the angular momenta of the atmosphere, the oceans, and the solid Earth are dynamically coupled. Sanchez has calculated the magnitude of atmospheric torque on the planet and has determined some of the possible effects that torque has on Earth's rotation.
15. Shot noise of spin-polarized charge currents as a probe of spin coherence in spin-orbit coupled nanostructures
Dragomirova, Ralitsa L.; Nikolić, Branislav K.
2007-02-01
We generalize the scattering theory of quantum shot noise to include the full spin-density matrix of electrons injected from a spin filtering or ferromagnetic electrode into a quantum-coherent nanostructure governed by arbitrary spin-dependent interactions. This formalism yields the spin-resolved shot noise power for different experimental measurement setups—with ferromagnetic source and ferromagnetic or normal drain electrodes—whose evaluation for the diffusive multichannel quantum wires with the Rashba spin-orbit (SO) coupling shows how spin decoherence and dephasing lead to substantial enhancement of charge current fluctuations (characterized by Fano factors >1/3 ). However, these processes and the corresponding shot-noise increase are suppressed in narrow wires, so that charge transport experiments measuring the Fano factor F↑→↑↓ in a ferromagnet/SO-coupled-wire/paramagnet setup also quantify the degree of phase coherence of transported spin—we predict a one-to-one correspondence between the magnitude of the spin-polarization vector and F↑→↑↓ .
16. An isotopic mass effect on the intermolecular potential
DOE PAGES
Herman, Michael F.; Currier, Robert Patrick; Clegg, Samuel M.
2015-09-28
The impact of isotopic variation on the electronic energy and intermolecular potentials is often suppressed when calculating isotopologue thermodynamics. Intramolecular potential energy surfaces for distinct isotopologues are in fact equivalent under the Born–Oppenheimer approximation, which is sometimes used to imply that the intermolecular interactions are independent of isotopic mass. In this paper, the intermolecular dipole–dipole interaction between hetero-nuclear diatomic molecules is considered. It is shown that the intermolecular potential contains mass-dependent terms even though each nucleus moves on a Born–Oppenheimer surface. Finally, the analysis suggests that mass dependent variations in intermolecular potentials should be included in comprehensive descriptions of isotopologuemore » thermodynamics.« less
17. X-ray Intermolecular Structure Factor (XISF): separation of intra- and intermolecular interactions from total X-ray scattering data
SciTech Connect
Mou, Q.; Benmore, C. J.; Yarger, J. L.
2015-06-01
XISF is a MATLAB program developed to separate intermolecular structure factors from total X-ray scattering structure factors for molecular liquids and amorphous solids. The program is built on a trust-region-reflective optimization routine with the r.m.s. deviations of atoms physically constrained. XISF has been optimized for performance and can separate intermolecular structure factors of complex molecules.
18. Probing the Efficiency of Electron-Proton Coupling in Relativistic Collisionless Shocks through the Radio Polarimetry of Gamma-Ray Burst Afterglows
SciTech Connect
Toma, Kenji; Nakamura, Takashi; Ioka, Kunihito
2008-05-22
The late-time optical/radio afterglows of {gamma}-ray bursts (GRBs) are believed to be synchrotron emission of electrons accelerated in relativistic collisionless shocks propagating in the ambient medium of the sources. However, the fraction f of electrons that are coupled to protons and accelerated remains unclear and a large number of thermal electrons that are not coupled to protons may be left behind. If f<1, the true explosion energies of GRBs are f{sup -1} times larger than those commonly estimated with f = 1. Thus the value of f gives an important constraint on the nature of the central engine of GRBs and the physics of collisionless shocks. Although early-time radio observations can probe the thermal electrons, they are difficult at present. We show that the Faraday rotation effects of the thermal electrons may suppress the linear polarization of the afterglow at frequencies higher than the absorption frequency in the late time, if the magnetic field is ordered at least in parts, and that f can be constrained through the observation of the effects. We find that those effects may be detected with late-time, {>=}1 day, polarimetry with ALMA for a burst occurring within 1 Gpc (i.e., z{approx_equal}0.2), if f{approx}10{sup -1}.
19. Mass Spectrometric and Langmuir Probe Measurements in Inductively Coupled Plasmas in Ar, CHF3/Ar and CHF3/Ar/O2 Mixtures
NASA Technical Reports Server (NTRS)
Kim, J. S.; Rao, M. V. V. S.; Cappelli, M. A.; Sharma, S. P.; Meyyappan, M.; Arnold, Jim (Technical Monitor)
2000-01-01
Absolute fluxes and energy distributions of ions in inductively coupled plasmas of Ar, CHF3/Ar, and CHF3/Ar/O2 have been measured. These plasmas were generated in a Gaseous Electronics Conference (GEC) cell modified for inductive coupling at pressures 10-50 mTorr and 100-300 W of 13.56 MHz radio frequency (RF) power in various feedgas mixtures. In pure Ar plasmas, the Ar(+) flux increases linearly with pressure as well as RF-power. Total ion flux in CHF3 mixtures decreases with increase in pressure and also CHF3 concentration. Relative ion fluxes observed in the present studies are analyzed with the help of available cross sections for electron impact ionization and charge-exchange ion-molecule reactions. Measurements of plasma potential, electron and ion number densities, electron energy distribution function, and mean electron energy have also been made in the center of the plasma with a RF compensated Langmuir probe. Plasma potential values are compared with the mean ion energies determined from the measured ion energy distributions and are consistent. Electron temperature, plasma potential, and mean ion energy vary inversely with pressure, but increase with CHF3 content in the mixture.
20. A novel inter-fibre light coupling sensor probe using plastic optical fibre for ethanol concentration monitoring at initial production rate
Memon, Sanober F.; Lewis, Elfed; Pembroke, J. Tony; Chowdhry, Bhawani S.
2017-04-01
A novel, low cost and highly sensitive optical fibre probe sensor for concentration measurement of ethanol solvent (C2H5OH) corresponding to bio-ethanol production rate by an algae is reported. The principle of operation of the sensor is based on inter-fibre light coupling through an evanescent field interaction to couple the light between two multimode fibres mounted parallel to each other at a minimum possible separation i.e. < 1mm. The sensor was fabricated using a low cost 1000um plastic optical fibre (POF) and was characterized for real time measurement in the broadband spectrum including visible and near infra-red. The wavelength dependency of this sensor design was also investigated by post processing analysis of real time data and hence the optimum wavelength range determined. The proposed sensor has shown significant response in the range of 0.005 - 0.1 %v/v (%volume/volume or volume concentration) which depicts the high sensitivity for monitoring very minute changes in concentration corresponding refractive index changes of the solution. Numerically, sensor has shown the sensitivity of 21945 intensity counts/%v/v or 109.7 counts per every 0.0050 %v/v.
1. Probing triple-W production and anomalous WWWW coupling at the CERN LHC and future TeV proton-proton collider
Wen, Yiwen; Qu, Huilin; Yang, Daneng; Yan, Qi-shu; Li, Qiang; Mao, Yajun
2015-03-01
Triple gauge boson production at the LHC can be used to test the robustness of the Standard Model and provide useful information for VBF di-boson scattering measurement. Especially, any derivations from SM prediction will indicate possible new physics. In this paper we present a detailed Monte Carlo study on measuring W ± W ± W ∓ production in pure leptonic and semileptonic decays, and probing anomalous quartic gauge WWWW couplings at the CERN LHC and future hadron collider, with parton shower and detector simulation effects taken into account. Apart from cut-based method, multivariate boosted decision tree method has been exploited for possible improvement. For the leptonic decay channel, our results show that at the TeV pp collider with integrated luminosity of 20(100)[3000] fb-1, one can reach a significance of 0.4(1.2)[10] σ to observe the SM W ± W ± W ∓ production. For the semileptonic decay channel, one can have 0.5(2)[14] σ to observe the SM W ± W ± W ∓ production. We also give constraints on relevant Dim-8 anomalous WWWW coupling parameters.
2. Multiple DNA Extractions Coupled with Stable-Isotope Probing of Anthracene-Degrading Bacteria in Contaminated Soil▿†
PubMed Central
Jones, Maiysha D.; Singleton, David R.; Sun, Wei; Aitken, Michael D.
2011-01-01
In many of the DNA-based stable-isotope probing (SIP) studies published to date in which soil communities were investigated, a single DNA extraction was performed on the soil sample, usually using a commercial DNA extraction kit, prior to recovering the 13C-labeled (heavy) DNA by density-gradient ultracentrifugation. Recent evidence suggests, however, that a single extraction of a soil sample may not lead to representative recovery of DNA from all of the organisms in the sample. To determine whether multiple DNA extractions would affect the DNA yield, the eubacterial 16S rRNA gene copy number, or the identification of anthracene-degrading bacteria, we performed seven successive DNA extractions on the same aliquot of contaminated soil either untreated or enriched with [U-13C]anthracene. Multiple extractions were necessary to maximize the DNA yield and 16S rRNA gene copy number from both untreated and anthracene-enriched soil samples. Sequences within the order Sphingomonadales, but unrelated to any previously described genus, dominated the 16S rRNA gene clone libraries derived from 13C-enriched DNA and were designated “anthracene group 1.” Sequences clustering with Variovorax spp., which were also highly represented, and sequences related to the genus Pigmentiphaga were newly associated with anthracene degradation. The bacterial groups collectively identified across all seven extracts were all recovered in the first extract, although quantitative PCR analysis of SIP-identified groups revealed quantitative differences in extraction patterns. These results suggest that performing multiple DNA extractions on soil samples improves the extractable DNA yield and the number of quantifiable eubacterial 16S rRNA gene copies but have little qualitative effect on the identification of the bacterial groups associated with the degradation of a given carbon source by SIP. PMID:21398486
3. Probing mechanical principles of focal contacts in cell–matrix adhesion with a coupled stochastic–elastic modelling framework
PubMed Central
Gao, Huajian; Qian, Jin; Chen, Bin
2011-01-01
Cell–matrix adhesion depends on the collective behaviours of clusters of receptor–ligand bonds called focal contacts between cell and extracellular matrix. While the behaviour of a single molecular bond is governed by statistical mechanics at the molecular scale, continuum mechanics should be valid at a larger scale. This paper presents an overview of a series of recent theoretical studies aimed at probing the basic mechanical principles of focal contacts in cell–matrix adhesion via stochastic–elastic models in which stochastic descriptions of molecular bonds and elastic descriptions of interfacial traction–separation are unified in a single modelling framework. The intention here is to illustrate these principles using simple analytical and numerical models. The aim of the discussions is to provide possible clues to the following questions: why does the size of focal adhesions (FAs) fall into a narrow range around the micrometre scale? How can cells sense and respond to substrates of varied stiffness via FAs? How do the magnitude and orientation of mechanical forces affect the binding dynamics of FAs? The effects of cluster size, cell–matrix elastic modulus, loading direction and cytoskeletal pretension on the lifetime of FA clusters have been investigated by theoretical arguments as well as Monte Carlo numerical simulations, with results showing that intermediate adhesion size, stiff substrate, cytoskeleton stiffening, low-angle pulling and moderate cytoskeletal pretension are factors that contribute to stable FAs. From a mechanistic point of view, these results provide possible explanations for a wide range of experimental observations and suggest multiple mechanisms by which cells can actively control adhesion and de-adhesion via cytoskeletal contractile machinery in response to mechanical properties of their surroundings. PMID:21632610
4. Multiple DNA extractions coupled with stable-isotope probing of anthracene-degrading bacteria in contaminated soil.
PubMed
Jones, Maiysha D; Singleton, David R; Sun, Wei; Aitken, Michael D
2011-05-01
In many of the DNA-based stable-isotope probing (SIP) studies published to date in which soil communities were investigated, a single DNA extraction was performed on the soil sample, usually using a commercial DNA extraction kit, prior to recovering the (13)C-labeled (heavy) DNA by density-gradient ultracentrifugation. Recent evidence suggests, however, that a single extraction of a soil sample may not lead to representative recovery of DNA from all of the organisms in the sample. To determine whether multiple DNA extractions would affect the DNA yield, the eubacterial 16S rRNA gene copy number, or the identification of anthracene-degrading bacteria, we performed seven successive DNA extractions on the same aliquot of contaminated soil either untreated or enriched with [U-(13)C]anthracene. Multiple extractions were necessary to maximize the DNA yield and 16S rRNA gene copy number from both untreated and anthracene-enriched soil samples. Sequences within the order Sphingomonadales, but unrelated to any previously described genus, dominated the 16S rRNA gene clone libraries derived from (13)C-enriched DNA and were designated "anthracene group 1." Sequences clustering with Variovorax spp., which were also highly represented, and sequences related to the genus Pigmentiphaga were newly associated with anthracene degradation. The bacterial groups collectively identified across all seven extracts were all recovered in the first extract, although quantitative PCR analysis of SIP-identified groups revealed quantitative differences in extraction patterns. These results suggest that performing multiple DNA extractions on soil samples improves the extractable DNA yield and the number of quantifiable eubacterial 16S rRNA gene copies but have little qualitative effect on the identification of the bacterial groups associated with the degradation of a given carbon source by SIP.
5. Open Port Probe Sampling Interface for the Direct Coupling of Biocompatible Solid-Phase Microextraction to Atmospheric Pressure Ionization Mass Spectrometry.
PubMed
Gómez-Ríos, Germán Augusto; Liu, Chang; Tascon, Marcos; Reyes-Garcés, Nathaly; Arnold, Don W; Covey, Thomas R; Pawliszyn, Janusz
2017-04-04
In recent years, the direct coupling of solid phase microextraction (SPME) and mass spectrometry (MS) has shown its great potential to improve limits of quantitation, accelerate analysis throughput, and diminish potential matrix effects when compared to direct injection to MS. In this study, we introduce the open port probe (OPP) as a robust interface to couple biocompatible SPME (Bio-SPME) fibers to MS systems for direct electrospray ionization. The presented design consisted of minimal alterations to the front-end of the instrument and provided better sensitivity, simplicity, speed, wider compound coverage, and high-throughput in comparison to the LC-MS based approach. Quantitative determination of clenbuterol, fentanyl, and buprenorphine was successfully achieved in human urine. Despite the use of short extraction/desorption times (5 min/5 s), limits of quantitation below the minimum required performance levels (MRPL) set by the world antidoping agency (WADA) were obtained with good accuracy (≥90%) and linearity (R(2) > 0.99) over the range evaluated for all analytes using sample volumes of 300 μL. In-line technologies such as multiple reaction monitoring with multistage fragmentation (MRM(3)) and differential mobility spectrometry (DMS) were used to enhance the selectivity of the method without compromising analysis speed. On the basis of calculations, once coupled to high throughput, this method can potentially yield preparation times as low as 15 s per sample based on the 96-well plate format. Our results demonstrated that Bio-SPME-OPP-MS efficiently integrates sampling/sample cleanup and atmospheric pressure ionization, making it an advantageous configuration for several bioanalytical applications, including doping in sports, in vivo tissue sampling, and therapeutic drug monitoring.
6. Linking proteins with anionic nanoparticles via protamine: ultrasmall protein-coupled probes for magnetic resonance imaging of apoptosis.
PubMed
Schellenberger, Eyk; Schnorr, Jörg; Reutelingsperger, Chris; Ungethüm, Liset; Meyer, Wolfdietrich; Taupitz, Matthias; Hamm, Bernd
2008-02-01
Magnetic resonance imaging (MRI) of a target in vivo depends on the surface, size, and particle relaxivity of the target-specific nanoparticles for MRI. Here a new method for decorating very small iron oxide particles (VSOPs) with target-specific ligands is described. The method is based on the electrostatic attraction of the strongly positively charged peptide protamine to the anionic citrate shell of the electrostatically stabilized VSOPs. The protamine coat allows linkage chemistry and chimera technology to functionalize VSOPs or other negative charged surfaces with biologics. Annexin A5 (anxA5)-VSOP utilizing thiol chemistry was generated to couple biologically active anxA5 to VSOPs for in vivo MRI of apoptosis. Annexin A5-VSOP comprises five anxA5 molecules per iron oxide nanoparticle with a high R2 particle relaxivity of 180 000 mM(-1) s(-1) yet small hydrodynamic diameter of only 14.7+/-2.9 nm beneficial for in vivo MRI of extravascular targets.
7. Intermolecular domain docking in the hairpin ribozyme
PubMed Central
Sumita, Minako; White, Neil A.; Julien, Kristine R.; Hoogstraten, Charles G.
2013-01-01
The hairpin ribozyme is a prototype small, self-cleaving RNA motif. It exists naturally as a four-way RNA junction containing two internal loops on adjoining arms. These two loops interact in a cation-driven docking step prior to chemical catalysis to form a tightly integrated structure, with dramatic changes occurring in the conformation of each loop upon docking. We investigate the thermodynamics and kinetics of the docking process using constructs in which loop A and loop B reside on separate molecules. Using a novel CD difference assay to isolate the effects of metal ions linked to domain docking, we find the intermolecular docking process to be driven by sub-millimolar concentrations of the exchange-inert Co(NH3)63+. RNA self-cleavage requires binding of lower-affinity ions with greater apparent cooperativity than the docking process itself, implying that, even in the absence of direct coordination to RNA, metal ions play a catalytic role in hairpin ribozyme function beyond simply driving loop-loop docking. Surface plasmon resonance assays reveal remarkably slow molecular association, given the relatively tight loop-loop interaction. This observation is consistent with a “double conformational capture” model in which only collisions between loop A and loop B molecules that are simultaneously in minor, docking-competent conformations are productive for binding. PMID:23324606
8. Intermolecular interaction studies of glyphosate with water
Manon, Priti; Juglan, K. C.; Kaur, Kirandeep; Sethi, Nidhi; Kaur, J. P.
2017-07-01
The density (ρ), viscosity (η) and ultrasonic velocity (U) of glyphosate with water have been measured on different ultrasonic frequency ranges from 1MHz, 2MHz, 3MHz & 5MHz by varying concentrations (0.05%, 0.10%, 0.15%, 0.20%, 0.25%, 0.30%, 0.35%, & 0.40%) at 30°C. The specific gravity bottle, Ostwald's viscometer and quartz crystal interferometer were used to determine density (ρ), viscosity (η) and ultrasonic velocity (U). These three factors contribute in evaluating the other parameters as acoustic impedance (Z), adiabatic compressibility (β), relaxation time (τ), intermolecular free length (Lf), free volume (Vf), ultrasonic attenuation (α/f2), Rao's constant (R), Wada's constant (W) and relative strength (R). Solute-solvent interaction is confirmed by ultrasonic velocity and viscosity values, which increases with increase in concentration indicates stronger association between solute and solvent molecules. With rise in ultrasonic frequency the interaction between the solute and solvent particles decreases. The linear variations in Rao's constant and Wada's constant suggest the absence of complex formation.
9. Mechanism of Intermolecular Electron Transfer in Bionanostructures
Gruodis, A.; Galikova, N.; Šarka, K.; Saulė, R.; Batiuškaitė, D.; Saulis, G.
Hepatocellular carcinoma (HCC) is one of the most common malignant tumors worldwide. Most patients are inoperable and hepatoma cells are resistant to conventional chemotherapies. Thus, the development of novel therapies for HCC treatment is of paramount importance. Amongst different alimentary factors, vitamin C and vitamin K3 In the present work, it has been shown that the treatment of mouse hepatoma MH-22A cells by vitamin C and vitamin K3 at the ratio of 100:1 greatly enhanced their cytotoxicity. When cells were subjected to vitamin C at 200 μM or to vitamin K3 at 2 μM separately, their viability reduced by only about 10%. However, when vitamins C and K3 were combined at the same concentrations, they killed more than 90% of cells. To elucidate the mechanism of the synergistic cytotoxicity of the C&K3 mixture, theoretical quantum-chemical analysis of the dynamics of intermolecular electron transfer (IET) processes within the complexes containing C (five forms) and K3 (one form) has been carried out. Optimization of the ground state complex geometry has been provided by means of GAUSSIAN03 package. Simulation of the IET has been carried out using NUVOLA package, in the framework of molecular orbitals (MO). The rate of IET has been calculated using Fermi Golden rule. The results of simulations allow us to create the preliminary model of the reaction pathway.
10. Interpolation of intermolecular potentials using Gaussian processes
Uteva, Elena; Graham, Richard S.; Wilkinson, Richard D.; Wheatley, Richard J.
2017-10-01
A procedure is proposed to produce intermolecular potential energy surfaces from limited data. The procedure involves generation of geometrical configurations using a Latin hypercube design, with a maximin criterion, based on inverse internuclear distances. Gaussian processes are used to interpolate the data, using over-specified inverse molecular distances as covariates, greatly improving the interpolation. Symmetric covariance functions are specified so that the interpolation surface obeys all relevant symmetries, reducing prediction errors. The interpolation scheme can be applied to many important molecular interactions with trivial modifications. Results are presented for three systems involving CO2, a system with a deep energy minimum (HF-HF), and a system with 48 symmetries (CH4-N2). In each case, the procedure accurately predicts an independent test set. Training this method with high-precision ab initio evaluations of the CO2-CO interaction enables a parameter-free, first-principles prediction of the CO2-CO cross virial coefficient that agrees very well with experiments.
11. Thermodynamics of systems with different geometric constraints and intermolecular correlations.
PubMed
Chen, Y; Kilburg, R R; Donohue, M D
2009-09-17
Four types of systems with different degrees of geometric constraint and intermolecular correlations were studied to determine the differences in their thermodynamics. The average configurational internal energies of these systems were calculated using Monte Carlo simulations, and the results are compared at the same temperatures and constant average bulk density. From the energy profiles for the four systems, the effects of geometry and intermolecular correlations on the systems' phase behavior are discussed. It was observed that indirect intermolecular correlations, rather than geometric constraints, are the key to achieving a first-order phase transition.
12. Intermolecular hydrogen bonding in chlorine dioxide photochemistry: A time-resolved resonance Raman study
Philpott, Matthew P.; Hayes, Sophia C.; Thomsen, Carsten L.; Reid, Philip J.
2001-01-01
The geminate-recombination and vibrational-relaxation dynamics of chlorine dioxide (OClO) dissolved in ethanol and 2,2,2-trifluoroethanol (TFE) are investigated using time-resolved resonance Raman spectroscopy. Stokes spectra are measured as a function of time following photoexcitation using degenerate pump and probe wavelengths of 398 nm. For OClO dissolved in ethanol, subpicosecond geminate recombination occurs resulting in the reformation of ground-state OClO with a quantum yield of 0.5±0.1. Following recombination, intermolecular-vibrational relaxation of OClO occurs with a time constant of 31±10 ps. For OClO dissolved in TFE, recombination occurs with a time constant of 1.8±0.8 ps and a quantum yield of only 0.3±0.1. The intermolecular-vibrational-relaxation time constant of OClO in TFE is 79±27 ps. The reduced geminate-recombination quantum yield, delayed recombination, and slower vibrational relaxation for OClO in TFE is interpreted in terms of greater self-association of the solvent. Degenerate pump-probe experiments are also presented that demonstrate decay of the Cl-solvent charge-transfer complex on the ˜1-ns time scale in ethanol and TFE. This time is significantly longer than the abstraction times observed for other systems demonstrating that Cl hydrogen abstraction from alcohols occurs in the presence of a significant energy barrier.
13. NMR detection of intermolecular interaction sites in the dimeric 5′-leader of the HIV-1 genome
PubMed Central
Keane, Sarah C.; Van, Verna; Frank, Heather M.; Sciandra, Carly A.; McCowin, Sayo; Santos, Justin; Heng, Xiao; Summers, Michael F.
2016-01-01
HIV type-1 (HIV-1) contains a pseudodiploid RNA genome that is selected for packaging and maintained in virions as a noncovalently linked dimer. Genome dimerization is mediated by conserved elements within the 5′-leader of the RNA, including a palindromic dimer initiation signal (DIS) that has been proposed to form kissing hairpin and/or extended duplex intermolecular contacts. Here, we have applied a 2H-edited NMR approach to directly probe for intermolecular interactions in the full-length, dimeric HIV-1 5′-leader (688 nucleotides; 230 kDa). The interface is extensive and includes DIS:DIS base pairing in an extended duplex state as well as intermolecular pairing between elements of the upstream Unique-5′ (U5) sequence and those near the gag start site (AUG). Other pseudopalindromic regions of the leader, including the transcription activation (TAR), polyadenylation (PolyA), and primer binding (PBS) elements, do not participate in intermolecular base pairing. Using a 2H-edited one-dimensional NMR approach, we also show that the extended interface structure forms on a time scale similar to that of overall RNA dimerization. Our studies indicate that a kissing dimer-mediated structure, if formed, exists only transiently and readily converts to the extended interface structure, even in the absence of the HIV-1 nucleocapsid protein or other RNA chaperones. PMID:27791166
14. Investigations of Diffuse Intermolecular Electronic Systems
Muguet, Francis Fabien Michel
1992-01-01
Diffuse intermolecular electronic systems, such as the hydrated electron or the ammonia and water dimers, present both a theoretical and a practical computational challenge. The hydrated electron was discovered more than 25 years ago, yet there is still no consensus on an explanation of this phenomenon. A novel model is presented here, whereby the hydrated electron consists in an itinerant diHydronium radical structure. Although electrostatically neutral, the itinerant radical is shown to behave as a negative charge carrier under the influence of an electric field. Within this perspective, the hydrated electron may be considered a quasiparticle. Contrary to the absence of agreement between many experiments and the old but still popular cavity model description, the energetics in the new model are shown to be consistent with photophysical experimental data. In order to understand negatively charged water clusters, it is also proposed that a metastable bifurcated water dimer structure is able to bind an extra electron. Prior to our studies, no ab initio computations had been able to reproduce the experimental geometry of the ammonia dimer or to predict any water dimer anion with the Franck-Condon factors agreeing with those recently found in molecular beam experiments. In both cases the potential energy surface is determined by attractors corresponding to nonlinear and linear hydrogen bonded geometries, respectively. One attractor receives an unfair advantage in the computational procedure mainly because of the basis set superposition error (BSSE). There is still no agreement on a scheme for correcting the BSSE. A widely employed error estimation method is the counterpoise correction. A completely different new method is proposed using reorthonormalization of purified localized molecular orbitals. In terms of a BSSE corrected potential energy surface of the water dimer, a multi-attractor model of liquid water is briefly discussed. For further water molecular dynamics
15. Intermolecular Vibrations of Hydrophobic Amino Acids
Williams, Michael Roy Casselman
Hydrophobic amino acids interact with their chemical environment through a combination of electrostatic, hydrogen bonding, dipole, induced dipole, and dispersion forces. These interactions all have their own characteristic energy scale and distance dependence. The low-frequency (0.1-5 THz, 5-150 cm-1) vibrational modes of amino acids in the solid state are a direct indicator of the interactions between the molecules, which include interactions between an amino acid functional group and its surroundings. This information is central to understanding the dynamics and morphology of proteins. The alpha-carbon is a chiral center for all of the hydrophobic amino acids, meaning that they exist in two forms, traditionally referred to as L- and D-enantiomers. This nomenclature indicates which direction the molecule rotates plane-polarized visible light (levorotory and dextrorotory). Chiral a-amino acids in proteins are exclusively the L-variety In the solid state, the crystal lattice of the pure L-enantiomer is the mirror image of the D-enantiomer crystal lattice. These solids are energetically identical. Enantiomers also have identical spectroscopic properties except when the measurement is polarization sensitive. A mixture of equal amounts D- and L-amino acid enantiomers can crystallize into a racemic (DL-) structure that is different from that of the pure enantiomers. Whether a solution of both enantiomers will crystallize into a racemic form or spontaneously resolve into a mixture of separate D- and L-crystals largely depends on the interactions between molecules available in the various possible configurations. This is an active area of research. Low-frequency vibrations with intermolecular character are very sensitive to changes in lattice geometry, and consequently the vibrational spectra of racemic crystals are usually quite distinct from the spectra of the crystals of the corresponding pure enantiomers in the far-infrared (far-IR). THz time-domain spectroscopy (THz
16. Self-diffusion studies by intra- and inter-molecular spin-lattice relaxometry using field-cycling: Liquids, plastic crystals, porous media, and polymer segments.
PubMed
Kimmich, Rainer; Fatkullin, Nail
2017-08-01
Field-cycling NMR relaxometry is a well-established technique for probing molecular dynamics in a frequency range from typically a few kHz up to several tens of MHz. For the interpretation of relaxometry data, it is quite often assumed that the spin-lattice relaxation process is of an intra-molecular nature so that rotational fluctuations dominate. However, dipolar interactions as the main type of couplings between protons and other dipolar species without quadrupole moments can imply appreciable inter-molecular contributions. These fluctuate due to translational displacements and to a lesser degree also by rotational reorientations in the short-range limit. The analysis of the inter-molecular proton spin-lattice relaxation rate thus permits one to evaluate self-diffusion variables such as the diffusion coefficient or the mean square displacement on a time scale from nanoseconds to several hundreds of microseconds. Numerous applications to solvents, plastic crystals and polymers will be reviewed. The technique is of particular interest for polymer dynamics since inter-molecular spin-lattice relaxation diffusometry bridges the time scales of quasi-elastic neutron scattering and field-gradient NMR diffusometry. This is just the range where model-specific intra-coil mechanisms are assumed to occur. They are expected to reveal themselves by characteristic power laws for the time-dependence of the mean-square segment displacement. These can be favorably tested on this basis. Results reported in the literature will be compared with theoretical predictions. On the other hand, there is a second way for translational diffusion phenomena to affect the spin-lattice relaxation dispersion. If rotational diffusion of molecules is restricted, translational diffusion properties can be deduced even from molecular reorientation dynamics detected by intra-molecular spin-lattice relaxation. This sort of scenario will be relevant for adsorbates on surfaces or polymer segments under
17. Synthesis and intermolecular interactions of N-benzylidenetyramines
2017-01-01
In this paper, the synthesis and intermolecular interactions between N-benzylidenetyramine molecules were investigated. The crystal structure of N-(4-nitrobenzylidene)tyramine shows a molecular organization in zigzag chains with intermolecular O-H⋯N hydrogen bonds between the azomethine and phenolic hydroxyl groups. Those chains are held together by C-H⋯O hydrogen bonds to generate layers, which are connected by C-H⋯O, π⋯π and NO2⋯π interactions.
18. Cavity Photons as a Probe for Charge Relaxation Resistance and Photon Emission in a Quantum Dot Coupled to Normal and Superconducting Continua
Bruhat, L. E.; Viennot, J. J.; Dartiailh, M. C.; Desjardins, M. M.; Kontos, T.; Cottet, A.
2016-04-01
Microwave cavities have been widely used to investigate the behavior of closed few-level systems. Here, we show that they also represent a powerful probe for the dynamics of charge transfer between a discrete electronic level and fermionic continua. We have combined experiment and theory for a carbon nanotube quantum dot coupled to normal metal and superconducting contacts. In equilibrium conditions, where our device behaves as an effective quantum dot-normal metal junction, we approach a universal photon dissipation regime governed by a quantum charge relaxation effect. We observe how photon dissipation is modified when the dot admittance turns from capacitive to inductive. When the fermionic reservoirs are voltage biased, the dot can even cause photon emission due to inelastic tunneling to/from a Bardeen-Cooper-Schrieffer peak in the density of states of the superconducting contact. We can model these numerous effects quantitatively in terms of the charge susceptibility of the quantum dot circuit. This validates an approach that could be used to study a wide class of mesoscopic QED devices.
19. Synthesis and Characterization of Tricarbonyl-Re/Tc(I) Chelate Probes Targeting the G Protein-Coupled Estrogen Receptor GPER/GPR30
PubMed Central
Burai, Ritwik; Ramesh, Chinnasamy; Nayak, Tapan K.; Dennis, Megan K.; Bryant, Bj K.; Prossnitz, Eric R.; Arterburn, Jeffrey B.
2012-01-01
The discovery of the G protein-coupled estrogen receptor GPER (also GPR30) and the resulting development of selective chemical probes have revealed new aspects of estrogen receptor biology. The potential clinical relevance of this receptor has been suggested from numerous studies that have identified GPER expression in breast, endometrial, ovarian and other cancers. Thus GPER can be considered a candidate biomarker and target for non-invasive imaging and therapy. We have designed and synthesized a series of organometallic tricarbonyl-rhenium complexes conjugated to a GPER-selective small molecule derived from tetrahydro-3H-cyclopenta[c]quinoline. The activity and selectivity of these chelates in GPER-mediated signaling pathways were evaluated. These results demonstrate that GPER targeting characteristics depend strongly on the structure of the chelate and linkage. Ethanone conjugates functioned as agonists, a 1,2,3-triazole spacer yielded an antagonist, and derivatives with increased steric volume exhibited decreased activities. Promising GPER selectivity was observed, as none of the complexes interacted with the nuclear estrogen receptors. Radiolabeling with technetium-99m in aqueous media was efficient and gave radioligands with high radiochemical yields and purity. These chelates have favorable physicochemical properties, show excellent stability in biologically relevant media, exhibit receptor specificity and are promising candidates for continuing development as diagnostic imaging agents targeting GPER expression in cancer. PMID:23077529
20. Design of a scanning probe microscope with advanced sample treatment capabilities: An atomic force microscope combined with a miniaturized inductively coupled plasma source.
PubMed
Hund, Markus; Herold, Hans
2007-06-01
We describe the design and performance of an atomic force microscope (AFM) combined with a miniaturized inductively coupled plasma source working at a radio frequency of 27.12 MHz. State-of-the-art scanning probe microscopes (SPMs) have limited in situ sample treatment capabilities. Aggressive treatments such as plasma etching or harsh treatments such as etching in aggressive liquids typically require the removal of the sample from the microscope. Consequently, time consuming procedures are required if the same sample spot has to be imaged after successive processing steps. We have developed a first prototype of a SPM which features a quasi in situ sample treatment using a modified commercial atomic force microscope. A sample holder is positioned in a special reactor chamber; the AFM tip can be retracted by several millimeters so that the chamber can be closed for a treatment procedure. Most importantly, after the treatment, the tip is moved back to the sample with a lateral drift per process step in the 20 nm regime. The performance of the prototype is characterized by consecutive plasma etching of a nanostructured polymer film.
1. Pd0-mediated rapid cross-coupling reactions, the rapid C-[11C]methylations, revolutionarily advancing the syntheses of short-lived PET molecular probes.
PubMed
Suzuki, Masaaki; Doi, Hisashi; Koyama, Hiroko; Zhang, Zhouen; Hosoya, Takamitsu; Onoe, Hirotaka; Watanabe, Yasuyoshi
2014-06-01
Positron emission tomography is a noninvasive method for monitoring drug (or diagnostic) behavior and its localization on the target molecules in the living systems, including the human body, using a short-lived positron-emitting radionuclide. New methodologies for introducing representative short-lived radionuclides, (11)C and (18)F, into the carbon frameworks of biologically active organic compounds have been established by developing rapid C-[(11)C]methylations and C-[(18)F]fluoromethylations using rapid Pd(0)-mediated cross-coupling reactions between [(11)C]methyl iodide (sp(3)-hybridized carbon) and an excess amount of organotributylstannane or organoboronic acid ester having sp(2) (phenyl, heteroaromatic, or alkenyl), sp(alkynyl), or sp(3) (benzyl and cinnamyl)-hybridized carbons; and [(18)F]fluoromethyl halide (iodide or bromide) and an organoboronic acid ester, respectively. These rapid reactions provide a firm foundation for an efficient and general synthesis of short-lived (11)C- or (18)F-labeled PET molecular probes to promote in vivo molecular imaging studies. Copyright © 2014 The Chemical Society of Japan and Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
2. Synergy between measurements of gravitational waves and the triple-Higgs coupling in probing the first-order electroweak phase transition
Hashino, Katsuya; Kakizaki, Mitsuru; Kanemura, Shinya; Matsui, Toshinori
2016-07-01
Probing the Higgs potential and new physics behind the electroweak symmetry breaking is one of the most important issues of particle physics. In particular, the nature of the electroweak phase transition is essential for understanding the physics of the early Universe, such that the strongly first-order phase transition is required for a successful scenario of electroweak baryogenesis. The strongly first-order phase transition is expected to be tested by precisely measuring the triple Higgs boson coupling at future colliders like the International Linear Collider. It can also be explored via the spectrum of stochastic gravitational waves to be measured at future space-based interferometers such as eLISA and DECIGO. We discuss the complementarity of both the methods in testing the strongly first-order phase transition of the electroweak symmetry in models with additional isospin singlet scalar fields with and without classical scale invariance. We find that they are synergetic in identifying specific models of electroweak symmetry breaking in more detail.
3. Long range intermolecular interactions between the alkali diatomics Na2, K2, and NaK
Zemke, Warren T.; Byrd, Jason N.; Michels, H. Harvey; Montgomery, John A.; Stwalley, William C.
2010-06-01
Long range interactions between the ground state alkali diatomics Na2-Na2, K2-K2, Na2-K2, and NaK-NaK are examined. Interaction energies are first determined from ab initio calculations at the coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] level of theory, including counterpoise corrections. Long range energies calculated from diatomic molecular properties (polarizabilities and dipole and quadrupole moments) are then compared with the ab initio energies. A simple asymptotic model potential ELR=Eelec+Edisp+Eind is shown to accurately represent the intermolecular interactions for these systems at long range.
4. Long range intermolecular interactions between the alkali diatomics Na(2), K(2), and NaK.
PubMed
Zemke, Warren T; Byrd, Jason N; Michels, H Harvey; Montgomery, John A; Stwalley, William C
2010-06-28
Long range interactions between the ground state alkali diatomics Na(2)-Na(2), K(2)-K(2), Na(2)-K(2), and NaK-NaK are examined. Interaction energies are first determined from ab initio calculations at the coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] level of theory, including counterpoise corrections. Long range energies calculated from diatomic molecular properties (polarizabilities and dipole and quadrupole moments) are then compared with the ab initio energies. A simple asymptotic model potential E(LR)=E(elec)+E(disp)+E(ind) is shown to accurately represent the intermolecular interactions for these systems at long range.
5. Intermolecular Singlet and Triplet Exciton Transfer Integrals from Many-Body Green's Functions Theory.
PubMed
Wehner, Jens; Baumeier, Björn
2017-03-08
A general approach to determine orientation and distance-dependent effective intermolecular exciton transfer integrals from many-body Green's functions theory is presented. On the basis of the GW approximation and the Bethe-Salpeter equation (BSE), a projection technique is employed to obtain the excitonic coupling by forming the expectation value of a supramolecular BSE Hamiltonian with electron-hole wave functions for excitations localized on two separated chromophores. Within this approach, accounting for the effects of coupling mediated by intermolecular charge transfer (CT) excitations is possible via perturbation theory or a reduction technique. Application to model configurations of pyrene dimers shows an accurate description of short-range exchange and long-range Coulomb interactions for the coupling of singlet and triplet excitons. Computational parameters, such as the choice of the exchange-correlation functional in the density-functional theory (DFT) calculations that underly the GW-BSE steps and the convergence with the number of included CT excitations, are scrutinized. Finally, an optimal strategy is derived for simulations of full large-scale morphologies by benchmarking various approximations using pairs of dicyanovinyl end-capped oligothiophenes (DCV5T), which are used as donor material in state-of-the-art organic solar cells.
6. Analysis of cytochrome P450 metabolites of arachidonic acid by stable isotope probe labeling coupled with ultra high-performance liquid chromatography/mass spectrometry.
PubMed
Zhu, Quan-Fei; Hao, Yan-Hong; Liu, Ming-Zhou; Yue, Jiang; Ni, Jian; Yuan, Bi-Feng; Feng, Yu-Qi
2015-09-04
Cytochrome P450 metabolites of arachidonic acid (AA) belong to eicosanoids and are potent lipid mediators of inflammation. It is well-known that eicosanoids play an important role in numerous pathophysiological processes. Therefore, quantitative analysis of cytochrome P450 metabolites of AA, including hydroxyeicosatetraenoic acids (HETEs), epoxyeicosatreinoic acids (EETs), and dihydroxyeicosatrienoic acids (DHETs) can provide crucial information to uncover underlying mechanisms of cytochrome P450 metabolites of AA related diseases. Herein, we developed a highly sensitive method to identify and quantify HETEs, EETs, and DHETs in lipid extracts of biological samples based on stable isotope probe labeling coupled with ultra high-performance liquid chromatography/mass spectrometry. To this end, a pair of stable isotope probes, 2-dimethylaminoethylamine (DMED) and d4-2-dimethylaminoethylamine (d4-DMED), were utilized to facilely label eicosanoids. The heavy labeled eicosanoid standards were prepared and used as internal standards for quantification to minimize the matrix and ion suppression effects in mass spectrometry analysis. In addition, the detection sensitivities of DMED labeled eicosanoids improved by 3-104 folds in standard solution and 5-138 folds in serum matrix compared with unlabeled analytes. Moreover, a good separation of eicosanoids isomers was achieved upon DMED labeling. The established method provided substantial sensitivity (limit of quantification at sub-picogram), high specificity, and broad linear dynamics range (3 orders of magnitude). We further quantified cytochrome P450 metabolites of AA in rat liver, heart, brain tissues and human serum using the developed method. The results showed that 19 eicosanoids could be distinctly detected and the contents of 11-, 15-, 16-, 20-HETE, 5,6-EET, and 14,15-EET in type 2 diabetes mellitus patients and 5-, 11-, 12-, 15-, 16-, 20-HETE, 8,9-EET, and 5,6-DHET in myeloid leukemia patients had significant changes
7. Probing Spin and Spin-Orbit Coupling effects in Narrow-gap Semiconductor Nano-structures by THz Magneto-photoresponse Spectroscopy and Magneto-transport Measurements
Pakmehr, Mehdi
Using the spin degree of freedom in a emergent field Known as Spintronics has motivated scientist in different disciplines including physicist within last 10 years. Due to different interaction mechanisms which affects the physical behavior of spin (eg its state and transport properties) within solid medium (Semiconductors in our case), one needs to distinguish these mechanisms and their importance for making any practical spin based devices. For example the idea of making spin based transistors with electrons being transported within InGaAs and their spin state is being controlled by Rashba type field has been around for around 25 years but injection of spin polarized currents from a source into the channel has not been solved yet. Spin orbit coupling (SOC) is one of the mechanisms which changes the spin state of electrons and avoid the existence of pure spin state as a favorable one from device point of view. SOC could have a different origin depending on material type or structure of device. One method of measuring and quantifying this mechanisms within semiconductor nanostructures is through measuring the parameters known as Lande g-factor. This parameters turns out to be a promising one to probe different effects on electronic band structure including quantum confinement, strain, electric filed, etc. We probe a combination of these effects (SOC, Strain, band mixing, etc) by measuring different g-factor tensor components of narrow gap Zinc blend semiconductor nanostructures which we hope finally serve to the purpose of making reliable spin based devices* (Spintronics). To reach this goal we have developed and implemented THz magneto-Photoresponse spectroscopy in conjunction with magneto-transport measurements at cryogenic temperatures. The samples include InAs and HgTe based Quantum wells as well as InAs based quantum point contact. Our findings clarify the situation where the combination of SOC, Strain, quantum confinements as well as many body electron effect
8. Energy transfer to a proton-transfer fluorescence probe: tryptophan to a flavonol in human serum albumin.
PubMed
Sytnik, A; Litvinyuk, I
1996-11-12
A protein fluorescence probe system, coupling excited-state intermolecular Förster energy transfer and intramolecular proton transfer (PT), is presented. As an energy donor for this system, we used tryptophan, which transfers its excitation energy to 3-hydroxyflavone (3-HF) as a flavonol prototype, an acceptor exhibiting excited-state intramolecular PT. We demonstrate such a coupling in human serum albumin-3-HF complexes, excited via the single intrinsic tryptophan (Trp-214). Besides the PT tautomer fluorescence (lambda max = 526 nm), these protein-probe complexes exhibit a 3-HF anion emission (lambda max = 500 nm). Analysis of spectroscopic data leads to the conclusion that two binding sites are involved in the human serum albumin-3-HF interaction. The 3-HF molecule bound in the higher affinity binding site, located in the IIIA subdomain, has the association constant (k1) of 7.2 x 10(5) M-1 and predominantly exists as an anion. The lower affinity site (k2 = 2.5 x 10(5) M-1), situated in the IIA subdomain, is occupied by the neutral form of 3-HF (normal tautomer). Since Trp-214 is situated in the immediate vicinity of the 3-HF normal tautomer bound in the IIA subdomain, the intermolecular energy transfer for this donor/ acceptor pair has a 100% efficiency and is followed by the PT tautomer fluorescence. Intermolecular energy transfer from the Trp-214 to the 3-HF anion bound in the IIIA subdomain is less efficient and has the rate of 1.61 x 10(8) s-1 thus giving for the donor/acceptor distance a value of 25.5 A.
9. Exciton dynamics reveal aggregates with intermolecular order at hidden interfaces in solution-cast organic semiconducting films.
PubMed
Wong, Cathy Y; Cotts, Benjamin L; Wu, Hao; Ginsberg, Naomi S
2015-01-12
Large-scale organic electronics manufacturing requires solution processing. For small-molecule organic semiconductors, solution processing results in crystalline domains with high charge mobility, but the interfaces between these domains impede charge transport, degrading device performance. Although understanding these interfaces is essential to improve device performance, their intermolecular and electronic structure is unknown: they are smaller than the diffraction limit, are hidden from surface probe techniques, and their nanoscale heterogeneity is not typically resolved using X-ray methods. Here we use transient absorption microscopy to isolate a unique signature of a hidden interface in a TIPS-pentacene thin film, exposing its exciton dynamics and intermolecular structure. Surprisingly, instead of finding an abrupt grain boundary, we reveal that the interface can be composed of nanoscale crystallites interleaved by a web of interfaces that compound decreases in charge mobility. Our novel approach provides critical missing information on interface morphology necessary to correlate solution-processing methods to optimal device performance.
10. Exciton dynamics reveal aggregates with intermolecular order at hidden interfaces in solution-cast organic semiconducting films
Wong, Cathy Y.; Cotts, Benjamin L.; Wu, Hao; Ginsberg, Naomi S.
2015-01-01
Large-scale organic electronics manufacturing requires solution processing. For small-molecule organic semiconductors, solution processing results in crystalline domains with high charge mobility, but the interfaces between these domains impede charge transport, degrading device performance. Although understanding these interfaces is essential to improve device performance, their intermolecular and electronic structure is unknown: they are smaller than the diffraction limit, are hidden from surface probe techniques, and their nanoscale heterogeneity is not typically resolved using X-ray methods. Here we use transient absorption microscopy to isolate a unique signature of a hidden interface in a TIPS-pentacene thin film, exposing its exciton dynamics and intermolecular structure. Surprisingly, instead of finding an abrupt grain boundary, we reveal that the interface can be composed of nanoscale crystallites interleaved by a web of interfaces that compound decreases in charge mobility. Our novel approach provides critical missing information on interface morphology necessary to correlate solution-processing methods to optimal device performance.
11. Intermolecular interactions between imidazole derivatives intercalated in layered solids. Substituent group effect
SciTech Connect
González, M.; Lemus-Santana, A.A.; Rodríguez-Hernández, J.; Aguirre-Velez, C.I.; Knobel, M.; Reguera, E.
2013-08-15
This study sheds light on the intermolecular interactions between imidazole derive molecules (2-methyl-imidazole, 2-ethyl-imidazole and benzimidazole) intercalated in T[Ni(CN){sub 4}] layers to form a solid of formula unit T(ImD){sub 2}[Ni(CN){sub 4}]. These hybrid inorganic–organic solids were prepared by soft chemical routes and their crystal structures solved and refined from X-ray powder diffraction data. The involved imidazole derivative molecules were found coordinated through the pyridinic N atom to the axial positions for the metal T in the T[Ni(CN){sub 4}] layer. In the interlayers region ligand molecules from neighboring layers remain stacked in a face-to-face configuration through dipole–dipole and quadrupole–quadrupole interactions. These intermolecular interactions show a pronounced dependence on the substituent group and are responsible for an ImD-pillaring concatenation of adjacent layers. This is supported by the structural information and the recorded magnetic data in the 2–300 K temperature range. The samples containing Co and Ni are characterized by presence of spin–orbit coupling and pronounced temperature dependence for the effective magnetic moment except for 2-ethyl-imidazole related to the local distortion for the metal coordination environment. For this last one ligand a weak ferromagnetic ordering ascribed to a super-exchange interaction between T metals from neighboring layers through the ligands π–π interaction was detected. - Graphical abstract: In the interlayers region imidazole derivative molecules are oriented according to their dipolar and quadrupolar interactions and minimizing the steric impediment. Highlights: • Imidazole derivatives intercalation compounds. • Intermolecular interaction between intercalated imidazole derivatives. • Hybrid inorganic–organic solids. • Pi–pi interactions and ferromagnetic coupling. • Dipolar and quadrupolar interactions between intercalated imidazole derivatives.
12. Long-term nitrogen fertilization of paddy soil shifts iron-reducing microbial community revealed by RNA-13C-acetate probing coupled with pyrosequencing
PubMed Central
Ding, Long-Jun; Su, Jian-Qiang; Xu, Hui-Juan; Jia, Zhong-Jun; Zhu, Yong-Guan
2015-01-01
Iron reduction is an important biogeochemical process in paddy soils, yet little is known about the microbial coupling between nitrogen and iron reduction. Here, we investigated the shift of acetate-metabolizing iron-reducers under long-term nitrogen fertilization using 13C-acetate-based ribosomal RNA (rRNA)-stable isotope probing (SIP) and pyrosequencing in an incubation experiment, and the shift of putative iron-reducers in original field samples were investigated by 16S rRNA gene-based pyrosequencing. During SIP incubations, in the presence of iron(III) oxyhydroxides, more iron(II) formation and less methane production were detected in nitrogen-fertilized (N) compared with non-fertilized (NF) soil. In 13C-rRNA from microcosms amended with ferrihydrite (FER), Geobacter spp. were the important active iron-reducers in both soils, and labeled to a greater extent in N (31% of the bacterial classified sequences) than NF soils (11%). Pyrosequencing of the total 16S rRNA transcripts from microcosms at the whole community level further revealed hitherto unknown metabolisms of potential FER reduction by microorganisms including Pseudomonas and Solibacillus spp. in N soil, Dechloromonas, Clostridium, Bacillus and Solibacillus spp. in NF soil. Goethite (GOE) amendment stimulated Geobacter spp. to a lesser extent in both soils compared with FER treatment. Pseudomonas spp. in the N soil and Clostridium spp. in the NF soil may also be involved in GOE reduction. Pyrosequencing results from field samples showed that Geobacter spp. were the most abundant putative iron-reducers in both soils, and significantly stimulated by long-term nitrogen fertilization. Overall, for the first time, we demonstrate that long-term nitrogen fertilization promotes iron(III) reduction and modulates iron-reducing bacterial community in paddy soils. PMID:25171335
13. Energy relaxation of intermolecular motions in supercooled water and ice: A molecular dynamics study
Yagasaki, Takuma; Saito, Shinji
2011-12-01
We investigate the energy relaxation of intermolecular motions in liquid water at temperatures ranging from 220 K to 300 K and in ice at 220 K using molecular dynamics simulations. We employ the recently developed frequency resolved transient kinetic energy analysis, which provides detailed information on energy relaxation in condensed phases like two-color pump-probe spectroscopy. It is shown that the energy cascading in liquid water is characterized by four processes. The temperature dependences of the earlier three processes, the rotational-rotational, rotational-translational, and translational-translational energy transfers, are explained in terms of the density of states of the intermolecular motions. The last process is the slow energy transfer arising from the transitions between potential energy basins caused by the excitation of the low frequency translational motion. This process is absent in ice because the hydrogen bond network rearrangement, which accompanies the interbasin transitions in liquid water, cannot take place in the solid phase. We find that the last process in supercooled water is well approximated by a stretched exponential function. The stretching parameter, β, decreases from 1 to 0.72 with decreasing temperature. This result indicates that the dynamics of liquid water becomes heterogeneous at lower temperatures.
14. Five intermolecular vibrations of the CO2 dimer observed via infrared combination bands.
PubMed
Norooz Oliaee, J; Dehghany, M; Rezaei, Mojtaba; McKellar, A R W; Moazzen-Ahmadi, N
2016-11-07
The weakly bound van der Waals dimer (CO2)2 has long been of considerable theoretical and experimental interest. Here, we study its low frequency intermolecular vibrations by means of combination bands in the region of the CO2 monomer ν3 fundamental (≈2350 cm(-1)), which are observed using a tunable infrared laser to probe a pulsed supersonic slit jet expansion. With the help of a recent high level ab initio calculation by Wang, Carrington, and Dawes, four intermolecular frequencies are assigned: the in-plane disrotatory bend (22.26 cm(-1)); the out-of-plane torsion (23.24 cm(-1)); twice the disrotatory bend (31.51 cm(-1)); and the in-plane conrotatory bend (92.25 cm(-1)). The disrotatory bend and torsion, separated by only 0.98 cm(-1), are strongly mixed by Coriolis interactions. The disrotatory bend overtone is well behaved, but the conrotatory bend is highly perturbed and could not be well fitted. The latter perturbations could be due to tunneling effects, which have not previously been observed experimentally for CO2 dimer. A fifth combination band, located 1.3 cm(-1) below the conrotatory bend, remains unassigned.
15. Five intermolecular vibrations of the CO2 dimer observed via infrared combination bands
Norooz Oliaee, J.; Dehghany, M.; Rezaei, Mojtaba; McKellar, A. R. W.; Moazzen-Ahmadi, N.
2016-11-01
The weakly bound van der Waals dimer (CO2)2 has long been of considerable theoretical and experimental interest. Here, we study its low frequency intermolecular vibrations by means of combination bands in the region of the CO2 monomer ν3 fundamental (≈2350 cm-1), which are observed using a tunable infrared laser to probe a pulsed supersonic slit jet expansion. With the help of a recent high level ab initio calculation by Wang, Carrington, and Dawes, four intermolecular frequencies are assigned: the in-plane disrotatory bend (22.26 cm-1); the out-of-plane torsion (23.24 cm-1); twice the disrotatory bend (31.51 cm-1); and the in-plane conrotatory bend (92.25 cm-1). The disrotatory bend and torsion, separated by only 0.98 cm-1, are strongly mixed by Coriolis interactions. The disrotatory bend overtone is well behaved, but the conrotatory bend is highly perturbed and could not be well fitted. The latter perturbations could be due to tunneling effects, which have not previously been observed experimentally for CO2 dimer. A fifth combination band, located 1.3 cm-1 below the conrotatory bend, remains unassigned.
16. Intermolecular Vibrational Modes Speed Up Singlet Fission in Perylenediimide Crystals.
PubMed
Renaud, Nicolas; Grozema, Ferdinand C
2015-02-05
We report numerical simulations based on a non-Markovian density matrix propagation scheme of singlet fission (SF) in molecular crystals. Ab initio electronic structure calculations were used to parametrize the exciton and phonon Hamiltonian as well as the interactions between the exciton and the intramolecular and intermolecular vibrational modes. We demonstrate that the interactions of the exciton with intermolecular vibrational modes are highly sensitive to the stacking geometry of the crystal and can, in certain cases, significantly accelerate SF. This result may help in understanding the fast SF experimentally observed in a broad range of molecular crystals and offers a new direction for the engineering of efficient SF sensitizers.
17. Insights into the Complexity of Weak Intermolecular Interactions Interfering in Host-Guest Systems.
PubMed
Zhang, Dawei; Chatelet, Bastien; Serrano, Eloisa; Perraud, Olivier; Dutasta, Jean-Pierre; Robert, Vincent; Martinez, Alexandre
2015-10-05
The recognition properties of heteroditopic hemicryptophane hosts towards anions, cations, and neutral pairs, combining both cation-π and anion-π interaction sites, were investigated to probe the complexity of interfering weak intermolecular interactions. It is suggested from NMR experiments, and supported by CASSCF/CASPT2 calculations, that the binding constants of anions can be modulated by a factor of up to 100 by varying the fluorination sites on the electron-poor aromatic rings. Interestingly, this subtle chemical modification can also reverse the sign of cooperativity in ion-pair recognition. Wavefunction calculations highlight how short- and long-range interactions interfere in this recognition process, suggesting that a disruption of anion-π interactions can occur in the presence of a co-bound cation. Such molecules can be viewed as prototypes for examining complex processes controlled by the competition of weak interactions.
18. Biaxial Dielectrophoresis Force Spectroscopy: A Stoichiometric Approach for Examining Intermolecular Weak Binding Interactions.
PubMed
Park, In Soo; Kwak, Tae Joon; Lee, Gyudo; Son, Myeonggu; Choi, Jeong Woo; Choi, Seungyeop; Nam, Kihwan; Lee, Sei-Young; Chang, Woo-Jin; Eom, Kilho; Yoon, Dae Sung; Lee, Sangyoup; Bashir, Rashid; Lee, Sang Woo
2016-04-26
The direct quantification of weak intermolecular binding interactions is very important for many applications in biology and medicine. Techniques that can be used to investigate such interactions under a controlled environment, while varying different parameters such as loading rate, pulling direction, rupture event measurements, and the use of different functionalized probes, are still lacking. Herein, we demonstrate a biaxial dielectrophoresis force spectroscopy (BDFS) method that can be used to investigate weak unbinding events in a high-throughput manner under controlled environments and by varying the pulling direction (i.e., transverse and/or vertical axes) as well as the loading rate. With the BDFS system, we can quantitatively analyze binding interactions related to hydrogen bonding or ionic attractions between functionalized microbeads and a surface within a microfluidic device. Our BDFS system allowed for the characterization of the number of bonds involved in an interaction, bond affinity, kinetic rates, and energy barrier heights and widths from different regimes of the energy landscape.
19. Intramolecular and intermolecular vibrational energy relaxation of CH 2I 2 dissolved in supercritical fluid
Sekiguchi, K.; Shimojima, A.; Kajimoto, O.
2002-04-01
A pump-probe experiment was performed to examine vibrational population relaxation of diiodomethane (CH 2I 2) molecule dissolved in supercritical CO 2. Using an apparatus with femtosecond time resolution, we observed the contributions of intramolecular vibrational energy redistribution (IVR) and intermolecular vibrational energy transfer (VET) separately. IVR and VET rates were measured with varying solvent densities at a constant temperature. It is shown that the IVR rate is not density dependent while the VET rate increases with increasing density from 0.4 to 0.8 g cm-3. This observation suggests that the rate of the VET process is determined by solute-solvent collisions whereas the IVR rate is not much affected by solute-solvent interaction.
20. Bead-probe complex capture a couple of SINE and LINE family from genomes of two closely related species of East Asian cyprinid directly using magnetic separation.
PubMed
Tong, Chaobo; Guo, Baocheng; He, Shunping
2009-02-19
Short and long interspersed elements (SINEs and LINEs, respectively), two types of retroposons, are active in shaping the architecture of genomes and powerful tools for studies of phylogeny and population biology. Here we developed special protocol to apply biotin-streptavidin bead system into isolation of interspersed repeated sequences rapidly and efficiently, in which SINEs and LINEs were captured directly from digested genomic DNA by hybridization to bead-probe complex in solution instead of traditional strategy including genomic library construction and screening. A new couple of SINEs and LINEs that shared an almost identical 3'tail was isolated and characterized in silver carp and bighead carp of two closely related species. These SINEs (34 members), designated HAmo SINE family, were little divergent in sequence and flanked by obvious TSD indicated that HAmo SINE was very young family. The copy numbers of this family was estimated to 2 x 105 and 1.7 x 105 per haploid genome by Real-Time qPCR, respectively. The LINEs, identified as the homologs of LINE2 in other fishes, had a conserved primary sequence and secondary structures of the 3'tail region that was almost identical to that of HAmo SINE. These evidences suggest that HAmo SINEs are active and amplified recently utilizing the enzymatic machinery for retroposition of HAmoL2 through the recognition of higher-order structures of the conserved 42-tail region. We analyzed the possible structures of HAmo SINE that lead to successful amplification in genome and then deduced that HAmo SINE, SmaI SINE and FokI SINE that were similar in sequence each other, were probably generated independently and created by LINE family within the same lineage of a LINE phylogeny in the genomes of different hosts. The presented results show the advantage of the novel method for retroposons isolation and a pair of young SINE family and its partner LINE family in two carp fishes, which strengthened the hypotheses containing the
1. Determination of hydrogen sulfide and volatile thiols in air samples by mercury probe derivatization coupled with liquid chromatography-atomic fluorescence spectrometry.
PubMed
Bramanti, Emilia; D'Ulivo, Lucia; Lomonte, Cristina; Onor, Massimo; Zamboni, Roberto; Raspi, Giorgio; D'Ulivo, Alessandro
2006-10-02
A new procedure is proposed for the sampling and storage of hydrogen sulphide (H2S) and volatile thiols (methanethiol or methyl mercaptan, ethanethiol and propanethiol) for their determination by liquid chromatography. The sampling procedure is based on the trapping/pre-concentration of the analytes in alkaline aqueous solution containing an organic mercurial probe p-hydroxymercurybenzoate, HO-Hg-C6H4-COO- (PHMB), where they are derivatized to stable PHMB complexes based on mercury-sulfur covalent bonds. PHMB complexes are separated on a C18 reverse phase column, allowing their determination by liquid chromatography coupled with sequential non-selective UV-vis (DAD) and mercury specific (chemical vapor generation atomic fluorescence spectrometry, CVGAFS) on-line detectors. PHMB complexes, S(PHMB)2CH3S-PHMB, C2H5S-PHMB and C3H7S-PHMB, are stable alt least for 12 h at room temperature and for 3 months if stored frozen (-20 degrees C). The best analytical figures of merits in the optimized conditions were obtained by CVGAFS detection, with detection limits (LODc) of 9.7 microg L(-1) for H2S, 13.7 microg L(-1) for CH(3)SH, 17.7 microg L(-1) for C2H5SH and 21.7 microg L(-1) for C3H7SH in the trapping solution in form of RS-PHMB complexes, the relative standard deviation (R.S.D.) ranging between 1.0 and 1.5%, and a linear dynamic range (LDR) between 10 and 9700 microg L(-1). Conventional UV absorbance detectors tuned at 254 nm can be employed as well with comparable R.S.D. and LDR, but with LODc one order of magnitude higher than AFS detector and lower specificity. The sampling procedure followed by LC-DAD-CVGAFS analysis has been validated, as example, for H2S determination by a certified gas permeation tube as a source of 3.071+/-0.154 microg min(-1) of H2S, giving a recovery of 99.8+/-7% and it has been applied to the determination of sulfur compounds in real gas samples (biogas and the air of a plant for fractional distillation of crude oil).
2. Bead-probe complex capture a couple of SINE and LINE family from genomes of two closely related species of East Asian cyprinid directly using magnetic separation
PubMed Central
Tong, Chaobo; Guo, Baocheng; He, Shunping
2009-01-01
Background Short and long interspersed elements (SINEs and LINEs, respectively), two types of retroposons, are active in shaping the architecture of genomes and powerful tools for studies of phylogeny and population biology. Here we developed special protocol to apply biotin-streptavidin bead system into isolation of interspersed repeated sequences rapidly and efficiently, in which SINEs and LINEs were captured directly from digested genomic DNA by hybridization to bead-probe complex in solution instead of traditional strategy including genomic library construction and screening. Results A new couple of SINEs and LINEs that shared an almost identical 3'tail was isolated and characterized in silver carp and bighead carp of two closely related species. These SINEs (34 members), designated HAmo SINE family, were little divergent in sequence and flanked by obvious TSD indicated that HAmo SINE was very young family. The copy numbers of this family was estimated to 2 × 105 and 1.7 × 105 per haploid genome by Real-Time qPCR, respectively. The LINEs, identified as the homologs of LINE2 in other fishes, had a conserved primary sequence and secondary structures of the 3'tail region that was almost identical to that of HAmo SINE. These evidences suggest that HAmo SINEs are active and amplified recently utilizing the enzymatic machinery for retroposition of HAmoL2 through the recognition of higher-order structures of the conserved 42-tail region. We analyzed the possible structures of HAmo SINE that lead to successful amplification in genome and then deduced that HAmo SINE, SmaI SINE and FokI SINE that were similar in sequence each other, were probably generated independently and created by LINE family within the same lineage of a LINE phylogeny in the genomes of different hosts. Conclusion The presented results show the advantage of the novel method for retroposons isolation and a pair of young SINE family and its partner LINE family in two carp fishes, which strengthened
3. Superior structure stability and selectivity of hairpin nucleic acid probes with an l-DNA stem
PubMed Central
Kim, Youngmi; Yang, Chaoyong James; Tan, Weihong
2007-01-01
Hairpin nucleic acid probes have been highly useful in many areas, especially for intracellular and in vitro nucleic acid detection. The success of these probes can be attributed to the ease with which their conformational change upon target binding can be coupled to a variety of signal transduction mechanisms. However, false-positive signals arise from the opening of the hairpin due mainly to thermal fluctuations and stem invasions. Stem invasions occur when the stem interacts with its complementary sequence and are especially problematic in complex biological samples. To address the problem of stem invasions in hairpin probes, we have created a modified molecular beacon that incorporates unnatural enantiomeric l-DNA in the stem and natural d-DNA or 2′-O-Me-modified RNA in the loop. l-DNA has the same physical characteristics as d-DNA except that l-DNA cannot form stable duplexes with d-DNA. Here we show that incorporating l-DNA into the stem region of a molecular beacon reduces intra- and intermolecular stem invasions, increases the melting temperature, improves selectivity to its target, and leads to enhanced bio-stability. Our results suggest that l-DNA is useful for designing functional nucleic acid probes especially for biological applications. PMID:17959649
4. Student Understanding of Intermolecular Forces: A Multimodal Study
ERIC Educational Resources Information Center
Cooper, Melanie M.; Williams, Leah C.; Underwood, Sonia M.
2015-01-01
The ability to use representations of molecular structure to predict the macroscopic properties of a substance is central to the development of a robust understanding of chemistry. Intermolecular forces (IMFs) play an important role in this process because they provide a mechanism for how and why molecules interact. In this study, we investigate…
5. Intermolecular atom-atom bonds in crystals - a chemical perspective.
PubMed
Thakur, Tejender S; Dubey, Ritesh; Desiraju, Gautam R
2015-03-01
Short atom-atom distances between molecules are almost always indicative of specific intermolecular bonding. These distances may be used to assess the significance of all hydrogen bonds, including the C-H⋯O and even weaker C-H⋯F varieties.
6. Connecting Protein Structure to Intermolecular Interactions: A Computer Modeling Laboratory
ERIC Educational Resources Information Center
Abualia, Mohammed; Schroeder, Lianne; Garcia, Megan; Daubenmire, Patrick L.; Wink, Donald J.; Clark, Ginevra A.
2016-01-01
An understanding of protein folding relies on a solid foundation of a number of critical chemical concepts, such as molecular structure, intra-/intermolecular interactions, and relating structure to function. Recent reports show that students struggle on all levels to achieve these understandings and use them in meaningful ways. Further, several…
7. Intermolecular potentials from shock structure experiments. [for monatomic gases
NASA Technical Reports Server (NTRS)
Sturtevant, B.; Steinhilper, E. A.
1974-01-01
Ground-state intermolecular interaction potentials determined from shock structure experiments with four monatomic gases are reported. These potentials are assessed for self-consistency, using the law of corresponding states, and their suitability for engineering applications in rarefied gas dynamics is discussed.
8. Dancing Crystals: A Dramatic Illustration of Intermolecular Forces
ERIC Educational Resources Information Center
Mundell, Donald W.
2007-01-01
Crystals of naphthalene form on the surface of an acetone solution and dance about in an animated fashion illustrating surface tension, crystallization, and intermolecular forces. Additional experiments reveal the properties of the solution. Flows within the solutions can be visualized by various means. Previous demonstrations of surface motion…
9. Learning about Intermolecular Interactions from the Cambridge Structural Database
ERIC Educational Resources Information Center
Battle, Gary M.; Allen, Frank H.
2012-01-01
A clear understanding and appreciation of noncovalent interactions, especially hydrogen bonding, are vitally important to students of chemistry and the life sciences, including biochemistry, molecular biology, pharmacology, and medicine. The opportunities afforded by the IsoStar knowledge base of intermolecular interactions to enhance the…
10. Learning about Intermolecular Interactions from the Cambridge Structural Database
ERIC Educational Resources Information Center
Battle, Gary M.; Allen, Frank H.
2012-01-01
A clear understanding and appreciation of noncovalent interactions, especially hydrogen bonding, are vitally important to students of chemistry and the life sciences, including biochemistry, molecular biology, pharmacology, and medicine. The opportunities afforded by the IsoStar knowledge base of intermolecular interactions to enhance the…
11. Connecting Protein Structure to Intermolecular Interactions: A Computer Modeling Laboratory
ERIC Educational Resources Information Center
Abualia, Mohammed; Schroeder, Lianne; Garcia, Megan; Daubenmire, Patrick L.; Wink, Donald J.; Clark, Ginevra A.
2016-01-01
An understanding of protein folding relies on a solid foundation of a number of critical chemical concepts, such as molecular structure, intra-/intermolecular interactions, and relating structure to function. Recent reports show that students struggle on all levels to achieve these understandings and use them in meaningful ways. Further, several…
12. Student Understanding of Intermolecular Forces: A Multimodal Study
ERIC Educational Resources Information Center
Cooper, Melanie M.; Williams, Leah C.; Underwood, Sonia M.
2015-01-01
The ability to use representations of molecular structure to predict the macroscopic properties of a substance is central to the development of a robust understanding of chemistry. Intermolecular forces (IMFs) play an important role in this process because they provide a mechanism for how and why molecules interact. In this study, we investigate…
13. Hydrogen-hydrogen intermolecular structure of polyethylene in the melt
Londono, J. D.; Annis, B. K.; Habenschuss, A.; Smith, G. D.; Borodin, O.; Tso, C.; Hsieh, E. T.; Soper, A. K.
1999-05-01
Three polyethylene samples, which differed in their degree of deuteration, were studied in neutron diffraction isotopic substitution (NDIS) experiments at 428 K. These results were complemented at small wavevectors by small angle neutron measurements. The intermolecular hydrogen-hydrogen (HH) structure function, hHH(Q), was obtained without recourse to intramolecular structure models, as demonstrated in a prior report. The PE experimental results are compared to computer simulation results for the alkanes C100 at 509 K and C44 at 350, 400, and 450 K. The small temperature dependence of the HH intermolecular radial distribution functions, gHH(r) for C44 indicates that the differences observed between the PE, C100, and C44 (450 K) results are, for the most part, not due to just temperature differences. It is shown that the string model, an analytic result from an integral equation theory of polymers (PRISM), can account approximately for the overall shape of the gHH(r) functions, and that this overall shape is dependent on the radius of gyration of the molecule. Further analysis shows that there are two other contributions to gHH(r), both of which are independent of chain length to first order. The first is due to chain-chain packing, and the second is due to local HH intermolecular correlations. These results are significant because they demonstrate that hHH(Q) is a useful function for studying intermolecular polymer structure, which has been shown to underpin phase behavior in polyolefin blends.
14. Dancing Crystals: A Dramatic Illustration of Intermolecular Forces
ERIC Educational Resources Information Center
Mundell, Donald W.
2007-01-01
Crystals of naphthalene form on the surface of an acetone solution and dance about in an animated fashion illustrating surface tension, crystallization, and intermolecular forces. Additional experiments reveal the properties of the solution. Flows within the solutions can be visualized by various means. Previous demonstrations of surface motion…
15. Morphology and the Strength of Intermolecular Contact in Protein Crystals
NASA Technical Reports Server (NTRS)
Matsuura, Yoshiki; Chernov, Alexander A.
2002-01-01
The strengths of intermolecular contacts (macrobonds) in four lysozyme crystals were estimated based on the strengths of individual intermolecular interatomic interaction pairs. The periodic bond chain of these macrobonds accounts for the morphology of protein crystals as shown previously. Further in this paper, the surface area of contact, polar coordinate representation of contact site, Coulombic contribution on the macrobond strength, and the surface energy of the crystal have been evaluated. Comparing location of intermolecular contacts in different polymorphic crystal modifications, we show that these contacts can form a wide variety of patches on the molecular surface. The patches are located practically everywhere on this surface except for the concave active site. The contacts frequently include water molecules, with specific intermolecular hydrogen-bonds on the background of non-specific attractive interactions. The strengths of macrobonds are also compared to those of other protein complex systems. Making use of the contact strengths and taking into account bond hydration we also estimated crystal-water interfacial energies for different crystal faces.
16. Improved Performance of DNA Microarray Multiplex Hybridization Using Probes Anchored at Several Points by Thiol-Ene or Thiol-Yne Coupling Chemistry.
PubMed
Bañuls, Maria-Jose; Jiménez-Meneses, Pilar; Meyer, Albert; Vasseur, Jean-Jacques; Morvan, François; Escorihuela, Jorge; Puchades, Rosa; Maquieira, Ángel
2017-02-15
Nucleic acid microarray-based assay technology has shown lacks in reproducibility, reliability, and analytical sensitivity. Here, a new strategy of probe attachment modes for silicon-based materials is built up. Thus, hybridization ability is enhanced by combining thiol-ene or thiol-yne click chemistry reactions with a multipoint attachment of polythiolated probes. The viability and performance of this approach was demonstrated by specifically determining Salmonella PCR products up to a 20 pM sensitivity level.
17. Intermolecular detergent-membrane protein noes for the characterization of the dynamics of membrane protein-detergent complexes.
PubMed
Eichmann, Cédric; Orts, Julien; Tzitzilonis, Christos; Vögeli, Beat; Smrt, Sean; Lorieau, Justin; Riek, Roland
2014-12-11
The interaction between membrane proteins and lipids or lipid mimetics such as detergents is key for the three-dimensional structure and dynamics of membrane proteins. In NMR-based structural studies of membrane proteins, qualitative analysis of intermolecular nuclear Overhauser enhancements (NOEs) or paramagnetic resonance enhancement are used in general to identify the transmembrane segments of a membrane protein. Here, we employed a quantitative characterization of intermolecular NOEs between (1)H of the detergent and (1)H(N) of (2)H-perdeuterated, (15)N-labeled α-helical membrane protein-detergent complexes following the exact NOE (eNOE) approach. Structural considerations suggest that these intermolecular NOEs should show a helical-wheel-type behavior along a transmembrane helix or a membrane-attached helix within a membrane protein as experimentally demonstrated for the complete influenza hemagglutinin fusion domain HAfp23. The partial absence of such a NOE pattern along the amino acid sequence as shown for a truncated variant of HAfp23 and for the Escherichia coli inner membrane protein YidH indicates the presence of large tertiary structure fluctuations such as an opening between helices or the presence of large rotational dynamics of the helices. Detergent-protein NOEs thus appear to be a straightforward probe for a qualitative characterization of structural and dynamical properties of membrane proteins embedded in detergent micelles.
18. Intermolecular vibrations of the CO2-CS2 complex: Experiment and theory agree, but understanding remains challenging
Dehghany, M.; Rezaei, Mojtaba; Moazzen-Ahmadi, N.; McKellar, A. R. W.; Brown, James; Wang, Xiao-Gang; Carrington, Tucker
2016-12-01
The infrared spectrum of the cross-shaped van der Waals complex CO2-CS2 is observed in the region of the CO2 ν3 fundamental band (≈2350 cm-1) using a tuneable diode laser to probe a pulsed supersonic slit jet expansion. Two combination bands are assigned, corresponding to the intermolecular torsion and CO2 bend modes, and their positions and rotational structure agree extremely well (<0.1 cm-1) with calculations based on a recent ab initio intermolecular potential. The b-type torsional band is well-behaved, but the a-type CO2 bending band is highly unusual, with large shifts between the subband origins for Ka = 0, 2, and 4. The shifts may be rationalized as due to tunnelling effects and Ka-dependent perturbations from other intermolecular modes. But even though they are well predicted by our calculations, there is no simple qualitative explanation. The predicted low-lying planar slipped parallel isomer of CO2-CS2 is not observed.
19. Intermolecular forces and the glass transition.
PubMed
Hall, Randall W; Wolynes, Peter G
2008-01-17
Random first-order transition theory is used to determine the role of attractive and repulsive interactions in the dynamics of supercooled liquids. Self-consistent phonon theory, an approximate mean field treatment consistent with random first-order transition theory, is used to treat individual glassy configurations, whereas the liquid phase is treated using common liquid-state approximations. Free energies are calculated using liquid-state perturbation theory. The transition temperature, T*A, the temperature where the onset of activated behavior is predicted by mean field theory; the lower crossover temperature, T*C, where barrierless motions actually occur through fractal or stringy motions (corresponding to the phenomenological mode coupling transition temperature); and T*K, the Kauzmann temperature (corresponding to an extrapolated entropy crisis), are calculated in addition to T*g, the glass transition temperature that corresponds to laboratory cooling rates. Relationships between these quantities agree well with existing experimental and simulation data on van der Waals liquids. Both the isobaric and isochoric behavior in the supercooled regime are studied, providing results for DeltaCV and DeltaCp that can be used to calculate the fragility as a function of density and pressure, respectively. The predicted variations in the alpha-relaxation time with temperature and density conform to the empirical density-temperature scaling relations found by Casalini and Roland. We thereby demonstrate the microscopic origin of their observations. Finally, the relationship first suggested by Sastry between the spinodal temperature and the Kauzmann temperatures, as a function of density, is examined. The present microscopic calculations support the existence of an intersection of these two temperatures at sufficiently low temperatures.
20. Tuning intermolecular non-covalent interactions for nanowires of organic semiconductors
Jiang, Lang; Gao, Jianhua; Fu, Yanyan; Dong, Huanli; Zhao, Huaping; Li, Hongxiang; Tang, Qingxin; Chen, Keqiu; Hu, Wenping
2010-12-01
Anthracene and its derivatives are used to demonstrate a simple way to cast assemble nanowires of organic semiconductors with tuning of intermolecular non-covalent interactions by molecular design. The tuning of intermolecular interactions could be achieved by (i) decreasing intermolecular hydrophobic interactions by linking hydrophilic side chains to anthracene rings, (ii) increasing intermolecular interaction for self-assembly with the assistance of hydrogen bonds, and (iii) enhancing molecular π-π interaction by increasing the conjugated dimension of the compounds.
1. Tuning intermolecular non-covalent interactions for nanowires of organic semiconductors.
PubMed
Jiang, Lang; Gao, Jianhua; Fu, Yanyan; Dong, Huanli; Zhao, Huaping; Li, Hongxiang; Tang, Qingxin; Chen, Keqiu; Hu, Wenping
2010-12-01
Anthracene and its derivatives are used to demonstrate a simple way to cast assemble nanowires of organic semiconductors with tuning of intermolecular non-covalent interactions by molecular design. The tuning of intermolecular interactions could be achieved by (i) decreasing intermolecular hydrophobic interactions by linking hydrophilic side chains to anthracene rings, (ii) increasing intermolecular interaction for self-assembly with the assistance of hydrogen bonds, and (iii) enhancing molecular π-π interaction by increasing the conjugated dimension of the compounds.
2. Long-range intermolecular interaction between broken DNA fragments
Pinchuk, Anatoliy O.; Vysotskii, Vladimir I.
2001-03-01
We analyzed the long-range intermolecular interaction between fragments of broken DNA. We considered two constituents of long-range intermolecular interaction. The first is a net electrostatic Coulomb interaction between charges, involved in a structure of opposite nucleotides, which we evaluate using Debye-Huckel theory. The second one is the Van der Waals interaction between the nucleotides. The general Lifshitz theory of Van der Waals forces was used to evaluate this interaction. Numerical calculations showed that a repulsive force between broken DNA fragments can arise in specific cases. This repulsion can prevent DNA from repairing itself after a double-strand break. The height of the barrier decreases with an increase of the ionic strength of the intracellular milieu, or with a reduction of its viscosity.
3. Intermolecular Hydrogen Bonding in Peptide and Modified Jeffamine Organogels
2011-03-01
In these studies, we present two systems whereby supramolecular assembly results in rigid organogels. First, a series of AB diblock copolymers consisting of poly(Lysine(Z)) (P(Lys(Z)) blocks were synthesized and found to form stable, rigid organogels in THF (ca. 1 - 1.5 wt.% solutions) and chloroform at room temperature. In these systems, the protecting group on the P(Lys) side-chains remains intact and gel formation results from the assembly of the solventphobic P(Lys(Z)) chains through intermolecular beta-sheet formation. The non-peptide block was found to have an effect on organogel properties due to interfacial frustration, which disrupts H-bonding. Second, Jeffamine polymers were modified in a facile way to incorporate intermolecular H-bonding groups to yield networks able to gel various solvents as well as mineral and canola oil. We present the physical and rheological properties of the organogels produced.
4. Separation of intra- and intermolecular contributions to the PELDOR signal
Schöps, Philipp; Plackmeyer, Jörn; Marko, Andriy
2016-08-01
Pulsed Electron-electron Double Resonance (PELDOR) is commonly used to measure distances between native paramagnetic centers or spin labels attached to complex biological macromolecules. In PELDOR the energies of electron magnetic dipolar interactions are measured by analyzing the oscillation frequencies of the recorded time resolved signal. Since PELDOR is an ensemble method, the detected signal contains contributions from intramolecular, as well as intermolecular electron spin interactions. The intramolecular part of the signal contains the information about the structure of the studied molecules, thus it is very important to accurately separate intra- and intermolecular contributions to the total signal. This separation can become ambiguous, when the length of the PELDOR signal is not much longer than twice the oscillation period of the signal. In this work we suggest a modulation depth scaling method, which can use short PELDOR signals in order to extract the intermolecular contribution. Using synthetic data we demonstrate the advantages of the new approach and analyze its stability with regard to signal noise. The method was also successfully tested on experimental data of three systems measured at Q-Band frequencies, two model compounds in deuterated and protonated solvents and one biological sample, namely BetP. The application of the new method with an assigned value of the signal modulation depth enables us to determine the interspin distances in all cases. This is especially interesting for the model compound with an interspin distance of 5.2 nm in the protonated solvent and the biological sample, since an accurate separation of the intra- and intermolecular PELDOR signal contributions would be difficult with the standard approach in those cases.
5. Highly Stereoselective Intermolecular Haloetherification and Haloesterification of Allyl Amides
PubMed Central
Soltanzadeh, Bardia; Jaganathan, Arvind; Staples, Richard J.
2016-01-01
An organocatalytic and highly regio-, diastereo-, and enantioselective intermolecular haloetherification and haloesterification reaction of allyl amides is reported. A variety of alkene substituents and substitution patterns are compatible with this chemistry. Notably, electronically unbiased alkene substrates exhibit exquisite regio- and diastereoselectivity for the title transformation. We also demonstrate that the same catalytic system can be used in both chlorination and bromination reactions of allyl amides with a variety of nucleophiles with little or no modification. PMID:26110812
6. Calciate-mediated intermolecular hydroamination of diphenylbutadiyne with secondary anilines.
PubMed
Glock, Carsten; Görls, Helmar; Westerhausen, Matthias
2012-07-18
Calciate-mediated intermolecular hydroamination of diphenylbutadiyne with N-phenyl and N-isopropyl-substituted anilines yields E- and Z-isomers of the corresponding 1-anilino-1,4-diphenylbut-1-ene-3-yne. In the case of HNPh(2) solely heterobimetallic K(2)Ca(NPh(2))(4) is able to effectively catalyze this hydroamination reaction in tetrahydrofuran at elevated temperatures.
7. Energetics of Intermolecular Hydrogen Bonds in a Hydrophobic Protein Cavity
Liu, Lan; Baergen, Alyson; Michelsen, Klaus; Kitova, Elena N.; Schnier, Paul D.; Klassen, John S.
2014-05-01
This work explores the energetics of intermolecular H-bonds inside a hydrophobic protein cavity. Kinetic measurements were performed on the gaseous deprotonated ions (at the -7 charge state) of complexes of bovine β-lactoglobulin (Lg) and three monohydroxylated analogs of palmitic acid (PA): 3-hydroxypalmitic acid (3-OHPA), 7-hydroxypalmitic acid (7-OHPA), and 16-hydroxypalmitic acid (16-OHPA). From the increase in the activation energy for the dissociation of the (Lg + X-OHPA)7- ions, compared with that of the (Lg + PA)7- ion, it is concluded that the -OH groups of the X-OHPA ligands participate in strong (5 - 11 kcal mol-1) intermolecular H-bonds in the hydrophobic cavity of Lg. The results of molecular dynamics (MD) simulations suggest that the -OH groups of 3-OHPA and 16-OHPA act as H-bond donors and interact with backbone carbonyl oxygens, whereas the -OH group of 7-OHPA acts as both H-bond donor and acceptor with nearby side chains. The capacity for intermolecular H-bonds within the Lg cavity, as suggested by the gas-phase measurements, does not necessarily lead to enhanced binding in aqueous solution. The association constant (Ka) measured for 7-OHPA [(2.3 ± 0.2) × 105 M-1] is similar to the value for the PA [(3.8 ± 0.1) × 105 M-1]; Ka for 3-OHPA [(1.1 ± 0.3) × 106 M-1] is approximately three-times larger, whereas Ka for 16-OHPA [(2.3 ± 0.2) × 104 M-1] is an order of magnitude smaller. Taken together, the results of this study suggest that the energetic penalty to desolvating the ligand -OH groups, which is necessary for complex formation, is similar in magnitude to the energetic contribution of the intermolecular H-bonds.
8. Covalent intermolecular interaction of the nitric oxide dimer (NO)2
Zhang, Hui; Zheng, Gui-Li; Lv, Gang; Geng, Yi-Zhao; Ji, Qing
2015-09-01
Covalent bonds arise from the overlap of the electronic clouds in the internucleus region, which is a pure quantum effect and cannot be obtained in any classical way. If the intermolecular interaction is of covalent character, the result from direct applications of classical simulation methods to the molecular system would be questionable. Here, we analyze the special intermolecular interaction between two NO molecules based on quantum chemical calculation. This weak intermolecular interaction, which is of covalent character, is responsible for the formation of the NO dimer, (NO)2, in its most stable conformation, a cis conformation. The natural bond orbital (NBO) analysis gives an intuitive illustration of the formation of the dimer bonding and antibonding orbitals concomitant with the breaking of the π bonds with bond order 0.5 of the monomers. The dimer bonding is counteracted by partially filling the antibonding dimer orbital and the repulsion between those fully or nearly fully occupied nonbonding dimer orbitals that make the dimer binding rather weak. The direct molecular mechanics (MM) calculation with the UFF force fields predicts a trans conformation as the most stable state, which contradicts the result of quantum mechanics (QM). The lesson from the investigation of this special system is that for the case where intermolecular interaction is of covalent character, a specific modification of the force fields of the molecular simulation method is necessary. Project supported by the National Natural Science Foundation of China (Grant Nos. 90403007 and 10975044), the Key Subject Construction Project of Hebei Provincial Universities, China, the Research Project of Hebei Education Department, China (Grant Nos. Z2012067 and Z2011133), the National Natural Science Foundation of China (Grant No. 11147103), and the Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Grant No. Y5
9. Bimorpholine-mediated enantioselective intramolecular and intermolecular aldol condensation.
PubMed
Kanger, Tõnis; Kriis, Kadri; Laars, Marju; Kailas, Tiiu; Müürisepp, Aleksander-Mati; Pehk, Tõnis; Lopp, Margus
2007-07-06
Monosalts of N-substituted bimorpholine derivatives are efficient organocatalysts in intramolecular and intermolecular aldol reactions. The properties of the catalysts can be tuned either by the selection of an appropriate acid for the salt formation or by the change of a substituent at the nitrogen atom. In aldol condensation, i-Pr-substituted bimorpholine is the most stereoselective catalyst affording products in high yield with enantioselectivities up to 95% ee.
10. Direction-dependent intermolecular interactions: catechol on TiO2(110)-1×1
Li, Shao-Chun; Diebold, Ulrike
2009-08-01
The adsorption of a submonolayer of catechol (C6H6O2) on the rutile TiO2(110)-1×1 surface has been investigated by Scanning Tunneling Microscopy (STM). The catechol molecules are preferentially adsorbed on the surface 5-fold coordinated Ti4+ sites, and occupy two neighboring lattice Ti sites. No preference for adsorption at surface step edges is observed at room temperature. A statistical analysis of intermolecular distances demonstrates that the interaction between the molecules strongly depends on the surface crystallographic direction: catechol molecules exhibit attractive interaction along [1-1 0], while they repel each other along the [001] direction. The attractive interaction is proposed to be caused by the coupling of π bonding electrons and the repulsive interaction is possibly mediated by substrate.
11. Intermolecular control of thermoswitching and photoswitching phenomena in two spin-crossover polymorphs
Buron-Le Cointe, M.; Hébert, J.; Baldé, C.; Moisan, N.; Toupet, L.; Guionneau, P.; Létard, J. F.; Freysz, E.; Cailleau, H.; Collet, E.
2012-02-01
We discuss here the important role of intermolecular coupling for the thermal- and light-induced molecular state switching in the solid state. Investigations were performed on the two crystalline polymorphs of the spin-crossover [Fe-(PM-BIA)2(NCS)2] material. In addition to structural studies at thermal equilibrium, light-induced phenomena were investigated through photocrystallography, photomagnetic, and dynamical optical measurements. Strong similarities between the thermal-equilibrium and the out-of-equilibrium light-induced transformations are observed in each polymorph: strong cooperative phenomena in one polymorph versus weak cooperative ones in the second polymorph. These different responses of the two crystalline forms of the compound to external perturbations are discussed at the microscopic level in terms of Ising-like model and two-mode description of on-site molecular potentials.
12. Intermolecular interactions in AST zeolites through (14)N NMR and DFT calculations.
PubMed
Dib, Eddy; Freire, Mélanie; Pralong, Valérie; Mineva, Tzonka; Alonso, Bruno
2017-03-01
The structure of the silica AST zeolites (octadecasil) synthesized in fluoride medium using tetramethylammonium (TMA) as the organic structure-directing agent has been reinvestigated using (14)N NMR quadrupolar parameters and DFT calculations. The value of the experimental (14)N quadrupolar coupling constant (CQ = 27 kHz) is larger than expected for a TMA cation possessing a high degree of motion. The analysis of a DFT-optimized octadecasil cluster along with the comparison between measured and calculated (14)N NMR parameters demonstrate the presence of weak C-H...O hydrogen bonds between the TMA in the [4(6)6(12)] cages and the silica skeleton. These intermolecular interactions can be related to the presence of Si...F tetrel bonds within the [4(6)] cages. These new results provide additional information with regard to the formation mechanisms and structure of the octadecasil zeolites.
13. Raman Q-branch line shapes as a test of the H2-Ar intermolecular potential
NASA Technical Reports Server (NTRS)
Green, Sheldon
1990-01-01
The line-shape cross sections of vibrational Raman Q-branch spectra are determined theoretically for D2 and H2 in Ar. The calculations are based on accurate close-coupling matrices and the intermolecular potential obtained by Le Roy and Hutson (1987) from spectra of van der Waals complexes. The calculation techniques applied are explained, and the results are presented in tables and graphs and discussed in detail with reference to published experimental data. Agreement to within about 25 percent is obtained for the line widths, but the line shifts are found to be a factor of two smaller than the measured values, and a temperature dependence of line-width cross sections is predicted which is not observed experimentally.
14. Nonresonant and resonant mode-specific intermolecular vibrational energy transfers in electrolyte aqueous solutions.
PubMed
Bian, Hongtao; Chen, Hailong; Li, Jiebo; Wen, Xiewen; Zheng, Junrong
2011-10-27
The donor/acceptor energy mismatch and vibrational coupling strength dependences of interionic vibrational energy transfer kinetics in electrolyte aqueous solutions were investigated with ultrafast multiple-dimensional vibrational spectroscopy. An analytical equation derived from the Fermi's Golden rule that correlates molecular structural parameters and vibrational energy transfer kinetics was found to be able to describe the intermolecular mode specific vibrational energy transfer. Under the assumption of the dipole-dipole approximation, the distance between anions in the aqueous solutions was obtained from the vibrational energy transfer measurements, confirmed with measurements on the corresponding crystalline samples. The result demonstrates that the mode-specific vibrational energy transfer method holds promise as an angstrom molecular ruler.
15. Spectrophotometric probe
DOEpatents
Prather, William S.; O'Rourke, Patrick E.
1994-01-01
A support structure bearing at least one probe for making spectrophotometric measurements of a fluid using a source of light and a spectrophotometer. The probe includes a housing with two optical fibers and a planoconvex lens. A sleeve bearing a mirror surrounds the housing. The lens is separated from the mirror by a fixed distance, defining an interior space for receiving a volume of the fluid sample. A plurality of throughholes extending through the sleeve communicate between the sample volume and the exterior of the probe, all but one hole bearing a screen. A protective jacket surrounds the probe. A hollow conduit bearing a tube is formed in the wall of the probe for venting any air in the interior space when fluid enters. The probe is held at an acute angle so the optic fibers carrying the light to and from the probe are not bent severely on emergence from the probe.
16. Spectrophotometric probe
DOEpatents
Prather, W.S.; O'Rourke, P.E.
1994-08-02
A support structure is described bearing at least one probe for making spectrophotometric measurements of a fluid using a source of light and a spectrophotometer. The probe includes a housing with two optical fibers and a planoconvex lens. A sleeve bearing a mirror surrounds the housing. The lens is separated from the mirror by a fixed distance, defining an interior space for receiving a volume of the fluid sample. A plurality of throughholes extending through the sleeve communicate between the sample volume and the exterior of the probe, all but one hole bearing a screen. A protective jacket surrounds the probe. A hollow conduit bearing a tube is formed in the wall of the probe for venting any air in the interior space when fluid enters. The probe is held at an acute angle so the optic fibers carrying the light to and from the probe are not bent severely on emergence from the probe. 3 figs.
17. Competing Intramolecular vs. Intermolecular Hydrogen Bonds in Solution
PubMed Central
Nagy, Peter I.
2014-01-01
A hydrogen bond for a local-minimum-energy structure can be identified according to the definition of the International Union of Pure and Applied Chemistry (IUPAC recommendation 2011) or by finding a special bond critical point on the density map of the structure in the framework of the atoms-in-molecules theory. Nonetheless, a given structural conformation may be simply favored by electrostatic interactions. The present review surveys the in-solution competition of the conformations with intramolecular vs. intermolecular hydrogen bonds for different types of small organic molecules. In their most stable gas-phase structure, an intramolecular hydrogen bond is possible. In a protic solution, the intramolecular hydrogen bond may disrupt in favor of two solute-solvent intermolecular hydrogen bonds. The balance of the increased internal energy and the stabilizing effect of the solute-solvent interactions regulates the new conformer composition in the liquid phase. The review additionally considers the solvent effects on the stability of simple dimeric systems as revealed from molecular dynamics simulations or on the basis of the calculated potential of mean force curves. Finally, studies of the solvent effects on the type of the intermolecular hydrogen bond (neutral or ionic) in acid-base complexes have been surveyed. PMID:25353178
18. Reliable prediction of three-body intermolecular interactions using dispersion-corrected second-order Møller-Plesset perturbation theory
SciTech Connect
Huang, Yuanhang; Beran, Gregory J. O.
2015-07-28
Three-body and higher intermolecular interactions can play an important role in molecular condensed phases. Recent benchmark calculations found problematic behavior for many widely used density functional approximations in treating 3-body intermolecular interactions. Here, we demonstrate that the combination of second-order Møller-Plesset (MP2) perturbation theory plus short-range damped Axilrod-Teller-Muto (ATM) dispersion accurately describes 3-body interactions with reasonable computational cost. The empirical damping function used in the ATM dispersion term compensates both for the absence of higher-order dispersion contributions beyond the triple-dipole ATM term and non-additive short-range exchange terms which arise in third-order perturbation theory and beyond. Empirical damping enables this simple model to out-perform a non-expanded coupled Kohn-Sham dispersion correction for 3-body intermolecular dispersion. The MP2 plus ATM dispersion model approaches the accuracy of O(N{sup 6}) methods like MP2.5 or even spin-component-scaled coupled cluster models for 3-body intermolecular interactions with only O(N{sup 5}) computational cost.
19. Reliable prediction of three-body intermolecular interactions using dispersion-corrected second-order Møller-Plesset perturbation theory
Huang, Yuanhang; Beran, Gregory J. O.
2015-07-01
Three-body and higher intermolecular interactions can play an important role in molecular condensed phases. Recent benchmark calculations found problematic behavior for many widely used density functional approximations in treating 3-body intermolecular interactions. Here, we demonstrate that the combination of second-order Møller-Plesset (MP2) perturbation theory plus short-range damped Axilrod-Teller-Muto (ATM) dispersion accurately describes 3-body interactions with reasonable computational cost. The empirical damping function used in the ATM dispersion term compensates both for the absence of higher-order dispersion contributions beyond the triple-dipole ATM term and non-additive short-range exchange terms which arise in third-order perturbation theory and beyond. Empirical damping enables this simple model to out-perform a non-expanded coupled Kohn-Sham dispersion correction for 3-body intermolecular dispersion. The MP2 plus ATM dispersion model approaches the accuracy of O(N6) methods like MP2.5 or even spin-component-scaled coupled cluster models for 3-body intermolecular interactions with only O(N5) computational cost.
20. Rubrene: The Interplay between Intramolecular and Intermolecular Interactions Determines the Planarization of Its Tetracene Core in the Solid State.
PubMed
Sutton, Christopher; Marshall, Michael S; Sherrill, C David; Risko, Chad; Brédas, Jean-Luc
2015-07-15
Rubrene is one of the most studied molecular semiconductors; its chemical structure consists of a tetracene backbone with four phenyl rings appended to the two central fused rings. Derivatization of these phenyl rings can lead to two very different solid-state molecular conformations and packings: One in which the tetracene core is planar and there exists substantive overlap among neighboring π-conjugated backbones; and another where the tetracene core is twisted and the overlap of neighboring π-conjugated backbones is completely disrupted. State-of-the-art electronic structure calculations show for all isolated rubrene derivatives that the twisted conformation is more favorable (by -1.7 to -4.1 kcal mol(-1)), which is a consequence of energetically unfavorable exchange-repulsion interactions among the phenyl side groups. Calculations based on available crystallographic structures reveal that planar conformations of the tetracene core in the solid state result from intermolecular interactions that can be tuned through well-chosen functionalization of the phenyl side groups and lead to improved intermolecular electronic couplings. Understanding the interplay of these intramolecular and intermolecular interactions provides insight into how to chemically modify rubrene and similar molecular semiconductors to improve the intrinsic materials electronic properties.
1. Second law considerations in Fourier heat conduction of a lattice chain in relation to intermolecular potentials
Jesudason, Christopher G.
2017-01-01
Two aspects of conductive heat are focused here (i) the nature of conductive heat, defined as that form of energy that is transferred as a result of a temperature difference and (ii) the nature of the intermolecular potentials that induces both thermal energy flow and the temperature profile at the steady state for a 1-D lattice chain. It is found that the standard presuppositions of people like Benofy and Quay (BQ) following Joseph Fourier do not obtain for at least a certain specified regime of intermolecular potential parameters related to harmonic (quadratic) potentials for nearest neighbor interactions. For these harmonic potentials, it appears from the simulation results that steady state solutions exist utilizing non-synthetic thermostats that couple not just the two particles at the extreme ends of the lattice chain, but to a control volume of N particles located at either ends of the chain that does not accord with the unique analytical solutions that obtains for single particle thermostatting at the ends of the lattice with a different thermostatting algorithm that utilizes coupling coefficients. If the method used here is considered a more "realistic" or feasible model of the physical reality, then a re-evaluation of some aspects of the standard theoretical methodology is warranted since the standard model solution profile does not accord with the simulation temperature profile determined here for this related model. We also note that the sinusoidal temperature profile generated suggests that thermal integrated circuits with several thermal P-N junctions may be constructed, opening a way to create more complex thermal transistor circuits. A stationary principle is proposed for regions that violate the Fourier principle Jq.∇T ≤ 0, where Jq is the heat current vector and T the temperature.
2. Probing the Structure of {sup 74}Ge Nucleus with Coupled-channels Analysis of {sup 74}Ge+{sup 74}Ge Fusion Reaction
SciTech Connect
Zamrun F, Muhammad; Kasim, Hasan Abu
2010-12-23
We study the fusion reaction of the {sup 74}Ge+{sup 74}Ge system in term of the full order coupled-channels formalism. We especially calculated the fusion cross section as well as the fusion barrier distribution of this reaction using transition matrix suggested by recent Coulomb excitation experiment. We compare the results with the one obtained by coupling matrix based on pure vibrational and rotational models. The present coupled-channels calculations for the barrier distributions obtained using experiment coupling matrix is in good agreement with the one obtained with vibrational model, in contrast to the rotational model. This is indicates that {sup 74}Ge nucleus favor a spherical shape than a deformed shape in its ground state. Our results will resolve the debates concerning the structure of this nucleus.
3. Difference between ²JC2H3 and ²JC3H2 spin-spin couplings in heterocyclic five- and six-membered rings as a probe for studying σ-ring currents: a quantum chemical analysis.
PubMed
Contreras, Rubén H; dos Santos, Francisco P; Ducati, Lucas C; Tormena, Cláudio F
2010-12-01
Adequate analyses of canonical molecular orbitals (CMOs) can provide rather detailed information on the importance of different σ-Fermi contact (FC) coupling pathways (FC term transmitted through the σ-skeleton). Knowledge of the spatial distribution of CMOs is obtained by expanding them in terms of natural bond orbitals (NBOs). Their relative importance for transmitting the σ-FC contribution to a given spin-spin coupling constants (SSCCs) is estimated by resorting to the expression of the FC term given by the polarisation propagator formalism. In this way, it is possible to classify the effects affecting such couplings in two different ways: delocalisation interactions taking place in the neighbourhood of the coupling nuclei and 'round the ring' effects. The latter, associated with σ-ring currents, are observed to yield significant differences between the FC terms of (2)J(C2H3) and (2)J(C3H2) SSCCs which, consequently, are taken as probes to gauge the differences in σ-ring currents for the five-membered rings (furan, thiophene, selenophene and pyrrol) and also for the six-membered rings (benzene, pyridine, protonated pyridine and N-oxide pyridine) used in the present study. Copyright © 2010 John Wiley & Sons, Ltd.
4. Intermolecular vibrations of fluorobenzene-Ar up to 130 cm(-1) in the ground electronic state.
PubMed
Gascooke, Jason R; Alexander, Ula N; Lawrance, Warren D
2012-08-28
Sixteen intermolecular vibrational levels of the S(0) state of the fluorobenzene-Ar van der Waals complex have been observed using dispersed fluorescence. The levels range up to ~130 cm(-1) in vibrational energy. The vibrational energies have been modelled using a complete set of harmonic and quartic anharmonic constants and a cubic anharmonic coupling between the stretch and long axis bend overtone that becomes near ubiquitous at higher energies. The constants predict the observed band positions with a root mean square deviation of 0.04 cm(-1). The set of vibrational levels predicted by the constants, which includes unobserved bands, has been compared with the predictions of ab initio calculations, which include all vibrational levels up to 70-75 cm(-1). There are small differences in energy, particularly above 60 cm(-1), however, the main differences are in the assignments and are largely due to the limitations of assigning the ab initio wavefunctions to a simple stretch, bend, or combination when the states are mixed by the cubic anharmonic coupling. The availability of these experimental data presents an opportunity to extend ab initio calculations to higher vibrational energies to provide an assessment of the accuracy of the calculated potential surface away from the minimum. The intermolecular modes of the fluorobenzene-Ar(2) trimer complex have also been investigated by dispersed fluorescence. The dominant structure is a pair of bands with a ~35 cm(-1) displacement from the origin band. Based on the set of vibrational modes calculated from the fluorobenzene-Ar frequencies, they are assigned to a Fermi resonance between the symmetric stretch and symmetric short axis bend overtone. The analysis of this resonance provides a measurement of the coupling strength between the stretch and short axis bend overtone in the dimer, an interaction that is not directly observed. The coupling matrix elements determined for the fluorobenzene-Ar stretch-long axis bend
5. Small-angle X-ray scattering probe of intermolecular interaction in red blood cells
Liu, Guan-Fen; Wang, We-Jia; Xu, Jia-Hua; Dong, Yu-Hui
2015-03-01
With high concentrations of hemoglobin (Hb) in red blood cells, self-interactions among these molecules could increase the propensities of their polymerization and aggregation. In the present work, high concentration Hb in solution and red blood cells were analyzed by small-angle X-ray scattering. Calculation of the effective structure factor indicates that the interaction of Hb molecules is the same when they are crowded together in both the cell and physiological saline. The Hb molecules stay individual without the formation of aggregates and clusters in cells. Supported by National Basic Research Program of China (2009CB918600) and National Natural Science Foundation of China (10979005)
6. Measurement of W+W- production in pp collisions at √s = 8 TeV and probing anomalous triple-gauge-boson couplings with the ATLAS detector
Feng, Haolu
This thesis presents the measurement of the vector boson pair W+W- production cross section in proton-proton collisions at the center-of-mass energy sqrt(s) = 8 TeV. The leptonic decay channels of the W+W- →ℓ +nuℓℓ-nu ℓor ℓ=(e,mu) are analyzed using data corresponding to 20.3 fb -1 of integrated luminosity collected by the ATLAS detector in 2012 at the Large Hadron Collider at CERN (in Geneva, Switzerland). The experimental signature of this measurement is two energetic isolated leptons ( e+e-, mu+mu-, e+mu-, e+/-mu∓) and associated large missing transverse energy (due to neutrinos in final states). A total of 6636 WW+ℓℓ candidate events is selected in ATLAS data with an estimation of 1547+/-28 background events from non-W+W- production processes. The measured total production cross section is 71+1.1 -1.1(stat)+5.7-5.0(syst)+2.1 -2.0)(lumi) pb, which is comparable with the theoretical prediction of 63.2+2.0-1.8 pb calculated with NNLO QCD and NLO EW corrections. The anomalous triple-gauge-boson couplings (WWZ and WWgamma) could signal new physics beyond the Standard Model at much higher energy scales compared to the directly detectable mass scale at the LHC. An effective Lagrangian is used to generalize the anomalous triple-gauge-boson couplings to describe the W ++W- productions at the LHC. These anomalous couplings can be experimentally probed by comparing the leading lepton transverse momentum spectrum with the theoretical predictions in different triple-gauge-boson coupling space. No observation of deviations from the Standard Model predicted couplings is found by a maximum likelihood fitting of the leading lepton transverse momentum. Therefore, the most stringent limits to date on the anomalous triple-gauge-boson couplings are set from this analysis.
7. Swan probe: A nanoliter-scale and high-throughput sampling interface for coupling electrospray ionization mass spectrometry with microfluidic droplet array and multiwell plate.
PubMed
Jin, Di-Qiong; Zhu, Ying; Fang, Qun
2014-11-04
Mass spectrometry provides a versatile detection method for high-throughput drug screening because it permits the use of native biological substrates and the direct quantification of unlabeled reaction products. This paper describes the design and application of a Swan-shaped probe for high-throughput and nanoliter-scale analysis of biological samples in both a microfluidic droplet array and a multiwell plate with electrospray ionization mass spectrometry (ESI-MS). The Swan probe is fabricated using a single capillary with quite low cost, and it consists of a U-shaped section with a micrometer-sized hole for sampling and a tapered tip for sample electrospray ionization. Continuous sample introduction was carried out under both sampling modes of push-pull and spontaneous injection by sequentially dipping the probe in the sample solutions and then removing them. High-throughput and reliable ESI-MS analysis was achieved in analyzing 256 droplets within 90 min with a peak height RSD of 12.6% (n = 256). To validate its potential in drug discovery, the present system was applied in the screening of inhibitors of acetylcholinesterase (AchE) and the measurement of the IC50 values of identified inhibitors.
8. In vivo absolute quantification for mouse muscle metabolites using an inductively coupled synthetic signal injection method and newly developed 1H/31P dual tuned probe
PubMed Central
Lee, Donghoon; Marro, Kenneth; Mathis, Mark; Shankland, Eric; Hayes, Cecil
2013-01-01
Purpose To obtain robust estimates of 31P metabolite content in mouse skeletal muscles using our recently developed MR absolute quantification method and a custom-built 1H/31P dual tuned radiofrequency (RF) coil optimized for mouse leg. Materials and Methods We designed and fabricated a probe consisting of two dual tuned 1H/31P solenoid coils: one leg was inserted to each solenoid. The mouse leg volume coil was incorporated with injector coils for MR absolute quantification. The absolute quantification method uses a synthetic reference signal injection approach and solves several challenges in MR absolute quantification including changes of coil loading and receiver gains. Results The 1H/31P dual tuned probe was composed of two separate solenoid coils, one for each leg, to increase coil filling factors and signal-to-noise ratio. Each solenoid was equipped with a second coil to allow injection of reference signals. 31P metabolite concentrations determined for normal mice were well within the expected range reported in the literature. Conclusion We developed an RF probe and an absolute quantification approach adapted for mouse skeletal muscle. PMID:24464912
9. Novel electronic ferroelectricity in an organic charge-order insulator investigated with terahertz-pump optical-probe spectroscopy
Yamakawa, H.; Miyamoto, T.; Morimoto, T.; Yada, H.; Kinoshita, Y.; Sotome, M.; Kida, N.; Yamamoto, K.; Iwano, K.; Matsumoto, Y.; Watanabe, S.; Shimoi, Y.; Suda, M.; Yamamoto, H. M.; Mori, H.; Okamoto, H.
2016-02-01
In electronic-type ferroelectrics, where dipole moments produced by the variations of electron configurations are aligned, the polarization is expected to be rapidly controlled by electric fields. Such a feature can be used for high-speed electric-switching and memory devices. Electronic-type ferroelectrics include charge degrees of freedom, so that they are sometimes conductive, complicating dielectric measurements. This makes difficult the exploration of electronic-type ferroelectrics and the understanding of their ferroelectric nature. Here, we show unambiguous evidence for electronic ferroelectricity in the charge-order (CO) phase of a prototypical ET-based molecular compound, α-(ET)2I3 (ET:bis(ethylenedithio)tetrathiafulvalene), using a terahertz pulse as an external electric field. Terahertz-pump second-harmonic-generation(SHG)-probe and optical-reflectivity-probe spectroscopy reveal that the ferroelectric polarization originates from intermolecular charge transfers and is inclined 27° from the horizontal CO stripe. These features are qualitatively reproduced by the density-functional-theory calculation. After sub-picosecond polarization modulation by terahertz fields, prominent oscillations appear in the reflectivity but not in the SHG-probe results, suggesting that the CO is coupled with molecular displacements, while the ferroelectricity is electronic in nature. The results presented here demonstrate that terahertz-pump optical-probe spectroscopy is a powerful tool not only for rapidly controlling polarizations, but also for clarifying the mechanisms of ferroelectricity.
10. Real-time dark-field light scattering imaging to monitor the coupling reaction with gold nanorods as an optical probe.
PubMed
Zhang, Hong Zhi; Li, Rong Sheng; Gao, Peng Fei; Wang, Ni; Lei, Gang; Huang, Cheng Zhi; Wang, Jian
2017-03-09
Gold nanorods (GNRs) have opened up promising applications based on their reshaping, due to the fact that a tiny change in shape or size could directly lead to optical changes. Herein, we report chemical reshaping of GNRs induced by the coupling reaction between Au, ferric chloride and thiourea. In the coupling reaction, Fe(3+) oxidizes the GNRs to yield Au(i), which complexes with the thiourea ligand, lowering the Gibbs free energy of the gold species and promoting the reaction equilibrium to enable the chemical reshaping of the GNRs. This coupling reaction process was monitored using a light-scattering dark-field microscopy (DFM) imaging technique and scanning electron microscopy (SEM). The light scattering underwent a colour change from bright red to yellow and finally to green, and the GNRs underwent a morphological change from rod-shaped to fusiform and finally to spherical, which is somewhat different from the results of other chemical etching processes of GNRs. It is believed that the coupling reaction induced chemical reshaping of GNRs not only provides an alternative way to monitor the coupling reaction, but also offers a facile way to obtain a desirable GNR morphology, which is important for the preparation of fusiform nanostructures.
11. Characterization of structure and properties of thin film crystals and ferroelectric BiFeO3: A coupled TEM, SPM, and optical probe approach
Jokisaari, Jacob Ragnar
Correlating advanced microscopy methods including transmission electron microscopy, scanning probe microscopy, and optical spectroscopy on the same materials and even the same specimens allows complimentary measurements to be obtained, revealing new details about structure-property relationships measured on a nanometer scale. Combining measurements not only corroborates the information obtained from any particular method, but also compensates for deficiencies of any single technique. An array of microscopy techniques including high resolution transmission electron microscopy, scanning probe microscopy, and Raman spectroscopy were applied to address scientific and engineering questions concerning the structure and properties of domain patterns in BiFeO3 ferroelectric thin films and to examine novel TiO2(B) thin films suitable for Li-ion battery applications. In BiFeO3, application of these combined techniques allowed a relationship between epitaxial strain and domain width to be established, two cases of strained films with unique domain structures to be identified, transformation of domain structures from all 109° to mixed to all 71° based on differing film thicknesses of 100 and 200 nm to be observed, and to identify growth-induced defects that control domain structure over very long range, 100 nm or more, compared to many studies. In TiO2(B) films, a combination of advanced microscopy and first principals calculations were applied with Raman spectroscopy to produce a definitive reference for further investigation of the crystallinity, structure, composition, and properties of TiO2(B) materials with Raman spectroscopy. Finally to extend these studies of nanostructures and allow direct measurement of electronic and optical properties, the design, development, and construction of proof-of-concept prototypes of specimen rods for in-situ transmission electron microcopy combining electrical probe, scanning tunneling measurements, and optical excitation and
12. Signatures of Solvation Thermodynamics in Spectra of Intermolecular Vibrations
PubMed Central
2017-01-01
This study explores the thermodynamic and vibrational properties of water in the three-dimensional environment of solvated ions and small molecules using molecular simulations. The spectrum of intermolecular vibrations in liquid solvents provides detailed information on the shape of the local potential energy surface, which in turn determines local thermodynamic properties such as the entropy. Here, we extract this information using a spatially resolved extension of the two-phase thermodynamics method to estimate hydration water entropies based on the local vibrational density of states (3D-2PT). Combined with an analysis of solute–water and water–water interaction energies, this allows us to resolve local contributions to the solvation enthalpy, entropy, and free energy. We use this approach to study effects of ions on their surrounding water hydrogen bond network, its spectrum of intermolecular vibrations, and resulting thermodynamic properties. In the three-dimensional environment of polar and nonpolar functional groups of molecular solutes, we identify distinct hydration water species and classify them by their characteristic vibrational density of states and molecular entropies. In each case, we are able to assign variations in local hydration water entropies to specific changes in the spectrum of intermolecular vibrations. This provides an important link for the thermodynamic interpretation of vibrational spectra that are accessible to far-infrared absorption and Raman spectroscopy experiments. Our analysis provides unique microscopic details regarding the hydration of hydrophobic and hydrophilic functional groups, which enable us to identify interactions and molecular degrees of freedom that determine relevant contributions to the solvation entropy and consequently the free energy. PMID:28783431
13. Computing free energy hypersurfaces for anisotropic intermolecular associations.
PubMed
Strümpfer, Johan; Naidoo, Kevin J
2010-01-30
We previously used an adaptive reaction coordinate force biasing method for calculating the free energy of conformation (Naidoo and Brady, J Am Chem Soc 1999, 121, 2244) and chemical reactions (Rajamani et al., J Comput Chem 2003, 24, 1775) amongst others. Here, we describe a generalized version able to produce free energies in multiple dimensions, descriptively named the free energies from adaptive reaction coordinate forces method. To illustrate it, we describe how we calculate a multidimensional intermolecular orientational free energy, which can be used to investigate complex systems such as protein conformation and liquids. This multidimensional intermolecular free energy W(r, theta(1), theta(2), phi) provides a measure of orientationally dependent interactions that are appropriate for applications in systems that inherently have molecular anisotropic features. It is a highly informative free energy volume, which can be used to parameterize key terms such as the Gay-Berne intermolecular potential in coarse grain simulations. To demonstrate the value of the information gained from the W(r, theta(1), theta(2), phi) hypersurfaces we calculated them for TIP3P, TIP4P, and TIP5P dimer water models in vacuum. A comparison with a commonly used one-dimensional distance free energy profile is made to illustrate the significant increase in configurational information. The W(r) plots show little difference between the three models while the W(r, theta(1), theta(2), phi) hypersurfaces reveal the underlying energetic reasons why these potentials reproduce tetrahedrality in the condensed phase so differently from each. Copyright 2009 Wiley Periodicals, Inc.
14. Search for W' boson resonances decaying to a top and a bottom quark and probing anomalous Wtb couplings with 1 fb{sup -1} of D0 Data
SciTech Connect
2008-11-23
With the first evidence for single top quark production in the D0 detector at the Fermilab Tevatron pp-bar collider, the single top quark cross section is measured, limits on the masses of heavy W' boson resonances are set and anomalous Wtb couplings are studied.
15. Intermolecular interactions of 4-pyrrolidino pyridine: a simulation study
Ranjan Bangal, Prakriti; Chakravorti, Sankar
1999-10-01
Simulations of intermolecular interaction by the AM1 method have been performed. The hydrogen bonding complex between and 4-pyrrolidino pyridine (PP) and water molecules with 1: n complexes have been considered to investigate possible stable complex configurations and to calculate the stable interaction energy. These calculations confirm the influence of water molecules on twisting of the pyrrolidino group in ground state. The excited state simulation predicts that the energy minimized geometry of the PP molecule takes an almost sandwich like structure, confirming the formation of an intramolecular exciplex in the gas phase as well as in nonpolar or in weakly polar solvents in line with the experimental findings.
16. INTERMOLECULAR FORCES IN ASSOCIATION OF PURINES WITH POLYBENZENOID HYDROCARBONS.
PubMed
PULLMAN, B; CLAVERIE, P; CAILLET, J
1965-03-12
The interactions in solution between purine or pyrimidine bases and polybenzenoid aromatic hydrocarbons probably consist in a vertical, stacking-type physical association. By molecular orbital calculations the role of the Van der Waals-London intermolecular forces in these interactions is determined. The electrostatic dipole-dipole forces are negligible, the polarization (or induction) dipole-induced dipole forces are contributory, but most important are the dispersion (or fluctuation) forces. This loose, physical type of interaction should not show any specificity with respect to the carcinogenic activity of the hydrocarbons.
17. Effects of intermolecular interaction on inelastic electron tunneling spectra
Kula, Mathias; Luo, Yi
2008-02-01
We have examined the effects of intermolecular interactions on the inelastic electron tunneling spectroscopy (IETS) of model systems: a pair of benzenethiol or a pair of benzenedithiol sandwiched between gold electrodes. The dependence of the IETS on the mutual position of and distance between the paired molecules has been predicted and discussed in detailed. It is shown that, although in most cases, there are clear spectral fingerprints present which allow identification of the actual structures of the molecules inside the junction. Caution must be exercised since some characteristic lines can disappear at certain symmetries. The importance of theoretical simulation is emphasized.
18. Structurally Defined Molecular Hypervalent Iodine Catalysts for Intermolecular Enantioselective Reactions
PubMed Central
Haubenreisser, Stefan; Wöste, Thorsten H.; Martínez, Claudio; Ishihara, Kazuaki
2015-01-01
Abstract Molecular structures of the most prominent chiral non‐racemic hypervalent iodine(III) reagents to date have been elucidated for the first time. The formation of a chirally induced supramolecular scaffold based on a selective hydrogen‐bonding arrangement provides an explanation for the consistently high asymmetric induction with these reagents. As an exploratory example, their scope as chiral catalysts was extended to the enantioselective dioxygenation of alkenes. A series of terminal styrenes are converted into the corresponding vicinal diacetoxylation products under mild conditions and provide the proof of principle for a truly intermolecular asymmetric alkene oxidation under iodine(I/III) catalysis. PMID:26596513
19. Electrophilic Cyclization and Intermolecular Acetalation of 2-(4-hydroxybut-1-yn-1-yl)benzaldehydes: Synthesis of Diiodinated Diepoxydibenzo[c,k][1,9]dioxacyclohexadecines.
PubMed
Wang, Jia; Zhu, Hai-Tao; Chen, Si; Luan, Cheng; Xia, Yu; Shen, Yi; Li, Ying-Xiu; Hua, Yingxi; Liang, Yong-Min
2017-09-01
An expedient strategy for the preparation of diiodinated diepoxydibenzo[c,k][1,9]dioxacyclohexadecines from readily available 2-(4-hydroxybut-1-yn-1-yl)benzaldehydes through electrophile-triggered tandem cyclization/intermolecular acetalation sequence has been presented. The electrophilic macrocyclization can be performed under mild conditions and up to gram quantities. Moreover, palladium-catalyzed coupling and reduction reactions of the resulting iodides could efficiently afford oxa-macrocycles.
20. Intermolecular potential and rovibrational states of the H2O-D2 complex
van der Avoird, Ad; Scribano, Yohann; Faure, Alexandre; Weida, Miles J.; Fair, Joanna R.; Nesbitt, David J.
2012-05-01
A five-dimensional intermolecular potential for H2O-D2 was obtained from the full nine-dimensional ab initio potential surface of Valiron et al. [P. Valiron, M. Wernli, A. Faure, L. Wiesenfeld, C. Rist, S. Kedžuch, J. Noga, J. Chem. Phys. 129 (2008) 134306] by averaging over the ground state vibrational wave functions of H2O and D2. On this five-dimensional potential with a well depth De of 232.12 cm-1 we calculated the bound rovibrational levels of H2O-D2 for total angular momentum J = 0-3. The method used to compute the rovibrational levels is similar to a scattering approach—it involves a basis of coupled free rotor wave functions for the hindered internal rotations and the overall rotation of the dimer—while it uses a discrete variable representation of the intermolecular distance coordinate R. The basis was adapted to the permutation symmetry associated with the para/ortho (p/o) nature of both H2O and D2, as well as to inversion symmetry. As expected, the H2O-D2 dimer is more strongly bound than its H2O-H2 isotopologue [cf. A. van der Avoird, D.J. Nesbitt, J. Chem. Phys. 134 (2011) 044314], with dissociation energies D0 of 46.10, 50.59, 67.43, and 73.53 cm-1 for pH2O-oD2, oH2O-oD2, pH2O-pD2, and oH2O-pD2. A rotationally resolved infrared spectrum of H2O-D2 was measured in the frequency region of the H2O bend mode. The ab initio calculated values of the rotational and distortion constants agree well with the values extracted from this spectrum.
1. Topology-based modeling of intrinsically disordered proteins: balancing intrinsic folding and intermolecular interactions.
PubMed
Ganguly, Debabani; Chen, Jianhan
2011-04-01
Coupled binding and folding is frequently involved in specific recognition of so-called intrinsically disordered proteins (IDPs), a newly recognized class of proteins that rely on a lack of stable tertiary fold for function. Here, we exploit topology-based Gō-like modeling as an effective tool for the mechanism of IDP recognition within the theoretical framework of minimally frustrated energy landscape. Importantly, substantial differences exist between IDPs and globular proteins in both amino acid sequence and binding interface characteristics. We demonstrate that established Gō-like models designed for folded proteins tend to over-estimate the level of residual structures in unbound IDPs, whereas under-estimating the strength of intermolecular interactions. Such systematic biases have important consequences in the predicted mechanism of interaction. A strategy is proposed to recalibrate topology-derived models to balance intrinsic folding propensities and intermolecular interactions, based on experimental knowledge of the overall residual structure level and binding affinity. Applied to pKID/KIX, the calibrated Gō-like model predicts a dominant multistep sequential pathway for binding-induced folding of pKID that is initiated by KIX binding via the C-terminus in disordered conformations, followed by binding and folding of the rest of C-terminal helix and finally the N-terminal helix. This novel mechanism is consistent with key observations derived from a recent NMR titration and relaxation dispersion study and provides a molecular-level interpretation of kinetic rates derived from dispersion curve analysis. These case studies provide important insight into the applicability and potential pitfalls of topology-based modeling for studying IDP folding and interaction in general. Copyright © 2011 Wiley-Liss, Inc.
2. The rotational spectrum, geometry, and intermolecular force constant of the heterodimer of hydrogen cyanide and fluoroform
Goodwin, Elizabeth J.; Legon, A. C.
1986-02-01
The ground-state rotational spectra of six isotopic species of an intermolecular complex formed by hydrogen cyanide and fluoroform have been measured using the pulsed-nozzle, Fourier-transform microwave technique. The rotational constant B0, the centrifugal distortion constants DJ,DJK,HJ, HJK, and HKJ, and, where appropriate, the nuclear quadrupole coupling constants χ(14N) and χ(D) have been determined for each of the species HC14NṡṡṡHCF3, DC14NṡṡṡHCF3, HC14ṡṡṡDCF3, HC15NṡṡṡHCF3, HC15NṡṡṡDCF3, and DC15NṡṡṡHCF3. For HC14NṡṡṡHCF3 the values are as follows: B0=1151.2991(4) MHz, DJ=1.91(1) kHz, DJK=282.75(6) kHz, HJ=-0.1(1) Hz, HJK=44.3(5) Hz, HKJ=53(5) Hz, and χ(14N)=3.948(8) MHz. The form of the spectra and magnitudes of the rotational constants allow the conclusion that the geometry of the complex is of C3V symmetry with the nuclei in the order HCNṡṡṡHCF3 and lead to r(NṡṡṡC)=3.489(2) Å for HCF3 species but 3.483(1) Å for DCF3 species. The intermolecular stretching force constant determined from DJ is kσ=3.52 N m-1.
3. Hybridization and electron-phonon coupling in ferroelectric BaTiO3 probed by resonant inelastic x-ray scattering
Fatale, S.; Moser, S.; Miyawaki, J.; Harada, Y.; Grioni, M.
2016-11-01
We investigated the ferroelectric perovskite material BaTiO3 by resonant inelastic x-ray scattering (RIXS) at the Ti L3 edge. We observe with decreasing temperature a transfer of spectral weight from the elastic to the charge-transfer spectral features, indicative of increasing Ti 3 d -O 2 p hybridization. When the incident photon energy selects transitions to the Ti 3 d eg manifold, the quasielastic RIXS response exhibits a tail indicative of phonon excitations. A fit of the spectral line shape by a theoretical model allows us to estimate the electron-phonon coupling strength M ˜0.25 eV, which places BaTiO3 in the intermediate coupling regime.
4. Photon counting as a probe of superfluidity in a two-band Bose-Hubbard system coupled to a cavity field.
PubMed
Rajaram, Sara; Trivedi, Nandini
2013-12-13
We show that photon number measurement can be used to detect superfluidity for a two-band Bose-Hubbard model coupled to a cavity field. The atom-photon coupling induces transitions between the two internal atomic levels and results in entangled polaritonic states. In the presence of a cavity field, we find different photon numbers in the Mott-insulating versus superfluid phases, providing a method of distinguishing the atomic phases by photon counting. Furthermore, we examine the dynamics of the photon field after a rapid quench to zero atomic hopping by increasing the well depth. We find a robust correlation between the field's quench dynamics and the initial superfluid order parameter, thereby providing a novel and accurate method of determining the order parameter.
5. Pd-Catalyzed Carbonylative Carboperfluoroalkylation of Alkynes. Through-Space (13)C-(19)F Coupling as a Probe for Configuration Assignment of Fluoroalkyl-Substituted Olefins.
PubMed
Domański, Sylwester; Staszewska-Krajewska, Olga; Chaładaj, Wojciech
2017-08-04
A four-component Pd-catalyzed protocol for direct synthesis of perfluoroalkyl-substituted enones is reported. Under mild conditions and low catalyst loading, alkynes, iodoperfluoroalkanes, (hetero)arylboronic acids, and carbon monoxide are assembled into highly elaborate products with good yields and excellent regio- and stereoselectivities. The configuration of the products was confirmed by the observation of through-space (13)C-(19)F couplings, accessible through the analysis of routine (13)C NMR spectra.
6. Suppressor analysis of the MotB(D33E) mutation to probe bacterial flagellar motor dynamics coupled with proton translocation.
PubMed
Che, Yong-Suk; Nakamura, Shuichi; Kojima, Seiji; Kami-ike, Nobunori; Namba, Keiichi; Minamino, Tohru
2008-10-01
MotA and MotB form the stator of the proton-driven bacterial flagellar motor, which conducts protons and couples proton flow with motor rotation. Asp-33 of Salmonella enterica serovar Typhimurium MotB, which is a putative proton-binding site, is critical for torque generation. However, the mechanism of energy coupling remains unknown. Here, we carried out genetic and motility analysis of a slowly motile motB(D33E) mutant and its pseudorevertants. We first confirmed that the poor motility of the motB(D33E) mutant is due to neither protein instability, mislocalization, nor impaired interaction with MotA. We isolated 17 pseudorevertants and identified the suppressor mutations in the transmembrane helices TM2 and TM3 of MotA and in TM and the periplasmic domain of MotB. The stall torque produced by the motB(D33E) mutant motor was about half of the wild-type level, while those for the pseudorevertants were recovered nearly to the wild-type levels. However, the high-speed rotations of the motors under low-load conditions were still significantly impaired, suggesting that the rate of proton translocation is still severely limited at high speed. These results suggest that the second-site mutations recover a torque generation step involving stator-rotor interactions coupled with protonation/deprotonation of Glu-33 but not maximum proton conductivity.
7. Intermolecular interactions and the thermodynamic properties of supercritical fluids
Yigzawe, Tesfaye M.; Sadus, Richard J.
2013-05-01
The role of different contributions to intermolecular interactions on the thermodynamic properties of supercritical fluids is investigated. Molecular dynamics simulation results are reported for the energy, pressure, thermal pressure coefficient, thermal expansion coefficient, isothermal and adiabatic compressibilities, isobaric and isochoric heat capacities, Joule-Thomson coefficient, and speed of sound of fluids interacting via both the Lennard-Jones and Weeks-Chandler-Andersen potentials. These properties were obtained for a wide range of temperatures, pressures, and densities. For each thermodynamic property, an excess value is determined to distinguish between attraction and repulsion. It is found that the contributions of intermolecular interactions have varying effects depending on the thermodynamic property. The maxima exhibited by the isochoric and isobaric heat capacities, isothermal compressibilities, and thermal expansion coefficient are attributed to interactions in the Lennard-Jones well. Repulsion is required to obtain physically realistic speeds of sound and both repulsion and attraction are necessary to observe a Joule-Thomson inversion curve. Significantly, both maxima and minima are observed for the isobaric and isochoric heat capacities of the supercritical Lennard-Jones fluid. It is postulated that the loci of these maxima and minima converge to a common point via the same power law relationship as the phase coexistence curve with an exponent of β = 0.32. This provides an explanation for the terminal isobaric heat capacity maximum in supercritical fluids.
8. Quantitative analysis of intermolecular interactions in orthorhombic rubrene
PubMed Central
Hathwar, Venkatesha R.; Sist, Mattia; Jørgensen, Mads R. V.; Mamakhel, Aref H.; Wang, Xiaoping; Hoffmann, Christina M.; Sugimoto, Kunihisa; Overgaard, Jacob; Iversen, Bo Brummerstedt
2015-01-01
Rubrene is one of the most studied organic semiconductors to date due to its high charge carrier mobility which makes it a potentially applicable compound in modern electronic devices. Previous electronic device characterizations and first principles theoretical calculations assigned the semiconducting properties of rubrene to the presence of a large overlap of the extended π-conjugated core between molecules. We present here the electron density distribution in rubrene at 20 K and at 100 K obtained using a combination of high-resolution X-ray and neutron diffraction data. The topology of the electron density and energies of intermolecular interactions are studied quantitatively. Specifically, the presence of Cπ⋯Cπ interactions between neighbouring tetracene backbones of the rubrene molecules is experimentally confirmed from a topological analysis of the electron density, Non-Covalent Interaction (NCI) analysis and the calculated interaction energy of molecular dimers. A significant contribution to the lattice energy of the crystal is provided by H—H interactions. The electron density features of H—H bonding, and the interaction energy of molecular dimers connected by H—H interaction clearly demonstrate an importance of these weak interactions in the stabilization of the crystal structure. The quantitative nature of the intermolecular interactions is virtually unchanged between 20 K and 100 K suggesting that any changes in carrier transport at these low temperatures would have a different origin. The obtained experimental results are further supported by theoretical calculations. PMID:26306198
9. Hybrid materials from intermolecular associations between cationic lipid and polymers.
PubMed
Pereira, Edla M A; Kosaka, Priscila M; Rosa, Heloísa; Vieira, Débora B; Kawano, Yoshio; Petri, Denise F S; Carmona-Ribeiro, Ana M
2008-08-07
Intermolecular associations between a cationic lipid and two model polymers were evaluated from preparation and characterization of hybrid thin films cast on silicon wafers. The novel materials were prepared by spin-coating of a chloroformic solution of lipid and polymer on silicon wafer. Polymers tested for miscibility with the cationic lipid dioctadecyldimethylammonium bromide (DODAB) were polystyrene (PS) and poly(methyl methacrylate) (PMMA). The films thus obtained were characterized by ellipsometry, wettability, optical and atomic force microscopy, Fourier transform infrared spectroscopy (FTIR), differential scanning calorimetry (DSC), and activity against Escherichia coli. Whereas intermolecular ion-dipole interactions were available for the PMMA-DODAB interacting pair producing smooth PMMA-DODAB films, the absence of such interactions for PS-DODAB films caused lipid segregation, poor film stability (detachment from the silicon wafer) and large rugosity. In addition, the well-established but still remarkable antimicrobial DODAB properties were transferred to the novel hybrid PMMA/DODAB coating, which is demonstrated to be highly effective against E. coli.
10. Intermolecular interactions and the thermodynamic properties of supercritical fluids.
PubMed
Yigzawe, Tesfaye M; Sadus, Richard J
2013-05-21
The role of different contributions to intermolecular interactions on the thermodynamic properties of supercritical fluids is investigated. Molecular dynamics simulation results are reported for the energy, pressure, thermal pressure coefficient, thermal expansion coefficient, isothermal and adiabatic compressibilities, isobaric and isochoric heat capacities, Joule-Thomson coefficient, and speed of sound of fluids interacting via both the Lennard-Jones and Weeks-Chandler-Andersen potentials. These properties were obtained for a wide range of temperatures, pressures, and densities. For each thermodynamic property, an excess value is determined to distinguish between attraction and repulsion. It is found that the contributions of intermolecular interactions have varying effects depending on the thermodynamic property. The maxima exhibited by the isochoric and isobaric heat capacities, isothermal compressibilities, and thermal expansion coefficient are attributed to interactions in the Lennard-Jones well. Repulsion is required to obtain physically realistic speeds of sound and both repulsion and attraction are necessary to observe a Joule-Thomson inversion curve. Significantly, both maxima and minima are observed for the isobaric and isochoric heat capacities of the supercritical Lennard-Jones fluid. It is postulated that the loci of these maxima and minima converge to a common point via the same power law relationship as the phase coexistence curve with an exponent of β = 0.32. This provides an explanation for the terminal isobaric heat capacity maximum in supercritical fluids.
11. Quantitative analysis of intermolecular interactions in orthorhombic rubrene
DOE PAGES
Hathwar, Venkatesha R.; Sist, Mattia; Jørgensen, Mads R. V.; ...
2015-08-14
Rubrene is one of the most studied organic semiconductors to date due to its high charge carrier mobility which makes it a potentially applicable compound in modern electronic devices. Previous electronic device characterizations and first principles theoretical calculations assigned the semiconducting properties of rubrene to the presence of a large overlap of the extended π-conjugated core between molecules. We present here the electron density distribution in rubrene at 20 K and at 100 K obtained using a combination of high-resolution X-ray and neutron diffraction data. The topology of the electron density and energies of intermolecular interactions are studied quantitatively. Specifically,more » the presence of Cπ...Cπinteractions between neighbouring tetracene backbones of the rubrene molecules is experimentally confirmed from a topological analysis of the electron density, Non-Covalent Interaction (NCI) analysis and the calculated interaction energy of molecular dimers. A significant contribution to the lattice energy of the crystal is provided by H—H interactions. The electron density features of H—H bonding, and the interaction energy of molecular dimers connected by H—H interaction clearly demonstrate an importance of these weak interactions in the stabilization of the crystal structure. Finally, the quantitative nature of the intermolecular interactions is virtually unchanged between 20 K and 100 K suggesting that any changes in carrier transport at these low temperatures would have a different origin. The obtained experimental results are further supported by theoretical calculations.« less
12. He-, Ne-, and Ar-phosgene intermolecular potential energy surfaces.
PubMed
Munteanu, Cristian R; Henriksen, Christian; Felker, Peter M; Fernández, Berta
2013-05-09
Using the CCSD(T) model, we evaluated the intermolecular potential energy surfaces of the He-, Ne-, and Ar-phosgene complexes. We considered a representative number of intermolecular geometries for which we calculated the corresponding interaction energies with the augmented (He complex) and double augmented (Ne and Ar complexes) correlation-consistent polarized valence triple-ζ basis sets extended with a set of 3s3p2d1f1g midbond functions. These basis sets were selected after systematic basis set studies carried out at geometries close to those of the surface minima. The He-, Ne-, and Ar-phosgene surfaces were found to have absolute minima of -72.1, -140.4, and -326.6 cm(-1) at distances between the rare-gas atom and the phosgene center of mass of 3.184, 3.254, and 3.516 Å, respectively. The potentials were further used in the evaluation of rovibrational states and the rotational constants of the complexes, providing valuable results for future experimental investigations. Comparing our results to those previously available for other phosgene complexes, we suggest that the results for Cl2-phosgene should be revised.
13. Quantitative analysis of intermolecular interactions in orthorhombic rubrene
SciTech Connect
Hathwar, Venkatesha R.; Sist, Mattia; Jørgensen, Mads R. V.; Mamakhel, Aref H.; Wang, Xiaoping; Hoffmann, Christina M.; Sugimoto, Kunihisa; Overgaard, Jacob; Iversen, Bo Brummerstedt
2015-08-14
Rubrene is one of the most studied organic semiconductors to date due to its high charge carrier mobility which makes it a potentially applicable compound in modern electronic devices. Previous electronic device characterizations and first principles theoretical calculations assigned the semiconducting properties of rubrene to the presence of a large overlap of the extended π-conjugated core between molecules. We present here the electron density distribution in rubrene at 20 K and at 100 K obtained using a combination of high-resolution X-ray and neutron diffraction data. The topology of the electron density and energies of intermolecular interactions are studied quantitatively. Specifically, the presence of Cπ...Cπinteractions between neighbouring tetracene backbones of the rubrene molecules is experimentally confirmed from a topological analysis of the electron density, Non-Covalent Interaction (NCI) analysis and the calculated interaction energy of molecular dimers. A significant contribution to the lattice energy of the crystal is provided by H—H interactions. The electron density features of H—H bonding, and the interaction energy of molecular dimers connected by H—H interaction clearly demonstrate an importance of these weak interactions in the stabilization of the crystal structure. Finally, the quantitative nature of the intermolecular interactions is virtually unchanged between 20 K and 100 K suggesting that any changes in carrier transport at these low temperatures would have a different origin. The obtained experimental results are further supported by theoretical calculations.
14. A Probe of magnetosphere-ionosphere coupling using Very Low Frequency (VLF) Radio Signal from North-West Cape (Australia) to Kolkata (India)
Nwankwo, Victor U. J.; Chakrabarti, Sandip Kumar
Very low frequency (VLF) radio waves has been employed for the detection and study of various terrestrial and extra-terrestrial high energy phenomena such as solar flares, solar eclipse, gamma ray burst, lightning induced electron precipitation etc., and the subsequent variations in the lower ionosphere driven by these events. In this study, we exploit the propagation characteristics of VLF signal through the Earth-ionosphere waveguide, to probe changes in ionospheric signatures, induced by solar driven variations in magnetospheric conditions. Our study is based on the VLF signal (amplitude and phase) received at the Ionospheric and Earthquake Research Centre (IERC), Sitapur, under Indian Centre for Space Physics (ICSP), which is transmitted by the Australian NWC station at about 19.8kHz.
15. Phase Separation in Ti-6Al-4V Alloys with Boron Additions for Biomedical Applications: Scanning Kelvin Probe Force Microscopy Investigation of Microgalvanic Couples and Corrosion Initiation
Davis, P. H.; Robles, K.; Livingston, K.; Johns, S.; Ravi, V. A.; Graugnard, E.; Hurley, M. F.
2017-08-01
To investigate the effect of boron additions on the corrosion behavior of Ti-6Al-4V for potential use in biomedical implants and devices, cast samples of Ti-6Al-4V were alloyed with 0.01% to 1.09% boron by weight and subjected to hot isostatic pressing. Subsequent analysis via scanning Kelvin probe force microscopy and scanning electron microscopy/energy-dispersive spectroscopy revealed the presence of both alpha ( α) and beta ( β) phase titanium, enriched in aluminum and vanadium, respectively. At all concentrations, boron additions affected the grain structure and were dispersed throughout both phases, but above the solubility limit, needle-like TiB structures also formed. The TiB needles and β phase exhibited similar surface potentials, whereas that of the α phase was found to be significantly lower. Nevertheless, when subjected to high applied electrochemical potentials in saline solutions, corrosion initiation was observed exclusively within the more noble β phase.
16. Intermolecular charge transfer enhances two-photon absorption in yellow fluorescent protein.
PubMed
Beerepoot, Maarten T P; Friese, Daniel H; Ruud, Kenneth
2014-04-07
We present a quantum chemical study of the two-photon absorption (TPA) properties of yellow fluorescent protein (YFP), a mutant of the extensively studied green fluorescent protein. The aromatic chromophore of YFP has a π-stacking interaction with the aromatic ring of a tyrosine residue (Tyr203) in a parallel-displaced structure with a distance of about 3.4 Å. We study the TPA spectrum of the π-stacking system of YFP using the well-established Coulomb-attenuated B3LYP density functional (CAM-B3LYP) and the second-order approximate coupled-cluster model CC2. This work presents both the first comprehensive study of the two-photon absorption spectrum of YFP and the largest-scale coupled-cluster calculation of two-photon absorption that has ever been performed. We analyze the intermolecular charge-transfer (ICT) transitions in this stacked system and show that the ICT transitions are an important mechanism for enhancing the TPA cross sections in YFP. We investigate the distance dependence of the ICT transitions and show that their TPA cross sections are strongly dependent on the separation of the aromatic moieties. This provides a means for tuning the TPA properties of YFP and other structurally related fluorescent proteins through molecular engineering.
17. On the effect of a radiation field in modifying the intermolecular interaction between two chiral molecules
Salam, A.
2006-01-01
The change in the mutual energy of interaction between a pair of chiral molecules coupled via the exchange of a single virtual photon and in the presence of an electromagnetic field is calculated using nonrelativistic quantum electrodynamics. The particular viewpoint adopted is one that has an intuitive physical appeal and resembles a classical treatment. It involves the coupling of electric and magnetic dipole moments induced at each center by the incident radiation field to the resonant dipole-dipole interaction tensor. The energy shift is evaluated for fixed as well as random orientations of the molecular pair with respect to the direction of propagation of the field. A complete polarization analysis is carried out for the former situation by examining the effect of incident radiation that is linearly or circularly polarized and traveling in a direction that is parallel or perpendicular to the intermolecular distance vector. After tumble averaging, all polarization dependence of the energy shift vanishes. In both cases the interaction energy is directly proportional to the irradiance of the applied field, and is discriminatory, changing sign when one optically active species is replaced by its enantiomer. The asymptotic behavior of the energy shift at the limits of large and small separations is also studied.
18. Probing Higgs width and top quark Yukawa coupling from t t¯ and t t¯ t¯ productions
Cao, Qing-Hong; Chen, Shao-Long; Liu, Yandong
2017-03-01
We demonstrate that four top-quark production is a powerful tool to constrain the top Yukawa coupling. The constraint is robust in the sense that it does not rely on the Higgs boson decay. Taking into account the projection of the t t ¯H production by the ATLAS Collaboration, we obtained a bound on the Higgs boson width, ΓH≤2.57 ΓHSM, at the 14 TeV Large Hadron Collider with an integrated luminosity of 300 fb-1.
19. Keto-enol tautomerization and intermolecular proton transfer in photoionized cyclopentanone dimer in the gas phase
SciTech Connect
Ghosh, Arup K.; Chatterjee, Piyali; Chakraborty, Tapas
2014-07-28
Time-of-flight mass spectra of cyclopentanone and its clusters cooled in a supersonic jet expansion have been measured following 4-, 3-, and 2-photon ionizations by the 2nd, 3rd, and 4th harmonic wavelengths, respectively, of a Q-switched Nd:YAG laser. The mass spectra reveal signatures of energetically favored keto to enol tautomerization of the molecular ion leading to intermolecular proton transfer, and this observation is found sharply dependent on the ionization wavelengths used. Electronic structure calculation predicts that in spite of the energetic preference, keto-enol conversion barrier of isolated molecular ion is high. However, the barrier is significantly reduced in a CH⋯O hydrogen-bonded dimer of the molecule. The transition states associated with tautomeric conversion of both cyclopentanone monomer and dimer cations have been identified by means of intrinsic reaction co-ordinate calculation. In a supersonic jet expansion, although a weakly bound dimer is readily generated, the corresponding cation and also the protonated counterpart are observed only for ionization by 532 nm. For other two ionization wavelengths, these species do not register in the mass spectra, where the competing reaction channels via α-cleavage of the ring become dominant. In contrast to the report of a recent study, we notice that the intact molecular ion largely survives fragmentations when ionized from the 2-photon resonant 3p Rydberg state as intermediate using nanosecond laser pulses, and the corresponding resonant 3-photon ionization spectrum has been recorded probing the intact molecular ion.
20. Experimental probes of axions
SciTech Connect
Chou, Aaron S.; /Fermilab
2009-10-01
Experimental searches for axions or axion-like particles rely on semiclassical phenomena resulting from the postulated coupling of the axion to two photons. Sensitive probes of the extremely small coupling constant can be made by exploiting familiar, coherent electromagnetic laboratory techniques, including resonant enhancement of transitions using microwave and optical cavities, Bragg scattering, and coherent photon-axion oscillations. The axion beam may either be astrophysical in origin as in the case of dark matter axion searches and solar axion searches, or created in the laboratory from laser interactions with magnetic fields. This note is meant to be a sampling of recent experimental results.
1. Diagnostics of capacitively-coupled hydrocarbon plasmas for deposition of diamond-like carbon films using quadrupole mass spectrometry and Langmuir probe
Oda, Akinori; Fukai, Shun; Kousaka, Hiroyuki; Ohta, Takayuki
2015-09-01
Diamond-like carbon (DLC) films are the hydrogenated amorphous carbon films, which contains a mixture of sp2- and sp3-bonded carbon. The DLC films have been widely used for various applications, such as automotive, semiconductors, medical devices, since have excellent material properties in lower friction, higher chemical stability, higher hardness, higher wear resistance. Until now, numerous investigations on the DLC films using plasma assisted chemical vapor deposition have been done. For precise control of coating technique of DLC films, it is enormously important to clarify the fundamental properties in hydrocarbon plasmas, as a source of hydrocarbon ions and radicals. In this paper, the fundamental properties in a low pressure radio-frequency hydrocarbon (Ar/CH4 (1 %) gas mixture) plasmas have been diagnosed using a quadrupole mass spectrometer (HIDEN ANARYTICAL Ltd., EQP-300) and Langmuir probe system (HIDEN ANARYTICAL Ltd., ESPion). This work was partly supported by KAKENHI (No.26420247), and a `Grant for Advanced Industrial Technology Development (No.11B06004d)'' in 2011 from the New Energy and Industrial Technology Development Organization (NEDO) of Japan.
2. Novel bacteria capable of degrading phenanthrene in activated sludge revealed by stable-isotope probing coupled with high-throughput sequencing.
PubMed
Li, Jibing; Zhang, Dayi; Song, Mengke; Jiang, Longfei; Wang, Yujie; Luo, Chunling; Zhang, Gan
2017-09-27
The indigenous microorganisms responsible for degrading phenanthrene (PHE) in activated biosludge were identified using DNA-based stable isotope probing. Besides the well-known PHE degraders Burkholderia, Ralstonia, Sinobacteraceae and Arthrobacter, we for the first time linked the taxa Paraburkholderia and Kaistobacter with in situ PHE biodegradation. Analysis of PAH-RHDα gene detected in the heavy DNA fraction of (13)C-PHE treatment suggested the mechanisms of horizontal gene transfer or inter-species hybridisation in PAH-RHD gene spread within the microbial community. Additionally, three cultivable PHE degraders, Microbacterium sp. PHE-1, Rhodanobacter sp. PHE-2 and Rhodococcus sp. PHE-3, were isolated from the same activated biosludge. Among them, Rhodanobacter sp. PHE-2 is the first identified strain in its genus with PHE-degrading ability. However, the involvement of these strains in PHE degradation in situ was questionable, due to their limited enrichment in the heavy DNA fraction of (13)C-PHE treatment and lack of PAH-RHDα gene found in these isolates. Collectively, our findings provide a deeper understanding of the diversity and functions of indigenous microbes in PHE degradation.
3. Electromechanical method coupling non-invasive skin impedance probing and in vivo subcutaneous liquid microinjection: controlling the diffusion pattern of nanoparticles within living soft tissues.
PubMed
Sung, Baeckkyoung; Kim, Se Hoon; Lee, Jin-Kyu; Lee, Byung-Cheon; Soh, Kwang-Sup
2014-08-01
Transdermal drug delivery is the way to transport drug carriers, such as nanoparticles, across the skin barrier to the dermal and/or subcutaneous layer. In order to control the transdermal drug delivery process, based on the heterogeneous and nonlinear structures of the skin tissues, we developed a novel electromechanical method combining in vivo local skin impedance probing, subcutaneous micro-injection of colloidal nanoparticles, and transcutaneous electrical stimulation. Experiments on the nude mice using in vivo fluorescence imaging exhibited significantly different apparent diffusion patterns of the nanoparticles depending on the skin impedance: Anisotropic and isotropic patterns were observed upon injection into low and high impedance points, respectively. This result implies that the physical complexity in living tissues may cause anisotropic diffusion of drug carriers, and can be used as a parameter for controlling drug delivery process. This method also can be combined with microneedle-based drug release systems, micro-fabricated needle-electrodes, and/or advanced in vivo targeting/imaging technologies using nanoparticles.
4. Intermolecular vibrations of (CH2)2O-HF and -DF hydrogen bonded complexes investigated by Fourier transform infrared spectroscopy and ab initio calculations.
PubMed
Cirtog, M; Asselin, P; Soulard, P; Madebène, B; Alikhani, M E
2010-10-14
A series of Fourier transform infrared spectra (FTIR) of the hydrogen bonded complexes (CH(2))(2)O-HF and -DF have been recorded in the 50-750 cm(-1) range up to 0.1 cm(-1) resolution in a static cell maintained at near room temperature. The direct observation of three intermolecular transitions enabled us to perform band contour analysis of congested cell spectra and to determine reliable rovibrational parameters such as intermolecular frequencies, rovibrational and anharmonic coupling constants involving two l(1) and l(2) librations and one σ stretching intermolecular motion. Inter-inter anharmonic couplings could be identified between ν(l(1)), ν(l(2)), ν(σ) and the two lowest frequency bending modes. The positive sign of coupling constants (opposite with respect to acid stretching intra-inter ones) reveals a weakening of the hydrogen bond upon intermolecular excitation. The four rovibrational parameters ν(σ) and x(σj) (j = σ, δ(1), δ(2)) derived in the present far-infrared study and also in a previous mid-infrared one [Phys. Chem. Chem. Phys. 2005, 1, 592] make deviations appear smaller than 1% for frequencies and 12% for coupling constants which gives confidence to the reliability of the data obtained. Anharmonic frequencies obtained at the MP2 level with Aug-cc-pvTZ basis set agree well with experimental values over a large set of frequencies and coupling constants. An estimated anharmonic corrected value of the dissociation energy D for both oxirane-HF (2424 cm(-1)) and -DF (2566 cm(-1)) has been derived using a level of theory as high as CCSD(T)/Aug-cc-pvQZ, refining the harmonic value previously calculated for oxirane-HF with the MP2 method and a smaller basis set. Finally, contrary to short predissociation lifetimes evidenced for acid stretching excited states, any homogeneous broadening related to vibrational dynamics of (CH(2))(2)O-HF and -DF has been observed within the three highest frequency intermolecular states, as expected with low
5. Thermodynamic curvature for attractive and repulsive intermolecular forces.
PubMed
May, Helge-Otmar; Mausbach, Peter; Ruppeiner, George
2013-09-01
The thermodynamic curvature scalar R for the Lennard-Jones system is evaluated in phase space, including vapor, liquid, and solid state. We paid special attention to the investigation of R along vapor-liquid, liquid-solid, and vapor-solid equilibria. Because R is a measure of interaction strength, we traced out the line R=0 dividing the phase space into regions with effectively attractive (R<0) or repulsive (R>0) interactions. Furthermore, we analyzed the dependence of R on the strength of attraction applying a perturbation ansatz proposed by Weeks-Chandler-Anderson. Our results show clearly a transition from R>0 (for poorly repulsive interaction) to R<0 when loading attraction in the intermolecular potential.
6. Intermolecular forces and energies between ligands and receptors.
PubMed
Moy, V T; Florin, E L; Gaub, H E
1994-10-14
The recognition mechanisms and dissociation pathways of the avidin-biotin complex and of actin monomers in actin filaments were investigated. The unbinding forces of discrete complexes of avidin or streptavidin with biotin analogs are proportional to the enthalpy change of the complex formation but independent of changes in the free energy. This result indicates that the unbinding process is adiabatic and that entropic changes occur after unbinding. On the basis of the measured forces and binding energies, an effective rupture length of 9.5 +/- 1 angstroms was calculated for all biotin-avidin pairs and approximately 1 to 3 angstroms for the actin monomer-monomer interaction. A model for the correlation among binding forces, intermolecular potential, and molecular function is proposed.
7. Transetherification on Polyols by Intra- and Intermolecular Nucleophilic Substitutions
PubMed Central
Muraoka, Takahiro; Adachi, Kota; Chowdhury, Rainy; Kinbara, Kazushi
2014-01-01
Transetherification on polyols involving intra- and intermolecular nucleophilic substitutions is reported. Di- or trialkoxide formation of propane-1,3-diol or 2-(hydroxymethyl)propane-1,3-diol derivatives by NaH triggers the reaction via oxetanes formation, where the order to add NaH and a polyol significantly influences the yields of products. It was demonstrated that the protective group on the pentaerythritol skeleton is apparently transferred to the hydrophilic and hydrophobic chain molecules bearing a leaving group in one-step, and a protective group conversion from tosyl to benzyl was successful using a benzyl-appending triol to afford a desired product in 67% yield. PMID:24663293
8. Intermolecular vibrational energy transfers in liquids and solids.
PubMed
Chen, Hailong; Wen, Xiewen; Guo, Xunmin; Zheng, Junrong
2014-07-21
Resonant and nonresonant intermolecular vibrational energy transfers in KSCN/KSC(13)N/KS(13)C(15)N aqueous and DMF solutions and crystals are studied. Both energy-gap and temperature dependent measurements reveal some surprising results, e.g. inverted energy-gap dependent energy transfer rates and opposite temperature dependences of resonant and nonresonant energy transfer rates. Two competing mechanisms are proposed to be responsible for the experimental observations. The first one is the dephasing mechanism in which the measured energy transfer rate originates from the dephasing of the energy donor-acceptor coherence, and the second one is the phonon-compensation mechanism derived from the second order perturbation. It is found that both the nonresonant energy transfers in the liquids and resonant energy transfers in both liquids and solids can be well described by the first mechanism. The second mechanism explains the nonresonant energy transfers in one series of the solid samples very well.
9. Dissecting Anion Effects in Gold(I)-Catalyzed Intermolecular Cycloadditions
PubMed Central
Homs, Anna; Obradors, Carla; Lebœuf, David; Echavarren, Antonio M
2014-01-01
From a series of gold complexes of the type [t-BuXPhosAu(MeCN)]X (X=anion), the best results in intermolecular gold(I)-catalyzed reactions are obtained with the complex with the bulky and soft anion BAr4F− [BAr4F−=3,5-bis(trifluoromethyl)phenylborate] improving the original protocols by 10–30% yield. A kinetic study on the [2+2] cycloaddition reaction of alkynes with alkenes is consistent with an scenario in which the rate-determining step is the ligand exchange to generate the (η2-phenylacetylene)gold(I) complex. We have studied in detail the subtle differences that can be attributed to the anion in this formation, which result in a substantial decrease in the formation of unproductive σ,π-(alkyne)digold(I) complexes by destabilizing the conjugated acid formed. PMID:26190958
10. Optical probe
DOEpatents
Hencken, Kenneth; Flower, William L.
1999-01-01
A compact optical probe is disclosed particularly useful for analysis of emissions in industrial environments. The instant invention provides a geometry for optically-based measurements that allows all optical components (source, detector, rely optics, etc.) to be located in proximity to one another. The geometry of the probe disclosed herein provides a means for making optical measurements in environments where it is difficult and/or expensive to gain access to the vicinity of a flow stream to be measured. Significantly, the lens geometry of the optical probe allows the analysis location within a flow stream being monitored to be moved while maintaining optical alignment of all components even when the optical probe is focused on a plurality of different analysis points within the flow stream.
11. X-ray Intermolecular Structure Factor ( XISF ): separation of intra- and intermolecular interactions from total X-ray scattering data
SciTech Connect
Mou, Q.; Benmore, C. J.; Yarger, J. L.
2015-05-09
XISFis a MATLAB program developed to separate intermolecular structure factors from total X-ray scattering structure factors for molecular liquids and amorphous solids. The program is built on a trust-region-reflective optimization routine with the r.m.s. deviations of atoms physically constrained.XISFhas been optimized for performance and can separate intermolecular structure factors of complex molecules.
12. Intermolecular vibrations and fast relaxations in supercooled ionic liquids
Ribeiro, Mauro C. C.
2011-06-01
Short-time dynamics of ionic liquids has been investigated by low-frequency Raman spectroscopy (4 < ω < 100 cm-1) within the supercooled liquid range. Raman spectra are reported for ionic liquids with the same anion, bis(trifluoromethylsulfonyl)imide, and different cations: 1-butyl-3-methylimidazolium, 1-hexyl-3-methylimidazolium, 1-butyl-1-methylpiperidinium, trimethylbutylammonium, and tributylmethylammonium. It is shown that low-frequency Raman spectroscopy provides similar results as optical Kerr effect (OKE) spectroscopy, which has been used to study intermolecular vibrations in ionic liquids. The comparison of ionic liquids containing aromatic and non-aromatic cations identifies the characteristic feature in Raman spectra usually assigned to librational motion of the imidazolium ring. The strength of the fast relaxations (quasi-elastic scattering, QES) and the intermolecular vibrational contribution (boson peak) of ionic liquids with non-aromatic cations are significantly lower than imidazolium ionic liquids. A correlation length assigned to the boson peak vibrations was estimated from the frequency of the maximum of the boson peak and experimental data of sound velocity. The correlation length related to the boson peak (˜19 Å) does not change with the length of the alkyl chain in imidazolium cations, in contrast to the position of the first-sharp diffraction peak observed in neutron and X-ray scattering measurements of ionic liquids. The rate of change of the QES intensity in the supercooled liquid range is compared with data of excess entropy, free volume, and mean-squared displacement recently reported for ionic liquids. The temperature dependence of the QES intensity in ionic liquids illustrates relationships between short-time dynamics and long-time structural relaxation that have been proposed for glass-forming liquids.
13. Intermolecular vibrations and fast relaxations in supercooled ionic liquids.
PubMed
Ribeiro, Mauro C C
2011-06-28
Short-time dynamics of ionic liquids has been investigated by low-frequency Raman spectroscopy (4 < ω < 100 cm(-1)) within the supercooled liquid range. Raman spectra are reported for ionic liquids with the same anion, bis(trifluoromethylsulfonyl)imide, and different cations: 1-butyl-3-methylimidazolium, 1-hexyl-3-methylimidazolium, 1-butyl-1-methylpiperidinium, trimethylbutylammonium, and tributylmethylammonium. It is shown that low-frequency Raman spectroscopy provides similar results as optical Kerr effect (OKE) spectroscopy, which has been used to study intermolecular vibrations in ionic liquids. The comparison of ionic liquids containing aromatic and non-aromatic cations identifies the characteristic feature in Raman spectra usually assigned to librational motion of the imidazolium ring. The strength of the fast relaxations (quasi-elastic scattering, QES) and the intermolecular vibrational contribution (boson peak) of ionic liquids with non-aromatic cations are significantly lower than imidazolium ionic liquids. A correlation length assigned to the boson peak vibrations was estimated from the frequency of the maximum of the boson peak and experimental data of sound velocity. The correlation length related to the boson peak (∼19 Å) does not change with the length of the alkyl chain in imidazolium cations, in contrast to the position of the first-sharp diffraction peak observed in neutron and X-ray scattering measurements of ionic liquids. The rate of change of the QES intensity in the supercooled liquid range is compared with data of excess entropy, free volume, and mean-squared displacement recently reported for ionic liquids. The temperature dependence of the QES intensity in ionic liquids illustrates relationships between short-time dynamics and long-time structural relaxation that have been proposed for glass-forming liquids.
14. Evaluation of intermolecular forces in a circulating system.
PubMed
Guo, Qiuquan; Liu, Mei; Yang, Jun
2011-11-01
Intercellular interactions, which are mediated by a variety of complex intercellular molecules through the processes of formation and dissociation of molecular bonds, play a critical role in regulating cellular functions in biological systems. Various approaches are applied to evaluate intercellular or molecular bonding forces. To quantify the intermolecular interaction forces, flow chamber has become a meaningful technique as it can ultimately mimic the cellular microenvironment in vivo under physiological flow conditions. Hydrodynamic forces are usually used to predict the intercellular forces down to the single molecular level. However, results show that only using hydrodynamic force will overestimate up to 30% of the receptor-ligand strength when the non-specific forces such as Derjaguin-Landau-Verway-Overbeek (DLVO) forces become un-neglected. Due to the nature of high ion concentration in the physiological condition, electrostatic force is largely screened which will cause DLVO force unbalanced. In this study, we propose to take account of the DLVO force, including van der Waals (VDW) force and electrostatic force, to predict the intermolecular forces of a cell doublet and cell-substrate model in a circulating system. Results also show that the DLVO force has a nonlinear effect as the cell-cell or cell-substrate distance changes. In addition, we used the framework of high accuracy hydrodynamic theories proved in colloidal systems. It is concluded that DLVO force could not be ignored in quantitative studies of molecular interaction forces in circulating system. More accurate prediction of intercellular forces needs to take account of both hydrodynamic force and DLVO force. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.
15. Intermolecular potential functions from spectroscopic properties of weakly bound complexes
SciTech Connect
Muenter, J.S.
1992-01-01
Goal is to consolidate the information from high resolution spectroscopy of weakly bound cluster molecules through a theoretical model of intermolecular potential energy surfaces. The ability to construct analytic intermolecular potential functions that accurately predict the interaction energy between small molecules will have a major impact in chemistry, biochemistry, and biology. This document presents the evolution and capabilities of a potential function model developed here, and then describes plans for future developments and applications. This potential energy surface (PES) model was first used on (HCCH){sub 2}, (CO{sub 2}){sub 2}, HCCH - CO{sub 2}; it had to be modified to work with HX dimers and CO{sub 2}-HX complexes. Potential functions have been calculated for 15 different molecular complexes containing 7 different monomer molecules. Current questions, logical extensions and new applications of the model are discussed. The questions are those raised by changing the repulsion and dispersion terms. A major extension of the PES model will be the inclusion of induction effects. Projects in progress include PES calculations on (HCCH){sub 3}, CO{sub 2} containing complexes, (HX){sub 2}, HX - CO{sub 2}, CO{sub 2} - CO, (CO{sub 2}){sub 3}, and (OCS){sub 2}. The first PES calculation for a nonlinear molecule will be for water and ammonia complexes. Possible long-term applications for biological molecules are discussed. Differences between computer programs used for molecular mechanics and dynamics in biological systems are discussed, as is the problem of errors. 12 figs, 74 refs. (DLC)
16. Intermolecular magnetic interactions in stacked DNA base pairs.
PubMed
Martínez, Fernando A; Aucar, Gustavo A
2017-10-09
The influence of pi-stacking on the magnetic properties of atoms that belong to adenine-thymine and guanine-cytosine pairs in sequences of three and five layers of DNA base pairs was analysed. As probes we used NMR spectroscopic parameters, which are among the most useful tools to learn about the transmission of magnetic interactions in molecules. Four DFT functionals were employed: B3LYP, BHANDLYP, KT2 and KT3, together with the SOPPA method. Besides, given that the number of non-hydrogen atoms of the supramolecular systems studied here is larger than 50 we applied a locally dense basis set scheme. Our results show that the piling up of a few Watson-Crick base pairs above and below a given pair modifies its NMR spectroscopic parameters by an amount that may be measurable and the percentage of variation does not depend on dispersion. We found that magnetic shieldings are more sensitive than J-couplings, and also that some atoms are more sensitive than others. Stacking affects the shielding of non-hydrogen atoms like nitrogens, that are donors in hydrogen bonds, HBs, and the carbons bonded to them. The amount of variation of these shieldings was found to be from 2% to 5% when the pairs are considered first as isolated, and then, placed in the middle of a sequence of three layers of base pairs. Such a variation becomes vanishingly small when the sequence contains more than three layers, showing that the stacking effect on NMR spectroscopic parameters has a local nature. We have also found a pattern for shieldings. First, equivalent atoms of similar monomers (thymine and adenine, or guanine and cytosine) have similar values of absolute shieldings in isolated pairs, and the amount of variation from isolated pairs to aggregates of a few pairs is also similar, meaning that equivalent atoms are affected in a similar manner by pi-stacking. Second, the hydrogen atoms which belong to hydrogen bonds are more sensitive to the piling up than the non-hydrogen atoms.
17. Final Project Report - Coupled Biogeochemical Process Evaluation for Conceptualizing Trichloriethylene Co-Metabolism: Co-Metabolic Enzyme Activity Probes and Modeling Co-Metabolism and Attenuation
SciTech Connect
Starr, Robert C; Orr, Brennon R; Lee, M Hope; Delwiche, Mark
2010-02-26
Trichloroethene (TCE) (also known as trichloroethylene) is a common contaminant in groundwater. TCE is regulated in drinking water at a concentration of 5 µg/L, and a small mass of TCE has the potential to contaminant large volumes of water. The physical and chemical characteristics of TCE allow it to migrate quickly in most subsurface environments, and thus large plumes of contaminated groundwater can form from a single release. The migration and persistence of TCE in groundwater can be limited by biodegradation. TCE can be biodegraded via different processes under either anaerobic or aerobic conditions. Anaerobic biodegradation is widely recognized, but aerobic degradation is less well recognized. Under aerobic conditions, TCE can be oxidized to non hazardous conditions via cometabolic pathways. This study applied enzyme activity probes to demonstrate that cometabolic degradation of TCE occurs in aerobic groundwater at several locations, used laboratory microcosm studies to determine aerobic degradation rates, and extrapolated lab-measured rates to in situ rates based on concentrations of microorganisms with active enzymes involved in cometabolic TCE degradation. Microcosms were constructed using basalt chips that were inoculated with microorganisms to groundwater at the Idaho National Laboratory Test Area North TCE plume by filling a set of Flow-Through In Situ Reactors (FTISRs) with chips and placing the FTISRs into the open interval of a well for several months. A parametric study was performed to evaluate predicted degradation rates and concentration trends using a competitive inhibition kinetic model, which accounts for competition for enzyme active sites by both a growth substrate and a cometabolic substrate. The competitive inhibition kinetic expression was programmed for use in the RT3D reactive transport package. Simulations of TCE plume evolution using both competitive inhibition kinetics and first order decay were performed.
18. Highly sensitive determination of nitric oxide in biologic samples by a near-infrared BODIPY-based fluorescent probe coupled with high-performance liquid chromatography.
PubMed
Zhang, Hui-Xian; Chen, Jian-Bo; Guo, Xiao-Feng; Wang, Hong; Zhang, Hua-Shan
2013-11-15
Nitric oxide (NO) acts as an important regulator and mediator in numerous processes of biological systems. In this work, the analytical potential of a novel near-infrared (NIR, >600 nm) BODIPY-based fluorescent probe for NO, 8-(3,4-diaminophenyl)-4,4-difluoro-4-bora-3a,4a-diaza-di(1,2-dihydro) naphtho[b, g]s-indacene (DANPBO-H) has been evaluated in high performance liquid chromatography (HPLC). In 25 mM pH 6.50 borate buffer, DANPBO-H reacted with NO to give the corresponding triazole, DANPBO-H-T, at 35 °C for 20 min. DANPBO-H-T was eluted using a mobile phase of methanol/tetrahydrofuran/50mM pH 7.00 H3Cit-NaOH buffer (81:7:12, v/v/v) in 4 min on a C8 column and detected with fluorescence detection at excitation and emission wavelengths of 621 and 631 nm, respectively. The limit of detection (LOD) (signal-to-noise=3) reached to 5.50×10(-10) M. Excellent selectivity was observed against other reactive oxygen/nitrogen species. Various representative biological matrixes including the whole blood and organs of mice, the pangen and radical of rice, human vascular endothelial (ECV-304) cells and mouse macrophage (RAW 264.7) cells were used to verify the feasibility and resistance to interfering effects from complex biological sample matrixes of the developed DANPBO-H-based HPLC method. Compared to the existing derivatization-based HPLC methods for NO, the proposed method eliminates interfering effects from complex biological sample matrixes efficiently owing to the fluorescence detection in the NIR region, and is more advantageous and robust for the sensitive and selective determination of NO in complex biological samples.
19. Coupling of laser excitation and inelastic neutron scattering: attempt to probe the dynamics of light-induced C-phycocyanin dynamics.
PubMed
Combet, Sophie; Pieper, Jörg; Coneggo, Frédéric; Ambroise, Jean-Pierre; Bellissent-Funel, Marie-Claire; Zanotti, Jean-Marc
2008-06-01
Excitation energy transfer (EET) in light-harvesting antennae is a highly efficient key event in photosynthesis, where light-induced dynamics of the antenna pigment-protein complexes may play a functional role. So far, however, the relationship between EET and protein dynamics remains unknown. C-phycocyanin (C-PC) is the main pigment/protein complex present in the cyanobacterial antenna, called "phycobilisome". The aim of the present study was to investigate light-induced C-PC internal thermal motions (ps timescale) measured by inelastic neutron scattering. To synchronize the beginning of the laser flash (6 ns duration) with that of the neutron test pulse ( approximately 87 micros duration), we developed a novel type of "time-resolved" experimental setup on MIBEMOL time-of-flight neutron spectrometer (LLB, France). Data acquisition has been modified to get quasi-simultaneously "light" and "dark" measurements (with and without laser, respectively) and eliminate many spurious effects that could occur on the sample during the experiment. The study was carried out on concentrated C-PC ( approximately 135 g/L protein in D(2)O phosphate buffer), contained in an aluminium/sapphire sample holder (almost "transparent" for neutrons) and homogeneously illuminated inside an "integrating sphere". We observed very similar incoherent dynamical structure factors of C-PC with or without light. The vibrational density of states showed two very slightly increased vibrational modes with light, at approximately 30 and approximately 50 meV ( approximately 240 and approximately 400 cm(-1), respectively). These effects have to be verified by further experiments before probing any temporal evolution, by introducing a time delay between the laser flash and the neutron test pulse.
20. Visualized detection of single-base difference in multiplexed loop-mediated isothermal amplification amplicons by invasive reaction coupled with oligonucleotide probe-modified gold nanoparticles.
PubMed
Lu, Yan; Ma, Xueping; Wang, Jianping; Sheng, Nan; Dong, Tianhui; Song, Qinxin; Rui, Jianzhong; Zou, Bingjie; Zhou, Guohua
2017-04-15
Loop-mediated isothermal amplification (LAMP) is a well-developed DNA amplification method with an ultra-high sensitivity, but it is difficult to recognize a single-base difference (like genotyping) in target-specific amplicons by conventional detection ways, such as the intercalation of dyes into dsDNA amplicons or the increase of solution turbidity along with the polymerization process. To allow genotyping based on LAMP suitable for POCT (point-of-care testing) or on-site testing, here we proposed a highly specific and cost-effective method for detecting a single-base difference in LAMP amplicons. The method includes three key steps, sequence amplifier to amplify multiple fragments containing the single nucleotide polymorphisms (SNPs) of interest, allele identifier to recognize a targeted base in the amplicons by invasive reaction, and signal generator to yield signals by hybridization-induced assembly of oligonucleotide probe-modified gold nanoparticles. Because the allele identifier is sensitive to one base difference, it is possible to use multiplexed LAMP (mLAMP) to generate amplicon mixtures for multiple SNP typing. Genotyping of 3 different SNPs (CYP2C19*2, CYP2C19*3 and MDR1-C3435T) for guiding the dosage of clopidogrel is successfully carried out in a 3-plex LAMP on real clinical samples. As our method relies on the naked-eye detection and constant-temperature reaction, no expensive instrument is required for both target amplification and sequence identification, thus much suitable for inexpensive gene-guided personalized medicine in source-limited regions.
1. General, mild, and intermolecular Ullmann-type synthesis of diaryl and alkyl aryl ethers catalyzed by diol-copper(I) complex.
PubMed
Naidu, Ajay B; Jaseer, E A; Sekar, Govindasamy
2009-05-15
A wide range of diaryl ethers and alkyl aryl ethers are synthesized through intermolecular C(aryl)-O bond formation from the corresponding aryl iodides/aryl bromides and phenols/alcohols through Ullmann-type coupling reaction in the presence of a catalytic amount of easily available (+/-)-diol L3-CuI complex under very mild reaction conditions. Less reactive aryl bromides can also be used for O-arylation of phenols under the same reaction conditions without increasing the reaction temperature, catalyst loading, and time. The catalytic system not only is capable of coupling hindered substrate but also tolerates a broad range of a series of functional groups.
2. Meeting the Challenge of Intermolecular Gold(I)-Catalyzed Cycloadditions of Alkynes and Allenes
PubMed Central
Muratore, Michael E; Homs, Anna; Obradors, Carla; Echavarren, Antonio M
2014-01-01
The development of gold(I)-catalyzed intermolecular carbo- and hetero-cycloadditions of alkynes and allenes has been more challenging than their intramolecular counterparts. Here we review, with a mechanistic perspective, the most fundamental intermolecular cycloadditions of alkynes and allenes with alkenes. PMID:25048645
3. The use of intermolecular potential functions in fitting pressure induced spectra
NASA Technical Reports Server (NTRS)
Goorvitch, D.; Silvaggio, P. M.; Boese, R. W.
1981-01-01
An example is presented which demonstrates the importance of using physically realistic derivatives of the intermolecular potential when fitting pressure-induced spectra. The use of nonrealistic derivatives may mask second-order temperature effects in the theory. As the temperature decreases, the intermolecular potential may have an important angular dependence.
4. Intermolecular interactions in rifabutin—2-hydroxypropyl-β-cyclodextrin—water solutions
Anshakova, A. V.; Yermolenko, Yu. V.; Konyukhov, V. Yu.; Polshakov, V. I.; Maksimenko, O. O.; Gelperina, S. E.
2015-05-01
The possibility of a intermolecular complex rifabutin (RB)-2-hydroxypropyl-β-cyclodextrin (HP-β-CD) formed as a result of the interaction of the piperidine fragment of the RB molecule and the hydrophobic cavity of the HP-β-CD molecule was found. The stability constant of the intermolecular complex was determined.
5. Quantifying intra- and intermolecular phenomena: challenging yet exciting territory for quantum chemistry.
PubMed
Corminboeuf, Clémence
2014-01-01
van der Waals interactions occur in all molecules and intermolecular complexes but are poorly described by the most widely used electronic structure framework. This paper addresses the efforts pursued in our laboratory to improve the performance of standard density functional approximations and deliver modern strategies to analyze and fine-tune the underlying physics of intra- and intermolecular interactions.
6. Problem-Based Learning in 9th Grade Chemistry Class: "Intermolecular Forces"
ERIC Educational Resources Information Center
Tarhan, Leman; Ayar-Kayali, Hulya; Urek, Raziye Ozturk; Acar, Burcin
2008-01-01
This research study aims to examine the effectiveness of a problem-based learning (PBL) on 9th grade students' understanding of intermolecular forces (dipole-dipole forces, London dispersion forces and hydrogen bonding). The student's alternate conceptions about intermolecular bonding and their beliefs about PBL were also measured. Seventy-eight…
7. Problem-Based Learning in 9th Grade Chemistry Class: "Intermolecular Forces"
ERIC Educational Resources Information Center
Tarhan, Leman; Ayar-Kayali, Hulya; Urek, Raziye Ozturk; Acar, Burcin
2008-01-01
This research study aims to examine the effectiveness of a problem-based learning (PBL) on 9th grade students' understanding of intermolecular forces (dipole-dipole forces, London dispersion forces and hydrogen bonding). The student's alternate conceptions about intermolecular bonding and their beliefs about PBL were also measured. Seventy-eight…
8. High pressure luminescence probes in polymers
SciTech Connect
Drickamer, H.G.
1980-01-01
High pressure luminescence has proved to be a very powerful tool for characterizing crystalline solids and liquids. Two problems involving glassy polymers are analyzed. In the first problem the excited states of azulene and its derivatives are used to probe intermolecular interactions in PMMA and PS. In the second problem the change in emission intensity with pressure from two excimer states of polyvinylcarbazole as a pure polymer and in dilute solution in polystyrene (PS), polymethylmethacrylate (PMMA) and polyisoliutylene (PIB) is studied. The relative emission from the two states depends strongly on the possibility for motion of polymer segments. The observations are related to the proximity to the glass transition.
9. Wave-wave and wave-particle interactions in the inner magnetosphere measured with Van Allen Probes: cross coupling between wave modes and its effect on radiation belt dynamics
Colpitts, C. A.; Cattell, C. A.; Broughton, M.; Engebretson, M. J.
2015-12-01
We will show observations of waveform bursts using the Electric Field and Waves (EFW) burst data on the Van Allen Probes satellites with intermediate frequency waves such as whistler mode, magnetosonic and lower hybrid. These observations show very strong modulation of these waves by lower frequency waves such as EMIC or ULF. We are analyzing the burst data and cross coupling between wave modes to determine how prevalent the cross coupling between wave modes is and under what conditions it occurs. To supplement the EFW data, each satellite is also equipped with a full complement of particle instruments, including the HOPE instrument measuring lower energy (1 eV - 50 keV) particles and MagEIS instruments measuring higher energy (20 keV - 5 MeV) particles. The energy and angular resolution of these detectors are sufficient to resolve the scattering and energization arising from the distinct wave modes, using the signatures in the trapped electron populations predicted by theory for the various mechanisms. Comparison of the burst waveform data with the electron data from HOPE and MagEIS, for times with and without coupling between the wave modes, will allow us to identify how the cross coupling affects electron dynamics in the radiation belts. The significance of wave-particle interactions in the formation and depletion of the radiation belts has long been established, but is still not completely understood. Specifically, pitch angle scattering from waves such as plasmaspheric hiss and electromagnetic ion cyclotron [EMIC] waves near the duskside plasmapause is known to contribute to electron loss from the radiation belts, primarily through precipitation into the atmosphere. Higher frequency waves such as whistler mode chorus and magnetosonic waves observed near the equator in the lower hybrid frequency range are widely believed to be primary means for electron energization. However, these and other competing processes often occur simultaneously, and an accurate model
10. Structural variability and the nature of intermolecular interactions in Watson-Crick B-DNA base pairs.
PubMed
Czyznikowska, Z; Góra, R W; Zaleśny, R; Lipkowski, P; Jarzembska, K N; Dominiak, P M; Leszczynski, J
2010-07-29
A set of nearly 100 crystallographic structures was analyzed using ab initio methods in order to verify the effect of the conformational variability of Watson-Crick guanine-cytosine and adenine-thymine base pairs on the intermolecular interaction energy and its components. Furthermore, for the representative structures, a potential energy scan of the structural parameters describing mutual orientation of the base pairs was carried out. The results were obtained using the hybrid variational-perturbational interaction energy decomposition scheme. The electron correlation effects were estimated by means of the second-order Møller-Plesset perturbation theory and coupled clusters with singles and doubles method adopting AUG-cc-pVDZ basis set. Moreover, the characteristics of hydrogen bonds in complexes, mimicking those appearing in B-DNA, were evaluated using topological analysis of the electron density. Although the first-order electrostatic energy is usually the largest stabilizing component, it is canceled out by the associated exchange repulsion in majority of the studied crystallographic structures. Therefore, the analyzed complexes of the nucleic acid bases appeared to be stabilized mainly by the delocalization component of the intermolecular interaction energy which, in terms of symmetry adapted perturbation theory, encompasses the second- and higher-order induction and exchange-induction terms. Furthermore, it was found that the dispersion contribution, albeit much smaller in terms of magnitude, is also a vital stabilizing factor. It was also revealed that the intermolecular interaction energy and its components are strongly influenced by four (out of six) structural parameters describing mutual orientation of bases in Watson-Crick pairs, namely shear, stagger, stretch, and opening. Finally, as a part of a model study, much of the effort was devoted to an extensive testing of the UBDB databank. It was shown that the databank quite successfully reproduces the
11. Vibrational dynamics of aqueous hydroxide solutions probed using broadband 2DIR spectroscopy
Mandal, Aritra; Tokmakoff, Andrei
2015-11-01
We employed ultrafast transient absorption and broadband 2DIR spectroscopy to study the vibrational dynamics of aqueous hydroxide solutions by exciting the O-H stretch vibrations of the strongly hydrogen-bonded hydroxide solvation shell water and probing the continuum absorption of the solvated ion between 1500 and 3800 cm-1. We observe rapid vibrational relaxation processes on 150-250 fs time scales across the entire probed spectral region as well as slower vibrational dynamics on 1-2 ps time scales. Furthermore, the O-H stretch excitation loses its frequency memory in 180 fs, and vibrational energy exchange between bulk-like water vibrations and hydroxide-associated water vibrations occurs in ˜200 fs. The fast dynamics in this system originate in strong nonlinear coupling between intra- and intermolecular vibrations and are explained in terms of non-adiabatic vibrational relaxation. These measurements indicate that the vibrational dynamics of the aqueous hydroxide complex are faster than the time scales reported for long-range transport of protons in aqueous hydroxide solutions.
12. Vibrational dynamics of aqueous hydroxide solutions probed using broadband 2DIR spectroscopy
SciTech Connect
Mandal, Aritra; Tokmakoff, Andrei
2015-11-21
We employed ultrafast transient absorption and broadband 2DIR spectroscopy to study the vibrational dynamics of aqueous hydroxide solutions by exciting the O–H stretch vibrations of the strongly hydrogen-bonded hydroxide solvation shell water and probing the continuum absorption of the solvated ion between 1500 and 3800 cm{sup −1}. We observe rapid vibrational relaxation processes on 150–250 fs time scales across the entire probed spectral region as well as slower vibrational dynamics on 1–2 ps time scales. Furthermore, the O–H stretch excitation loses its frequency memory in 180 fs, and vibrational energy exchange between bulk-like water vibrations and hydroxide-associated water vibrations occurs in ∼200 fs. The fast dynamics in this system originate in strong nonlinear coupling between intra- and intermolecular vibrations and are explained in terms of non-adiabatic vibrational relaxation. These measurements indicate that the vibrational dynamics of the aqueous hydroxide complex are faster than the time scales reported for long-range transport of protons in aqueous hydroxide solutions.
13. Complexities of bloom dynamics in the toxic dinoflagellate Alexandrium fundyense revealed through DNA measurements by imaging flow cytometry coupled with species-specific rRNA probes
PubMed Central
Brosnahan, Michael L.; Farzan, Shahla; Keafer, Bruce A.; Sosik, Heidi M.; Olson, Robert J.; Anderson, Donald M.
2013-01-01
Measurements of the DNA content of different protist populations can shed light on a variety of processes, including cell division, sex, prey ingestion, and parasite invasion. Here, we modified an Imaging FlowCytobot (IFCB), a custom-built flow cytometer that records images of microplankton, to measure the DNA content of large dinoflagellates and other high-DNA content species. The IFCB was also configured to measure fluorescence from Cy3-labeled rRNA probes, aiding the identification of Alexandrium fundyense (syn. A. tamarense Group I), a photosynthetic dinoflagellate that causes paralytic shellfish poisoning (PSP). The modified IFCB was used to analyze samples from the development, peak and termination phases of an inshore A. fundyense bloom (Salt Pond, Eastham, MA USA), and from a rare A. fundyense ‘red tide’ that occurred in the western Gulf of Maine, offshore of Portsmouth, NH (USA). Diploid or G2 phase (‘2C’) A. fundyense cells were frequently enriched at the near-surface, suggesting an important role for aggregation at the air-sea interface during sexual events. Also, our analysis showed that large proportions of A. fundyense cells in both the Salt Pond and red tide blooms were planozygotes during bloom decline, highlighting the importance of sexual fusion to bloom termination. At Salt Pond, bloom decline also coincided with a dramatic rise in infections by the parasite genus Amoebophrya. The samples that were most heavily infected contained many large cells with higher DNA-associated fluorescence than 2C vegetative cells, but these cells’ nuclei were also frequently consumed by Amoebophrya trophonts. Neither large cell size nor increased DNA-associated fluorescence could be replicated by infecting an A. fundyense culture of vegetative cells. Therefore we attribute these characteristics of the large Salt Pond cells to planozygote maturation rather than Amoebophrya infection, though an interaction between infection and planozygote maturation may
14. Complexities of bloom dynamics in the toxic dinoflagellate Alexandrium fundyense revealed through DNA measurements by imaging flow cytometry coupled with species-specific rRNA probes
Brosnahan, Michael L.; Farzan, Shahla; Keafer, Bruce A.; Sosik, Heidi M.; Olson, Robert J.; Anderson, Donald M.
2014-05-01
Measurements of the DNA content of different protist populations can shed light on a variety of processes, including cell division, sex, prey ingestion, and parasite invasion. Here, we modified an Imaging FlowCytobot (IFCB), a custom-built flow cytometer that records images of microplankton, to measure the DNA content of large dinoflagellates and other high-DNA content species. The IFCB was also configured to measure fluorescence from Cy3-labeled rRNA probes, aiding the identification of Alexandrium fundyense (syn. A. tamarense Group I), a photosynthetic dinoflagellate that causes paralytic shellfish poisoning (PSP). The modified IFCB was used to analyze samples from the development, peak and termination phases of an inshore A. fundyense bloom (Salt Pond, Eastham, MA, USA), and from a rare A. fundyense ‘red tide’ that occurred in the western Gulf of Maine, offshore of Portsmouth, NH (USA). Diploid or G2 phase (‘2C’) A. fundyense cells were frequently enriched at the near-surface, suggesting an important role for aggregation at the air-sea interface during sexual events. Also, our analysis showed that large proportions of A. fundyense cells in both the Salt Pond and red tide blooms were planozygotes during bloom decline, highlighting the importance of sexual fusion to bloom termination. At Salt Pond, bloom decline also coincided with a dramatic rise in infections by the parasite genus Amoebophrya. The samples that were most heavily infected contained many large cells with higher DNA-associated fluorescence than 2C vegetative cells, but these cells' nuclei were also frequently consumed by Amoebophrya trophonts. Neither large cell size nor increased DNA-associated fluorescence could be replicated by infecting an A. fundyense culture of vegetative cells. Therefore, we attribute these characteristics of the large Salt Pond cells to planozygote maturation rather than Amoebophrya infection, though an interaction between infection and planozygote maturation may
15. Diffusion and molecular interactions in a methanol/polyimide system probed by coupling time-resolved FTIR spectroscopy with gravimetric measurements.
PubMed
Musto, Pellegrino; Galizia, Michele; La Manna, Pietro; Pannico, Marianna; Mensitieri, Giuseppe
2014-01-01
In this contribution the diffusion of methanol in a commercial polyimide (PMDA-ODA) is studied by coupling gravimetric measurements with in-situ, time-resolved FTIR spectroscopy. The spectroscopic data have been treated with two complementary techniques, i.e., difference spectroscopy (DS) and least-squares curve fitting (LSCF). These approaches provided information about the overall diffusivity, the nature of the molecular interactions among the system components and the dynamics of the various molecular species. Additional spectroscopic measurements on thin film samples (about 2 μm) allowed us to identify the interaction site on the polymer backbone and to propose likely structures for the H-bonding aggregates. Molar absorptivity values from a previous literature report allowed us to estimate the population of first-shell and second-shell layers of methanol in the polymer matrix. In terms of diffusion kinetics, the gravimetric and spectroscopic estimates of the diffusion coefficients were found to be in good agreement with each other and with previous literature reports. A Fickian behavior was observed throughout, with diffusivity values markedly affected by the total concentration of sorbed methanol.
16. Transport-related triplet states and hyperfine couplings in organic tandem solar cells probed by pulsed electrically detected magnetic resonance spectroscopy.
PubMed
Kraffert, Felix; Bahro, Daniel; Meier, Christoph; Denne, Maximilian; Colsmann, Alexander; Behrends, Jan
2017-09-01
Tandem solar cells constitute the most successful organic photovoltaic devices with power conversion efficiencies comparable to thin-film silicon solar cells. Especially their high open-circuit voltage - only achievable by a well-adjusted layer stacking - leads to their high efficiencies. Nevertheless, the microscopic processes causing the lossless recombination of charge carriers within the recombination zone are not well understood yet. We show that advanced pulsed electrically detected magnetic resonance techniques such as electrically detected (ED)-Rabi nutation measurements and electrically detected hyperfine sublevel correlation (ED-HYSCORE) spectroscopy help to understand the role of triplet excitons in these microscopic processes. We investigate fully working miniaturised organic tandem solar cells and detect current-influencing doublet states in different layers as well as triplet excitons located on the fullerene-based acceptor. We apply ED-HYSCORE in order to study the nuclear spin environment of the relevant electron/hole spins and detect a significant amount of the low abundant (13)C nuclei coupled to the observer spins. Copyright © 2017 Elsevier Inc. All rights reserved.
17. Probing the photoexcited states of rhodium corroles by time-resolved Q-band EPR. Observation of strong spin-orbit coupling effects.
PubMed
Rozenshtein, V; Wagnert, L; Berg, A; Stavitski, E; Berthold, T; Kothe, G; Saltsman, I; Gross, Z; Levanon, H
2008-06-19
The photoexcited states of two 5,10,15-tris(pentafluorophenyl)corroles (tpfc), hosting Rh(III) in their core, namely Rh(pyr)(PPh 3)(tpfc) and Rh(PPh 3)(tpfc), have been studied by time-resolved electron paramagnetic resonance (TREPR) combined with pulsed laser excitation. Using the transient nutation technique, the spin polarized spectra are assigned to photoexcited triplet states. The spectral widths observed for the two Rh(III) corroles crucially depend on the axial ligands at the Rh(III) metal ion. In case of Rh(PPh 3)(tpfc), the TREPR spectra are found to extend over 200 mT, which exceeds the spectral width of non-transition-metal corroles by more than a factor of 3. Moreover, the EPR lines of the Rh(III) corroles are less symmetric than those of the non-transition-metal corrroles. The peculiarities in the TREPR spectra of the Rh(III) corroles can be rationalized in terms of strong spin-orbit coupling (SOC) associated with the transition-metal character of the Rh(III) ion. It is assumed that SOC in the photoexcited Rh(III) corroles effectively admixes metal centered (3)dd-states to the corrole centered (3)pipi*-states detected in the TREPR experiments. This admixture leads to an increased zero-field splitting and a large g-tensor anisotropy as manifested by the excited Rh(III) corroles.
18. Diffusion and molecular interactions in a methanol/polyimide system probed by coupling time-resolved FTIR spectroscopy with gravimetric measurements
PubMed Central
Musto, Pellegrino; Galizia, Michele; La Manna, Pietro; Pannico, Marianna; Mensitieri, Giuseppe
2013-01-01
In this contribution the diffusion of methanol in a commercial polyimide (PMDA-ODA) is studied by coupling gravimetric measurements with in-situ, time-resolved FTIR spectroscopy. The spectroscopic data have been treated with two complementary techniques, i.e., difference spectroscopy (DS) and least-squares curve fitting (LSCF). These approaches provided information about the overall diffusivity, the nature of the molecular interactions among the system components and the dynamics of the various molecular species. Additional spectroscopic measurements on thin film samples (about 2 μm) allowed us to identify the interaction site on the polymer backbone and to propose likely structures for the H-bonding aggregates. Molar absorptivity values from a previous literature report allowed us to estimate the population of first-shell and second-shell layers of methanol in the polymer matrix. In terms of diffusion kinetics, the gravimetric and spectroscopic estimates of the diffusion coefficients were found to be in good agreement with each other and with previous literature reports. A Fickian behavior was observed throughout, with diffusivity values markedly affected by the total concentration of sorbed methanol. PMID:24809042
19. Transport-related triplet states and hyperfine couplings in organic tandem solar cells probed by pulsed electrically detected magnetic resonance spectroscopy
Kraffert, Felix; Bahro, Daniel; Meier, Christoph; Denne, Maximilian; Colsmann, Alexander; Behrends, Jan
2017-09-01
Tandem solar cells constitute the most successful organic photovoltaic devices with power conversion efficiencies comparable to thin-film silicon solar cells. Especially their high open-circuit voltage - only achievable by a well-adjusted layer stacking - leads to their high efficiencies. Nevertheless, the microscopic processes causing the lossless recombination of charge carriers within the recombination zone are not well understood yet. We show that advanced pulsed electrically detected magnetic resonance techniques such as electrically detected (ED)-Rabi nutation measurements and electrically detected hyperfine sublevel correlation (ED-HYSCORE) spectroscopy help to understand the role of triplet excitons in these microscopic processes. We investigate fully working miniaturised organic tandem solar cells and detect current-influencing doublet states in different layers as well as triplet excitons located on the fullerene-based acceptor. We apply ED-HYSCORE in order to study the nuclear spin environment of the relevant electron/hole spins and detect a significant amount of the low abundant 13C nuclei coupled to the observer spins.
20. Probing the Role of Interlayer Coupling and Coulomb Interactions on Electronic Structure in Few-Layer MoSe 2 Nanostructures
DOE PAGES
2015-03-16
Despite the weak nature of interlayer forces in transition metal dichalcogenide (TMD) materials, their properties are highly dependent on the number of layers in the few-layer two-dimensional (2D) limit. Here, we present a combined scanning tunneling microscopy/spectroscopy and GW theoretical study of the electronic structure of high quality single- and few-layer MoSe2 grown on bilayer graphene. We find that the electronic (quasiparticle) bandgap, a fundamental parameter for transport and optical phenomena, decreases by nearly one electronvolt when going from one layer to three due to interlayer coupling and screening effects. Our results paint a clear picture of the evolution ofmore » the electronic wave function hybridization in the valleys of both the valence and conduction bands as the number of layers is changed. This demonstrates the importance of layer number and electron-electron interactions on van der Waals heterostructures and helps to clarify how their electronic properties might be tuned in future 2D nanodevices.« less
1. Probing the Role of Interlayer Coupling and Coulomb Interactions on Electronic Structure in Few-Layer MoSe 2 Nanostructures
SciTech Connect
Bradley, Aaron J.; M. Ugeda, Miguel; da Jornada, Felipe H.; Qiu, Diana Y.; Ruan, Wei; Zhang, Yi; Wickenburg, Sebastian; Riss, Alexander; Lu, Jiong; Mo, Sung-Kwan; Hussain, Zahid; Shen, Zhi-Xun; Louie, Steven G.; Crommie, Michael F.
2015-03-16
Despite the weak nature of interlayer forces in transition metal dichalcogenide (TMD) materials, their properties are highly dependent on the number of layers in the few-layer two-dimensional (2D) limit. Here, we present a combined scanning tunneling microscopy/spectroscopy and GW theoretical study of the electronic structure of high quality single- and few-layer MoSe2 grown on bilayer graphene. We find that the electronic (quasiparticle) bandgap, a fundamental parameter for transport and optical phenomena, decreases by nearly one electronvolt when going from one layer to three due to interlayer coupling and screening effects. Our results paint a clear picture of the evolution of the electronic wave function hybridization in the valleys of both the valence and conduction bands as the number of layers is changed. This demonstrates the importance of layer number and electron-electron interactions on van der Waals heterostructures and helps to clarify how their electronic properties might be tuned in future 2D nanodevices.
2. Gold Nanoparticle Internal Structure and Symmetry Probed by Unified Small-Angle X-ray Scattering and X-ray Diffraction Coupled with Molecular Dynamics Analysis.
PubMed
Fleury, Blaise; Cortes-Huerto, Robinson; Taché, Olivier; Testard, Fabienne; Menguy, Nicolas; Spalla, Olivier
2015-09-09
Shape and size are known to determine a nanoparticle's properties. Hardly ever studied in synthesis, the internal crystal structure (i.e., particle defects, crystallinity, and symmetry) is just as critical as shape and size since it directly impacts catalytic efficiency, plasmon resonance, and orients anisotropic growth of metallic nanoparticles. Hence, its control cannot be ignored any longer in today's research and applications in nanotechnology. This study implemented an unprecedented reliable measurement combining these three structural aspects. The unified small-angle X-ray scattering and diffraction measurement (SAXS/XRD) was coupled with molecular dynamics to allow simultaneous determination of nanoparticles' shape, size, and crystallinity at the atomic scale. Symmetry distribution (icosahedra-Ih, decahedra-Dh, and truncated octahedra-TOh) of 2-6 nm colloidal gold nanoparticles synthesized in organic solvents was quantified. Nanoparticle number density showed the predominance of Ih, followed by Dh, and little, if any, TOh. This result contradicts some theoretical predictions and highlights the strong effect of the synthesis environment on structure stability. We foresee that this unified SAXS/XRD analysis, yielding both statistical and quantitative counts of nanoparticles' symmetry distribution, will provide new insights into nanoparticle formation, growth, and assembly.
3. Isotope Probing of the UDP‐Apiose/UDP‐Xylose Synthase Reaction: Evidence of a Mechanism via a Coupled Oxidation and Aldol Cleavage
PubMed Central
Eixelsberger, Thomas; Horvat, Doroteja; Gutmann, Alexander; Weber, Hansjörg
2017-01-01
Abstract The C‐branched sugar d‐apiose (Api) is essential for plant cell‐wall development. An enzyme‐catalyzed decarboxylation/pyranoside ring‐contraction reaction leads from UDP‐α‐d‐glucuronic acid (UDP‐GlcA) to the Api precursor UDP‐α‐d‐apiose (UDP‐Api). We examined the mechanism of UDP‐Api/UDP‐α‐d‐xylose synthase (UAXS) with site‐selectively 2H‐labeled and deoxygenated substrates. The analogue UDP‐2‐deoxy‐GlcA, which prevents C‐2/C‐3 aldol cleavage as the plausible initiating step of pyranoside‐to‐furanoside conversion, did not give the corresponding Api product. Kinetic isotope effects (KIEs) support an UAXS mechanism in which substrate oxidation by enzyme‐NAD+ and retro‐aldol sugar ring‐opening occur coupled in a single rate‐limiting step leading to decarboxylation. Rearrangement and ring‐contracting aldol addition in an open‐chain intermediate then give the UDP‐Api aldehyde, which is intercepted via reduction by enzyme‐NADH. PMID:28102965
4. PROBING THE CARBON–PHOSPHORUS BOND COUPLING IN LOW-TEMPERATURE PHOSPHINE (PH{sub 3})–METHANE (CH{sub 4}) INTERSTELLAR ICE ANALOGUES
SciTech Connect
Turner, Andrew M.; Abplanalp, Matthew J.; Kaiser, Ralf I.
2016-03-10
Phosphine, which has now been confirmed around the carbon-rich star IRC+10216, provides the first example of a phosphorus-containing single bond in interstellar or circumstellar media. While four compounds containing both phosphorus and carbon have been discovered, none contain a carbon–phosphorus single bond. Here, we show that this moiety is plausible from the reaction of phosphine with methane in electron-irradiated interstellar ice analogues. Fractional sublimation allows for detection of individual products at distinct temperatures using reflectron time-of-flight mass spectrometry (ReTOF) coupled with vacuum ultraviolet photoionization. This method produced phosphanes and methylphosphanes as large as P{sub 8}H{sub 10} and CH{sub 3}P{sub 8}H{sub 9}, which demonstrates that a phosphorus–carbon bond can readily form and that methylphosphanes sublime at 12–17 K higher temperatures than the non-organic phosphanes. Also, irradiated ices of phosphine with deuterated-methane untangle the reaction pathways through which these methylphosphanes were formed and identified radical recombination to be preferred over carbene/phosphinidene insertion reactions. In addition, these ReTOF results confirm that CH{sub 3}PH{sub 2} and CH{sub 6}P{sub 2} can form via insertion of carbene and phosphinidene and that the methylenediphosphine (PH{sub 2}CH{sub 2}PH{sub 2}) isomer forms in the ices, although methylphosphine (CH{sub 3}P{sub 2}H{sub 3}) is likely the more abundant isomer and that phosphanes and organophosphanes preferentially fragment via the loss of a phosphino group when photoionized. While the formation of methylphosphine is overall endoergic, the intermediates produced by interactions with energetic electrons proceed toward methylphosphine favorably and barrierlessly and provide plausible mechanisms toward hitherto unidentified interstellar compounds.
5. Electrophoresis-mass spectrometry probe
DOEpatents
Andresen, Brian D.; Fought, Eric R.
1987-01-01
The invention involves a new technique for the separation of complex mixtures of chemicals, which utilizes a unique interface probe for conventional mass spectrometers which allows the electrophoretically separated compounds to be analyzed in real-time by a mass spectrometer. This new chemical analysis interface, which couples electrophoresis with mass spectrometry, allows complex mixtures to be analyzed very rapidly, with much greater specificity, and with greater sensitivity. The interface or probe provides a means whereby large and/or polar molecules in complex mixtures to be completely characterized. The preferred embodiment of the probe utilizes a double capillary tip which allows the probe tip to be continually wetted by the buffer, which provides for increased heat dissipation, and results in a continually operating interface which is more durable and electronically stable than the illustrated single capillary tip probe interface.
6. Electrophoresis-mass spectrometry probe
DOEpatents
Andresen, B.D.; Fought, E.R.
1987-11-10
The invention involves a new technique for the separation of complex mixtures of chemicals, which utilizes a unique interface probe for conventional mass spectrometers which allows the electrophoretically separated compounds to be analyzed in real-time by a mass spectrometer. This new chemical analysis interface, which couples electrophoresis with mass spectrometry, allows complex mixtures to be analyzed very rapidly, with much greater specificity, and with greater sensitivity. The interface or probe provides a means whereby large and/or polar molecules in complex mixtures to be completely characterized. The preferred embodiment of the probe utilizes a double capillary tip which allows the probe tip to be continually wetted by the buffer, which provides for increased heat dissipation, and results in a continually operating interface which is more durable and electronically stable than the illustrated single capillary tip probe interface. 8 figs.
7. Excitonic couplings between molecular crystal pairs by a multistate approximation
SciTech Connect
Aragó, Juan Troisi, Alessandro
2015-04-28
In this paper, we present a diabatization scheme to compute the excitonic couplings between an arbitrary number of states in molecular pairs. The method is based on an algebraic procedure to find the diabatic states with a desired property as close as possible to that of some reference states. In common with other diabatization schemes, this method captures the physics of the important short-range contributions (exchange, overlap, and charge-transfer mediated terms) but it becomes particularly suitable in presence of more than two states of interest. The method is formulated to be usable with any level of electronic structure calculations and to diabatize different types of states by selecting different molecular properties. These features make the diabatization scheme presented here especially appropriate in the context of organic crystals, where several excitons localized on the same molecular pair may be found close in energy. In this paper, the method is validated on the tetracene crystal dimer, a well characterized case where the charge transfer (CT) states are closer in energy to the Frenkel excitons (FE). The test system was studied as a function of an external electric field (to explore the effect of changing the relative energy of the CT excited state) and as a function of different intermolecular distances (to probe the strength of the coupling between FE and CT states). Additionally, we illustrate how the approximation can be used to include the environment polarization effect.
8. Astrophysical probes of fundamental physics
Martins, C. J. A. P.
2009-10-01
I review the motivation for varying fundamental couplings and discuss how these measurements can be used to constrain fundamental physics scenarios that would otherwise be inaccessible to experiment. I highlight the current controversial evidence for varying couplings and present some new results. Finally I focus on the relation between varying couplings and dark energy, and explain how varying coupling measurements might be used to probe the nature of dark energy, with some advantages over standard methods. In particular I discuss what can be achieved with future spectrographs such as ESPRESSO and CODEX.
9. Ice-Borehole Probe
NASA Technical Reports Server (NTRS)
Behar, Alberto; Carsey, Frank; Lane, Arthur; Engelhardt, Herman
2006-01-01
An instrumentation system has been developed for studying interactions between a glacier or ice sheet and the underlying rock and/or soil. Prior borehole imaging systems have been used in well-drilling and mineral-exploration applications and for studying relatively thin valley glaciers, but have not been used for studying thick ice sheets like those of Antarctica. The system includes a cylindrical imaging probe that is lowered into a hole that has been bored through the ice to the ice/bedrock interface by use of an established hot-water-jet technique. The images acquired by the cameras yield information on the movement of the ice relative to the bedrock and on visible features of the lower structure of the ice sheet, including ice layers formed at different times, bubbles, and mineralogical inclusions. At the time of reporting the information for this article, the system was just deployed in two boreholes on the Amery ice shelf in East Antarctica and after successful 2000 2001 deployments in 4 boreholes at Ice Stream C, West Antarctica, and in 2002 at Black Rapids Glacier, Alaska. The probe is designed to operate at temperatures from 40 to +40 C and to withstand the cold, wet, high-pressure [130-atm (13.20-MPa)] environment at the bottom of a water-filled borehole in ice as deep as 1.6 km. A current version is being outfitted to service 2.4-km-deep boreholes at the Rutford Ice Stream in West Antarctica. The probe (see figure) contains a sidelooking charge-coupled-device (CCD) camera that generates both a real-time analog video signal and a sequence of still-image data, and contains a digital videotape recorder. The probe also contains a downward-looking CCD analog video camera, plus halogen lamps to illuminate the fields of view of both cameras. The analog video outputs of the cameras are converted to optical signals that are transmitted to a surface station via optical fibers in a cable. Electric power is supplied to the probe through wires in the cable at a
10. Oriented covalent immobilization of antibodies for measurement of intermolecular binding forces between zipper-like contact surfaces of split inteins
PubMed Central
Sorci, Mirco; Dassa, Bareket; Liu, Hongwei; Anand, Gaurav; Dutta, Amit K.; Pietrokovski, Shmuel; Belfort, Marlene; Belfort, Georges
2013-01-01
In order to measure the intermolecular binding forces between two halves (or partners) of naturally split protein splicing elements called inteins, a novel thiol-hydrazide linker was designed and used to orient immobilized antibodies specific for each partner. Activation of the surfaces was achieved in one step allowing direct force measurements of the formation of a peptide bond catalyzed by the binding of the two partners of the split intein (called protein trans-splicing). Through this binding process, a whole functional intein is formed resulting in subsequent splicing. Atomic force microscopy (AFM) was used to directly measure the split intein partner binding at 1µm/s between native (wild-type) and mixed pairs of C- and N-terminal partners of naturally occurring split inteins from three cyanobacteria. Native and mixed pairs exhibit similar binding forces within the error of the measurement technique (~52 pN). Bioinformatic sequence analysis and computational structural analysis discovered a zipper-like contact between the two partners with electrostatic and non-polar attraction between multiple aligned ion pairs and hydrophobic residues. Also, we tested the Jarzynski’s equality and demonstrated, as expected, that non-equilibrium dissipative measurements obtained here gave larger energies of interaction as compared with those for equilibrium. Hence, AFM coupled with our immobilization strategy and computational studies provides a useful analytical tool for the direct measurement of intermolecular association of split inteins and could be extended to any interacting protein pair. PMID:23679912
11. A quantum chemical study of H2S2: Intramolecular torsional mode and intermolecular interactions with rare gases
Maciel, Glauciete S.; Barreto, Patricia R. P.; Palazzetti, Federico; Lombardi, Andrea; Aquilanti, Vincenzo
2008-10-01
The structural and energetic properties of the H2S2 molecule have been studied using density functional theory, second-order Møller-Plesset method, and coupled cluster theory with several basis sets. In order to extend previous work on intra- and intermolecular dynamics of the chirality changing modes for H2O2 and its derivatives, our focus has been on the torsion around the S-S bond, along with an extensive characterization of the intermolecular potentials of H2S2 with the rare gases (He, Ne, Ar, and Kr). Use is made of previously defined coordinates and expansion formulas for the potentials which allow for a faithful representation of geometrical and symmetry properties of these systems that involve the interaction of an atom with a floppy molecule. The potential energy surfaces obtained in this work are useful for classical and quantum mechanical simulations of molecular collisions responsible for chirality changing processes of possible interest in the modeling of prebiotic phenomena.
12. Ab initio intermolecular potential energy surfaces for the Ar-NCCN van der Waals complexes
2014-11-01
The intermolecular potential energy surface of complex pairing argon with cyanogen molecule (NCCN) was calculated using the coupled cluster with single and double and perturbative triple excitations (CCSD(T)) with aug-cc-pvdz basis set extended with a set of mid-bond (3s3p2d1f1g) functions. The interaction energies were calculated by the supermolecular approach with the full counterpoise correction for the basis set superposition error. The calculated potential energies were fitted to an analytical expression. The calculated Ar-NCCN potential energy surface shows a global minimum at 3.35 Å, the distance between argon and centre of mass of cyanogen, for the T-shaped geometry and two local minimum at distance of 5.54 Å for the linear geometry on one side of cyanogen. Finally, the interaction second virial coefficients were calculated using the fitted potential energy surface and were compared with those obtained by the parameters of the Beattie-Bridgeman equation of states of pure argon and cyanogens fluids, approximately.
13. Intermolecular forces between low generation PAMAM dendrimer condensed DNA helices: role of cation architecture.
PubMed
An, Min; Parkin, Sean R; DeRouchey, Jason E
2014-01-28
In recent years, dendriplexes, complexes of cationic dendrimers with DNA, have become attractive DNA delivery vehicles due to their well-defined chemistries. To better understand the nature of the forces condensing dendriplexes, we studied low generation poly(amidoamine) (PAMAM) dendrimer-DNA complexes and compared them to comparably charged linear arginine peptides. Using osmotic stress coupled with X-ray scattering, we have investigated the effect of molecular chain architecture on DNA-DNA intermolecular forces that determine the net attraction and equilibrium interhelical distance within these polycation condensed DNA arrays. In order to compact DNA, linear cations are believed to bind in DNA grooves and to interact with the phosphate backbone of apposing helices. We have previously shown a length dependent attraction resulting in higher packaging densities with increasing charge for linear cations. Hyperbranched polycations, such as polycationic dendrimers, presumably would not be able to bind to DNA and correlate their charges in the same manner as linear cations. We show that attractive and repulsive force amplitudes in PAMAM-DNA assemblies display significantly different trends than comparably charged linear arginines resulting in lower DNA packaging densities with increasing PAMAM generation. The salt and pH dependencies of packaging in PAMAM dendrimer-DNA and linear arginine-DNA complexes were also investigated. Significant differences in the force curve behaviour and salt and pH sensitivities suggest that different binding modes may be present in DNA condensed by dendrimers when compared to linear polycations.
14. Liquid chloroform structure from computer simulation with a full ab initio intermolecular interaction potential
Yin, Chih-Chien; Li, Arvin Huang-Te; Chao, Sheng D.
2013-11-01
We have calculated the intermolecular interaction energies of the chloroform dimer in 12 orientations using the second-order Møller-Plesset perturbation theory. Single point energies of important geometries were calibrated by the coupled cluster with single and double and perturbative triple excitation method. Dunning's correlation consistent basis sets up to aug-cc-pVQZ have been employed in extrapolating the interaction energies to the complete basis set limit values. With the ab initio potential data we constructed a 5-site force field model for molecular dynamics simulations. We compared the simulation results with recent experiments and obtained quantitative agreements for the detailed atomwise radial distribution functions. Our results were also consistent with previous results using empirical force fields with polarization effects. Moreover, the calculated diffusion coefficients reproduced the experimental data over a wide range of thermodynamic conditions. To the best of our knowledge, this is the first ab initio force field which is capable of competing with existing empirical force fields for liquid chloroform.
15. Intercalation of organic molecules in 2D copper (II) nitroprusside: Intermolecular interactions and magnetic properties
SciTech Connect
Osiry, H.; Cano, A.; Lemus-Santana, A.A.; Rodríguez, A.; Carbonio, R.E.; Reguera, E.
2015-10-15
This contribution discusses the intercalation of imidazole and its 2-ethyl derivative, and pyridine in 2D copper nitroprusside. In the interlayer region, neighboring molecules remain interacting throu gh their dipole and quadrupole moments, which supports the solid 3D crystal structure. The crystal structure of this series of intercalation compounds was solved and refined from powder X-ray diffraction patterns complemented with spectroscopic information. The intermolecular interactions were studied from the refined crystal structures and low temperature magnetic measurements. Due to strong attractive forces between neighboring molecules, the resulting π–π cloud overlapping enables the ferromagnetic coupling between metal centers on neighboring layers, which was actually observed for the solids containing imidazole and pyridine as intercalated molecules. For these two solids, the magnetic data were properly described with a model of six neighbors. For the solid containing 2-ethylimidazole and for 2D copper nitroprusside, a model of four neighbors in a plane is sufficient to obtain a reliable data fitting. - Highlights: • Intercalation of organic molecules in 2D copper (II) nitroprusside. • Molecular properties of intercalation compounds of 2D copper (II) nitroprusside. • Magnetic properties of hybrid inorganic–organic solids. • Hybrid inorganic–organic 3D framework.
16. Ground state analytical ab initio intermolecular potential for the Cl{sub 2}-water system
SciTech Connect
Hormain, Laureline; Monnerville, Maurice Toubin, Céline; Duflot, Denis; Pouilly, Brigitte; Briquez, Stéphane; Bernal-Uruchurtu, Margarita I.; Hernández-Lamoneda, Ramón
2015-04-14
The chlorine/water interface is of crucial importance in the context of atmospheric chemistry. Modeling the structure and dynamics at this interface requires an accurate description of the interaction potential energy surfaces. We propose here an analytical intermolecular potential that reproduces the interaction between the Cl{sub 2} molecule and a water molecule. Our functional form is fitted to a set of high level ab initio data using the coupled-cluster single double (triple)/aug-cc-p-VTZ level of electronic structure theory for the Cl{sub 2} − H{sub 2}O complex. The potential fitted to reproduce the three minima structures of 1:1 complex is validated by the comparison of ab initio results of Cl{sub 2} interacting with an increasing number of water molecules. Finally, the model potential is used to study the physisorption of Cl{sub 2} on a perfectly ordered hexagonal ice slab. The calculated adsorption energy, in the range 0.27 eV, shows a good agreement with previous experimental results.
17. Resolution enhancement in in vivo NMR spectroscopy: detection of intermolecular zero-quantum coherences
Faber, Cornelius; Pracht, Eberhard; Haase, Axel
2003-04-01
Intermolecular zero-quantum coherences are insensitive to magnetic field inhomogeneities. For this reason we have applied the HOMOGENIZED sequence [Vathyam et al., Science 272 (1996) 92] to phantoms containing metabolites at low concentrations, phantoms with air inclusions, an intact grape, and the head of a rat in vivo at 750 MHz. In the 1H-spectra, the water signal is efficiently suppressed and line broadening due to susceptibility gradients is effectively removed along the indirectly detected dimension. We have obtained a 1H-spectrum of a 2.5 mM solution of γ-aminobutyric acid in 12 min scan time. In the phantom with air inclusions a reduction of line widths from 0.48 ppm in the direct dimension to 0.07 ppm in the indirect dimension was observed, while in a deshimmed grape the reduction was from 1.4 to 0.07 ppm. In a spectrum of the grape we were able to resolve glucose resonances at 0.3 ppm from the water in 6 min scan time. J-coupling information was partly retained. In the in vivo spectra of the rat brain five major metabolites were observed.
18. Impact of Intermolecular Distance on Singlet Fission in a Series of TIPS Pentacene Compounds.
PubMed
Wu, Yishi; Liu, Ke; Liu, Huiying; Zhang, Yi; Zhang, Haoli; Yao, Jiannian; Fu, Hongbing
2014-10-16
Singlet fission has attracted considerable interest for its potential application in organic photovoltaics. However, the underlying microscopic mechanism is not well understood and the molecular parameters that govern SF efficiency remain unclear. We herein study the primary exciton photogeneration and evolution in the thin film of a series of pentacene derivatives (TIPS-Pn and ADPD-Pn) using femtosecond transient absorption spectroscopy. With a favorable "long-edge on" packing motif, the singlet-excited slip-stacked TIPS-Pn and ADPD-Pn molecules undergo ultrafast fission to produce triplet excitonic states with time constants of ∼0.3 ps. More importantly, the ADPD-Pn compound features a considerably higher triplet yield than TIPS-Pn (162 ± 10% vs 114 ± 15%). The enhanced electronic coupling as a result of closer interchromophore distance (3.33 Å for ADPD-Pn vs 3.40 Å for TIPS-Pn) is suggested to account for the much higher triplet yield for ADPD-Pn relative to that for TIPS-Pn, proving SF can be readily modulated by adjusting the intermolecular distance.
19. Role of Amino Acid Insertions on Intermolecular Forces between Arginine Peptide Condensed DNA Helices
PubMed Central
DeRouchey, Jason E.; Rau, Donald C.
2011-01-01
In spermatogenesis, chromatin histones are replaced by arginine-rich protamines to densely compact DNA in sperm heads. Tight packaging is considered necessary to protect the DNA from damage. To better understand the nature of the forces condensing protamine-DNA assemblies and their dependence on amino acid content, the effect of neutral and negatively charged amino acids on DNA-DNA intermolecular forces was studied using model peptides containing six arginines. We have previously observed that the neutral amino acids in salmon protamine decrease the net attraction between protamine-DNA helices compared with the equivalent homo-arginine peptide. Using osmotic stress coupled with x-ray scattering, we have investigated the component attractive and repulsive forces that determine the net attraction and equilibrium interhelical distance as a function of the chemistry, position, and number of the amino acid inserted. Neutral amino acids inserted into hexa-arginine increase the short range repulsion while only slightly affecting longer range attraction. The amino acid content alone of salmon protamine is enough to rationalize the forces that package DNA in sperm heads. Inserting a negatively charged amino acid into hexa-arginine dramatically weakens the net attraction. Both of these observations have biological implications for protamine-DNA packaging in sperm heads. PMID:21994948
20. Infrared Chemical Nano-Imaging: Accessing Structure, Coupling, and Dynamics on Molecular Length Scales
SciTech Connect
Muller, Eric A.; Pollard, Benjamin; Raschke, Markus Bernd
2015-04-02
This Perspective highlights recent advances in infrared vibrational chemical nano-imaging. In its implementations of scattering scanning near-field optical microscopy (s-SNOM) and photothermal-induced resonance (PTIR), IR nanospectroscopy provides few-nanometer spatial resolution for the investigation of polymer, biomaterial, and related soft-matter surfaces and nanostructures. Broad-band IR s-SNOM with coherent laser and synchrotron sources allows for chemical recognition with small-ensemble sensitivity and the potential for sensitivity reaching the single-molecule limit. Probing selected vibrational marker resonances, it gives access to nanoscale chemical imaging of composition, domain morphologies, order/disorder, molecular orientation, or crystallographic phases. Local intra- and intermolecular coupling can be measured through frequency shifts of a vibrational marker in heterogeneous environments and associated inhomogeneities in vibrational dephasing. In combination with ultrafast spectroscopy, the vibrational coherent evolution of homogeneous sub-ensembles coupled to their environment can be observed. Outstanding challenges are discussed in terms of extensions to coherent and multidimensional spectroscopies, implementation in liquid and in situ environments, general sample limitations, and engineering s-SNOM scanning probes to better control the nano-localized optical excitation and to increase sensitivity.
1. Effect of donor orientation on ultrafast intermolecular electron transfer in coumarin-amine systems
SciTech Connect
Singh, P. K.; Nath, S.; Bhasikuttan, A. C.; Kumbhakar, M.; Mohanty, J.; Sarkar, S. K.; Mukherjee, T.; Pal, H.
2008-09-21
Effect of donor amine orientation on nondiffusive ultrafast intermolecular electron transfer (ET) reactions in coumarin-amine systems has been investigated using femtosecond fluorescence upconversion measurements. Intermolecular ET from different aromatic and aliphatic amines used as donor solvents to the excited coumarin-151 (C151) acceptor occurs with ultrafast rates such that the shortest fluorescence lifetime component ({tau}{sub 1}) is the measure of the fastest ET rate ({tau}{sub 1}={tau}{sub ET}{sup fast}=(k{sub ET}{sup fast}){sup -1}), assigned to the C151-amine contact pairs in which amine donors are properly oriented with respect to C151 to maximize the acceptor-donor electronic coupling (V{sub el}). It is interestingly observed that as the amine solvents are diluted by suitable diluents (either keeping solvent dielectric constant similar or with increasing dielectric constant), the {tau}{sub 1} remains almost in the similar range as long as the amine dilution does not cross a certain critical limit, which in terms of the amine mole fraction (x{sub A}) is found to be {approx}0.4 for aromatic amines and {approx}0.8 for aliphatic amines. Beyond these dilutions in the two respective cases of the amine systems, the {tau}{sub 1} values are seen to increase very sharply. The large difference in the critical x{sub A} values involving aromatic and aliphatic amine donors has been rationalized in terms of the largely different orientational restrictions for the ET reactions as imposed by the aliphatic (n-type) and aromatic ({pi}-type) nature of the amine donors [A. K. Satpati et al., J. Mol. Struct. 878, 84 (2008)]. Since the highest occupied molecular orbital (HOMO) of the n-type aliphatic amines is mostly centralized at the amino nitrogen, only some specific orientations of these amines with respect to the close-contact acceptor dye [also of {pi}-character; A. K. Satpati et al., J. Mol. Struct. 878, 84 (2008) and E. W. Castner et al., J. Phys. Chem. A 104, 2869
2. Pollution Probe.
ERIC Educational Resources Information Center
Chant, Donald A.
This book is written as a statement of concern about pollution by members of Pollution Probe, a citizens' anti-pollution group in Canada. Its purpose is to create public awareness and pressure for the eventual solution to pollution problems. The need for effective government policies to control the population explosion, conserve natural resources,…
3. Pollution Probe.
ERIC Educational Resources Information Center
Chant, Donald A.
This book is written as a statement of concern about pollution by members of Pollution Probe, a citizens' anti-pollution group in Canada. Its purpose is to create public awareness and pressure for the eventual solution to pollution problems. The need for effective government policies to control the population explosion, conserve natural resources,…
4. Phosphite-oxazole/imidazole ligands in asymmetric intermolecular Heck reaction.
PubMed
Mazuela, Javier; Tolstoy, Paivi; Pàmies, Oscar; Andersson, Pher G; Diéguez, Montserrat
2011-02-07
We describe the application of a new class of ligands--the phosphite-oxazole/imidazole (L1-L5a-g)--in asymmetric intermolecular Pd-catalyzed Heck reactions under thermal and microwave conditions. These ligands combine the advantages of the oxazole/imidazole moiety with those of the phosphite moiety: they are more stable than their oxazoline counterparts, less sensitive to air and other oxidizing agents than phosphines and phosphinites, and easy to synthesize from readily available alcohols. The results indicate that activities, regio- and enantioselectivities, are highly influenced by the type of nitrogen donor group (oxazole or imidazole), the oxazole and biaryl-phosphite substituents and the axial chirality of the biaryl moiety of the ligand. By carefully selecting the ligand components, we achieved high activities, regio- (up to 99%) and enantioselectivities (up to 99%) using several triflate sources. Under microwave-irradiation conditions, reaction times were considerably shorter (from 24 h to 30 min) and regio- and enantioselectivities were still excellent.
5. Thermal selectivity of intermolecular versus intramolecular reactions on surfaces.
PubMed
Cirera, Borja; Giménez-Agulló, Nelson; Björk, Jonas; Martínez-Peña, Francisco; Martin-Jimenez, Alberto; Rodriguez-Fernandez, Jonathan; Pizarro, Ana M; Otero, Roberto; Gallego, José M; Ballester, Pablo; Galan-Mascaros, José R; Ecija, David
2016-03-11
On-surface synthesis is a promising strategy for engineering heteroatomic covalent nanoarchitectures with prospects in electronics, optoelectronics and photovoltaics. Here we report the thermal tunability of reaction pathways of a molecular precursor in order to select intramolecular versus intermolecular reactions, yielding monomeric or polymeric phthalocyanine derivatives, respectively. Deposition of tetra-aza-porphyrin species bearing ethyl termini on Au(111) held at room temperature results in a close-packed assembly. Upon annealing from room temperature to 275 °C, the molecular precursors undergo a series of covalent reactions via their ethyl termini, giving rise to phthalocyanine tapes. However, deposition of the tetra-aza-porphyrin derivatives on Au(111) held at 300 °C results in the formation and self-assembly of monomeric phthalocyanines. A systematic scanning tunnelling microscopy study of reaction intermediates, combined with density functional calculations, suggests a [2+2] cycloaddition as responsible for the initial linkage between molecular precursors, whereas the monomeric reaction is rationalized as an electrocyclic ring closure.
6. Thermal selectivity of intermolecular versus intramolecular reactions on surfaces
PubMed Central
Cirera, Borja; Giménez-Agulló, Nelson; Björk, Jonas; Martínez-Peña, Francisco; Martin-Jimenez, Alberto; Rodriguez-Fernandez, Jonathan; Pizarro, Ana M.; Otero, Roberto; Gallego, José M.; Ballester, Pablo; Galan-Mascaros, José R.; Ecija, David
2016-01-01
On-surface synthesis is a promising strategy for engineering heteroatomic covalent nanoarchitectures with prospects in electronics, optoelectronics and photovoltaics. Here we report the thermal tunability of reaction pathways of a molecular precursor in order to select intramolecular versus intermolecular reactions, yielding monomeric or polymeric phthalocyanine derivatives, respectively. Deposition of tetra-aza-porphyrin species bearing ethyl termini on Au(111) held at room temperature results in a close-packed assembly. Upon annealing from room temperature to 275 °C, the molecular precursors undergo a series of covalent reactions via their ethyl termini, giving rise to phthalocyanine tapes. However, deposition of the tetra-aza-porphyrin derivatives on Au(111) held at 300 °C results in the formation and self-assembly of monomeric phthalocyanines. A systematic scanning tunnelling microscopy study of reaction intermediates, combined with density functional calculations, suggests a [2+2] cycloaddition as responsible for the initial linkage between molecular precursors, whereas the monomeric reaction is rationalized as an electrocyclic ring closure. PMID:26964764
7. Polyelectrolyte brushes in mixed ionic medium studied via intermolecular forces
Farina, Robert; Laugel, Nicolas; Pincus, Philip; Tirrell, Matthew
2011-03-01
The vast uses and applications of polyelectrolyte brushes make them an attractive field of research especially with the growing interest in responsive materials. Polymers which respond via changes in temperature, pH, and ionic strength are increasingly being used for applications in drug delivery, chemical gating, etc. When polyelectrolyte brushes are found in either nature (e.g., surfaces of cartilage and mammalian lung interiors) or commercially (e.g., skin care products, shampoo, and surfaces of medical devices) they are always surrounded by mixed ionic medium. This makes the study of these brushes in varying ionic environments extremely relevant for both current and future potential applications. The polyelectrolyte brushes in this work are diblock co-polymers of poly-styrene sulfonate (N=420) and poly-t-butyl styrene (N=20) which tethers to a hydrophobic surface allowing for a purely thermodynamic study of the polyelectrolyte chains. Intermolecular forces between two brushes are measured using the SFA. As multi-valent concentrations are increased, the brushes collapse internally and form strong adhesion between one another after contact (properties not seen in a purely mono-valent environment).
8. Intermolecular Structural Change for Thermo-Switchable Polymeric photosensitizer
SciTech Connect
Park, Wooram; Park, Sin-Jung; Cho, Soojeong; Shin, Heejun; Jung, Young-Seok; Lee, Byeongdu; Na, Kun; Kim, Dong-Hyun
2016-08-31
A switchable photosensitizer (PS), which can be activated at a spe-cific condition beside light, has tremendous advantages for photo-dynamic therapy (PDT). Herein, we developed a thermo-switchable polymeric photosensitizer (T-PPS) by conjugating PS (Pheophor-bide-a, PPb-a) to a temperature-responsive polymer backbone of biocompatible hydroxypropyl cellulose (HPC). Self-quenched PS molecules linked in close proximity by pi-pi stacking in T-PPS were easily transited to an active monomeric state by the tempera-ture induced phase transition of polymer backbones. The tempera-ture responsive inter-molecular interaction changes of PS molecules in T-PPS were demonstrated in synchrotron small-angle X-ray scattering (SAXS) and UV-Vis spectrophotometer analysis. The T-PPS allowed switchable activation and synergistically enhanced cancer cell killing effect at the hyperthermia temperature (45 °C). Our developed T-PPS has the considerable potential not only as a new class of photomedicine in clinics but also as a biosensor based on temperature responsiveness.
9. Thermal selectivity of intermolecular versus intramolecular reactions on surfaces
Cirera, Borja; Giménez-Agulló, Nelson; Björk, Jonas; Martínez-Peña, Francisco; Martin-Jimenez, Alberto; Rodriguez-Fernandez, Jonathan; Pizarro, Ana M.; Otero, Roberto; Gallego, José M.; Ballester, Pablo; Galan-Mascaros, José R.; Ecija, David
2016-03-01
On-surface synthesis is a promising strategy for engineering heteroatomic covalent nanoarchitectures with prospects in electronics, optoelectronics and photovoltaics. Here we report the thermal tunability of reaction pathways of a molecular precursor in order to select intramolecular versus intermolecular reactions, yielding monomeric or polymeric phthalocyanine derivatives, respectively. Deposition of tetra-aza-porphyrin species bearing ethyl termini on Au(111) held at room temperature results in a close-packed assembly. Upon annealing from room temperature to 275 °C, the molecular precursors undergo a series of covalent reactions via their ethyl termini, giving rise to phthalocyanine tapes. However, deposition of the tetra-aza-porphyrin derivatives on Au(111) held at 300 °C results in the formation and self-assembly of monomeric phthalocyanines. A systematic scanning tunnelling microscopy study of reaction intermediates, combined with density functional calculations, suggests a [2+2] cycloaddition as responsible for the initial linkage between molecular precursors, whereas the monomeric reaction is rationalized as an electrocyclic ring closure.
10. Noncovalent Intermolecular Forces in Phycobilisomes of Porphyridium cruentum.
PubMed
Zilinskas, B A; Glick, R E
1981-08-01
Using sensitized fluorescence as a measure of intactness of phycobilisomes isolated from Porphyridium cruentum, the effects of various environmental perturbations on phycobilisome integrity were investigated. The rate of phycobilisome dissociation in 0.75 ionic strength sodium salts proceeds in the order: SCN(-) > NO(3) (-) > Cl(-) > C(6)H(5)O(7) (3-) > SO(4) (2-) > PO(4) (3-), as predicted from the lyotropic series of anions and their effects on hydrophobic interactions in proteins. Similarly, increasing temperature (to 30 C) and pH values approaching the isoelectric points of the biliproteins stabilize phycobilisomes. Deuterium substitution at exchangeable sites on the phycobiliproteins decreases the rate of phycobilisome dissociation, while substitution at nonexchangeable sites increases rates of dissociation. It is concluded that hydrophobic intermolecular interactions are the most important forces in maintaining the phycobilisome structure. Dispersion forces also seem to contribute to phycobilisome stabilization. The adverse effects of electrostatic repulsion must not be ignored; however, it seems that the requirement of phycobilisomes of high salt concentrations is not simply countershielding of charges on the proteins.
11. Intermolecular forces between the motor protein and the filament.
PubMed
Suda, H; Taylor, T W
1993-03-07
Intermolecular forces between motor proteins and filaments were evaluated on the basis of the experimental data of an in vitro motility assay by considering the molecular friction in the movement system. The molecular friction was caused by a different mechanism from that of the hydrodynamic drag. However, the molecular frictional forces apparently gave the same expression as the hydrodynamic frictional forces. The resulting equation was very effective in examining the physical properties of the weak interaction in the dynein-microtubules system from basic experiments carried out by Vale et al. (1989). From careful analysis of their experimental data, it was concluded that the hydrodynamic friction was not dominant, even in the weak binding state. The electrostatic interaction between dynein-heads and microtubules in the weak binding state was analyzed by applying the DLVO (Derjaguin-Landau-Verway-Overbeek) theory in colloid science through the ionic dependence of one-dimensional diffusion. The interacting distance between charges which took part in the weak adhesion was estimated to be 3 nm. In the present study, the molecular mechanism of the sliding velocity was also investigated for the myosin-actin filaments and the kinesin-microtubules systems by fitting the ATP-dependence and the ionic dependence in ATP-driven active sliding.
12. Resonant Auger decay driving intermolecular Coulombic decay in molecular dimers.
PubMed
Trinter, F; Schöffler, M S; Kim, H-K; Sturm, F P; Cole, K; Neumann, N; Vredenborg, A; Williams, J; Bocharova, I; Guillemin, R; Simon, M; Belkacem, A; Landers, A L; Weber, Th; Schmidt-Böcking, H; Dörner, R; Jahnke, T
2014-01-30
In 1997, it was predicted that an electronically excited atom or molecule placed in a loosely bound chemical system (such as a hydrogen-bonded or van-der-Waals-bonded cluster) could efficiently decay by transferring its excess energy to a neighbouring species that would then emit a low-energy electron. This intermolecular Coulombic decay (ICD) process has since been shown to be a common phenomenon, raising questions about its role in DNA damage induced by ionizing radiation, in which low-energy electrons are known to play an important part. It was recently suggested that ICD can be triggered efficiently and site-selectively by resonantly core-exciting a target atom, which then transforms through Auger decay into an ionic species with sufficiently high excitation energy to permit ICD to occur. Here we show experimentally that resonant Auger decay can indeed trigger ICD in dimers of both molecular nitrogen and carbon monoxide. By using ion and electron momentum spectroscopy to measure simultaneously the charged species created in the resonant-Auger-driven ICD cascade, we find that ICD occurs in less time than the 20 femtoseconds it would take for individual molecules to undergo dissociation. Our experimental confirmation of this process and its efficiency may trigger renewed efforts to develop resonant X-ray excitation schemes for more localized and targeted cancer radiation therapy.
13. Localized-overlap approach to calculations of intermolecular interactions
Rob, Fazle
Symmetry-adapted perturbation theory (SAPT) based on the density functional theory (DFT) description of the monomers [SAPT(DFT)] is one of the most robust tools for computing intermolecular interaction energies. Currently, one can use the SAPT(DFT) method to calculate interaction energies of dimers consisting of about a hundred atoms. To remove the methodological and technical limits and extend the size of the systems that can be calculated with the method, a novel approach has been proposed that redefines the electron densities and polarizabilities in a localized way. In the new method, accurate but computationally expensive quantum-chemical calculations are only applied for the regions where it is necessary and for other regions, where overlap effects of the wave functions are negligible, inexpensive asymptotic techniques are used. Unlike other hybrid methods, this new approach is mathematically rigorous. The main benefit of this method is that with the increasing size of the system the calculation scales linearly and, therefore, this approach will be denoted as local-overlap SAPT(DFT) or LSAPT(DFT). As a byproduct of developing LSAPT(DFT), some important problems concerning distributed molecular response, in particular, the unphysical charge-flow terms were eliminated. Additionally, to illustrate the capabilities of SAPT(DFT), a potential energy function has been developed for an energetic molecular crystal of 1,1-diamino-2,2-dinitroethylene (FOX-7), where an excellent agreement with the experimental data has been found.
14. Cobalt complex of cinchonine: intermolecular interactions in two crystalline modifications.
PubMed
Skórska, Agnieszka; Oleksyn, Barbara J; Sliwiński, Jan
2002-01-01
Two crystalline modifications of cinchonine cobalt complex, C19H23Cl3CoN2O, were obtained from mixture of saturated alcohol solutions of CoCl3 x 6H2O and cinchonine. The X-ray structure analysis revealed that the asymmetric unit of one modification, CoCn1, contains only zwitterionic molecules of the complex. In the asymmetric unit of the other, CoCn2, there are two molecules of the title compound and two molecules of ethanol. The influence of the absolute configuration, the CoCl3 coordination with quinoline, and the presence of alcohol molecules on the studied structures was established by comparison of the crystal and molecular structures of both cobalt complexes with the analogous quinine complex and zinc complex of cinchonine. The interactions that dominate in the packing of the molecules in both structures are intermolecular hydrogen bonds. They form characteristic ring systems, depending on the presence of the alcohol molecules. The ring features are also related to the absolute configuration of the alkaloid.
15. Determination of stepsize parameters for intermolecular vibrational energy transfer
SciTech Connect
Tardy, D.C.
1992-03-01
Intermolecular energy transfer of highly excited polyatomic molecules plays an important role in many complex chemical systems: combustion, high temperature and atmospheric chemistry. By monitoring the relaxation of internal energy we have observed trends in the collisional efficiency ({beta}) for energy transfer as a function of the substrate's excitation energy and the complexities of substrate and deactivator. For a given substrate {beta} increases as the deactivator's mass increase to {approximately}30 amu and then exhibits a nearly constant value; this is due to a mass mismatch between the atoms of the colliders. In a homologous series of substrate molecules (C{sub 3}{minus}C{sub 8}) {beta} decreases as the number of atoms in the substrate increases; replacing F with H increases {beta}. All substrates, except for CF{sub 2}Cl{sub 2} and CF{sub 2}HCl below 10,000 cm{sup {minus}1}, exhibited that {beta} is independent of energy, i.e. <{Delta}E>{sub all} is linear with energy. The results are interpreted with a simple model which considers that {beta} is a function of the ocillators energy and its vibrational frequency. Limitations of current approximations used in high temperature unimolecular reactions were evaluated and better approximations were developed. The importance of energy transfer in product yields was observed for the photoactivation of perfluorocyclopropene and the photoproduction of difluoroethyne. 3 refs., 18 figs., 4 tabs.
16. Quantitative tomographic imaging of intermolecular FRET in small animals
PubMed Central
Venugopal, Vivek; Chen, Jin; Barroso, Margarida; Intes, Xavier
2012-01-01
Forster resonance energy transfer (FRET) is a nonradiative transfer of energy between two fluorescent molecules (a donor and an acceptor) in nanometer range proximity. FRET imaging methods have been applied to proteomic studies and drug discovery applications based on intermolecular FRET efficiency measurements and stoichiometric measurements of FRET interaction as quantitative parameters of interest. Importantly, FRET provides information about biomolecular interactions at a molecular level, well beyond the diffraction limits of standard microscopy techniques. The application of FRET to small animal imaging will allow biomedical researchers to investigate physiological processes occurring at nanometer range in vivo as well as in situ. In this work a new method for the quantitative reconstruction of FRET measurements in small animals, incorporating a full-field tomographic acquisition system with a Monte Carlo based hierarchical reconstruction scheme, is described and validated in murine models. Our main objective is to estimate the relative concentration of two forms of donor species, i.e., a donor molecule involved in FRETing to an acceptor close by and a nonFRETing donor molecule. PMID:23243567
17. Cantilevered probe detector with piezoelectric element
SciTech Connect
Adams, Jesse D; Sulchek, Todd A; Feigin, Stuart C
2014-04-29
A disclosed chemical detection system for detecting a target material, such as an explosive material, can include a cantilevered probe, a probe heater coupled to the cantilevered probe, and a piezoelectric element disposed on the cantilevered probe. The piezoelectric element can be configured as a detector and/or an actuator. Detection can include, for example, detecting a movement of the cantilevered probe or a property of the cantilevered probe. The movement or a change in the property of the cantilevered probe can occur, for example, by adsorption of the target material, desorption of the target material, reaction of the target material and/or phase change of the target material. Examples of detectable movements and properties include temperature shifts, impedance shifts, and resonant frequency shifts of the cantilevered probe. The overall chemical detection system can be incorporated, for example, into a handheld explosive material detection system.
18. Cantilevered probe detector with piezoelectric element
DOEpatents
Adams, Jesse D; Sulchek, Todd A; Feigin, Stuart C
2013-04-30
A disclosed chemical detection system for detecting a target material, such as an explosive material, can include a cantilevered probe, a probe heater coupled to the cantilevered probe, and a piezoelectric element disposed on the cantilevered probe. The piezoelectric element can be configured as a detector and/or an actuator. Detection can include, for example, detecting a movement of the cantilevered probe or a property of the cantilevered probe. The movement or a change in the property of the cantilevered probe can occur, for example, by adsorption of the target material, desorption of the target material, reaction of the target material and/or phase change of the target material. Examples of detectable movements and properties include temperature shifts, impedance shifts, and resonant frequency shifts of the cantilevered probe. The overall chemical detection system can be incorporated, for example, into a handheld explosive material detection system.
19. Cantilevered probe detector with piezoelectric element
DOEpatents
Adams, Jesse D.; Sulchek, Todd A.; Feigin, Stuart C.
2010-04-06
A disclosed chemical detection system for detecting a target material, such as an explosive material, can include a cantilevered probe, a probe heater coupled to the cantilevered probe, and a piezoelectric element disposed on the cantilevered probe. The piezoelectric element can be configured as a detector and/or an actuator. Detection can include, for example, detecting a movement of the cantilevered probe or a property of the cantilevered probe. The movement or a change in the property of the cantilevered probe can occur, for example, by adsorption of the target material, desorption of the target material, reaction of the target material and/or phase change of the target material. Examples of detectable movements and properties include temperature shifts, impedance shifts, and resonant frequency shifts of the cantilevered probe. The overall chemical detection system can be incorporated, for example, into a handheld explosive material detection system.
20. Cantilevered probe detector with piezoelectric element
DOEpatents
Adams, Jesse D; Sulchek, Todd A; Feigin, Stuart C
2013-04-30
A disclosed chemical detection system for detecting a target material, such as an explosive material, can include a cantilevered probe, a probe heater coupled to the cantilevered probe, and a piezoelectric element disposed on the cantilevered probe. The piezoelectric element can be configured as a detector and/or an actuator. Detection can include, for example, detecting a movement of the cantilevered probe or a property of the cantilevered probe. The movement or a change in the property of the cantilevered probe can occur, for example, by adsorption of the target material, desorption of the target material, reaction of the target material and/or phase change of the target material. Examples of detectable movements and properties include temperature shifts, impedance shifts, and resonant frequency shifts of the cantilevered probe. The overall chemical detection system can be incorporated, for example, into a handheld explosive material detection system.
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https://www.sosto.net/205/margins-in-a-latex-document.html
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#linux
Margins in a LaTex document
Yesterday I wanted to modify the margins of a LaTex document: the first thing I tried was simply to modify the following variables:
\oddsidemargin 0.0in
\evensidemargin 0.0in
\textwidth 6.5in
However, this modifies only the width of the document's body but not the width of the header and the footer (I am using the package fancyhdr).
It is possible to fix this problem using the package geometry, like this:
\usepackage[body={6.0in, 9.2in},left=1.25in,right=1.25in]{geometry}
The document attached to this post is a LaTex "template" I use for my the exercise series at school.
Centering elements using CSS
I found this useful page: Centering things.
nome* (massimo 20 caratteri)
e-mail di contatto (non sarà pubblicato)
commento*
Per evitare lo spam, per favore copia questo codice:
ricerca
galleries
clemspace.ch
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https://calculus7.org/tag/iteration/
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Iterating the logistic map: limsup of nonperiodic orbits
Last time we found that when a sequence with ${x_1\in (0,1)}$ and ${x_{n+1} = 4x_n(1-x_n)}$ does not become periodic, its upper limit ${\limsup x_n}$ must be at least ${\approx 0.925}$. This time we’ll see that ${\limsup x_n}$ can be as low as ${(2+\sqrt{3})/4\approx 0.933}$ and determine for which ${x_1}$ it is equal to 1.
The quadratic polynomial ${f(x)=4x(1-x)}$ maps the interval ${[0,1]}$ onto itself. Since the linear function ${g(x) = 1-2x}$ maps ${[0,1]}$ onto ${[-1,1]}$, it follows that the composition ${h=g\circ f\circ g^{-1}}$ maps ${[-1,1]}$ onto ${[-1,1]}$. This composition is easy to compute: ${h(x) = 2x^2-1 }$.
We want to know whether the iteration of ${f}$, starting from ${x_1}$, produces numbers arbitrarily close to ${1}$. Since ${f\circ f \circ \cdots \circ f = g^{-1}\circ h \circ h \circ \cdots \circ h\circ g}$ the goal is equivalent to finding whether the iteration of ${h}$, starting from ${g(x_1)}$, produces numbers arbitrarily close to ${g(1) = -1}$. To shorten formulas, let’s write ${h_n}$ for the ${n}$th iterate of ${h}$, for example, ${h_3 = h\circ h\circ h}$.
So far we traded one quadratic polynomial ${f}$ for another, ${h}$. But ${h}$ satisfies a nice identity: ${h(\cos t)=2\cos^2 t-1 = \cos(2t)}$, hence ${h_n(\cos t) = \cos (2^n t)}$ for all ${n\in\mathbb N}$. It’s convenient to introduce ${\alpha = \frac{1}{\pi}\cos^{-1}(1-2x_1)}$, so that ${ h_n(g(x_1)) = h_n(\cos 2\pi \alpha ) = \cos(2^n\cdot 2\pi \alpha) }$.
The problem becomes to determine whether the numbers ${2^n\cdot 2\pi \alpha}$ come arbitrarily close to ${\pi}$, modulo an integer multiple of ${2\pi}$. Dividing by ${2\pi}$ rephrases this as: does the fractional part of ${2^n \alpha}$ come arbitrarily close to ${1/2}$?
A number that is close to ${1/2}$ has the binary expansion beginning either with ${0.01111111\dots}$ or with ${0.10000000\dots}$. Since the binary expansion of ${2^n\alpha}$ is just the binary expansion of ${\alpha}$ shifted ${n}$ digits to the left, the property ${\limsup x_n=1}$ is equivalent to the following: for every ${k\in\mathbb N}$ the binary expansion of ${\alpha}$ has infinitely many groups of the form “1 followed by k zeros” or “0 followed by k ones”.
A periodic expansion cannot have the above property; this, ${\alpha}$ must be irrational. The property described above can then be simplified to “irrational and has arbitrarily long runs of the same digit”, since a long run of ${0}$s will be preceded by a ${1}$, and vice versa.
For example, combining the pairs 01 and 10 in some non-periodic way, we get an irrational number ${\alpha}$ such that the fractional part of ${2^n\alpha}$ does not get any closer to 1/2 than ${0.01\overline{10}_2 = 5/12}$ or ${0.10\overline{01}_2 = 7/12}$. Hence, ${\cos 2^n 2\pi \alpha \ge -\sqrt{3}/2}$, which leads to the upper bound ${x_n\le (2+\sqrt{3})/4\approx 0.933}$ for the sequence with the starting value ${x_1=(1-\cos\pi\alpha)/2}$.
Let us summarize the above observations about ${\limsup x_n}$.
Theorem: ${\limsup x_n=1}$ if and only if (A) the number ${\alpha = \frac{1}{\pi}\cos^{-1}(1-2x_1)}$ is irrational, and (B) the binary expansion of ${\alpha}$ has arbitrarily long runs of the same digit.
Intuitively, one expects that a number that satisfies (A) will also satisfy (B) unless it was constructed specifically to fail (B). But to verify that (B) holds for a given number is not an easy task.
As a bonus, let’s prove that for every rational number ${y\in (-1,1)}$, except 0, 1/2 and -1/2, the number ${\alpha = \frac{1}{\pi}\cos^{-1}y}$ is irrational. This will imply, in particular, that ${x_1=1/3}$ yields a non-periodic sequence. The proof follows a post by Robert Israel and requires a lemma (which could be replaced with an appeal to Chebyshev polynomials, but the lemma keeps things self-contained).
Lemma. For every ${n\in \mathbb N}$ there exists a monic polynomial ${P_n}$ with integer coefficients such that ${P_n(2 \cos t) = 2\cos nt }$ for all ${t}$.
Proof. Induction, the base case ${n=1}$ being ${P_1(x)=x}$. Assuming the result for integers ${\le n}$, we have ${2 \cos (n+1)t = e^{i(n+1)t} + e^{-i(n+1)t} }$ ${ = (e^{int} + e^{-int})(e^{it} + e^{-it}) - (e^{i(n-1)t} + e^{-i(n-1)t}) }$ ${ = P_n(2 \cos t) (2\cos t) - P_{n-1}(2\cos t) }$
which is a monic polynomial of ${2\cos t}$. ${\Box}$
Suppose that there exists ${n}$ such that ${n\alpha \in\mathbb Z}$. Then ${2\cos(\pi n\alpha)=\pm 2}$. By the lemma, this implies ${P_n(2\cos(\pi \alpha)) =\pm 2}$, that is ${P_n(2y)=\pm 2}$. Since ${2y}$ is a rational root of a monic polynomial with integer coefficients, the Rational Root Theorem implies that it is an integer. ${\Box}$
A limsup exercise: iterating the logistic map
Define the sequence ${\{x_n\}}$ as follows: ${x_1=1/3}$ and ${x_{n+1} = 4x_n(1-x_n)}$ for ${n=1,2,\dots}$. What can we say about its behavior as ${n\rightarrow\infty}$?
The logistic map ${f(x)=4x(1-x)}$ leaves the interval [0,1] invariant (as a set), so ${0\le x_n\le 1}$ for all ${n}$. There are two fixed points: 0 and 3/4.
Can ${x_n}$ ever be 0? If ${n}$ is the first index this happens, then ${x_{n-1}}$ must be ${1}$. Working backwards, we find ${x_{n-2}=1/2}$, and ${x_{n-3}\in \{1/2 \pm \sqrt{2}/4\}}$. But this is impossible since all elements of the sequence are rational. Similarly, if ${n}$ is the first index when ${x_n = 3/4}$, then ${x_{n-1}=1/4}$ and ${x_{n-2}\in \{1/2\pm \sqrt{3}/4\}}$, a contradiction again. Thus, the sequence never stabilizes.
If ${x_n}$ had a limit, it would have to be one of the two fixed points. But both are repelling: ${f'(x) = 4 - 8x}$, so ${|f'(0)|=4>1 }$ and ${|f'(3/4)| = 2 > 1}$. This means that a small nonzero distance to a fixed point will increase under iteration. The only way to converge to a repelling fixed point is to hit it directly, but we already know this does not happen. So the sequence ${\{x_n\}}$ does not converge.
But we can still consider its upper and lower limits. Let’s try to estimate ${S = \limsup x_n}$ from below. Since ${f(x)\ge x}$ for ${x\in [0,3/4]}$, the sequence ${\{x_n\}}$ increases as long as ${x_n\le 3/4}$. Since we know it doesn’t have a limit, it must eventually break this pattern, and therefore exceed 3/4. Thus, ${S\ge 3/4}$.
This can be improved. The second iterate ${f_2(x)=f(f(x))}$ satisfies ${f_2(x)\ge x}$ for ${x}$ between ${3/4}$ and ${a = (5+\sqrt{5})/8 \approx 0.9}$. So, once ${x_n>3/4}$ (which, by above, happens infinitely often), the subsequence ${x_n, x_{n+2}, x_{n+4},\dots}$ increases until it reaches ${a}$. Hence ${S\ge a}$.
The bound ${\limsup x_n\ge a}$ is best possible if the only information about ${x_1}$ is that the sequence ${x_n}$ does not converge. Indeed, ${a}$ is a periodic point of ${f}$, with the corresponding iteration sequence ${\{(5+ (-1)^n\sqrt{5})/8\}}$.
Further improvement is possible if we recall that our sequence is rational and hence cannot hit ${a}$ exactly. By doubling the number of iterations (so that the iterate also fixes ${a}$ but also has positive derivative there) we arrive at the fourth iterate ${f_4}$. Then ${f_4(x)\ge x}$ for ${a\le x\le b}$, where ${b }$ is the next root of ${f_4(x)-x}$ after ${a}$, approximately ${0.925}$. Hence ${S\ge b}$.
This is a colorful illustration of the estimation process (made with Sage): we are covering the line ${y=x}$ with the iterates of ${f}$, so that each subsequent one rises above the line the moment the previous one falls. This improves the lower bound on ${S}$ from 0.75 to 0.9 to 0.92.
Although this process can be continued, the gains diminish so rapidly that it seems unlikely one can get to 1 in this way. In fact, one cannot because we are not using any properties of ${x_1}$ other than “the sequence ${x_n}$ is not periodic.” And it’s not true that ${\limsup x_n = 1}$ for every non-periodic orbit of ${f}$. Let’s return to this later.
From boring to puzzling in 30 iterative steps
The function ${f(x)=2\cos x }$ may be nice and important as a part of trigonometric basis, but there is nothing exciting in its graph:
Let’s look at its iterations ${f^n=f\circ f\circ \dots \circ f}$ where ${n }$ is the number of iterations, not an exponent. Here is the graph of ${f^{14}}$:
A rectangular pattern is already visible above; further iterations only make it stronger. For example, ${f^{30} }$:
It may be impossible to see on the graph, but the rectangles are slightly apart from one another (though of course they are connected by the graph of continuous function). This is easier to see on the histogram of the values ${f^{n}(0) }$ for ${n=0,\dots, 10000 }$, which contains two small gaps in addition to a large one:
What goes on here? The range of ${f}$ on ${[-2,2]}$, as well as the range of any of its iterates, is of course connected: it is the closed interval ${[f^{2}(0),f(0)] = [2 \cos 2, 2]}$. But the second iterate ${f^2=f\circ f}$ also has two invariant subintervals, marked here by horizontal lines:
Namely, they are ${I_1=[f^{2}(0), f^{4}(0)]}$ and ${I_2=[f^{3}(0),2]}$. It is easy to see that ${f(I_1)=I_2}$ and ${f(I_2)=I_1}$. The gap between ${I_1}$ and ${I_2}$ contains the repelling fixed point of ${f}$, approximately ${x=1.03}$. Every orbit except for the fixed point itself is pushed away from this point and is eventually trapped in the cycle between ${I_1}$ and ${I_2}$.
But there is more. A closer look at the fourth iterate reveals smaller invariant subintervals of ${f^4}$. Here is what it does on ${I_2}$:
Here the gap contains a repelling fixed point of ${f^2}$, approximately ${1.8}$. The invariant subintervals of ${I_2}$ are ${I_{21}=[f^{3}(0), f^{7}(0)]}$ and ${I_{22}=[f^9(0), 2]}$. Also, ${I_1}$ contains invariant subintervals ${I_{11}=[f^{2}(0), f^{6}(0)]}$ and ${I_{12}=[f^8(0), f^4(0)]}$. These are the projections of the rectangles in the graph of ${f^{30}}$ onto the vertical axes.
No more such splitting occurs. The histogram of the values of iterates of ${f}$ indeed consists of four disjoint intervals. Can one get a Cantor-type set in this way, starting from some boring function?
Fun with TI-83: billions upon billions of cosines
Okay, maybe not billions. But by taking cosines repeatedly, one can find the solution of the equation ${\cos x = x}$ with high precision in under a minute.
Step 1: Enter any number, for example 0, and press Enter.
Step 2: Enter cos(Ans) and press Enter
Step 3: Keep pushing Enter. (Unfortunately, press-and-hold-to-repeat does not work on TI-83). This will repeatedly execute the command cos(Ans).
After a few iterations, the numbers begin to settle down:
and eventually stabilize at 0.7390851332
Explanation: the graph of cosine meets the line ${y = x}$ at one point: this is a unique fixed point of the function ${f(x)=\cos x}$.
Since the derivative ${f'(x)=-\sin x}$ at the fixed point is less than 1 in absolute value, the fixed point is attracting.
Now try the same with the equation ${10 \cos x =x}$.
This time, the numbers flat out refuse to converge:
Explanation: the graph of ${f(x)=10\cos x}$ meets the line ${y = x}$ at seven point: thus, this function has seven fixed points.
And it so happens that ${|f'(x)|>1}$ at each of those fixed points. This makes them repelling. The sequence has nowhere to converge, because every candidate for the limit pushes it away. All that’s left to it is to jump chaotically around the interval ${[-10,10]}$. Here are the first 1024 terms, plotted with OpenOffice:
Clearly, the distribution of the sequence is not uniform. I divided the interval ${[-10,10]}$ into subintervals of length ${0.05}$ and counted the number of terms falling into each.
What is going on here? Stay tuned.
|
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http://talkstats.com/threads/fleeting-random-thoughts.17635/page-2
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# Fleeting/Random Thoughts
#### spunky
##### Doesn't actually exist
But isn't planning a usable sample size part of sitting down and planning a well-designed experiment? I think it's emphasized too much as the only thing that matters because there are definitely aspects of a study designed that don't get considered nearly as much as they should but sample sizes still plays an important part don't you think?
yeah... i guess i didnt explain myself correctly there. you certainly have a point in the fact that you need to have some idea of how many people, dogs, galaxies, neurons or whatever you're gonna measure but, as you said, at least here in the world of social/behavioural/health sciences, people line outside my office asking for power analysis this and power analysis that and if they're "guaranteed" to get significance if they can get their sample size right and i'm like "no, no, no... focus on your research, on what you should be doing... the research question should guide the analysis and not vice-versa" now, i understand where they're coming from in a way because nowadays a lot of people ask for power stuff to even consider an application for funding, but still... it's weird here how people sometimes grab on to something for dear life and change it into something it was not meant for (like factor analysis, people pretty much get married to their factors)... one aspect that i would love people pay more attention to are confounders or missing variables instead of only sample size and statistical significance... i've been doing a lot of research on suppression effects in multiple regression and i think it's surprising, at least to me, the lengths people go to dump or just blatantly ignore suppression effects in the social sciences...
how's the RA position going, btw?
#### Dason
The RA position is interesting. There are some unique challenges involved with the data and I might end up seeking help from a couple of users here in the future. It should be fun.
#### spunky
##### Doesn't actually exist
hey, glad to hear that... at the risk of sounding too nosey could i ask what are you doing? or what kind of data analysis are you doing?
#### Dason
Right now I'm working with some RNA-seq data trying to find differential expression between control snakes and heat stressed snakes . The design of the experiment (which we weren't consulted on but logistically they were constrained to this design) is less than optimal (story of all research right?).
I'm working solely in R though which makes me happy. When I was consulting I worked almost solely with SAS which is not my platform of choice.
#### trinker
##### ggplot2orBust
2. Why are peer reviewers in psych more interested in pushing their pet theories than, I don't know, actually making useful comments about data analysis?
Peer reviewers actually read the article that's sent to them? You've got one up on others then even if they are pusing pet theories.
#### CowboyBear
##### Super Moderator
Peer reviewers actually read the article that's sent to them? You've got one up on others then even if they are pusing pet theories.
Lol! Guess I should be thankful for small mercies
#### TheEcologist
##### Global Moderator
Wow! Congratulations Dason! And how did it go Link?
I am getting to the point that I should pop the question soon too.... in the next few months I should try and find the courage
Tricky questions like when, where and how are still bothering me though....
#### TheEcologist
##### Global Moderator
Good news: Just got a new house! Got the keys on Friday! Finally moving from a one room apartment to something with a garden..
Bad news: Just when I started working on RBattleship, now I will be spending my free time painting and building stuff
#### Dason
Well that sounds awesome. Congratulations! I can't wait to get a house but it'll probably be quite a few years until that happens.
By the way: a few friends of mine saw my minesweeper clone and loved the idea of implementing games in R. One wants to make a version of "Guess Who" but I'm not sure if they'll actually follow through with that. I also don't know exactly what they planned on doing for the AI of the opponent. I mentioned that to them and said that it really only works well as a multiplayer game without some amazing AI. Then he went on to say "well why not just make it multiplayer". I don't think he really thought much about it...
I worked on the gWidgets version of minesweeper and implemented an option to right click to place flags. I also finally figured out how to change the color of glabels so the numbers can be colored. Sometimes I wish gWidgets was documented a lot better than it currently is (and it's not even that bad of documentation)... there's just a lot there that they don't mention at all in the documentation or the vignette.
#### Lazar
##### Phineas Packard
Lol! Guess I should be thankful for small mercies
bah I just got a review back from a guy who said more or less "how come you did not use this theory. I know it is not based on the area you are studying but....." Drives me bonkers. Trying to figure out how to tell the guy "I did not use the theory because it is irrelavent to this area of research" but in a nice way.
#### Dason
Well just because it's irrelevant doesn't mean you can't use it. Just to be safe you should also stick in some SEM and some HLMs and some GLMs. Then you'll have your bases covered.
#### Lazar
##### Phineas Packard
lol actually it is a sequential logit model using latent predictors with clustered data so I already have all those bases covered
#### CowboyBear
##### Super Moderator
here in the world of social/behavioural/health sciences, people line outside my office asking for power analysis this and power analysis that and if they're "guaranteed" to get significance if they can get their sample size right
This attitude to research really bugs me. Not only is the enterprise oriented towards confirming theory rather than subjecting it to potential falsification, but the researcher actually wants a guarantee that they'll get the result that they want?
I wonder if it's worth asking: But what if your theory is wrong? How will we know that it's wrong? And if it is wrong, does this study you're planning have any realistic chance of showing that your theory is wrong? (remembering that a non-significant p value isn't falsifying evidence, just inconclusive)
IMO figuring out how to subject a social science -type theory to genuinely risky tests with the potential for falsification is rather harder than power level calculations.
(Ok, so I've been reading a bit of Popper lately... )
#### TheEcologist
##### Global Moderator
By the way: a few friends of mine saw my minesweeper clone and loved the idea of implementing games in R. One wants to make a version of "Guess Who" but I'm not sure if they'll actually follow through with that. I also don't know exactly what they planned on doing for the AI of the opponent. I mentioned that to them and said that it really only works well as a multiplayer game without some amazing AI. Then he went on to say "well why not just make it multiplayer". I don't think he really thought much about it...
Oke some random thoughts: The 'multiplayer' option may be more interesting than I first realized. You know it may be useful if there was a way to run two R sessions on multiple pc's simultaneously in one synced workspace (besides it use for gaming), you establish a connection between two machines and you can work on data with your collaborators/supervisor simultaneously. This kind of thing is getting pretty popular and can be darn useful when your collaborator lives in another continent. Guess it would work through VPN.. or something.
#### Dason
Nice! My wife and I were looking for ways to get some additional income. I've been wanting to do some more teaching for a while (I love my RA but teaching is something I miss terribly). What do I hear about today? An elementary statistics course that needs a teacher at the hospital! I talked to the contact here at the department and I got a number to call and it looks like I got the job. I guess the person they was going to teach the course had to cancel at the last minute so they were pretty desperately looking for somebody.
*Excited*
#### TheEcologist
##### Global Moderator
Nice! My wife and I were looking for ways to get some additional income. I've been wanting to do some more teaching for a while (I love my RA but teaching is something I miss terribly). What do I hear about today? An elementary statistics course that needs a teacher at the hospital! I talked to the contact here at the department and I got a number to call and it looks like I got the job. I guess the person they was going to teach the course had to cancel at the last minute so they were pretty desperately looking for somebody.
*Excited*
Congratulations! I bet you will be a great teacher, through teaching the basics I have learned so much. its surprising how much you can learn from questions of people who are trying to understand stats
Today, I am just frustrated that those grant deadlines always seem to sneak up on you ;-) Its evening and I'm still at the university.... oh well.
#### Dragan
##### Super Moderator
Nice! My wife and I were looking for ways to get some additional income. I've been wanting to do some more teaching for a while (I love my RA but teaching is something I miss terribly). What do I hear about today? An elementary statistics course that needs a teacher at the hospital! I talked to the contact here at the department and I got a number to call and it looks like I got the job. I guess the person they was going to teach the course had to cancel at the last minute so they were pretty desperately looking for somebody.
*Excited*
Teaching Statistics in a hospital???...Now, there's one I haven't heard of
Who are the students?
#### trinker
##### ggplot2orBust
I'm trying to write an [R] code to bake me some cookies. I just can't get it to work. Here's what I have so far; any suggestions?
Code:
bake.cookies<-(type="choc.chip"){
switch(type,
choc.chip=,
oatmeal.raisin=,
peanut.butter=,
sugar=,)
}
#### Dason
If you had an automated cookie maker connected to your computer that you could control through the command line you could use the "system" command to control it.
#### trinker
##### ggplot2orBust
Dason,
bake.cookies<-function(type="choc.chip"){
}
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https://collegephysicsanswers.com/openstax-solutions/how-many-lines-centimeter-are-there-diffraction-grating-gives-first-order
|
Change the chapter
Question
How many lines per centimeter are there on a diffraction grating that gives a first-order maximum for 470-nm blue light at an angle of $25.0^\circ$?
$8990 \textrm{ lines/cm}$
Solution Video
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http://comisef.wikidot.com/concept:forwards
|
Forward Contracts
Raquel Fonseca
## Keywords
Currencies, Derivatives, Foreign Exchange Rates
Unreviewed
# Definition
Probably the most simple form of derivatives, forward contracts are agreements to buy or sell at a certain point in the future an asset for a pre-specified price. Forwards are a common instrument to hedge the currency risk, when the investor is expecting to receive or pay a certain amount of money expressed in foreign currency in the near future. There are no costs in entering into a forward agreement apart from the differences in the bid-ask spread proposed by the financial institutions.
A very important feature of the forward contracts is that these are binding contracts (contrary to options), and therefore both parts are obliged to honour the contract and deliver the asset at that price. This condition impacts the calculation of the payoff of the forward.
Forward and spot prices are closely related. Assuming continuous compounding, we can determine the forward price of an asset as:
(1)
$$F = Se^{rT}$$
where $F$ and $S$ are the forward and the spot prices of the underlying asset respectively, $r$ is the risk free rate and $T$ is the period of time for compounding. This formulation implies there are no arbitrage opportunities. Note that if $F > Se^{rT}$, speculators may buy the asset now and enter into a short forward agreement, fixing now the sale price at a later date. The inverse applies if $F < Se^{rT}$. If the underlying asset is an investment asset which provides a known dividend yield, the above formula must be corrected to account for the rate of return of the investment, $q$:
(2)
$$F = Se^{(r-q)T}$$
The initial cost of a forward contract is zero. Luenberger [3]: “The forward price is the price that applies at delivery. This price is negotiated so that the initial payment is zero; that is, the value of the contract is zero when it is initiated”. At each point in time, until maturity, the value of a forward contract $f$ with a delivery price of $F$ is calculated as:
(3)
$$f = S - Fe^{(r-q)T}$$
When the contract is first established, the price of the forward contract $K$ is determined so as to ensure that its value $f$ is zero.
# Forward exchange rate contracts
We can also define forward contracts on foreign currencies, where the underlying asset is the exchange rate, or a certain number of units of a foreign currency. We start be defining $S$ as the spot exchange rate and $F$ as the forward price, both expressed as units of the base currency per unit of foreign currency. Holding currency provides the investor with an interest gain at the risk-free rate prevailing in the respective country. If we take $r$ as the domestic risk-free rate and $r_f$ as the risk-free rate in the foreign country, the forward price is then as before:
(4)
$$F = Se^{(r-r_f)T}$$
This is known as the ‘interest-rate parity’. If this was not the case arbitrage opportunities would arise, forcing the prices back to equilibrium. If $F > Se^{(r-r_f)T}$, a profit could be obtained by:
• Borrowing $Se^{(-r_fT)}$ in domestic currency at rate $r$ for time $T$
• Buying $e^{-r_fT}$ of the foreign currency and invest this at the rate $r_f$
• Short sell a forward contract on one unit of the foreign currency
At time $T$, the arbitrageur will receive one unit of foreign currency from the deposit, which he sells at the forward price $F$. From this results, he is able to repay the loan $Se^{(r-r_f)T}$ and still obtain a net profit of $F - Se^{(r-r_f)T}$.
# Hedging
Forwards on exchange rates are a commonly used hedging instrument for its simplicity and practicality. Suppose an US investor is expecting to receive in three months time the amount of Eur 150,000. Not wanting to take the risk of a depreciation in the exchange rate, he can enter into a forward rate agreement to sell Eur 150,000 in three months at the forward price of $F$, therefore fixing the foreign exchange rate at the level $F$. Forward contracts are quite effective when the agent knows exactly the amount he/she expects to receive at a future date, and allow him/her to hedge completely the risk of a change in the exchange rate. Nevertheless, while eliminating completely the risk of a currency depreciation, in the opposite case the potential gain is lost as the exchange rate is already determined and is binding.
|
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http://blog.nothinguntoward.eu/?p=38
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# An 88 Byte Bare-Metal Mandelbrot Generator
A while back, I was playing around with a bit of 8086 assembly. I’m not much of a programmer, but I’ve done some C{,++}, Python, PHP (sorry) and bits of a few others in the past. All of these are quite high level though, and I felt like going back to basics a bit. I chose to start with MS-DOS, since I thought (perhaps incorrectly?) that it would be easier to program. And I figured it would probably be a nice bit of computing history to learn anyway.
I soon moved on from MS-DOS and decided to set myself a programming challenge of a bare-metal Mandelbrot generator. In this post, I’ll give a bit of background about the Mandelbrot set, and explain my code.
## MS-DOS
I started off with this MS-DOS assembly tutorial. It seems to be broadly unchanged since it was first crawled by the Wayback Machine in 2002. Nice. I chose to use NASM instead of A86 but otherwise the tutorial’s pretty good. If you’re lazy, here’s a virtualbox image, with MSDOS 6.22 and NASM installed. My code is all in C:\PROGRAMM, in case anyone wants to use it as a reference.
This was fun for a while, but eventually I got bored of DOS programming and decided to try some bare metal stuff – and somehow, perhaps vaguely influenced by demoscene style demos, I ended up setting myself the challenge of writing a bare-metal Mandelbrot generator within a 512-byte bootsector.
## The Mandelbrot Set
The Mandelbrot Set is the set of points, c, on the complex plane such that the sequence zn+1=zn2+c (where z0=0) remains bounded. To clarify, here’s an example:
• Let’s check if the point (-0.5+0.5j) is in the set. Set c=(-0.5+0.5j)
• Now let’s perform the first iteration. (-0.5+0.5j)²+(-0.5+0.5j)=-0.5
• And another iteration: (-0.5)²+(-0.5+0.5j)=-0.25+0.5j
• And another: (0.25+0.5j)²+(-0.5+0.5j)=-0.6875+0.25j
• We can keep on iterating again and again like this, and we find that the numbers stay small. Eventually, we might conclude that the sequence is bounded, and the point is therefore in the set.
In fact, if we plot each iteration, we can see that it’s going around in a strange, almost spirograph-like shape:
But overall, the general trend seems to be going around in a closed circle, rather than shooting off to infinity, so it would probably be fairly safe to say here that the sequence is bounded. If you’re not convinced, here’s a plot of the magnitude at each iteration:
To take another example, let’s try it with the point (0.5,0.5). The iterations go:
• 0.5+1j
• -0.25+1.5j
• -1.69-0.25j
• 3.28+1.34j
• 990294279-77569977j
• So, this looks like it’s shooting off to infinity… and fast.
But this raises an interesting question: at what point do we decide whether the sequence is or isn’t bounded? In general we’d have to continue iterating to infinity to know for sure. Perhaps we should set a threshold, beyond which we declare it to be unbounded? But where should it be? And how do we know that sequences which exceed that threshold aren’t coming back?
Well, as it turns out, it can be proven (see A6d) that if any point leaves a circle of radius 2, (ie |zn|>2), it will never return. So a reasonable approach is to compute a fixed number of iterations, and then check whether the result is less than 2 in absolute value.
Here are two simple implementations I wrote just to demonstrate the idea. First, this is for the C++-minded people:
#include <iostream>
#include <complex>
using namespace std;
int main(){
cout << "P1 800 800 ";
for(int i=0;i<800;i++){
for(int j=0;j<800;j++){
complex<float> c((j-400)/200.0,(i-400)/200.0); //scale the indicies to floats in the range -2..2
complex<float> z(0,0); // initialise z to 0
for (int iter=0;iter<64;iter++) //iterate 64 times
z=z*z+c;
cout << (abs(z)<2)?"1 ":"0 "; //output a black pixel if in the set, white otherwise
}
}
cout<<endl;
return 0;
}
This goes through each pixel one-by-one and for each one runs 64 iterations. The output is a PBM file to stdout, so you’ll have to pipe it and open it in a compatible viewer (GIMP works) or convert it to a more common format.
Or, if you’re more of a MATLAB fan:
c=ones(800,1)*linspace(-2,2,800);
c=complex(c,c');
z=zeros(800,800);
for i=1:50
z=z.^2+c;
end
imshow(abs(z)<2)
The same idea as the C++ example, but using vectorisation rather than iterating through pixels, and using MATLAB’s internal imshow command to display the image.
## The Bare-Metal Version
With all that setting the scene done, let’s get down to how I wrote an 88-byte 8086 bare-metal mandelbrot generator.
### A note on arithmetic
The general structure of the C++ example can be carried over, but the arithmetic gets difficult. Firstly, the complex number datatype in C++ is an abstraction. The processor doesn’t understand complex numbers (not an 8086 at least). So we’ll have to treat them as two reals. Addition and subtraction are trivial. For multiplication we just have to remember that:
$(a+bj)(c+dj)=(ac-bd)+(ad+bc)j$
and specifically:
$(a+bj)^2=(a^2-b^2)+2abj$
This is conceptually not too difficult, but it does mean that complex operations take up a lot of program space.
The second thing to consider is that floating point operations don’t exist in 16-bit intel. We’re going to have to work in integer instructions instead. With a little bit of trickery though, we can create a very simple fixed-point system. Essentially, we just represent every number as a fixed multiple of its true value. Say, this could be 10. Addition (and by extension, subtraction) is consistent:
$(10a)+(10b)=10(a+b)$
Multiplication works too, with the caveat that we have to divide by the scale factor after:
$\frac{(10a)(10b)}{10}=10ab$
It’s for this reason that it’s best for that multiple to be a power of two: this reduces the division to a right shift.
For example, here is how we might multiply two numbers with a scaling of 1/32:
mov al,73 ; move the number 2.28 (73/32) into al
mov bl,-193 ;move -6.03 (-193/32) into bl
imul bl ; multiply bl (implicitly, with al). stores result in ax.
sar ax,5 ; shift right by 5 places to divide by 2^5=32
Note the use of sar rather than shr to preserve the sign.
### The code
So, without further ado, let’s start deconstructing my code, a section at a time:
[bits 16]
[org 7c00h]
mov ax,0fh
int 10h
First a bit of initialisation – instructions to the assembler that the code should be 16-bit, and will be loaded into memory at location 0x7c00.
Then, we call BIOS interrupt 10h with AH=0 (change video mode) and AL=0fh (640×350 mono resolution).
This video mode will fit a nice big 512×256 canvas on the screen.
Total assembled size so far: 5 bytes
mov dx,-128 ;start on the first line
yloop:
mov di,-256 ;go to the beginning of the line
xloop:
;set z=c initially - start on iteration 1
mov si,di
mov bp,dx
xor ax,ax ; set colour to black (al=0) and iteration counter to zero (ah=0)
So, here we initialise the two variables for our c value. DX will contain the y value and DI the x value. I’m starting at y=-1 and x=-2, using a scaling factor of 1/128. My canvas is to be y from -1 to 1 and x from -2 to 2. The z variable is stored with its real part in SI and its imaginary part in BP. We skip out the zeroth iteration here by initialising z=c.
Later, the interrupt to write a pixel to the screen will read the pixel value from AL. This wants to be initialised to zero (black). If the pixel is in the set, this will be changed to one (white) later. Otherwise it will be unchanged.
At the same time, I want to set an iteration counter to zero. Sneakily, I’ve chosen to use the other byte of AX for this, so that I can set both the pixel value and the iteration counter to zero in a single instruction. This single xor saves two bytes vs two 8-bit literal moves.
This block: 12 bytes, So far: 17 bytes.
iterate:
;calculate Im(z^2)=2xy
mov cx,bp
imul cx,si
jo overflow
sar cx,6 ;maybe mov 6 into a register first?
;cx contains Im(z^2)
At each iteration step we need to calculate $z_{n+1}=z_n^2+c$. To do this we need to calculate the real and imaginary parts of $z_n$, then add these to the real and imaginary parts of c.
As the comment suggests, here we’re calculating $Im(z_n^2)$, which as I showed previously is $2Re(z_n)Im(z_n)$. We copy $Im(z_n)$ into CX, since we’ll need it again later and we don’t want to clobber it. Then we multiply this by SI ($Re(z_n)$) and store the result in CX. The value in this register should now be $128Re(z_n)Im(z_n)$ (note what I said about fixed-point multiplication earlier). Ignoring the conditional jump for now, we would then want to divide by 128 to get $Re(z_n)Im(z_n)$. Except what we want is actually $2Re(z_n)Im(z_n)$, so we can save ourselves a multiplication by just dividing by 64 instead (right shift by 6).
Now, back to the jump. This is how we catch the sequences which go off to infinity – we’ll see where it goes later. In the C++ example, we used abs(z) to check whether we were inside an r=2 circle. But calculating an abs value is expensive. It requires us to square two numbers and sum them. But consider this: any point which leaves the r=2 circle will eventually go off to infinity. If I wanted to I could use an r=3 circle, or an r=1,000,000 circle – it would just potentially take more iterations. Any region which completely contains the r=2 circle will do the job. So how about a rectangle?
My jump is conditional on $128Re(z_n)Im(z_n)=64Im(z_n^2)$ being greater than 32768/128 in magnitude (the signed 16-bit max, after scaling). That is, $|Im(z_n^2)|>8$
So, provided that |Im(c)|<6 - which it always will be since we're only working with y in the range of -1 to 1 - this will contain the whole of the r=2 circle. Perfect. This block: 10 bytes, So far: 27 bytes [code];calculate Re(z^2)=x^2-y^2 mov bx,si ;we will work in the BX register for now add bx,bp ;bx contains x+y sub si,bp ;si contains x-y imul si,bx jo overflow sar si,7 ;si contains Re(z^2)[/code] And now to calculate $Re(z_n^2)$. As noted previously, this is given by $Re(z_n)^2-Im(z_n)^2$. Earlier versions of my code calculated exactly this – multiplying each part by itself, then subtracting one from the other. Then I realised I was missing a trick here – I could factorise $a^2-b^2=(a+b)(a-b)$, thus gaining an ADD (+2 bytes), but losing an IMUL (-3 bytes). A saving of 1 byte – score!
After we’ve calculated $Re(z_n)+Im(z_n)$ with the add bx,bp, we no longer need $Re(z_n)$ (SI), so we save ourselves an MOV by clobbering it in the SUB instruction.
Again, we check for overflow and SAR 7 to take out the factor of 128. Here, the overflow checks if $|128Re(z_n^2)|>\frac{32768}{128}$, ie $|Re(z_n^2)|>4$. Over the range of |Re(c)|<2 - exactly the space we're working in - this completely contains the r=2 circle. In fact, at the far left and right edges of the canvas, they just touch. An illustration is shown to the right: including the $abs(z^2)<2$ criterion in grey and the rectangular criterion we're using here in blue. The rectangle moves around relative to the axes depending on the point being calculated. This block: 14 bytes, So far: 41 bytes [code];calculate z'=z^2+c add si,di add cx,dx mov bp,cx ;do another iteration inc ah jno iterate[/code] Here are the final steps to calculate $z_{n+1}$. We then increment the iteration counter, AH, and unless it overflows (passes 255), we go round again. Whee! 255 iterations is thoroughly excessive, but it allows us to just check overflow, rather than doing a CMP with an immediate value, which would cost 3 bytes. This block: 10 bytes, So far: 51 bytes [code];iterations are over inc al ; if we've gotten all this way, set the colour to white overflow:[/code] If we get here just by the natural progression of the program, that will be because we went through 255 iterations without overflowing. Therefore the pixel is in the set, so we set it to white - a value of 1. Since I know its value before is zero, I can use an INC (2 bytes) instead of a MOV immediate (3 bytes). If we get here via one of the jump on overflows, we skip out of this instruction and the pixel remains black. This block: 2 bytes, So far: 53 bytes [code];now write a pixel mov ah,0ch ; write pixel interrupt xor bh,bh mov cx,di add cx,320 add dx,175 int 10h sub dx,175[/code] Here we use another INT 10h interrupt to write the pixel to the screen. We set AH=0Ch for the "write a pixel" command, set BH=0 for page zero (using XOR- no size advantage over MOV immediate here, but faster), and stick the coordinates in CX and DX (in fact, I chose to use DX to store the y coordinate anyway, to save a MOV instruction here). Since our coordinate system was centred around zero, we add 320 and 175 to the x and y coordinates respectively, to centre the image on the screen. After the interrupt, we have to take the 175 back off DX, since it serves as our loop counter so we can't clobber it. All of these ADD and SUB immediates are VERY expensive instructions - each one takes 4 bytes. I haven't thought of a way to optimise this though. This block: 20 bytes, So far: 73 bytes [code];loop around, do the next pixel inc di cmp di,255 jne xloop ;or if we've gotten to here, draw the next row inc dx cmp dx,127 jne yloop[/code] And some loop logic. We go onto the next pixel in the line (inc DI), and loop around unless the pixel value's 255 (end of the line). This CMP literal is expensive (4 bytes) but not easily avoided - since it's a signed type (and we're only using the lower 9 bits anyway), we can't just test for overflow. Outside of this, we have the same structure to loop through lines. This block: 13 bytes, So far: 86 bytes [code]cli hlt db $-$$;tell us the length of the code times 510 - ( -$$) db 0 dw 0xAA55[/code] And finally a little bit of boilerplate: clear BIOS interrupts and halt. The db$- line is a little hack to make it easier to see the size of the program - it just inserts a byte of value (this memory location-memory location of program start). Then I just look at the code in xxd and the last byte before the long run of zeros is the size of the program. It needs to be padded up to 512 bytes (the size of a boot sector), with the magic word AA55h at the end to indicate that it's bootable. And so that's a final 2 bytes of executable code (I'm not counting the padding, of course), bringing us up to 88 bytes! The complete code is here: mandelbrot-bootsector.asm
### The result
The code is compiled with nasm:
$nasm -o mandelbrot mandelbrot-bootsector.asm And run in qemu: $ qemu-system-i386 -video cirrus -fda mandelbrot -net none
Here’s a screenshot and a video of it running:
### Possible Optimisations
I’ve no doubt this code could be made smaller by someone more skilled than I am. I can see a few areas for potential optimisation, but can’t think how to implement them without breaking other things. For example, when writing the pixels to the screen, there are 3 ADD/SUB immediate instructions. These take up 4 bytes each – if I could have the immediate values in a register instead, that would save two bytes per instruction. But alas, I’m already scraping the bottom of the barrel for registers (I tried using SP, but since BIOS interrupts apparently use the stack, that breaks things).
Similarly, the CMP literals for the loop logic are pretty expensive. Avoiding literals is always desirable.
Perhaps it’s possible to save operations by foregoing the BIOS interrupt to write pixels and just write to video memory instead? I haven’t looked into this at all.
### Dissolve Animation
I made another version of my code which makes the set “dissolve” in. Essentially it uses an LFSR to cycle through pixel values, rather than a loop. I think it gives a pretty cool visual effect. I was going to write more on it, but this post is getting long enough already, so I’ll just leave the code and a video here if anyone’s interested. It’s not as heavily optimised as the code above.
mandelbrot2-ver4.asm
## Conclusion
This has turned out to be a very long blog post (my word count is saying over 2,700 words) but hey, I guess I had a lot to say. I had great fun learning assembly with this programming challenge, and I hope you’ve found my explanation interesting interesting too. If you can optimise it any more, I’d be interested to see your results, so do let me know in the comments!
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http://conversion.org/speed/kilometre-per-day/speed-of-light
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# kilometre per day to speed of light conversion
Conversion number between kilometre per day [km/d] and speed of light [c] is 3.8606955462749 × 10-11. This means, that kilometre per day is smaller unit than speed of light.
### Contents [show][hide]
Switch to reverse conversion:
from speed of light to kilometre per day conversion
### Enter the number in kilometre per day:
Decimal Fraction Exponential Expression
[km/d]
eg.: 10.12345 or 1.123e5
Result in speed of light
?
precision 0 1 2 3 4 5 6 7 8 9 [info] Decimal: Exponential:
### Calculation process of conversion value
• 1 kilometre per day = (exactly) ((1000/86400)) / (299792458) = 3.8606955462749 × 10-11 speed of light
• 1 speed of light = (exactly) (299792458) / ((1000/86400)) = 25902068371.2 kilometre per day
• ? kilometre per day × ((1000/86400) ("m/s"/"kilometre per day")) / (299792458 ("m/s"/"speed of light")) = ? speed of light
### High precision conversion
If conversion between kilometre per day to metre-per-second and metre-per-second to speed of light is exactly definied, high precision conversion from kilometre per day to speed of light is enabled.
Decimal places: (0-800)
kilometre per day
Result in speed of light:
?
### kilometre per day to speed of light conversion chart
Start value: [kilometre per day] Step size [kilometre per day] How many lines? (max 100)
visual:
kilometre per dayspeed of light
00
103.8606955462749 × 10-10
207.7213910925498 × 10-10
301.1582086638825 × 10-9
401.54427821851 × 10-9
501.9303477731375 × 10-9
602.3164173277649 × 10-9
702.7024868823924 × 10-9
803.0885564370199 × 10-9
903.4746259916474 × 10-9
1003.8606955462749 × 10-9
1104.2467651009024 × 10-9
Copy to Excel
## Multiple conversion
Enter numbers in kilometre per day and click convert button.
One number per line.
Converted numbers in speed of light:
Click to select all
## Details about kilometre per day and speed of light units:
Convert Kilometre per day to other unit:
### kilometre per day
Definition of kilometre per day unit: ≡ 1 km / 86400 s. The speed with which the body moves 1 km in 1 day.
Convert Speed of light to other unit:
### speed of light
Definition of speed of light unit: ≡ 299 792 458 m/s. Light velocity (in vacuum) is one of the basic physical constants. Sign c (Latin celeritas = speed). Its value is exactly: 299792458 m/s. Example: electromagnetic waves propagation speed 1 c.
← Back to Speed units
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https://trac-hacks.org/ticket/7053
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Opened 7 years ago
Closed 23 months ago
# Render text from repository
Reported by: Owned by: simon@… Ryan J Ollos normal PlantUmlMacro normal Steffen Hoffmann 0.11
### Description
It would be nice if it would be possible to render a UML graph from text in the repository rather than text inlined in the wiki page.
### comment:1 follow-up: 6 Changed 7 years ago by Álvaro Iradier
Owner: changed from robert_martin to Álvaro Iradier new → assigned
Indeed it would be nice. I'll take a look to implement rendering from source: (repository) and from attach: too.
### comment:2 Changed 5 years ago by Ryan J Ollos
Owner: changed from Álvaro Iradier to Ryan J Ollos assigned → new
The CodeExampleMacro implements a similar feature.
### comment:4 follow-up: 5 Changed 5 years ago by Ryan J Ollos
Cc: Steffen Hoffmann added; anonymous removed
I have a working implementation of this feature, which just needs some unit tests added. I also have some questions about the syntax. What is the proper way to pass arguments to WikiProcessors? The only example I could find in Trac 0.12 is the div processor: t:WikiProcessors#Examples. Following that example, the proper syntax would be:
{{{
#!PlantUML path=/somepath
}}}
but I'm not sure how the argument gets passed to the WikiProcessor, and whether this could be made to work with both Trac 0.11 and 0.12.
Maybe a better option would be to provide a WikiMacro for rendering text from the repository. For example,
[[PlantUML(somepath)]]
If we go that route, then I think #9906 should be implemented, and the WikiProcessor should be named plantuml and the macro named PlantUml.
### comment:5 in reply to: 4 Changed 5 years ago by Ryan J Ollos
but I'm not sure how the argument gets passed to the WikiProcessor, and whether this could be made to work with both Trac 0.11 and 0.12.
I found that this is actually clearly described in the documentation: trac/wiki/api.py.
### comment:6 in reply to: 1 Changed 5 years ago by Ryan J Ollos
Indeed it would be nice. I'll take a look to implement rendering from source: (repository) and from attach: too.
It seems like the ideal approach here would be to pattern this after the ImageMacro syntax. As I'm writing the code for this, I'm finding it is very similar to code that I've recently written for the IncludeMacro.
### comment:7 follow-up: 9 Changed 5 years ago by Ryan J Ollos
(In [11637]) Refs #7053: Added support for rendering markup from the repository. NOTE: This is work in progress and the calling syntax will change as support for additional realms is added. Feedback is welcome and appreciated.
The following are supported:
[[PlantUml(/path/to/repository)]]
[[PlantUml(/repos/path/to/repository@rev)]] (i.e. multi-repository installations and specific revisions are supported).
{{{
#!plantuml path="/path/to/repository"
...
}}}
{{{
#!plantuml path="/repos/path/to/repository@rev"
...
}}}
The Trac convention is to use camelcase names for macro calls and lowercase names for WikiProcessors, therefore PlantUml and plantuml have been added as valid casings. However, PlantUML is still a valid casing, retained for backwards compatibility.
### comment:8 Changed 5 years ago by Ryan J Ollos
(In [11638]) Refs #7053: Added support for translation of error messages.
### comment:9 in reply to: 7 ; follow-up: 10 Changed 5 years ago by tom.ghyselinck@…
Hi,
I would be great if we could diversify between two figures in a single file.
e.g. /path/to/source/file.txt contains:
@startuml{figure1.png}
title figure1
@enduml
...
@startuml{figure2.png}
title figure2
@enduml
You could provide something like [[PlantUml(/path/to/source/file.txt#figure1)]] or [[PlantUml(/path/to/source/file.txt@rev#figure1)]] ?
I don't know by heart what's the correct (Trac) syntax for such references.
### comment:10 in reply to: 9 Changed 5 years ago by Ryan J Ollos
I would be great if we could diversify between two figures in a single file.
Thanks for your feedback. That seems like a good feature to have, and I will see if I can add it after I add the other plantuml markup sources I have planned to support (wiki, attachment, ...).
### comment:11 Changed 4 years ago by Ryan J Ollos
(In [12389]) Refs #10229, #7053:
• Fixed error reported on Trac 0.11.7 in which calls containing the uml in the body of the wikiprocessor would fail with Path not specified.
• A message with the file path is now reported when the file is not found in the repository.
### comment:12 Changed 23 months ago by Ryan J Ollos
Resolution: → fixed new → closed
### Modify Ticket
Change Properties
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http://math.stackexchange.com/questions/495413/is-it-still-possible-for-mathematicians-to-contribute-to-the-theory-of-music
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# Is it still possible for mathematicians to contribute to the theory of music?
Is it still possible that mathematicians contribute to the theory of music? Is the mathematical foundation of music still an area of research? If yes, what new researches have been done regarding that?
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math.stackexchange.com/questions/79885/… possibly related. – Daniel Rust Sep 16 '13 at 13:43
@DanielRust: No, I had read that but that topic is mostly about book suggestions and reference request. On the other hand, this one is about the recent research done in this area, if there's any. – some1.new4u Sep 16 '13 at 13:46
@some1.new4u How does that contradict that that link is related to this question? – Git Gud Sep 16 '13 at 13:49
When you ask "new researches", what do you mean by "new"? New since when? – MJD Sep 16 '13 at 13:49
It seems that IRCAM researches on this. – Voyska Sep 16 '13 at 14:13
I know that a member of Mathoverflow Tobias Schlemmer works in this topic, you can consult with him.
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Yes, specifically in the area of musical tuning theory: the xenharmonic wiki is a good place to read about this. Harmonic entropy and xenharmonic temperament theory are two relatively new topics with a lot of current (albeit somewhat obscure) research going on in them.
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Key reference:
That set theory is useful with digital music, especially MIDI, seems not to be widely known.
Consider a sequence consisting of the following chords: $F^1 , C^2 , G7^4$ .
Changing the chords means that the set of notes $F^1 = \{F,A,C\}$ is replaced by the set of notes $C^2 = \{E,G,C\}$ is replaced by the set of notes $G7^4 = \{F,G,B\}$ . Mind the notes in common; these are joined by bows in the score.
In MIDI, first the notes in $F^1$ are set On (Note On). After a duration of four beats, the notes in $C^2$ should sound. In order to accomplish smooth transition of the chords, this should be done by first hitting the chord $C^2$ before (immediately) releasing the chord $F^1$. More in detail, apply a Note On event to the elements in $\{E,G,C\}$ minus $\{F,A,C\} = \{E,G\}$ immediately followed (timestep $0$) by a Note Off event applied to the elements in $\{F,A,C\}$ minus $\{E,G,C\} = \{F,A\}$ . Note that nothing happens with the note $C$ .
After a duration of four beats again, the notes in $G7^4$ should sound. This should be done by first hitting the chord $G7^4$ before (immediately) releasing the chord $C^2$. More in detail, apply a Note On event to the members of the set $G7^4 \setminus C^2$ immediately followed by a Note Off event applied to the members of the set $C^2 \setminus G7^4$ .
This is in a nutshell how chord transition works - or rather should work - in MIDI. It's implemented in my personal mathematical contribution to music : MidiDoos .
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https://blog.flyingcoloursmaths.co.uk/ask-uncle-colin-a-binary-fraction/
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Dear Uncle Colin,
How would you write $\frac{1}{10}$ in binary?
Binary Is Totally Stupid
Hi, BITS, and thanks for your message!
I have two ways to deal with this: the standard, long-division sort of method, and a much nicer geometric series approach.
Long division-esque
While I can do the long division method, I can’t easily typeset it. So I’m going to tackle it by the double-and-remainder method.
Let $x = \frac{1}{10}$.
Then I find:
• $2x = \frac{1}{5}$
• $4x = \frac{2}{5}$
• $8x = \frac{4}{5}$
• $16x = 1 + \frac{3}{5}$
• $32x = 3 + \frac{1}{5}$
Now, I know what 3 is in binary - it’s $11_2$. If you’ll forgive me mixing decimal and binary representations, I know that that $2^5 x = 11_2 + 2x$.
Dividing both sides by $2^5$ gives $x = 0.00011_2 + 2^{-4} x$, which gives the recursive result $x = 0.0001100110011…_2$.
Geometric series
It’s always been a source of delight for me that, in base 10, $0.\dot{9} = 1$ exactly. This is a result that can be shown using the sum of a geometric sequence: $S =\frac{a}{1-r}$, where $a$ is the first term and $r$ is the common ratio (as long as it’s between -1 and 1). (In that example, $0.\dot{9} = \frac{9}{10} + \frac{9}{100} + \dots$; we have $a = \frac{9}{10}$, $r =\frac{1}{10}$ and the result follows.)
Now, can we engineer a similar result for $\frac{1}{10}$ using “nice” binary numbers? Let’s have a think. We want $\frac{a}{1-r} = \frac{1}{10}$, or $10a = 1-r$, where $a$ and $r$ are numbers easy to express in binary.
One possibility is $r = -\frac{1}{4}$ and $a = \frac{1}{8}$, but this would give me a bit of a headache with negative numbers.
Suppose $a$ and $r$ have the same denominator, $2^k$, and numerators $A$ and $R$. Then we can rewrite our target expression as $10A = 2^k - R$ - we’re looking for a “nice” multiple of 10 that’s a nice distance away from a power of 2. For example, with $k=5$, we get $A=3$ and $R=2$ - which gives us $a = \frac{3}{32}$ and $r = \frac{1}{16}$.
A geometric series with first term $\frac{3}{32}$ and common ratio $\frac{1}{16}$ would look like: $0.0001100110011…_2$, as we had before!
Hope that helps,
- Uncle Colin
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https://www.ourxanadu.net/info/1115/18633.htm
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Nondivergence of reductive group actions on homogeneous spaces
Let $G/\Gamma$ be the quotient of a semisimple Lie group $G$ by its arithmetic lattice. Let $H$ be a reductive algebraic subgroup of $G$ acting on $G/\Gamma$. The question we are interested in is whether there is a compact set of $G/\Gamma$ that intersects every H-orbit.
We show that the failure of this can be explained by a single algebraic reason, which generalizes several previous results towards this question. We also obtain a way to find this algebraic obstruction, if there is any.
This talk is based on joint work with Runlin Zhang.
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https://www.askiitians.com/forums/Algebra/if-the-roots-and-0-of-the-quadratic_108355.htm
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If the roots α and β (α + β ≠ 0) of the quadratic equation ax^2 + bx + c = 0 are real and of opposite sign. Then show that roots of the equation α(x - β)^2 + β(x - α)^2 = 0 are also real and of opposite sign.
mycroft holmes
272 Points
7 years ago
Product of roots is $\frac{\alpha \beta^2 + \alpha^2 \beta}{(\alpha + \beta)}=\alpha \beta<0$
This immediately means that both roots are real and of opposite signs
(if they were complex, then they are conjugates and their product is always positive)
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http://www.logicmatters.net/2015/12/04/book-note-tony-roy-symbolic-logic-2/
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# Book Note: Tony Roy, Symbolic Logic, #2
To continue, then, with the comments on Tony Roy’s Symbolic Logic: An Accessible Introduction to Serious Mathematical Logic, Part II is called “Transition: Reasoning about Logic”, and is almost another 100 pages, though it consists of just two chapters.
Chapter 7 is a curious affair. It’s called “Direct Semantic Reasoning”, and the aim is to get the student to be able to use their understanding of the official semantics to demonstrate that, e.g., (i) $\exists xFx \vDash \exists y(Fx \lor Gy)$ or more challengingly (ii) $\exists x \forall y Rxy \vDash \forall y \exists x Rxy$, while also being able to show e.g. (iii) $\forall x \exists y Rxy \nvDash \exists y\forall x Rxy$. And yes, we of course want students to be able to do these things. Or rather more carefully, we want a student to able to produce informal but rigorous proofs of entailments given the definition of semantic consequence, and to produce counterexamples to witness non-entailments. This amounts to learning how to do some bits of (pretty elementary) mathematical reasoning, and students coming from a non-maths background need to be given some exemplars and models of this sort of informal reasoning done with the right amount of detail to pass muster.
But Roy is keen to replace informal proofs with formal derivations set out in natural deduction style, and the results seem to me to be rebarbative and consequently unhelpful. It is difficult to believe that students will find their abilities at informal reasoning actually improved by the sort of messy regimentations we find in this chapter. Have a look at p. 364 and ask if this is likely to help a student who doesn’t immediately see why, morally, (ii) should be true.
In his Preface, Roy tries to make a case for his approach in this chapter, but I’m not convinced. And to the extent that the idea is to give students an example of working formally in reasoning about logic, then we have to hand a framework for formalizing semantic reasoning which is much, much more elegant — i.e. use semantic tableaux, which are designed for the job!
Chapter 8 is on Mathematical Induction. This starts with a general discussion of induction, with some simple arithmetical and geometrical examples. Roy then goes on to give some applications of induction to prove syntactic and semantic facts about his formal languages. The chapter seems pretty clear, though as before things are perhaps rather stretched out. However, philosophy students needing to get their heads round the idea of induction and struggling with brisker presentations could very well find this a useful compendium.
To be continued.
This entry was posted in This and that. Bookmark the permalink.
### One Response to Book Note: Tony Roy, Symbolic Logic, #2
1. Tony Roy says:
Even though (perhaps because) they are not terribly positive, I very much appreciate Peter’s comments on my book. I will definitely pay close attention as the manuscript is revised. In some cases, however, it may be that comments reflect differences about ends.
Peter is right that the text (especially in the beginning) is aimed at students without mathematical background. The aim is to begin where they are, and gradually bring them to increasing levels of sophistication. My students are not admitted to Cambridge! With this in mind,
Peter’s Comment #1
1. I agree that chapter 3 (on axiomatic deduction) is too quick for a neophyte audience. As Peter observes I do suggest that students not attempt the chapter until they have worked all the way through natural derivations. At that stage, they aren’t quite neophytes. The chapter’s location immediately after presentation of syntax (and its prickly nature) is intended to make vivid that derivations are defined purely with respect to form.
2. Again, I agree that chapter 4 (on semantics) remains entirely at the level of valuations (what I call ‘interpretations’) so that formal languages are not tied to anything in ordinary language. Even the standard valuation of the language for arithmetic is presented as one among others. But that is the point: I am concerned to present the formal languages “as themselves” and without connection to ordinary language. This is supposed to mitigate the objections as, “the table for ‘’ is wrong insofar as it does not always correspond to the ordinary ‘if. . . then. . .’”
3. Chapter 5 (on translation) finally makes connections to ordinary language. I do wheel in the semantics – but that is because it’s only relative to the semantics that I have any account about how the formal language works. (The approach may mitigate the objection that tilde, caret and wedge are better primitive symbols than tilde and arrow – at this stage all the usual operators are defined, and we can begin with the cases that make the best fit to ordinary expressions.) Also, I do have an elaborate method for translations especially in the sentential case – but, theory to the side, my experience is that beginning students struggle with translations and take the method as a lifeline (in contrast to the way many of us learned).
4. Peter is right that chapter 6 (on natural deduction) has more by way of heuristics than the is required by the mathematically ept, and more detail than required for a bare account of how proofs work. But, again, the chapter is meant to bring along students who struggle at the simplest of derivations. The “strategies” are offered as a lifeline to students who would otherwise drown.
Peter’s Comment #2
5. In chapter 7 (on elementary mathematical reasoning) I do introduce a formal system in a natural deduction style. But I am not keen to replace informal proofs with formal derivations! Rather the formal derivations are intended as an aid for producing informal reasoning. Again, I have not found that simple provision of examples is generally sufficient. And the reason for natural rather than tableaux formalization is precisely because the formal derivations are supposed to aid (natural) informal reasoning.
6. Peter suggests that chapter 8 (on mathematical induction) is a bit stretched out – though it might be useful to students struggling with brisker presentations. Perhaps some of this comes down to the difference between students at my institution and those at Cambridge (and so a contrast with the way most of us learned)!
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https://arxiv.org/abs/1212.0137
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math.QA
(what is this?)
# Title: Bispectral extensions of the Askey-Wilson polynomials
Authors: Plamen Iliev
Abstract: Following the pioneering work of Duistermaat and Gr\"unbaum, we call a family $\{p_n(x)\}_{n=0}^{\infty}$ of polynomials bispectral, if the polynomials are simultaneously eigenfunctions of two commutative algebras of operators: one consisting of difference operators acting on the degree index $n$, and another one of operators acting on the variable $x$. The goal of the present paper is to construct and parametrize bispectral extensions of the Askey-Wilson polynomials, where the second algebra consists of $q$-difference operators. In particular, we describe explicitly measures on the real line for which the corresponding orthogonal polynomials satisfy (higher-order) $q$-difference equations extending all known families of orthogonal polynomials satisfying $q$-difference, difference or differential equations in $x$.
Comments: comments and references added Subjects: Quantum Algebra (math.QA); Classical Analysis and ODEs (math.CA) Journal reference: J. Funct. Anal. 266 (2014), no. 4, 2294--2318 DOI: 10.1016/j.jfa.2013.06.018 Cite as: arXiv:1212.0137 [math.QA] (or arXiv:1212.0137v2 [math.QA] for this version)
## Submission history
From: Plamen Iliev [view email]
[v1] Sat, 1 Dec 2012 17:40:31 GMT (19kb)
[v2] Mon, 27 May 2013 19:48:19 GMT (21kb)
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http://copper.math.buffalo.edu/309/hw09.html
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# HW #9, due 3:50pm Friday, April 20
Note: Webwork sets for 6.1 and 6.2 are also due on April 20.
# 5.4
6. (A linear transformation of polynomials)
30. (Find the B-matrix of a transformation.)
Note that to invert an nxn matrix P, you can augment it with the nxn identity matrix, get the reduced row echelon form of that, and your inverse is the last n columns. For example if P is 3x3:
Pinv = rre( augmented( P, eye(3) ) )[:,3:]
# Note to self: Maybe I should add a function inverse() to the mth309 module.
32. (Find a diagonalizing matrix.)
Help for this:
from mth309 import *
from numpy import *
A = Matrix([[15,-66,-44, ...
vals = linalg.eigvals(array(A,dtype=float))
vals
If the eigevalues happen to be integers, you can use the function nullbasis() in mth309.py to find a basis for the eigenspace corresponding to each eigenvalue (i.e. a basis for the nullspace of A − λI):
If 7 were an eigenvalue of A (it isn't!), then do
I = Matrix(eye(4))
N7 = nullbasis( A - 7*I )
You can then stack all your nullspace bases together using hstack:
P = Matrix(hstack([N7,...]))
P
You should check that
dot(Pinv,dot(A,P))
is diagonal.
## 5.5 Complex eigenvalues
4. and 6. (Eigenvalues and eigenvectors of a 2x2 matrix.)
8. (2x2 matrices that already are just rotation and scaling: what's the angle and the scaling.)
## 5.6 Discrete dynamical systems
2. (Solution and asymptotics of 3D linear dynamical system.)
6. (Owls and rats. See the note above Ex. 3.)
10, 12, 14. (Attractor, repellor, saddle?) You are welcome to use Python or any other tool to find the eigendata.
## 6.1 Inner product, length, and orthogonality
2, 4, 6, 8. (Compute some dot products, length, etc.)
20. (True or False.)
28. (If y orthogonal to u and v, show it's orthogonal to all vectors in span(u,v).)
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http://mathhelpforum.com/advanced-applied-math/174231-delay-state-space-system.html
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# Thread: Delay in a state-space system...
1. ## Delay in a state-space system...
Apologies if this is in the incorrect forum, it seemed the most appropriate from the choices given.
I have a state-space equation of the form
$\dot{x} = Ax + Bu + Ew$
where $x \in \mathbb{R}^n$ are my states, $u \in \mathbb{R}^m$ are my user-defined controls, and $w \in \mathbb{R}^p$ are disturbances to the system, and $A$, $B$, and $C$ are appropriately sized matrices.
The problem I have is that certain entries of $w$ are sort of related to others, in that, some terms in the $w$ vector are the same as other terms, but at some time later...so essentially I have a delay in the system, but only on certain elements of $w$. I can essentially split the $w$ vector into two groups; one group being the disturbance itself, and the other being the same disturbance at some time later.
Is there a way I can include this delay into the system, so that it's of the same form as the first equation I wrote? I can obviously enforce this delay when solving the equation numerically, but I ideally need the matrices to be of this form so that I can use it later for control synthesis.
Any ideas would be welcome.
2. I'm not sure what you have would be called a 'delay', would it? What you are saying is that elements of $w$ are predictions of what the disturbance will be in future time points, and so the derivatives of the system are affected by what's going to be happening in the future.
Unless, of course, I have wildly misunderstood.
3. I'm not sure. I may not have described it properly.
One example would be is if you imagine a car driving over a bump. The disturbances would be the bump acting on the wheels. However, the bumps on the wheels are related. Wherever hits the front wheel will hit the back wheel at some time later.
Ideally I wanted to include this additional piece of information, rather than just keep the disturbance inputs separate, to design a better controller. However, the very nature of what I'm suggesting appears to be nonlinear, and unsuitable for the linear control methods I'm proposing. I was just wondering if there was a trick to include it.
4. Originally Posted by Guffmeister
I'm not sure. I may not have described it properly.
One example would be is if you imagine a car driving over a bump. The disturbances would be the bump acting on the wheels. However, the bumps on the wheels are related. Wherever hits the front wheel will hit the back wheel at some time later.
Ideally I wanted to include this additional piece of information, rather than just keep the disturbance inputs separate, to design a better controller. However, the very nature of what I'm suggesting appears to be nonlinear, and unsuitable for the linear control methods I'm proposing. I was just wondering if there was a trick to include it.
Yes, but with the car, the vehicle's dynamics will not feel the effect of the back wheel hitting the bump until this event has happened.
The time derivative of your system is being affected by an event which is yet to occur, which for all intents and purposes isn't applicable to any real-world systems.
Sometimes linear control methods apply very well to systems with non-linear behaviour. I myself have certainly used simple PID controllers to adequately autopilot the controls of nonlinear models of aircraft.
Out of interest, what is the physical system you are trying to model/control?
5. I'm sure you're right, but I'm not sure I understand.
I agree that the back wheel won't feel the effects of the bump until it hits it, which is why I want to include the delay. Going back to the car example, I'd have 4 disturbances (one for each wheel). What I want to do is reduce that to two (just the front wheels) but formulate the $E$ matrix above so that it delivers the inputs that hit the front wheel into the system dynamics some time later. I don't believe what I've proposed violates any problems with hitting something in the future, but rather, you've provided the problem with additional information about the system, and the way the disturbances act on it. Imagine you were driving a car, and drove into a huge bump in the road...if you had the time to react, and your objective was to drive as carefully as possible, surely your brain would tell you to slow the car down so that the back wheel doesn't hit the same bump so hard. Essentially you're adding feedforward control to the problem. I wanted to have this as an additional bit of information, so a control scheme could do a similar thought process when controlling the system, rather than just having all the disturbances independent.
I meant to comment on your name in my last post! I should have guessed you were somehow involved in aeronautics! In fact, the system above is looking at planes through gusts.
6. Originally Posted by Guffmeister
Apologies if this is in the incorrect forum, it seemed the most appropriate from the choices given.
I have a state-space equation of the form
$\dot{x} = Ax + Bu + Ew$
where $x \in \mathbb{R}^n$ are my states, $u \in \mathbb{R}^m$ are my user-defined controls, and $w \in \mathbb{R}^p$ are disturbances to the system, and $A$, $B$, and $C$ are appropriately sized matrices.
The problem I have is that certain entries of $w$ are sort of related to others, in that, some terms in the $w$ vector are the same as other terms, but at some time later...so essentially I have a delay in the system, but only on certain elements of $w$. I can essentially split the $w$ vector into two groups; one group being the disturbance itself, and the other being the same disturbance at some time later.
Is there a way I can include this delay into the system, so that it's of the same form as the first equation I wrote? I can obviously enforce this delay when solving the equation numerically, but I ideally need the matrices to be of this form so that I can use it later for control synthesis.
Any ideas would be welcome.
If I understand this correctly, some of the coordinates of $w$ at time t are the same as other coordinates at some earlier time, so that for example the j-coordinate at time $t$ is the same as the i-coordinate at time $t-t_0$, where $t_0$ is fixed.
One way to handle this would be to remove all such earlier-time-dependent coordinates from w (so that w acts on a smaller dimensional space). Then use two different matrices to describe the instantaneous effect of w and the delayed effect of w. You would then get the equation in the form
$\dot{x}(t) = Ax(t) + Bu(t) + E_1w(t) + E_2w(t-t_0)$.
This is a subject I have never studied, but I believe there is a substantial literature on these delay-differential equations.
7. Originally Posted by Guffmeister
I meant to comment on your name in my last post! I should have guessed you were somehow involved in aeronautics! In fact, the system above is looking at planes through gusts.
Okay I think I understand what you mean now. Allow me to use an example and you can confirm if I'm right here.
So yo have $\dot{x} = Ax+Bu+Ew$.
Let's take a very simple case of the states being only the surge and heave of the vehicle, so $x = (u,v)^T$.
Then, you say we have four disturbances, so we can formulate the state space as so...
$\left( \begin{array}{ccc}
\dot{u}(t) \\
\dot{v}(t) \end{array} \right) = \left( \begin{array}{ccc}
A_{11} & A_{12} \\
A_{21} & A_{22} \end{array} \right) \left( \begin{array}{ccc}
u(t) \\
v(t) \end{array} \right) + \left( \begin{array}{ccc}
B_{11} & B_{12} \\
B_{21} & B_{22} \end{array} \right) \left( \begin{array}{ccc}
\delta_r(t) \\
\delta_a(t) \end{array} \right) + \left( \begin{array}{cccc}
E_{11} & E_{12} & E_{13} & E_{14} \\
E_{21} & E_{22} & E_{23} & E_{24} \end{array} \right)\left( \begin{array}{ccc}
w_{1}(t) & \\
w_{2}(t) & \\
w_{3}(t) & \\
w_{4}(t) & \end{array} \right)$
But, you're saying that, for example $w_{3}(t) = w_{1}(t-\tau)$, $w_{4}(t) = w_{2}(t-\tau)$
Given that 2 disturbances are dependent on each other, you want to reformulate the matrix $E$ such that it extracts the same information, but from only two variables, i.e.
$\left( \begin{array}{cccc}
E_{11} & E_{12} & E_{13} & E_{14} \\
E_{21} & E_{22} & E_{23} & E_{24} \end{array} \right)\left( \begin{array}{ccc}
w_{1}(t) & \\
w_{2}(t) & \\
w_{3}(t) & \\
w_{4}(t) & \end{array} \right) = \left( \begin{array}{ccc}
N_{11} & N_{12} \\
N_{21} & N_{22} \end{array} \right)\left( \begin{array}{ccc}
w_{1}(t) & \\
w_{2}(t) & \end{array} \right)$
Am I right?
If this is indeed the case, it should be sufficient to solve the linear system that I have just presented, so long as you are able to write the delayed variables as functions of the original variable.
For example, expanding the first row....
$E_{11}w_1(t) + E_{12}w_2(t) + E_{13} w_3(t) + E_{14}w_4(t) = N_{11}w_1(t) + N_{12}w_2(t)$
$\therefore E_{11}w_1(t) + E_{12}w_2(t) + E_{13} w_1(t-\tau) + E_{14}w_2(t-\tau) = N_{11}w_1(t) + N_{12}w_2(t)$
From here, you will have to write $w_1(t-\tau) = f(w_1(t))$, and $w_2(t-\tau) = f(w_2(t))$. Then take $w_1(t)$ and $w_2(t)$ out as factors on the LHS and coefficients you get there are going to be equal to $N_{11}$ and $N_{12}$.
This should be straight forward if, for example, there is a pattern between the varios disturbances. But if they are random, as disturbances tend to be, then you'll have a bit more trouble writing the delayed variables as functis of the originals.
Does this help?
And indeed, aeronautics is my forte.
8. Thanks for all your help.
Phugoid - indeed this is what I was getting at. I'm glad it made sense in the end, I'm just terrible at explaining things. Hehe.
What you've proposed was what I'd been trying so far, but unless I'm wrong, the equation is no longer linear is it?
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https://root-forum.cern.ch/t/compiling-error/11559
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# Compiling error
Hi rooter
I am trying to recompile cint from root 5.28.00
my command are
sudo make clean
sudo ./configure
sudo make
# cd cint/src/dict && PATH=…/…/…/lib:\$PATH LD_LIBRARY_PATH=…/…/…/lib:\$LD_LIBRARY_PATH DYLD_LIBRARY_PATH=…/lib:.:\$DYLD_LIBRARY_PATH …/…/…/bin/cint_tmp -nApiif.cxx -NG__API -Z0 -D__MAKECINT__ -c-1 -I…/…/inc -I…/…/…/reflex/inc -I… Api.h Error: cannot open file “math.h” FILE:…/…/inc/G__ci.h LINE:459 !!!Removing Apiif.cxx Apiif.h !!! make: *** [cint/src/dict/Apiif.cxx] Error 1
Hi,
I can not reproduce this problem. Is CINTSYSDIR set properly (or unset)? Can you re-try with a fresh check-out (of just the cint directories)?
Philippe.
hello mhoroub
I encounter the same problem as you when do the compiling 。Can you give some guide or clue ，Thank you very much
[quote=“Francis. Liu”]hello mhoroub
I encounter the same problem as you when do the compiling 。Can you give some guide or clue ，Thank you very much[/quote]
Hi Francis ,
I am not sure how I solved it, but perhaps you need to disable xrootd.
This can be done by reconfiguring root and then you can compile.
Cheers
Hi,
There is no need (nor is it possible) to compile CINT as part of ROOT. If you want to build CINT without ROOT then only check out the cint subdirectory, and run CINT’s ./configure (not ROOT’s!)
Cheers, Axel.
|
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|
http://www.let.rug.nl/~gosse/termpedia2/termpedia.php?language=dutch_general&density=7&link_color=000000&termpedia_system=perl_db&url=http%3A%2F%2Fen.wikipedia.org%2Fwiki%2FAlpha
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# Alpha
Alpha (uppercase Α, lowercase α; Ancient Greek: ἄλφα, álpha, modern pronunciation álfa) is the first letter of the Greek alphabet. In the system of Greek numerals, it has a value of 1.
It was derived from the Phoenician and Hebrew letter aleph - an ox or leader.[1]
Letters that arose from alpha include the Latin A and the Cyrillic letter А.
In English, the noun "alpha" is used as a synonym for "beginning", or "first" (in a series), reflecting its Greek roots.[2]
## Uses
### Greek
In Ancient Greek, alpha was pronounced [a] and could be either phonemically long ([aː]) or short ([a]). Where there is ambiguity, long and short alpha are sometimes written with a macron and breve today: Ᾱᾱ, Ᾰᾰ.
In Modern Greek, vowel length has been lost, and all instances of alpha simply represent IPA: [a].
In the polytonic orthography of Greek, alpha, like other vowel letters, can occur with several diacritic marks: any of three accent symbols (ά, ὰ, ᾶ), and either of two breathing marks (ἁ, ἀ), as well as combinations of these. It can also combine with the iota subscript ().
#### Greek grammar
In the AtticIonic dialect of Ancient Greek, long alpha [aː] fronted to [ɛː] (eta). In Ionic, the shift took place in all positions. In Attic, the shift did not take place after epsilon, iota, and rho (ε, ι, ρ; e, i, r). In Doric and Aeolic, long alpha is preserved in all positions.[3]
• Doric, Aeolic, Attic χώρᾱ chṓrā — Ionic χώρη chṓrē, "country"
• Doric, Aeolic φᾱ́μᾱ phā́mā — Attic, Ionic φήμη phḗmē, "report"
Privative a is the Ancient Greek prefix ἀ- or ἀν- a-, an-, added to words to negate them. It originates from the Proto-Indo-European *n̥- (syllabic nasal) and is cognate with English un-.
Copulative a is the Greek prefix ἁ- or ἀ- ha-, a-. It comes from Proto-Indo-European *sm̥.
### Math and science
The letter alpha represents various concepts in physics and chemistry, including alpha radiation, angular acceleration, alpha particles, alpha carbon and strength of electromagnetic interaction (as Fine-structure constant). Alpha also stands for thermal expansion coefficient of a compound in physical chemistry. It is also commonly used in mathematics in algebraic solutions representing quantities such as angles. Furthermore, in mathematics, the letter alpha is used to denote the area underneath a normal curve in statistics to denote significance level[4] when proving null and alternative hypotheses. In zoology, it is used to name the dominant individual in a wolf or dog pack. In aerodynamics, the letter is used as a symbol for the angle of attack of an aircraft and the word "alpha" is used as a synonym for this property.
The proportionality operator "" (in Unicode: U+221D) is sometimes mistaken for alpha.
The uppercase letter alpha is not generally used as a symbol because it tends to be rendered identically to the uppercase Latin A.
### International Phonetic Alphabet
In the International Phonetic Alphabet, the letter ɑ, which looks similar to the lower-case alpha, represents the open back unrounded vowel.
## History and symbolism
### Etymology
Alpha was derived from aleph, which in Phoenician means "ox".[5]
### Plutarch
Plutarch, in Moralia,[6] presents a discussion on why the letter alpha stands first in the alphabet. Ammonius asks Plutarch what he, being a Boeotian, has to say for Cadmus, the Phoenician who reputedly settled in Thebes and introduced the alphabet to Greece, placing alpha first because it is the Phoenician name for ox—which, unlike Hesiod,[7] the Phoenicians considered not the second or third, but the first of all necessities. "Nothing at all," Plutarch replied. He then added that he would rather be assisted by Lamprias, his own grandfather, than by Dionysus' grandfather, i.e. Cadmus. For Lamprias had said that the first articulate sound made is "alpha", because it is very plain and simple—the air coming off the mouth does not require any motion of the tongue—and therefore this is the first sound that children make.
According to Plutarch's natural order of attribution of the vowels to the planets, alpha was connected with the Moon.
### Alpha and Omega
Memorial Stained Glass window, Royal Military College of Canada features Alpha and Omega
Alpha, both as a symbol and term, is used to refer to or describe a variety of things, including the first or most significant occurrence of something. The New Testament has God declaring himself to be the "Alpha and Omega, the beginning and the end, the first and the last." (Revelation 22:13, KJV, and see also 1:8). Because of this symbolism, the characters ⍺ and ⍵ denote the left and right arguments in the APL programming language.
### Language
The term "alpha" has been used to denote position in social hierarchy, examples being "alpha males" or pack leaders.
## Computer encodings
• Greek alpha / Coptic alfa[8]
Character Α α
Unicode name GREEK CAPITAL LETTER ALPHA GREEK SMALL LETTER ALPHA COPTIC CAPITAL LETTER ALFA COPTIC SMALL LETTER ALFA
Encodings decimal hex decimal hex decimal hex decimal hex
Unicode 913 U+0391 945 U+03B1 11392 U+2C80 11393 U+2C81
UTF-8 206 145 CE 91 206 177 CE B1 226 178 128 E2 B2 80 226 178 129 E2 B2 81
Numeric character reference Α Α α α Ⲁ Ⲁ ⲁ ⲁ
Named character reference Α α
CP 437 224 E0
DOS Greek 128 80 152 98
DOS Greek-2 164 A4 214 D6
Windows 1253 193 C1 225 E1
TeX \alpha
For accented Greek characters, see Greek diacritics: Computer encoding.
• Latin / IPA alpha
Character ɑ ɒ
Unicode name LATIN SMALL LETTER ALPHA LATIN SMALL LETTER TURNED ALPHA LATIN SMALL LETTER ALPHA
WITH RETROFLEX HOOK
MODIFIER LETTER
SMALL ALPHA
MODIFIER LETTER
SMALL TURNED ALPHA
Encodings decimal hex decimal hex decimal hex decimal hex decimal hex
Unicode 593 U+0251 594 U+0252 7568 U+1D90 7493 U+1D45 7579 U+1D9B
UTF-8 201 145 C9 91 201 146 C9 92 225 182 144 E1 B6 90 225 181 133 E1 B5 85 225 182 155 E1 B6 9B
Numeric character reference ɑ ɑ ɒ ɒ ᶐ ᶐ ᵅ ᵅ ᶛ ᶛ
• Mathematical / Technical alpha
Character 𝚨 𝛂 𝛢 𝛼
Unicode name APL FUNCTIONAL SYMBOL ALPHA APL FUNCTIONAL SYMBOL
ALPHA UNDERBAR
MATHEMATICAL BOLD
CAPITAL ALPHA
MATHEMATICAL BOLD
SMALL ALPHA
MATHEMATICAL ITALIC
CAPITAL ALPHA
MATHEMATICAL ITALIC
SMALL ALPHA
Encodings decimal hex decimal hex decimal hex decimal hex decimal hex decimal hex
Unicode 9082 U+237A 9078 U+2376 120488 U+1D6A8 120514 U+1D6C2 120546 U+1D6E2 120572 U+1D6FC
UTF-8 226 141 186 E2 8D BA 226 141 182 E2 8D B6 240 157 154 168 F0 9D 9A A8 240 157 155 130 F0 9D 9B 82 240 157 155 162 F0 9D 9B A2 240 157 155 188 F0 9D 9B BC
UTF-16 9082 237A 9078 2376 55349 57000 D835 DEA8 55349 57026 D835 DEC2 55349 57058 D835 DEE2 55349 57084 D835 DEFC
Numeric character reference ⍺ ⍺ ⍶ ⍶ 𝚨 𝚨 𝛂 𝛂 𝛢 𝛢 𝛼 𝛼
Character 𝜜 𝜶 𝝖 𝝰 𝞐 𝞪
Unicode name MATHEMATICAL BOLD ITALIC
CAPITAL ALPHA
MATHEMATICAL BOLD ITALIC
SMALL ALPHA
MATHEMATICAL SANS-SERIF
BOLD CAPITAL ALPHA
MATHEMATICAL SANS-SERIF
BOLD SMALL ALPHA
MATHEMATICAL SANS-SERIF
BOLD ITALIC CAPITAL ALPHA
MATHEMATICAL SANS-SERIF
BOLD ITALIC SMALL ALPHA
Encodings decimal hex decimal hex decimal hex decimal hex decimal hex decimal hex
Unicode 120604 U+1D71C 120630 U+1D736 120662 U+1D756 120688 U+1D770 120720 U+1D790 120746 U+1D7AA
UTF-8 240 157 156 156 F0 9D 9C 9C 240 157 156 182 F0 9D 9C B6 240 157 157 150 F0 9D 9D 96 240 157 157 176 F0 9D 9D B0 240 157 158 144 F0 9D 9E 90 240 157 158 170 F0 9D 9E AA
UTF-16 55349 57116 D835 DF1C 55349 57142 D835 DF36 55349 57174 D835 DF56 55349 57200 D835 DF70 55349 57232 D835 DF90 55349 57258 D835 DFAA
Numeric character reference 𝜜 𝜜 𝜶 𝜶 𝝖 𝝖 𝝰 𝝰 𝞐 𝞐 𝞪 𝞪
## References
1. ^ Chambers concise dictionary p.30 Allied Publishers, 2004 ISBN 9798186062363 Retrieved 2017-02-06
2. ^ Alpha - Definition and More from the Free Merriam-Webster Dictionary
3. ^ Herbert Weir Smyth. Greek grammar for colleges. paragraph 30 and note.
4. ^ "Chapter 5: Analysing the Data Part II : Inferential Statistics". Research Methods and Statistics PESS202 Lecture and Commentary Notes. Archived from the original on 22 August 2011.
5. ^ alpha on the Online Etymology Dictionary
6. ^ Symposiacs, Book IX, questions II & III On-line text Archived 13 October 2008 at the Wayback Machine at Adelaide library
7. ^ Hesiod, in Works and Days (see on Perseus Project), advises the early Greek farmers, "First of all, get a house, then a woman and third, an ox for the plough."
8. ^ "Character Encodings". Retrieved 14 January 2013.
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http://math.stackexchange.com/questions/275303/kx-y-a-closed-subset-of-bx-y-for-normed-spaces-x-y/275354
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$K(X,Y)$ a closed subset of $B(X,Y)$ for normed spaces $X,Y$
Note this is a homework problem so I am looking for a hint not a solution:
For normed linear spaces $X$ and $Y$, I'm trying to show that $K(X,Y)$, the set of compact operators $X\to Y$ is a closed subset of $B(X,Y)$ the set of bounded operators $X\to Y$.
At first I thought it might be similar to showing that $c_{0}$ is a closed subspace of $c$. But the standard argument for that (if I am not mistaken) relies on the fact that the scalar field is complete.
Note: It turns out that $Y$ must be complete in order for the result to be true.
I start by assuming $f_{n}\in K(X,Y)$ is compact, and that $f_{n}\to f$ for some $f\in B(X,Y)$.
I want to show $f\in K(X,Y)$ using the criterion that for every sequence $x_{n}\in B_{X}$, $f(x_{n})$ has a convergent subsequence.
For each $m \geq 1$, by the compactness of $f_{m}$, there is a subsequence $x_{n_{k}}$ such that $f_{m}(x_{n_{k}})$ is convergent to some value in $Y$, say $y_{m}$.
If the same subsequence served as an appropriate witness for each $m\geq 1$, I think I may be able to get somewhere by changing orders of limits using an upper bound for the sequence $(f_{n})$. But I doubt this is the case, and thus I am stuck.
-
I think it would be easier to show that $f(B_X)$ is totally bounded. To do this, let $\epsilon>0$, then choose $N$ so that $\Vert f_N-f\Vert<\epsilon$. Choose a finite $\epsilon$-net, $\{f_N(x_1),\ldots , f_N(x_n)\}$ for $f_N(B_X)$. Then show this is a $3\epsilon$-net for $f(B_X)$. – David Mitra Jan 10 '13 at 18:12
Thank you. I will try this. – roo Jan 10 '13 at 18:26
I didnt use the concept of totally bounded, but I applied your choice of $N$ and immediately got the convergent subsequence I require. Thanks again! – roo Jan 10 '13 at 18:47
If you define a compact operator as one that maps bounded sets to sets with compact closure, then I'm not sure this is true. With $Y$ Banach, this is a standard result. But for arbitrary $Y$ I don't see how to get anything stronger than the result that $f$ maps bounded sets to totally bounded sets. What is your definition of a compact operator? – David Mitra Jan 10 '13 at 21:25
As you suggested, in my course an operator $T:X\to Y$ is compact if $\overline{T(B_{X})}$ is norm compact in $Y$. The issue you mention is actually why I avoided the totally bounded approach. It seems easy to go from compact to totally bounded, but not the other way around. Some google-browsing reveals that the other direction definitely holds in metric spaces but these facts are not available to me. – roo Jan 10 '13 at 21:30
2 Answers
A sequential argument that works when $Y$ is a Banach space is given below:
Hint: We take take subsequences of subsequences and diagonalize.
Below are the details:
Let $X_1=(x_n)$ be a sequence in $B_X$. Choose a subsequence $X_2=(x_n^1)_n$ of $X_1$ such that $f_1(x_n^1)$ is convergent. Now choose a subsequence $X_3=(x_n^2)_n$ of $X_2$ such that $f_2(x_n^2)$ converges. Continue in this manner...
We thus have subsequences $$(x_n^1)\supset (x_n^2)\supset (x_n^3)\supset\cdots$$so that $(f_m x_n^m)_n$ is convergent for each $m$.
Now set $y_n=x_n^n$. Then $(f_m y_n)_n$ is a convergent sequence for each $m$.
We also have \eqalign{\Vert f(y_n)-f(y_l)\Vert &\le\Vert (f-f_m)(y_n)\Vert +\Vert f_m(y_n-y_l)\Vert+\Vert (f_m-f)(y_l)\Vert \cr &\le 2\Vert f-f_m\Vert +\Vert f_m(y_n-y_l)\Vert } It follows from the above that $(f(y_n))_n$ is a Cauchy sequence and, thus, convergent.
I'm not sure how to make the above argument go through when $Y$ is only assumed to be a normed space; however, you can show that $f(B_X)$ is totally bounded as in my comment above.
-
This looks like the proof of Arzela-Ascoli (or some version of it I saw in an ODE's course). $Y$ is only a Normed space, not a Banach space, so this may not work in general. But I used your first hint in the comment above and the problem worked out fine. – roo Jan 10 '13 at 18:52
Unaccepted as you asked, but deleting it doesn't seem right as it is still valuable. – roo Jan 10 '13 at 21:25
Reaccepting this as it turns out completeness of $Y$ was a missing hypothesis. – roo Jan 12 '13 at 19:37
The following is incorrect:
Let $x_{n}$ be a sequence in $B_{X}$. Choose $N\geq 1$ so that $\|f_{N} - f\| < \epsilon$.
Choose a subsequence $x_{n_{k}}$ such that $f_{N}(x_{n_{k}})\to y$ for some $y\in Y$, and then $K\geq 1$ such that $\|f_{N}(x_{n_{K}}) - y\| < \epsilon$.
Then $\|f(x_{n_{K}}) - y\| \leq \|f(x_{n_{K}}) - f_{N}(x_{n_{K}})\| + \|f_{N}(x_{n_{K}}) - y\| < 2\epsilon$.
This allows arbitrarily close approximation of $y$ by elements of the sequence $f(x_{n})$, which gives the subsequence which is needed.
-
But, for different $\epsilon$, and thus different $N$, how do you know you can use the same limit $y$? Or am I missing something? (Also, would you unaccept my answer? I'd like to delete it as I misread (or rather didn't read carefully) your question.) – David Mitra Jan 10 '13 at 19:20
You're absolutely right. I was jumping to conclusions. Thanks for pointing out my error. – roo Jan 10 '13 at 21:25
I think I can take smaller and smaller values of $\epsilon$, and form a sequence from the resulting $y$ values, and then cross my fingers that it has a convergent subsequence. I think this will fix it. – roo Jan 10 '13 at 21:49
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http://writinginmediasres.blogspot.com/2012/04/quotation-of-week_09.html
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## Monday, April 9, 2012
### Quotation of the Week
Every week, I’ll put up a quotation related to writing or creation and tell you a little bit about the person who said it. I’ll try to vary the speakers as much as possible.
"In going where you have to go, and doing what you have to do, and seeing what you have to see, you dull and blunt the instrument you write with. But I would rather have it bent and dulled and know I had to put it on the grindstone again and hammer it into shape and put a whetstone to it, and know that I had something to write about, than to have it bright and shining and nothing to say, or smooth and well oiled in the closet, but unused." - Ernest Hemingway
Hemingway is a fairly known writer, having published classics like The Old man and the Sea and For Whom the Bell Tolls. He is also known for his drinking (and apparently he frequently embarked on “alcoholic sprees” with James Joyce). His writing style is very heavily ice-berg based, meaning that very little is said explicitly, but a lot is going on under the surface.
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https://ncar.github.io/esds/posts/2021/matplotlib-faq/
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# Matplotlib Tutorial FAQ#
Here is a compilation of questions and issues that arose during the Matplotlib session of the Python Tutorial Seminar Series.
Q. Are all the colormaps perceptually ordered?
A. They are not all perceptually ordered. Any color map you can think of exists or can be made. The Matplotlib Documentation has a good guide for choosing colormaps.
Q. How do you set the x-axis boundary to remove the padding left and right of where the data begins/ends?
A. You would use ax.set_xlim and provide the minimum and maximum x-values as input. You can infer these from your x data with the full command ax.set_xlim([min(x), max(x)]).
Q. How do you create a .png from a notebook?
A. You can save a figure by running plt.savefig(‘filename.png’) in the cell you plotted the figure. The file type is inferred from the filename. png, pdf, ps, eps, jpg, and svg are all supported image formats on most backends.
Q. How can we set resolution (dpi) when saving plots?
A. dpi is a keyword argument to savefig. So you can call plt.savefig(FIGURENAME.EXT, dpi=FLOAT) where you specify your desired dots per inch as a float.
Q. How can I add a shared colorbar for the subplots?
A. There are many of examples of how to do this in the GeoCAT-examples documentation. Here is an example that does so while plotting EOFs of the Sea Level Pressure over the North Atlantic. The Matplotlib documentation also has great instructions on how to manipulate colorbars.
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