id
int64 39
11.1M
| section
stringlengths 3
4.51M
| length
int64 2
49.9k
| title
stringlengths 1
182
| chunk_id
int64 0
68
|
|---|---|---|---|---|
17,945 |
# Lie group
In mathematics, a **Lie group** (pronounced `{{IPAc-en|l|iː}}`{=mediawiki} `{{respell|LEE}}`{=mediawiki}) is a group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable.
A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additional properties it must have to be thought of as a \"transformation\" in the abstract sense, for instance multiplication and the taking of inverses (to allow division), or equivalently, the concept of addition and subtraction. Combining these two ideas, one obtains a continuous group where multiplying points and their inverses is continuous. If the multiplication and taking of inverses are smooth (differentiable) as well, one obtains a Lie group.
Lie groups provide a natural model for the concept of continuous symmetry, a celebrated example of which is the circle group. Rotating a circle is an example of a continuous symmetry. For any rotation of the circle, there exists the same symmetry, and concatenation of such rotations makes them into the circle group, an archetypal example of a Lie group. Lie groups are widely used in many parts of modern mathematics and physics.
Lie groups were first found by studying matrix subgroups $G$ contained in $\text{GL}_n(\mathbb{R})$ or `{{tmath|1= \text{GL}_{n}(\mathbb{C}) }}`{=mediawiki}, the groups of $n\times n$ invertible matrices over $\mathbb{R}$ or `{{tmath|1= \mathbb{C} }}`{=mediawiki}. These are now called the classical groups, as the concept has been extended far beyond these origins. Lie groups are named after Norwegian mathematician Sophus Lie (1842--1899), who laid the foundations of the theory of continuous transformation groups. Lie\'s original motivation for introducing Lie groups was to model the continuous symmetries of differential equations, in much the same way that finite groups are used in Galois theory to model the discrete symmetries of algebraic equations.
| 300 |
Lie group
| 0 |
17,945 |
# Lie group
## History
Sophus Lie considered the winter of 1873--1874 as the birth date of his theory of continuous groups. Thomas Hawkins, however, suggests that it was \"Lie\'s prodigious research activity during the four-year period from the fall of 1869 to the fall of 1873\" that led to the theory\'s creation. Some of Lie\'s early ideas were developed in close collaboration with Felix Klein. Lie met with Klein every day from October 1869 through 1872: in Berlin from the end of October 1869 to the end of February 1870, and in Paris, Göttingen and Erlangen in the subsequent two years. Lie stated that all of the principal results were obtained by 1884. But during the 1870s all his papers (except the very first note) were published in Norwegian journals, which impeded recognition of the work throughout the rest of Europe. In 1884 a young German mathematician, Friedrich Engel, came to work with Lie on a systematic treatise to expose his theory of continuous groups. From this effort resulted the three-volume *Theorie der Transformationsgruppen*, published in 1888, 1890, and 1893. The term *groupes de Lie* first appeared in French in 1893 in the thesis of Lie\'s student Arthur Tresse.
Lie\'s ideas did not stand in isolation from the rest of mathematics. In fact, his interest in the geometry of differential equations was first motivated by the work of Carl Gustav Jacobi, on the theory of partial differential equations of first order and on the equations of classical mechanics. Much of Jacobi\'s work was published posthumously in the 1860s, generating enormous interest in France and Germany. Lie\'s *idée fixe* was to develop a theory of symmetries of differential equations that would accomplish for them what Évariste Galois had done for algebraic equations: namely, to classify them in terms of group theory. Lie and other mathematicians showed that the most important equations for special functions and orthogonal polynomials tend to arise from group theoretical symmetries. In Lie\'s early work, the idea was to construct a theory of *continuous groups*, to complement the theory of discrete groups that had developed in the theory of modular forms, in the hands of Felix Klein and Henri Poincaré. The initial application that Lie had in mind was to the theory of differential equations. On the model of Galois theory and polynomial equations, the driving conception was of a theory capable of unifying, by the study of symmetry, the whole area of ordinary differential equations. However, the hope that Lie theory would unify the entire field of ordinary differential equations was not fulfilled. Symmetry methods for ODEs continue to be studied, but do not dominate the subject. There is a differential Galois theory, but it was developed by others, such as Picard and Vessiot, and it provides a theory of quadratures, the indefinite integrals required to express solutions.
Additional impetus to consider continuous groups came from ideas of Bernhard Riemann, on the foundations of geometry, and their further development in the hands of Klein. Thus three major themes in 19th century mathematics were combined by Lie in creating his new theory:
- The idea of symmetry, as exemplified by Galois through the algebraic notion of a group;
- Geometric theory and the explicit solutions of differential equations of mechanics, worked out by Poisson and Jacobi;
- The new understanding of geometry that emerged in the works of Plücker, Möbius, Grassmann and others, and culminated in Riemann\'s revolutionary vision of the subject.
Although today Sophus Lie is rightfully recognized as the creator of the theory of continuous groups, a major stride in the development of their structure theory, which was to have a profound influence on subsequent development of mathematics, was made by Wilhelm Killing, who in 1888 published the first paper in a series entitled *Die Zusammensetzung der stetigen endlichen Transformationsgruppen* (*The composition of continuous finite transformation groups*). The work of Killing, later refined and generalized by Élie Cartan, led to classification of semisimple Lie algebras, Cartan\'s theory of symmetric spaces, and Hermann Weyl\'s description of representations of compact and semisimple Lie groups using highest weights.
In 1900 David Hilbert challenged Lie theorists with his Fifth Problem presented at the International Congress of Mathematicians in Paris.
Weyl brought the early period of the development of the theory of Lie groups to fruition, for not only did he classify irreducible representations of semisimple Lie groups and connect the theory of groups with quantum mechanics, but he also put Lie\'s theory itself on firmer footing by clearly enunciating the distinction between Lie\'s *infinitesimal groups* (i.e., Lie algebras) and the Lie groups proper, and began investigations of topology of Lie groups. The theory of Lie groups was systematically reworked in modern mathematical language in a monograph by Claude Chevalley.
| 790 |
Lie group
| 1 |
17,945 |
# Lie group
## Overview
Lie groups are smooth differentiable manifolds and as such can be studied using differential calculus, in contrast with the case of more general topological groups. One of the key ideas in the theory of Lie groups is to replace the *global* object, the group, with its *local* or linearized version, which Lie himself called its \"infinitesimal group\" and which has since become known as its Lie algebra.
Lie groups play an enormous role in modern geometry, on several different levels. Felix Klein argued in his Erlangen program that one can consider various \"geometries\" by specifying an appropriate transformation group that leaves certain geometric properties invariant. Thus Euclidean geometry corresponds to the choice of the group E(3) of distance-preserving transformations of the Euclidean space `{{tmath|1= \mathbb{R}^3 }}`{=mediawiki}, conformal geometry corresponds to enlarging the group to the conformal group, whereas in projective geometry one is interested in the properties invariant under the projective group. This idea later led to the notion of a *G*-structure, where *G* is a Lie group of \"local\" symmetries of a manifold.
Lie groups (and their associated Lie algebras) play a major role in modern physics, with the Lie group typically playing the role of a symmetry of a physical system. Here, the representations of the Lie group (or of its Lie algebra) are especially important. Representation theory is used extensively in particle physics. Groups whose representations are of particular importance include the rotation group SO(3) (or its double cover SU(2)), the special unitary group SU(3) and the Poincaré group.
On a \"global\" level, whenever a Lie group acts on a geometric object, such as a Riemannian or a symplectic manifold, this action provides a measure of rigidity and yields a rich algebraic structure. The presence of continuous symmetries expressed via a Lie group action on a manifold places strong constraints on its geometry and facilitates analysis on the manifold. Linear actions of Lie groups are especially important, and are studied in representation theory.
In the 1940s--1950s, Ellis Kolchin, Armand Borel, and Claude Chevalley realised that many foundational results concerning Lie groups can be developed completely algebraically, giving rise to the theory of algebraic groups defined over an arbitrary field. This insight opened new possibilities in pure algebra, by providing a uniform construction for most finite simple groups, as well as in algebraic geometry. The theory of automorphic forms, an important branch of modern number theory, deals extensively with analogues of Lie groups over adele rings; *p*-adic Lie groups play an important role, via their connections with Galois representations in number theory.
| 429 |
Lie group
| 2 |
17,945 |
# Lie group
## Definitions and examples {#definitions_and_examples}
A **real Lie group** is a group that is also a finite-dimensional real smooth manifold, in which the group operations of multiplication and inversion are smooth maps. Smoothness of the group multiplication
: $\mu:G\times G\to G\quad \mu(x,y)=xy$
means that *μ* is a smooth mapping of the product manifold `{{nowrap|''G'' × ''G''}}`{=mediawiki} into *G*. The two requirements can be combined to the single requirement that the mapping
: $(x,y)\mapsto x^{-1}y$
be a smooth mapping of the product manifold into *G*.
### First examples {#first_examples}
- The 2×2 real invertible matrices form a group under multiplication, called general linear group of degree 2 and denoted by $\operatorname{GL}(2, \mathbb{R})$ or by `{{tmath|1= \operatorname{GL}_2(\mathbb{R}) }}`{=mediawiki}: $\operatorname{GL}(2, \mathbb{R}) = \left\{A = \begin{pmatrix}a & b\\c & d\end{pmatrix} : \det A = ad-bc \ne 0\right\}.$ This is a four-dimensional noncompact real Lie group; it is an open subset of `{{tmath|1= \mathbb R^4 }}`{=mediawiki}. This group is disconnected; it has two connected components corresponding to the positive and negative values of the determinant.
- The rotation matrices form a subgroup of `{{tmath|1= \operatorname{GL}(2, \mathbb{R}) }}`{=mediawiki}, denoted by `{{tmath|1= \operatorname{SO}(2, \mathbb{R}) }}`{=mediawiki}. It is a Lie group in its own right: specifically, a one-dimensional compact connected Lie group which is diffeomorphic to the circle. Using the rotation angle $\varphi$ as a parameter, this group can be parametrized as follows: $\operatorname{SO}(2, \mathbb{R}) = \left\{\begin{pmatrix} \cos\varphi & -\sin\varphi \\ \sin\varphi & \cos\varphi \end{pmatrix} : \varphi \in \mathbb{R}\ /\ 2\pi\mathbb{Z}\right\}.$ Addition of the angles corresponds to multiplication of the elements of `{{tmath|1= \operatorname{SO}(2, \mathbb{R}) }}`{=mediawiki}, and taking the opposite angle corresponds to inversion. Thus both multiplication and inversion are differentiable maps.
- The affine group of one dimension is a two-dimensional matrix Lie group, consisting of $2 \times 2$ real, upper-triangular matrices, with the first diagonal entry being positive and the second diagonal entry being 1. Thus, the group consists of matrices of the form $A= \left( \begin{array}{cc} a & b\\ 0 & 1 \end{array}\right),\quad a>0,\, b \in \mathbb{R}.$
### Non-example {#non_example}
We now present an example of a group with an uncountable number of elements that is not a Lie group under a certain topology. The group given by
: $H = \left\{\left(\begin{matrix}e^{2\pi i\theta} & 0\\0 & e^{2\pi ia\theta}\end{matrix}\right) :\, \theta \in \mathbb{R}\right\} \subset \mathbb{T}^2 = \left\{\left(\begin{matrix}e^{2\pi i\theta} & 0\\0 & e^{2\pi i\phi}\end{matrix}\right) :\, \theta, \phi \in \mathbb{R}\right\},$
with $a \in \mathbb R \setminus \mathbb Q$ a *fixed* irrational number, is a subgroup of the torus $\mathbb T^2$ that is not a Lie group when given the subspace topology. If we take any small neighborhood $U$ of a point $h$ in `{{tmath|1= H }}`{=mediawiki}, for example, the portion of $H$ in $U$ is disconnected. The group $H$ winds repeatedly around the torus without ever reaching a previous point of the spiral and thus forms a dense subgroup of `{{tmath|1= \mathbb T^2 }}`{=mediawiki}.
The group $H$ can, however, be given a different topology, in which the distance between two points $h_1,h_2\in H$ is defined as the length of the shortest path *in the group* $H$ joining $h_1$ to `{{tmath|1= h_2 }}`{=mediawiki}. In this topology, $H$ is identified homeomorphically with the real line by identifying each element with the number $\theta$ in the definition of `{{tmath|1= H }}`{=mediawiki}. With this topology, $H$ is just the group of real numbers under addition and is therefore a Lie group.
The group $H$ is an example of a \"Lie subgroup\" of a Lie group that is not closed. See the discussion below of Lie subgroups in the section on basic concepts.
### Matrix Lie groups {#matrix_lie_groups}
Let $\operatorname{GL}(n, \mathbb{C})$ denote the group of $n\times n$ invertible matrices with entries in `{{tmath|1= \mathbb{C} }}`{=mediawiki}. Any closed subgroup of $\operatorname{GL}(n, \mathbb{C})$ is a Lie group; Lie groups of this sort are called **matrix Lie groups.** Since most of the interesting examples of Lie groups can be realized as matrix Lie groups, some textbooks restrict attention to this class, including those of Hall, Rossmann, and Stillwell. Restricting attention to matrix Lie groups simplifies the definition of the Lie algebra and the exponential map. The following are standard examples of matrix Lie groups.
- The special linear groups over $\mathbb{R}$ and `{{tmath|1= \mathbb{C} }}`{=mediawiki}, $\operatorname{SL}(n, \mathbb{R})$ and `{{tmath|1= \operatorname{SL}(n, \mathbb{C}) }}`{=mediawiki}, consisting of $n\times n$ matrices with determinant one and entries in $\mathbb{R}$ or $\mathbb{C}$
- The unitary groups and special unitary groups, $\operatorname{U}(n,\mathbb{C})$ and `{{tmath|1= \operatorname{SU}(n,\mathbb{C}) }}`{=mediawiki}, consisting of $n\times n$ complex matrices satisfying $U^*=U^{-1}$ (and also $\det(U)=1$ in the case of $\operatorname{SU}(n)$)
- The orthogonal groups and special orthogonal groups, $\operatorname{O}(n,\mathbb{R})$ and `{{tmath|1= \operatorname{SO}(n,\mathbb{R}) }}`{=mediawiki}, consisting of $n\times n$ real matrices satisfying $R^\mathrm{T}=R^{-1}$ (and also $\det(R)=1$ in the case of $\operatorname{SO}(n,\mathbb{R})$)
All of the preceding examples fall under the heading of the classical groups.
### Related concepts {#related_concepts}
A **complex Lie group** is defined in the same way using complex manifolds rather than real ones (example: $\operatorname{SL}(2, \mathbb{C})$), and holomorphic maps. Similarly, using an alternate metric completion of `{{tmath|1= \mathbb{Q} }}`{=mediawiki}, one can define a ***p*-adic Lie group** over the *p*-adic numbers, a topological group which is also an analytic *p*-adic manifold, such that the group operations are analytic. In particular, each point has a *p*-adic neighborhood.
Hilbert\'s fifth problem asked whether replacing differentiable manifolds with topological or analytic ones can yield new examples. The answer to this question turned out to be negative: in 1952, Gleason, Montgomery and Zippin showed that if *G* is a topological manifold with continuous group operations, then there exists exactly one analytic structure on *G* which turns it into a Lie group (see also Hilbert--Smith conjecture). If the underlying manifold is allowed to be infinite-dimensional (for example, a Hilbert manifold), then one arrives at the notion of an infinite-dimensional Lie group. It is possible to define analogues of many Lie groups over finite fields, and these give most of the examples of finite simple groups.
The language of category theory provides a concise definition for Lie groups: a Lie group is a group object in the category of smooth manifolds. This is important, because it allows generalization of the notion of a Lie group to Lie supergroups. This categorical point of view leads also to a different generalization of Lie groups, namely Lie groupoids, which are groupoid objects in the category of smooth manifolds with a further requirement.
| 1,054 |
Lie group
| 3 |
17,945 |
# Lie group
## Definitions and examples {#definitions_and_examples}
### Topological definition {#topological_definition}
A Lie group can be defined as a (Hausdorff) topological group that, near the identity element, looks like a transformation group, with no reference to differentiable manifolds. First, we define an **immersely linear Lie group** to be a subgroup *G* of the general linear group $\operatorname{GL}(n, \mathbb{C})$ such that
1. for some neighborhood *V* of the identity element *e* in *G*, the topology on *V* is the subspace topology of $\operatorname{GL}(n, \mathbb{C})$ and *V* is closed in `{{tmath|1= \operatorname{GL}(n, \mathbb{C}) }}`{=mediawiki}.
2. *G* has at most countably many connected components.
(For example, a closed subgroup of `{{tmath|1= \operatorname{GL}(n, \mathbb{C}) }}`{=mediawiki}; that is, a matrix Lie group satisfies the above conditions.)
Then a *Lie group* is defined as a topological group that (1) is locally isomorphic near the identities to an immersely linear Lie group and (2) has at most countably many connected components. Showing the topological definition is equivalent to the usual one is technical (and the beginning readers should skip the following) but is done roughly as follows:
1. Given a Lie group *G* in the usual manifold sense, the Lie group--Lie algebra correspondence (or a version of Lie\'s third theorem) constructs an immersed Lie subgroup $G' \subset \operatorname{GL}(n, \mathbb{C})$ such that $G, G'$ share the same Lie algebra; thus, they are locally isomorphic. Hence, $G$ satisfies the above topological definition.
2. Conversely, let $G$ be a topological group that is a Lie group in the above topological sense and choose an immersely linear Lie group $G'$ that is locally isomorphic to `{{tmath|1= G }}`{=mediawiki}. Then, by a version of the closed subgroup theorem, $G'$ is a real-analytic manifold and then, through the local isomorphism, *G* acquires a structure of a manifold near the identity element. One then shows that the group law on *G* can be given by formal power series; so the group operations are real-analytic and $G$ itself is a real-analytic manifold.
The topological definition implies the statement that if two Lie groups are isomorphic as topological groups, then they are isomorphic as Lie groups. In fact, it states the general principle that, to a large extent, *the topology of a Lie group* together with the group law determines the geometry of the group.
| 380 |
Lie group
| 4 |
17,945 |
# Lie group
## More examples of Lie groups {#more_examples_of_lie_groups}
Lie groups occur in abundance throughout mathematics and physics. Matrix groups or algebraic groups are (roughly) groups of matrices (for example, orthogonal and symplectic groups), and these give most of the more common examples of Lie groups.
### Dimensions one and two {#dimensions_one_and_two}
The only connected Lie groups with dimension one are the real line $\mathbb{R}$ (with the group operation being addition) and the circle group $S^1$ of complex numbers with absolute value one (with the group operation being multiplication). The $S^1$ group is often denoted as `{{tmath|1= \operatorname{U}(1) }}`{=mediawiki}, the group of $1\times 1$ unitary matrices.
In two dimensions, if we restrict attention to simply connected groups, then they are classified by their Lie algebras. There are (up to isomorphism) only two Lie algebras of dimension two. The associated simply connected Lie groups are $\mathbb{R}^2$ (with the group operation being vector addition) and the affine group in dimension one, described in the previous subsection under \"first examples\".
### Additional examples {#additional_examples}
- The group SU(2) is the group of $2\times 2$ unitary matrices with determinant `{{tmath|1= 1 }}`{=mediawiki}. Topologically, $\text{SU}(2)$ is the `{{tmath|1= 3 }}`{=mediawiki}-sphere `{{tmath|1= S^3 }}`{=mediawiki}; as a group, it may be identified with the group of unit quaternions.
- The Heisenberg group is a connected nilpotent Lie group of dimension `{{tmath|1= 3 }}`{=mediawiki}, playing a key role in quantum mechanics.
- The Lorentz group is a 6-dimensional Lie group of linear isometries of the Minkowski space.
- The Poincaré group is a 10-dimensional Lie group of affine isometries of the Minkowski space.
- The exceptional Lie groups of types G~2~, F~4~, E~6~, E~7~, E~8~ have dimensions 14, 52, 78, 133, and 248. Along with the A--B--C--D series of simple Lie groups, the exceptional groups complete the list of simple Lie groups.
- The symplectic group $\text{Sp}(2n,\mathbb{R})$ consists of all $2n \times 2n$ matrices preserving a *symplectic form* on `{{tmath|1= \mathbb{R}^{2n} }}`{=mediawiki}. It is a connected Lie group of dimension `{{tmath|1= 2n^2 + n }}`{=mediawiki}.
### Constructions
There are several standard ways to form new Lie groups from old ones:
- The product of two Lie groups is a Lie group.
- Any topologically closed subgroup of a Lie group is a Lie group. This is known as the closed subgroup theorem or **Cartan\'s theorem**.
- The quotient of a Lie group by a closed normal subgroup is a Lie group.
- The universal cover of a connected Lie group is a Lie group. For example, the group $\mathbb{R}$ is the universal cover of the circle group `{{tmath|1= S^1 }}`{=mediawiki}. In fact any covering of a differentiable manifold is also a differentiable manifold, but by specifying *universal* cover, one guarantees a group structure (compatible with its other structures).
### Related notions {#related_notions}
Some examples of groups that are *not* Lie groups (except in the trivial sense that any group having at most countably many elements can be viewed as a 0-dimensional Lie group, with the discrete topology), are:
- Infinite-dimensional groups, such as the additive group of an infinite-dimensional real vector space, or the space of smooth functions from a manifold $X$ to a Lie group `{{tmath|1= G }}`{=mediawiki}, `{{tmath|1= C^\infty(X,G) }}`{=mediawiki}. These are not Lie groups as they are not *finite-dimensional* manifolds.
- Some totally disconnected groups, such as the Galois group of an infinite extension of fields, or the additive group of the *p*-adic numbers. These are not Lie groups because their underlying spaces are not real manifolds. (Some of these groups are \"*p*-adic Lie groups\".) In general, only topological groups having similar local properties to **R**^*n*^ for some positive integer *n* can be Lie groups (of course they must also have a differentiable structure).
| 620 |
Lie group
| 5 |
17,945 |
# Lie group
## Basic concepts {#basic_concepts}
### The Lie algebra associated with a Lie group {#the_lie_algebra_associated_with_a_lie_group}
To every Lie group we can associate a Lie algebra whose underlying vector space is the tangent space of the Lie group at the identity element and which completely captures the local structure of the group. Informally we can think of elements of the Lie algebra as elements of the group that are \"infinitesimally close\" to the identity, and the Lie bracket of the Lie algebra is related to the commutator of two such infinitesimal elements. Before giving the abstract definition we give a few examples:
- The Lie algebra of the vector space **R**^*n*^ is just **R**^*n*^ with the Lie bracket given by\
\[*A*, *B*\] = 0.\
(In general the Lie bracket of a connected Lie group is always 0 if and only if the Lie group is abelian.)
- The Lie algebra of the general linear group GL(*n*, **C**) of invertible matrices is the vector space M(*n*, **C**) of square matrices with the Lie bracket given by\
\[*A*, *B*\] = *AB* − *BA*.
- If *G* is a closed subgroup of GL(*n*, **C**) then the Lie algebra of *G* can be thought of informally as the matrices *m* of M(*n*, **C**) such that 1 + ε*m* is in *G*, where ε is an infinitesimal positive number with ε^2^ = 0 (of course, no such real number ε exists). For example, the orthogonal group O(*n*, **R**) consists of matrices *A* with *AA*^T^ = 1, so the Lie algebra consists of the matrices *m* with (1 + ε*m*)(1 + ε*m*)^T^ = 1, which is equivalent to *m* + *m*^T^ = 0 because ε^2^ = 0.
- The preceding description can be made more rigorous as follows. The Lie algebra of a closed subgroup *G* of GL(*n*, **C**), may be computed as
: $\operatorname{Lie}(G) = \{ X \in M(n;\mathbb{C}) | \operatorname{exp}(tX) \in G \text{ for all } t \text{ in } \mathbb{\mathbb{R}} \},$ where exp(*tX*) is defined using the matrix exponential. It can then be shown that the Lie algebra of *G* is a real vector space that is closed under the bracket operation, `{{tmath|1= [X,Y]=XY-YX }}`{=mediawiki}.
The concrete definition given above for matrix groups is easy to work with, but has some minor problems: to use it we first need to represent a Lie group as a group of matrices, but not all Lie groups can be represented in this way, and it is not even obvious that the Lie algebra is independent of the representation we use. To get around these problems we give the general definition of the Lie algebra of a Lie group (in 4 steps):
1. Vector fields on any smooth manifold *M* can be thought of as derivations *X* of the ring of smooth functions on the manifold, and therefore form a Lie algebra under the Lie bracket \[*X*, *Y*\] = *XY* − *YX*, because the Lie bracket of any two derivations is a derivation.
2. If *G* is any group acting smoothly on the manifold *M*, then it acts on the vector fields, and the vector space of vector fields fixed by the group is closed under the Lie bracket and therefore also forms a Lie algebra.
3. We apply this construction to the case when the manifold *M* is the underlying space of a Lie group *G*, with *G* acting on *G* = *M* by left translations *L~g~*(*h*) = *gh*. This shows that the space of left invariant vector fields (vector fields satisfying *L~g~*~\*~*X~h~* = *X~gh~* for every *h* in *G*, where *L~g~*~\*~ denotes the differential of *L~g~*) on a Lie group is a Lie algebra under the Lie bracket of vector fields.
4. Any tangent vector at the identity of a Lie group can be extended to a left invariant vector field by left translating the tangent vector to other points of the manifold. Specifically, the left invariant extension of an element *v* of the tangent space at the identity is the vector field defined by *v*\^~*g*~ = *L~g~*~\*~*v*. This identifies the tangent space *T~e~G* at the identity with the space of left invariant vector fields, and therefore makes the tangent space at the identity into a Lie algebra, called the Lie algebra of *G*, usually denoted by a Fraktur $\mathfrak{g}.$ Thus the Lie bracket on $\mathfrak{g}$ is given explicitly by \[*v*, *w*\] = \[*v*\^, *w*\^\]~*e*~.
This Lie algebra $\mathfrak{g}$ is finite-dimensional and it has the same dimension as the manifold *G*. The Lie algebra of *G* determines *G* up to \"local isomorphism\", where two Lie groups are called **locally isomorphic** if they look the same near the identity element. Problems about Lie groups are often solved by first solving the corresponding problem for the Lie algebras, and the result for groups then usually follows easily. For example, simple Lie groups are usually classified by first classifying the corresponding Lie algebras.
We could also define a Lie algebra structure on *T~e~* using right invariant vector fields instead of left invariant vector fields. This leads to the same Lie algebra, because the inverse map on *G* can be used to identify left invariant vector fields with right invariant vector fields, and acts as −1 on the tangent space *T~e~*.
The Lie algebra structure on *T~e~* can also be described as follows: the commutator operation
: (*x*, *y*) → *xyx*^−1^*y*^−1^
on *G* × *G* sends (*e*, *e*) to *e*, so its derivative yields a bilinear operation on *T~e~G*. This bilinear operation is actually the zero map, but the second derivative, under the proper identification of tangent spaces, yields an operation that satisfies the axioms of a Lie bracket, and it is equal to twice the one defined through left-invariant vector fields.
### Homomorphisms and isomorphisms {#homomorphisms_and_isomorphisms}
If *G* and *H* are Lie groups, then a Lie group homomorphism *f* : *G* → *H* is a smooth group homomorphism. In the case of complex Lie groups, such a homomorphism is required to be a holomorphic map. However, these requirements are a bit stringent; every continuous homomorphism between real Lie groups turns out to be (real) analytic.
The composition of two Lie homomorphisms is again a homomorphism, and the class of all Lie groups, together with these morphisms, forms a category. Moreover, every Lie group homomorphism induces a homomorphism between the corresponding Lie algebras. Let $\phi : G \to H$ be a Lie group homomorphism and let $\phi_{*}$ be its derivative at the identity. If we identify the Lie algebras of *G* and *H* with their tangent spaces at the identity elements, then $\phi_{*}$ is a map between the corresponding Lie algebras:
: $\phi_{*} : \mathfrak g \to \mathfrak h,$
which turns out to be a Lie algebra homomorphism (meaning that it is a linear map which preserves the Lie bracket). In the language of category theory, we then have a covariant functor from the category of Lie groups to the category of Lie algebras which sends a Lie group to its Lie algebra and a Lie group homomorphism to its derivative at the identity.
Two Lie groups are called *isomorphic* if there exists a bijective homomorphism between them whose inverse is also a Lie group homomorphism. Equivalently, it is a diffeomorphism which is also a group homomorphism. Observe that, by the above, a continuous homomorphism from a Lie group $G$ to a Lie group $H$ is an isomorphism of Lie groups if and only if it is bijective.
| 1,240 |
Lie group
| 6 |
17,945 |
# Lie group
## Basic concepts {#basic_concepts}
### Lie group versus Lie algebra isomorphisms {#lie_group_versus_lie_algebra_isomorphisms}
Isomorphic Lie groups necessarily have isomorphic Lie algebras; it is then reasonable to ask how isomorphism classes of Lie groups relate to isomorphism classes of Lie algebras.
The first result in this direction is Lie\'s third theorem, which states that every finite-dimensional, real Lie algebra is the Lie algebra of some (linear) Lie group. One way to prove Lie\'s third theorem is to use Ado\'s theorem, which says every finite-dimensional real Lie algebra is isomorphic to a matrix Lie algebra. Meanwhile, for every finite-dimensional matrix Lie algebra, there is a linear group (matrix Lie group) with this algebra as its Lie algebra.
On the other hand, Lie groups with isomorphic Lie algebras need not be isomorphic. Furthermore, this result remains true even if we assume the groups are connected. To put it differently, the *global* structure of a Lie group is not determined by its Lie algebra; for example, if *Z* is any discrete subgroup of the center of *G* then *G* and *G*/*Z* have the same Lie algebra (see the table of Lie groups for examples). An example of importance in physics are the groups SU(2) and SO(3). These two groups have isomorphic Lie algebras, but the groups themselves are not isomorphic, because SU(2) is simply connected but SO(3) is not.
On the other hand, if we require that the Lie group be simply connected, then the global structure is determined by its Lie algebra: two simply connected Lie groups with isomorphic Lie algebras are isomorphic. (See the next subsection for more information about simply connected Lie groups.) In light of Lie\'s third theorem, we may therefore say that there is a one-to-one correspondence between isomorphism classes of finite-dimensional real Lie algebras and isomorphism classes of simply connected Lie groups.
### Simply connected Lie groups {#simply_connected_lie_groups}
A Lie group $G$ is said to be **simply connected** if every loop in $G$ can be shrunk continuously to a point in `{{tmath|1= G }}`{=mediawiki}. This notion is important because of the following result that has simple connectedness as a hypothesis:
: **Theorem**: Suppose $G$ and $H$ are Lie groups with Lie algebras $\mathfrak g$ and $\mathfrak h$ and that $f:\mathfrak{g}\rightarrow\mathfrak{h}$ is a Lie algebra homomorphism. If $G$ is simply connected, then there is a unique Lie group homomorphism $\phi:G\rightarrow H$ such that `{{tmath|1= \phi_*=f }}`{=mediawiki}, where $\phi_*$ is the differential of $\phi$ at the identity.
Lie\'s third theorem says that every finite-dimensional real Lie algebra is the Lie algebra of a Lie group. It follows from Lie\'s third theorem and the preceding result that every finite-dimensional real Lie algebra is the Lie algebra of a *unique* simply connected Lie group.
An example of a simply connected group is the special unitary group SU(2), which as a manifold is the 3-sphere. The rotation group SO(3), on the other hand, is not simply connected. (See *Topology of SO(3)*.) The failure of SO(3) to be simply connected is intimately connected to the distinction between integer spin and half-integer spin in quantum mechanics. Other examples of simply connected Lie groups include the special unitary group SU(n), the spin group (double cover of rotation group) Spin(*n*) for `{{tmath|1= n\geq 3 }}`{=mediawiki}, and the compact symplectic group Sp(n).
Methods for determining whether a Lie group is simply connected or not are discussed in the article on fundamental groups of Lie groups.
| 569 |
Lie group
| 7 |
17,945 |
# Lie group
## Basic concepts {#basic_concepts}
### Exponential map {#exponential_map}
The exponential map from the Lie algebra $\mathrm{M}(n;\mathbb C)$ of the general linear group $\mathrm{GL}(n;\mathbb C)$ to $\mathrm{GL}(n;\mathbb C)$ is defined by the matrix exponential, given by the usual power series:
: $\exp(X) = 1 + X + \frac{X^2}{2!} + \frac{X^3}{3!} + \cdots$
for matrices `{{tmath|1= X }}`{=mediawiki}. If $G$ is a closed subgroup of `{{tmath|1= \mathrm{GL}(n;\mathbb C) }}`{=mediawiki}, then the exponential map takes the Lie algebra of $G$ into `{{tmath|1= G }}`{=mediawiki}; thus, we have an exponential map for all matrix groups. Every element of $G$ that is sufficiently close to the identity is the exponential of a matrix in the Lie algebra.
The definition above is easy to use, but it is not defined for Lie groups that are not matrix groups, and it is not clear that the exponential map of a Lie group does not depend on its representation as a matrix group. We can solve both problems using a more abstract definition of the exponential map that works for all Lie groups, as follows.
For each vector $X$ in the Lie algebra $\mathfrak{g}$ of $G$ (i.e., the tangent space to $G$ at the identity), one proves that there is a unique one-parameter subgroup $c:\mathbb R\rightarrow G$ such that `{{tmath|1= c'(0)=X }}`{=mediawiki}. Saying that $c$ is a one-parameter subgroup means simply that $c$ is a smooth map into $G$ and that
: $c(s + t) = c(s) c(t)\$
for all $s$ and `{{tmath|1= t }}`{=mediawiki}. The operation on the right hand side is the group multiplication in `{{tmath|1= G }}`{=mediawiki}. The formal similarity of this formula with the one valid for the exponential function justifies the definition
: $\exp(X) = c(1) .$
This is called the **exponential map**, and it maps the Lie algebra $\mathfrak{g}$ into the Lie group `{{tmath|1= G }}`{=mediawiki}. It provides a diffeomorphism between a neighborhood of 0 in $\mathfrak{g}$ and a neighborhood of $e$ in `{{tmath|1= G }}`{=mediawiki}. This exponential map is a generalization of the exponential function for real numbers (because $\mathbb{R}$ is the Lie algebra of the Lie group of positive real numbers with multiplication), for complex numbers (because $\mathbb{C}$ is the Lie algebra of the Lie group of non-zero complex numbers with multiplication) and for matrices (because $M(n, \mathbb{R})$ with the regular commutator is the Lie algebra of the Lie group $\mathrm{GL}(n, \mathbb{R})$ of all invertible matrices).
Because the exponential map is surjective on some neighbourhood $N$ of `{{tmath|1= e }}`{=mediawiki}, it is common to call elements of the Lie algebra **infinitesimal generators** of the group `{{tmath|1= G }}`{=mediawiki}. The subgroup of $G$ generated by $N$ is the identity component of `{{tmath|1= G }}`{=mediawiki}.
The exponential map and the Lie algebra determine the *local group structure* of every connected Lie group, because of the Baker–Campbell–Hausdorff formula: there exists a neighborhood $U$ of the zero element of `{{tmath|1= \mathfrak{g} }}`{=mediawiki}, such that for $X,Y\in U$ we have
: $\exp(X)\,\exp(Y) = \exp\left(X + Y + \tfrac{1}{2}[X,Y] + \tfrac{1}{12}[\,[X,Y],Y] - \tfrac{1}{12}[\,[X,Y],X] - \cdots \right),$
where the omitted terms are known and involve Lie brackets of four or more elements. In case $X$ and $Y$ commute, this formula reduces to the familiar exponential law `{{tmath|1= \exp(X)\exp(Y)=\exp(X+Y) }}`{=mediawiki}.
The exponential map relates Lie group homomorphisms. That is, if $\phi : G \to H$ is a Lie group homomorphism and $\phi_* : \mathfrak{g} \to \mathfrak{h}$ the induced map on the corresponding Lie algebras, then for all $x \in \mathfrak g$ we have
: $\phi(\exp(x)) = \exp(\phi_{*}(x)) .$
In other words, the following diagram commutes,
(In short, exp is a natural transformation from the functor Lie to the identity functor on the category of Lie groups.)
The exponential map from the Lie algebra to the Lie group is not always onto, even if the group is connected (though it does map onto the Lie group for connected groups that are either compact or nilpotent). For example, the exponential map of `{{nowrap|[[SL2(R)|SL(2, '''R''')]]}}`{=mediawiki} is not surjective. Also, the exponential map is neither surjective nor injective for infinite-dimensional (see below) Lie groups modelled on *C*^∞^ Fréchet space, even from arbitrary small neighborhood of 0 to corresponding neighborhood of 1.
### Lie subgroup {#lie_subgroup}
A **Lie subgroup** $H$ of a Lie group $G$ is a Lie group that is a subset of $G$ and such that the inclusion map from $H$ to $G$ is an injective immersion and group homomorphism. According to Cartan\'s theorem, a closed subgroup of $G$ admits a unique smooth structure which makes it an embedded Lie subgroup of $G$---i.e. a Lie subgroup such that the inclusion map is a smooth embedding.
Examples of non-closed subgroups are plentiful; for example take $G$ to be a torus of dimension 2 or greater, and let $H$ be a one-parameter subgroup of *irrational slope*, i.e. one that winds around in *G*. Then there is a Lie group homomorphism $\varphi:\mathbb{R}\to G$ with `{{tmath|1= \mathrm{im}(\varphi) = H }}`{=mediawiki}. The closure of $H$ will be a sub-torus in `{{tmath|1= G }}`{=mediawiki}.
The exponential map gives a one-to-one correspondence between the connected Lie subgroups of a connected Lie group $G$ and the subalgebras of the Lie algebra of `{{tmath|1= G }}`{=mediawiki}. Typically, the subgroup corresponding to a subalgebra is not a closed subgroup. There is no criterion solely based on the structure of $G$ which determines which subalgebras correspond to closed subgroups.
| 890 |
Lie group
| 8 |
17,945 |
# Lie group
## Representations
One important aspect of the study of Lie groups is their representations, that is, the way they can act (linearly) on vector spaces. In physics, Lie groups often encode the symmetries of a physical system. The way one makes use of this symmetry to help analyze the system is often through representation theory. Consider, for example, the time-independent Schrödinger equation in quantum mechanics, `{{tmath|1= \hat{H}\psi = E\psi }}`{=mediawiki}. Assume the system in question has the rotation group SO(3) as a symmetry, meaning that the Hamiltonian operator $\hat{H}$ commutes with the action of SO(3) on the wave function `{{tmath|1= \psi }}`{=mediawiki}. (One important example of such a system is the hydrogen atom, which has a spherically symmetric potential.) This assumption does not necessarily mean that the solutions $\psi$ are rotationally invariant functions. Rather, it means that the *space* of solutions to $\hat{H}\psi = E\psi$ is invariant under rotations (for each fixed value of $E$). This space, therefore, constitutes a representation of SO(3). These representations have been classified and the classification leads to a substantial simplification of the problem, essentially converting a three-dimensional partial differential equation to a one-dimensional ordinary differential equation.
The case of a connected compact Lie group *K* (including the just-mentioned case of SO(3)) is particularly tractable. In that case, every finite-dimensional representation of *K* decomposes as a direct sum of irreducible representations. The irreducible representations, in turn, were classified by Hermann Weyl. The classification is in terms of the \"highest weight\" of the representation. The classification is closely related to the classification of representations of a semisimple Lie algebra.
One can also study (in general infinite-dimensional) unitary representations of an arbitrary Lie group (not necessarily compact). For example, it is possible to give a relatively simple explicit description of the representations of the group SL(2, **R**) and the representations of the Poincaré group.
| 310 |
Lie group
| 9 |
17,945 |
# Lie group
## Classification
Lie groups may be thought of as smoothly varying families of symmetries. Examples of symmetries include rotation about an axis. What must be understood is the nature of \'small\' transformations, for example, rotations through tiny angles, that link nearby transformations. The mathematical object capturing this structure is called a Lie algebra (Lie himself called them \"infinitesimal groups\"). It can be defined because Lie groups are smooth manifolds, so have tangent spaces at each point.
The Lie algebra of any compact Lie group (very roughly: one for which the symmetries form a bounded set) can be decomposed as a direct sum of an abelian Lie algebra and some number of simple ones. The structure of an abelian Lie algebra is mathematically uninteresting (since the Lie bracket is identically zero); the interest is in the simple summands. Hence the question arises: what are the simple Lie algebras of compact groups? It turns out that they mostly fall into four infinite families, the \"classical Lie algebras\" A~*n*~, B~*n*~, C~*n*~ and D~*n*~, which have simple descriptions in terms of symmetries of Euclidean space. But there are also just five \"exceptional Lie algebras\" that do not fall into any of these families. E~8~ is the largest of these.
Lie groups are classified according to their algebraic properties (simple, semisimple, solvable, nilpotent, abelian), their connectedness (connected or simply connected) and their compactness.
A first key result is the Levi decomposition, which says that every simply connected Lie group is the semidirect product of a solvable normal subgroup and a semisimple subgroup.
- Connected compact Lie groups are all known: they are finite central quotients of a product of copies of the circle group *S*^1^ and simple compact Lie groups (which correspond to connected Dynkin diagrams).
- Any simply connected solvable Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices of some rank, and any finite-dimensional irreducible representation of such a group is 1-dimensional. Solvable groups are too messy to classify except in a few small dimensions.
- Any simply connected nilpotent Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices with 1s on the diagonal of some rank, and any finite-dimensional irreducible representation of such a group is 1-dimensional. Like solvable groups, nilpotent groups are too messy to classify except in a few small dimensions.
- Simple Lie groups are sometimes defined to be those that are simple as abstract groups, and sometimes defined to be connected Lie groups with a simple Lie algebra. For example, SL(2, **R**) is simple according to the second definition but not according to the first. They have all been classified (for either definition).
- Semisimple Lie groups are Lie groups whose Lie algebra is a product of simple Lie algebras. They are central extensions of products of simple Lie groups.
The identity component of any Lie group is an open normal subgroup, and the quotient group is a discrete group. The universal cover of any connected Lie group is a simply connected Lie group, and conversely any connected Lie group is a quotient of a simply connected Lie group by a discrete normal subgroup of the center. Any Lie group *G* can be decomposed into discrete, simple, and abelian groups in a canonical way as follows. Write
: *G*~con~ for the connected component of the identity
: *G*~sol~ for the largest connected normal solvable subgroup
: *G*~nil~ for the largest connected normal nilpotent subgroup
so that we have a sequence of normal subgroups
: .
Then
: *G*/*G*~con~ is discrete
: *G*~con~/*G*~sol~ is a central extension of a product of simple connected Lie groups.
: *G*~sol~/*G*~nil~ is abelian. A connected abelian Lie group is isomorphic to a product of copies of **R** and the circle group *S*^1^.
: *G*~nil~/1 is nilpotent, and therefore its ascending central series has all quotients abelian.
This can be used to reduce some problems about Lie groups (such as finding their unitary representations) to the same problems for connected simple groups and nilpotent and solvable subgroups of smaller dimension.
- The diffeomorphism group of a Lie group acts transitively on the Lie group
- Every Lie group is parallelizable, and hence an orientable manifold (there is a bundle isomorphism between its tangent bundle and the product of itself with the tangent space at the identity)
| 729 |
Lie group
| 10 |
17,945 |
# Lie group
## Infinite-dimensional Lie groups {#infinite_dimensional_lie_groups}
Lie groups are often defined to be finite-dimensional, but there are many groups that resemble Lie groups, except for being infinite-dimensional. The simplest way to define infinite-dimensional Lie groups is to model them locally on Banach spaces (as opposed to Euclidean space in the finite-dimensional case), and in this case much of the basic theory is similar to that of finite-dimensional Lie groups. However this is inadequate for many applications, because many natural examples of infinite-dimensional Lie groups are not Banach manifolds. Instead one needs to define Lie groups modeled on more general locally convex topological vector spaces. In this case the relation between the Lie algebra and the Lie group becomes rather subtle, and several results about finite-dimensional Lie groups no longer hold.
The literature is not entirely uniform in its terminology as to exactly which properties of infinite-dimensional groups qualify the group for the prefix *Lie* in *Lie group*. On the Lie algebra side of affairs, things are simpler since the qualifying criteria for the prefix *Lie* in *Lie algebra* are purely algebraic. For example, an infinite-dimensional Lie algebra may or may not have a corresponding Lie group. That is, there may be a group corresponding to the Lie algebra, but it might not be nice enough to be called a Lie group, or the connection between the group and the Lie algebra might not be nice enough (for example, failure of the exponential map to be onto a neighborhood of the identity). It is the \"nice enough\" that is not universally defined.
Some of the examples that have been studied include:
- The group of diffeomorphisms of a manifold. Quite a lot is known about the group of diffeomorphisms of the circle. Its Lie algebra is (more or less) the Witt algebra, whose central extension the Virasoro algebra (see Virasoro algebra from Witt algebra for a derivation of this fact) is the symmetry algebra of two-dimensional conformal field theory. Diffeomorphism groups of compact manifolds of larger dimension are regular Fréchet Lie groups; very little about their structure is known.
- The diffeomorphism group of spacetime sometimes appears in attempts to quantize gravity.
- The group of smooth maps from a manifold to a finite-dimensional Lie group is an example of a gauge group (with operation of pointwise multiplication), and is used in quantum field theory and Donaldson theory. If the manifold is a circle these are called loop groups, and have central extensions whose Lie algebras are (more or less) Kac–Moody algebras.
- There are infinite-dimensional analogues of general linear groups, orthogonal groups, and so on. One important aspect is that these may have *simpler* topological properties: see for example Kuiper\'s theorem. In M-theory, for example, a 10-dimensional SU(*N*) gauge theory becomes an 11-dimensional theory when *N* becomes infinite
| 470 |
Lie group
| 11 |
17,968 |
# Louchébem
***Louchébem*** or ***loucherbem*** (`{{IPA|fr|luʃebɛm}}`{=mediawiki}) is Parisian and Lyonnaise butchers\' (French *boucher*) slang, similar to Pig Latin and Verlan. It originated in the mid-19th century and was in common use until the 1950s.
## Process
The *louchébem* word-creation process resembles that of *largonji*, *\[\[verlan\]\]*, and *\[\[javanais\]\]*, in that existing words are camouflaged according to a set of rules. Strictly speaking, *louchébem* is a more rigid variety of *largonji* in which the ending *-èm* is obligatory. *Largonji* substitutes `{{angle bracket|l}}`{=mediawiki} for the consonant or consonant cluster at the beginning of the word, or, if the word begins with an `{{angle bracket|l}}`{=mediawiki} or a vowel, the second syllable; the initial consonant is then reattached to the end of the word along with a suffix particular to the argot: *-ji* `{{IPA|fr|ʒi|}}`{=mediawiki}, *-oc* `{{IPA|fr|ɔk|}}`{=mediawiki}, *-ic* `{{IPA|fr|ik|}}`{=mediawiki}, *-uche* `{{IPA|fr|yʃ|}}`{=mediawiki}, *-ès* `{{IPA|fr|ɛs|}}`{=mediawiki}, or in the case of louchébem, *-em/ème* `{{IPA|fr|ɛm|}}`{=mediawiki}.
Note that *louchébem* is first and foremost an oral language, and spelling is usually phoneticized.
## History
Despite the name, *louchébem* seems to have been created not by butchers, but by inmates at Brest Prison, with records dating back to 1821.
Edmund Clerihew Bentley used the language as a plot point in his 1937 short story \"The Old-Fashioned Apache\".
During the Nazi occupation *louchébem* was used by Parisian members of the Resistance.
Even today, *louchébem* is still well-known and used among those working at point-of-sale in the meat retail industry. Some words have even leaked into common, everyday use by the masses; an example is the word `{{wikt-lang|fr|loufoque}}`{=mediawiki}, meaning \"eccentric\".
## Examples
Here are a few example Louchébem words.
English French Louchébem
------------------------ ---------- -------------------------------------------------------
slang
butcher
customer
coffeehouse
(don\'t) understand (*pas*) (*dans le lap*)
woman (lady) (*dame*) (*lamdé*)
blunder
boy/waiter
Roma (ethnicity)
leg (of mutton, etc.)
insane ; *loufoque*; *louftingue*
pork
mackerel
Sir; Mister; gentleman
piece
overcoat (*lardeussupem*)
excuse me?; sorry
to talk
manager
tip
bag
expensive ; *lerchem* (often in the negative, as *pas lerchem*)
sneakily ; *en loucedoc*
wallet ; *lortefeuillepem*
thief, crook
knife
There is another French argot called *largonji*, which differs from *louchébem* only in the suffix that is added (*-i* instead of *-em*); the term is derived from *jargon*
| 360 |
Louchébem
| 0 |
17,974 |
# Long gun
A **long gun** is a category of firearms with long barrels. In small arms, a *long gun* or **longarm** is generally designed to be held by both hands and braced against the shoulder, in contrast to a handgun, which can be fired being held with a single hand. In the context of cannons and mounted firearms, an artillery *long gun* would be contrasted with a field gun or howitzer.
## Small arms {#small_arms}
thumb\|upright=1.35\|U.S. Army Brigadier General Claudius Miller Easley practicing with an M1 Garand\|left The actual length of the barrels of a long gun is subject to various laws in many jurisdictions, mainly concerning minimum length, sometimes as measured in a specific position or configuration. The National Firearms Act in the United States sets a minimum length of 16 inch for rifle barrels and 18 inch for shotgun barrels. Canada sets a minimum of 18.5 inch for either. In addition, Canada sets a minimum fireable length for long guns with detachable or folding stocks 26 inch. In the United States, the minimum length for long guns with detachable or folding stocks is 26 in with the stock in the extended position.
Examples of various classes of small arms generally considered long arms include, but are not limited to shotguns, personal defense weapons, submachine guns, carbines, assault rifles, designated marksman rifles, sniper rifles, anti-material rifles, light machine guns, medium machine guns, and heavy machine guns.
### Advantages and disadvantages {#advantages_and_disadvantages}
Almost all long arms have front grips (forearms) and shoulder stocks, which provide the user the ability to hold the firearm more steadily than a handgun. In addition, the long barrel of a long gun usually provides a longer distance between the front and rear sights, providing the user with more precision when aiming. The presence of a stock makes the use of a telescopic sight or red dot sight easier than with a handgun.
The mass of a long gun is usually greater than that of a handgun, making the long gun more expensive to transport, and more difficult and tiring to carry. The increased moment of inertia makes the long gun slower and more difficult to traverse and elevate, and it is thus slower and more difficult to adjust the aim. However, this also results in greater stability in aiming. The greater amount of material in a long gun tends to make it more expensive to manufacture, other factors being equal. The greater size makes it more difficult to conceal, and more inconvenient to use in confined quarters, as well as requiring larger storage space.
As long guns include a stock that is braced against the shoulder, the recoil when firing is transferred directly into the body of the user. This allows better control of aim than handguns, which do not include stock, and thus all their recoil must be transferred to the arms of the user. It also makes it possible to manage larger amounts of recoil without damage or loss of control; in combination with the higher mass of long guns, this means more propellant (such as gunpowder) can be used and thus larger projectiles can be fired at higher velocities. This is one of the main reasons for the use of long guns over handguns---faster or heavier projectiles help with penetration and accuracy over longer distances.
Shotguns are long guns that are designed to fire many small projectiles at once. This makes them very effective at close ranges, but with diminished usefulness at long ranges, even with shotgun slugs they are mostly only effective to about 100 yd.
## Naval long guns {#naval_long_guns}
In historical navy usage, a **long gun** was the standard type of cannon mounted by a sailing vessel, called such to distinguish it from the much shorter carronades. In informal usage, the length was combined with the weight of the shot, yielding terms like \"long 9s\", referring to full-length cannons firing a 9-pound round shot
| 656 |
Long gun
| 0 |
17,981 |
# Law of definite proportions
In chemistry, the **law of definite proportions**, sometimes called **Proust\'s law** or the **law of constant composition**, states that a given chemical compound contains its constituent elements in a fixed ratio (by mass) and does not depend on its source or method of preparation. For example, oxygen makes up about ^8^/~9~ of the mass of any sample of pure water, while hydrogen makes up the remaining ^1^/~9~ of the mass: the mass of two elements in a compound are always in the same ratio. Along with the law of multiple proportions, the law of definite proportions forms the basis of stoichiometry.
## History
The law of definite proportion was given by Joseph Proust in 1797.
At the end of the 18th century, when the concept of a chemical compound had not yet been fully developed, the law was novel. In fact, when first proposed, it was a controversial statement and was opposed by other chemists, most notably Proust\'s fellow Frenchman Claude Louis Berthollet, who argued that the elements could combine in any proportion. The existence of this debate demonstrates that, at the time, the distinction between pure chemical compounds and mixtures had not yet been fully developed.
The law of definite proportions contributed to the atomic theory that John Dalton promoted beginning in 1805, which explained matter as consisting of discrete atoms, that there was one type of atom for each element, and that the compounds were made of combinations of different types of atoms in fixed proportions.
A related early idea was Prout\'s hypothesis, formulated by English chemist William Prout, who proposed that the hydrogen atom was the fundamental atomic unit. From this hypothesis was derived the whole number rule, which was the rule of thumb that atomic masses were whole number multiples of the mass of hydrogen. This was later rejected in the 1820s and 30s following more refined measurements of atomic mass, notably by Jöns Jacob Berzelius, which revealed in particular that the atomic mass of chlorine was 35.45, which was incompatible with the hypothesis. Since the 1920s this discrepancy has been explained by the presence of isotopes; the atomic mass of any isotope is very close to satisfying the whole number rule, with the mass defect caused by differing binding energies being significantly smaller.
## Non-stoichiometric compounds and isotopes {#non_stoichiometric_compounds_and_isotopes}
Although very useful in the foundation of modern chemistry, the law of definite proportions is not universally true. There exist non-stoichiometric compounds whose elemental composition can vary from sample to sample. Such compounds follow the law of multiple proportion. An example is the iron oxide wüstite, which can contain between 0.83 and 0.95 iron atoms for every oxygen atom, and thus contain anywhere between 23% and 25% oxygen by mass. The ideal formula is FeO, but it is about Fe~0.95~O due to crystallographic vacancies. In general, Proust\'s measurements were not precise enough to detect such variations.
In addition, the isotopic composition of an element can vary depending on its source, hence its contribution to the mass of even a pure stoichiometric compound may vary. This variation is used in radiometric dating since astronomical, atmospheric, oceanic, crustal and deep Earth processes may concentrate some environmental isotopes preferentially. With the exception of hydrogen and its isotopes, the effect is usually small, but is measurable with modern-day instrumentation.
Many natural polymers vary in composition (for instance DNA, proteins, carbohydrates) even when \"pure\". Polymers are generally not considered \"pure chemical compounds\" except when their molecular weight is uniform (mono-disperse) and their stoichiometry is constant
| 589 |
Law of definite proportions
| 0 |
17,982 |
# Limbo
`{{Roman Catholic Church}}`{=mediawiki} The unofficial term **Limbo** `{{IPAc-en|ˈ|l|ɪ|m|b|oʊ}}`{=mediawiki} (*limbus\]\]*, `{{gloss|edge}}`{=mediawiki} or `{{gloss|boundary}}`{=mediawiki}, referring to the edge of Hell) is the afterlife condition in medieval Catholic theology, of those who die in original sin without being assigned to the Hell of the Damned. However, it has become the general term to refer to nothing between time and space in general.
Some medieval theologians of Western Europe described the underworld (\"hell\", \"hades\", \"infernum\") as divided into three distinct parts: Hell of the Damned, Limbo of the Fathers or Patriarchs, and Limbo of the Infants.
The Limbo of the Fathers is the state or place for people who were friends of God but died before the death of Jesus Christ; when Jesus died he descended into hell and rescued the souls of those who had died before him: this is traditionally known as the harrowing of hell.
The Limbo of the Infants was the hope that just because a child died before baptism, it does not mean they deserve punishment (or are developed enough to be cognizant of separation from God), though they cannot have full salvation (or experience the Beatific Vision.) The Limbo of the Infants is neither affirmed nor denied by Catholic doctrine.
## Limbo of the Patriarchs {#limbo_of_the_patriarchs}
The \"Limbo of the Patriarchs\" or \"Limbo of the Fathers\" (Latin *limbus patrum*) is seen as the temporary state of those who, despite the sins they may have committed, died in the friendship of God but could not enter heaven until redemption by Jesus Christ made it possible. The term *Limbo of the Fathers* was a medieval name for the part of the underworld (Hades) where the patriarchs of the Old Testament were believed to be kept until Christ\'s soul descended into it by his death through crucifixion and freed them.
The Catechism of the Catholic Church describes Christ\'s descent into Hell as meaning primarily that \"the crucified one sojourned in the realm of the dead prior to his resurrection. This was the first meaning given in the apostolic preaching to Christ\'s descent into Hell: that Jesus, like all men, experienced death and in his soul joined the others in the realm of the dead.\" It adds: \"But he descended there as Saviour, proclaiming the Good News to the spirits imprisoned there.\" It does not use the word *Limbo*.
This concept of Limbo affirms that admittance to heaven is possible only through the intervention of Jesus Christ, but does not portray Moses, etc. as being punished eternally in Hell. The concept of Limbo of the Patriarchs is not spelled out in Scripture, but is seen by some`{{who|date=September 2021}}`{=mediawiki} as implicit in various references:
- Luke 16:22 speaks of the \"bosom of Abraham\", which both the Roman Catholic Church and the Eastern Orthodox Church, following early Christian writers, understand as a temporary state of souls awaiting entrance into heaven. The end of that state is set either at the Resurrection of the Dead, the most common interpretation in the East, or at the Harrowing of Hell, the most common interpretation in the West, but adopted also by some in the East.
- Jesus told the Good Thief that the two of them would be together \"this day\" in Paradise (Luke 23:43; see also Matthew 27:38); but on the Sunday of his resurrection he said that he had \"not yet ascended to the Father\" (John 20:17). At least one Medieval devotional source and a course of Catholic religious instruction dating to or before the early 1900s posit the view that the descent of Jesus Christ to the abode of the dead, his presence among them, turned it into a paradise. It is also possible that the intended text was not \"I say to you, This day you will be with me in paradise\", but \"I say to you this day, You will be with me in paradise\". Timothy Radcliffe explained the \"today\" as a reference to the \"Today of eternity\".
- Jesus is also described as preaching to \"the spirits in prison\" (1 Peter 3:19). Medieval drama sometimes portrayed Christ leading a dramatic assault -- the Harrowing of Hell -- during the three days between the Crucifixion and the resurrection. In this assault, Jesus freed the souls of the just and escorted them triumphantly into heaven. This imagery is still used in the Eastern Orthodox Church\'s Holy Saturday liturgy (between Good Friday and Pascha) and in Eastern Orthodox icons of the Resurrection of Jesus.
- The doctrine expressed by the term *Limbo of the Fathers* was taught, for instance, by Clement of Alexandria (`{{c.|150|215}}`{=mediawiki}), who maintained: \"It is not right that these should be condemned without trial, and that those alone who lived after the coming \[of Christ\] should have the advantage of the divine righteousness.\"
According to Saint Thomas Aquinas, unlike Purgatory and Hell, in the Limbo of Patriarchs there was not the penalty of sense (the affliction by fire in which the soul burns after death and also the body after the resurrection of the flesh), but solely the penalty of harm, which is the privation of the beatific vision of God. However, the souls in Limbo of Patriarchs enjoyed the natural knowledge of God and experienced great joy because of the future glory that awaited them in Paradise.
| 879 |
Limbo
| 0 |
17,982 |
# Limbo
## Limbo of Infants {#limbo_of_infants}
right\|thumb\|upright=1.4\|Byzantine depiction in the Church of Chora of the resurrection of Christ, raising Adam and Eve who represent all humankind, with the righteous prophets of the Old Testament observing
The Limbo of Infants (Latin *limbus infantium* or *limbus puerorum*) is the hypothetical permanent status of the unbaptised who die in infancy, too young to have committed actual sins, but not having been freed from original sin. Recent Catholic theological speculation tends to stress the hope, although not the certainty, that these infants may attain heaven instead of the state of Limbo. Many Catholic priests and prelates say that the souls of unbaptized children must simply be \"entrusted to the mercy of God\", and whatever their status is cannot be known.
While the Catholic Church has a defined doctrine on original sin, it has none on the eternal fate of unbaptised infants, leaving theologians free to propose different theories, which magisterium is free to accept or reject. Nonetheless, according to Catholic dogma, baptism, or at least the desire for it, along with supernatural faith or at least the \"habit of faith\", are necessary for salvation. Hence, it is not immediately clear how to reconcile the mercy of God for unbaptized infants with the necessity of baptism and Catholic faith for salvation. Several theories have been proposed. Limbo is one such theory, although the word *limbo* itself is never mentioned in the Catechism of the Catholic Church. Nonetheless, the theory of limbo has weighty support in the traditional teaching of the Doctors of the Church, such as Saint Thomas Aquinas, Saint Augustine, and Saint Alphonsus Liguori.
### Latin Fathers {#latin_fathers}
In countering Pelagius, who denied original sin, Saint Augustine of Hippo was led to state that because of original sin, \"such infants as quit the body without being baptized will be involved in the mildest condemnation of all. That person, therefore, greatly deceives both himself and others, who teaches that they will not be involved in condemnation; whereas the apostle says: \'Judgment from one offence to condemnation\' (Romans 5:16), and again a little after: \'By the offence of one upon all persons to condemnation\'.\"
In 418, the Council of Carthage, a synod of North African bishops which included Augustine of Hippo, did not explicitly endorse all aspects of Augustine\'s stern view about the destiny of infants who die without baptism, but stated in some manuscripts \"that there is no intermediate or other happy dwelling place for children who have left this life without Baptism, without which they cannot enter the kingdom of heaven, that is, eternal life\". So great was Augustine\'s influence in the West, however, that the Latin Fathers of the 5th and 6th centuries (e.g., Jerome, Avitus of Vienne, and Gregory the Great) did adopt his position.
### Medieval theologians {#medieval_theologians}
In the later Medieval period, some theologians continued to hold Augustine\'s view. In the 12th century, Peter Abelard (1079--1142) said that these infants suffered no material torment or positive punishment, just the pain of loss at being denied the beatific vision. Others held that unbaptised infants suffered no pain at all: unaware of being deprived of the beatific vision, they enjoyed a state of natural, not supernatural happiness. This theory was associated with but independent of the term \"Limbo of Infants\", which was coined about the year 1300.
If heaven is a state of supernatural happiness and union with God, and Hell is understood as a state of torture and separation from God then, in this view, the Limbo of Infants, although technically part of hell (the outermost part, *limbo* meaning \'outer edge\' or \'hem\') is seen as a sort of intermediate state.
The question of Limbo is not treated in the parts of the *\[\[Summa Theologica\]\]* by Thomas Aquinas, but is dealt with in an appendix to the supplement added after his death compiled from his earlier writings. The Limbo of Infants is there described as an eternal state of natural joy, untempered by any sense of loss at how much greater their joy might have been had they been baptised:
The natural happiness possessed in this place would consist in the perception of God mediated through creatures. As stated in the International Theological Commission\'s document on the question:
The afterdeath life cartography that runs through Christian thought from Bernard of Clairvaux to Aquinas is thus composed of five real and physical places: Paradise, Limbo of Patriarchs, Limbo of the Infants, Purgatory and Hell.
| 743 |
Limbo
| 1 |
17,982 |
# Limbo
## Limbo of Infants {#limbo_of_infants}
### Modern era {#modern_era}
In 1442, the Ecumenical Council of Florence spoke of baptism as necessary even for children, and required that they be baptised soon after birth. This had earlier been affirmed at the Council of Carthage in 418. The Council of Florence also stated that those who die in original sin alone go to Hell, but with pains unequal to those suffered by those who had committed actual mortal sins. John Wycliffe\'s attack on the necessity of infant baptism was condemned by another general council, the Council of Constance. In 1547, the Council of Trent explicitly decreed that baptism (or desire for baptism) was the means by which one is transferred \"from that state wherein man is born a child of the first Adam, to the state of grace, and of the adoption of the sons of God, through the second Adam, Jesus Christ, our Saviour. Pope Pius X taught of Limbo\'s existence in his Catechism.
However, throughout the 18th and 19th centuries, individual theologians (Bianchi in 1768, H. Klee in 1835, Caron in 1855, H. Schell in 1893) continued to formulate theories of how children who died unbaptised might still be saved. By 1952 a theologian such as Ludwig Ott could, in a widely used and well-regarded manual, openly teach the possibility that children who die unbaptised might be saved for heaven. He also told about Thomas Cajetan, a major 16th-century theologian, that suggested infants dying in the womb before birth, and so before ordinary sacramental baptism could be administered, might be saved through their mother\'s wish for their baptism. In its 1980 instruction on children\'s baptism the Congregation for the Doctrine of the Faith stated that \"with regard to children who die without having received baptism, the Church can only entrust them to the mercy of God, as indeed she does in the funeral rite established for them\", leaving all theories as to their fate, including Limbo, as viable possibilities. In 1984, when Joseph Ratzinger, then Cardinal Prefect of that Congregation, stated that he rejected the claim that children who die unbaptised cannot attain salvation, he was speaking for many academic theologians of his training and background.
The Church\'s teaching, expressed in the 1992 Catechism of the Catholic Church, is that \"Baptism is necessary for salvation for those to whom the Gospel has been proclaimed and who have had the possibility of asking for this sacrament\", and that \"God has bound salvation to the sacrament of Baptism, but he himself is not bound by his sacraments\". It recalls that, apart from the sacrament, baptism of blood (as in the case of Christian martyrs) and in the case of catechumens who die before receiving the sacrament, explicit desire for baptism, together with Catholic faith, repentance for their sins (specifically perfect contrition, in the case of catechumens) and charity, ensures salvation. It also states that since Christ died for all and all are called to the same divine destiny, \"every man who is ignorant of the Gospel of Christ and of his Church, but seeks the truth and does the will of God in accordance with his understanding of it, can be saved\", seeing that, if they had known of the necessity of baptism, they would have desired it explicitly. Additionally, at the Council of Trent and in the Vatican\'s response to Feeneyism in the 1940s, the Church affirmed in every case the necessity of Catholic faith (also called \"supernatural faith\"), or at least the \"habit of faith\", for salvation.
It then states:
Merely stating that one can \"hope\" in a way of salvation other than baptism, the Church thus urgently reiterates its appeal to baptize infants, the only certain means to \"not prevent\" their \"coming to Christ\" for salvation.
On 20 April 2007, the advisory body known as the International Theological Commission released a document, originally commissioned by Pope John Paul II, entitled \"The Hope of Salvation for Infants Who Die without Being Baptized.\" After tracing the history of the various opinions that have been and are held on the eternal fate of unbaptized infants, including that connected with the theory of the Limbo of Infants, and after examining the theological arguments, the document stated its conclusion as follows:
Pope Benedict XVI authorized publication of this document, indicating that he considers it consistent with the Church\'s teaching, though it is not an official expression of that teaching. Media reports that by the document \"the Pope closed Limbo\" are thus without foundation. In fact, the document explicitly states that \"the theory of *limbo* \[\...\] never entered into the dogmatic definitions of the Magisterium. Still, that same Magisterium did at times mention the theory in its ordinary teaching up until the Second Vatican Council. It remains therefore a possible theological hypothesis\". The document thus allows the limbo hypothesis to be held as one of the existing theories about the fate of children who die without being baptised, a question on which there is \"no explicit answer\" from Scripture or tradition. The traditional theological alternative to Limbo was not heaven, but rather some degree of suffering in Hell. At any rate, these theories are not the official teaching of the Catholic Church but rather opinions that the Church permits to be held by its members, just as is the theory of possible salvation for infants dying without baptism.
| 895 |
Limbo
| 2 |
17,982 |
# Limbo
## In other denominations and religions {#in_other_denominations_and_religions}
### Judaism
While Jewish sources are conflicted about what happens to individuals after they die, the concept of limbo does not arise. Furthermore, even the conception of Hell in Judaism is presented as a temporary stage, typically transpiring over a short period of time. According to Talmud, the judgment of the wicked in Gehenna lasts for twelve months. This teaching is attributed to Rabbi Akiva (50-135 AD).
### Christianity
#### Protestant and Eastern Orthodox {#protestant_and_eastern_orthodox}
Neither the Eastern Orthodox Church nor Protestantism accepts the concept of a limbo of infants; but, while not using the expression \"Limbo of the Patriarchs\", the Eastern Orthodox Church lays much stress on the resurrected Christ\'s action of liberating Adam and Eve and other righteous figures of the Old Testament, such as Abraham and David, from Hades (see Harrowing of Hell).
Some Protestants have a similar understanding of those who died as believers prior to the crucifixion of Jesus residing in a place that is not Heaven, but not Hell. The doctrine holds that Hades has two \"compartments\", one an unnamed place of torment, the other named \"Abraham\'s bosom\". Luke 16:19--16:26 speaks of a chasm fixed between the two which cannot be crossed. Those in the unnamed \"compartment\" have no hope, and will ultimately be consigned to hell. Those in Abraham\'s bosom are those of whom it is written of Jesus, \"When He ascended on high, He led captive a host of captives\" (Ephesians 4:8), quoting Psalm 68:18). These individuals, the captives, now reside with God in Heaven. Both \"Compartments\" still exist, but Abraham\'s bosom is now empty, while the other chamber is not, according to this doctrine.
#### Nontrinitarian
Latter-day Saints teach that \"there is a space between death and the resurrection of the body \[\...\] a state of the soul in happiness or in misery until the time \[\...\] that the dead shall come forth, and be reunited, both soul and body, and be brought to stand before God, and be judged according to their works.\" It is also taught that \"all who have died without a knowledge of \[the\] gospel, who would have received it if they had been permitted to tarry, shall be heirs of the celestial kingdom of God.\".
Jehovah\'s Witnesses, Christadelphians, and others have taught that the dead are unconscious (or even nonexistent), awaiting their destiny on Judgment Day.
### Zoroastrianism
The Zoroastrian concept of *hamistagan* is similar to Limbo. Hamistagan is a neutral state in which a soul that was neither good nor evil awaits Judgment Day.
### Islam
In Islam, which denies the existence of original sin in totality, the concept of Limbo exists as `{{transliteration|ar|[[Barzakh]]}}`{=mediawiki}, the state that exists after death, prior to the day of resurrection. During this period, sinners are punished and the adequately purified rest in comfort. Children, however, are exempt from this stage, as they are regarded as innocent and are automatically classed as Muslims (despite religious upbringing). After death, they go directly to Heaven, where they are cared for by Abraham. According to Christian Louis Lange, Islam also possesses a `{{transliteration|ar|al-aʿrāf}}`{=mediawiki} (cf. Q.7:46) \"a residual place or limbo\" situated between heaven and hell where there is \"neither punishment nor reward\".
### Greek mythology {#greek_mythology}
In Classical Greek mythology, the section of Hades known as the Fields of Asphodel were a realm much resembling Limbo, to which the vast majority of people who were held to have deserved neither the Elysian Fields (Heaven) nor Tartarus (Hell) were consigned for eternity.
### Buddhism
In Buddhism, *Bardo* (Sanskrit: `{{transliteration|sa|antarabhāva}}`{=mediawiki}) is sometimes described as similar to limbo. It is an intermediate state in which the recently deceased experiences various phenomena before being reborn in another state, including heaven or hell. According to Mahāyāna Buddhism, the arhat must ultimately embrace the path of the bodhisattva, despite having reached enlightenment. The Laṅkāvatāra Sūtra states that an arhat obtains a `{{transliteration|sa|samādhikāya}}`{=mediawiki} (`{{gloss|rapture-body}}`{=mediawiki}) and is reborn in a lotus in a transitory state of existence, unable to awaken for a whole eon. This is likened to a person intoxicated who must spend a certain period of time before becoming sober
| 690 |
Limbo
| 3 |
17,994 |
# Learning theory (education)
**Learning theory** attempts to describe how students receive, process, and retain knowledge during learning. Cognitive, emotional, and environmental influences, as well as prior experience, all play a part in how understanding, or a worldview, is acquired or changed and knowledge and skills retained.
Behaviorists look at learning as an aspect of conditioning and advocating a system of rewards and targets in education. Educators who embrace cognitive theory believe that the definition of learning as a change in behaviour is too narrow, and study the learner rather than their environment---and in particular the complexities of human memory. Those who advocate constructivism believe that a learner\'s ability to learn relies largely on what they already know and understand, and the acquisition of knowledge should be an individually tailored process of construction. Transformative learning theory focuses on the often-necessary change required in a learner\'s preconceptions and worldview. Geographical learning theory focuses on the ways that contexts and environments shape the learning process.
Outside the realm of educational psychology, techniques to directly observe the functioning of the brain during the learning process, such as event-related potential and functional magnetic resonance imaging, are used in educational neuroscience. The theory of multiple intelligences, where learning is seen as the interaction between dozens of different functional areas in the brain each with their own individual strengths and weaknesses in any particular human learner, has also been proposed, but empirical research has found the theory to be unsupported by evidence.
## Educational philosophy {#educational_philosophy}
### Classical theorists {#classical_theorists}
#### Plato
Plato (428 BC--347 BC) proposed the question: \"How does an individual learn something new when the topic is brand new to that person?\", This question may seem trivial; however, think of a human-like a computer. The question would then become: How does a computer take in any factual information without previous programming? Plato answered his own question by stating that knowledge is present at birth and all information learned by a person is merely a recollection of something the soul has already learned previously, which is called the Theory of Recollection or Platonic epistemology. This answer could be further justified by a paradox: If a person knows something, they don\'t need to question it, and if a person does not know something, they don\'t know to question it. Plato says that if one did not previously know something, then they cannot learn it. He describes learning as a passive process, where information and knowledge are ironed into the soul over time. However, Plato\'s theory elicits even more questions about knowledge: If we can only learn something when we already had the knowledge impressed onto our souls, then how did our souls gain that knowledge in the first place? Plato\'s theory can seem convoluted; however, his classical theory can still help us understand knowledge today.
#### Locke
John Locke (1632--1704) offered an answer to Plato\'s question as well. Locke offered the \"blank slate\" theory where humans are born into the world with no innate knowledge and are ready to be written on and influenced by the environment. The thinker maintained that knowledge and ideas originate from two sources, which are sensation and reflection. The former provides insights regarding external objects (including their properties) while the latter provides the ideas about one\'s mental faculties (volition and understanding). In the theory of empiricism, these sources are direct experience and observation. Locke, like David Hume, is considered an empiricist because he locates the source of human knowledge in the empirical world.
Locke recognized that something had to be present, however. This something, to Locke, seemed to be \"mental powers\". Locke viewed these powers as a biological ability the baby is born with, similar to how a baby knows how to biologically function when born. So as soon as the baby enters the world, it immediately has experiences with its surroundings and all of those experiences are being transcribed to the baby\'s \"slate\". All of the experiences then eventually culminate into complex and abstract ideas. This theory can still help teachers understand their students\' learning today.
| 677 |
Learning theory (education)
| 0 |
17,994 |
# Learning theory (education)
## Educational psychology {#educational_psychology}
### Behavior analysis {#behavior_analysis}
The term \"behaviorism\" was coined by American psychologist John Watson (1878--1959). Watson believed the behaviorist view is a purely objective experimental branch of natural science with a goal to predict and control behavior. In an article in the *Psychological Review*, he stated that, \"Its theoretical goal is the prediction and control of behavior. Introspection forms no essential part of its methods, nor is the scientific value of its data dependent upon the readiness with which they lend themselves to interpretation in terms of consciousness.\"
Methodological behaviorism is based on the theory of only explaining public events, or observable behavior. B.F. Skinner introduced another type of behaviorism called radical behaviorism, or the conceptual analysis of behavior, which is based on the theory of also explaining private events; particularly, thinking and feelings. Radical behaviorism forms the conceptual piece of behavior analysis.
In behavior analysis, learning is the acquisition of a new behavior through conditioning and social learning.
#### Learning and conditioning {#learning_and_conditioning}
The three main types of conditioning and learning:
- Classical conditioning, where the behavior becomes a reflex response to an antecedent stimulus.
- Operant conditioning, where antecedent stimuli results from the consequences that follow the behavior through a reward (reinforcement) or a punishment.
- Social learning theory, where an observation of behavior is followed by modeling.
Ivan Pavlov discovered classical conditioning. He observed that if dogs come to associate the delivery of food with a white lab coat or the ringing of a bell, they produce saliva, even when there is no sight or smell of food. Classical conditioning considers this form of learning the same, whether in dogs or in humans. Operant conditioning reinforces this behavior with a reward or a punishment. A reward increases the likelihood of the behavior recurring, a punishment decreases its likelihood. Social learning theory observes behavior and is followed with modeling.
These three learning theories form the basis of applied behavior analysis, the application of behavior analysis, which uses analyzed antecedents, functional analysis, replacement behavior strategies, and often data collection and reinforcement to change behavior. The old practice was called behavior modification, which only used *assumed* antecedents and consequences to change behavior without acknowledging the conceptual analysis; analyzing the function of behavior and teaching of new behaviors that would serve the same function was never relevant in behavior modification.
Behaviorists view the learning process as a change in behavior, and arrange the environment to elicit desired responses through such devices as behavioral objectives, Competency-based learning, and skill development and training. Educational approaches such as Early Intensive Behavioral Intervention, curriculum-based measurement, and direct instruction have emerged from this model.
#### Transfer of learning {#transfer_of_learning}
Transfer of learning is the idea that what one learns in school somehow carries over to situations different from that particular time and that particular setting. Transfer was amongst the first phenomena tested in educational psychology. Edward Lee Thorndike was a pioneer in transfer research. He found that though transfer is extremely important for learning, it is a rarely occurring phenomenon. In fact, he held an experiment where he had the subjects estimate the size of a specific shape and then he would switch the shape. He found that the prior information did not help the subjects; instead it impeded their learning.
One explanation of why transfer does not occur often involves surface structure and deep structure. The surface structure is the way a problem is framed. The deep structure is the steps for the solution. For example, when a math story problem changes contexts from asking how much it costs to reseed a lawn to how much it costs to varnish a table, they have different surface structures, but the steps for getting the answers are the same. However, many people are more influenced by the surface structure. In reality, the surface structure is unimportant. Nonetheless, people are concerned with it because they believe that it provides background knowledge on how to do the problem. Consequently, this interferes with their understanding of the deep structure of the problem. Even if somebody tries to concentrate on the deep structure, transfer still may be unsuccessful because the deep structure is not usually obvious. Therefore, surface structure gets in the way of people\'s ability to see the deep structure of the problem and transfer the knowledge they have learned to come up with a solution to a new problem.
Current learning pedagogies focus on conveying rote knowledge, independent of the context that gives it meaning. Because of this, students often struggle to transfer this stand-alone information into other aspects of their education. Students need much more than abstract concepts and self-contained knowledge; they need to be exposed to learning that is practiced in the context of authentic activity and culture. Critics of situated cognition, however, would argue that by discrediting stand-alone information, the transfer of knowledge across contextual boundaries becomes impossible. There must be a balance between situating knowledge while also grasping the deep structure of material, or the understanding of how one arrives to know such information.
Some theorists argue that transfer does not even occur at all. They believe that students transform what they have learned into the new context. They say that transfer is too much of a passive notion. They believe students, instead, transform their knowledge in an active way. Students don\'t simply carry over knowledge from the classroom, but they construct the knowledge in a way that they can understand it themselves. The learner changes the information they have learned to make it best adapt to the changing contexts that they use the knowledge in. This transformation process can occur when a learner feels motivated to use the knowledge---however, if the student does not find the transformation necessary, it is less likely that the knowledge will ever transform.
#### Techniques and benefits of transfer of learning {#techniques_and_benefits_of_transfer_of_learning}
There are many different conditions that influence transfer of learning in the classroom. These conditions include features of the task, features of the learner, features of the organization and social context of the activity. The features of the task include practicing through simulations, problem-based learning, and knowledge and skills for implementing new plans. The features of learners include their ability to reflect on past experiences, their ability to participate in group discussions, practice skills, and participate in written discussions. All the unique features contribute to a student\'s ability to use transfer of learning. There are structural techniques that can aid learning transfer in the classroom. These structural strategies include hugging and bridging.
Hugging uses the technique of simulating an activity to encourage reflexive learning. An example of the hugging strategy is when a student practices teaching a lesson or when a student role plays with another student. These examples encourage critical thinking that engages the student and helps them understand what they are learning---one of the goals of transfer of learning and desirable difficulties.
Bridging is when instruction encourages thinking abstractly by helping to identify connections between ideas and to analyze those connections. An example is when a teacher lets the student analyze their past test results and the way they got those results. This includes amount of study time and study strategies. Looking at their past study strategies can help them come up with strategies to improve performance. These are some of the ideas important to successful to hugging and bridging practices.
There are many benefits of transfer of learning in the classroom. One of the main benefits is the ability to quickly learn a new task. This has many real-life applications such as language and speech processing. Transfer of learning is also very useful in teaching students to use higher cognitive thinking by applying their background knowledge to new situations.
| 1,293 |
Learning theory (education)
| 1 |
17,994 |
# Learning theory (education)
## Educational psychology {#educational_psychology}
### Cognitivism
#### Gestalt theory {#gestalt_theory}
Cognitive theories grew out of Gestalt psychology. Gestalt psychology was developed in Germany in the early 1900s by Wolfgang Kohler and was brought to America in the 1920s. The German word *Gestalt* is roughly equivalent to the English \"emergence (of a form-as in the game pictionary, when all of a sudden one recognises what the person is trying to convey - the form and meaning \"emerge\")\", *configuration* or *organization* and emphasizes the whole of human experience. Over the years, the Gestalt psychologists provided demonstrations and described principles to explain the way we organize our sensations into perceptions. Max Wertheimer, one of the founding fathers of Gestalt Theory, observed that sometimes we interpret motion when there is no motion at all. For example: a powered sign used at a convenience store to indicate that the store is open or closed might be seen as a sign with \"constant light\". However, the lights are actually flashing. Each light has been programmed to blink rapidly at their own individual pace. Perceived as a whole however, the sign appears fully lit without flashes. If perceived individually, the lights turn off and on at designated times. Another example of this would be a brick house: As a whole, it is viewed as a standing structure. However, it is actually composed of many smaller parts, which are individual bricks. People tend to see things from a holistic point of view rather than breaking it down into sub units.
In Gestalt theory, psychologists say that instead of obtaining knowledge from what\'s in front of us, we often learn by making sense of the relationship between what\'s new and old. Because we have a unique perspective of the world, humans have the ability to generate their own learning experiences and interpret information that may or may not be the same for someone else.
Gestalt psychologists criticize behaviorists for being too dependent on overt behavior to explain learning. They propose looking at the patterns rather than isolated events. Gestalt views of learning have been incorporated into what have come to be labeled *cognitive theories*. Two key assumptions underlie this cognitive approach: that the memory system is an active organized processor of information and that prior knowledge plays an important role in learning. Gestalt theorists believe that for learning to occur, prior knowledge must exist on the topic. When the learner applies their prior knowledge to the advanced topic, the learner can understand the meaning in the advanced topic, and learning can occur. Cognitive theories look beyond behavior to consider how human memory works to promote learning, and an understanding of short-term memory and long-term memory is important to educators influenced by cognitive theory. They view learning as an internal mental process (including insight, information processing, memory and perception) where the educator focuses on building intelligence and cognitive development. The individual learner is more important than the environment.
#### Other cognitive theories {#other_cognitive_theories}
Once memory theories like the Atkinson--Shiffrin memory model and Baddeley\'s working memory model were established as a theoretical framework in cognitive psychology, new cognitive frameworks of learning began to emerge during the 1970s, 80s, and 90s. Today, researchers are concentrating on topics like cognitive load and information processing theory. These theories of learning play a role in influencing instructional design. Cognitive theory is used to explain such topics as social role acquisition, intelligence and memory as related to age.
In the late twentieth century, situated cognition emerged as a theory that recognized current learning as primarily the transfer of decontextualized and formal knowledge. Bredo (1994) depicts situated cognition as \"shifting the focus from individual in environment to individual and environment\". In other words, individual cognition should be considered as intimately related with the context of social interactions and culturally constructed meaning. Learning through this perspective, in which knowing and doing become inseparable, becomes both applicable and whole.
Much of the education students receive is limited to the culture of schools, without consideration for authentic cultures outside of education. Curricula framed by situated cognition can bring knowledge to life by embedding the learned material within the culture students are familiar with. For example, formal and abstract syntax of math problems can be transformed by placing a traditional math problem within a practical story problem. This presents an opportunity to meet that appropriate balance between situated and transferable knowledge. Lampert (1987) successfully did this by having students explore mathematical concepts that are continuous with their background knowledge. She does so by using money, which all students are familiar with, and then develops the lesson to include more complex stories that allow for students to see various solutions as well as create their own. In this way, knowledge becomes active, evolving as students participate and negotiate their way through new situations.
| 805 |
Learning theory (education)
| 2 |
17,994 |
# Learning theory (education)
## Educational psychology {#educational_psychology}
### Constructivism
Founded by Jean Piaget, constructivism emphasizes the importance of the active involvement of learners in constructing knowledge for themselves. Students are thought to use background knowledge and concepts to assist them in their acquisition of novel information. On approaching such new information, the learner faces a loss of equilibrium with their previous understanding, and this demands a change in cognitive structure. This change effectively combines previous and novel information to form an improved cognitive schema. Constructivism can be both subjectively and contextually based. Under the theory of radical constructivism, coined by Ernst von Glasersfeld, understanding relies on one\'s subjective interpretation of experience as opposed to objective \"reality\". Similarly, William Cobern\'s idea of contextual constructivism encompasses the effects of culture and society on experience.
Constructivism asks why students do not learn deeply by listening to a teacher, or reading from a textbook. To design effective teaching environments, it believes one needs a good understanding of what children already know when they come into the classroom. The curriculum should be designed in a way that builds on the pupil\'s background knowledge and is allowed to develop with them. Begin with complex problems and teach basic skills while solving these problems. The learning theories of John Dewey, Maria Montessori, and David A. Kolb serve as the foundation of the application of constructivist learning theory in the classroom. Constructivism has many varieties such as active learning, discovery learning, and knowledge building, but all versions promote a student\'s free exploration within a given framework or structure. The teacher acts as a facilitator who encourages students to discover principles for themselves and to construct knowledge by working answering open-ended questions and solving real-world problems. To do this, a teacher should encourage curiosity and discussion among his/her students as well as promoting their autonomy. In scientific areas in the classroom, constructivist teachers provide raw data and physical materials for the students to work with and analyze.
### Transformative learning theory {#transformative_learning_theory}
Transformative learning theory seeks to explain how humans revise and reinterpret meaning. Transformative learning is the cognitive process of effecting change in a frame of reference. A frame of reference defines our view of the world. The emotions are often involved. Adults have a tendency to reject any ideas that do not correspond to their particular values, associations and concepts.
Our frames of reference are composed of two dimensions: habits of mind and points of view. Habits of mind, such as ethnocentrism, are harder to change than points of view. Habits of mind influence our point of view and the resulting thoughts or feelings associated with them, but points of view may change over time as a result of influences such as reflection, appropriation and feedback. Transformative learning takes place by discussing with others the \"reasons presented in support of competing interpretations, by critically examining evidence, arguments, and alternative points of view\". When circumstances permit, transformative learners move toward a frame of reference that is more inclusive, discriminating, self-reflective, and integrative of experience.
| 507 |
Learning theory (education)
| 3 |
17,994 |
# Learning theory (education)
## Educational neuroscience {#educational_neuroscience}
American Universities such as Harvard, Johns Hopkins, and University of Southern California began offering majors and degrees dedicated to educational neuroscience or neuroeducation in the first decade of the twenty-first century. Such studies seek to link an understanding of brain processes with classroom instruction and experiences. Neuroeducation analyzes biological changes in the brain from processing new information. It looks at what environmental, emotional, and social situations best help the brain store and retain new information via the linking of neurons---and best keep the dendrites from being reabsorbed, losing the information. The 1990s were designated \"The Decade of the Brain\", and advances took place in neuroscience at an especially rapid pace. The three dominant methods for measuring brain activities are event-related potential, functional magnetic resonance imaging and magnetoencephalography (MEG).
The integration and application to education of what we know about the brain was strengthened in 2000 when the American Federation of Teachers stated: \"It is vital that we identify what science tells us about how people learn in order to improve the education curriculum.\" What is exciting about this new field in education is that modern brain imaging techniques now make it possible, in some sense, to watch the brain as it learns, and the question then arises: can the results of neuro-scientific studies of brains as they are learning usefully inform practice in this area? The neuroscience field is young. Researchers expected that new technologies and ways of observing will produce new scientific evidence that helps refine the paradigms of what students need and how they learn best. In particular, it may bring more informed strategies for teaching students with learning disabilities.
### Formal and mental discipline {#formal_and_mental_discipline}
All individuals have the ability to develop mental discipline and the skill of mindfulness, the two go hand in hand. Mental discipline is huge in shaping what people do, say, think and feel. It\'s critical in terms of the processing of information and involves the ability to recognize and respond appropriately to new things and information people come across, or have recently been taught. Mindfulness is important to the process of learning in many aspects. Being mindful means to be present with and engaged in whatever you are doing at a specific moment in time. Being mindful can aid in helping us to more critically think, feel and understand the new information we are in the process of absorbing. The formal discipline approach seeks to develop causation between the advancement of the mind by exercising it through exposure to abstract school subjects such as science, language and mathematics. With student\'s repetitive exposure to these particular subjects, some scholars feel that the acquisition of knowledge pertaining to science, language and math is of \"secondary importance\", and believe that the strengthening and further development of the mind that this curriculum provides holds far greater significance to the progressing learner in the long haul. D.C. Phillips and Jonas F. Soltis provide some skepticism to this notion. Their skepticism stems largely in part from feeling that the relationship between formal discipline and the overall advancement of the mind is not as strong as some would say. They illustrate their skepticism by opining that it is foolish to blindly assume that people are better off in life, or at performing certain tasks, because of taking particular, yet unrelated courses.
## Multiple intelligences {#multiple_intelligences}
The existence of multiple intelligences is proposed by psychologist Howard Gardner, who suggests that different kinds of intelligence exists in human beings. It is a theory that has been fashionable in continuous professional development (CPD) training courses for teachers. However, the theory of multiple intelligences is often cited as an example of pseudoscience because it lacks empirical evidence or falsifiability.
| 624 |
Learning theory (education)
| 4 |
17,994 |
# Learning theory (education)
## Multimedia learning {#multimedia_learning}
*Main article: Multimedia learning* Multimedia learning refers to the use of visual and auditory teaching materials that may include video, computer and other information technology. Multimedia learning theory focuses on the principles that determine the effective use of multimedia in learning, with emphasis on using both the visual and auditory channels for information processing.
The auditory channel deals with information that is heard, and the visual channel processes information that is seen. The visual channel holds less information than the auditory channel. If both the visual and auditory channels are presented with information, more knowledge is retained. However, if too much information is delivered it is inadequately processed, and long-term memory is not acquired. Multimedia learning seeks to give instructors the ability to stimulate both the visual and auditory channels of the learner, resulting in better progress.
### Using online games for learning {#using_online_games_for_learning}
Many educators and researchers believe that information technology could bring innovation on traditional educational instructions. Teachers and technologists are searching for new and innovative ways to design learner-centered learning environments effectively, trying to engage learners more in the learning process. Claims have been made that online games have the potential to teach, train and educate and they are effective means for learning skills and attitudes that are not so easy to learn by rote memorization.
There has been a lot of research done in identifying the learning effectiveness in game based learning. Learner characteristics and cognitive learning outcomes have been identified as the key factors in research on the implementation of games in educational settings. In the process of learning a language through an online game, there is a strong relationship between the learner\'s prior knowledge of that language and their cognitive learning outcomes. For the people with prior knowledge of the language, the learning effectiveness of the games is much more than those with none or less knowledge of the language.
| 324 |
Learning theory (education)
| 5 |
17,994 |
# Learning theory (education)
## Other learning theories {#other_learning_theories}
Other learning theories have also been developed for more specific purposes. For example, andragogy is the art and science to help adults learn. Connectivism is a recent theory of networked learning, which focuses on learning as making connections. The Learning as a Network (LaaN) theory builds upon connectivism, complexity theory, and double-loop learning. It starts from the learner and views learning as the continuous creation of a personal knowledge network (PKN).
### Learning style theories {#learning_style_theories}
Learning style theories propose that individuals learn in different ways, that there are distinct learning styles and that knowledge of a learner\'s preferred learning style leads to faster and more satisfactory improvement. However, the current research has not been able to find solid scientific evidence to support the main premises of learning styles theory.
### Affective Context Model {#affective_context_model}
People remember how things made them feel, and use those emotional imprints to create memories on demand.
### Informal and post-modern theories {#informal_and_post_modern_theories}
In theories that make use of cognitive restructuring, an informal curriculum promotes the use of prior knowledge to help students gain a broad understanding of concepts. New knowledge cannot be told to students, it believes, but rather the students\' current knowledge must be challenged. In this way, students adjust their ideas to more closely resemble actual theories or concepts. By using this method students gain the broad understanding they\'re taught and later are more willing to learn and keep the specifics of the concept or theory. This theory further aligns with the idea that teaching the concepts and the language of a subject should be split into multiple steps.
Other informal learning theories look at the sources of motivation for learning. Intrinsic motivation may create a more self-regulated learner, yet schools undermine intrinsic motivation. Critics argue that the average student learning in isolation performs significantly less well than those learning with collaboration and mediation. Students learn through talk, discussion, and argumentation.
| 328 |
Learning theory (education)
| 6 |
17,994 |
# Learning theory (education)
## Educational anthropology {#educational_anthropology}
### Philosophical anthropology {#philosophical_anthropology}
According to Theodora Polito, \"every well-constructed theory of education \[has\] at \[its\] center a philosophical anthropology,\" which is \"a philosophical reflection on some basic problems of mankind.\" Philosophical anthropology is an exploration of human nature and humanity. Aristotle, an early influence on the field, deemed human nature to be \"rational animality,\" wherein humans are closely related to other animals but still set apart by their ability to form rational thought. Philosophical anthropology expanded upon these ideas by clarifying that rationality is, \"determined by the biological and social conditions in which the lives of human beings are embedded.\" Fully developed learning theories address some of the \"basic problems of mankind\" by examining these biological and social conditions to understand and manipulate the rationality of humanity in the context of learning.
Philosophical anthropology is evident in behaviorism, which requires an understanding of humanity and human nature in order to assert that the similarities between humans and other animals are critical and influential to the process of learning. Situated cognition focuses on how humans interact with each other and their environments, which would be considered the \"social conditions\" explored within the field of philosophical anthropology. Transformative learning theories operate with the assumption that humans are rational creatures capable of examining and redefining perspectives, something that is heavily considered within philosophical anthropology.
An awareness and understanding of philosophical anthropology contributes to a greater comprehension and practice of any learning theory. In some cases, philosophy can be used to further explore and define uncertain terms within the field of education. Philosophy can also be a vehicle to explore the purpose of education, which can greatly influence an educational theory.
## Criticism
Critics of learning theories that seek to displace traditional educational practices claim that there is no need for such theories; that the attempt to comprehend the process of learning through the construction of theories creates problems and inhibits personal freedom
| 328 |
Learning theory (education)
| 7 |
17,996 |
# List of Latin phrases
This is a list of Wikipedia articles of Latin phrases and their translation into English.
To view all phrases on a single, lengthy document, see: List of Latin phrases (full)
| 35 |
List of Latin phrases
| 0 |
17,998 |
# List of Latin words with English derivatives
This is a list of Latin words with derivatives in English language.
Ancient orthography did not distinguish between *i* and *j* or between *u* and *v*. Many modern works distinguish *u* from *v* but not *i* from *j*. In this article, both distinctions are shown as they are helpful when tracing the origin of English words. See also Latin phonology and orthography.
## Nouns and adjectives {#nouns_and_adjectives}
The citation form for nouns (the form normally shown in Latin dictionaries) is the Latin nominative singular, but that typically does not exhibit the root form from which English nouns are generally derived
| 108 |
List of Latin words with English derivatives
| 0 |
18,000 |
# Latin conjugation
*Pandoc failed*: ```
Error at (line 1087, column 2):
unexpected '-'
|-
^
``
| 17 |
Latin conjugation
| 0 |
18,004 |
# LALR parser
In computer science, an **LALR parser** (**look-ahead, left-to-right, rightmost derivation parser**) is part of the compiling process where human readable text is converted into a structured representation to be read by computers. An LALR parser is a software tool to process (parse) text into a very specific internal representation that other programs, such as compilers, can work with. This process happens according to a set of production rules specified by a formal grammar for a computer language.
An LALR parser is a simplified version of a canonical LR parser.
The LALR parser was invented by Frank DeRemer in his 1969 PhD dissertation, *Practical Translators for LR(k) languages*, in his treatment of the practical difficulties at that time of implementing LR(1) parsers. He showed that the LALR parser has more language recognition power than the LR(0) parser, while requiring the same number of states as the LR(0) parser for a language that can be recognized by both parsers. This makes the LALR parser a memory-efficient alternative to the LR(1) parser for languages that are LALR. It was also proven that there exist LR(1) languages that are not LALR. Despite this weakness, the power of the LALR parser is sufficient for many mainstream computer languages, including Java, though the reference grammars for many languages fail to be LALR due to being ambiguous.
The original dissertation gave no algorithm for constructing such a parser given a formal grammar. The first algorithms for LALR parser generation were published in 1973. In 1982, DeRemer and Tom Pennello published an algorithm that generated highly memory-efficient LALR parsers. LALR parsers can be automatically generated from a grammar by an LALR parser generator such as Yacc or GNU Bison. The automatically generated code may be augmented by hand-written code to augment the power of the resulting parser.
## History
In 1965, Donald Knuth invented the LR parser (**L**eft to Right, **R**ightmost derivation). The LR parser can recognize any deterministic context-free language in linear-bounded time. Rightmost derivation has very large memory requirements and implementing an LR parser was impractical due to the limited memory of computers at that time. To address this shortcoming, in 1969, Frank DeRemer proposed two simplified versions of the LR parser, namely the **Look-Ahead LR** (LALR) and the **Simple LR parser** (SLR) that had much lower memory requirements at the cost of less language-recognition power, with the LALR parser being the most-powerful alternative. In 1977, memory optimizations for the LR parser were invented but still the LR parser was less memory-efficient than the simplified alternatives.
In 1979, Frank DeRemer and Tom Pennello announced a series of optimizations for the LALR parser that would further improve its memory efficiency. Their work was published in 1982.
## Overview
Generally, the LALR parser refers to the LALR(1) parser, just as the LR parser generally refers to the LR(1) parser. The \"(1)\" denotes one-token lookahead, to resolve differences between rule patterns during parsing. Similarly, there is an LALR(2) parser with two-token lookahead, and LALR(*k*) parsers with *k*-token lookup, but these are rare in actual use. The LALR parser is based on the LR(0) parser, so it can also be denoted LALR(1) = LA(1)LR(0) (1 token of lookahead, LR(0)) or more generally LALR(*k*) = LA(*k*)LR(0) (k tokens of lookahead, LR(0)). There is in fact a two-parameter family of LA(*k*)LR(*j*) parsers for all combinations of *j* and *k*, which can be derived from the LR(*j* + *k*) parser, but these do not see practical use.
As with other types of LR parsers, an LALR parser is quite efficient at finding the single correct bottom-up parse in a single left-to-right scan over the input stream, because it does not need to use backtracking. Being a lookahead parser by definition, it always uses a lookahead, with `{{nowrap|LALR(1)}}`{=mediawiki} being the most-common case.
| 631 |
LALR parser
| 0 |
18,004 |
# LALR parser
## Relation to other parsers {#relation_to_other_parsers}
### LR parsers {#lr_parsers}
The LALR(1) parser is less powerful than the LR(1) parser, and more powerful than the SLR(1) parser, though they all use the same production rules. The simplification that the LALR parser introduces consists in merging rules that have identical **kernel item sets**, because during the LR(0) state-construction process the lookaheads are not known. This reduces the power of the parser because not knowing the lookahead symbols can confuse the parser as to which grammar rule to pick next, resulting in **reduce/reduce conflicts**. All conflicts that arise in applying a LALR(1) parser to an unambiguous LR(1) grammar are reduce/reduce conflicts. The SLR(1) parser performs further merging, which introduces additional conflicts.
The standard example of an LR(1) grammar that cannot be parsed with the LALR(1) parser, exhibiting such a reduce/reduce conflict, is:
` S → a E c`\
` → a F d`\
` → b F c`\
` → b E d`\
` E → e`\
` F → e`
In the LALR table construction, two states will be merged into one state and later the lookaheads will be found to be ambiguous. The one state with lookaheads is:
` E → e. {c,d}`\
` F → e. {c,d}`
An LR(1) parser will create two different states (with non-conflicting lookaheads), neither of which is ambiguous. In an LALR parser this one state has conflicting actions (given lookahead c or d, reduce to E or F), a \"reduce/reduce conflict\"; the above grammar will be declared ambiguous by a LALR parser generator and conflicts will be reported.
To recover, this ambiguity is resolved by choosing E, because it occurs before F in the grammar. However, the resultant parser will not be able to recognize the valid input sequence `b e c`, since the ambiguous sequence `e c` is reduced to `(E → e) c`, rather than the correct `(F → e) c`, but `b E c` is not in the grammar.
### LL parsers {#ll_parsers}
The LALR(*j*) parsers are incomparable with LL(*k*) parsers: for any *j* and *k* both greater than 0, there are LALR(*j*) grammars that are not LL(*k*) grammars and vice versa. In fact, it is undecidable whether a given LL(1) grammar is LALR(*k*) for any $k > 0$.
Depending on the presence of empty derivations, a LL(1) grammar can be equal to a SLR(1) or a LALR(1) grammar. If the LL(1) grammar has no empty derivations it is SLR(1) and if all symbols with empty derivations have non-empty derivations it is LALR(1). If symbols having only an empty derivation exist, the grammar may or may not be LALR(1)
| 441 |
LALR parser
| 1 |
18,008 |
# Language center
In neuroscience and psychology, the term **language center** refers collectively to the areas of the brain which serve a particular function for speech processing and production. Language is a core system that gives humans the capacity to solve difficult problems and provides them with a unique type of social interaction. Language allows individuals to attribute symbols (e.g. words or signs) to specific concepts, and utilize them through sentences and phrases that follow proper grammatical rules. Finally, speech is the mechanism by which language is orally expressed.
Information is exchanged in a larger system, including language-related regions. These regions are connected by white matter fiber tracts that make possible the transmission of information between regions. The white matter fiber bunches were recognized to be important for language production after suggesting that it is possible to make a connection between multiple language centers. The three classical language areas that are involved in language production and processing are Broca\'s and Wernicke\'s areas, and the angular gyrus.
## Broca\'s area {#brocas_area}
Broca\'s Area was first suggested to play a role in speech function by the French neurologist and anthropologist Paul Broca in 1861. The basis for this discovery was analyzing speech problems resulting from injuries to this brain region, located in the inferior frontal gyrus. Paul Broca had a patient called Leborgne who could only pronounce the word \"tan\" when speaking. After working with another patient with a similar impairment, Paul Broca concluded that damage in the inferior frontal gyrus affected articulate language.
Broca\'s area is well known for being the syntactic processing \"center\". It has been known of since Paul Broca associated speech production with an area in the posterior inferior frontal gyrus, which he called \"Broca\'s area\". Although this area is in charge of speech production, the specific details of its role in the language system is unknown. However, it is involved in phonological, semantic, and syntactic processing, and working memory. The anterior region of Broca\'s area is involved in semantic processing, while the posterior region involves phonological processing (Bohsali, 2015). The whole of Broca\'s area has been shown to have a higher activation while doing reading tasks than other types of tasks.
In a simple explanation of speech production, this area approaches phonological word representation chronologically divided into segments of syllables which then is sent to different motor areas where they are converted into a phonetic code. The study of how this area produces speech has been made with paradigms using both single and complex words.
Broca\'s area is correlated with phonological segmentation, unification, and syntactic processing, all connected to linguistic information. This area, although it synchronizes the transformation of information within cortical systems involved in spoken word production, does not contribute to the production of single words. The inferior frontal lobe is the one in charge of word production.
Furthermore, Broca\'s area is structurally related to the thalamus, and both are engaged in language processing. The connectivity between both areas is two thalamic nuclei, the pulvinar, and the ventral nucleus, which are involved in language processing and linguistic functions similar to BA 44 and 45 in Broca\'s area. Pulvinar is connected to many frontal regions of the frontal cortex and the ventral nucleus is involved in speech production. The frontal speech regions of the brain have been shown to participate in speech sound perception.
Broca\'s Area is today still considered an important language center, playing a central role in processing syntax, grammar, and sentence structure.
## Wernicke\'s area {#wernickes_area}
Wernicke\'s area was named for German doctor Carl Wernicke, who discovered it in 1874 in the course of his research into aphasias (loss of ability to speak). This area of the brain is involved in language comprehension. Therefore, Wernicke\'s area is for understanding oral language. Besides Wernicke\'s area, the left posterior superior temporal gyrus (pSTG), middle temporal gyrus (MTG), inferior temporal gyrus (ITG), supramarginal gyrus (SMG), and angular gyrus (AG) participate in language comprehension. Therefore, language comprehension is not located in a specific area. Contrarily, it involves large regions of the inferior parietal lobe and left temporal.
While the finale of speech production is a sequence of muscle movements, activating knowledge about the sequence of phonemes (consonants and vowel speech sounds) that creates a word is a phonological retrieval. Wernicke\'s area contributes to phonological retrieval. All speech production tasks (e.g. word retrieval, repetition, and reading aloud) require phonological retrieval. The phonological retrieval system involved in speech repetition is the auditory phoneme perception system, and the visual letter perception system is the one that serves for reading aloud. Communicative speech production entails a phase preceding phonological retrieval. Speech comprehension involves mapping sequences of phonemes onto word meaning.
| 778 |
Language center
| 0 |
18,008 |
# Language center
## Angular gyrus {#angular_gyrus}
The angular gyrus is important in processing concrete and abstract concepts. It also has a role in verbal working memory during retrieval of verbal information and in visual memory when turning written language into spoken language. The left AG is activated in semantic processing that requires concept retrieval and conceptual integration. Also, the left AG is activated during problems of multiplication and addition requiring return of arithmetic factors in verbal memory. Thus, it is involved in verbal coding of numbers.
## Insular cortex {#insular_cortex}
The insula is implicated in speech and language, taking part in functional and structural connections with motor neurons, linguistic, sensory, and limbic brain areas. The knowledge about the function of the insula in speech production comes from different studies with patients having speech apraxia. These studies have led researchers to learn of the involvement of different parts of the insula. These parts are the left anterior insula, which is related to speech production, and the bilateral anterior insula, which is involved in misleading speech comprehension.
## Speech and language disorders {#speech_and_language_disorders}
Many different sources state that the study of the brain, and therefore, language disorders, originated in the 19th century, and linguistic analysis of those disorders began in the 20th century. Studying language impairments in the brain after injuries aids in comprehending how the brain works and changes after an injury. When this happens, the brain\'s impairment is referred to as \"aphasia\". Lesions to Broca\'s Area results primarily in disruptions to speech production; damage to Wernicke\'s Area, which is located in the lower part of the temporal lobe, leads mainly to disruptions in speech reception.
There are numerous distinctive ways in which language can be affected. Phonemic paraphasia, an attribute of conduction aphasia and Wernicke aphasia, does not involve speech comprehension impairment. Instead, it requires speech production damage, where the desired phonemes are selected erroneously or in an incorrect sequence. Therefore, although Wernicke\'s aphasia, a combination of phonological retrieval and semantic systems impairment, affects speech comprehension, it also involves speech production damage. Phonemic paraphasia and anomia (impaired word retrieval) are the results of phonological retrieval impairment.
Another lesion that involves impairment in language production and processing is apraxia of speech, a difficulty synchronizing articulators essential for speech production. This type of lesion is located in the superior pre-central gyrus of the insula, and is more likely to occur in patients with Broca\'s aphasia. Lesions of the dominant ventral anterior nucleus may result in semantic paraphasias and difficulty in word-finding. Also, individuals with thalamic lesions experience difficulties linking semantic concepts with correct phonological representations in word production.
Dyslexia is a language-processing disorder. It involves learning difficulties in reading, writing, word recognition, phonological recording, numeracy, and spelling. Even with access to appropriate intervention during childhood, these difficulties continue throughout the lifespan. Children are diagnosed with dyslexia when more than one factor affecting learning (e.g. reading or writing) appears. When children diagnosed with dyslexia have difficulties in concrete cognitive functioning, this is called an assumption of specificity, and it aids in the diagnosis of dyslexia.
Some characteristics that distinguish dyslexics include errors in phonological processing, causing misreading of unfamiliar words, affecting comprehension; inadequacy of working memory, affecting speaking, reading, and writing; errors in oral reading; oral skill difficulties such as expressing oneself; and writing skill problems in areas such as spelling and general expression. Dyslexics not only experience learning difficulties, but also other secondary characteristics, such as having difficulties in organizing, planning, social interaction, motor skills, visual perception, and short-term memory. These characteristics affect personal and academic life.
Dysarthria is a motor speech disorder caused by damage to the central and/or peripheral nervous system, and it is related to degenerative neurological diseases, such as Parkinson\'s disease, cerebrovascular accident (CVA), and traumatic brain injury (TBI). Dysarthria can be caused by a mechanical difficulty in the vocal cords, or neurological disease, and produces abnormal articulation of phonemes, such as using \"b\" in place of \"p\". Apraxic dysarthria is a type of dyspraxia that involves distortions of words. This type is related to facial apraxia and motor aphasia if Broca\'s area is involved.`{{Clarify|date=June 2023}}`{=mediawiki}
| 689 |
Language center
| 1 |
18,008 |
# Language center
## Current scientific consensus {#current_scientific_consensus}
Improvement in computer technology in the late 20th century has allowed a better understanding of the correlation between brain and language, in the disorders that this entails. This improvement has permitted better visualization of the brain structure in high-resolution three-dimensional images. It has also allowed observation of brain activity through blood flow (Dronkers, Ivanova, & Baldo, 2017).
New medical imaging techniques such as PET and fMRI have allowed researchers to generate pictures showing which areas of a living brain are active at a given time. Functional magnetic resonance imaging (fMRI) localizes specific brain functions to particular brain regions by observing blood flow in different areas. This technique shows the location and magnitude of neural activity variations, influenced by external stimulation and fluctuation at rest. MRI is a technique that was developed in the 20th century to observe brain activity in healthy and abnormal brains. Diffusion-weighted magnetic resonance imaging, or diffusion tensor imaging (DTI), is a technique used for tracking white matter bundles *in vivo*, and gives information on the internal fibrous structure via measuring water diffusion. This diffusion tensor is used for inferring white matter connectivity.
In the past, research was primarily based on observations of loss of ability resulting from damage to the cerebral cortex. In the modern era, medical imaging has represented a radical step forward for research on speech processing. It is now known that a whole series of relatively large brain areas are involved in speech processing. In more recent research, subcortical regions (those lying below the cerebral cortex such as the putamen and the caudate nucleus), as well as the pre-motor areas (BA 6), have received increased attention. It is now generally assumed that the following structures of the cerebral cortex near the primary and secondary auditory cortices play a fundamental role in speech processing:
- Superior temporal gyrus (STG): morphosyntactic processing (anterior section), integration of syntactic and semantic information (posterior section)
```{=html}
<!-- -->
```
- Inferior frontal gyrus (IFG, Brodmann area (BA) 45/47): syntactic processing, working memory
```{=html}
<!-- -->
```
- Inferior frontal gyrus (IFG, BA 44): syntactic processing, working memory
```{=html}
<!-- -->
```
- Middle temporal gyrus (MTG): lexical semantic processing
```{=html}
<!-- -->
```
- Angular gyrus (AG): semantic processes (posterior temporal cortex)
The left hemisphere is usually dominant in right-handed people, although bilateral activations are not uncommon in syntactic processing. It is now accepted that the right hemisphere plays an important role in the processing of suprasegmental acoustic features like prosody, which is \"the rhythmic and melodic variations in speech\". There are two types of prosodic information: emotional prosody (right hemisphere), which is the emotional content of the speech, and linguistic prosody (left hemisphere), the syntactic and thematic structure of the speech.
Most areas of speech processing develop in the second year of life in the dominant half (hemisphere) of the brain, which often (though not necessarily) corresponds to the opposite of the dominant hand. 98% of right-handed people are left-hemisphere dominant, and the majority of left-handed people are as well.
Computerized tomographic (CT) scans are a technique dating to the 1970s, and produce low spatial resolution, but are capable of providing the location of injuries *in vivo*. Also, Voxel-based Lesion Symptom Mapping (VLSM) and Voxel-Based Morphometry (VBM) techniques have contributed to the understanding that specific brain regions have different roles when supporting speech processing. VLSM has been used to observe complex language functions supported by multiple brain regions. VBM is a helpful technique for analyzing language impairments related to neurodegenerative disease.
| 592 |
Language center
| 2 |
18,008 |
# Language center
## Older models {#older_models}
The differentiation of speech production into only two large sections of the brain (i.e. Broca\'s and Wernicke\'s areas), which was accepted long before medical imaging techniques, is now considered outdated. Broca\'s area was first suggested to play a role in speech function by the French neurologist and anthropologist Paul Broca in 1861. The basis for this discovery was the analysis of speech problems resulting from injuries to this brain region, located in the inferior frontal gyrus. Lesions to Broca\'s Area result primarily in disruptions to speech production.
Damage to Wernicke\'s area, located in the lower part of the temporal lobe, mainly leads to speech reception disruptions. This area was named for German doctor Carl Wernicke, who discovered it in 1874 in the course of his research into aphasias (loss of ability to speak).
Broca\'s area is today still considered an important language center, playing a central role in processing syntax, grammar, and sentence structure
| 161 |
Language center
| 3 |
18,026 |
# Luigi Alamanni
**Luigi Alamanni** (sometimes spelt **Alemanni**) (6 March 1495`{{snd}}`{=mediawiki}18 April 1556) was an Italian poet and statesman. He was regarded as a prolific and versatile poet. He was credited with introducing the epigram into Italian poetry.
## Biography
Alamanni was born in Florence. His father was a devoted adherent of the Medici party, but Luigi, smarting under a supposed injustice, joined an unsuccessful conspiracy against Giulio de\' Medici, soon to be elected Pope Clement VII. Consequently, he was forced to take refuge in Venice, and, on the accession of Medici to pope, to flee to France. When Florence had exiled the Medici in 1527, Alamanni returned, and took a prominent part in the management of the affairs of the short-lived republic.
The Florentines had thrown off Medici rule and established a republic after the Sack of Rome in 1527; the Florentine Republic had continued to participate in the war on the side of the French. The French defeats at Naples in 1528 and Landriano in 1529, however, led to Francis I of France concluding the Treaty of Cambrai with the Holy Roman Emperor Charles V. When Pope Clement VII and the Republic of Venice also concluded treaties with the Emperor, Florence was left to fight alone. Charles, attempting to gain Clement\'s favor, ordered his armies to seize Florence and return the Medici to power.
After the siege of Florence in 1530 by Imperial forces, succeeded in restoring the Medici to the duchy, Alamanni again fled, this time to France, where he composed the greater part of his works. He was a favourite with the French King Francis I, who sent him as ambassador to the Holy Roman Emperor Charles V after the Peace of Crépy in 1544.
An instance of Alammani\'s diplomatic tact is reflected in an encounter with the emperor. Alamanni, while giving a complimentary address to Charles, was interrupted by the emperor who quoted a line from a satirical poem of Alamanni: *\"l\'aquila grifagna, Che per piu devorar, duoi rostri porta*\" (*\"Two crooked bills the ravenous eagle bears, The better to devour*\"). The double eagle was a symbol of the Hapsburg monarchy. Upon this interruption, Alamanni immediately replied that he spoke that line only as a poet using fictions, now as an ambassador, he could only speak the truth. The ready reply pleased Charles, who added some complimentary words.
After the death of Francis, Alamanni enjoyed the confidence of his successor Henry II, and in 1551 was sent as his ambassador to Genoa. He died at Amboise on 18 April 1556.
He wrote a large number of poems, distinguished by the purity and excellence of their style. The best is a didactic poem, *La Coltivazione* (Paris, 1546; see 1546 in poetry), written in imitation of Virgil\'s *Georgics*. His *Opere Toscane* (Lyon, 1532) consists of satirical pieces written in blank verse. His use of Horatian epistolary satire is important and his tenth satire was used as a model by Sir Thomas Wyatt in his poem \'Mine own John Poyntz\' which introduced the form into English literature. An unfinished poem, *Avarchide*, in imitation of the Iliad, was the work of his old age and has little merit.
It has been said by some that Alamanni was the first to use blank verse in Italian poetry, but that distinction belongs rather to his contemporary Giangiorgio Trissino.
The contemporary poet Isabella di Morra dedicated a sonnet to Alamanni called *Non sol il ciel vi fu largo e cortese* (*\"Not only was heaven generous and courteous to you\"*).
Alamanni is a minor speaker in Machiavelli\'s *The Art of War*, a book structured as a dialogue between real people known to Machiavelli, and set in the gardens of Cosimo Rucellai. In this book, Alamanni is present as a loyal friend of the host, and is mentioned to be the youngest of Rucellai\'s friends present
| 642 |
Luigi Alamanni
| 0 |
18,028 |
# Louis Aleman
**Louis Aleman** (c. February 1390`{{snd}}`{=mediawiki}16 September 1450) was a French Roman Catholic cardinal and a professed member of the now-suppressed Canons Regular of Saint John Baptist. He served as the Archbishop of Arles from 1423 until his resignation in 1440 when he had resigned from the cardinalate. But he was later reinstated as a cardinal on 19 December 1449 at which point he served as the Protopriest and also reclaimed his titular church.
Aleman served as the Bishop of Maguelonne from 1418 until his archepiscopal elevation at which point he was later named a cardinal. Aleman once led opposition to Pope Eugene IV while pledging allegiance to an antipope which led to Eugene IV stripping Aleman of all ecclesiastical dignities that he had been entitled to. But he later convinced the antipope to abdicate as a means of ending the Western Schism at which stage Aleman was restored to the cardinalate and returned to full communion with the Roman see under Pope Nicholas V. He has often been dubbed as the \"Cardinal of Arles\".
His beatification received approval on 9 April 1527 from Pope Clement VII.
## Life
Louis Aleman was born to nobles circa 1390 at the castle in Arbent to Jean Aleman and Marie de Châtillon de Michaille. His archbishop grand-uncle was François de Conzie (c.1356-31.12.1431/2).
He was present at the Council of Pisa in 1409. He studied canon law and graduated in that area with a doctorate in 1414 at the college in Avignon. In 1417 he was made the abbot commendatario of Saint-Pierre de la Tour.
Aleman served as the governor of the Romagna since 1424 and had to face the ongoing struggles between the Guelphs and the Ghibellines in Bologna. One of the Guelph families - the Canetols - even imprisoned Aleman for several weeks but Aleman was later released and moved to Rome to serve in the court of Pope Martin V. Aleman served as a noted advisor to the pope and also served as a courtier while in the papal court. He had served in the papal court for Martin V since July 1417.
On 22 June 1418 he was appointed as the Bishop of Maguelonne and he was installed into his new see on 17 May 1419. The pope himself granted episcopal consecration to Aleman in Mantua. He later became a diplomat to Siena in 1422. Aleman was later promoted as the newest Archbishop of Arles on 3 December 1423 and was installed in that see on 16 May 1424. Martin V named him a cardinal on 24 May 1426 as the Cardinal-Priest of Santa Cecilia - he received that title on 27 May. From 1427 until 1431 he served as the Camerlengo for the College of Cardinals. He served as a legate to Bologna from 1426 to 1428 and did not participate in the conclave of 1431.
He was a prominent member of the Council of Basel since 1432 and together with Cardinal Julian Cesarini led the forces that maintained the power of the general councils over the pope\'s own control of the Church. It was while the council was proceeding that he tended to victims of the plague. He later led opposition to the pope but Cesarini was reconciled with Pope Eugene IV and had a prominent part in the pope\'s convoked Council of Florence. In 1439 he led the effort to depose Eugene IV and the election of a successor. In 1440 he placed the tiara upon Antipope Felix V and consecrated him as a bishop. This was a misguided attempt at reforming the Church which Aleman believed was vital. Eugene IV was responded to this and excommunicated the antipope while also depriving Aleman of all his ecclesiastical dignities. This also meant that Aleman could no longer be considered a cardinal and he was deprived of the dignities that came with the cardinalate. This occurred on 11 April 1440: he was stripped of Arles as his archdiocese and was stripped of his titular church.
Antipope Felix V made him the legate to the Diet of Frankfurt to the court of Emperor Friedrich III. He was further involved in the unsuccessful efforts to win over Europe\'s princes to Basel\'s antipope. In order to make an end of the schism the former cardinal advised Felix V to abdicate at which stage Pope Nicholas V restored the cardinal to all his honors and appointed him as a papal legate to the German kingdom\] in 1449; his full restoration was on 19 December 1449. He was granted back his titular church as well and from that moment until his death served as the Protopriest of the College of Cardinals. It was due to his estrangement to the Roman see that he was not permitted to participate in the conclave of 1447. He returned to his former archdiocese where he dedicated himself with great zeal to the catechetical formation of the people.
He died on 16 September 1450 at the Franciscan convent in Salon at Arles. Aleman\'s remains are housed in Saint-Trophine d\'Arles.
## Beatification
His beatification was approved and celebrated on 9 April 1527 after Pope Clement VII confirmed that there had been a longstanding and popular cultus (otherwise known as an enduring public veneration) of the late cardinal
| 879 |
Louis Aleman
| 0 |
18,030 |
# LR parser
In computer science, **LR parsers** are a type of bottom-up parser that analyse deterministic context-free languages in linear time. There are several variants of LR parsers: SLR parsers, LALR parsers, canonical LR(1) parsers, minimal LR(1) parsers, and generalized LR parsers (GLR parsers). LR parsers can be generated by a parser generator from a formal grammar defining the syntax of the language to be parsed. They are widely used for the processing of computer languages.
An LR parser (left-to-right, rightmost derivation in reverse) reads input text from left to right without backing up (this is true for most parsers), and produces a rightmost derivation in reverse: it does a bottom-up parse -- not a top-down LL parse or ad-hoc parse. The name \"LR\" is often followed by a numeric qualifier, as in \"LR(1)\" or sometimes \"LR(*k*)\". To avoid backtracking or guessing, the LR parser is allowed to peek ahead at *k* lookahead input symbols before deciding how to parse earlier symbols. Typically *k* is 1 and is not mentioned. The name \"LR\" is often preceded by other qualifiers, as in \"SLR\" and \"LALR\". The \"LR(*k*)\" notation for a grammar was suggested by Knuth to stand for \"translatable from left to right with bound *k*.\"
LR parsers are deterministic; they produce a single correct parse without guesswork or backtracking, in linear time. This is ideal for computer languages, but LR parsers are not suited for human languages which need more flexible but inevitably slower methods. Some methods which can parse arbitrary context-free languages (e.g., Cocke--Younger--Kasami, Earley, GLR) have worst-case performance of O(`{{var|n}}`{=mediawiki}^3^) time. Other methods which backtrack or yield multiple parses may even take exponential time when they guess badly.
The above properties of **L**, **R**, and ***k*** are actually shared by all shift-reduce parsers, including precedence parsers. But by convention, the LR name stands for the form of parsing invented by Donald Knuth, and excludes the earlier, less powerful precedence methods (for example Operator-precedence parser). LR parsers can handle a larger range of languages and grammars than precedence parsers or top-down LL parsing. This is because the LR parser waits until it has seen an entire instance of some grammar pattern before committing to what it has found. An LL parser has to decide or guess what it is seeing much sooner, when it has only seen the leftmost input symbol of that pattern.
| 396 |
LR parser
| 0 |
18,030 |
# LR parser
## Overview
### Bottom-up parse tree for example A \* 2 + 1 {#bottom_up_parse_tree_for_example_a_2_1}
An LR parser scans and parses the input text in one forward pass over the text. The parser builds up the parse tree incrementally, bottom up, and left to right, without guessing or backtracking. At every point in this pass, the parser has accumulated a list of subtrees or phrases of the input text that have been already parsed. Those subtrees are not yet joined together because the parser has not yet reached the right end of the syntax pattern that will combine them.
At step 6 in an example parse, only \"A \* 2\" has been parsed, incompletely. Only the shaded lower-left corner of the parse tree exists. None of the parse tree nodes numbered 7 and above exist yet. Nodes 3, 4, and 6 are the roots of isolated subtrees for variable A, operator \*, and number 2, respectively. These three root nodes are temporarily held in a parse stack. The remaining unparsed portion of the input stream is \"+ 1\".
### Shift and reduce actions {#shift_and_reduce_actions}
As with other shift-reduce parsers, an LR parser works by doing some combination of Shift steps and Reduce steps.
- A **Shift** step advances in the input stream by one symbol. That shifted symbol becomes a new single-node parse tree.
- A **Reduce** step applies a completed grammar rule to some of the recent parse trees, joining them together as one tree with a new root symbol.
If the input has no syntax errors, the parser continues with these steps until all of the input has been consumed and all of the parse trees have been reduced to a single tree representing an entire legal input.
LR parsers differ from other shift-reduce parsers in how they decide when to reduce, and how to pick between rules with similar endings. But the final decisions and the sequence of shift or reduce steps are the same.
Much of the LR parser\'s efficiency is from being deterministic. To avoid guessing, the LR parser often looks ahead (rightwards) at the next scanned symbol, before deciding what to do with previously scanned symbols. The lexical scanner works one or more symbols ahead of the parser. The **lookahead** symbols are the \'right-hand context\' for the parsing decision.
### Bottom-up parse stack {#bottom_up_parse_stack}
Like other shift-reduce parsers, an LR parser lazily waits until it has scanned and parsed all parts of some construct before committing to what the combined construct is. The parser then acts immediately on the combination instead of waiting any further. In the parse tree example, the phrase A gets reduced to Value and then to Products in steps 1-3 as soon as lookahead \* is seen, rather than waiting any later to organize those parts of the parse tree. The decisions for how to handle A are based only on what the parser and scanner have already seen, without considering things that appear much later to the right.
Reductions reorganize the most recently parsed things, immediately to the left of the lookahead symbol. So the list of already-parsed things acts like a stack. This **parse stack** grows rightwards. The base or bottom of the stack is on the left and holds the leftmost, oldest parse fragment. Every reduction step acts only on the rightmost, newest parse fragments. (This accumulative parse stack is very unlike the predictive, leftward-growing parse stack used by top-down parsers.)
### Bottom-up parse steps for example A \* 2 + 1 {#bottom_up_parse_steps_for_example_a_2_1}
Step Parse Stack Unparsed Shift/Reduce
------ ------------------- ------------ ------------------------------
0 *empty* A \* 2 + 1 shift
1 *id* \* 2 + 1 Value → *id*
2 Value \* 2 + 1 Products → Value
3 Products \* 2 + 1 shift
4 Products \* 2 + 1 shift
5 Products \* *int* \+ 1 Value → *int*
6 Products \* Value \+ 1 Products → Products \* Value
7 Products \+ 1 Sums → Products
8 Sums \+ 1 shift
9 Sums + 1 shift
10 Sums + *int* *eof* Value → *int*
11 Sums + Value *eof* Products → Value
12 Sums + Products *eof* Sums → Sums + Products
13 Sums *eof* accept
Step 6 applies a grammar rule with multiple parts:
: Products → Products \* Value
This matches the stack top holding the parsed phrases \"\... Products \* Value\". The reduce step replaces this instance of the rule\'s right hand side, \"Products \* Value\" by the rule\'s left hand side symbol, here a larger Products. If the parser builds complete parse trees, the three trees for inner Products, \*, and Value are combined by a new tree root for Products. Otherwise, semantic`{{Broken anchor|date=2025-04-28|bot=User:Cewbot/log/20201008/configuration|target_link=Semantics#Programming languages|reason=Anchor "Semantics#Programming languages" links to a specific web page: "Programming languages". The anchor (Programming languages) [[Special:Diff/1208968924|has been deleted]].|diff_id=1208968924}}`{=mediawiki} details from the inner Products and Value are output to some later compiler pass, or are combined and saved in the new Products symbol.
| 828 |
LR parser
| 1 |
18,030 |
# LR parser
## Overview
### LR parse steps for example A \* 2 + 1 {#lr_parse_steps_for_example_a_2_1}
In LR parsers, the shift and reduce decisions are potentially based on the entire stack of everything that has been previously parsed, not just on a single, topmost stack symbol. If done in an unclever way, that could lead to very slow parsers that get slower and slower for longer inputs. LR parsers do this with constant speed, by summarizing all the relevant left context information into a single number called the LR(0) **parser state**. For each grammar and LR analysis method, there is a fixed (finite) number of such states. Besides holding the already-parsed symbols, the parse stack also remembers the state numbers reached by everything up to those points.
At every parse step, the entire input text is divided into a stack of previously parsed phrases, a current look-ahead symbol, and the remaining unscanned text. The parser\'s next action is determined by its current LR(0) `{{color|#928|state number}}`{=mediawiki} (rightmost on the stack) and the lookahead symbol. In the steps below, all the black details are exactly the same as in other non-LR shift-reduce parsers. LR parser stacks add the state information in purple, summarizing the black phrases to their left on the stack and what syntax possibilities to expect next. Users of an LR parser can usually ignore state information. These states are explained in a later section.
`{{br}}`{=mediawiki}Step Parse Stack`{{br}}`{=mediawiki}~`{{color|#928|state}}`{=mediawiki}~ \[Symbol~`{{color|#928|state}}`{=mediawiki}~\]\* Look`{{br}}`{=mediawiki}Ahead `{{br}}`{=mediawiki}Unscanned Parser`{{br}}`{=mediawiki}Action `{{br}}`{=mediawiki}Grammar Rule Next`{{br}}`{=mediawiki}State
-------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------- ------------------------------- ---------------------------------- ---------------------------------- -------------------------------
0 ~`{{color|#928|0}}`{=mediawiki}~ *id* \* 2 + 1 shift
1 ~`{{color|#928|0}}`{=mediawiki}~ *id*~`{{color|#928|9}}`{=mediawiki}~ \* 2 + 1 reduce Value → *id*
2 ~`{{color|#928|0}}`{=mediawiki}~ Value~`{{color|#928|7}}`{=mediawiki}~ \* 2 + 1 reduce Products → Value
3 ~`{{color|#928|0}}`{=mediawiki}~ Products~`{{color|#928|4}}`{=mediawiki}~ \* 2 + 1 shift
4 ~`{{color|#928|0}}`{=mediawiki}~ Products~`{{color|#928|4}}`{=mediawiki}~ \*~`{{color|#928|5}}`{=mediawiki}~ *int* \+ 1 shift
5 ~`{{color|#928|0}}`{=mediawiki}~ Products~`{{color|#928|4}}`{=mediawiki}~ \*~`{{color|#928|5}}`{=mediawiki}~ *int*~`{{color|#928|8}}`{=mediawiki}~ \+ 1 reduce Value → *int*
6 ~`{{color|#928|0}}`{=mediawiki}~ Products~`{{color|#928|4}}`{=mediawiki}~ \*~`{{color|#928|5}}`{=mediawiki}~ Value~`{{color|#928|6}}`{=mediawiki}~ \+ 1 reduce Products → Products \* Value
7 ~`{{color|#928|0}}`{=mediawiki}~ Products~`{{color|#928|4}}`{=mediawiki}~ \+ 1 reduce Sums → Products
8 ~`{{color|#928|0}}`{=mediawiki}~ Sums~`{{color|#928|1}}`{=mediawiki}~ \+ 1 shift
9 ~`{{color|#928|0}}`{=mediawiki}~ Sums~`{{color|#928|1}}`{=mediawiki}~ +~`{{color|#928|2}}`{=mediawiki}~ *int* *eof* shift
10 ~`{{color|#928|0}}`{=mediawiki}~ Sums~`{{color|#928|1}}`{=mediawiki}~ +~`{{color|#928|2}}`{=mediawiki}~ *int*~`{{color|#928|8}}`{=mediawiki}~ *eof* reduce Value → *int*
11 ~`{{color|#928|0}}`{=mediawiki}~ Sums~`{{color|#928|1}}`{=mediawiki}~ +~`{{color|#928|2}}`{=mediawiki}~ Value~`{{color|#928|7}}`{=mediawiki}~ *eof* reduce Products → Value
12 ~`{{color|#928|0}}`{=mediawiki}~ Sums~`{{color|#928|1}}`{=mediawiki}~ +~`{{color|#928|2}}`{=mediawiki}~ Products~`{{color|#928|3}}`{=mediawiki}~ *eof* reduce Sums → Sums + Products
13 ~`{{color|#928|0}}`{=mediawiki}~ Sums~`{{color|#928|1}}`{=mediawiki}~ *eof* accept
At initial step 0, the input stream \"A \* 2 + 1\" is divided into
- an empty section on the parse stack,
- lookahead text \"A\" scanned as an *id* symbol, and
- the remaining unscanned text \"\* 2 + 1\".
The parse stack begins by holding only initial state 0. When state 0 sees the lookahead *id*, it knows to shift that *id* onto the stack, and scan the next input symbol **\***, and advance to state 9.
At step 4, the total input stream \"A \* 2 + 1\" is currently divided into
- the parsed section \"A \*\" with 2 stacked phrases Products and **\***,
- lookahead text \"2\" scanned as an *int* symbol, and
- the remaining unscanned text \" + 1\".
The states corresponding to the stacked phrases are 0, 4, and 5. The current, rightmost state on the stack is state 5. When state 5 sees the lookahead *int*, it knows to shift that *int* onto the stack as its own phrase, and scan the next input symbol **+**, and advance to state 8.
At step 12, all of the input stream has been consumed but only partially organized. The current state is 3. When state 3 sees the lookahead *eof*, it knows to apply the completed grammar rule
:
: Sums → Sums + Products
by combining the stack\'s rightmost three phrases for Sums, **+**, and Products into one thing. State 3 itself doesn\'t know what the next state should be. This is found by going back to state 0, just to the left of the phrase being reduced. When state 0 sees this new completed instance of a Sums, it advances to state 1 (again). This consulting of older states is why they are kept on the stack, instead of keeping only the current state.
| 686 |
LR parser
| 2 |
18,030 |
# LR parser
## Overview
### Grammar for the example A \* 2 + 1 {#grammar_for_the_example_a_2_1}
LR parsers are constructed from a grammar that formally defines the syntax of the input language as a set of patterns. The grammar doesn\'t cover all language rules, such as the size of numbers, or the consistent use of names and their definitions in the context of the whole program. LR parsers use a context-free grammar that deals just with local patterns of symbols.
The example grammar used here is a tiny subset of the Java or C language:
:
: r0: Goal → Sums *eof*
: r1: Sums → Sums + Products
: r2: Sums → Products
: r3: Products → Products \* Value
: r4: Products → Value
: r5: Value → *int*
: r6: Value → *id*
The grammar\'s terminal symbols are the multi-character symbols or \'tokens\' found in the input stream by a lexical scanner. Here these include **+** **\*** and *int* for any integer constant, and *id* for any identifier name, and *eof* for end of input file. The grammar doesn\'t care what the *int* values or *id* spellings are, nor does it care about blanks or line breaks. The grammar uses these terminal symbols but does not define them. They are always leaf nodes (at the bottom bushy end) of the parse tree.
The capitalized terms like Sums are nonterminal symbols. These are names for concepts or patterns in the language. They are defined in the grammar and never occur themselves in the input stream. They are always internal nodes (above the bottom) of the parse tree. They only happen as a result of the parser applying some grammar rule. Some nonterminals are defined with two or more rules; these are alternative patterns. Rules can refer back to themselves, which are called *recursive*. This grammar uses recursive rules to handle repeated math operators. Grammars for complete languages use recursive rules to handle lists, parenthesized expressions, and nested statements.
Any given computer language can be described by several different grammars. An LR(1) parser can handle many but not all common grammars. It is usually possible to manually modify a grammar so that it fits the limitations of LR(1) parsing and the generator tool.
The grammar for an LR parser must be unambiguous itself, or must be augmented by tie-breaking precedence rules. This means there is only one correct way to apply the grammar to a given legal example of the language, resulting in a unique parse tree with just one meaning, and a unique sequence of shift/reduce actions for that example. LR parsing is not a useful technique for human languages with ambiguous grammars that depend on the interplay of words. Human languages are better handled by parsers like Generalized LR parser, the Earley parser, or the CYK algorithm that can simultaneously compute all possible parse trees in one pass.
| 481 |
LR parser
| 3 |
18,030 |
# LR parser
## Overview
### Parse table for the example grammar {#parse_table_for_the_example_grammar}
Most LR parsers are table driven. The parser\'s program code is a simple generic loop that is the same for all grammars and languages. The knowledge of the grammar and its syntactic implications are encoded into unchanging data tables called **parse tables** (or **parsing tables**). Entries in a table show whether to shift or reduce (and by which grammar rule), for every legal combination of parser state and lookahead symbol. The parse tables also tell how to compute the next state, given just a current state and a next symbol.
The parse tables are much larger than the grammar. LR tables are hard to accurately compute by hand for big grammars. So they are mechanically derived from the grammar by some parser generator tool like Bison.
Depending on how the states and parsing table are generated, the resulting parser is called either a **SLR** (simple LR) parser, **LALR** (look-ahead LR) parser, or canonical LR parser. LALR parsers handle more grammars than SLR parsers. Canonical LR parsers handle even more grammars, but use many more states and much larger tables. The example grammar is SLR.
LR parse tables are two-dimensional. Each current LR(0) parser state has its own row. Each possible next symbol has its own column. Some combinations of state and next symbol are not possible for valid input streams. These blank cells trigger syntax error messages.
The **Action** left half of the table has columns for lookahead terminal symbols. These cells determine whether the next parser action is shift (to state *n*), or reduce (by grammar rule **r**~*n*~).
The **Goto** right half of the table has columns for nonterminal symbols. These cells show which state to advance to, after some reduction\'s Left Hand Side has created an expected new instance of that symbol. This is like a shift action but for nonterminals; the lookahead terminal symbol is unchanged.
The table column \"Current Rules\" documents the meaning and syntax possibilities for each state, as worked out by the parser generator. It is not included in the actual tables used at parsing time. The `{{color|#f7f|•}}`{=mediawiki} (pink dot) marker shows where the parser is now, within some partially recognized grammar rules. The things to the left of `{{color|#f7f|•}}`{=mediawiki} have been parsed, and the things to the right are expected soon. A state has several such current rules if the parser has not yet narrowed possibilities down to a single rule.
Curr Lookahead
------- ---------------------------------------------------------------------------------------------------------------------------------------- ----------- ------ ------
State Current Rules *int* *id* \*
0 Goal → `{{color|#f7f|•}}`{=mediawiki} Sums *eof* 8 9
1 Goal → Sums `{{color|#f7f|•}}`{=mediawiki} *eof* `{{br}}`{=mediawiki} Sums → Sums `{{color|#f7f|•}}`{=mediawiki} + Products
2 Sums → Sums + `{{color|#f7f|•}}`{=mediawiki} Products 8 9
3 Sums → Sums + Products `{{color|#f7f|•}}`{=mediawiki} `{{br}}`{=mediawiki} Products → Products `{{color|#f7f|•}}`{=mediawiki} \* Value 5
4 Sums → Products `{{color|#f7f|•}}`{=mediawiki} `{{br}}`{=mediawiki} Products → Products `{{color|#f7f|•}}`{=mediawiki} \* Value 5
5 Products → Products \* `{{color|#f7f|•}}`{=mediawiki} Value 8 9
6 Products → Products \* Value `{{color|#f7f|•}}`{=mediawiki} r3
7 Products → Value `{{color|#f7f|•}}`{=mediawiki} r4
8 Value → *int* `{{color|#f7f|•}}`{=mediawiki} r5
9 Value → *id* `{{color|#f7f|•}}`{=mediawiki} r6
In state 2 above, the parser has just found and shifted-in the **+** of grammar rule
:
: r1: Sums → Sums + `{{color|#f7f|•}}`{=mediawiki} Products
The next expected phrase is Products. Products begins with terminal symbols *int* or *id*. If the lookahead is either of those, the parser shifts them in and advances to state 8 or 9, respectively. When a Products has been found, the parser advances to state 3 to accumulate the complete list of summands and find the end of rule r0. A Products can also begin with nonterminal Value. For any other lookahead or nonterminal, the parser announces a syntax error.
In state 3, the parser has just found a Products phrase, that could be from two possible grammar rules:
:
: r1: Sums → Sums + Products `{{color|#f7f|•}}`{=mediawiki}
: r3: Products → Products `{{color|#f7f|•}}`{=mediawiki} \* Value
The choice between r1 and r3 can\'t be decided just from looking backwards at prior phrases. The parser has to check the lookahead symbol to tell what to do. If the lookahead is **\***, it is in rule 3, so the parser shifts in the **\*** and advances to state 5. If the lookahead is *eof*, it is at the end of rule 1 and rule 0, so the parser is done.
In state 9 above, all the non-blank, non-error cells are for the same reduction r6. Some parsers save time and table space by not checking the lookahead symbol in these simple cases. Syntax errors are then detected somewhat later, after some harmless reductions, but still before the next shift action or parser decision.
Individual table cells must not hold multiple, alternative actions, otherwise the parser would be nondeterministic with guesswork and backtracking. If the grammar is not LR(1), some cells will have shift/reduce conflicts between a possible shift action and reduce action, or reduce/reduce conflicts between multiple grammar rules. LR(*k*) parsers resolve these conflicts (where possible) by checking additional lookahead symbols beyond the first.
### LR parser loop {#lr_parser_loop}
The LR parser begins with a nearly empty parse stack containing just the start state 0, and with the lookahead holding the input stream\'s first scanned symbol. The parser then repeats the following loop step until done, or stuck on a syntax error:
The topmost state on the parse stack is some state *s*, and the current lookahead is some terminal symbol *t*. Look up the next parser action from row *s* and column *t* of the Lookahead Action table. That action is either Shift, Reduce, Accept, or Error:
- Shift *n*:
:
: Shift the matched terminal *t* onto the parse stack and scan the next input symbol into the lookahead buffer.
: Push next state *n* onto the parse stack as the new current state.
- Reduce r~*m*~: Apply grammar rule r~*m*~: Lhs → S~1~ S~2~ \... S~L~
:
: Remove the matched topmost L symbols (and parse trees and associated state numbers) from the parse stack.
: This exposes a prior state *p* that was expecting an instance of the Lhs symbol.
: Join the L parse trees together as one parse tree with new root symbol Lhs.
: Lookup the next state *n* from row *p* and column *Lhs* of the LHS Goto table.
: Push the symbol and tree for Lhs onto the parse stack.
: Push next state *n* onto the parse stack as the new current state.
: The lookahead and input stream remain unchanged.
- Accept: Lookahead *t* is the *eof* marker. End of parsing. If the state stack contains just the start state report success. Otherwise, report a syntax error.
- Error: Report a syntax error. The parser ends, or attempts some recovery.
LR parser stack usually stores just the LR(0) automaton states, as the grammar symbols may be derived from them (in the automaton, all input transitions to some state are marked with the same symbol, which is the symbol associated with this state). Moreover, these symbols are almost never needed as the state is all that matters when making the parsing decision.
| 1,192 |
LR parser
| 4 |
18,030 |
# LR parser
## LR generator analysis {#lr_generator_analysis}
This section of the article can be skipped by most users of LR parser generators.
### LR states {#lr_states}
State 2 in the example parse table is for the partially parsed rule
:
: r1: Sums → Sums + `{{color|#f7f|•}}`{=mediawiki} Products
This shows how the parser got here, by seeing Sums then **+** while looking for a larger Sums. The `{{color|#f7f|•}}`{=mediawiki} marker has advanced beyond the beginning of the rule. It also shows how the parser expects to eventually complete the rule, by next finding a complete Products. But more details are needed on how to parse all the parts of that Products.
The partially parsed rules for a state are called its \"core LR(0) items\". The parser generator adds additional rules or items for all the possible next steps in building up the expected Products:
:
: r3: Products → `{{color|#f7f|•}}`{=mediawiki} Products \* Value
: r4: Products → `{{color|#f7f|•}}`{=mediawiki} Value
: r5: Value → `{{color|#f7f|•}}`{=mediawiki} *int*
: r6: Value → `{{color|#f7f|•}}`{=mediawiki} *id*
The `{{color|#f7f|•}}`{=mediawiki} marker is at the beginning of each of these added rules; the parser has not yet confirmed and parsed any part of them. These additional items are called the \"closure\" of the core items. For each nonterminal symbol immediately following a `{{color|#f7f|•}}`{=mediawiki}, the generator adds the rules defining that symbol. This adds more `{{color|#f7f|•}}`{=mediawiki} markers, and possibly different follower symbols. This closure process continues until all follower symbols have been expanded. The follower nonterminals for state 2 begins with Products. Value is then added by closure. The follower terminals are *int* and *id*.
The kernel and closure items together show all possible legal ways to proceed from the current state to future states and complete phrases. If a follower symbol appears in only one item, it leads to a next state containing only one core item with the `{{color|#f7f|•}}`{=mediawiki} marker advanced. So *int* leads to next state 8 with core
:
: r5: Value → *int* `{{color|#f7f|•}}`{=mediawiki}
If the same follower symbol appears in several items, the parser cannot yet tell which rule applies here. So that symbol leads to a next state that shows all remaining possibilities, again with the `{{color|#f7f|•}}`{=mediawiki} marker advanced. Products appears in both r1 and r3. So Products leads to next state 3 with core
:
: r1: Sums → Sums + Products `{{color|#f7f|•}}`{=mediawiki}
: r3: Products → Products `{{color|#f7f|•}}`{=mediawiki} \* Value
In words, that means if the parser has seen a single Products, it might be done, or it might still have even more things to multiply together. All the core items have the same symbol preceding the `{{color|#f7f|•}}`{=mediawiki} marker; all transitions into this state are always with that same symbol.
Some transitions will be to cores and states that have been enumerated already. Other transitions lead to new states. The generator starts with the grammar\'s goal rule. From there it keeps exploring known states and transitions until all needed states have been found.
These states are called \"LR(0)\" states because they use a lookahead of *k*=0, i.e. no lookahead. The only checking of input symbols occurs when the symbol is shifted in. Checking of lookaheads for reductions is done separately by the parse table, not by the enumerated states themselves.
### Finite state machine {#finite_state_machine}
The parse table describes all possible LR(0) states and their transitions. They form a finite-state machine (FSM). An FSM is a simple engine for parsing simple unnested languages, without using a stack. In this LR application, the FSM\'s modified \"input language\" has both terminal and nonterminal symbols, and covers any partially parsed stack snapshot of the full LR parse.
Recall step 5 of the Parse Steps Example:
\<`{{br}}`{=mediawiki}Step Parse Stack`{{br}}`{=mediawiki}~`{{color|#928|state}}`{=mediawiki}~ Symbol ~`{{color|#928|state}}`{=mediawiki}~ \... Look`{{br}}`{=mediawiki}Ahead `{{br}}`{=mediawiki}Unscanned
---------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------- -------------------------------
5 ~`{{color|#928|0}}`{=mediawiki}~ Products~`{{color|#928|4}}`{=mediawiki}~ \*~`{{color|#928|5}}`{=mediawiki}~ *int*~`{{color|#928|8}}`{=mediawiki}~ \+ 1
The parse stack shows a series of state transitions, from the start state 0, to state 4 and then on to 5 and current state 8. The symbols on the parse stack are the shift or goto symbols for those transitions. Another way to view this, is that the finite state machine can scan the stream \"Products \* *int* + 1\" (without using yet another stack) and find the leftmost complete phrase that should be reduced next. And that is indeed its job!
How can a mere FSM do this when the original unparsed language has nesting and recursion and definitely requires an analyzer with a stack? The trick is that everything to the left of the stack top has already been fully reduced. This eliminates all the loops and nesting from those phrases. The FSM can ignore all the older beginnings of phrases, and track just the newest phrases that might be completed next. The obscure name for this in LR theory is \"viable prefix\".
| 797 |
LR parser
| 5 |
18,030 |
# LR parser
## LR generator analysis {#lr_generator_analysis}
### Lookahead sets {#lookahead_sets}
The states and transitions give all the needed information for the parse table\'s shift actions and goto actions. The generator also needs to calculate the expected lookahead sets for each reduce action.
In **SLR** parsers, these lookahead sets are determined directly from the grammar, without considering the individual states and transitions. For each nonterminal S, the SLR generator works out Follows(S), the set of all the terminal symbols which can immediately follow some occurrence of S. In the parse table, each reduction to S uses Follow(S) as its LR(1) lookahead set. Such follow sets are also used by generators for LL top-down parsers. A grammar that has no shift/reduce or reduce/reduce conflicts when using Follow sets is called an SLR grammar.
**LALR** parsers have the same states as SLR parsers, but use a more complicated, more precise way of working out the minimum necessary reduction lookaheads for each individual state. Depending on the details of the grammar, this may turn out to be the same as the Follow set computed by SLR parser generators, or it may turn out to be a subset of the SLR lookaheads. Some grammars are okay for LALR parser generators but not for SLR parser generators. This happens when the grammar has spurious shift/reduce or reduce/reduce conflicts using Follow sets, but no conflicts when using the exact sets computed by the LALR generator. The grammar is then called LALR(1) but not SLR.
An SLR or LALR parser avoids having duplicate states. But this minimization is not necessary, and can sometimes create unnecessary lookahead conflicts. **Canonical LR** parsers use duplicated (or \"split\") states to better remember the left and right context of a nonterminal\'s use. Each occurrence of a symbol S in the grammar can be treated independently with its own lookahead set, to help resolve reduction conflicts. This handles a few more grammars. Unfortunately, this greatly magnifies the size of the parse tables if done for all parts of the grammar. This splitting of states can also be done manually and selectively with any SLR or LALR parser, by making two or more named copies of some nonterminals. A grammar that is conflict-free for a canonical LR generator but has conflicts in an LALR generator is called LR(1) but not LALR(1), and not SLR.
SLR, LALR, and canonical LR parsers make exactly the same shift and reduce decisions when the input stream is the correct language. When the input has a syntax error, the LALR parser may do some additional (harmless) reductions before detecting the error than would the canonical LR parser. And the SLR parser may do even more. This happens because the SLR and LALR parsers are using a generous superset approximation to the true, minimal lookahead symbols for that particular state.
| 471 |
LR parser
| 6 |
18,030 |
# LR parser
## LR generator analysis {#lr_generator_analysis}
### Syntax error recovery {#syntax_error_recovery}
LR parsers can generate somewhat helpful error messages for the first syntax error in a program, by simply enumerating all the terminal symbols that could have appeared next instead of the unexpected bad lookahead symbol. But this does not help the parser work out how to parse the remainder of the input program to look for further, independent errors. If the parser recovers badly from the first error, it is very likely to mis-parse everything else and produce a cascade of unhelpful spurious error messages.
In the yacc and bison parser generators, the parser has an ad hoc mechanism to abandon the current statement, discard some parsed phrases and lookahead tokens surrounding the error, and resynchronize the parse at some reliable statement-level delimiter like semicolons or braces. This often works well for allowing the parser and compiler to look over the rest of the program.
Many syntactic coding errors are simple typos or omissions of a trivial symbol. Some LR parsers attempt to detect and automatically repair these common cases. The parser enumerates every possible single-symbol insertion, deletion, or substitution at the error point. The compiler does a trial parse with each change to see if it worked okay. (This requires backtracking to snapshots of the parse stack and input stream, normally unneeded by the parser.) Some best repair is picked. This gives a very helpful error message and resynchronizes the parse well. However, the repair is not trustworthy enough to permanently modify the input file. Repair of syntax errors is easiest to do consistently in parsers (like LR) that have parse tables and an explicit data stack.
### Variants of LR parsers {#variants_of_lr_parsers}
The LR parser generator decides what should happen for each combination of parser state and lookahead symbol. These decisions are usually turned into read-only data tables that drive a generic parser loop that is grammar- and state-independent. But there are also other ways to turn those decisions into an active parser.
Some LR parser generators create separate tailored program code for each state, rather than a parse table. These parsers can run several times faster than the generic parser loop in table-driven parsers. The fastest parsers use generated assembler code.
In the recursive ascent parser variation, the explicit parse stack structure is also replaced by the implicit stack used by subroutine calls. Reductions terminate several levels of subroutine calls, which is clumsy in most languages. So recursive ascent parsers are generally slower, less obvious, and harder to hand-modify than recursive descent parsers.
Another variation replaces the parse table by pattern-matching rules in non-procedural languages such as Prolog.
**GLR** Generalized LR parsers use LR bottom-up techniques to find all possible parses of input text, not just one correct parse. This is essential for ambiguous grammar such as used for human languages. The multiple valid parse trees are computed simultaneously, without backtracking. GLR is sometimes helpful for computer languages that are not easily described by a conflict-free LALR(1) grammar.
**LC** Left corner parsers use LR bottom-up techniques for recognizing the left end of alternative grammar rules. When the alternatives have been narrowed down to a single possible rule, the parser then switches to top-down LL(1) techniques for parsing the rest of that rule. LC parsers have smaller parse tables than LALR parsers and better error diagnostics. There are no widely used generators for deterministic LC parsers. Multiple-parse LC parsers are helpful with human languages with very large grammars.
### Theory
LR parsers were invented by Donald Knuth in 1965 as an efficient generalization of precedence parsers. Knuth proved that LR parsers were the most general-purpose parsers possible that would still be efficient in the worst cases.
: \"LR(*k*) grammars can be efficiently parsed with an execution time essentially proportional to the length of the string.\"
: For every `{{nowrap|''k'' ≥ 1}}`{=mediawiki}, \"a language can be generated by an LR(*k*) grammar if and only if it is deterministic \[and context-free\], if and only if it can be generated by an LR(1) grammar.\"
In other words, if a language was reasonable enough to allow an efficient one-pass parser, it could be described by an LR(*k*) grammar. And that grammar could always be mechanically transformed into an equivalent (but larger) LR(1) grammar. So an LR(1) parsing method was, in theory, powerful enough to handle any reasonable language. In practice, the natural grammars for many programming languages are close to being LR(1).
The canonical LR parsers described by Knuth had too many states and very big parse tables that were impractically large for the limited memory of computers of that era. LR parsing became practical when Frank DeRemer invented SLR and LALR parsers with much fewer states.
For full details on LR theory and how LR parsers are derived from grammars, see *The Theory of Parsing, Translation, and Compiling, Volume 1* (Aho and Ullman).
Earley parsers apply the techniques and `{{color|#f7f|•}}`{=mediawiki} notation of LR parsers to the task of generating all possible parses for ambiguous grammars such as for human languages.
While LR(*k*) grammars have equal generative power for all *k*≥1, the case of LR(0) grammars is slightly different. A language *L* is said to have the *prefix property* if no word in *L* is a proper prefix of another word in *L*. A language *L* has an LR(0) grammar if and only if *L* is a deterministic context-free language with the prefix property. As a consequence, a language *L* is deterministic context-free if and only if *L*\$ has an LR(0) grammar, where \"\$\" is not a symbol of *L*{{\'}}s alphabet.
| 932 |
LR parser
| 7 |
18,030 |
# LR parser
## Additional example 1 + 1 {#additional_example_1_1}
right\|framed\|Bottom-up parse of 1+1
This example of LR parsing uses the following small grammar with goal symbol E:
: \(1\) E → E \* B
: \(2\) E → E + B
: \(3\) E → B
: \(4\) B → 0
: \(5\) B → 1
to parse the following input:
: **1 + 1**
### Action and goto tables {#action_and_goto_tables}
The two LR(0) parsing tables for this grammar look as follows:
------------- -------------- -------
***state*** ***action***
**\*** **+**
**0**
**1** r4 r4
**2** r5 r5
**3** s5 s6
**4** r3 r3
**5**
**6**
**7** r1 r1
**8** r2 r2
------------- -------------- -------
The **action table** is indexed by a state of the parser and a terminal (including a special terminal \$ that indicates the end of the input stream) and contains three types of actions:
- *shift*, which is written as \"s*n*\" and indicates that the next state is *n*
- *reduce*, which is written as \"r*m*\" and indicates that a reduction with grammar rule *m* should be performed
- *accept*, which is written as \"acc\" and indicates that the parser accepts the string in the input stream.
The **goto table** is indexed by a state of the parser and a nonterminal and simply indicates what the next state of the parser will be if it has recognized a certain nonterminal. This table is important to find out the next state after every reduction. After a reduction, the next state is found by looking up the **goto table** entry for top of the stack (i.e. current state) and the reduced rule\'s LHS (i.e. non-terminal).
### Parsing steps {#parsing_steps}
The table below illustrates each step in the process. Here the state refers to the element at the top of the stack (the right-most element), and the next action is determined by referring to the action table above. A \$ is appended to the input string to denote the end of the stream.
State Input stream Output stream Stack Next action
------- -------------- --------------- ------------- -------------
0 1 + 1 \$ \[0\] Shift 2
2 \+ 1 \$ \[0,2\] Reduce 5
4 \+ 1 \$ 5 \[0,4\] Reduce 3
3 \+ 1 \$ 5,3 \[0,3\] Shift 6
6 1 \$ 5,3 \[0,3,6\] Shift 2
2 \$ 5,3 \[0,3,6,2\] Reduce 5
8 \$ 5,3,5 \[0,3,6,8\] Reduce 2
3 \$ 5,3,5,2 \[0,3\] Accept
| 401 |
LR parser
| 8 |
18,030 |
# LR parser
## Additional example 1 + 1 {#additional_example_1_1}
### Walkthrough
The parser starts out with the stack containing just the initial state (\'0\'):
: \[**0**\]
The first symbol from the input string that the parser sees is \'1\'. To find the next action (shift, reduce, accept or error), the action table is indexed with the current state (the \"current state\" is just whatever is on the top of the stack), which in this case is 0, and the current input symbol, which is \'1\'. The action table specifies a shift to state 2, and so state 2 is pushed onto the stack (again, all the state information is in the stack, so \"shifting to state 2\" is the same as pushing 2 onto the stack). The resulting stack is
: \[**0** \'1\' **2**\]
where the top of the stack is 2. For the sake of explaining the symbol (e.g., \'1\', B) is shown that caused the transition to the next state, although strictly speaking it is not part of the stack.
In state 2, the action table says to reduce with grammar rule 5 (regardless of what terminal the parser sees on the input stream), which means that the parser has just recognized the right-hand side of rule 5. In this case, the parser writes 5 to the output stream, pops one state from the stack (since the right-hand side of the rule has one symbol), and pushes on the stack the state from the cell in the goto table for state 0 and B, i.e., state 4. The resulting stack is:
: \[**0** B **4**\]
However, in state 4, the action table says the parser should now reduce with rule 3. So it writes 3 to the output stream, pops one state from the stack, and finds the new state in the goto table for state 0 and E, which is state 3. The resulting stack:
: \[**0** E **3**\]
The next terminal that the parser sees is a \'+\' and according to the action table it should then shift to state 6:
: \[**0** E **3** \'+\' **6**\]
The resulting stack can be interpreted as the history of a finite-state machine that has just read a nonterminal E followed by a terminal \'+\'. The transition table of this automaton is defined by the shift actions in the action table and the goto actions in the goto table.
The next terminal is now \'1\' and this means that the parser performs a shift and go to state 2:
: \[**0** E **3** \'+\' **6** \'1\' **2**\]
Just as the previous \'1\' this one is reduced to B giving the following stack:
: \[**0** E **3** \'+\' **6** B **8**\]
The stack corresponds with a list of states of a finite automaton that has read a nonterminal E, followed by a \'+\' and then a nonterminal B. In state 8 the parser always performs a reduce with rule 2. The top 3 states on the stack correspond with the 3 symbols in the right-hand side of rule 2. This time we pop 3 elements off of the stack (since the right-hand side of the rule has 3 symbols) and look up the goto state for E and 0, thus pushing state 3 back onto the stack
: \[**0** E **3**\]
Finally, the parser reads a \'\$\' (end of input symbol) from the input stream, which means that according to the action table (the current state is 3) the parser accepts the input string. The rule numbers that will then have been written to the output stream will be \[5, 3, 5, 2\] which is indeed a rightmost derivation of the string \"1 + 1\" in reverse.
| 618 |
LR parser
| 9 |
18,030 |
# LR parser
## Constructing LR(0) parsing tables {#constructing_lr0_parsing_tables}
### Items
The construction of these parsing tables is based on the notion of *LR(0) items* (simply called *items* here) which are grammar rules with a special dot added somewhere in the right-hand side. For example, the rule E → E + B has the following four corresponding items:
: E → `{{color|#f7f|•}}`{=mediawiki} E + B
: E → E `{{color|#f7f|•}}`{=mediawiki} + B
: E → E + `{{color|#f7f|•}}`{=mediawiki} B
: E → E + B `{{color|#f7f|•}}`{=mediawiki}
Rules of the form *A* → ε have only a single item *A* → `{{color|#f7f|•}}`{=mediawiki}. The item E → E `{{color|#f7f|•}}`{=mediawiki} + B, for example, indicates that the parser has recognized a string corresponding with E on the input stream and now expects to read a \'+\' followed by another string corresponding with B.
### Item sets {#item_sets}
It is usually not possible to characterize the state of the parser with a single item because it may not know in advance which rule it is going to use for reduction. For example, if there is also a rule E → E \* B then the items E → E `{{color|#f7f|•}}`{=mediawiki} + B and E → E `{{color|#f7f|•}}`{=mediawiki} \* B will both apply after a string corresponding with E has been read. Therefore, it is convenient to characterize the state of the parser by a set of items, in this case the set { E → E `{{color|#f7f|•}}`{=mediawiki} + B, E → E `{{color|#f7f|•}}`{=mediawiki} \* B }.
### Extension of Item Set by expansion of non-terminals {#extension_of_item_set_by_expansion_of_non_terminals}
An item with a dot before a nonterminal, such as E → E + `{{color|#f7f|•}}`{=mediawiki} B, indicates that the parser expects to parse the nonterminal B next. To ensure the item set contains all possible rules the parser may be in the midst of parsing, it must include all items describing how B itself will be parsed. This means that if there are rules such as B → 1 and B → 0 then the item set must also include the items B → `{{color|#f7f|•}}`{=mediawiki} 1 and B → `{{color|#f7f|•}}`{=mediawiki} 0. In general this can be formulated as follows:
: If there is an item of the form *A* → *v* `{{color|#f7f|•}}`{=mediawiki} *Bw* in an item set and in the grammar there is a rule of the form *B* → *w\'* then the item *B* → `{{color|#f7f|•}}`{=mediawiki} *w\'* should also be in the item set.
### Closure of item sets {#closure_of_item_sets}
Thus, any set of items can be extended by recursively adding all the appropriate items until all nonterminals preceded by dots are accounted for. The minimal extension is called the *closure* of an item set and written as **clos**(*I*) where *I* is an item set. It is these closed item sets that are taken as the states of the parser, although only the ones that are actually reachable from the begin state will be included in the tables.
### Augmented grammar {#augmented_grammar}
Before the transitions between the different states are determined, the grammar is augmented with an extra rule
: \(0\) S → E eof
where S is a new start symbol and E the old start symbol. The parser will use this rule for reduction exactly when it has accepted the whole input string.
For this example, the same grammar as above is augmented thus:
: \(0\) S → E eof
: \(1\) E → E \* B
: \(2\) E → E + B
: \(3\) E → B
: \(4\) B → 0
: \(5\) B → 1
It is for this augmented grammar that the item sets and the transitions between them will be determined.
| 612 |
LR parser
| 10 |
18,030 |
# LR parser
## Table construction {#table_construction}
### Finding the reachable item sets and the transitions between them {#finding_the_reachable_item_sets_and_the_transitions_between_them}
The first step of constructing the tables consists of determining the transitions between the closed item sets. These transitions will be determined as if we are considering a finite automaton that can read terminals as well as nonterminals. The begin state of this automaton is always the closure of the first item of the added rule: S → `{{color|#f7f|•}}`{=mediawiki} E eof:
: **Item set 0**
: S → `{{color|#f7f|•}}`{=mediawiki} E eof
: **+** E → `{{color|#f7f|•}}`{=mediawiki} E \* B
: **+** E → `{{color|#f7f|•}}`{=mediawiki} E + B
: **+** E → `{{color|#f7f|•}}`{=mediawiki} B
: **+** B → `{{color|#f7f|•}}`{=mediawiki} 0
: **+** B → `{{color|#f7f|•}}`{=mediawiki} 1
The boldfaced \"**+**\" in front of an item indicates the items that were added for the closure (not to be confused with the mathematical \'+\' operator which is a terminal). The original items without a \"**+**\" are called the *kernel* of the item set.
Starting at the begin state (S0), all of the states that can be reached from this state are now determined. The possible transitions for an item set can be found by looking at the symbols (terminals and nonterminals) found following the dots; in the case of item set 0 those symbols are the terminals \'0\' and \'1\' and the nonterminals E and B. To find the item set that each symbol $x \in \{0, 1, E, B\}$ leads to, the following procedure is followed for each of the symbols:
1. Take the subset, *S*, of all items in the current item set where there is a dot in front of the symbol of interest, *x*.
2. For each item in *S*, move the dot to the right of *x*.
3. Close the resulting set of items.
For the terminal \'0\' (i.e. where x = \'0\') this results in:
: **Item set 1**
: B → 0 `{{color|#f7f|•}}`{=mediawiki}
and for the terminal \'1\' (i.e. where x = \'1\') this results in:
: **Item set 2**
: B → 1 `{{color|#f7f|•}}`{=mediawiki}
and for the nonterminal E (i.e. where x = E) this results in:
: **Item set 3**
: S → E `{{color|#f7f|•}}`{=mediawiki} eof
: E → E `{{color|#f7f|•}}`{=mediawiki} \* B
: E → E `{{color|#f7f|•}}`{=mediawiki} + B
and for the nonterminal B (i.e. where x = B) this results in:
: **Item set 4**
: E → B `{{color|#f7f|•}}`{=mediawiki}
The closure does not add new items in all cases - in the new sets above, for example, there are no nonterminals following the dot.
Above procedure is continued until no more new item sets are found. For the item sets 1, 2, and 4 there will be no transitions since the dot is not in front of any symbol. For item set 3 though, we have dots in front of terminals \'\*\' and \'+\'. For symbol $x = \texttt{*}$ the transition goes to:
: **Item set 5**
: E → E \* `{{color|#f7f|•}}`{=mediawiki} B
: **+** B → `{{color|#f7f|•}}`{=mediawiki} 0
: **+** B → `{{color|#f7f|•}}`{=mediawiki} 1
and for $x = \texttt{+}$ the transition goes to:
: **Item set 6**
: E → E + `{{color|#f7f|•}}`{=mediawiki} B
: **+** B → `{{color|#f7f|•}}`{=mediawiki} 0
: **+** B → `{{color|#f7f|•}}`{=mediawiki} 1
Now, the third iteration begins.
For item set 5, the terminals \'0\' and \'1\' and the nonterminal B must be considered, but the resulting closed item sets for the terminals are equal to already found item sets 1 and 2, respectively. For the nonterminal B, the transition goes to:
: **Item set 7**
: E → E \* B `{{color|#f7f|•}}`{=mediawiki}
For item set 6, the terminal \'0\' and \'1\' and the nonterminal B must be considered, but as before, the resulting item sets for the terminals are equal to the already found item sets 1 and 2. For the nonterminal B the transition goes to:
: **Item set 8**
: E → E + B `{{color|#f7f|•}}`{=mediawiki}
These final item sets 7 and 8 have no symbols beyond their dots so no more new item sets are added, so the item generating procedure is complete. The finite automaton, with item sets as its states is shown below.
The transition table for the automaton now looks as follows:
Item Set \* \+ 0 1 E B
---------- ---- ---- --- --- --- ---
0 1 2 3 4
1
2
3 5 6
4
5 1 2 7
6 1 2 8
7
8
### Constructing the action and goto tables {#constructing_the_action_and_goto_tables}
From this table and the found item sets, the action and goto table are constructed as follows:
1. The columns for nonterminals are copied to the goto table.
2. The columns for the terminals are copied to the action table as shift actions.
3. An extra column for \'\$\' (end of input) is added to the action table. An *acc* action is added to the \'\$\' column for each item set that contains an item of the form S → w `{{color|#f7f|•}}`{=mediawiki} eof.
4. If an item set *i* contains an item of the form *A* → *w* `{{color|#f7f|•}}`{=mediawiki} and *A* → *w* is rule *m* with *m* \> 0 then the row for state *i* in the action table is completely filled with the reduce action r*m*.
The reader may verify that these steps produce the action and goto table presented earlier.
#### A note about LR(0) versus SLR and LALR parsing {#a_note_about_lr0_versus_slr_and_lalr_parsing}
Only step 4 of the above procedure produces reduce actions, and so all reduce actions must occupy an entire table row, causing the reduction to occur regardless of the next symbol in the input stream. This is why these are LR(0) parse tables: they don\'t do any lookahead (that is, they look ahead zero symbols) before deciding which reduction to perform. A grammar that needs lookahead to disambiguate reductions would require a parse table row containing different reduce actions in different columns, and the above procedure is not capable of creating such rows.
Refinements to the **LR**(0) table construction procedure (such as SLR and LALR) are capable of constructing reduce actions that do not occupy entire rows. Therefore, they are capable of parsing more grammars than LR(0) parsers.
| 1,037 |
LR parser
| 11 |
18,030 |
# LR parser
## Table construction {#table_construction}
### Conflicts in the constructed tables {#conflicts_in_the_constructed_tables}
The automaton is constructed in such a way that it is guaranteed to be deterministic. However, when reduce actions are added to the action table it can happen that the same cell is filled with a reduce action and a shift action (a *shift-reduce conflict*) or with two different reduce actions (a *reduce-reduce conflict*). However, it can be shown that when this happens the grammar is not an LR(0) grammar. A classic real-world example of a shift-reduce conflict is the dangling else problem.
A small example of a non-LR(0) grammar with a shift-reduce conflict is:
: \(1\) E → 1 E
: \(2\) E → 1
One of the item sets found is:
: **Item set 1**
: E → 1 `{{color|#f7f|•}}`{=mediawiki} E
: E → 1 `{{color|#f7f|•}}`{=mediawiki}
: **+** E → `{{color|#f7f|•}}`{=mediawiki} 1 E
: **+** E → `{{color|#f7f|•}}`{=mediawiki} 1
There is a shift-reduce conflict in this item set: when constructing the action table according to the rules above, the cell for \[item set 1, terminal \'1\'\] contains **s1** (shift to state 1) **and r2** (reduce with grammar rule 2).
A small example of a non-LR(0) grammar with a reduce-reduce conflict is:
: \(1\) E → A 1
: \(2\) E → B 2
: \(3\) A → 1
: \(4\) B → 1
In this case the following item set is obtained:
: **Item set 1**
: A → 1 `{{color|#f7f|•}}`{=mediawiki}
: B → 1 `{{color|#f7f|•}}`{=mediawiki}
There is a reduce-reduce conflict in this item set because in the cells in the action table for this item set there will be both a reduce action for rule 3 and one for rule 4.
Both examples above can be solved by letting the parser use the follow set (see LL parser) of a nonterminal *A* to decide if it is going to use one of *A*s rules for a reduction; it will only use the rule *A* → *w* for a reduction if the next symbol on the input stream is in the follow set of *A*. This solution results in so-called Simple LR parsers
| 359 |
LR parser
| 12 |
18,031 |
# Leon Battista Alberti
**Leon Battista Alberti** (`{{IPA|it|leombatˈtista alˈbɛɾti|lang}}`{=mediawiki}; 14 February 1404 -- 25 April 1472) was an Italian Renaissance humanist author, artist, architect, poet, priest, linguist, philosopher, and cryptographer; he epitomised the nature of those identified now as polymaths. He is considered the founder of European cryptography, a claim he shares with Johannes Trithemius.
He is often considered primarily an architect. However, according to James Beck, \"to single out one of Leon Battista\'s \'fields\' over others as somehow functionally independent and self-sufficient is of no help at all to any effort to characterize Alberti\'s extensive explorations in the fine arts\". Although Alberti is known mostly as an artist, he was also a mathematician and made significant contributions to that field. Among the most famous buildings he designed are the churches of San Sebastiano (1460) and Sant\'Andrea (1472), both in Mantua.
Alberti\'s life was told in Giorgio Vasari\'s *Lives of the Most Excellent Painters, Sculptors, and Architects*.
## Biography
### Early life {#early_life}
Leon Battista Alberti was born in 1404 in Genoa. His mother was Bianca Fieschi. His father, Lorenzo di Benedetto Alberti, was a wealthy Florentine who had been exiled from his own city, but allowed to return in 1428. Alberti was sent to boarding school in Padua, then studied law at Bologna. He lived for a time in Florence, then in 1431 travelled to Rome, where he took holy orders and entered the service of the papal court. During this time he studied the ancient ruins, which excited his interest in architecture and strongly influenced the form of the buildings that he designed.
Leon Battista Alberti was gifted in many ways. He was tall, strong, and a fine athlete who could ride the wildest horse and jump over a person\'s head. He distinguished himself as a writer while still a child at school, and by the age of twenty had written a play that was successfully passed off as a genuine piece of Classical literature. In 1435 he began his first major written work, *Della pittura*, which was inspired by the burgeoning pictorial art in Florence in the early fifteenth century. In this work he analysed the nature of painting and explored the elements of perspective, composition, and colour.
In 1438 he began to focus more on architecture and was encouraged by the Marchese Leonello d\'Este of Ferrara, for whom he built a small triumphal arch to support an equestrian statue of Leonello\'s father. In 1447 Alberti became architectural advisor to Pope Nicholas V and was involved in several projects at the Vatican.
### First major commission {#first_major_commission}
His first major architectural commission was in 1446 for the façade of the Rucellai Palace in Florence. This was followed in 1450 by a commission from Sigismondo Malatesta to transform the Gothic church of San Francesco in Rimini into a memorial chapel, the Tempio Malatestiano. In Florence, he designed the upper parts of the façade for the Dominican church of Santa Maria Novella, famously bridging the nave and lower aisles with two ornately inlaid scrolls, solving a visual problem and setting a precedent to be followed by architects of churches for four hundred years. In 1452, he completed *\[\[De re aedificatoria\]\]*, a treatise on architecture, using as its basis the work of Vitruvius and influenced by the ancient roman buildings. The work was not published until 1485. It was followed in 1464 by his less influential work, *De statua*, in which he examines sculpture. Alberti\'s only known sculpture is a self-portrait medallion, sometimes attributed to Pisanello. Alberti was employed to design two churches in Mantua, San Sebastiano, which was never completed and for which Alberti\'s intention can only be speculated upon, and the Basilica of Sant\'Andrea. The design for the latter church was completed in 1471, a year before Alberti\'s death: the construction was completed after his death and is considered as his most significant work.
### Alberti as artist {#alberti_as_artist}
As an artist, Alberti distinguished himself from the contemporary ordinary craftsmen educated in workshops. He was a humanist who studied Aristotle and Plotinus. He was among the rapidly growing group of intellectuals and artists who at that time were supported by the courts of nobility. As a member of a noble family and as part of the Roman curia, Alberti enjoyed special status. He was a welcomed guest at the Este court in Ferrara, and spent time with the soldier-prince Federico III da Montefeltro in Urbino. The Duke of Urbino was a shrewd military commander, who generously funded artists. Alberti planned to dedicate his treatise on architecture to him.
Among Alberti\'s minor but pioneering studies, were an essay on cryptography, *De componendis cifris*, and the first Italian grammar. He collaborated with the Florentine cosmographer Paolo Toscanelli in astronomy, a science close to geography at that time. He also wrote a small Latin work on geography, *Descriptio urbis Romae* (*The Panorama of the City of Rome*). Just a few years before his death, Alberti completed *De iciarchia* (*On Ruling the Household*), a dialogue about Florence during the Medici rule.
Alberti took holy orders and never married. He loved animals and had a pet dog, a mongrel, about whom he wrote a panegyric (*Canis*). Vasari describes Alberti as \"an admirable citizen, a man of culture\... a friend of talented men, open and courteous with everyone. He always lived honourably and like the gentleman he was.\" Alberti died in Rome on 25 April 1472 at the age of 68.
| 907 |
Leon Battista Alberti
| 0 |
18,031 |
# Leon Battista Alberti
## Publications
Alberti considered mathematics as the foundation of arts and sciences. \"To make clear my exposition in writing this brief commentary on painting,\" Alberti began his treatise, *Della Pittura* (On Painting) dedicated to Brunelleschi, \"I will take first from the mathematicians those things with which my subject is concerned.\"
*Della pittura* (also known in Latin as *De Pictura*) relied on the study classical optics to approach the perspective in artistic and architectural representations. Alberti was well-versed in the sciences of his age. His knowledge of optics was connected to the tradition of the *Kitab al-manazir* (*The Optics*; *De aspectibus*) of the Arab polymath Alhazen (Ibn al-Haytham, d. c. 1041), which was transmitted by Franciscan optical workshops of the thirteenth-century *Perspectivae* traditions of scholars such as Roger Bacon, John Peckham, and Witelo (similar influences are also traceable in the third commentary of Lorenzo Ghiberti, *Commentario terzo*). In both *Della pittura* and *De statua*, Alberti stressed that \"all steps of learning should be sought from nature\". The ultimate aim of an artist is to imitate nature. Painters and sculptors strive \"through by different skills, at the same goal, namely that as nearly as possible the work they have undertaken shall appear to the observer to be similar to the real objects of nature\". However, Alberti did not mean that artists should imitate nature objectively, as it is, but the artist should be especially attentive to beauty, \"for in painting beauty is as pleasing as it is necessary\". The work of art is, according to Alberti, so constructed that it is impossible to take anything away from it or to add anything to it, without impairing the beauty of the whole. Beauty was for Alberti \"the harmony of all parts in relation to one another,\" and subsequently \"this concord is realized in a particular number, proportion, and arrangement demanded by harmony\". Alberti\'s thoughts on harmony were not new---they could be traced back to Pythagoras---but he set them in a fresh context, which fit in well with the contemporary aesthetic discourse.
In Rome, Alberti spent considerable time studying its ancient sites, ruins, and arts. His detailed observations, included in his *\[\[De re aedificatoria\]\]* (1452, *On the Art of Building*), were inspired by the essay *De architectura* written by the Roman architect and engineer Vitruvius (fl. 46--30 BC). Alberti\'s work was the first architectural treatise of the Renaissance. It covered a wide range of subjects, from history to town planning, from engineering to the aesthetics. *De re aedificatoria*, a large and expensive book, was not published until 1485, after which it became a major reference for architects. However, the book was written \"not only for craftsmen but also for anyone interested in the noble arts\", as Alberti put it. Originally published in Latin, the first Italian edition came out in 1546. and the standard Italian edition by Cosimo Bartoli was published in 1550. Pope Nicholas V, to whom Alberti dedicated the whole work, dreamed of rebuilding the city of Rome, but he managed to realize only a fragment of his visionary plans. Through his book, Alberti opened up his theories and ideals of the Florentine Renaissance to architects, scholars, and others.
Alberti wrote *I Libri della famiglia*---which discussed education, marriage, household management, and money---in the Tuscan dialect. The work was not printed until 1843. Like Erasmus decades later, Alberti stressed the need for a reform in education. He noted that \"the care of very young children is women\'s work, for nurses or the mother\", and that at the earliest possible age children should be taught the alphabet. With great hopes, he gave the work to his family to read, but in his autobiography Alberti confesses that \"he could hardly avoid feeling rage, moreover, when he saw some of his relatives openly ridiculing both the whole work and the author\'s futile enterprise along it\". *Momus*, written between 1443 and 1450, was a notable comedy about the Olympian deities. It has been considered as a roman à clef---Jupiter has been identified in some sources as Pope Eugenius IV and Pope Nicholas V. Alberti borrowed many of its characters from Lucian, one of his favorite Greek writers. The name of its hero, Momus, refers to the Greek word for blame or criticism. After being expelled from heaven, Momus, the god of mockery, is eventually castrated. Jupiter and the other deities come down to earth also, but they return to heaven after Jupiter breaks his nose in a great storm.
| 746 |
Leon Battista Alberti
| 1 |
18,031 |
# Leon Battista Alberti
## Architectural works {#architectural_works}
Alberti did not concern himself with engineering, and very few of his major projects were built. As a designer and a student of Vitruvius and of ancient Roman architecture, he studied column and lintel based architecture, from a visual rather than structural viewpoint. He correctly employed the Classical orders, unlike his contemporary, Brunelleschi, who used the Classical column and pilaster in a free interpretation. Alberti reflected on the social effects of architecture, and was attentive to the urban landscape. This is demonstrated by his inclusion, at the Rucellai Palace, of a continuous bench for seating at the level of the basement. Alberti anticipated the principle of street hierarchy, with wide main streets connected to secondary streets, and buildings of equal height.
In Rome he was employed by Pope Nicholas V for the restoration of the Roman aqueduct of Acqua Vergine, which debouched into a simple basin designed by Alberti, which was later replaced by the Baroque Trevi Fountain.
Some researchers suggested that the Villa Medici in Fiesole might have been designed by Alberti, rather than by Michelozzo. This hilltop residence commissioned by Giovanni de\' Medici, Cosimo il Vecchio\'s second son, with its view over the city, is sometimes considered the first example of a Renaissance villa: it reflects the writing by Alberti about country residential buildings as \"villa suburbana\". The building later inspired numerous other similar projects buildings from the end of the fifteenth century.
### Tempio Malatestiano, Rimini {#tempio_malatestiano_rimini}
The Tempio Malatestiano in Rimini (1447, 1453--60) is the rebuilding of a Gothic church. The façade, with its dynamic play of forms, was left incomplete.
### Façade of Palazzo Rucellai {#façade_of_palazzo_rucellai}
The design of the façade of the Palazzo Rucellai (1446--51) was one of several commissioned by the Rucellai family. The design overlays a grid of shallow pilasters and cornices in classical style onto rusticated masonry, and is surmounted by a heavy cornice. The inner courtyard has Corinthian columns. The palace introduced set the use of classical building elements in civic buildings in Florence, and became very influential. The work was executed by Bernardo Rossellino.
### Santa Maria Novella {#santa_maria_novella}
At Santa Maria Novella, Florence, between (1448--70) the upper façade was constructed to the design of Alberti. It was a challenging task, as the lower level already had three doorways and six Gothic niches containing tombs and employing the polychrome marble typical of Florentine churches, such as San Miniato al Monte and the Baptistery of Florence. The design also incorporates an ocular window that was already in place. Alberti introduced Classical features around the portico and spread the polychromy over the entire façade in a manner that includes Classical proportions and elements such as pilasters, cornices, and a pediment in the Classical style, ornamented with a sunburst in tesserae, rather than sculpture. The best known feature of this typically aisled church is the manner in which Alberti has solved the problem of visually bridging the different levels of the central nave and much lower side aisles. He employed two large scrolls, which were to become a standard feature of church façades in the later Renaissance, Baroque, and Classical Revival buildings.
### Pienza
thumb\|upright= 1.5\|Piazza Pio II in Pienza, looking toward the Palazzo Piccolomini Alberti is considered to have been the consultant for the design of the Piazza Pio II, Pienza. The village, previously called Corsignano, was redesigned beginning around 1459. It was the birthplace of Aeneas Silvius Piccolomini, Pope Pius II, in whose employ Alberti served. Pius II wanted to use the village as a retreat, but needed for it to reflect the dignity of his position.
The piazza is a trapezoid shape defined by four buildings, with a focus on Pienza Cathedral and passages on either side opening onto a landscape view. The principal residence, *Palazzo Piccolomini*, is on the western side. It has three stories, articulated by pilasters and entablature courses, with a twin-lighted cross window set within each bay. This structure is similar to Alberti\'s Palazzo Rucellai in Florence and other later palaces. Noteworthy is the internal court of the palazzo. The back of the palace, to the south, is defined by loggia on all three floors that overlook an enclosed Italian Renaissance garden with *Giardino all\'italiana* era modifications, and spectacular views into the distant landscape of the Val d\'Orcia and Pope Pius\'s beloved Mount Amiata beyond. Below this garden is a vaulted stable that had stalls for a hundred horses. The design, which radically transformed the center of the town, included a palace for the pope, a church, a town hall, and a building for the bishops who would accompany the Pope on his trips. Pienza is considered an early example of Renaissance urban planning.
### Sant\' Andrea, Mantua {#sant_andrea_mantua}
The Basilica of Sant\'Andrea, Mantua was begun in 1471, the year before Alberti\'s death. It was brought to completion and is his most significant work employing the triumphal arch motif, both for its façade and interior, and influencing many works that were to follow. Alberti perceived the role of architect as designer. Unlike Brunelleschi, he had no interest in the construction, leaving the practicalities to builders and the oversight to others.
| 863 |
Leon Battista Alberti
| 2 |
18,031 |
# Leon Battista Alberti
## Architectural works {#architectural_works}
### Other buildings {#other_buildings}
- San Sebastiano, Mantua, (begun 1458) the unfinished façade of which has promoted much speculation as to Alberti\'s intention
- Sepolcro Rucellai in San Pancrazio, 1467)
- The Tribune for Santissima Annunziata, Florence (1470, completed with alterations, 1477)
| 50 |
Leon Battista Alberti
| 3 |
18,031 |
# Leon Battista Alberti
## Painting
Giorgio Vasari, who argued that historical progress in art reached its peak in Michelangelo, emphasized Alberti\'s scholarly achievements, not his artistic talents: \"He spent his time finding out about the world and studying the proportions of antiquities; but above all, following his natural genius, he concentrated on writing rather than on applied work.\" In *On Painting*, Alberti uses the expression \"We Painters\", but as a painter, or sculptor, he was a dilettante. \"In painting Alberti achieved nothing of any great importance or beauty\", wrote Vasari. \"The very few paintings of his that are extant are far from perfect, but this is not surprising since he devoted himself more to his studies than to draughtsmanship.\" Jacob Burckhardt portrayed Alberti in *The Civilization of the Renaissance in Italy* as a truly universal genius. \"And Leonardo Da Vinci was to Alberti as the finisher to the beginner, as the master to the dilettante. Would only that Vasari\'s work were here supplemented by a description like that of Alberti! The colossal outlines of Leonardo\'s nature can never be more than dimly and distantly conceived.\"
Alberti is said to appear in Mantegna\'s great frescoes in the Camera degli Sposi, as the older man dressed in dark red clothes, who whispers in the ear of Ludovico Gonzaga, the ruler of Mantua. In Alberti\'s self-portrait, a large plaquette, he is clothed as a Roman. To the left of his profile is a winged eye. On the reverse side is the question, *Quid tum?* (what then), taken from Virgil\'s *Eclogues*: \"So what, if Amyntas is dark? (*quid tum si fuscus Amyntas?*) Violets are black, and hyacinths are black.\"
| 276 |
Leon Battista Alberti
| 4 |
18,031 |
# Leon Battista Alberti
## Contributions and cultural influence {#contributions_and_cultural_influence}
Alberti made a variety of contributions to several fields:
- Alberti was the creator of a theory called \"historia\". In his treatise *De pictura* (1435) he explains the theory of the accumulation of people, animals, and buildings, which create harmony amongst each other, and \"hold the eye of the learned and unlearned spectator for a long while with a certain sense of pleasure and emotion\". *De pictura* (\"On Painting\") contained the first scientific study of perspective. An Italian translation of *De pictura* (*Della pittura*) was published in 1436, one year after the original Latin version and addressed Filippo Brunelleschi in the preface. The Latin version had been dedicated to Alberti\'s humanist patron, Gianfrancesco Gonzaga of Mantua. He also wrote works on sculpture, *De statua*.
- Alberti used his artistic treatises to propound a new humanistic theory of art. He drew on his contacts with early Quattrocento artists such as Brunelleschi, Donatello, and Ghiberti to provide a practical handbook for the renaissance artist.
- Alberti wrote an influential work on architecture, *\[\[De re aedificatoria\]\]*, which by the sixteenth century had been translated into Italian (by Cosimo Bartoli), French, Spanish, and English. An English translation was by Giacomo Leoni in the early eighteenth century. Newer translations are now available.
- Whilst Alberti\'s treatises on painting and architecture have been hailed as the founding texts of a new form of art, breaking from the Gothic past, it is impossible to know the extent of their practical impact during his lifetime. His praise of the *Calumny of Apelles* led to several attempts to emulate it, including paintings by Botticelli and Signorelli. His stylistic ideals have been put into practice in the works of Mantegna, Piero della Francesca, and Fra Angelico. But how far Alberti was responsible for these innovations and how far he was simply articulating the trends of the artistic movement, with which his practical experience had made him familiar, is impossible to ascertain.
- He was so a skilled composer of Latin verse: a comedy he wrote when twenty years old, entitled *Philodoxius*, would later deceive the younger Aldus Manutius, who edited and published it as the genuine work of \'Lepidus Comicus\'.
- He has been credited with being the author, or alternatively, the designer of the woodcut illustrations, of the *Hypnerotomachia Poliphili*, a strange fantasy novel.
- Apart from his treatises on the arts, Alberti also wrote: *Philodoxus* (\"Lover of Glory\", 1424), *De commodis litterarum atque incommodis* (\"On the Advantages and Disadvantages of Literary Studies\", 1429), *Intercoenales* (\"Table Talk\", c. 1429), *Della famiglia* (\"On the Family\", begun 1432), *Vita S. Potiti* (\"Life of St. Potitus\", 1433), *De iure* (On Law, 1437), *Theogenius* (\"The Origin of the Gods\", c. 1440), *Profugorium ab aerumna* (\"Refuge from Mental Anguish\",), *Momus* (1450), and *De Iciarchia* (\"On the Prince\", 1468). These and other works were translated and printed in Venice by the humanist Cosimo Bartoli in 1586.
- Alberti was an accomplished cryptographer by the standard of his day and invented the first polyalphabetic cipher, which is now known as the Alberti cipher, and machine-assisted encryption using his Cipher Disk. The polyalphabetic cipher was, at least in principle (for it was not properly used for several hundred years) the most significant advance in cryptography since classical times. Cryptography historian David Kahn called him the \"Father of Western Cryptography\", pointing to three significant advances in the field that can be attributed to Alberti: \"the earliest Western exposition of cryptanalysis, the invention of polyalphabetic substitution, and the invention of enciphered code\".
- According to Alberti, in a short autobiography written c. 1438 in Latin and in the third person, (many but not all scholars consider this work to be an autobiography) he was capable of \"standing with his feet together, and springing over a man\'s head.\" The autobiography survives thanks to an eighteenth-century transcription by Antonio Muratori. Alberti also claimed that he \"excelled in all bodily exercises; could, with feet tied, leap over a standing man; could in the great cathedral, throw a coin far up to ring against the vault; amused himself by taming wild horses and climbing mountains\". Needless to say, many in the Renaissance promoted themselves in various ways and Alberti\'s eagerness to promote his skills should be understood, to some extent, within that framework.
- Alberti claimed in his \"autobiography\" to be an accomplished musician and organist, but there is no hard evidence to support this claim. In fact, musical posers were not uncommon in his day (see the lyrics to the song *Musica Son*, by Francesco Landini, for complaints to this effect.) He held the appointment of canon in the metropolitan church of Florence, and thus -- perhaps -- had the leisure to devote himself to this art, but this is only speculation. Vasari also agreed with this.
- He was interested in the drawing of maps and worked with the astronomer, astrologer, and cartographer Paolo Toscanelli.
- In the domain of Aesthetics Alberti is recognized for his definition of art as imitation of nature, exactly as a selection of its most beautiful parts: \"So let\'s take from nature what we are going to paint, and from nature we choose the most beautiful and worthy things\".
- Borsi states that Alberti\'s writings on architecture continue to influence modern and contemporary architecture stating: \"The organicism and nature-worship of Wright, the neat classicism of van der Mies, the regulatory outlines and anthropomorphic, harmonic, modular systems of Le Corbusier, and Kahn\'s revival of the \'antique\' are all elements that tempt one to trace Alberti\'s influence on modern architecture.\"
| 932 |
Leon Battista Alberti
| 5 |
18,031 |
# Leon Battista Alberti
## Works in print {#works_in_print}
- *De Pictura*, 1435. *On Painting*, in English, *De Pictura*, in Latin, ; *Della Pittura*, in Italian (1804 \[1434\]).
- *Momus,* Latin text and English translation, 2003 `{{ISBN|0-674-00754-9}}`{=mediawiki}
- *De re aedificatoria* (1452, Ten Books on Architecture). Alberti, Leon Battista. De re aedificatoria. On the art of building in ten books. (translated by Joseph Rykwert, Robert Tavernor and Neil Leach). Cambridge, Mass.: MIT Press, 1988. `{{ISBN|0-262-51060-X}}`{=mediawiki}. `{{ISBN|978-0-262-51060-8}}`{=mediawiki}. [Latin, French and Italian editions](http://architectura.cesr.univ-tours.fr/Traite/Auteur/Alberti.asp?param=en) `{{Webarchive|url=https://web.archive.org/web/20160305013659/http://architectura.cesr.univ-tours.fr/Traite/Auteur/Alberti.asp?param=en |date=2016-03-05 }}`{=mediawiki} and in [English translation](http://93.174.95.29/main/2337000/40d2623e3f6de2653824375370cf0915/%28Dover%20Architecture%29%20Leon%20Battista%20Alberti%20-%20The%20Ten%20Books%20of%20Architecture_%20The%201755%20Leoni%20Edition-Dover%20Puplications%20%281986%29.pdf)`{{Dead link|date=April 2023 |bot=InternetArchiveBot |fix-attempted=yes }}`{=mediawiki}.
- *De Cifris* A Treatise on Ciphers (1467), trans. A. Zaccagnini. Foreword by David Kahn, Galimberti, Torino 1997.
-
- \"Leon Battista Alberti. On Painting. A New Translation and Critical Edition\", Edited and Translated by Rocco Sinisgalli, Cambridge University Press, New York, May 2011, `{{ISBN|978-1-107-00062-9}}`{=mediawiki}, ([books.google.de](https://books.google.com/books?id=K3bCI-yhadMC) `{{Webarchive|url=https://web.archive.org/web/20230723080815/https://books.google.com/books?id=K3bCI-yhadMC |date=2023-07-23 }}`{=mediawiki})
- *I libri della famiglia*, Italian edition
- \"Dinner pieces\". A Translation of the *Intercenales* by David Marsh. Center for Medieval and Early Renaissance Studies, State University of New York, Binghamton 1987.
- \"Descriptio urbis Romae. Leon Battista Alberti\'s Delineation of the city of Rome\". Peter Hicks, Arizona Board of Regents for Arizona State university 2007.
```{=html}
<!-- -->
```
- (LA) Leon Battista Alberti, De re aedificatoria, Argentorati, excudebat M. Iacobus Cammerlander Moguntinus, 1541.
- (LA) Leon Battista Alberti, De re aedificatoria, Florentiae, accuratissime impressum opera magistri Nicolai Laurentii Alamani.
- Leon Battista Alberti, Opere volgari. 1, Firenze, Tipografia Galileiana, 1843.
- Leon Battista Alberti, Opere volgari. 2, Firenze, Tipografia Galileiana, 1844.
- Leon Battista Alberti, Opere volgari. 4, Firenze, Tipografia Galileiana, 1847.
- Leon Battista Alberti, Opere volgari. 5, Firenze, Tipografia Galileiana, 1849.
- Leon Battista Alberti, Opere, Florentiae, J. C. Sansoni, 1890.
- Leon Battista Alberti, Trattati d\'arte, Bari, Laterza, 1973.
- Leon Battista Alberti, Ippolito e Leonora, Firenze, Bartolomeo de\' Libri, prima del 1495.
- Leon Battista Alberti, Ecatonfilea, Stampata in Venesia, per Bernardino da Cremona, 1491.
- Leon Battista Alberti, Deifira, Padova, Lorenzo Canozio, 1471.
- Leon Battista Alberti, Teogenio, Milano, Leonard Pachel, circa 1492.
- Leon Battista Alberti, Libri della famiglia, Bari, G. Laterza, 1960.
- Leon Battista Alberti, Rime e trattati morali, Bari, Laterza, 1966.
- Franco Borsi, Leon Battista Alberti: Opera completa, Electa, Milano, 1973;
| 375 |
Leon Battista Alberti
| 6 |
18,031 |
# Leon Battista Alberti
## In popular culture {#in_popular_culture}
- Leon Battista Alberti is a major character in Roberto Rossellini\'s three-part television film *The Age of the Medici* (1973), with the third and final part, *Leon Battista Alberti: Humanism*, centering on him, his works (such as Santa Maria Novella), and his thought. He is played by Italian actor Virginio Gazzolo.
- Mentioned in the 1994 film *Renaissance Man* or ***Army Intelligence*** starring Danny DeVito.
- Mentioned in the 2004 book *The Rule of Four* by Ian Caldwell and Dustin Thomason
- Mentioned in the board game [Alma mater](https://boardgamegeek.com/boardgame/299960/alma-mater) in cards with special powers
| 103 |
Leon Battista Alberti
| 7 |
18,033 |
# Little Nemo
**Little Nemo** is a fictional character created by American cartoonist Winsor McCay. He originated in an early comic strip by McCay, *Dream of the Rarebit Fiend*, before receiving his own spin-off series, ***Little Nemo in Slumberland***. The full-page weekly strip depicted Nemo having fantastic dreams that were interrupted by his awakening in the final panel. The strip is considered McCay\'s masterpiece for its experiments with the form of the comics page, its use of color and perspective, its timing and pacing, the size and shape of its panels, and its architectural and other details.
*Little Nemo in Slumberland* ran in the *New York Herald* from October 15, 1905 until July 23, 1911. The strip was renamed ***In the Land of Wonderful Dreams*** when McCay brought it to William Randolph Hearst\'s *New York American*, where it ran from September 3, 1911 until July 26, 1914. When McCay returned to the *Herald* in 1924, he revived the strip, and it ran under its original title from August 3, 1924 until January 9, 1927, when McCay returned to Hearst.
## Concept
A weekly fantasy adventure, *Little Nemo in Slumberland* featured the young Nemo (\"No one\" in Latin) who dreamed himself into wondrous predicaments from which he awoke in bed in the last panel.
The first episode begins with a command from King Morpheus of Slumberland to a minion to collect Nemo. Nemo was to be the playmate of Slumberland\'s Princess, but it took months of adventures before Nemo finally arrived. A green, cigar-chewing clown named Flip was determined to disturb Nemo\'s sleep with a top hat emblazoned with the words \"Wake Up\". Nemo and Flip eventually become companions and are joined by an African Imp whom Flip finds in the Candy Islands. The group travels far and wide, from shanty towns to Mars, to Jack Frost\'s palace, to the bizarre architecture and distorted funhouse-mirror illusions of Befuddle Hall.
The strip shows McCay\'s understanding of dream psychology, particularly of dream fears---falling, drowning, impalement. This dream world has its own moral code, perhaps difficult to understand. Breaking it has terrible consequences as when Nemo ignores instructions not to touch Queen Crystalette who inhabits a cave of glass. Overcome with his infatuation, he causes her and her followers to shatter and awakens with \"the groans of the dying guardsmen still ringing in his ears\".
Although the strip began October 15, 1905, with King Morpheus, ruler of Slumberland, making his first attempt to bring Little Nemo to his realm. Nemo did not get into Slumberland until March 4, 1906. Due to Flip\'s interfering, Nemo did not get to see the Princess until July 8. His dream quest is always interrupted, either by his falling out of bed, Nemo suddenly waking up, or by his parents forcing him to wake up.
On July 12, 1908, McCay made a major change of direction: Flip visits Nemo and tells him that he has had his uncle destroy Slumberland (it had been dissolved before, into day, but this time it appeared to be permanent). After this, Nemo\'s dreams take place in his home town, though Flip---and a curious-looking boy named the Professor---accompany him. These adventures range from the down-to-earth to Rarebit-fiend type fantasy; one very commonplace dream had the Professor pelting people with snowballs. The famous \"walking bed\" story was in this period. Slumberland continued to make sporadic appearances until it returned for good on December 26, 1909.
Story-arcs included Befuddle Hall, a voyage to Mars (with a well-realized Martian civilization), and a trip around the world (including a tour of New York City).
| 596 |
Little Nemo
| 0 |
18,033 |
# Little Nemo
## Style
McCay experimented with the form of the comics page, its timing and pacing, the size and shape of its panels, perspective, and architectural and other detail. From the second installment, McCay had the panel sizes and layouts conform to the action in the strip: as a forest of mushrooms grew, so did the panels, and the panels shrank as the mushrooms collapsed on Nemo. In an early Thanksgiving episode, the focal action of a giant turkey gobbling Nemo\'s house receives an enormous circular panel in the center of the page. McCay also accommodated a sense of proportion with panel size and shape, showing elephants and dragons at a scale the reader could feel in proportion to the regular characters. McCay controlled narrative pacing through variation or repetition, as with equally-sized panels whose repeated layouts and minute differences in movement conveyed a feeling of buildup to some climactic action.
In his familiar Art Nouveau-influenced style, McCay outlined his characters in heavy blacks. Slumberland\'s ornate architecture was reminiscent of the architecture designed by McKim, Mead & White for the 1893 World\'s Columbian Exposition in Chicago, as well as Luna Park and Dreamland in Coney Island, and the Parisian Luxembourg Palace.
s ornate architecture was inspired by McCay\'s memories of the 1893 World\'s Columbian Exposition in Chicago, and his experience working at Coney Island (Luna Park pictured). \|align = center
\|image1 = Little Nemo 1905-12-17 panel nine.jpg \|width1 = 197 \|alt1 = A comic strip panel. A character in a frilled red suit points a boy at a city with ostentatious architecture.
\|image2 = The Dragon\'s Gorge, Luna Park, Coney Island, NY.jpg \|width2 = 303 \|alt2 = A colored photograph of an ornately-decorated amusement park. }}
McCay made imaginative use of color, sometimes changing the backgrounds\' or characters\' colors from panel to panel in a psychedelic imitation of a dream experience. The colors were enhanced by the careful attention and advanced Ben Day lithographic process employed by the *Herald*{{\'}}s printing staff. McCay annotated the *Nemo* pages for the printers with the precise color schemes he wanted.
For the first five months the pages were accompanied with captions beneath them, and at first the captions were numbered. In contrast to the high level of skill in the artwork, the dialogue in the speech balloons is crude, sometimes approaching illegibility, and \"disfigur`{{interp|ing McCay's}}`{=mediawiki} otherwise flawless work\", according to critic R. C. Harvey. The level of effort and skill apparent in the title lettering highlights what seems to be the little regard for the dialogue balloons, their content, and their placement in the visual composition.
McCay used ethnic stereotypes prominently in *Little Nemo*, as in the ill-tempered Irishman Flip, and the nearly-mute African Impie.
| 453 |
Little Nemo
| 1 |
18,033 |
# Little Nemo
## Background
Winsor McCay (c. 1867--71 -- 1934) had worked prolifically as a commercial artist and cartoonist in carnivals and dime museums before he began working for newspapers and magazines in 1898. In 1903, he joined the staff of the *New York Herald* family of newspapers, where he had success with comic strips such as *Little Sammy Sneeze* (1904--06). and *Dream of the Rarebit Fiend* (1904--11)
In 1905, McCay got \"an idea from the *Rarebit Fiend* to please the little folk\". That October, the full-page Sunday strip *Little Nemo in Slumberland* debuted in the *Herald*. Considered McCay\'s masterpiece, its child protagonist, whose appearance was based on McCay\'s son Robert, had fabulous dreams that would be interrupted with his awakening in the last panel. McCay experimented with the form of the comics page, its timing and pacing, the size and shape of its panels, perspective, architectural and other detail.
## Publication history {#publication_history}
*Little Nemo in Slumberland* debuted on the last page of the Sunday comics section of *The New York Herald* newspaper, on October 15, 1905. The full-page, color comic strip ran until July 23, 1911. In spring 1911, McCay moved to William Randolph Hearst\'s *New York American* and took *Little Nemo*{{\'}}s characters with him. The *Herald* held the strip\'s copyright, but McCay won a lawsuit that allowed him to continue using the characters. In the *American*, the strip ran under the title *In the Land of Wonderful Dreams*. The *Herald* was unsuccessful in finding another cartoonist to continue the original strip.
McCay left Hearst in May 1924 and returned to the *Herald Tribune*. He began *Little Nemo in Slumberland* afresh on August 3 of that year. The new strip displayed the virtuoso technique of the old, but the panels were laid out in an unvarying grid. Nemo took a more passive role in the stories, and there was no continuity. The strip came to an end in January 1927, as it was not popular with readers. Hearst executives had been trying to convince McCay to return to the *American*, and they succeeded in 1927. Due to the lack of the 1920s Nemo\'s success, the *Herald Tribune* signed over all copyrights to the strip to McCay for one dollar.
In 1937, McCay\'s son Robert attempted to carry on his father\'s legacy by reviving *Little Nemo*. Comic book packager Harry \"A\" Chesler\'s syndicate announced a Sunday and daily *Nemo* strip, credited to \"Winsor McCay, Jr.\" Robert also drew a comic-book version for Chesler called *Nemo in Adventureland* featuring grown-up versions of Nemo and the Princess. Neither project lasted long. Production continued on both after the syndicate was closed in 1938, being utilized in various comic books including Cocomalt Comics and Blue Ribbon, published by MLJ Publications (later Archie Publications). Chesler closed his shop (the first of several times) around 1940. Street & Smith ran Little Nemo in 1942 in *Shadow Comics*. In 1945, McCay was again with Chesler's shop, producing Little Nemo in Adventureland for Red Seal and Punch Comics until 1947, when the shop closed down for the final time.
In 1947, Robert and fabric salesman Irving Mendelsohn organized the McCay Feature Syndicate, Inc. to revive the original *Nemo* strip from McCay\'s original art, modified to fit the size of modern newspaper pages. This revival also did not last. The McCay-Richardson Syndicate distributed this version from approximately March to December 1947.
In 1966, cartoonist Woody Gelman discovered the original artwork for many *Little Nemo* strips at a cartoon studio where McCay\'s son Bob had worked. In 1973, Gelman published a collection of *Little Nemo* strips in Italy. His collection of McCay originals is preserved at the Billy Ireland Cartoon Library & Museum at Ohio State University.
In 2005, collector Peter Maresca self-published a 21 xx volume of *Nemo* Sundays as *Little Nemo in Slumberland: So Many Splendid Sundays!* via his Sunday Press Books. The volume was large enough to reproduce the pages at their original size, as they appeared in newspapers. Restoration work took Maresca between five and twenty hours per page. A second volume, *Little Nemo in Slumberland: Many More Splendid Sundays!*, appeared in 2008.
| 689 |
Little Nemo
| 2 |
18,033 |
# Little Nemo
## Adaptations
### Theatre
As early as 1905, several abortive attempts were made to put *Little Nemo* on stage. In summer 1907, Marcus Klaw and A. L. Erlanger announced they would put on an extravagant *Little Nemo* show for an unprecedented \$100,000, with a score by Victor Herbert and lyrics by Harry B. Smith. It starred Gabriel Weigel, an actor with dwarfism, as Nemo, Joseph Cawthorn as Dr. Pill, and Billy B. Van as Flip. Reviews were positive, and it played to sold-out houses in New York. It went on the road for two seasons. McCay brought his vaudeville act to each city where *Little Nemo* played. When a Keith circuit refused to let McCay perform in Boston without a new act, McCay switched to the William Morris circuit, with a \$100-a-week raise. In several cities, McCay brought his son, who sat on a small throne dressed as Nemo as publicity.
As part of an improvised story, Cawthorn introduced a mythical creature he called a \"Whiffenpoof\". The word stuck with the public, and became the name of a hit song and a singing group. One reviewer of the 1908 operetta gave a paragraph of praise to the comic hunting tales presented in a scene in which three hunters are trying to outdo each other with hunting stories about the \"montimanjack\", the \"peninsula\", and the \"whiffenpoof\". He calls it \"one of the funniest yarns ever spun\" and compares it favorably to Lewis Carroll\'s The Hunting of the Snark. One source indicates that the dialogue in fact began as an ad lib by actor Joseph Cawthorn, covering for some kind of backstage problem during a performance. The whiffenpoof is also referred in one of the Little Nemo comic strips published in 1909 (April 11). After being held down by nine policemen during a hysteria crisis, Nemo\'s father tells the doctor: \"Just keep those whiffenpoofs away. Will you?\". The strip for September 26 starts with a hunt for whiffenpoofs but instead the hunters find a \"montemaniac\" and a \"peninsula\".
Despite the show\'s success, it failed to make back its investment due to its enormous expenses, and came to an end in December 1910. In mid-2012 Toronto-based theatre company Frolick performed an adaptation of the strip into *Adventures in Slumberland*, a multimedia show featuring puppets large and small and a score that included as a refrain \"Wake Up Little Nemo\", set to the tune of The Everly Brothers\' 1957 hit \"Wake Up Little Susie\". Talespinner Children\'s Theatre in Cleveland, OH produced a scaled-down, \"colorful and high-energy 45-minute\" adaptation in 2013, *Adventures In Slumberland* by David Hansen.
In March 2017, a short, one-act adaptation of the \"Little Nemo\" adventures was staged at Fordham University in New York City. The play, simply entitled *Little Nemo in Slumberland*, was written by Aladdin Lee Grant Rutledge Collar, and directed by student Peter McNally. The six person cast, as well as creative team, consisted of students and alums at the university.
| 495 |
Little Nemo
| 3 |
18,033 |
# Little Nemo
## Adaptations
### Film
McCay played an important role in the early history of animation. In 1911, he completed his first film, *Winsor McCay, the Famous Cartoonist of the N.Y. Herald and His Moving Comics* (also known as *Little Nemo*), first in theatres and then as part of his vaudeville act. McCay made the 4,000 rice-paper drawings for the animated portion of the film. The animated portion took up about four minutes of the film\'s total length. Photography was done at the Vitagraph Studios under the supervision of animation pioneer James Stuart Blackton. During the live-action portion of the film, McCay bets his colleagues he can make his drawings move. He wins the bet by animating his *Little Nemo* characters, who shapeshift and transform.
In 1984, Arnaud Sélignac produced and directed a film titled *Nemo*, a.k.a. *Dream One*, starring Jason Connery, Harvey Keitel, and Carole Bouquet. It involves a little boy called Nemo, who wears pajamas and travels to a fantasy world, but otherwise the connection to McCay\'s strip is a loose one. The fantasy world is a dark and dismal beach, and Nemo encounters characters from other works of fiction rather than those from the original strip. Instead of Flip or the Princess, Nemo meets Zorro, Alice, and Jules Verne\'s Nautilus (which was led by Captain Nemo).
A joint American-Japanese feature-length film *Little Nemo: Adventures in Slumberland* was released in Japan in 1989 and in the United States in August 1992 from Hemdale Film Corporation, with contributions by Ray Bradbury, Chris Columbus, and Moebius, and music by the Sherman Brothers. The story tells of a quest by Nemo and friends to rescue King Morpheus from the Nightmare King. The Princess is named Princess Camille, Flip has a bird companion named Flap, and Nemo has a pet flying squirrel named Icarus. It received mixed reviews from critics, where it earned \$11.4 million on a \$35 million budget and was a box-office bomb, but it sold well on home video and has since developed into a cult film.
A live-action film adaptation, *Slumberland*, directed by Francis Lawrence, was released in 2022. It features a gender-swapped version of the title character played by Marlow Barkley. Jason Momoa stars as a radically altered version of Flip, who is described as a \"nine-foot tall creature that is half-man, half-beast, has shaggy fur and long curved tusks\". The plot centers on Nemo and Flip traveling to Slumberland in search of the former\'s father.
### Opera
The Sarasota Opera commissioned composer Daron Hagen and librettist J. D. McClatchy to create an opera based on *Little Nemo*. Two casts of children alternated performances when it debuted in November 2012. The dreamlike nonlinear story told of Nemo, the Princess, and their comrades trying to prevent the Emperor of Sol and the Guardian of Dawn from bringing daylight to Slumberland. Special effects and shifting backgrounds were produced with projections onto a scaffolding of boxes. The work was first performed on November 10 and 11, by members of the Sarasota Opera, Sarasota Youth Opera, Sarasota Prep Chorus, The Sailor Circus and students from Booker High school.
### Other media {#other_media}
In 1990, Capcom produced a video game for the NES, titled *Little Nemo: The Dream Master* (known as *Pajama Hero Nemo* in Japan), a licensed game based on the 1989 film. The film would not see a US release until 1992, two years after the game\'s Japanese release, so the game is often thought to be a standalone adaptation of *Little Nemo*, not related to the film. An arcade game called simply *Nemo* was also released in 1990. In 2021, a new game, titled *Little Nemo and the Nightmare Fiends* based on the original comic strip was launched on Kickstarter. It is developed by Chris Totten of Pie For Breakfast Studios and Benjamin Cole of PXLPLZ. In 2022, a new game, titled *Little Nemo and the Guardians of Slumberland* based on the original comic strip was launched on Kickstarter. It is developed by Dave Mauro of DIE SOFT.
Throughout the years, various pieces of Little Nemo merchandise have been produced. In 1941, Rand, McNally & Co. published a Little Nemo children\'s storybook. *Little Nemo in Slumberland in 3-D* was released by Blackthorne Publishing in 1987; this reprinted Little Nemo issues with 3-D glasses. A set of 30 Little Nemo postcards was available through Stewart Tabori & Chang in 1996. In 1993, as promotion for the 1989 animated film, Hemdale produced a Collector\'s Set which includes a VHS movie, illustrated storybook, and cassette soundtrack. In 2001, Dark Horse Comics released a Little Nemo statue and tin lunchbox.
| 769 |
Little Nemo
| 4 |
18,033 |
# Little Nemo
## Cultural influence {#cultural_influence}
Little Nemo itself is influenced by children stories in general, and some French comic pages in particular. Since its publishing, *Little Nemo* has had an influence on other artists, including Peter Newell (*The Naps of Polly Sleepyhead*), Frank King (*Bobby Make-Believe*), Clare Briggs (*Danny Dreamer*) or George McManus (*Nibsy the Newsboy in Funny Fairyland*). Through the Paris edition of the New York Herald, his influence reached France and other European countries.
In children\'s literature, Maurice Sendak said that this strip inspired his book *In the Night Kitchen*, and William Joyce included several elements from Little Nemo in his children\'s book *Santa Calls*, including appearances by Flip and the walking bed. Another tribute to Little Nemo is the comic, then made into a short film, *Little Remo in Pinchmeland*, by Ellen Duthie and Daniela Martagón.
The character and themes from the comic strip *Little Nemo* were used in a song \"Scenes from a Night\'s Dream\" written by Tony Banks and Phil Collins of the progressive rock group Genesis on their 1978 recording, *\...And Then There Were Three\...*.
A progressive rock group from Germany named Scara Brae also recorded a musical impression of the comic on their rare self-titled disc from 1981 (the track was actually recorded 2 years earlier). Their concept piece was revived on the second album by the Greek band Anger Department, titled *The Strange Dreams of a Rarebit Fiend*, again after a McCay-comic. Their *Little Nemo* was chosen for a theatre play, which was suggested for the cultural program for the Olympic Games in 2004.
In 1984, Italian comic artist Vittorio Giardino started producing a number of stories under the title *Little Ego*, a parodic adaptation of *Little Nemo*, in the shape of adult-oriented erotic comics. Brian Bolland\'s early comic strip *Little Nympho in Slumberland* employed a similar technique.
The bar in *A Nightmare on Elm Street 3: Dream Warriors* is called \'Little Nemo\'s\'.
The strip influenced Alan Moore, in *Miracleman* #4, when the Miracleman family end up in a palace called \"Sleepy Town\", which has imagery similar to Little Nemo\'s. In Moore (and J.H. Williams III)\'s *Promethea*, a more direct pastiche -- \"Little Margie in Misty Magic Land\" -- showed Moore\'s inspiration and debt to McCay\'s landmark 1905 strip. Little Nemo makes a visual cameo in Volume 4, issue #4 of Moore and Kevin O\'Neill\'s *League of Extraordinary Gentleman*, during the Shakespearean Theatre scene that includes many other cameos.
The Sandman comics and graphic novel series occasionally references *Little Nemo* as well. Examples include *The Sandman: The Doll\'s House*, where an abused child escapes into dreams styled after McCay\'s comics and using a similar \"wake-up\" mechanism, and *The Sandman: Book of Dreams* (pub. 1996), which features George Alec Effinger\'s short \"Seven Nights in Slumberland\" (where Nemo interacts with Neil Gaiman\'s characters The Endless).
In 1989, teen comic book Power Pack ran an issue (#47) which paid direct homage to one of McCay\'s Nemo storylines, featuring a castle that was drawn sideways and Katie Power re-enacting a classic Nemo panel with a sideways-drawn hallway that served as a bottomless pit with the line \"Don\'t fall in, y\'hear?\"
The video of the 1989 song for \"Runnin\' Down a Dream\" by Tom Petty is directly inspired by *Little Nemo in Slumberland* by Winsor McCay, which features a drawing style reminiscent of McCay\'s and showing Petty and a character who resembles Flip travelling through Slumberland.
The band Queensrÿche paid homage to Little Nemo in their 1990 video Silent Lucidity.
In 1994--1995, French artist Moebius wrote the story to a sequel comic series, *Little Nemo*, drawn by Bruno Marchand in two albums. In 2000--2002, Marchand continued the story with two additional albums.
In 2006, electronic artist Daedelus used Little Nemo artwork for his album *Denies the Day\'s Demise*.
The comic strip *Cul de Sac* includes a strip-within-the-strip, *Little Neuro*, a parody of Little Nemo. Neuro is a little boy who hardly ever leaves his bed.
In 2009, the Pittsburgh ToonSeum established its NEMO Award, given to notable individuals \"for excellence in the cartoon arts\". Recipients to date include veteran comic-book artist, Ron Frenz, editorial and comic-strip artist, Dick Locher, cartoonist and comics historian, Trina Robbins, and comics artist, editorial cartoonist and artists\' rights advocate Jerry Robinson.
On October 15, 2012, celebrating the 107th anniversary of the first *Little Nemo* story, Google displayed an interactive animated \"Google Doodle\" called \"Little Nemo in Google-land\" on its homepage. The doodle showed a typical Little Nemo adventure through a series of panels, each featuring a letter from the word \"Google\". The doodle also ends in the same way as the comic strips, with Nemo falling from his bed.
Eric Shanower and Gabriel Rodriguez revived the characters in 2014 in an IDW comic book series entitled *Little Nemo: Return to Slumberland*. That same year, Locust Moon Press released a new anthology and Taschen published the complete series (1905--1926).
A comic strip *Mutts* has one of the strip\'s recurring characters, a naughty squirrel, \"bonking\" Nemo with an acorn, and wishing him \"sweet dreams\".
## Legacy
Comics historian R. C. Harvey has called McCay \"the first original genius of the comic strip medium\". Harvey claims that McCay\'s contemporaries lacked the skill to continue with his innovations, so that they were left for future generations to rediscover and build upon. Cartoonist Robert Crumb called McCay a \"genius\" and one of his favorite cartoonists. Art Spiegelman\'s *In the Shadow of No Towers* (2004) appropriated some of McCay\'s imagery, and included a page of *Little Nemo* in its appendix. Federico Fellini read *Little Nemo* in the children\'s magazine *Il corriere dei piccoli*, and the strip was a \"powerful influence\" on the filmmaker, according to Fellini biographer Peter Bondanella.
McCay\'s original artwork has been poorly preserved. McCay insisted on having his originals returned to him, and a large collection survived him, but much of it was destroyed in a fire in the late 1930s. His wife was unsure how to handle the surviving pieces, so his son took on the responsibility and moved the collection into his own house. The family sold off some of the artwork when they were in need of cash. Responsibility for it passed to Mendelsohn, then later to daughter Marion. By the early twenty-first century, most of McCay\'s surviving artwork remained in family hands
| 1,053 |
Little Nemo
| 5 |
18,041 |
# Liber Memorialis
The ***Liber Memorialis*** is an ancient book in Latin featuring an extremely concise summary---a kind of index---of universal history from earliest times to the reign of Trajan. It was written by Lucius Ampelius, who was possibly a tutor or schoolmaster.
## Description
The book is dedicated to a Macrinus, who may have been the emperor who reigned 217--218, but that name was not uncommon, and it seems more likely he was simply a young man with a thirst for universal knowledge, which the book was compiled to satisfy.
The book\'s object and scope are indicated in its dedication: `{{Blockquote|Since you desire to know everything, I have written this 'book of notes,' that you may learn of what the universe and its elements consist, what the world contains, and what the human race has done.}}`{=mediawiki}
The *Liber Memorialis* seems to have been intended as a textbook to be learned by heart. This little work, in fifty chapters, gives a sketch of cosmography, geography, mythology (Chapters I-X), and history (Chapters X to end). The historical portion, dealing mainly with the republican period, is untrustworthy and the text in many places corrupt; the earlier chapters are more valuable, and contain some interesting information.
Chapter VIII (*Miracula Mundi*) contains the following, the only reference by an ancient writer to the famous sculptures of the Pergamon Altar, which were discovered in 1871, excavated in 1878, and are now in Berlin:
## Date
Nothing is known of the date at which the work was written; the times of Trajan, Hadrian, Antoninus Pius, the beginning of the 3rd century have all been suggested. However, in Chapter V De Orbe Terrarum (The World), Ampelius refers to the \"Tigris and Euphrates in Parthia,\" which suggests that Ampelius wrote before the Sassanians overthrew the Parthians in 224.
## Editions
The first edition of the *Liber Memorialis* was published in 1638 by Claudius Salmasius (Saumaise) from the Dijon manuscript, now lost, together with the *Epitome* of Florus. An 1873 edition by Wölfflin was based on Salmasius\'s copy of the lost codex. The more recent editions are
- Erwin Assmann\'s Teubner edition of 1935
- Nicola Terzaghi\'s edition, published by Chiantore in Turin ca
| 365 |
Liber Memorialis
| 0 |
18,043 |
# Lancelot Andrewes
**Lancelot Andrewes** (1555`{{snd}}`{=mediawiki}25 September 1626) was an English bishop and scholar, who held high positions in the Church of England during the reigns of Elizabeth I and James I. During the latter\'s reign, Andrewes served successively as Bishop of Chichester, of Ely, and of Winchester and oversaw the translation of the King James Version of the Bible (or Authorized Version). In the Church of England he is commemorated on 25 September with a lesser festival.
## Early life, education and ordination {#early_life_education_and_ordination}
Andrewes was born in 1555 near All Hallows, Barking, by the Tower of London, of an ancient Suffolk family later domiciled at Chichester Hall, at Rawreth in Essex; his father, Thomas, was master of Trinity House. Andrewes attended the Cooper\'s free school in Ratcliff in the parish of Stepney and then the Merchant Taylors\' School under Richard Mulcaster. In 1571 he entered Pembroke Hall, Cambridge, and graduated with a Bachelor of Arts degree, proceeding to a Master of Arts degree in 1578. His academic reputation spread so quickly that on the foundation in 1571 of Jesus College, Oxford he was named in the charter as one of the founding scholars \"without his privity\" (Isaacson, 1650); his connection with the college seems to have been purely notional, however. In 1576 he was elected fellow of Pembroke College; on 11 June 1580 he was ordained a priest by William Chaderton, Bishop of Chester, and in 1581 was incorporated Master of Arts (MA) at Oxford. As catechist at his college he read lectures on the Decalogue (published in 1630), which aroused great interest.
Once a year he would spend a month with his parents and, during this vacation, he would find a master from whom he would learn a language of which he had no previous knowledge. In this way, after a few years, he acquired most of the modern languages of Europe.
Andrewes was the elder brother of the scholar and cleric Roger Andrewes, who also served as a translator for the King James Version of the Bible.
| 341 |
Lancelot Andrewes
| 0 |
18,043 |
# Lancelot Andrewes
## During Elizabeth\'s reign {#during_elizabeths_reign}
In 1588, following a period as chaplain to Henry Hastings, 3rd Earl of Huntingdon, Lord President of the Council in the North, he became vicar of St Giles, Cripplegate, in the City of London, where he delivered striking sermons on the temptation in the wilderness and the Lord\'s Prayer. In a sermon (during Easter week) on 10 April 1588, he stoutly vindicated the Reformed character of the Church of England against the claims of Roman Catholicism and adduced John Calvin as a new writer, with lavish praise and affection.
Yet, Andrewes was certainly no Calvinist. It has been said that he developed a proto-Arminian soteriology while at Cambridge and that he maintained this non-Calvinist theology throughout his life. He made it a point to refuse to repeat the common Calvinist slogans of his time. During the first half of the seventeenth century, he claimed that Calvinism was incompatible with civil government, preaching, and ministry. Throughout his sermons, he unashamedly criticized Calvinist doctrine and practice. He has been referred to as an avant-garde conformist, which is understood as an implicitly proto-Arminian precursor to Laudianism and explicit English-Arminianism. He outright decried the translation and Calvinistic notes in the Geneva translation of the Bible. He taught that God condemned Cain for his own freely chosen sin and he denied that God unconditionally predestined any to salvation or that he unconditionally condemned anyone. He argued for soteriological synergism, using Lot\'s wife as a picture that one\'s salvation is not secure post-conversion apart from an ongoing and freely chosen cooperation with God\'s saving grace. John Overall and Andrewes were more sympathetic to the Remonstrants than the Calvinists at the time of the Synod of Dort. Andrewes, out of fear, denied his support for the Remonstrants when letters sent to him from that party were intercepted. He was not on friendly terms with the delegates to the synod and he made it clear that he did not support the results. He and the Remonstrants attempted to use the ecclesiological similarities between the Contra-Remonstrants and the Puritans to persuade James I not to involve himself in the Synod of Dort or to support the Remonstrant cause if he did.
Through the influence of Francis Walsingham, Andrewes was appointed prebendary of St Pancras in St Paul\'s Cathedral, in 1589, and subsequently became master of his own college of Pembroke, as well as a chaplain to John Whitgift, Archbishop of Canterbury. From 1589 to 1609 he was prebendary of Southwell. On 4 March 1590, as a chaplain of Elizabeth I, he preached before her an outspoken sermon and, in October that year, gave his introductory lecture at St Paul\'s, undertaking to comment on the first four chapters of the Book of Genesis. These were later compiled as *The Orphan Lectures* (1657).
Andrewes liked to move among the people, yet found time to join a society of antiquaries, of which Walter Raleigh, Philip Sidney, Burghley, Arundel, the Herberts, Saville, John Stow and William Camden were members. Elizabeth I had not advanced him further on account of his opposition to the alienation of ecclesiastical revenues. In 1598 he declined the bishoprics of Ely and Salisbury, because of the conditions attached. On 23 November 1600, he preached at Whitehall a controversial sermon on justification. In July 1601 he was appointed Dean of Westminster and gave much attention to the school there.
When plague struck in 1603 he retreated to Chiswick to teach the boys of Westminster School, where he preached a plague sermon on 21 August arguing in favour of leaving London under such circumstances. His argumentation rested on the Old Testament\'s commands to avoid exposing oneself to contagion, to avoid contact with lepers, etc. Andrewes claimed that the plague was caused by \"inventions\" like \"new meats in diet\" and \"new fashions in apparel\" that had roused the wrath of God. He condemns changes in Christian tradition that \"our fathers never knew of\".
| 659 |
Lancelot Andrewes
| 1 |
18,043 |
# Lancelot Andrewes
## During the reign of James I {#during_the_reign_of_james_i}
On the accession of James I, Andrewes rose into great favour. He assisted at the coronation of James I and Anne, and in 1604 took part in the Hampton Court Conference.
Andrewes\' name is the first on the list of divines appointed to compile the *Authorized Version* of the Bible, which was commissioned in 1604 and published in 1611. He headed the \"First Westminster Company\" which took charge of the first books of the Old Testament (Genesis to 2 Kings). He acted, furthermore, as a sort of general editor for the project as well.
On 31 October 1605 his election as Bishop of Chichester was confirmed, he was consecrated a bishop on 3 November, installed at Chichester Cathedral on 18 November and made Lord High Almoner (until 1619). Following the discovery of the Gunpowder Plot, Andrewes was asked to prepare a sermon to be presented to the king in 1606 (Sermons Preached upon the V of November, in Lancelot Andrewes, XCVI Sermons, 3rd. Edition (London,1635) pp. 889, 890, 900--1008 ). In this sermon Andrewes justified the need to commemorate the deliverance and defined the nature of celebrations. This sermon became the foundation of celebrations which continue 400 years later. In 1609 he published *Tortura Torti*, a learned work which grew out of the Gunpowder Plot controversy and was written in answer to Bellarmine\'s *Matthaeus Tortus*, which attacked James I\'s book on the oath of allegiance. After moving to Ely (his election to that see was confirmed on 22 September), he again controverted Bellarmine in the *Responsio ad Apologiam*.
In 1617 he accompanied James I to Scotland with a view to persuading the Scots that Episcopacy was preferable to Presbyterianism. He was made dean of the Chapel Royal and translated (by the confirmation of his election to that see in February 1619) to Winchester, a diocese that he administered with great success.
Following his death in 1626 in Winchester Palace, the bishop\'s residence in Southwark, he was mourned alike by leaders in church and state, and buried in St Saviour\'s Church (now Southwark Cathedral, then in the Diocese of Winchester). He was buried in a small chapel at the east end. After the destruction of the Bishop\'s Chapel in 1830, his tomb was moved to a new position, immediately behind the high altar. His monument is by Gerard Janssen; the canopy was restored by Arthur Blomfield with colouring by Ninian Comper.
| 411 |
Lancelot Andrewes
| 2 |
18,043 |
# Lancelot Andrewes
## Legacy
Two generations later, Richard Crashaw caught up the universal sentiment, when in his lines \"Upon Bishop Andrewes\' Picture before his Sermons\" he exclaims:
:
: This reverend shadow cast that setting sun,
: Whose glorious course through our horizon run,
: Left the dim face of this dull hemisphere,
: All one great eye, all drown\'d in one great teare.
Andrewes was a friend of Hugo Grotius, and one of the foremost contemporary scholars, but is chiefly remembered for his style of preaching. As a churchman he was typically Anglican, equally removed from the Puritan and the Roman positions. A good summary of his position is found in his *First Answer to Cardinal Perron*, who had challenged James I\'s use of the title \"Catholic\". His position in regard to the Eucharist is naturally more mature than that of the first reformers.
> As to the Real Presence we are agreed; our controversy is as to the mode of it. As to the mode we define nothing rashly, nor anxiously investigate, any more than in the Incarnation of Christ we ask how the human is united to the divine nature in One Person. There is a real change in the elements---we allow *ut panis iam consecratus non-sit panis quem natura formavit; sed, quem benedictio consecravit, et consecrando etiam immutavit* \[i.e., \"that the bread once consecrated is not the bread which nature has formed, but that which the blessing has consecrated and, by consecrating it, has also changed\"\]. (*Responsio*, p. 263).
> Adoration is permitted, and the use of the terms \"sacrifice\" and \"altar\" maintained as being consonant with scripture and antiquity. Christ is \"a sacrifice---so, to be slain; a propitiatory sacrifice---so, to be eaten.\" (*Sermons*, vol. ii. p. 296).
> By the same rules that the Passover was, by the same may ours be termed a sacrifice. In rigour of speech, neither of them; for to speak after the exact manner of divinity, there is but one only sacrifice, *veri nominis*, that is Christ\'s death. And that sacrifice but once actually performed at His death, but ever before represented in figure, from the beginning; and ever since repeated in memory to the world\'s end. That only absolute, all else relative to it, representative of it, operative by it \... Hence it is that what names theirs carried, ours do the like, and the Fathers make no scruple at it---no more need we.(*Sermons,* vol. ii. p. 300).
Andrewes preached regularly and submissively before James I and his court on the anniversaries of the Gowrie Conspiracy and the Gunpowder Plot. These sermons were used to promulgate the doctrine of the Divine Right of Kings.
His *Life* was written by Alexander Whyte (Edinburgh, 1896), M. Wood (New York, 1898), and Robert Lawrence Ottley (Boston, 1894). His services to his church have been summed up thus: (1) he has a keen sense of the proportion of the faith and maintains a clear distinction between what is fundamental, needing ecclesiastical commands, and subsidiary, needing only ecclesiastical guidance and suggestion; (2) as distinguished from the earlier protesting standpoint, e.g. of the Thirty-nine Articles, he emphasised a positive and constructive statement of the Anglican position.
His best-known work is the *Preces Privatae* or *Private Prayers*, edited by Alexander Whyte (1896), which has widespread appeal and has remained in print since renewed interest in Andrewes developed in the 19th century. The *Preces Privatae* were first published by R. Drake in 1648; an improved edition by F. E. Brightman appeared in 1903. John Rutter set some of those prayers to music. Andrewes\'s other works occupy eight volumes in the *Library of Anglo-Catholic Theology* (1841--1854). Ninety-six of his sermons were published in 1631 by command of Charles I, have been occasionally reprinted, and are considered among the most rhetorically developed and polished sermons of the late-sixteenth and early-seventeenth centuries. Because of these, Andrewes has been commemorated by literary greats including T. S. Eliot.
Andrewes was considered, next to James Ussher, to be the most learned churchman of his day, and enjoyed a great reputation as an eloquent and impassioned preacher, but the stiffness and artificiality of his style render his sermons unsuited to modern taste. Nevertheless, there are passages of extraordinary beauty and profundity. His doctrine was High Church, and in his life he was humble, pious and charitable. He continues to influence religious thinkers to the present day, and was cited as an influence by T. S. Eliot, among others. Eliot borrowed, almost word for word and without his usual acknowledgement, a passage from Andrewes\' 1622 Christmas Day sermon for the opening of his poem \"Journey of the Magi\". In his 1997 novel *Timequake*, Kurt Vonnegut suggested that Andrewes was \"the greatest writer in the English language\", citing as proof the first few verses of the 23rd Psalm. His translation work has also led him to appear as a character in three plays dealing with the King James Bible, Howard Brenton\'s *Anne Boleyn* (2010), Jonathan Holmes\' *Into Thy Hands* (2011) and David Edgar\'s *Written on the Heart* (2011).
He has an academic cap named after him, known as the Bishop Andrewes cap, which is like a mortarboard but made of velvet, floppy and has a tump or tuff instead of a tassel. This was in fact the ancient version of the mortarboard before the top square was stiffened and the tump replaced by a tassel and button. This cap is still used by Cambridge DDs and at certain institutions as part of their academic dress.
A block of flats in the [Barbican Residential Estate](https://www.barbicanliving.co.uk/), central London, is named [Andrewes House](https://www.barbicanliving.co.uk/blocks/andrewes-house/). All the Barbican\'s residential buildings are named after famous people with a connection to the locale.
There is a stained glass window depicting Bishop Andrewes in [Grays Inn Chapel](https://www.graysinn.org.uk/the-inn/history/the-historic-estate/stained-glass/), central London
## Collected works {#collected_works}
Andrewes created a significant personal library. In his will, he bequeathed approximately 400 volumes to Pembroke College (Cambridge) where they remain.
His collection included:
- Works of Lancelot Andrewes, 11 volumes (Oxford, 1841--1854),
- Lancelot Andrewes Collection, 7 volumes
| 1,009 |
Lancelot Andrewes
| 3 |
18,043 |
# Lancelot Andrewes
## Styles and titles {#styles_and_titles}
- 1555--c. 1579: Lancelot Andrewes Esq.
- --1589: *The Reverend* Lancelot Andrewes
- 1589--bef. 1590: *The Reverend* Prebendary Lancelot Andrewes
- bef
| 30 |
Lancelot Andrewes
| 4 |
18,051 |
# Labour Day
alt=\|thumb\|upright=2\|Countries and dependencies coloured by observance of International Workers\' Day or a different variant of May Day or Labour Day: `{{legend|#dd3333|Labour Day falls on 1 May}}`{=mediawiki} `{{legend|#ffcc33|Another public holiday on 1 May or the first Monday in May}}`{=mediawiki} `{{legend|#00af89|No public holiday on 1 May, but Labour Day on a different date}}`{=mediawiki} `{{legend|#cccccc|No public holiday on 1 May and no Labour Day}}`{=mediawiki} **Labour Day** is an annual day of celebration of the labour movement and its achievements. It has its origins in the labour union movement, specifically the eight-hour day movement, which advocated eight hours for work, eight hours for recreation, and eight hours for rest.
In most countries, Labour Day is synonymous with, or linked with, International Workers\' Day, which happens on 1 May, originally chosen to commemorate the 1886 general strike which culminated in the Haymarket affair. For other countries, Labour Day is celebrated on a different date, often one with special significance for the labour movement in that country. Labour Day is a public holiday in many countries.
## International Workers\' Day {#international_workers_day}
For most countries, \"Labour Day\" is synonymous with, or linked with, International Workers\' Day, which occurs on 1 May. Some countries vary the actual date of their celebrations so that the holiday occurs on a Monday close to 1 May.
Some countries have a holiday at or around this date, but it is not a \'Labour Day\' celebration.
## Other dates {#other_dates}
### Australia
Labour Day is a public holiday in Australia on dates which vary between states and territories. In some states the date commemorates the Eight Hours Day march (see below). It is the first Monday in October in the Australian Capital Territory, New South Wales and South Australia. In Victoria and Tasmania, it is the second Monday in March (though the latter calls it the Eight Hours Day). In Western Australia, Labour Day is the first Monday in March. In Queensland and the Northern Territory, Labour Day occurs on the first Monday in May (though the latter calls it May Day). It is on the fourth Monday of March in the territory of Christmas Island.
#### Victoria
The first march for an eight-hour day by the labour movement occurred in Melbourne on 21 April 1856. On this day, stonemasons and building workers on building sites around Melbourne stopped work and marched from the University of Melbourne to Parliament House to achieve an eight-hour day. Their direct action protest was a success, and they are noted as being among the first organised workers in the world to achieve an eight-hour day, with no loss of pay.
#### Queensland
Labour Day was first celebrated with a public holiday in Queensland in 1865 as Eight Hours Celebration Day. It occurred on 1 March (Saint David\'s Day) and celebrated the winning of an eight-hour work day by Brisbane workers in 1858. The date was moved to May Day around 1896, in solidarity with the attack on United States workers on the first May Day parade in the Haymarket affair. In 1901, the holiday was moved to the first Monday in May, to ensure a long weekend.
### Bangladesh
Bangladesh Garment Sramik Sanghati, an organisation working for the welfare of garment workers, has requested that 24 April be declared Labour Safety Day in Bangladesh, in memory of the victims of the 2013 Rana Plaza collapse. However, Bangladesh does observe May Day on 1 May.
### The Bahamas {#the_bahamas}
Labour Day is a national holiday in The Bahamas, celebrated on the first Friday in June in order to create a long weekend for workers. The traditional date of Labour Day in The Bahamas, however, is 7 June, in commemoration of a significant workers\' strike that began on that day in 1942. Labour Day is meant to honour and celebrate workers and the importance of their contributions to the nation and society. In the capital city, Nassau, thousands of people come to watch a parade through the streets, which begins at mid-morning. Bands in colourful uniforms, traditional African Junkanoo performers, and members of various labour unions and political parties are all part of the procession, which ends up at the Southern Recreation Grounds, where government officials make speeches for the occasion.
### Canada
Labour Day (*Fête du Travail*) has been marked as a statutory public holiday in Canada on the first Monday in September since 1894. Its origins can be traced back to numerous local demonstrations and celebrations in earlier decades. Such events assumed political significance when a labour demonstration in Toronto in April 1872, in support of striking printers, led directly to the enactment of the Trade Union Act, a law that confirmed the legality of unions. On 22 July 1882, a labour celebration in Toronto attracted the attention of American labour leader Peter J. McGuire, who organised a similar parade in New York City on 5 September that year. Labour parades were held in several Canadian cities that day as well.
Unions associated with the Knights of Labor and the American Federation of Labor in both Canada and the United States subsequently promoted parades and festivals on the first Monday in September. In Canada, local celebrations took place in Hamilton, Oshawa, Montreal, St. Catharines, Halifax, Ottawa, Vancouver and London during these years. Montreal declared a civic holiday in 1889. In Nova Scotia, coal miners had been holding picnics and parades since 1880 to celebrate the anniversary of their union, the Provincial Workmen\'s Association, first organised in 1879.
In addition, in 1889, the Royal Commission on the Relations of Labour and Capital in Canada, chaired by James Sherrard Armstrong (1886--88) and Augustus Toplady Freed (1888--89), recommended recognition of an official \"labour day\" by the federal government. In March and April 1894, unions lobbied Parliament to recognise Labour Day as a public holiday. Legislation was introduced in May by prime minister Sir John Thompson and received royal assent in July 1894.
| 985 |
Labour Day
| 0 |
18,051 |
# Labour Day
## Other dates {#other_dates}
### China
1 May is a statutory holiday in the People\'s Republic of China. It was a three-day holiday until 2008, but was only one day after 2008. However, the actual time off is often longer than the time off in the regulations, and the extra time off is usually supplemented by another two weekends, but since the extra time is not under an official holiday, the extra days must be \"made up\" by working on the preceding or following weekend. For example, in 2013, 1 May fell on Wednesday. Most workplaces, including all government offices, took 29 April (Monday) to 1 May (Wednesday) as days off. As the first two days were not statutory holidays, they had to be \"made up\" by working the preceding weekend (27 and 28 April).
### Hong Kong S.A.R. {#hong_kong_s.a.r.}
Labour Day, observed 1 May, has been considered a public holiday in Hong Kong since 1999.
### India
The first Labour Day was celebrated in India on 1 May 1923, in Chennai (then known as Madras), organised by the Labour Kisan Party of Hindustan.
### Jamaica
Labour Day in Jamaica has a rich history tied to the struggles of the working class and the country's shift away from colonial traditions. Originally, May 24 was observed as Empire Day, celebrating Queen Victoria's birthday. In British history, she was credited with granting enslaved people in the colonies their freedom. Empire Day was widely observed across the Commonwealth, including Jamaica, but as the country moved toward independence, there was growing sentiment to replace it with something more reflective of Jamaica's own labour struggles.
Premier Norman Manley led this change in 1960 by introducing a bill to abolish Empire Day and replace it with Labour Day to commemorate the 1938 labour strikes. These strikes were a turning point in Jamaican history, as grossly underpaid workers across the island organized in protest. By May 23, 1938, public sector and transport workers in Kingston had joined the movement, halting activity in the capital. The unrest led to 46 deaths, 429 injuries, and numerous arrests, marking a major push for labour rights in the country. Manley's proposal to commemorate these events gained unanimous support in Parliament, officially establishing Labour Day on May 23.
In the 1960s, Labour Day celebrations were heavily tied to politics, with the two major trade unions---the Bustamante Industrial Trade Union (JLP) and the National Workers Union (PNP)---leading marches and rallies in Kingston. However, these events often turned violent. In 1962, a politically motivated clash during a Labour Day march resulted in the death of a woman and injuries to several police officers, who resorted to using tear gas to control the crowd. Additional conflicts in 1966 led authorities to ban Labour Day marches in Kingston, marking a shift in how the holiday was observed.
It was Prime Minister Michael Manley who redefined Labour Day in 1972 with the theme "Put Work into Labour Day." Rather than focusing on rallies and marches, Manley encouraged Jamaicans to actively participate in community projects. His vision emphasized the role of labour in nation-building, inspiring voluntary efforts across the island. The first national project focused on beautifying the Palisadoes Road, with Manley himself participating in tree planting. The response was overwhelming, with 600 projects completed that year, cementing Labour Day as a day of national pride and community service.
However, this momentum slowed under Prime Minister Edward Seaga in 1980, when large-scale Labour Day activities were halted, leading to an eight-year absence of organized projects. It was not until 1989, when Michael Manley returned to office, that Labour Day was fully revived. The Jamaican government began introducing themes to guide national activities, ensuring that community development remained central to the celebrations. Since then, Labour Day has continued as a tradition that blends historical remembrance with civic responsibility.
### Japan
A public holiday in Japan, Labour Day is officially conflated with Thanksgiving on 23 November, as Labor Thanksgiving Day.
### Kazakhstan
Labour Day, a public holiday in Kazakhstan, is celebrated on the last Sunday in September. The holiday was officially established in late 2013. In 1995, the government of Kazakhstan replaced International Workers\' Day with Kazakhstan People\'s Unity Day. Kazakh president Nursultan Nazarbayev also instituted a special medal that is awarded to veterans of labour on the occasion of the holiday. Labour Day it is widely celebrated across the country with official speeches, award ceremonies, cultural events, etc. It is a non-working holiday for most citizens of Kazakhstan because it always falls on a weekend.
### Kenya
A public holiday in Kenya, Labour Day is commemorated yearly every 1 May. This celebration is usually marked with song and dance as Kenyans gather at designated locations to celebrate and listen to speeches from the leadership of the country. Francis Atwoli, Secretary General of the Central Organization of Trade Unions (COTU) has been vocal in spearheading the celebrations in the country while advocating for favourable working conditions for the Kenyan people.
| 833 |
Labour Day
| 1 |
18,051 |
# Labour Day
## Other dates {#other_dates}
### Macau S.A.R. {#macau_s.a.r.}
In Macau, 1 May is a public holiday and is officially known as *Dia do Trabalhador* (Portuguese for \'Workers\' Day\').
### Malaysia
On 1 May, people in Malaysia take the time to remember the economic and social accomplishments of the labour movement.
Also known as May Day, this public holiday is sometimes celebrated with groups organising parades, rallies or both, to promote and protect workers\' rights.
### New Zealand {#new_zealand}
Labour Day (*Te Rā Whakanui i ngā Kaimahi*) is a public holiday in New Zealand and is held on the fourth Monday in October. Its origins are traced back to the eight-hour working day movement that arose in the newly founded Wellington colony in 1840, primarily because of carpenter Samuel Duncan Parnell\'s refusal to work more than eight hours a day. That year, Parnell reportedly told a prospective employer: \"There are twenty-four hours per day given us; eight of these should be for work, eight for sleep, and the remaining eight for recreation\".
The first Labour Day in New Zealand was celebrated on 28 October 1890, which marked the first anniversary of the Maritime Council, an organisation of transport and mining unions. Several thousand trade union members and supporters attended parades in the main city centres. Government employees were given the day off to attend, and many businesses closed for at least part of the day. Initially, the day was variously called Labour Day or Labour Demonstration Day.
In 1899, the government legislated that the day be a public holiday through the Labour Day Act of 1899. The day was set as the second Wednesday in October and first celebrated the following year, in 1900. In 1910, the holiday was moved to the fourth Monday in October.
### Pakistan
Labour Day, or *Youm-e-Mazdoor*, is observed in Pakistan on May 1st as a public holiday to recognize the contributions and rights of workers. Officially declared a holiday in 1972 under Prime Minister Zulfikar Ali Bhutto, it was part of the country\'s first labor policy, which also introduced welfare initiatives for workers. The day is marked by rallies, seminars, and demonstrations organized by trade unions to highlight labor issues such as fair wages and safe working conditions. Government offices, banks, and many businesses remain closed in observance.
### Poland
Labour Day is a public holiday in Poland, celebrated on 1 May. Together with Polish National Flag Day on 2 May and Constitution Day on 3 May - the latter also being a public holiday, coinciding with the Catholic holiday of The Most Holy Virgin Mary, Queen of Poland - it typically forms a long May weekend, referred to as *majówka*, widely regarded as the informal start of the spring outdoor leisure season, marked with picnics, barbecues, local events and travel.
### Philippines
In the Philippines, Labor Day is a public holiday commemorated nationwide on 1 May. Initially observed in 1903 through a protest by the Unión Obrera Democrática Filipina in Manila during the American colonial era, it was officially recognised as a holiday in 1908, with the first official commemoration taking place in 1913.
### Switzerland
In Switzerland, Labour Day on 1 May is not a federal holiday across the entire country, but several of the Swiss cantons have made it one of their cantonal holidays. In the Canton of Fribourg, it is traditional for children to go singing at people\'s doors in exchange for sweets and money.
### Taiwan
Labour Day, observed 1 May, in Taiwan, is an official holiday, though not everybody gets a day off. Public servants, teachers and students do not have this day off.
### Tajikistan
Labour Day was celebrated on 1 May in the Soviet Union, and the tradition lives on in Tajikistan as International Labour Day Although Labour Day is a working day, folk festivals, performances and fairs organised throughout the country create a holiday atmosphere.
### Trinidad and Tobago {#trinidad_and_tobago}
In Trinidad and Tobago, Labour Day is celebrated every 19 June. This public holiday was proposed in 1973 to be commemorated on the anniversary of the labour riots led by Tubal Uriah Butler in 1937, part of the British West Indian labour unrest of 1934--1939.
### Turkey
In Turkey, \"Labour and Solidarity Day\" (*Emek ve Dayanışma Günü*) became an official holiday in 2009. Prior to that, the day had been observed by workers and unions but had been banned for many years after the 1980 military coup. The turning point came in 2009, when the Turkish government, led by Prime Minister Recep Tayyip Erdoğan, officially recognized May 1st as a public holiday again. Demonstrations at Taksim Square carries historical significance due to the Taksim Square Massacre on 1 May 1977.
### United States {#united_states}
*Main article: Labor Day* In the United States, Labor Day is a federal holiday and public holiday observed on the first Monday of September. It is customarily viewed as the end of the summer vacation season. Many schools open for the year on the day after Labor Day. [The origins of Labor Day](https://archives.nupge.ca/content/celebrating-labour-day-holiday-canada-gave-world) can be traced back to 1872
| 850 |
Labour Day
| 2 |
18,056 |
# Laws of infernal dynamics
The **laws of infernal dynamics** are an adage about the cursedness of the universe. Attributed to science fiction author David Gerrold, the laws are as follows:
1. An object in motion will be moving in the wrong direction.
2. An object at rest will be in the wrong place.
3. The energy required to move an object in the correct direction, or put it in the right place, will be more than you wish to expend but not so much as to make the task impossible.
The laws are a parody on the first and second of Newton\'s laws of motion in the spirit of Murphy\'s law. Newton\'s first law of motion has here been split into two parts, the first two laws. Newton\'s third law of motion is left unparodied, though a separate adage states that \"for every action, there is an equal and opposite criticism
| 152 |
Laws of infernal dynamics
| 0 |
18,060 |
# Leonard Bloomfield
**Leonard Bloomfield** (April 1, 1887 -- April 18, 1949) was an American linguist who led the development of structural linguistics in the United States during the 1930s and the 1940s. He is considered to be the father of American distributionalism. His influential textbook *Language*, published in 1933, presented a comprehensive description of American structural linguistics. He made significant contributions to Indo-European historical linguistics, the description of Austronesian languages, and description of languages of the Algonquian family.
Bloomfield\'s approach to linguistics was characterized by its emphasis on the scientific basis of linguistics and emphasis on formal procedures for the analysis of linguistic data. The influence of Bloomfieldian structural linguistics declined in the late 1950s and 1960s as the theory of generative grammar developed by Noam Chomsky came to predominate.
## Early life and education {#early_life_and_education}
Bloomfield was born in Chicago, Illinois, on April 1, 1887, to Jewish parents (Sigmund Bloomfield and Carola Buber Bloomfield). His father immigrated to the United States as a child in 1868; the original family name *Blumenfeld* was changed to Bloomfield after their arrival. In 1896 his family moved to Elkhart Lake, Wisconsin, where he attended elementary school, but returned to Chicago for secondary school. His uncle Maurice Bloomfield was a prominent linguist at Johns Hopkins University, and his aunt Fannie Bloomfield Zeisler was a well-known concert pianist.
Bloomfield attended Harvard College from 1903 to 1906, graduating with the A.B. degree. He subsequently began graduate work at the University of Wisconsin, taking courses in German and Germanic philology, in addition to courses in other Indo-European languages. A meeting with Indo-Europeanist Eduard Prokosch, a faculty member at the University of Wisconsin, convinced Bloomfield to pursue a career in linguistics. In 1908 Bloomfield moved to the University of Chicago, where he took courses in German and Indo-European philology with Frances A. Wood and Carl Darling Buck. His doctoral dissertation in Germanic historical linguistics, *A semasiologic differentiation in Germanic secondary ablaut*, was supervised by Wood, and he graduated in 1909.
He undertook further studies at the University of Leipzig and the University of Göttingen in 1913 and 1914 with leading Indo-Europeanists August Leskien, Karl Brugmann, as well as Hermann Oldenberg, a specialist in Vedic Sanskrit. Bloomfield also studied at Göttingen with Sanskrit specialist Jacob Wackernagel, and considered both Wackernagel and the Sanskrit grammatical tradition of rigorous grammatical analysis associated with Pāṇini as important influences on both his historical and descriptive work. Further training in Europe was a condition for promotion at the University of Illinois from Instructor to the rank of assistant professor.
## Career
Bloomfield was instructor in German at the University of Cincinnati, 1909--1910; Instructor in German at the University of Illinois at Urbana--Champaign, 1910--1913; promoted to assistant professor of Comparative Philology and German, also University of Illinois, 1913--1921; Professor of German and Linguistics at the Ohio State University, 1921--1927; Professor of Germanic Philology at the University of Chicago, 1927--1940; Sterling Professor of Linguistics at Yale University, 1940--1949. During the summer of 1925 Bloomfield worked as Assistant Ethnologist with the Geological Survey of Canada in the Canadian Department of Mines, undertaking linguistic field work on Plains Cree; this position was arranged by Edward Sapir, who was then Chief of the Division of Anthropology, Victoria Museum, Geological Survey of Canada, Canadian Department of Mines. In May 1946, he suffered a debilitating stroke, which ended his career.
Bloomfield was one of the founding members of the Linguistic Society of America. In 1924, along with George M. Bolling (Ohio State University) and Edgar Sturtevant (Yale University) he formed a committee to organize the creation of the Society, and drafted the call for the Society\'s foundation. He contributed the lead article to the inaugural issue of the Society\'s journal *Language*, and was President of the Society in 1935. He taught in the Society\'s summer Linguistic Institute in 1938--1941, with the 1938--1940 Institutes being held in Ann Arbor, Michigan, and the 1941 Institute in Chapel Hill, North Carolina. Bloomfield was also a member of the American Philosophical Society.
| 668 |
Leonard Bloomfield
| 0 |
18,060 |
# Leonard Bloomfield
## Indo-European linguistics {#indo_european_linguistics}
Bloomfield\'s earliest work was in historical Germanic studies, beginning with his dissertation, and continuing with a number of papers on Indo-European and Germanic phonology and morphology. His post-doctoral studies in Germany further strengthened his expertise in the Neogrammarian tradition, which still dominated Indo-European historical studies. Bloomfield throughout his career, but particularly during his early career, emphasized the Neogrammarian principle of regular sound change as a foundational concept in historical linguistics.
Bloomfield\'s work in Indo-European beyond his dissertation was limited to an article on palatal consonants in Sanskrit and one article on the Sanskrit grammatical tradition associated with Pāṇini, in addition to a number of book reviews. Bloomfield made extensive use of Indo-European materials to explain historical and comparative principles in both of his textbooks, *An introduction to language* (1914), and his seminal *Language* (1933). In his textbooks he selected Indo-European examples that supported the key Neogrammarian hypothesis of the regularity of sound change, and emphasized a sequence of steps essential to success in comparative work: (a) appropriate data in the form of texts which must be studied intensively and analysed; (b) application of the comparative method; (c) reconstruction of proto-forms. He further emphasized the importance of dialect studies where appropriate, and noted the significance of sociological factors such as prestige, and the impact of meaning. In addition to regular linguistic change, Bloomfield also allowed for borrowing and analogy.
It is argued that Bloomfield\'s Indo-European work had two broad implications: \"He stated clearly the theoretical bases for Indo-European linguistics\" and \"he established the study of Indo-European languages firmly within general linguistics.\"
### Sanskrit studies {#sanskrit_studies}
As part of his training with leading Indo-Europeanists in Germany in 1913 and 1914 Bloomfield studied the Sanskrit grammatical tradition originating with Pāṇini, who lived in northwestern India during the fifth or fourth century BC. Pāṇini\'s grammar is characterized by its extreme thoroughness and explicitness in accounting for Sanskrit linguistic forms, and by its complex context-sensitive, rule-based generative structure. Bloomfield noted that \"Pāṇini gives the formation of every inflected, compounded, or derived word, with an exact statement of the sound-variations (including accent) and of the meaning\". In a letter to Algonquianist Truman Michelson, Bloomfield noted \"My models are Pāṇini and the kind of work done in Indo-European by my teacher, Professor Wackernagel of Basle.\"
Pāṇini\'s systematic approach to analysis includes components for: (a) forming grammatical rules, (b) an inventory of sounds, (c) a list of verbal roots organized into sublists, and (d) a list of classes of morphs. Bloomfield\'s approach to key linguistic ideas in his textbook *Language* reflect the influence of Pāṇini in his treatment of basic concepts such as *linguistic form*, *free form*, and others. Similarly, Pāṇini is the source for Bloomfield\'s use of the terms *exocentric* and *endocentric* used to describe compound words. Concepts from Pāṇini are found in *Eastern Ojibwa*, published posthumously in 1958, in particular his use of the concept of a morphological zero, a morpheme that has no overt realization. Pāṇini\'s influence is also present in Bloomfield\'s approach to determining parts of speech (Bloomfield uses the term \"form-classes\") in both *Eastern Ojibwa* and in the later *Menomini language*, published posthumously in 1962.
| 529 |
Leonard Bloomfield
| 1 |
18,060 |
# Leonard Bloomfield
## Austronesian linguistics {#austronesian_linguistics}
While at the University of Illinois Bloomfield undertook research on Tagalog, an Austronesian language spoken in the Philippines. He carried out linguistic field work with Alfredo Viola Santiago, who was an engineering student at the university from 1914 to 1917. The results were published as *Tagalog texts with grammatical analysis*, which includes a series of texts dictated by Santiago in addition to an extensive grammatical description and analysis of every word in the texts. Bloomfield\'s work on Tagalog, from the beginning of field research to publication, took no more than two years. His study of Tagalog has been described as \"the best treatment of any Austronesian language \... The result is a description of Tagalog which has never been surpassed for completeness, accuracy, and wealth of exemplification.\"
Bloomfield\'s only other publication on an Austronesian language was an article on the syntax of Ilocano, based upon research undertaken with a native speaker of Ilocano who was a student at Yale University. This article has been described as a \"tour de force, for it covers in less than seven pages the entire taxonomic syntax of Ilocano\".
## Algonquian linguistics {#algonquian_linguistics}
Bloomfield\'s work on Algonquian languages had both descriptive and comparative components. He published extensively on four Algonquian languages: Fox, Cree, Menominee, and Ojibwe, publishing grammars, lexicons, and text collections. Bloomfield used the materials collected in his descriptive work to undertake comparative studies leading to the reconstruction of Proto-Algonquian, with an early study reconstructing the sound system of Proto-Algonquian, and a subsequent more extensive paper refining his phonological analysis and adding extensive historical information on general features of Algonquian grammar.
Bloomfield undertook field research on Cree, Menominee, and Ojibwe, and analysed the material in previously published Fox text collections. His first Algonquian research, beginning around 1919, involved study of text collections in the Fox language that had been published by William Jones and Truman Michelson. Working through the texts in these collections, Bloomfield excerpted grammatical information to create a grammatical sketch of Fox. A lexicon of Fox based on his excerpted material was published posthumously.
Bloomfield undertook field research on Menominee in the summers of 1920 and 1921, with further brief field research in September 1939 and intermittent visits from Menominee speakers in Chicago in the late 1930s, in addition to correspondence with speakers during the same period. Material collected by Morris Swadesh in 1937 and 1938, often in response to specific queries from Bloomfield, supplemented his information. Significant publications include a collection of texts, a grammar and a lexicon (both published posthumously), in addition to a theoretically significant article on Menomini phonological alternations.
Bloomfield undertook field research in 1925 among Plains Cree speakers in Saskatchewan at the Sweet Grass reserve, and also at the Star Blanket reserve, resulting in two volumes of texts and a posthumous lexicon. He also undertook brief field work on Swampy Cree at The Pas, Manitoba. Bloomfield\'s work on Swampy Cree provided data to support the predictive power of the hypothesis of exceptionless phonological change.
Bloomfield\'s initial research on Ojibwe was through study of texts collected by William Jones, in addition to nineteenth century grammars and dictionaries. During the 1938 Linguistic Society of America Linguistic Institute held at the University of Michigan in Ann Arbor, Michigan, he taught a field methods class with Andrew Medler, a speaker of the Ottawa dialect who was born in Saginaw, Michigan, but spent most of his life on Walpole Island, Ontario. The resulting grammatical description, transcribed sentences, texts, and lexicon were published posthumously in a single volume. In 1941 Bloomfield worked with Ottawa dialect speaker Angeline Williams at the 1941 Linguistic Institute held at the University of North Carolina in Chapel Hill, North Carolina, resulting in a posthumously published volume of texts.
| 627 |
Leonard Bloomfield
| 2 |
18,060 |
# Leonard Bloomfield
## Selected publications {#selected_publications}
- Bloomfield, Leonard. 1909/1910. \"A semasiological differentiation in Germanic secondary ablaut\". *Modern Philology* 7:245--288; 345--382.
-
- Bloomfield, Leonard. 1914. *Introduction to the Study of Language*. New York: Henry Holt. Reprinted 1983, John Benjamins. Retrieved April 19, 2009. `{{ISBN|90-272-1892-7}}`{=mediawiki}.
-
-
- Bloomfield, Leonard. 1917. *Tagalog texts with grammatical analysis*. University of Illinois studies in language and literature, 3.2-4. Urbana, Illinois.
-
-
- Bloomfield, Leonard. 1925--1927. \"Notes on the Fox language.\" *International Journal of American Linguistics* 3:219-232; 4: 181--219
- (reprinted in: Martin Joos, ed., *Readings in Linguistics I*, Chicago and London: The University of Chicago Press 1957, 26--31).
-
-
- Bloomfield, Leonard. 1928. *Menomini texts.* Publications of the American Ethnological Society 12. New York: G. E. Stechert, Agents. \[reprinted 1974. New York: AMS Press\] `{{ISBN|0-404-58162-5}}`{=mediawiki}
-
- Bloomfield, Leondard. 1929. Review of Bruno Liebich, 1928, *Konkordanz Pāṇini-Candra*, Breslau: M. & H. Marcus. *Language* 5:267--276. Reprinted in Hockett, Charles. 1970, pp. 219--226.
- Bloomfield, Leonard. 1930. *Sacred stories of the Sweet Grass Cree*. National Museum of Canada Bulletin, 60 (Anthropological Series 11). Ottawa. \[reprinted 1993, Saskatoon, SK: Fifth House\]. `{{ISBN|1-895618-27-4}}`{=mediawiki}
- Bloomfield, Leonard. 1933. *Language*. New York: Henry Holt. `{{ISBN|0-226-06067-5}}`{=mediawiki}, `{{ISBN|90-272-1892-7}}`{=mediawiki}
- Bloomfield, Leonard. 1934. *Plains Cree texts*. American Ethnological Society Publications 16. New York. \[reprinted 1974, New York: AMS Press\]
- Bloomfield, Leonard. 1935. \"Linguistic aspects of science\". *Philosophy of Science* 2/4:499--517.
- Bloomfield, Leonard. 1939. \"Menomini morphophonemics\". *Etudes phonologiques dédiées à la mémoire de M. le prince N.S. Trubetzkoy*, 105--115. Travaux du Cercle Linguistique de Prague 8. Prague.
- Bloomfield, Leonard. 1939a. *Linguistic aspects of science*. Chicago: University of Chicago Press. `{{ISBN|0-226-57579-9}}`{=mediawiki}
-
- Bloomfield, Leonard. 1942a. *Outline guide for the practical study of foreign languages.* Baltimore: Linguistic Society of America.
- Bloomfield, Leonard. 1946. \"Algonquian.\" Harry Hoijer et al., eds., *Linguistic structures of native America*, pp. 85--129. Viking Fund Publications in Anthropology 6. New York: Wenner-Gren Foundation.
- Bloomfield, Leonard. 1958. *Eastern Ojibwa.* Ed. Charles F. Hockett. Ann Arbor: University of Michigan Press.
- Bloomfield, Leonard. 1962. *The Menomini language.* Ed. Charles F. Hockett. New Haven: Yale University Press.
- Bloomfield, Leonard. 1975. *Menomini lexicon.* Ed. Charles F. Hockett. Milwaukee Public Museum Publications in Anthropology and History. Milwaukee: Milwaukee Public Museum.
- Bloomfield, Leonard. 1984. *Cree-English lexicon.* Ed. Charles F. Hockett. New Haven: Human Relations Area Files. `{{ISBN|99954-923-9-3}}`{=mediawiki}
- Bloomfield, Leonard. 1984b. *Fox-English lexicon.* Ed. Charles F. Hockett. New Haven: Human Relations Area Files
| 406 |
Leonard Bloomfield
| 3 |
18,065 |
# Long Parliament
The **Long Parliament** was an English Parliament which lasted from 1640 until 1660, making it the longest-lasting Parliament in English and British history. It followed the fiasco of the Short Parliament, which had convened for only three weeks during the spring of 1640 after an 11-year parliamentary absence. In September 1640, King Charles I issued writs summoning a parliament to convene on 3 November 1640. He intended it to pass financial bills, a step made necessary by the costs of the Bishops\' Wars against Scotland. The Long Parliament received its name from the fact that, by Act of Parliament, it stipulated it could be dissolved only with agreement of the members; and those members did not agree to its dissolution until 16 March 1660, after the English Civil War and near the close of the Interregnum.
The parliament first sat from 1640 until 1653. Following Pride\'s Purge in 1648, the remaining members sat as the Rump Parliament until Oliver Cromwell suspended it in April 1653, replacing it with a succession of nominated and elected parliaments.
In the chaos following the death of Cromwell in September 1658, the Rump was reinstalled in May 1659, and in February 1660 General George Monck allowed the members barred in 1648 to retake their seats, so that they could pass the necessary legislation to allow the Stuart Restoration and dissolve the Long Parliament. This cleared the way for a new parliament to be elected, which was known as the Convention Parliament. Some key members of the Long Parliament, such as Sir Henry Vane the Younger and General Edmond Ludlow, were barred from the final acts of the Long Parliament. They claimed the parliament was not legally dissolved, its final votes a procedural irregularity (the words used contemporaneously were \"device\" and \"conspiracy\") by Monck to ensure the restoration of King Charles II of England. On the restoration Monck was rewarded with a dukedom.
The Long Parliament later became a key moment in Whig histories of the seventeenth century. American Whig historian Charles Wentworth Upham believed the Long Parliament comprised \"a set of the greatest geniuses for government that the world ever saw embarked together in one common cause\" and whose actions produced an effect which, at the time, made their country the wonder and admiration of the world, and is still felt and exhibited far beyond the borders of that country, in the progress of reform, and the advancement of popular liberty. He believed its republican principles made it a precursor to the American Revolutionary War.
| 423 |
Long Parliament
| 0 |
18,065 |
# Long Parliament
## Execution of Strafford {#execution_of_strafford}
thumb\|left\|upright=1\|Charles signed a bill agreeing that the present Parliament should not be dissolved without its own consent. Charles found himself unable to fund the Bishops\' Wars without taxes; in April 1640, Parliament was recalled for the first time in eleven years, but when it refused to vote taxes without concessions, he dissolved it after only three weeks. The humiliating terms imposed by the Scots Covenanters after a second defeat forced him to hold fresh elections in November, which produced a large majority for the opposition, led by John Pym.
Parliament was almost immediately presented with a series of \"Root and Branch petitions\". These demanded the expulsion of bishops from the Church of England, reflecting widespread concern at the growth of \"Catholic practices\" within the church. Charles\' willingness to make war on the Protestant Scots, but not to assist his exiled nephew Charles Louis, led to fears he was about to sign an alliance with Spain, a view shared by the experienced Venetian and French ambassadors.
This meant ending arbitrary rule was important not just for England, but the Protestant cause in general. Since direct attacks on the monarch were considered unacceptable, the usual route was to prosecute his \"evil counsellors\". Doing so showed even if the king was above the law, his subordinates were not, and he could not protect them; the intention was to make others think twice about their actions. Further, they started to create a series of committees and sub-committees starting with the Grand Committee for Religion appointed on 6 November 1640.
Their main target was the Earl of Strafford, former Lord Deputy of Ireland; aware of this, he urged Charles to use military force to seize the Tower of London, and arrest any MP or peer guilty of \"treasonable correspondence with the Scots\". While Charles hesitated, Pym struck first; on 11 November Strafford was impeached, arrested, and sent to the Tower. Other targets, including John Finch, fled abroad; Archbishop William Laud---by then sufficiently unpopular that in May 1640 a large armed mob attacked Lambeth Palace, seeking to kill him---was impeached in December, joining Strafford in the Tower.
At his trial in March 1641, Strafford was indicted on 28 counts of \"arbitrary and tyrannical government\". Even if these charges were proved, it was not clear they constituted a crime against the king, the legal definition of treason. If he went free, his opponents would replace him in the Tower, and so Pym immediately moved a bill of attainder, asserting Strafford\'s guilt and ordering his execution.
Although Charles announced he would not sign the attainder, on 21 April 204 MPs voted in favour, 59 against, while 250 abstained. On 1 May, rumours of a military plot to release Strafford from the Tower led to widespread demonstrations in London, and on 7th, the Lords voted for execution by 51 to 9. Claiming to fear for his family\'s safety, Charles signed the death warrant on 10 May, and Strafford was beheaded two days later.
## Committees established by the Long Parliament {#committees_established_by_the_long_parliament}
On 5 November 1640 parliament created several committees to parcel out the work they intended to address. The first committee was the Committee for Privileges and Elections under the leadership of John Maynard, MP for Totnes. On the next day, 6 November, parliament established the Grand Committee for Religion.
| 559 |
Long Parliament
| 1 |
18,065 |
# Long Parliament
## The Grand Remonstrance {#the_grand_remonstrance}
thumb\|right\|upright=1.0\|Viscount Falkland; killed at Newbury in 1643, typical of those moderates who supported reforms, but opposed the Grand Remonstrance and became Royalists This seemed to provide a basis for a programme of constitutional reforms, and Parliament voted Charles an immediate grant of £400,000. The Triennial Acts required Parliament meet at least every three years, and if the King failed to issue proper summons, the members could assemble on their own. Levying taxes without consent of Parliament was declared unlawful, including Ship money and forced loans, while the Star Chamber and High Commission courts abolished.
These reforms were supported by many who later became Royalists, including Edward Hyde, Viscount Falkland, and Sir John Strangways. Where they differed from Pym and his supporters was their refusal to accept Charles would not keep his commitments, despite evidence to the contrary. He reneged on those made in the 1628 Petition of Right, and agreed terms with the Scots in 1639, while preparing another attack. Both he and Henrietta Maria openly told foreign ambassadors any concessions were temporary, and would be retrieved by force if needed.
In this period, \'true religion\' and \'good government\' were seen as one and the same. Although the vast majority believed a \'well-ordered\' monarchy was a divinely mandated requirement, they disagreed on what \'well-ordered\' meant, and who held ultimate authority in clerical affairs. Royalists generally supported a Church of England governed by bishops, appointed by, and answerable to, the king; most Parliamentarians were Puritans, who believed he was answerable to the leaders of the church, appointed by their congregations.
However, Puritan meant anyone who wanted to reform, or \'purify\', the Church of England, and contained many different opinions. Some simply objected to Laud\'s reforms; Presbyterians like Pym wanted to reform the Church of England, along the same lines as the Church of Scotland. Independents believed any state church was wrong, while many were also political radicals like the Levellers. Presbyterians in England and Scotland gradually came to see them as more dangerous than the Royalists; an alliance between these three groups eventually led to the Second English Civil War in 1648.
While it is not clear there was a majority for removing bishops from the Church, their presence in the House of Lords became increasingly resented due to their role in blocking many of these reforms. Tensions came to a head in October 1641 with the outbreak of the Irish Rebellion; both Charles and Parliament supported raising troops to suppress it, but neither trusted the other with their control.
On 22 November, the Commons passed the Grand Remonstrance by 159 votes to 148, and presented it to Charles on 1 December. The first half listed over 150 perceived \'misdeeds\', the second proposed solutions, including church reform and Parliamentary control over the appointment of royal ministers. In the Militia Ordinance, Parliament asserted control over appointment of army and navy commanders; Charles rejected the Grand Remonstrance and refused to assent to the Militia Ordinance. It was at this point moderates like Hyde decided Pym and his supporters had gone too far, and switched sides.
| 520 |
Long Parliament
| 2 |
18,065 |
# Long Parliament
## First English Civil War {#first_english_civil_war}
thumb\|right\|upright=1.2\|King Charles\' attempt to arrest the Five Members of the Commons Increasing unrest in London culminated in 23 to 29 December 1641 with widespread riots in Westminster, while the hostility of the crowd meant the bishops stopped attending the Lords. On 30 December, Charles induced John Williams, Archbishop of York and eleven other bishops, to sign a complaint, disputing the legality of any laws passed by the Lords during their exclusion. This was viewed by the Commons as inviting the king to dissolve Parliament; all twelve were arrested.
On 3 January 1642, Charles ordered his Attorney-general to bring charges of treason against Edward Montagu, 2nd Earl of Manchester, and Five Members of the Commons; Pym, John Hampden, Denzil Holles, Arthur Haselrig, and William Strode. This confirmed fears he intended to use force to shut down Parliament. The members were pre-warned, and evaded arrest.
Soon after, Charles left London, accompanied by many Royalist MPs, and members of the Lords, a major tactical mistake. By doing so, he abandoned the largest arsenal in England and the commercial power of the City of London and guaranteed his opponents majorities in both houses. In February, Parliament passed the Clergy Act, excluding bishops from the Lords; Charles approved it, since he had already decided to retrieve all such concessions by assembling an army.
In March 1642, Parliament decreed its own Parliamentary Ordinances were valid laws, even without royal assent. The Militia Ordinance gave them control of the local militia, or Trained Bands; those in London were the most strategically critical, because they could protect Parliament from armed intervention by any soldiers which Charles had near the capital. Charles declared Parliament in rebellion and began raising an army, by issuing a competing Commission of Array.
At the end of 1642, he set up his court at Oxford, where the Royalist MPs formed the Oxford Parliament. In 1645 Parliament reaffirmed its determination to fight the war to a finish. It passed the Self-denying Ordinance, by which all members of either House of Parliament resigned any military commands, and formed the New Model Army under the command of Fairfax and Cromwell. The New Model Army soon destroyed Charles\' armies, and by early 1646, he was on the verge of defeat.
Charles left Oxford in disguise on 27 April; on 6 May, Parliament received a letter from David Leslie, commander of Scottish forces besieging Newark, announcing that he had the king in custody. Charles ordered the Royalist governor, Lord Belasyse, to surrender Newark, and the Scots withdrew to Newcastle, taking the king with them. This marked the end of the First English Civil War.
| 444 |
Long Parliament
| 3 |
18,065 |
# Long Parliament
## Second English Civil War {#second_english_civil_war}
Many Parliamentarians had assumed military defeat would force Charles to compromise, which proved a fundamental misunderstanding of his character. When Prince Rupert suggested in August 1645 the war was lost, Charles responded he was correct from a military viewpoint, but \'God will not suffer rebels and traitors to prosper\'. This deeply-held conviction meant he refused any substantial concessions. Aware of divisions among his opponents, he used his position as king of both Scotland and England to deepen them, assuming that he was essential to any government; while this was true in 1646, by 1648 key actors believed it was pointless to negotiate with someone who could not be trusted to keep any agreement.
Unlike in England, where Presbyterians were a minority, the Bishops\' Wars resulted in a Covenanter, or Presbyterian government, and Presbyterian kirk, or Church of Scotland. The Scots wanted to preserve these achievements; the 1643 Solemn League and Covenant was driven by their concern at the implications for this settlement if Charles defeated Parliament. By 1646, they viewed Charles as a lesser threat than the Independents, who opposed their demand for a unified, Presbyterian church of England and Scotland; Cromwell claimed he would fight rather than agree to it.
In July, the Scots and English commissioners presented Charles with the Newcastle Propositions, which he rejected. His refusal to negotiate created a dilemma for the Covenanters. Even if Charles agreed to a Presbyterian union, there was no guarantee it would be approved by Parliament. Keeping him was too dangerous; as subsequent events proved, whether Royalist or Covenanter, many Scots supported his retention. In February 1647, they agreed to a financial settlement, handed Charles over to Parliament, and retreated into Scotland. In England, Parliament was struggling with the economic cost of the war, a poor 1646 harvest, and a recurrence of the plague. The Presbyterian faction had the support of the London Trained Bands, the Army of the Western Association, leaders like Rowland Laugharne in Wales, and parts of the Royal Navy. By March 1647, the New Model was owed more than £3 million in unpaid wages; Parliament ordered it to Ireland, stating that only those who agreed would be paid. When their representatives demanded full payment for all in advance, it was disbanded.
The New Model refused to be disbanded; in early June, Charles was removed from his Parliamentary guards, and taken to Thriplow, where he was presented with the Army Council\'s terms. Though they were more lenient than the Newcastle Propositions, Charles rejected them; on 26 July, pro-Presbyterian rioters burst into Parliament, demanding he be invited to London. In early August, Fairfax and the New Model Army took control of the city, while on 20 August Cromwell went to Parliament with a military escort, and forced the passing of the Null and Void Ordinance annulling all Parliamentary proceedings since 26 July, leading to the withdrawal of most of the Presbyterian MPs and presaging Pride\'s Purge the following year. The Putney Debates attempted to address radicals\' objectives, but the return of royalist threats in November led to Fairfax demanding a declaration of loyalty; this re-established command authority over the rank and file, completed at Corkbush.
In late November, the king escaped from his guards, and made his way to Carisbrooke Castle. In April 1648, the Engagers became a majority in the Scottish Parliament; in return for restoring him to the English throne, Charles agreed to impose Presbyterianism in England for three years, and suppress the Independents. His refusal to take the Covenant himself split the Scots; the Kirk Party did not trust Charles, objected to an alliance with English and Scots Royalists, and denounced the Engagement as \'sinful.\'
After two years of constant negotiation, and refusal to compromise, Charles finally had the pieces in place for a rising by Royalists, supported by some English Presbyterians, and Scots Covenanters. However, lack of co-ordination meant the Second English Civil War was quickly suppressed.
| 661 |
Long Parliament
| 4 |
18,065 |
# Long Parliament
## Rump Parliament (6 December 1648 -- 20 April 1653) {#rump_parliament_6_december_1648_20_april_1653}
*Main article: Rump Parliament* Divisions emerged between various factions, culminating in Pride\'s Purge on 7 December 1648, when, under the orders of Oliver Cromwell\'s son-in-law Henry Ireton, Colonel Pride physically barred and arrested 41 of the members of Parliament. Many of the excluded members were Presbyterians. Henry Vane the Younger removed himself from Parliament in protest of this unlawful action by Ireton. He was not party to the execution of Charles I, although Cromwell was. In the wake of the ejections, the remnant, the *Rump Parliament*, arranged for the trial and execution of Charles I on 30 January 1649. It was also responsible for the setting up of the Commonwealth of England in 1649.
Henry Vane the Younger was persuaded to rejoin Parliament on 17 February 1649 and a Council of state was installed, into whose hands the executive government of the nation was committed. Sir Henry Vane was appointed a member of the Council. Cromwell took great pains to induce Vane to accept the appointment, and after many consultations, he so far prevailed in satisfying Vane of the purity of his principles in reference to the Commonwealth, as to overcome his reluctance again to enter the public service. Sir Henry Vane was for some time President of the Council, and, as Treasurer and Commissioner for the Navy, he had almost the exclusive direction of that branch of public service.
Cromwell \"well knew that while the Long Parliament, that noble company, who had fought the great battle of liberty from the beginning, remained in session, and such men as Vane were enabled to mingle in its deliberations, it would be utterly useless for him to think of executing his purposes\" (to set up a Protectorate or Dictatorship). Henry Vane was working on a Reform Bill. Cromwell knew \"that if the Reform Bill should be suffered to pass, and a House of Commons be convened, freely elected on popular principles, and constituting a full and fair and equal representation, it would be impossible ever after to overthrow the liberties of the people, or break down the government of the country\". According to General Edmund Ludlow (an unapologetic supporter of the Good Old Cause who lived in exile after the Restoration), this reform bill provided for an equal representation of the people, disfranchised several boroughs which had ceased to have a population in proportion to representation, fixed the number of the House at four hundred\". It would have \"secured to England and to the rest of the world the blessings of republican institutions, two centuries earlier than can now be expected\".
\"Harrison, who was in Cromwell\'s confidence on this occasion, rose to debate the motion, merely in order to gain time. Word was carried to Cromwell, that the House were on the point of putting the final motion; and Colonel Ingoldby hastened to Whitehall to tell him, that, if he intended to do anything decisive, he had no time to lose\". Once the troops were in place Cromwell entered the assembly. He was dressed in a suit of plain black; with grey worsted stockings. He took his seat; and appeared to be listening to the debate. As the Speaker was about to rise to put the question, Cromwell whispered to Harrison, \"Now is the time; I must do it\". As he rose, his countenance became flushed and blacked by the terrific passions which the crisis awakened. With the most reckless violence of manner and language, he abused the character of the House; and, after the first burst of his denunciations had passed, suddenly changing his tone, he exclaimed, \"You think, perhaps, this is not parliamentary language; I know it; nor are you to expect such from me\". He then advanced out into the middle of the hall, and walked to and fro, like a man beside himself. In a few moments he stamped upon the floor, the doors flew open and a file of musketeers entered. As they advanced, Cromwell exclaimed, looking over the House, \"You are no Parliament; I say you are no Parliament; begone, and give place to honester men\".
\"While this extraordinary scene was transacting, the members, hardly believing their own ears and eyes, sat in mute amazement, horror, and pity of the maniac traitor who was storming and raving before them. At length Vane rose to remonstrate, and call him to his senses; but Cromwell, instead of listening to him, drowned his voice, repeating with great vehemence, and as though with the desperate excitement of the moment, \"Sir Harry Vane! Sir Harry Vane! Good Lord deliver me from Sir Harry Vane!\" He then seized the records, snatched the bill from the hands of the clerk, drove the members out at the point of the bayonet, locked the doors, put the key in his pocket, and returned to Whitehall.
Oliver Cromwell forcibly disbanded the Rump in 1653 when it seemed to be planning to perpetuate itself rather than call new elections as had been agreed. It was followed by Barebone\'s Parliament and then the First, Second and Third Protectorate Parliaments.
| 855 |
Long Parliament
| 5 |
18,065 |
# Long Parliament
## Recall of the Rump (7 May 1659 -- 20 February 1660) {#recall_of_the_rump_7_may_1659_20_february_1660}
After Richard Cromwell, who had succeeded his father Oliver as Lord Protector in 1658, was effectively deposed by an officers\' coup in April 1659, the officers re-summoned the Rump Parliament to sit. It convened on 7 May 1659, but after five months in power it again clashed with the army (led by John Lambert) and was again forcibly dissolved on 13 October 1659. Once again, Sir Henry Vane was the leading catalyst for the republican cause in opposition to force by the military.
The persons connected with the administration as it existed at the death of Oliver were, of course, interested in keeping things as they were. Also, it was necessary for someone to assume the reins of government until the public will could be ascertained and brought into exercise. Henry Vane was elected to Parliament at Kingston upon Hull, but the certificate was given to another. Vane proceeded to Bristol, entered the canvass, and received the majority. Again the certificate was given to another. Finally Vane proceeded to Whitechurch in Hampshire and was elected a third time and was this time seated in Parliament. Vane managed the debates on behalf of the House of Commons. One of Vane\'s speeches effectively ended Richard Cromwell\'s career:
This speech swept everything before it. The Rump Parliament which Oliver Cromwell had dispersed in 1653 was once more summoned to assemble, by a declaration from the Council of Officers dated on 6 May 1659.
Edmond Ludlow made several attempts to reconcile the army and parliament in this time period but was ultimately unsuccessful. Parliament ordered the regiments of Colonel Morley and Colonel Moss to march to Westminster for their security, and sent for the rest of the troops that were about London to draw down to them also with all speed.
In October 1659, Colonel Lambert and various subordinate members of the army, acting in the military interest, resisted Colonel Morley and others who were defending the rump Parliament. Colonel Lambert, Major Grimes, and Colonel Sydenham eventually gained their points, and placed guards both by land and water, to hinder the members of Parliament from approaching the House. Colonel Lambert subsequently acquitted himself to Henry Vane the Younger, Edmond Ludlow and the \"Committee on Safety,\" an instrument of the Wallingford House party acting under their misdirection.
Nevertheless, Parliament was closed once again by military force until such time that the army and leaders of Parliament could effect a resolution. Rule then passed to an unelected *Committee of Safety*, including Lambert and Vane; pending a resolution or compromise with the Army.
During these disorders, the Council of State still assembled at the usual place, and:
The Council of Officers at first attempted to come to some agreement with the leaders of Parliament. On 15 October 1659, the Council of Officers appointed ten persons to \"consider of fit ways and means to carry on the affairs and government of the Commonwealth\". On 26 October 1659 the Council of Officers appointed a new Committee of Safety of twenty-three members.
On 1 November 1659, the Committee of Safety nominated a committee \"to consider of and prepare a form of government to be settled over the three nations in the way of a free state and Commonwealth, and afterwards to present it to the Committee of Safety for their further considerations\".
The designs of General Fleetwood of the army and the Wallingford House party were now suspected as being in a possible alliance with Charles II. According to Edmond Ludlow:
Edmond Ludlow warned both the Army and key members of Parliament that unless a compromise could be made it would \"render all the blood and treasure that had been spent in asserting our liberties of no use to us, but also force us under such a yoke of servitude, that neither we nor our posterity should be able to bear\".
Starting on 17 December 1659, Henry Vane representing the Parliament, Major Saloway and Colonel Salmon with powers from the officers of the army to treat with the fleet, and Vice-Admiral Lawson met in negotiating a compromise. The navy was very adverse to any proposal of terms to be made with the Parliament before Parliament\'s readmission, insisting upon the absolute submission of the army to the authority of Parliament. A plan was then put in place declaring a resolution to join with the Generals at Portsmouth, Colonel Monck, and Vice-Admiral Lawson, but it was still unknown to the republican party that Colonel Monck was in league with King Charles II.
Colonel Monck, though a hero to the restoration of King Charles II, was also treacherously disloyal to the Long Parliament, to his oath to the present Parliament, and to the Good Old Cause. Ludlow stated in early January 1660 when in conversation with several key officers of the army:
This statement may be verified by the many executions of key Parliament members and Generals after the restoration of King Charles II. Therefore, the restoration of King Charles II could not be an act of the Long Parliament acting freely under its own authority, but only under the influence of the sword by Colonel Monck, who traded his loyalties for the present Long Parliament, in preference to a reformed Long Parliament and to the restoration of King Charles II.
General George Monck, who had been Cromwell\'s viceroy in Scotland, feared that the military stood to lose power and secretly shifted his loyalty to the Crown. As he began to march south, Lambert, who had ridden out to face him, lost support in London. However, the Navy declared for Parliament, and on 26 December 1659 the Rump was restored to power.
On 9 January 1660, Monck arrived in London and his plans were communicated. Whereupon Henry Vane the Younger was discharged from being a member of the Long Parliament; and Major Saloway was reproved for his role and committed to the Tower during the pleasure of the house. Lieutenant-General Fleetwood, Col. Sydenham, Lord Commissioner Whitlock, Cornelius Holland, and Mr. Strickland were required to clear themselves touching their deportment in that affair. High treason was also declared against Miles Corbet, Cor. John Jones, Col. Thomlinson, and Edmond Ludlow on 19 January 1660. 1,500 other officers were removed from their command and \"scarce one of ten of the old officers of the army were continued\". Any known Anabaptists in the army were specifically discharged. So tame had Parliament become, that though it was most visible that Monck\'s letters and Arthur Haslerig\'s instructions were designed for the dissolution of the Long Parliament, they were obeyed by the remainder of the members and all these designs were to be put into execution. Though named by Parliament for treason, Miles Corbet and Edmond Ludlow were for a while were permitted to continue to sit with Parliament, and for a time the charges against these men were dropped.
| 1,156 |
Long Parliament
| 6 |
18,065 |
# Long Parliament
## Restoration and dissolution of the Long Parliament (21 February -- 16 March 1660) {#restoration_and_dissolution_of_the_long_parliament_21_february_16_march_1660}
After his initial show of deference to the Rump, Monck quickly found them unwilling to continue in cooperation with his plan for an election of a new parliament (the Rump Parliament believed Monck was accountable to them and had its own plan for free elections); so on 21 February 1660 he forcibly reinstated the members \'secluded\' by Pride\'s purge in 1648, so that they could prepare legislation for the Convention Parliament. Some of the Rump Parliament were opposed and refused to sit with the Secluded Members.
On 27 February 1660, \"the new Council of State being informed of some designs against the usurped power, issued out warrants for apprehending divers officers of the army; and having some jealousy of others that were members of Parliament, they procured an order of their House to authorize them to seize any member who had not sat since the coming in of the Secluded Members, if there should be occasion.
When the house was ready to pass the act for dissolution, Crew who had been as forward as any man in beginning and carrying on the war against the last King, moved, that before they dissolved themselves, they would bear their witness against the horrid murder, as he called it, of the King. According to Ludlow:
Having called for elections for a new Parliament to meet on 25 April, the Long Parliament was dissolved on 16 March 1660.
Finally, on 22 April 1660, \"Major-General Lambert\'s party was dispersed\" and General Lambert taken prisoner by Colonel Ingoldsby.
| 270 |
Long Parliament
| 7 |
18,065 |
# Long Parliament
## Aftereffects: royalist and republican theories {#aftereffects_royalist_and_republican_theories}
\"Hitherto Monk had continued to make solemn protestations of his affection and fidelity to the Commonwealth interest, against a King and House of Lords; but the new militia being settled, and a Convention, calling themselves a Parliament and fit for his purpose, being met at Westminster, he sent to such lords as had sat with the Parliament till 1648, to return to the place where they used to sit, which they did, upon assurance from him, that no others should be permitted to sit with them; which promise he also broke, and let in not only such as had deserted to Oxford, but the late created lords. And Charles Stuart, eldest son of the late King, being informed of these transactions, left the Spanish territories where he then resided, and by the advice of Monk went to Breda, a town belonging to the States of Holland: from when he sent his letters and a declaration to the two House by Sir John Greenvil; whereupon the nominal House of Commons, though called by a Commonwealth writ in the name of the Keepers of the Liberties of England, passed a vote \[on about April 25, 1660\], \'That the government of the nation should be by a King, Lords and Commons, and that Charles Stuart should be proclaimed King of England\'\".
\"The Lord Mayor, Sheriffs and Aldermen of the City, treated their King with a collation under a tent, placed in St. George\'s Fields; and five or six hundred citizens cloathed in coats of black velvet, and (not improperly) wearing chains about their necks, by an order of the Common Council, attended on the triumph of that day; \... and those who had been so often defeated in the field, and had contributed nothing either of bravery or policy to this change, in ordering the souldiery to ride with swords drawn through the city of London to White Hall, the Duke of York and Monk leading the way; and intimating (as was supposed) a resolution to maintain that by force which had been obtained by fraud\".
Initially seven, and later \'twenty persons were put to death for life and estate.\' These included: Chief Justice Coke, who had been Solicitor to the High Court of Justice, Major-General Harrison, Col. John Jones (also a member of the High Court of Justice), Mr. Thomas Scot, Sir. Henry Vane, Sir. Arthur Haslerig, Sir. Henry Mildmay, Mr. Robert Wallop, the Lord Mounson, Sir. James Harrington, Mr. James Challoner, Mr. John Phelps, Mr. John Carew, Mr. Hugh Peters, Mr. Gregory Clement, Colonel Adrian Scroop, Col. Francis Hacker, Col. Daniel Axtel. Among those who appeared the most basely subservient to these \'exorbitancies\' of the Court, \'Mr. William Prynn was singularly remarkable\' and attempted to add to these all who \'abjured the family of the Stuarts\' previously, though this motion failed.
\"John Finch who had been accused of high treason twenty years before, by a full Parliament, and who by flying from their justice had saved his life, was appointed to judge some of those who should have been his judges; and Sir. Orlando Bridgman, who upon his submission to Cromwell had been permitted to practice the law in a private manner, and under that colour had served both as spy and agent for his master, was entrusted with the principal management of this tragic scene; and in his charge to the Grand Jury, had the assurance to tell them \'That no authority, no single person, or community of men; not the people collectively or representatively, had any coercive power over the King of England\'\".
In framing the Act of Indemnity and Oblivion, the House of Commons were unwilling to except Sir Henry Vane, Sir. Arthur Haslerig, and Major-General Lambert as they had no immediate hand in the death of the King, and there was as much reason to except them as most of the members of Parliament from its benefits. In Henry Vane\'s case the House of Lords were desirous of having him specifically excepted, so as to leave him at the mercy of the government and thus restrain him from the exercise of his great talents in promoting his favourite republican principles at any time during the remainder of his life. At a conference between the two Houses, it was concluded that the Commons should consent to except him from the act of indemnity, the Lords agreeing, on their part, to concur with the other House in petitioning the King, in case of the condemnation of Vane, not to carry the sentence into execution. General Edmond Ludlow, still loyal to the Rump Parliament was also excepted.
According to contemporary royalist legal theory, the Long Parliament was regarded as having been automatically dissolved from the moment of Charles I\'s execution on 30 January 1649. This view was confirmed by a court ruling during the treason trial of Henry Vane the Younger -- a ruling that Henry Vane himself had concurred with in opposition to Oliver Cromwell years earlier.
The trial given to Vane as to his own person, and defence of his own part played for the Long Parliament was a foregone conclusion. It was not a fair trial as both his defence, and deportment at the time of defence bears out. He was not given legal counsel (other than the judges that sat at his trial); and was left to conduct his own defence after years in prison. Sir Henry Vane maintained the following at his trial:
1. Whether the collective body of the Parliament can be impeached of high treason?
2. Whether any person, acting by authority of Parliament, can (so long as he acting by that authority) commit treason?
3. Whether matters, acted by that authority, can be called in question in an inferior court?
4. Whether a king *de jure*, and out of possession, can have treason committed against him?
King Charles II did not keep the promise made to the house but executed the sentence of death on Sir Henry Vane the Younger. The solicitor, openly declared in his speech afterwards \"that he (Henry Vane) must be made a public sacrifice\". One of his judges stated: \"We knew not how to answer him, but we know what to do with him\".
Edmond Ludlow one of the members of Parliament excepted by the act of indemnity, fled to Switzerland after the restoration of King Charles II, where he wrote his memoirs of these events.
The Long Parliament began with the execution of Lord Stafford, and effectively ended with the execution of Henry Vane the Younger.
The republican theory is that the goal and aim of the Long Parliament was to institute a constitutional, balanced, and equally representative form of government along similar lines as were later accomplished in America by the American Revolution. It is clear from the writings of both Ludlow, Vane, and historians of the early American period such as Upham, that this is what they were striving for and why they were excepted from the acts of indemnity. The republican theory also suggests that the Long Parliament would have been successful in these necessary reforms except through the forceful intervention of Oliver Cromwell (and others) in removing the loyalists party, the unlawful execution of King Charles I, later dissolving the Rump Parliament; and finally the forceful dissolution of the reconvened Rump Parliament by Monck when less than a fourth of the required members were present. It is believed that in many ways this struggle was but a precursor to the American Revolution.
## Notable members of the Long Parliament {#notable_members_of_the_long_parliament}
- Sir Arthur Haselrig
- Sir Benjamin Rudyerd
- Carew Raleigh
- Denzil Holles, 1st Baron Holles
- Edmond Ludlow
- Edward Hyde, 1st Earl of Clarendon
- Sir Francis Seymour, 1st Baron Seymour of Trowbridge
- George Digby, 2nd Earl of Bristol
- Sir Henry Vane the Elder
- Sir Henry Vane the Younger
- James Temple
- Sir John Coolepeper
- John Hampden
- John Pym
- Lucius Cary, 2nd Viscount Falkland
- Sir Nicholas Crisp
- Nicholas Slanning
- Oliver Cromwell
- Oliver St John
- Sir Robert Harley
- Samuel Vassall
- Simonds D\'Ewes
- Major-General Harrison
- William Lenthall
- William Russell, 1st Duke of Bedford
- William Strode
| 1,381 |
Long Parliament
| 8 |
18,065 |
# Long Parliament
## Timeline
- Archbishop William Laud impeached December 1640, imprisoned 26 February 1641
- *Triennial Act*, passed 15 February 1641
- Act against Dissolving the Long Parliament without its own Consent 11 May 1641
- Thomas Wentworth, 1st Earl of Strafford executed 12 May 1641
- Abolition of the Star Chamber 5 July 1641
- *Ship Money* declared illegal 7 August 1641
- Grand Remonstrance 22 November 1641
- *Militia Bill* December 1641
- The King\'s answer to the petition accompanying the *Grand Remonstrance* 23 December 1641
- The King\'s attempt to seize the Five Members 4 January 1642
- The King and Royal Family leave Whitehall for Hampton Court
| 113 |
Long Parliament
| 9 |
18,073 |
# L cut
In film editing, an **L cut** is a variant of a split edit technique in which the audio from the preceding scene overlaps the picture from the following scene, so that the audio cuts after the picture, and continues playing over the beginning of the next scene.
The name of the cut refers to the shape of audio and video pieces of the second of two scenes cut together when it was done on analog film. This creates a shape similar to the letter \"L\" on the timeline, with the main body representing the video from the previous clip and the foot of the \"L\" representing the continuing audio. The L-Cut frequently appears in interviews, documentaries, and dialogue-heavy video scenes
| 123 |
L cut
| 0 |
18,077 |
# Lexicon
A **lexicon** (plural: **lexicons**, rarely **lexica**) is the vocabulary of a language or branch of knowledge (such as nautical or medical). In linguistics, a lexicon is a language\'s inventory of lexemes. The word *lexicon* derives from Greek word *λεξικόν* (*lexikon*), neuter of *λεξικός* (*lexikos*) meaning \'of or for words\'.
Linguistic theories generally regard human languages as consisting of two parts: a lexicon, essentially a catalogue of a language\'s words (its wordstock); and a grammar, a system of rules which allow for the combination of those words into meaningful sentences. The lexicon is also thought to include bound morphemes, which cannot stand alone as words (such as most affixes). In some analyses, compound words and certain classes of idiomatic expressions, collocations and other phrasemes are also considered to be part of the lexicon. Dictionaries are lists of the lexicon, in alphabetical order, of a given language; usually, however, bound morphemes are not included.
## Size and organization {#size_and_organization}
Items in the lexicon are called lexemes, lexical items, or word forms. Lexemes are not atomic elements but contain both phonological and morphological components. When describing the lexicon, a reductionist approach is used, trying to remain general while using a minimal description. To describe the size of a lexicon, lexemes are grouped into lemmas. A lemma is a group of lexemes generated by inflectional morphology. Lemmas are represented in dictionaries by headwords that list the citation forms and any irregular forms, since these must be learned to use the words correctly. Lexemes derived from a word by derivational morphology are considered new lemmas. The lexicon is also organized according to open and closed categories. Closed categories, such as determiners or pronouns, are rarely given new lexemes; their function is primarily syntactic. Open categories, such as nouns and verbs, have highly active generation mechanisms and their lexemes are more semantic in nature.
| 310 |
Lexicon
| 0 |
18,077 |
# Lexicon
## Lexicalization and other mechanisms in the lexicon {#lexicalization_and_other_mechanisms_in_the_lexicon}
A central role of the lexicon is documenting established *lexical norms and conventions*. Lexicalization is the process by which new words, having gained widespread usage, enter the lexicon. Since lexicalization may modify lexemes phonologically and morphologically, it is possible that a single etymological source may be inserted into a single lexicon in two or more forms. These pairs, called a doublet, are often close semantically. Two examples are *aptitude* versus *attitude* and *employ* versus *imply*.
The mechanisms, not mutually exclusive, are:
- Innovation, the planned creation of new roots (often on a large-scale), such as *slang*, *branding*.
- Borrowing of foreign words.
- Compounding (composition), the combination of lexemes to make a single word.
- Abbreviation of compounds.
- Acronyms, the reduction of compounds to their initial letters, such as NASA and laser (from \"LASER\").
- Inflection, a morphology change with a category, such as a number or tense.
- Derivation, a morphological change resulting in a change of category.
- Agglutination, the compounding of morphemes into a single word.
### Neologisms (new words) {#neologisms_new_words}
Neologisms are new lexeme candidates which, if they gain wide usage over time, become part of a language\'s lexicon. Neologisms are often introduced by children who produce erroneous forms by mistake. Other common sources are slang and advertising.
### Neologisms that maintain the sound of their external source {#neologisms_that_maintain_the_sound_of_their_external_source}
There are two types of borrowings (neologisms based on external sources) that retain the sound of the source language material:
- Borrowing using the source language lexical item as the basic material for the neologization: guestwords, foreignisms and loanwords
- Borrowing using a target language lexical items as the basic material for the neologization: phono-semantic matching, semanticized phonetic matching and phonetic matching.
#### Guestwords, foreignisms and loanwords {#guestwords_foreignisms_and_loanwords}
The following are examples of external lexical expansion using the source language lexical item as the basic material for the neologization, listed in decreasing order of phonetic resemblance to the original lexical item (in the source language):
- Guestword (in German: *Gastwort*): unassimilated borrowing.
- Foreignism (in German: *Fremdwort*): foreign word, e.g. phonetic adaptation.
- Loanword (in German: *Lehnwort*): totally assimilated borrowing, e.g. morphemic adaptation.
#### Phono-semantic matches, semanticized phonetic matches and phonetic matches {#phono_semantic_matches_semanticized_phonetic_matches_and_phonetic_matches}
The following are examples of simultaneous external and internal lexical expansion using target language lexical items as the basic material for the neologization but still resembling the sound of the lexical item in the source language:
- Phono-semantic matching (PSM): the target language material is originally similar to the source language lexical item both phonetically and semantically.
- Semanticized phonetic matching (SPM): the target language material is originally similar to the source language lexical item phonetically, and only in a loose way semantically.
- Phonetic matching (PM): the target language material is originally similar to the source language lexical item phonetically but not semantically.
### Role of morphology {#role_of_morphology}
Another mechanism involves generative devices that combine morphemes according to a language\'s rules. For example, the suffix \"-able\" is usually only added to transitive verbs, as in \"readable\" but not \"cryable\".
### Compounding
A compound word is a lexeme composed of several established lexemes, whose semantics is not the sum of that of their constituents. They can be interpreted through analogy, common sense and, most commonly, context. Compound words can have simple or complex morphological structures. Usually, only the head requires inflection for agreement. Compounding may result in lexemes of unwieldy proportion. This is compensated by mechanisms that reduce the length of words. A similar phenomenon has been recently shown to feature in social media also where hashtags compound to form longer-sized hashtags that are at times more popular than the individual constituent hashtags forming the compound. Compounding is the most common of word formation strategies cross-linguistically.
## Diachronic mechanisms {#diachronic_mechanisms}
Comparative historical linguistics studies the evolution of languages and takes a diachronic view of the lexicon. The evolution of lexicons in different languages occurs through a parallel mechanism. Over time historical forces work to shape the lexicon, making it simpler to acquire and often creating an illusion of great regularity in language.
- Phonological assimilation, the modification of loanwords to fit a new language\'s sound structure more effectively. If, however, a loanword sounds too \"foreign\", inflection or derivation rules may not be able to transform it.
- Analogy, where new words undergo inflection and derivation analogous to that of words with a similar sound structure.
- Emphasis, the modification of words\' stress or accent.
- Metaphor, a form of semantic extension.
| 759 |
Lexicon
| 1 |
18,077 |
# Lexicon
## Second-language lexicon {#second_language_lexicon}
The term \"lexicon\" is generally used in the context of a single language. Therefore, multi-lingual speakers are generally thought to have multiple lexicons. Speakers of language variants (Brazilian Portuguese and European Portuguese, for example) may be considered to possess a single lexicon. Thus a *cash dispenser* (British English) as well as an automatic teller machine or ATM in American English would be understood by both American and British speakers, despite each group using different dialects.
When linguists study a lexicon, they consider such things as what constitutes a word; the word/concept relationship; lexical access and lexical access failure; how a word\'s phonology, syntax, and meaning intersect; the morphology-word relationship; vocabulary structure within a given language; language use (pragmatics); language acquisition; the history and evolution of words (etymology); and the relationships between words, often studied within philosophy of language.
Various models of how lexicons are organized and how words are retrieved have been proposed in psycholinguistics, neurolinguistics and computational linguistics
| 165 |
Lexicon
| 2 |
18,087 |
# Lonsdaleite
**Lonsdaleite** (named in honour of Kathleen Lonsdale), also called **hexagonal diamond** in reference to the crystal structure, is an allotrope of carbon with a hexagonal lattice, as opposed to the cubical lattice of conventional diamond. It is found in nature in meteorite debris; when meteors containing graphite strike the Earth, the immense heat and stress of the impact transforms the graphite into diamond, but retains graphite\'s hexagonal crystal lattice. Lonsdaleite was first identified in 1967 from the Canyon Diablo meteorite, where it occurs as microscopic crystals associated with ordinary diamond.
It is translucent and brownish-yellow and has an index of refraction of 2.40--2.41 and a specific gravity of 3.2--3.3. Its hardness is theoretically superior to that of cubic diamond (up to 58% more), according to computational simulations, but natural specimens exhibited somewhat lower hardness through a large range of values (from 7--8 on Mohs hardness scale). The cause is speculated to be due to the samples having been riddled with lattice defects and impurities.
In addition to meteorite deposits, hexagonal diamond has been synthesized in the laboratory (1966 or earlier; published in 1967) by compressing and heating graphite either in a static press or using explosives.
## Hardness
According to the conventional interpretation of the results of examining the meagre samples collected from meteorites or manufactured in the lab, lonsdaleite has a hexagonal unit cell, related to the diamond unit cell in the same way that the hexagonal and cubic close packed crystal systems are related. Its diamond structure can be considered to be made up of interlocking rings of six carbon atoms, in the chair conformation. In lonsdaleite, some rings are in the boat conformation instead. At nanoscale dimensions, cubic diamond is represented by *diamondoids* while hexagonal diamond is represented by *wurtzoids*.
In diamond, all the carbon-to-carbon bonds, both within a layer of rings and between them, are in the staggered conformation, thus causing all four cubic-diagonal directions to be equivalent; whereas in lonsdaleite the bonds between layers are in the eclipsed conformation, which defines the axis of hexagonal symmetry.
Mineralogical simulation predicts lonsdaleite to be 58% harder than diamond on the \<100\> face, and to resist indentation pressures of 152 GPa, whereas diamond would break at 97 GPa.
- This is yet exceeded by IIa diamond\'s \<111\> tip hardness of 162 GPa.
The extrapolated properties of lonsdaleite have been questioned, particularly its superior hardness, since specimens under crystallographic inspection have not shown a bulk hexagonal lattice structure, but instead a conventional cubic diamond dominated by structural defects that include hexagonal sequences. A quantitative analysis of the X-ray diffraction data of lonsdaleite has shown that about equal amounts of hexagonal and cubic stacking sequences are present. Consequently, it has been suggested that \"stacking disordered diamond\" is the most accurate structural description of lonsdaleite. On the other hand, recent shock experiments with in situ X-ray diffraction show strong evidence for creation of relatively pure lonsdaleite in dynamic high-pressure environments comparable to meteorite impacts.
## Occurrence
Lonsdaleite occurs as microscopic crystals associated with diamond in several meteorites: Canyon Diablo, Kenna, and Allan Hills 77283. It is also naturally occurring in non-bolide diamond placer deposits in the Sakha Republic. Material with d-spacings consistent with Lonsdaleite has been found in sediments with highly uncertain dates at Lake Cuitzeo, in the state of Guanajuato, Mexico, by proponents of the controversial Younger Dryas impact hypothesis, which is now refuted by earth scientists and planetary impact specialists. Claims of Lonsdaleite and other nanodiamonds in a layer of the Greenland ice sheet that could be of Younger Dryas age have not been confirmed and are now disputed. Its presence in local peat deposits is claimed as evidence for the Tunguska event being caused by a meteor rather than by a cometary fragment.
## Manufacture
In addition to laboratory synthesis by compressing and heating graphite either in a static press or using explosives, lonsdaleite has also been produced by chemical vapor deposition, and also by the thermal decomposition of a polymer, poly(hydridocarbyne), at atmospheric pressure, under argon atmosphere, at 1000 °C.
In 2020, researchers at Australian National University found by accident they were able to produce lonsdaleite at room temperatures using a diamond anvil cell.
In 2021, Washington State University\'s Institute for Shock Physics published a paper stating that they created lonsdaleite crystals large enough to measure their stiffness, confirming that they are stiffer than common cubic diamonds. However, the explosion used to create these crystals also destroys them nanoseconds later, providing just enough time to measure stiffness with lasers.
| 754 |
Lonsdaleite
| 0 |
18,087 |
# Lonsdaleite
## Scams
Since the characteristics of lonsdaleite are unknown to most people outside of scientists trained in geology and mineralogy, the names \"lonsdaleite\" and \"hexagonal diamond\" have frequently been used in the fraudulent sale of ceramic artifacts passed off as meteorites on online e-commerce sites and at street fairs and street markets, with prices ranging from a few dollars to thousands of dollars
| 65 |
Lonsdaleite
| 1 |
18,089 |
# Lettres de cachet
***Lettres de cachet*** (`{{IPA|fr|lɛtʁ də kaʃɛ|lang}}`{=mediawiki}; `{{literal translation|"letters of the sign/signet"}}`{=mediawiki}) were letters signed by the king of France, countersigned by one of his ministers, and closed with the royal seal. They contained orders directly from the king, often to enforce actions and judgments that could not be appealed.
In the case of organized bodies, *lettres de cachet* were issued for the purpose of preventing assembly, or to accomplish some other definite act. The provincial estates were convoked (called to assembly) in this manner, and it was by a *lettre de cachet* (in this case, a *lettre de jussipri*), or by showing in person in a *lit de justice*, that the king ordered a *parlement* to register a law despite that *parlement*{{\'}}s refusal to pass it.
The best-known *lettres de cachet*, however, were penal, by which a subject was imprisoned without trial and without an opportunity of defense (after inquiry and due diligence by the *lieutenant de police*) in a state prison or an ordinary jail, confined in a convent or the General Hospital of Paris, transported to the colonies, or expelled to another part of the realm, or from the realm altogether. The *lettres* were mainly used against drunkards, troublemakers, prostitutes, squanderers of the family fortune, or insane persons. The wealthy sometimes petitioned such *lettres* to dispose of inconvenient individuals, especially to prevent unequal marriages (nobles with commoners), or to prevent a scandal (the *lettre* could prevent court cases that might otherwise dishonour a family).
In this respect, the *lettres de cachet* were a prominent symbol of the abuses of the *ancien régime* monarchy, and as such were suppressed during the French Revolution. In 1789 and 1790, all cases were reviewed by a commission which confirmed most of the sentences. Historian Claude Quétel has interpreted these confirmations as indicating that the *lettres* were not as arbitrary and unjust as they have been represented after the Revolution, and he hence speaks of a *Légende noire*.
| 329 |
Lettres de cachet
| 0 |
18,089 |
# Lettres de cachet
## History
The power to issue *lettres de cachet* was a royal privilege recognized by the French monarchic civil law that developed during the 13th century, as the Capetian monarchy overcame its initial distrust of Roman law. The principle can be traced to a maxim which furnished a text of the *Pandects* of Justinian: in their Latin version, \"*Rex solutus est a legibus*\", or \"The king is released from the laws\". \"The French legal scholars interpreted the imperial office of the Justinian code generically and arrived at the conclusion that every \'king is an emperor in his own kingdom\', that is, he possesses the prerogatives of legal absolutism that the *Corpus Juris Civilis* attributes to the Roman emperor.\"
This meant that when the king intervened directly, he could decide without heeding the laws, and even contrary to the laws. This was an early conception, and in early times the order in question was simply verbal; some letters patent of Henry III in 1576 state that François de Montmorency was \"prisoner in our castle of the Bastille in Paris by verbal command\" of the late king Charles IX.
In the 14th century, the principle was introduced that the order should be written, and hence arose the *lettre de cachet*. The *lettre de cachet* belonged to the class of *lettres closes*, as opposed to *lettres patentes*, which contained the expression of the legal and permanent will of the king, and had to be furnished with the seal of state affixed by the chancellor.
The *lettres de cachet*, on the contrary, were signed simply by a secretary of state for the king; they bore merely the imprint of the king\'s privy seal, from which circumstance they were often called, in the 14th and 15th centuries, *lettres de petit signet* or *lettres de petit cachet*, and were entirely exempt from the control of the chancellor.
## As a tool {#as_a_tool}
In addition to serving the government as a silent weapon against political adversaries or controversial writers and as a means of punishing culprits of high birth without the scandal of a lawsuit, the *lettres de cachet* had many other uses. They were employed by the police in dealing with prostitutes, and on their authority lunatics were shut up in hospitals and sometimes in prisons.
They were also often used by heads of families as a means of correction, for example, to protect the family honour from the disorderly or criminal conduct of sons. The case of the Marquis de Sade (imprisoned 1777--1790 under a *lettre de cachet* obtained by his wealthy and influential mother-in-law) is a prominent example. Wives, too, took advantage of them to curb the profligacy of husbands, and vice versa.
In reality, the secretary of state had delegated powers, and could issue them at his own discretion, and in most cases the king was unaware of their issue. In the 18th century the letters were often issued blank, i.e. without containing the name of the person against whom they were directed; the recipient, or mandatary, filled in the name in order to make the letter effective.
| 519 |
Lettres de cachet
| 1 |
18,089 |
# Lettres de cachet
## Protests
Protests against the *lettres de cachet* were made continually by the *Parlement* of Paris and by the provincial *parlements*, and also by the Estates-General. In 1648, during the Fronde, the sovereign courts of Paris, by their *Arrêt d\'Union*, procured their momentary suppression in a kind of charter of liberties which they imposed upon the crown, but which was short-lived.
It was not until the reign of Louis XVI that a reaction against the abuse became clearly perceptible. At the beginning of that reign Malesherbes during his short ministry endeavoured to infuse some measure of justice into the system, and in March 1784 the baron de Breteuil, a minister of the king\'s household, addressed a circular to the intendants and the lieutenant of police with a view to preventing the most serious abuses connected with the issue of *lettres de cachet*.
The Comte de Mirabeau wrote a scathing indictment of *lettres de cachet* while imprisoned in the dungeon of Vincennes (by *lettre de cachet* obtained by his father). The treatise was published after his liberation in 1782 under the title *Les Lettres de cachet et des prisons d\'etat* and was widely read throughout Europe.
Besides the Bastille, there were thirty prisons in Paris by 1779 in which a person could be detained without trial. Convents were used for the same purpose.
They were reported to have been openly sold, in the reign of Louis XV, by the mistress of one of his ministers.
In Paris, in 1779, the Cour des Aides demanded their suppression, and in March 1788 the *Parlement* of Paris made some exceedingly energetic remonstrances, which are important for the light they throw upon old French public law. The crown, however, did not decide to lay aside this weapon, and in a declaration to the States-General in the royal session of June 23, 1789 (art. 15) it did not renounce it absolutely.
## Abolition and reinstatement {#abolition_and_reinstatement}
*Lettres de cachet* were abolished after the French Revolution by the Constituent Assembly, but Napoleon reestablished their penal equivalent by a political measure in the decree of 8 March 1801 on the state prisons. This was one of the acts brought up against him by the senatus-consulte of 3 April 1814, which pronounced his fall \"considering that he has violated the constitutional laws by the decrees on the state prisons.\"
| 394 |
Lettres de cachet
| 2 |
18,089 |
# Lettres de cachet
## Victims of *lettres de cachet* {#victims_of_lettres_de_cachet}
- Charles Simon Favart (because a nobleman was interested in his wife)
- Luke Joseph Hooke (deprived of his academic chair in theology for awarding a PhD to a candidate without having read the (heretical) thesis.)
- Honoré Gabriel Riqueti, comte de Mirabeau (several times, on request of his father, as protection against creditors and once to prevent a death penalty for kidnapping and eloping with a married woman)
- Marguerite Monvoisin (complicity in a poisoning affair. A *lettre de cachet* was used to avoid a scandal that might have affected Françoise-Athénaïs, marquise de Montespan, a mistress of the King who was assumed to have been involved).
- Pigault-Lebrun (twice, for eloping with two successive young women)
- Alexandre Balthazar Laurent Grimod de La Reynière (misconduct: sent away to an abbey by his father)
- Marquis de Sade (rape and torture. The *lettre* was petitioned by the marquis\' wife, to avoid a court case)
- Comte de Sanois (domestic disputes and debt. His wife petitioned a Lettre, claiming her husband insane)
- Voltaire (once for slander, a second time for violent menaces against the Prince de Rohan)
- Jean-François Marmontel, accused to be the author of a satire against the Duke d\'Aumont. His account of his short stay in the Bastille contains a description of the food he received, the room he was imprisoned with his servant, and the goodwill shown to him.
- Giacomo Casanova (dueling)
- Marie-Anne de La Ville (practiced black magic. A scandalous trial was avoided by a *lettre*)
- Jean-Baptiste Forqueray (request of his father)
## In literature {#in_literature}
- Honoré de Mirabeau, [*Des Lettres de Cachet et des prisons d\'état*](https://books.google.com/books?id=b1sGAAAAQAAJ&pg=PR1) (Hamburg, 1782), written in the dungeon at Vincennes into which his father had thrown him by a *lettre de cachet*, one of the ablest and most eloquent of his works, which had an immense circulation and was translated into English in 1788.
- *The Castle of Wolfenbach*, one of the \"Horrid Novels\" mentioned in *Northanger Abbey* by Jane Austen, features a *lettre de cachet* as a major plot point when the main villain, the guardian of a young lady who has run away, tries to use a *lettre de cachet* to obligate her to be returned to him so he can force her into marriage.
- Doctor Alexandre Manette, in Charles Dickens\' *A Tale of Two Cities*, was thrown into the Bastille prison by means of a *lettre de cachet*. In addition, Charles Darnay suspected that his uncle, a marquis, would have used a *lettre de cachet* to put Darnay himself into prison had the Marquis not fallen out of favour with the royal court
| 452 |
Lettres de cachet
| 3 |
18,090 |
# Lilia Podkopayeva
**Lilia Oleksandrivna Podkopayeva** (*Лілія Олександрівна Подкопаєва*; born 15 August 1978) is a Ukrainian former artistic gymnast. She is the 1995 world all-around champion, and the 1996 Olympic all-around and floor exercise champion. Often thought of as a complete athlete, Podkopayeva was known for combining power, style, and balletic grace.
## Gymnastics career {#gymnastics_career}
### 1993--95
In March 1993, Lilia won her only National All Around Title in Ukraine. In April 1993, Podkopayeva competed at the World Artistic Gymnastics Championships in Birmingham, England. She qualified for the vault final, but crashed on her first attempt and finished last with a score of 8.893.
At the 1994 World Championships in Brisbane, Australia, she placed sixth in the all-around with a score of 38.942. In event finals, she placed eighth on vault, scoring 9.424; fifth on uneven bars, scoring 9.350; and second on balance beam, scoring 9.737. In November 1994, at the World Team Championships in Dortmund, Germany, she contributed an all-around score of 38.099 toward the Ukrainian team\'s fifth-place finish.
The following year, Podkopayeva competed at the 1995 World Championships in Sabae, Japan. She helped Ukraine place fifth and qualify a full team to the 1996 Olympics. Podkopayeva then won the all-around final with a score of 39.248. In event finals, she placed first on vault (9.781), second on uneven bars (9.837), second on balance beam (9.837), and seventh on floor (9.087).
### 1996 {#section_1}
At the beginning of the year, Podkopayeva was seriously injured when she fell from the beam in practice, fracturing two ribs. However, in May, she competed at the European Championships in Birmingham, where she helped the Ukrainian team place third and won the individual all-around with a score of 39.205. In event finals, she placed third on balance beam (9.756), first on uneven bars (9.825), and first on floor (9.862).
#### Atlanta Olympics {#atlanta_olympics}
In July, Podkopayeva competed at the 1996 Summer Olympics in Atlanta, Georgia. In the team final, she contributed a combined compulsory and optional score of 78.061 toward the Ukrainian team\'s fifth-place finish. She then won the all-around final with a score of 39.255. In event finals, she placed fifth on uneven bars (9.787), second on balance beam (9.825), and first on floor (9.887). She was the fourth gymnast to win the Olympic all-around title as the reigning world champion, and the first gymnast to win the all-around without winning a team medal. She was also the last female gymnast to win the all-around title and an event-final gold medal until Simone Biles did this in 2016.
### 1997 {#section_2}
Podkopayeva originally intended to continue competing after the 1996 Olympics, and she was named to the Ukrainian team for the 1997 World Championships. However, injuries forced her to sit out the competition and, later, to retire.
## Eponymous skills {#eponymous_skills}
Podkopayeva has two eponymous skills listed in the Code of Points.
Apparatus Name Description Difficulty
---------------- ------------- ------------------------------------------------------------------------------------------------------------------------------------------ ------------
Vault Podkopayeva Round-off flic-flac with `{{frac|1|2}}`{=mediawiki} turn (180°) on - piked salto forward with `{{frac|1|2}}`{=mediawiki} turn (180°) off 4.2
Floor exercise Podkopayeva Double salto forward tucked with `{{frac|1|2}}`{=mediawiki} turn (180°) F (0.6)
## Post-retirement {#post_retirement}
In 2002, Podkopayeva started the Golden Lilia International Sports Festival, an exhibition featuring artistic and rhythmic gymnasts, acrobats, and dancers. She said, \"It\'s important to us to show outstanding people and brightest talent so that the next generation can follow the best of the best.\"
In December 2004, she married a Ukrainian businessman Tymofiy Nahornyi. They have two children: Vadym, adopted in Ukraine in July 2006, and Karolina, born in November 2006. The couple divorced in 2009.
In 2005, Podkopayeva became a United Nations goodwill ambassador on HIV/AIDS in Ukraine. She is also an Ambassador of the Council of Europe for Sport, Tolerance, and Fair Play.
In 2007, she won Ukraine\'s *Dancing With the Stars* with partner Sergiy Kostetskyi. The next year, she represented Ukraine in the Eurovision Dance Contest. Along with partner Kyrylo Khytrov, she placed third in the competition.
In 2014, Podkopayeva did a gala event in Mexico, using similar choreography to the floor routine she performed in Atlanta, as well as doing back handsprings and round-offs.
In 2019, Podkopayeva joined the coaching staff at Marcus Jewish Community Center of Atlanta\'s Perimeter Gymnastics
| 708 |
Lilia Podkopayeva
| 0 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.