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Dynkin diagram

In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line). Dynkin diagrams arise in the classification of semisimple Lie algebras over algebraically closed fields, in the classification of Weyl groups and other finite reflection groups, and in other contexts. Various properties of the Dynkin diagram (such as whether it contains multiple edges, or its symmetries) correspond to important features of the associated Lie algebra.

The term "Dynkin diagram" can be ambiguous. In some cases, Dynkin diagrams are assumed to be directed, in which case they correspond to root systems and semi-simple Lie algebras, while in other cases they are assumed to be undirected, in which case they correspond to Weyl groups. In this article, "Dynkin diagram" means directed Dynkin diagram, and undirected Dynkin diagrams will be explicitly so named.

Classification of semisimple Lie algebras
The fundamental interest in Dynkin diagrams is that they classify semisimple Lie algebras over algebraically closed fields. One classifies such Lie algebras via their root system, which can be represented by a Dynkin diagram. One then classifies Dynkin diagrams according to the constraints they must satisfy, as described below.

Dropping the direction on the graph edges corresponds to replacing a root system by the finite reflection group it generates, the so-called Weyl group, and thus undirected Dynkin diagrams classify Weyl groups.

They have the following correspondence for the Lie algebras associated to classical groups over the complex numbers: For the exceptional groups, the names for the Lie algebra and the associated Dynkin diagram coincide.
 * $$A_n$$: $$\mathfrak {sl}_{n+1}$$, the special linear Lie algebra.
 * $$B_n$$: $$\mathfrak{so}_{2n+1}$$, the odd-dimensional special orthogonal Lie algebra.
 * $$C_n$$: $$\mathfrak {sp}_{2n}$$, the symplectic Lie algebra.
 * $$D_n$$: $$\mathfrak{so}_{2n}$$, the even-dimensional special orthogonal Lie algebra ($$n>1$$).

Related classifications
Dynkin diagrams can be interpreted as classifying many distinct, related objects, and the notation "An, Bn, ..." is used to refer to all such interpretations, depending on context; this ambiguity can be confusing.

The central classification is that a simple Lie algebra has a root system, to which is associated an (oriented) Dynkin diagram; all three of these may be referred to as Bn, for instance.

The unoriented Dynkin diagram is a form of Coxeter diagram, and corresponds to the Weyl group, which is the finite reflection group associated to the root system. Thus Bn may refer to the unoriented diagram (a special kind of Coxeter diagram), the Weyl group (a concrete reflection group), or the abstract Coxeter group.

Although the Weyl group is abstractly isomorphic to the Coxeter group, a specific isomorphism depends on an ordered choice of simple roots. Likewise, while Dynkin diagram notation is standardized, Coxeter diagram and group notation is varied and sometimes agrees with Dynkin diagram notation and sometimes does not.

Lastly, sometimes associated objects are referred to by the same notation, though this cannot always be done regularly. Examples include: These latter notations are mostly used for objects associated with exceptional diagrams – objects associated to the regular diagrams (A, B, C, D) instead have traditional names.
 * The root lattice generated by the root system, as in the E8 lattice. This is naturally defined, but not one-to-one – for example, A2 and G2 both generate the hexagonal lattice.
 * An associated polytope – for example Gosset 421 polytope may be referred to as "the E8 polytope", as its vertices are derived from the E8 root system and it has the E8 Coxeter group as symmetry group.
 * An associated quadratic form or manifold – for example, the E8 manifold has intersection form given by the E8 lattice.

The index (the n) equals to the number of nodes in the diagram, the number of simple roots in a basis, the dimension of the root lattice and span of the root system, the number of generators of the Coxeter group, and the rank of the Lie algebra. However, n does not equal the dimension of the defining module (a fundamental representation) of the Lie algebra – the index on the Dynkin diagram should not be confused with the index on the Lie algebra. For example, $$B_4$$ corresponds to $$\mathfrak{so}_{2\cdot 4 + 1} = \mathfrak{so}_9,$$ which naturally acts on 9-dimensional space, but has rank 4 as a Lie algebra.

The simply laced Dynkin diagrams, those with no multiple edges (A, D, E) classify many further mathematical objects; see discussion at ADE classification.

Example: A2

For example, the symbol $$A_2$$ may refer to:
 * The Dynkin diagram with 2 connected nodes,, which may also be interpreted as a Coxeter diagram.
 * The root system with 2 simple roots at a $$2\pi/3$$ (120 degree) angle.
 * The Lie algebra $$\mathfrak{sl}_{2+1} = \mathfrak{sl}_3$$ of rank 2.
 * The Weyl group of symmetries of the roots (reflections in the hyperplane orthogonal to the roots), isomorphic to the symmetric group $$S_3$$ (of order 6).
 * The abstract Coxeter group, presented by generators and relations, $$\left\langle r_1,r_2 \mid (r_1)^2=(r_2)^2=(r_ir_j)^3=1\right\rangle.$$

Construction from root systems
Consider a root system, assumed to be reduced and integral (or "crystallographic"). In many applications, this root system will arise from a semisimple Lie algebra. Let $$\Delta$$ be a set of positive simple roots. We then construct a diagram from $$\Delta$$ as follows. Form a graph with one vertex for each element of $$\Delta$$. Then insert edges between each pair of vertices according to the following recipe. If the roots corresponding to the two vertices are orthogonal, there is no edge between the vertices. If the angle between the two roots is 120 degrees, we put one edge between the vertices. If the angle is 135 degrees, we put two edges, and if the angle is 150 degrees, we put three edges. (These four cases exhaust all possible angles between pairs of positive simple roots. ) Finally, if there are any edges between a given pair of vertices, we decorate them with an arrow pointing from the vertex corresponding to the longer root to the vertex corresponding to the shorter one. (The arrow is omitted if the roots have the same length.) Thinking of the arrow as a "greater than" sign makes it clear which way the arrow should go. Dynkin diagrams lead to a classification of root systems. The angles and length ratios between roots are related. Thus, the edges for non-orthogonal roots may alternatively be described as one edge for a length ratio of 1, two edges for a length ratio of $$\sqrt{2}$$, and three edges for a length ratio of $$\sqrt{3}$$. (There are no edges when the roots are orthogonal, regardless of the length ratio.)

In the $$A_2$$ root system, shown at right, the roots labeled $$\alpha$$ and $$\beta$$ form a base. Since these two roots are at angle of 120 degrees (with a length ratio of 1), the Dynkin diagram consists of two vertices connected by a single edge:.

Constraints
Dynkin diagrams must satisfy certain constraints; these are essentially those satisfied by finite Coxeter–Dynkin diagrams, together with an additional crystallographic constraint.

Connection with Coxeter diagrams
Dynkin diagrams are closely related to Coxeter diagrams of finite Coxeter groups, and the terminology is often conflated.

Dynkin diagrams differ from Coxeter diagrams of finite groups in two important respects:
 * Partly directed: Dynkin diagrams are partly directed – any multiple edge (in Coxeter terms, labeled with "4" or above) has a direction (an arrow pointing from one node to the other); thus Dynkin diagrams have more data than the underlying Coxeter diagram (undirected graph).
 * At the level of root systems the direction corresponds to pointing towards the shorter vector; edges labeled "3" have no direction because the corresponding vectors must have equal length. (Caution: Some authors reverse this convention, with the arrow pointing towards the longer vector.)

 * Crystallographic restriction: Dynkin diagrams must satisfy an additional restriction, namely that the only allowable edge labels are 2, 3, 4, and 6, a restriction not shared by Coxeter diagrams, so not every Coxeter diagram of a finite group comes from a Dynkin diagram.
 * At the level of root systems this corresponds to the crystallographic restriction theorem, as the roots form a lattice.

A further difference, which is only stylistic, is that Dynkin diagrams are conventionally drawn with double or triple edges between nodes (for p = 4, 6), rather than an edge labeled with "p".

The term "Dynkin diagram" at times refers to the directed graph, at times to the undirected graph. For precision, in this article "Dynkin diagram" will mean directed, and the underlying undirected graph will be called an "undirected Dynkin diagram". Then Dynkin diagrams and Coxeter diagrams may be related as follows: By this is meant that Coxeter diagrams of finite groups correspond to point groups generated by reflections, while Dynkin diagrams must satisfy an additional restriction corresponding to the crystallographic restriction theorem, and that Coxeter diagrams are undirected, while Dynkin diagrams are (partly) directed.

The corresponding mathematical objects classified by the diagrams are: The blank in the upper right, corresponding to directed graphs with underlying undirected graph any Coxeter diagram (of a finite group), can be defined formally, but is little-discussed, and does not appear to admit a simple interpretation in terms of mathematical objects of interest.

There are natural maps down – from Dynkin diagrams to undirected Dynkin diagrams; respectively, from root systems to the associated Weyl groups – and right – from undirected Dynkin diagrams to Coxeter diagrams; respectively from Weyl groups to finite Coxeter groups.

The down map is onto (by definition) but not one-to-one, as the Bn and Cn diagrams map to the same undirected diagram, with the resulting Coxeter diagram and Weyl group thus sometimes denoted BCn.

The right map is simply an inclusion – undirected Dynkin diagrams are special cases of Coxeter diagrams, and Weyl groups are special cases of finite Coxeter groups – and is not onto, as not every Coxeter diagram is an undirected Dynkin diagram (the missed diagrams being H3, H4 and I2(p) for p = 5 p ≥ 7), and correspondingly not every finite Coxeter group is a Weyl group.

Isomorphisms
Dynkin diagrams are conventionally numbered so that the list is non-redundant: $$n \geq 1$$ for $$A_n,$$ $$n \geq 2$$ for $$B_n,$$ $$n \geq 3$$ for $$C_n,$$ $$n \geq 4$$ for $$D_n,$$ and $$E_n$$ starting at $$n=6.$$ The families can however be defined for lower n, yielding exceptional isomorphisms of diagrams, and corresponding exceptional isomorphisms of Lie algebras and associated Lie groups.

Trivially, one can start the families at $$n=0$$ or $$n=1,$$ which are all then isomorphic as there is a unique empty diagram and a unique 1-node diagram. The other isomorphisms of connected Dynkin diagrams are:
 * $$A_1 \cong B_1 \cong C_1$$
 * $$B_2 \cong C_2$$
 * $$D_2 \cong A_1 \times A_1$$
 * $$D_3 \cong A_3$$
 * $$E_3 \cong A_1 \times A_2$$
 * $$E_4 \cong A_4$$
 * $$E_5 \cong D_5$$

These isomorphisms correspond to isomorphism of simple and semisimple Lie algebras, which also correspond to certain isomorphisms of Lie group forms of these. They also add context to the En family.

Automorphisms

In addition to isomorphism between different diagrams, some diagrams also have self-isomorphisms or "automorphisms". Diagram automorphisms correspond to outer automorphisms of the Lie algebra, meaning that the outer automorphism group Out = Aut/Inn equals the group of diagram automorphisms.

The diagrams that have non-trivial automorphisms are An ($$n > 1$$), Dn ($$n > 1$$), and E6. In all these cases except for D4, there is a single non-trivial automorphism (Out = C2, the cyclic group of order 2), while for D4, the automorphism group is the symmetric group on three letters (S3, order 6) – this phenomenon is known as "triality". It happens that all these diagram automorphisms can be realized as Euclidean symmetries of how the diagrams are conventionally drawn in the plane, but this is just an artifact of how they are drawn, and not intrinsic structure.

For An, the diagram automorphism is reversing the diagram, which is a line. The nodes of the diagram index the fundamental weights, which (for An−1) are $$\bigwedge^i C^n$$ for $$i=1,\dots,n$$, and the diagram automorphism corresponds to the duality $$\bigwedge^i C^n \mapsto \bigwedge^{n-i} C^n.$$ Realized as the Lie algebra $$\mathfrak{sl}_{n+1},$$ the outer automorphism can be expressed as negative transpose, $$T \mapsto -T^{\mathrm T}$$, which is how the dual representation acts.

For Dn, the diagram automorphism is switching the two nodes at the end of the Y, and corresponds to switching the two chiral spin representations. Realized as the Lie algebra $$\mathfrak{so}_{2n},$$ the outer automorphism can be expressed as conjugation by a matrix in O(2n) with determinant −1. When n = 3, one has $$\mathrm{D}_3 \cong \mathrm{A}_3,$$ so their automorphisms agree, while $$\mathrm{D}_2 \cong \mathrm{A}_1 \times \mathrm{A}_1$$ is disconnected, and the automorphism corresponds to switching the two nodes.

For D4, the fundamental representation is isomorphic to the two spin representations, and the resulting symmetric group on three letter (S3, or alternatively the dihedral group of order 6, Dih3) corresponds both to automorphisms of the Lie algebra and automorphisms of the diagram.

The automorphism group of E6 corresponds to reversing the diagram, and can be expressed using Jordan algebras.

Disconnected diagrams, which correspond to semisimple Lie algebras, may have automorphisms from exchanging components of the diagram.

In positive characteristic there are additional "diagram automorphisms" – roughly speaking, in characteristic p one is sometimes allowed to ignore the arrow on bonds of multiplicity p in the Dynkin diagram when taking diagram automorphisms. Thus in characteristic 2 there is an order 2 automorphism of $$\mathrm{B}_2 \cong \mathrm{C}_2$$ and of F4, while in characteristic 3 there is an order 2 automorphism of G2. But doesn't apply in all circumstances: for example, such automorphisms need not arise as automorphisms of the corresponding algebraic group, but rather on the level of points valued in a finite field.

Construction of Lie groups via diagram automorphisms
Diagram automorphisms in turn yield additional Lie groups and groups of Lie type, which are of central importance in the classification of finite simple groups.

The Chevalley group construction of Lie groups in terms of their Dynkin diagram does not yield some of the classical groups, namely the unitary groups and the non-split orthogonal groups. The Steinberg groups construct the unitary groups 2An, while the other orthogonal groups are constructed as 2Dn, where in both cases this refers to combining a diagram automorphism with a field automorphism. This also yields additional exotic Lie groups 2E6 and 3D4, the latter only defined over fields with an order 3 automorphism.

The additional diagram automorphisms in positive characteristic yield the Suzuki–Ree groups, 2B2, 2F4, and 2G2.

Folding
A (simply-laced) Dynkin diagram (finite or affine) that has a symmetry (satisfying one condition, below) can be quotiented by the symmetry, yielding a new, generally multiply laced diagram, with the process called folding (due to most symmetries being 2-fold). At the level of Lie algebras, this corresponds to taking the invariant subalgebra under the outer automorphism group, and the process can be defined purely with reference to root systems, without using diagrams. Further, every multiply laced diagram (finite or infinite) can be obtained by folding a simply-laced diagram.

The one condition on the automorphism for folding to be possible is that distinct nodes of the graph in the same orbit (under the automorphism) must not be connected by an edge; at the level of root systems, roots in the same orbit must be orthogonal. At the level of diagrams, this is necessary as otherwise the quotient diagram will have a loop, due to identifying two nodes but having an edge between them, and loops are not allowed in Dynkin diagrams.

The nodes and edges of the quotient ("folded") diagram are the orbits of nodes and edges of the original diagram; the edges are single unless two incident edges map to the same edge (notably at nodes of valence greater than 2) – a "branch point" of the map, in which case the weight is the number of incident edges, and the arrow points towards the node at which they are incident – "the branch point maps to the non-homogeneous point". For example, in D4 folding to G2, the edge in G2 points from the class of the 3 outer nodes (valence 1), to the class of the central node (valence 3).

The foldings of finite diagrams are:
 * $$A_{2n-1} \to C_n$$
 * (The automorphism of A2n does not yield a folding because the middle two nodes are connected by an edge, but in the same orbit.)

 * $$D_{n+1} \to B_n$$
 * $$D_4 \to G_2$$ (if quotienting by the full group or a 3-cycle, in addition to $$D_4 \to B_3$$ in 3 different ways, if quotienting by an involution)
 * $$E_6 \to F_4$$

Similar foldings exist for affine diagrams, including:
 * $$\tilde A_{2n-1} \to \tilde C_n$$
 * $$\tilde D_{n+1} \to \tilde B_n$$
 * $$\tilde D_4 \to \tilde G_2$$
 * $$\tilde E_6 \to \tilde F_4$$

The notion of foldings can also be applied more generally to Coxeter diagrams – notably, one can generalize allowable quotients of Dynkin diagrams to Hn and I2(p). Geometrically this corresponds to projections of uniform polytopes. Notably, any simply laced Dynkin diagram can be folded to I2(h), where h is the Coxeter number, which corresponds geometrically to projection to the Coxeter plane.

Folding can be applied to reduce questions about (semisimple) Lie algebras to questions about simply-laced ones, together with an automorphism, which may be simpler than treating multiply laced algebras directly; this can be done in constructing the semisimple Lie algebras, for instance. See Math Overflow: Folding by Automorphisms for further discussion.

Other maps of diagrams
Some additional maps of diagrams have meaningful interpretations, as detailed below. However, not all maps of root systems arise as maps of diagrams.

For example, there are two inclusions of root systems of A2 in G2, either as the six long roots or the six short roots. However, the nodes in the G2 diagram correspond to one long root and one short root, while the nodes in the A2 diagram correspond to roots of equal length, and thus this map of root systems cannot be expressed as a map of the diagrams.

Some inclusions of root systems can be expressed as one diagram being an induced subgraph of another, meaning "a subset of the nodes, with all edges between them". This is because eliminating a node from a Dynkin diagram corresponds to removing a simple root from a root system, which yields a root system of rank one lower. By contrast, removing an edge (or changing the multiplicity of an edge) while leaving the nodes unchanged corresponds to changing the angles between roots, which cannot be done without changing the entire root system. Thus, one can meaningfully remove nodes, but not edges. Removing a node from a connected diagram may yield a connected diagram (simple Lie algebra), if the node is a leaf, or a disconnected diagram (semisimple but not simple Lie algebra), with either two or three components (the latter for Dn and En). At the level of Lie algebras, these inclusions correspond to sub-Lie algebras.

The maximal subgraphs are as follows; subgraphs related by a diagram automorphism are labeled "conjugate":
 * An+1: An, in 2 conjugate ways.
 * Bn+1: An, Bn.
 * Cn+1: An, Cn.
 * Dn+1: An (2 conjugate ways), Dn.
 * En+1: An, Dn, En.
 * For E6, two of these coincide: $$\mathrm{D}_5 \cong \mathrm{E}_5$$ and are conjugate.
 * F4: B3, C3.
 * G2: A1, in 2 non-conjugate ways (as a long root or a short root).

Finally, duality of diagrams corresponds to reversing the direction of arrows, if any: Bn and Cn are dual, while F4, and G2 are self-dual, as are the simply-laced ADE diagrams.

Simply laced

A Dynkin diagram with no multiple edges is called simply laced, as are the corresponding Lie algebra and Lie group. These are the $$A_n, D_n, E_n$$ diagrams, and phenomena that such diagrams classify are referred to as an ADE classification. In this case the Dynkin diagrams exactly coincide with Coxeter diagrams, as there are no multiple edges.

Satake diagrams
Dynkin diagrams classify complex semisimple Lie algebras. Real semisimple Lie algebras can be classified as real forms of complex semisimple Lie algebras, and these are classified by Satake diagrams, which are obtained from the Dynkin diagram by labeling some vertices black (filled), and connecting some other vertices in pairs by arrows, according to certain rules.

History

Dynkin diagrams are named for Eugene Dynkin, who used them in two papers (1946, 1947) simplifying the classification of semisimple Lie algebras; see. When Dynkin left the Soviet Union in 1976, which was at the time considered tantamount to treason, Soviet mathematicians were directed to refer to "diagrams of simple roots" rather than use his name.

Undirected graphs had been used earlier by Coxeter (1934) to classify reflection groups, where the nodes corresponded to simple reflections; the graphs were then used (with length information) by Witt (1941) in reference to root systems, with the nodes corresponding to simple roots, as they are used today. Dynkin then used them in 1946 and 1947, acknowledging Coxeter and Witt in his 1947 paper.

Conventions
Dynkin diagrams have been drawn in a number of ways; the convention followed here is common, with 180° angles on nodes of valence 2, 120° angles on the valence 3 node of Dn, and 90°/90°/180° angles on the valence 3 node of En, with multiplicity indicated by 1, 2, or 3 parallel edges, and root length indicated by drawing an arrow on the edge for orientation. Beyond simplicity, a further benefit of this convention is that diagram automorphisms are realized by Euclidean isometries of the diagrams.

Alternative convention include writing a number by the edge to indicate multiplicity (commonly used in Coxeter diagrams), darkening nodes to indicate root length, or using 120° angles on valence 2 nodes to make the nodes more distinct.

There are also conventions about numbering the nodes. The most common modern convention had developed by the 1960s and is illustrated in.

Rank 2 Dynkin diagrams
Dynkin diagrams are equivalent to generalized Cartan matrices, as shown in this table of rank 2 Dynkin diagrams with their corresponding $22$ Cartan matrices.

For rank 2, the Cartan matrix form is:
 * $$A = \left [\begin{matrix}2&a_{12}\\a_{21}&2\end{matrix}\right ]$$

A multi-edged diagram corresponds to the nondiagonal Cartan matrix elements $-a_{21}, -a_{12}$, with the number of edges drawn equal to $\max(-a_{21}, -a_{12})$, and an arrow pointing towards nonunity elements.

A generalized Cartan matrix is a square matrix $$A = (a_{ij})$$ such that:
 * 1) For diagonal entries, $$a_{ii} = 2$$.
 * 2) For non-diagonal entries, $$a_{ij} \leq 0 $$.
 * 3) $$a_{ij} = 0$$ if and only if $$a_{ji} = 0$$

The Cartan matrix determines whether the group is of finite type (if it is a positive-definite matrix, i.e. all eigenvalues are positive), of affine type (if it is not positive-definite but positive-semidefinite, i.e. all eigenvalues are non-negative), or of indefinite type. The indefinite type often is further subdivided, for example a Coxeter group is Lorentzian if it has one negative eigenvalue and all other eigenvalues are positive. Moreover, multiple sources refer to hyberbolic Coxeter groups, but there are several non-equivalent definitions for this term. In the discussion below, hyperbolic Coxeter groups are a special case of Lorentzian, satisfying an extra condition. For rank 2, all negative determinant Cartan matrices correspond to hyperbolic Coxeter group. But in general, most negative determinant matrices are neither hyperbolic nor Lorentzian.

Finite branches have $$(-a_{21}, -a_{12}) = (1,1), (2,1), (3,1)$$, and affine branches (with a zero determinant) have $(-a_{21}, -a_{12}) =(2,2)\text{ or }(4,1)$.

Affine Dynkin diagrams
There are extensions of Dynkin diagrams, namely the affine Dynkin diagrams; these classify Cartan matrices of affine Lie algebras. These are classified in, specifically listed on. Affine diagrams are denoted as $$X_l^{(1)}, X_l^{(2)},$$ or $$X_l^{(3)},$$ where X is the letter of the corresponding finite diagram, and the exponent depends on which series of affine diagrams they are in. The first of these, $$X_l^{(1)},$$ are most common, and are called extended Dynkin diagrams and denoted with a tilde, and also sometimes marked with a + superscript. as in $$\tilde A_5 = A_5^{(1)} = A_5^{+}$$. The (2) and (3) series are called twisted affine diagrams.

See Dynkin diagram generator for diagrams.

Here are all of the Dynkin graphs for affine groups up to 10 nodes. Extended Dynkin graphs are given as the ~ families, the same as the finite graphs above, with one node added. Other directed-graph variations are given with a superscript value (2) or (3), representing foldings of higher order groups. These are categorized as Twisted affine diagrams.

Hyperbolic and higher Dynkin diagrams
The set of compact and noncompact hyperbolic Dynkin graphs has been enumerated. All rank 3 hyperbolic graphs are compact. Compact hyperbolic Dynkin diagrams exist up to rank 5, and noncompact hyperbolic graphs exist up to rank 10.

Noncompact (over-extended) forms
Some notations used in theoretical physics, such as M-theory, use a "+" superscript for extended groups instead of a "~" and this allows higher extensions groups to be defined.
 * 1) Extended Dynkin diagrams (affine) are given "+" and represent one added node. (Same as "~")
 * 2) Over-extended Dynkin diagrams (hyperbolic) are given "^" or "++" and represent two added nodes.
 * 3) Very-extended Dynkin diagrams with 3 nodes added are given "+++".

238 Hyperbolic groups (compact and noncompact)
The 238 hyperbolic groups (compact and noncompact) of rank $$n \ge 3$$ are named as $$H_i^{(n)}$$ and listed as $$i=1,2,3...$$ for each rank.

Very-extended
Very-extended groups are Lorentz groups, defined by adding three nodes to the finite groups. The E8, E7, E6, F4, and G2 offer six series ending as very-extended groups. Other extended series not shown can be defined from An, Bn, Cn, and Dn, as different series for each n. The determinant of the associated Cartan matrix determine where the series changes from finite (positive) to affine (zero) to a noncompact hyperbolic group (negative), and ending as a Lorentz group that can be defined with the use of one time-like dimension, and is used in M theory.

title: Dynkin diagram


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User talk:Aamiller

Hello Aamiller and welcome to wikipedia! I see you are making important contributions for medical articles. Maybe you should take a look at the tyle conventions in the Manual of Style. I also formatted a few of your articles as an example. Have fun! Cheers, Muriel Gottrop 13:36 25 Jul 2003 (UTC)

Category:Wikipedians in New Zealand
Hi, You might want to consider adding User NZ res to the top of your user page, which will add you to this category automatically and also add a nice graphic. Onco_p53 07:42, 14 November 2005 (UTC)

Speedy deletion nomination of Isocentric technique

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As reviewing administrator, I removed the speedy because this does not at all sound luke nonsense. But it needs considerable improvement to be an acceptable article. First, it must be more than a definition--it needs to be an explanation. Then,m the explanation must be accompanied and supported by references providing substantial coverage from 3rd party independent published reliable sources, print or online, but not blogs or press releases, or material derived from press releases. I advise you to fix the problem, and do this very quickly, before the article gets nominated for deletion by a regular deletion process.

I  urge you to write a proper article if it is possible; if it is not yet possible, please help us by improving our other articles on related topics.  DGG ( talk ) 22:08, 3 June 2011 (UTC)

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Howard Kaloogian

Howard James Kaloogian (born December 30, 1959) is an American politician and a former Republican member of the California State Assembly, having served in the State Assembly for the 74th district from 1994 to 2000. After leaving office, he was active in the 2003 California recall, and unsuccessfully ran in 2004 for the United States Senate and in a special election in 2006 to the United States House of Representatives.

Biography
Kaloogian grew up in Michigan, of Armenian-born parents. Kaloogian earned a Bachelor's from Michigan State University and a J.D. degree from Pepperdine University School of Law. During 1988–1996, he was an estate attorney. He got his start in politics at the suggestion of Bill Morrow, after Morrow read a strongly worded letter Kaloogian wrote to the editor of the San Diego Union-Tribune purporting to correct a reader's misleading interpretation of the preamble to the Constitution of the United States.

From 1994–2000, Kaloogian was a member of the California Assembly, representing California District 74, which covers portions of northern San Diego County. He won his seat in the 1994 legislative elections, with 61% of the votes counted. He endorsed Senator Phil Gramm's presidential bid in 1995.

Kaloogian was twice re-elected to the Assembly. He recorded an unchanged majority, 61%, in the 1996 legislative election and was re-elected again in the 1998 election, where his share of the vote fell to 57%.

In 2003, Kaloogian became the chairman of the Recall Gray Davis Committee, dedicated to the ousting of governor Gray Davis.

Kaloogian is a founder and co-chairman of Move America Forward, a political action group. Kaloogian considers President Ronald Reagan to be one of his political heroes. Kaloogian serves on the Ronald Reagan Legacy Project and was the Chairman of the Defend Reagan Project, which campaigned in 2003 for CBS to drop a docudrama about Reagan, The Reagans. The campaign was successful, as CBS did not show the mini-series, but handed it off to Showtime.

In 2004 Kaloogian ran for the U.S. Senate from California but lost the Republican primary with 11% of the vote, placing him 3rd out of 11 candidates. He also ran unsuccessfully in the special election to fill the opening created by the resignation of disgraced Congressman Duke Cunningham in California's 50th Congressional District.

In 2008 Kaloogian chaired an Anti-Barack Obama political action committee called "Our country deserves better". He appeared in a video ad for that group.

Howard Kaloogian is married to Martha Lynn, and has a step-son.

2006 campaign for Congress
Kaloogian ran in the special election to fill the opening in California's 50th District to the House of Representatives caused by the resignation of disgraced former Congressman Duke Cunningham. In the special elections where the top vote-getter from each party moves to the next round, Kaloogian finished a distant third among the Republican candidates. The next round took place at the same time as the primary for the term that commenced January 3, 2007. On April 17, Kaloogian announced his withdrawal from the primary for the next congressional term. State Senator Bill Morrow, who was running against Kaloogian, challenged an implied endorsement by him of Kaloogian on Kaloogian's website.

Altered photo and Other Controversies
During the 2006 campaign, an image showing "a busy urban street scene" in Baghdad was posted on Kaloogian's web site. The image was removed after bloggers at the Daily Kos noted that the image was actually of Istanbul. Kaloogian later said using the photo was "a stupid mistake".

Kaloogian was involved with another controversy with Lowell Robert "Bob" Fuselier, "Business Law Group PC" and "Ambassador Property Management," Vista, CA, and both of Kaloogian and Fuselier, LLP law firm in Carlsbad, CA. NBC San Diego News reports that Howard Kaloogian and Bob Fuselier stole over $150,000 of their client's money. Bob Fuselier admitted to cashing a check made out to their client and withdrawing $60,000. Fuselier refused to disclose where the rest of the money was being held. A criminal complaint was filed with the Carlsbad Police Department. Kaloogian and Fuselier convinced the DA and the Superior Court of California, San Diego, North County Division, that they had a right to keep their client's money for charges in a separate and unconnected case. Kaloogian & Fuselier won by default. The client reports that Kaloogian & Fuselier told so many lies, papered him and the courts over with so many false allegations and trumped up lawsuits to keep the money, that he ended up defaulting.

title: Howard Kaloogian


text:
Tangible investment

A tangible investment is something physical that you can touch. It is an investment in a tangible, hard or real asset or personal property. This contrasts with financial investments such as stocks, bonds, mutual funds and other financial instruments.

Some assets are held purely for their ability to appreciate, such as collectibles, while others are held for the income they generate while they depreciate, such as equipment held for lease. Others exhibit a combination of properties, appreciating in market value while depreciating in book value, such as rental real estate. Timberland exhibits depletion of timber combined with appreciation of land. Other assets’ values fluctuate with supply and demand, such as commodities, which are liquid investments unlike most other tangible investments.

These various properties, together with the lack of correlation to traditional asset class values, make tangible investments a means of reducing overall investment risk through diversification.

Types
All of the following are tangible investments:
 * Businesses
 * Real estate and land
 * Infrastructure as an asset class (as opposed to traditional government-funded infrastructure)
 * Commodities and natural resources such as industrial and precious metals and minerals, oil, agricultural commodities, fish, livestock and forestry
 * Collectibles of all kinds, including:
 * Antiques and ancient artifacts
 * Fine art
 * Postage stamps (see philatelic investment)
 * Coins (see coin collecting) and banknotes
 * Autographs and historic documents
 * Memorabilia, such as political, celebrity, and sports memorabilia
 * Firearms and militaria
 * Trading cards
 * Jewelry and timepieces
 * Fine wines and spirits
 * Classic cars
 * Rare books
 * Musical instruments
 * Toys

title: Tangible investment


text:
Superrationality

In economics and game theory, a participant is considered to have superrationality (or renormalized rationality) if they have perfect rationality (and thus maximize their utility) but assume that all other players are superrational too and that a superrational individual will always come up with the same strategy as any other superrational thinker when facing the same problem. Applying this definition, a superrational player playing against a superrational opponent in a prisoner's dilemma will cooperate while a rationally self-interested player would defect.

This decision rule is not a mainstream model in game theory and was suggested by Douglas Hofstadter in his article, series, and book Metamagical Themas as an alternative type of rational decision making different from the widely accepted game-theoretic one. Hofstadter provided this definition: "Superrational thinkers, by recursive definition, include in their calculations the fact that they are in a group of superrational thinkers."

Unlike the supposed "reciprocating human", the superrational thinker will not always play the equilibrium that maximizes the total social utility and is thus not a philanthropist.

Prisoner's dilemma
The idea of superrationality is that two logical thinkers analyzing the same problem will think of the same correct answer. For example, if two people are both good at math and both have been given the same complicated problem to do, both will get the same right answer. In math, knowing that the two answers are going to be the same doesn't change the value of the problem, but in the game theory, knowing that the answer will be the same might change the answer itself.

The prisoner's dilemma is usually framed in terms of jail sentences for criminals, but it can be stated equally well with cash prizes instead. Two players are each given the choice to cooperate (C) or to defect (D). The players choose without knowing what the other is going to do. If both cooperate, each will get $100. If they both defect, they each get $1. If one cooperates and the other defects, then the defecting player gets $150, while the cooperating player gets nothing.

The four outcomes and the payoff to each player are listed below.

One valid way for the players to reason is as follows:

 * 1) Assuming the other player defects, if I cooperate I get nothing and if I defect I get a dollar.
 * 2) Assuming the other player cooperates, I get $100 if I cooperate and $150 if I defect.
 * 3) So whatever the other player does, my payoff is increased by defecting, if only by one dollar.

The conclusion is that the rational thing to do is to defect. This type of reasoning defines game-theoretic rationality and two game-theoretic rational players playing this game both defect and receive a dollar each.

Superrationality is an alternative method of reasoning. First, it is assumed that the answer to a symmetric problem will be the same for all the superrational players. Thus the sameness is taken into account before knowing what the strategy will be. The strategy is found by maximizing the payoff to each player, assuming that they all use the same strategy. Since the superrational player knows that the other superrational player will do the same thing, whatever that might be, there are only two choices for two superrational players. Both will cooperate or both will defect depending on the value of the superrational answer. Thus the two superrational players will both cooperate since this answer maximizes their payoff. Two superrational players playing this game will each walk away with $100.

Note that a superrational player playing against a game-theoretic rational player will defect, since the strategy only assumes that the superrational players will agree.

Although standard game theory assumes common knowledge of rationality, it does so in a different way. The game-theoretic analysis maximizes payoffs by allowing each player to change strategies independently of the others, even though in the end, it assumes that the answer in a symmetric game will be the same for all. This is the definition of a game-theoretic Nash equilibrium, which defines a stable strategy as one where no player can improve the payoffs by unilaterally changing course. The superrational equilibrium in a symmetric game is one where all the players' strategies are forced to be the same before the maximization step. (There is no agreed-upon extension of the concept of superrationality to asymmetric games.)

Some argue that superrationality implies a kind of magical thinking in which each player supposes that their decision to cooperate will cause the other player to cooperate, even though there is no communication. Hofstadter points out that the concept of "choice" doesn't apply when the player's goal is to figure something out, and that the decision does not cause the other player to cooperate, but rather the same logic leads to the same answer independent of communication or cause and effect. This debate is over whether it is reasonable for human beings to act in a superrational manner, not over what superrationality means, and is similar to arguments about whether it is reasonable for humans to act in a 'rational' manner, as described by game theory (wherein they can figure out what other players will or have done by asking themselves, what would I do if I was them, and applying backward induction and iterated elimination of dominated strategies).

Probabilistic strategies
For simplicity, the foregoing account of superrationality ignored mixed strategies: the possibility that the best choice could be to flip a coin, or more generally to choose different outcomes with some probability. In the prisoner's dilemma, it is superrational to cooperate with probability 1 even when mixed strategies are admitted, because the average payoff when one player cooperates and the other defects are the same as when both cooperate and so defecting increases the risk of both defecting, which decreases the expected payout. But in some cases, the superrational strategy is mixed.

For example, if the payoffs in are as follows:

 * CC – $100/$100
 * CD – $0/$1,000,000
 * DC – $1,000,000/$0
 * DD – $1/$1

So that defecting has a huge reward, the superrational strategy is defecting with a probability of 499,900/999,899 or a little over 49.995%. As the reward increases to infinity, the probability only approaches 1/2 further, and the losses for adopting the simpler strategy of 1/2 (which are already minimal) approach 0. In a less extreme example, if the payoff for one cooperator and one defector was $400 and $0, respectively, the superrational mixed strategy world be defecting with probability 100/299 or about 1/3.

In similar situations with more players, using a randomising device can be essential. One example discussed by Hofstadter is the platonia dilemma: an eccentric trillionaire contacts 20 people, and tells them that if one and only one of them send him or her a telegram (assumed to cost nothing) by noon the next day, that person will receive a billion dollars. If they receive more than one telegram or none at all, no one will get any money, and communication between players is forbidden. In this situation, the superrational thing to do (if it is known that all 20 are superrational) is to send a telegram with probability p=1/20—that is, each recipient essentially rolls a 20-sided die and only sends a telegram if it comes up "1". This maximizes the probability that exactly one telegram is received.

Notice though that this is not the solution in the conventional game-theoretical analysis. Twenty game-theoretically rational players would each send in telegrams and therefore receive nothing. This is because sending telegrams is the dominant strategy; if an individual player sends telegrams they have a chance of receiving money, but if they send no telegrams they cannot get anything. (If all telegrams were guaranteed to arrive, they would only send one, and no one would expect to get any money).

Formalizations and related concepts
The question of whether to cooperate in a one-shot Prisoner's Dilemma in some circumstances has also come up in the decision theory literature sparked by Newcomb's problem. Causal decision theory suggests that superrationality is irrational, while evidential decision theory endorses lines of reasoning similar to superrationality and recommends cooperation in a Prisoner's Dilemma against a similar opponent.

Program equilibrium has been proposed as a mechanistic model of superrationality.

title: Superrationality


text:
Wikipedia talk:Nupedia and Wikipedia

differences between Nupedia and Wikipedia
This page does not discuss the differences between Nupedia and Wikipedia. I am not very much enlightened! i.e. are they simply in competition, or are the trying to achieve different aims?

Nupedia Chalkboard
I see that we shouldn't add articles from the Nupedia Chalkboard, but what about Nupedia's articles in progress?. There are articles that have been stranded in there, with no visible movement, since late 2001. Do these have the same status as chalkboard articles, or can they be assumed to be released under the GFDL? It would be a pity to not use them as many of them would make excellent stubs and it would be a pity if they disappeared down into /dev/null simply through inactivity at Nupedia. -- Lexor 09:19, 13 Aug 2003 (UTC)

 * Jimbo and others on the wikipedia-l list archive thread: http://mail.wikipedia.org/pipermail/wikipedia-l/2003-August/thread.html#11582 seem to concur that nupedia a-i-p qualify under the GFDL. Also mav confirmed this on my talk page:

 * Yes. Jimbo said it is OK so go ahead and use the Nupedia articles under development under the GNU FDL. It was the intent of the authors anyway to have their work under the GNU FDL, so I don't see a problem so long as proper credit is given. --mav

 * so I'm going to update this meta page saying that Nupedia a-i-p can be ported to wikipedia. --Lexor 08:34, 3 Sep 2003 (UTC)

Copying from the village pump so that it somebody who looks for Nupedia from this page will know that it's been reported: -- Lexor 13:16, 26 Sep 2003 (UTC)

Nupedia.com/Nupedia.org is gone, please bring it back
It appears that http://nupedia.org and http://nupedia.com are both gone, which is a great pity because I was trying to port across some of the articles in process, see Nupedia and Wikipedia. There was no mention that this site was going to disappear, no announcement that it was about to go. Most unceremonius.

In discussion with Jimbo and Mav, (see above) it appears that I could port the old articles in progress under the GFDL, further, there were actually at least one officially posted article that hadn't been transferred at all. Not mention all the attribution links for the source material, history of Nupedia, etc. that are now gone and old contributors to Nupedia might be a little miffed about this. Can we get it back please (at very least the content of the database so I can continue the port)? I certainly hope something like this doesn't happen to wikipedia some day. --Lexor 11:24, 26 Sep 2003 (UTC)

GFDL license statement and the Title page
Looking at the article Imperative programming I see that there is some attribution text atop the article that the history comments says should not be removed because it is a "Title Page" required by the GFDL. Is this advice correctly stated? Bevo 01:18, 15 Feb 2004 (UTC)

 * I removed it. It is non-standard and ugly. See Copyrights. We deal with that issue by having detailed history pages linked before articles. RMS is well-aware of us and how we operate - he would have said something ages ago if we were doing something wrong. --mav 01:50, 15 Feb 2004 (UTC)

 * It may be non-standard. It may be ugly. It is also correct. RMS is not god, nor is he well aware of the precise details of how we operate, nor has he stated a position on this particular issue. If you disagree with my interpretation of copyright law, you are welcome to explain why. Martin 19:48, 15 Feb 2004 (UTC)

 * It's certainly not like anything I've seen elsewhere on the 'pedia - articles based on the 1911 Britannica or FOLDOC generally have a note at the bottom, but this seems to be out of politeness rather than anything else. - IMSoP 01:55, 15 Feb 2004 (UTC) [Comment written simultaneously to mav's]

From the article talk page

Mav, why did you remove the history and title page text? It's required under the GFDL for making a modified version, in this case from Nupedia. You said "see copyrights", but I can't tell to what you refer. Martin 16:10, 15 Feb 2004 (UTC)

 * He's under the delusion that the convoluted interpretation of the GFDL given on copyrights is the only interpretation that can be made. Anthony DiPierro 16:19, 15 Feb 2004 (UTC)

If so, the point is that just because Wikipedia has a certain interpretation of the GFDL when others use our work, doesn't mean that we're allowed to use the same interpretation of the GFDL when we use the work of others. Now, if the authors of the Nupedia article in question to indicate that they share our interpretation, then that's great. However, if they do not (and they have not yet to date, AFAICT) then we should follow a comparatively strict interpretation to ensure that we are not violating copyright. Martin 16:38, 15 Feb 2004 (UTC)

 * If the text is felt to be needed, I would favour a note at the bottom of the page similar to the one used for 1911 or FOLDOC articles, which would seem to contain the same information in a less obtrusive and more standard (in the sense of consistent within Wikipedia) way. Something like:
 * This text, or a previous version of it, was written by Stan Seibert for Nupedia.
 * Would that cover the potential copyright issues do you think? - IMSoP 18:56, 15 Feb 2004 (UTC)

 * No, the text needs to go on the "Title Page", as that text is defined in the GFDL:

 * The "Title Page" means, for a printed book, the title page itself, plus such following pages as are needed to hold, legibly, the material this License requires to appear in the title page. For works in formats which do not have any title page as such, "Title Page" means the text near the most prominent appearance of the work's title, preceding the beginning of the body of the text.

 * See sections 4A, 4B, 4C of the Text of the GNU Free Documentation License. Martin 19:48, 15 Feb 2004 (UTC)

 * Hmmm, that is pretty clear isn't it. I guess we need to hash out a standard text to go unobtrusively at the top of the articles then. Taking the suggested text on Nupedia and Wikipedia as starting point, how about:
 * An earlier version of this article was posted on Nupedia; editor: Robert Dyer, lead reviewer: James Allan Evans, lead copyeditors: Charles Peyser and Jeri Bates. This version has been modified by Wikipedia users and published by Wikimedia
 * Unwieldy, I know, but seemingly necessary for strict adherence to the licence. - IMSoP 20:51, 15 Feb 2004 (UTC)

 * I thought it would look better to have a short note at the top of the page, and a longer note at the bottom of the page, but I'm open to suggestions. :) Martin 21:19, 15 Feb 2004 (UTC)

 * Well, as I understand it, that would be fudging the licence requirement somewhat (as you quote above: "...preceding the beginning of the body of the text...") - but I guess not by much, and let's face it, the FDL wasn't written with such short texts in mind. - IMSoP 22:19, 15 Feb 2004 (UTC)

 * In fact, the page on Nupedia and Wikipedia has a suggested text, but of the half-dozen links I followed, only one had actually used it, and no two were alike. Perhaps someone needs to go through and make them consistent? [Although the attribution may be awkward with the site unavailable] - IMSoP 19:06, 15 Feb 2004 (UTC)

 * The Internet Archive sees all. The other articles will be fixed in due course. Martin 19:48, 15 Feb 2004 (UTC)

 * Aha, good thinking! Now we just need to decide how to format the information... - IMSoP 20:51, 15 Feb 2004 (UTC)

 * As a side note - in our article about Nupedia, don't you think it's time we declared them dead? The site has been gone since september. I think it's fair to say they aren't coming back. →Raul654 19:09, Feb 15, 2004 (UTC)

If this is, indeed, a requirement, it's going to be impossible to do it by editing every single article and putting it there, and making sure it stays there. It's going to have to be done by the operating system in an section which is not editable. RickK 21:14, 15 Feb 2004 (UTC)

 * There aren't that many Nupedia articles, so it shouldn't be too difficult. The FOLDOC articles are more of a challenge, though. Martin 21:42, 15 Feb 2004 (UTC)

Taking a comment out of line...

Imsop: there are two seperate pieces of text we require: firstly, we require some text on the "title page", under 4A, 4B, 4C. I think Imperative programming satisfies that, so I don't think we need to add any more to it.

Secondly, we require some "History" text on the article. Now the History text doesn't have to go on the title page, so we can shuffle it off to the bottom and put it in small. Does that clarify? Martin 22:34, 15 Feb 2004 (UTC)

 * Blimey, aren't licences hard work! I suppose you're right that the current note at Imperative programming is OK for the "Title Page", as long as Stan Seibert can be considered the sole "principal author" of the original work. I'm not overly fond of the wording - I'd certainly prefer it if "a previous version" was in there somewhere, because potentially there may be very little of the original text left, so we don't want to make it look like the Nupedia author was the principal author of this text. Oh, and you spelled "modified" wrong :p - IMSoP 22:49, 15 Feb 2004 (UTC)

 * OK, I'm an idiot. :)

 * I guess a longer wording would be much clearer - that's a fair point. I like what you've just done regards "incorporates text written by..."

 * One alternative to all this is to put something on the main page, and consider Wikipedia a single "Document" with that as its "Title Page", but I think that would be heavily resisted, so I'll stick to fixing things on a per-article basis.

 * And yes, licenses suck. :-/ Martin 23:15, 15 Feb 2004 (UTC)

 * Considering the Wikipedia a single work would be a really bad idea. In a single work a site which wished to infringe the GFDL could do so by making a single contribution, then exploiting precednets saying that joint authors may not sue each other. It's important that each article be the single work. Note how we're reacting to it as well and consider that our use of GFDL imposes what we dislike on reusers of the WiKipeida. There's more to be learned from this than just what we need to do in this case - the GFDL requirements are causing us to choose to rewrite rather than reuse a GFDL work.  Jamesday 03:26, 17 Feb 2004 (UTC)

On Wikipedia the title page is the article itself and the history section and list of authors are combined on the article's history page. So moving the author note from the start of the article to the references section and indicating that the history section you wrote was on this talk page, is above and beyond what is needed. --mav

 * The main problem I see is that the GFDL seems to stipulate that the author list go on the Title page, not in the history section. --Delirium 11:55, Feb 16, 2004 (UTC)

 * Mav, your interpretation of the GFDL is a novel one. You appear to be claiming that the entire article plus the "page history", plus the Talk page is all one big "Title Page". However, the Text of the GFDL states:

 * The "Title Page" means, for a printed book, the title page itself, plus such following pages as are needed to hold, legibly, the material this License requires to appear in the title page. For works in formats which do not have any title page as such, "Title Page" means the text near the most prominent appearance of the work's title, preceding the beginning of the body of the text.

 * The entire article cannot be considered to be "near" the most prominent appearance of the work's title. Nor can it be considered to be "preceding the beginning of the body of the text", as it is the body of the text. A plain reading of the text of the GFDL does not support your interpretation. Martin 19:46, 16 Feb 2004 (UTC)

 * Further, your interpretation has severe negative consequences for Wikipedia or another person producing a printed version, as to do so they would be absolutely forced to print out the entire page history. Nobody can sanely argue that some text is "near the most prominent appearance of the work's title", when it is in fact only available by logging on to the internet (and the user may not have internet access) and browsing to a URL. This interpretation, even if it were valid, would thus severely damage the freeness of Wikipedia. Martin 19:46, 16 Feb 2004 (UTC)

 * My point is indeed that it is not "near the most prominent appearance of the work's title" currently, while the GFDL requires that it be in that location. Note that this is onoly for materials the license requires on the title page, which does not include the history.  It does however, include the authors list.  To my reading, the GFDL does not anywhere allow the authors list to be buried in a link on the internet.  It requires the authors list to be on the Title page, or in materials lacking a title page, to be "near the most prominent apperance of the work's title".  In fact, I don't understand your argument at all: you seem to be arguing that because Wikipedia does not place this in a prominent location, that it is therefore not in a prominent location, which is true.  But it doesn't change the fact that the GFDL requires it in a prominent location. --Delirium 00:50, Feb 17, 2004 (UTC)

 * Ahh, I was replying to mav, and it seems I misread his comments: I thought he said "On Wikipedia the title page is the article itself and the history section and list of authors", whereas in fact he said "On Wikipedia the title page is the article itself", and the mention of the history section is a seperate clause. My apologies: I have edited the text in question. Martin 01:01, 17 Feb 2004 (UTC)

Is the title page notice a permanent mark? Can I simply rewrite the article entirely and avoid it? Bevo 14:56, 16 Feb 2004 (UTC)

 * Certainly if you rewrite the article from scratch you can delete the title page notice (and the history section). That's absolutely fine.
 * If you rewrite the article so that it shares nothing in common with the original external GFDL article, then you can probably (99% sure) likewise remove the title page notice and history section.
 * You can also ask the contributing author to license their text under a less restrictive license than the GFDL.
 * Of course, IANAL, and this is not legal advice. Martin 19:46, 16 Feb 2004 (UTC)

 * Thanks for the comments. Bevo 20:09, 16 Feb 2004 (UTC)

Nupedia attribution
Read http://en.wikipedia.org/wiki/Wikipedia:Nupedia_and_Wikipedia. In reviewing Nupedia sourced articles from the list kept there, I don't see any uniformity of attribution style for this requirement. I also see that the links to the original Nupedia articles are now deadends. Is there a simple phrase that would suffice to meet the requirement? - Bevo 19:54, 2 Jun 2004 (UTC)

title: Wikipedia talk:Nupedia and Wikipedia


text:
Talk:Dirk Gently's Holistic Detective Agency

Plot synopsis
I intentionally did not put a plot synopsis of the book in the article. I feel that a spoiler warning would not be sufficient to stop people from reading the synopsis, and that it would be a shame to ruin a book that is this complex. (Summarizing up to the canal scene might be acceptable.) Besides, with the way the book is written, every detail begs to be summarized (especially if the summary reaches the end, where all the details come together), so the book is its own best summary.

I also think that the character descriptions serve the purpose of a plot synopsis -- to get the tone and character of the book across. Paullusmagnus 13:50 25 Jul 2003 (UTC)

 * Hi. I added a detailed plot synopsis to the article before seeing your note on the Talk page. I see your point, but would argue that a detailed synopsis that does show how the apparently disparate strands of the book's convoluted plot are connected (especially by the back story) is of use. If people don't want to read it, they don't have to. Conversely, if a synopsis is absent or removed, they don't have a choice! Any corrections are welcome. I couldn't work out exactly when the Salaxan ghost shifts to Richard. Even Dirk's comments are guesswork, as he wasn't factoring in the Electric Monk. Vivamancer 15:39, 9 April 2007 (UTC)

I was under the impression that the poem of import in the book was Rime of the Ancient Mariner, not Kubla Kahn. --Jherico 23:16, 2 Jul 2004 (UTC)

 * They're both relevant, but "Kubla Khan" is the really significant one. --Paul A 02:40, 20 Jul 2004 (UTC)
 * Corrected article to reflect this.-- jet 57  (u∴t) 10:56, 24 April 2007 (UTC) 14:59, 14 May 2005 (UTC)

I have no idea what is meant by the end of this line: 'Dirk Gently's Holistic Detective Agency has been compared to Gödel, Escher, Bach: an Eternal Golden Braid because Dirk Gently is actually based on the "fundamental interconnectedness of all things"—which is virtually the same thing as the chaos theory.' Godel Escher Bach was certainly not about chaos theory, it explored mathematical formalism, truth, proof and the emergence of meaning and possibly consciousness from self-reference. Chaos theory describes the unpredictable behaviour of a system with total sensitivity to initial variables, a totally different topic. --Remy B

 * See here: http://www.forum2.org/tal/books/dirk.html The reviewer Tal Cohen e-mailed Douglas Adams about this, and he said that although he had read Hofstadter's book, he didn't feel it was connected really.

 * I agree that the "connection" to GEB seems both tenuous and not terribly relevant. "Has been compared to" is misleading as it stands, because the comparison isn't from a noteworthy source. I'm going to take this out. Bombyx 04:31, 13 February 2006 (UTC)

 * SPOILERS TO FOLLOW?
 * One thing that, as far as I know, none of the discussions of the ending of DGHDA have mentioned is the true significance of the "albatross" - i.e. the new editor of Fathom magazine, described in the book as "A.K. Ross" or "Al", i.e. "Albert Ross". The Rime of the Ancient Mariner, following Dirk's conversation with Coleridge, attains the structure we know today, with the part about killing the albatross. However, Wenton-Weakes is already heard complaining about "the part with the bird" making no sense, before Dirk goes back and plants the albatross idea in Coleridge's mind. How is this, I wonder? Umop ap!sdn 11:31, 29 Apr 2005 (UTC)
 * It would seem from the context that the albatross was already in the poem. Otherwise why would Richard tell Dirk to ask about it? I think it's just a joke on the fact the no one knows what the albatross means, and no one ever will.67.85.254.111 18:30, 4 July 2007 (UTC)

I've moved the section on the sofa from Richard's bulletpoint in Characters to Notes, since it was out of place when you included the reference to Adams' RL experience. Tyrhinis 18:30, August 30, 2005 (UTC)

Should the salmon of doubt be mentioned here too? 131.111.8.99

 * You COULD mention Salmon of Doubt, in the context that that was slated to be the third Dirk Gently novel, never finished, etc etc. --JohnDBuell 12:28, 2 March 2006 (UTC)

Origins in Doctor Who
I have corrected the reference which said Professor Chronotis' longevity as being due to his "eccentric time machine". Chronotis is the one who is eccentric, not his time machine (I haven't seen it for years, but at one point I swear he says he's trying to have undergraduates "banned" from his College). My restoration is relevant inasmuch as it shows Adams's humour. That being said, I do wonder how much of the two Who stories needs to be described here. Any thoughts? ZarhanFastfire (talk) 03:38, 19 April 2013 (UTC)

How many it sold
Is it at all possible to get some figures as to how well this, as well as it's sequel, sold? Especially compared to The Guide? I've never had a clue as to how popular this was in relativity and can't imagine how to get such numbers myself.

 * Probably your only choices would be to contact the publishers (William Heinemann in the UK, and Pocket Books/Simon and Shuster in the US) and ask for figures. Another possibility would be to contact Nielsen Bookdata, http://www.nielsenbookdata.co.uk/nbd/index.asp - but be prepared to pay for figures received from the latter service. There are also ways to track Amazon's sales data, including the book's Amazon rank.... --JohnDBuell 12:01, 12 April 2006 (UTC)

Calculator
Wasn't the weird calculator that Dirk bought called the I Ching? —The preceding unsigned comment was added by Deathgecko (talk • contribs).
 * Yes, but that was in the second book. --JohnDBuell 22:19, 6 December 2006 (UTC)
 * Oops, sorry. I knew that. --ArtifexCrastinus 18:31, 8 December 2006 (UTC)

Removed links to common words
I've removed many of the extraneous links (to words like "cat," "bathroom," and so on, and will get to the layout in a week or so unless someone beats me to it.

Fabulous Creature 17:21, 10 April 2007 (UTC)

Output of the "Lazy peer review" program
The following suggestions were generated by a semi-automatic javascript program. You may wish to browse through User:AndyZ/Suggestions for further ideas. Thanks, Kweeket 21:49, 29 June 2007 (UTC)
 * Consider adding more links to the article; per Manual of Style (links) and Build the web, create links to relevant articles.[?]
 * Per Wikipedia:Context and Wikipedia:Manual of Style (dates), months and days of the week generally should not be linked. Years, decades, and centuries can be linked if they provide context for the article.[?]
 * As per Wikipedia:Manual of Style (dates), dates shouldn't use th; for example, instead of using January 30th was a great day, use January 30 was a great day.[?]
 * Please reorder/rename the last few sections to follow guidelines at Guide to layout.[?]
 * There are a few occurrences of weasel words in this article- please observe WP:AWT. Certain phrases should specify exactly who supports, considers, believes, etc., such a view.
 * it has been
 * might be weasel words, and should be provided with proper citations (if they already do, or are not weasel terms, please strike this comment).[?]
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 * "It has been" is used twice.
 * Due to these malfunctions, it has been ejected from civilisation with only a horse, as horses are rather cheap to produce. — Clearly not weasel words, but a statement of the plot.
 * Chaos theory, as it has been popularized, is therefore an appropriate context for this novel. — Not weasel words, per se, but it is an unsubstantiated opinion due to the second half, "Is therefore an appropriate context for this novel". I'm not sure what to do about it. Does that need a source?

 * In either case I crossed that line out of the review, as weasel words are not the issue.67.85.254.111 18:49, 4 July 2007 (UTC)

 * Chaos theory, as it has been popularized, is therefore an appropriate context for this novel. - I changed this line to read, Chaos theory, in its accessible form popularized by writers such as James Gleick, is therefore an appropriate context for this novel.  Gleick wrote those books that made chaos theory a household word. Kweeket 00:49, 6 July 2007 (UTC)
 * That's that then, but I take it there is more to do? —67.85.254.111 01:31, 6 July 2007 (UTC)
 * Well, there is redundancy in the plot introduction and the plot summary that could be eliminated, as well as "Vague terms of size" somewhere... Kweeket 07:29, 6 July 2007 (UTC)

Instructions in Kubla Khan
What were these instructions? The book certainly doesn't say, other than that the ghost will never be able to end his torment and destroy life without them. Kubla Khan would also not be of much help here, as our version contains no instructions.

Clearly the plan involved going forward in time to change Kubla Khan before Wenton-Weakes went back 4 billion years in the past. But what he needed in Coleridge is purposely vague. Did Adams ever mention anything more specific? Right now we have two competing hypotheses. 1) That Kubla Khan was used to control Wenton-Weakes or any possible future host or 2) That the instructions for averting the disaster were in Kubla Khan, and Weakes wouldn't be able to change the past, by averting the launch and properly fixing the lander, without them. Is there any definitive proof for either of the hypotheses. 67.85.254.111 00:59, 6 July 2007 (UTC)

 * It's a joke that you don't get to find out. They go back and interrupt the poet in mid-flow so he can't recall all of his dream in the changed time-line at the end of the story (ie, our reality).  It's not just the instructions that get erased, but also the reading at the collage that Richard and Reg have heard which is just referred to in passing.  It's Douglas having a good old joke on the reader.  BRIANTIST   (talk) 18:33, 14 August 2007 (UTC)

THE FOLLOWING IS FULL OF SPOILERS Who needs the second part of 'Kubla Khan' anyway? The Ghost's problem is not that he did not know how to prevent the explosion (he is the engineer after all) but that he did not properly check that he had done so (by sending out a Monk rather than going himself). He will behave the same way without the extended 'Kubla Khan' (and it is not his possession of Michael which is prevented - Reg notes there will be two identical ghosts after Dirk has interrupted Coleridge, so Michael's walk to the landing craft at the end is made anyway). So what we need to know is: Ghost-in-Michael is on his way to tell Original-Ghost to be more careful about mending the landing craft, while Dirk & Co quickly sabotage 'Kubla Khan' and in so doing also sabotage Ghost-in-Michael's mission. How does that work? I haven't an answer to this question, and it's bothered me for 25 years. I can see that Adams might enjoy a joke at the reader's expense, but this is such a key part of understanding how the ending fits together that the explanation of a joke is just not enough. I'd be delighted to read a better analysis.

There are after all already clear inconsistencies in the book which do look like errors, even if they are made for the sake of humour: see the analysis of the albatross question above by other commentators.

Less importantly, can anyone work out how Reg manages to introduce Bach's music into our reality? Seems to me he has to live out Bach's whole life, starting as a well-documented baby in Eisenach. This really is a joke on the reader, and rather a good one which doesn't affect the main narrative. - Skraff, 15 March 2012 — Preceding unsigned comment added by 92.22.186.137 (talk) 09:58, 15 April 2012 (UTC)

It is also worth noting that in a thread on the official Message Boards on Douglas Adams' website when a reader inquired about the specific mechanics of how the ending worked out, Adams responded: "Ahem. All I can say is that it was as clear as day to me when I wrote it and now I can't figure it out myself. Sorry about that. I'm actually thinking about it at the moment as I've been re-reading the book in preparation for doing a screenplay. I've got a little bit of sorting out to do..." 75.72.30.75 (talk) 12:24, 31 July 2016 (UTC)

New BBC Adaptation
In the article it says

"o make an 18 x 30 minute adaptation of Douglas Adams' Dirk Gently books. It will run over 3 series of 6 episodes and will begin in October of 2007"

There are only two completed books, which are this book and Long Dark. The Salmon of Doubt is unfinished. The press release makes clear that there is a "first series of six 30-minute episodes" but I thought that "and we've finished the last book too!!!!" would be an important element of a Press Release? Otherwise the page needs some trimming.  BRIANTIST  (talk) 18:38, 14 August 2007 (UTC)

http://www.abovethetitle.com/hda_home.php/hda_home.php states there will be three series. The third will presumably be Salmon of Doubt. It does not state that each series will be 6 episodes long. Perhaps series 2 and 3 will be shorter, as were the Qandary and Quintessential phases of H2G2.71.205.219.229 17:14, 26 October 2007 (UTC)

ah, but the amazon.co.uk product synopsis states this is the first of three 6X30-minute series - so 18 episodes it is, at least by their info. 71.205.219.229 02:36, 13 November 2007 (UTC)

The sofa
I got the impression that they prevented the sofa from getting stuck at the end, rather than causing it to get stuck, because if they'd caused the sofa to get stuck then that contradicts the entire rest of the book. The novel shows examples of changing the past, and alternate timelines - but if they caused the sofa to get stuck then that'd mean they were destined to time-travel and change the past... well, you get it. It's a contradiction.

Of course, if they prevented the sofa from getting stuck then it leaves unexplained how the sofa got stuck in the first place. —Preceding unsigned comment added by 220.239.97.10 (talk) 02:26, 21 March 2008 (UTC)

~They actually _did_ get it stuck. "Who was that in the hall?" "That was the delivery man, bringing in your sofa. He asked if we could open the door so he could get it around the corner, and I said we'd be delighted." —Preceding unsigned comment added by 66.122.77.82 (talk) 02:53, 28 January 2009 (UTC)

Misleading Plot Synopsis?
seems to me that the synopsis discusses mcduff erasing susan's answering machine to erase possible implicating evidence of his involvement in way's murder. however, in the book i have read (far too many times by now), he has no idea way is even murdered by then, and decided to erase his voice because he promised to take susan out the following weekend, when in fact (due to work concerns) he could not. am i incorrect in this? --Snideology (talk) 19:53, 10 March 2009 (UTC)

yes, you're right, it is misleading --Chnt (talk) 03:13, 11 March 2009 (UTC)

 * There is more misleading stuff in this synopsis. i cannot remember anything in the book suggesting that Reg saved the aliens "a millisecond before the explosion" and sent them into the future. And I have read the "flare of light in the night sky" being interpreted as the ship being blown up, not it departing, which is why Reg says "sorry, Richard". I fear there is a lot of personal interpretation in this synopsis, which might be up for debate. 2A02:8071:884:B300:25F6:F018:3F78:ABF (talk) 11:50, 23 May 2022 (UTC)

The exam: a prank?
In the Characters section the exam papers is said to be very coincidently duplicated, but my guess is that it's a prank from Reg. I'm thinking this is alluded to just after Dirk tells Reg that he broke his rule for the salt trick. Richard realizes something and tells Reg never to follow Dirk next to the Cam river, I guess out of fear of being pushed/hypnotized to plunge into it in revenge of the prank whose consequences went way too far for Dirk. --SamuelThibault (talk) 00:32, 5 August 2022 (UTC)

When the Salaxalan ghost switched from the Electric Monk to Richard?
I'm not sure that the Salaxalan ghost switch from the Electric Monk to Richard in Reg's room. What is sure is that he is next to Richard in the car when the car "hits" Gordon's ghost, which is after Richard encountered the Monk carrying Gordon's body. I would rather think the switch happened at that time, after the Monk made various dumb things, the last (really last before just trying to ride a tree, then his horse) being to carry back the body to his home. --SamuelThibault (talk) 08:03, 5 August 2022 (UTC)

US Paperback Information
Published by Pocket Books, (May 1988), ISBN 0-671-66063-2. Looking at the article, just throwing this info in is no help. Someone may want to work it in (or not). PAV5150 (talk) 01:43, 3 April 2010 (UTC)

TV - 'Adaptation'
Should there be a separate linked page to this one off drama? Apart from the character names it bares little relation to the original book save the character of Dirk. I am not saying it was bad and should be dis-owned although I did find it disappointing it was not even an attempt at brining the original plot to the screen? —Preceding unsigned comment added by 217.154.113.158 (talk) 12:40, 17 December 2010 (UTC)

 * Possibly, but we would need some reliable sources that demonstrate that this adaption is notable on its own. Regards  So Why  13:08, 17 December 2010 (UTC)
 * I think its affinities with the original novel are close enough to merit keeping it on this article as it stands. If not, we can note that this televised version has a different plot, in the lede. --TS 17:58, 17 December 2010 (UTC)

 * I think for now it should stay where it is. If the BBC shoots more episodes then we might consider moving the show to its own page, but for now it's close enough to the original work and thus the two should be kept together. --Chnt (talk) 20:17, 26 December 2010 (UTC)

 * I've split this off now, as there was plenty of external coverage and other details that I think justified a separate article. Is there any chance that the radio adaptation/s could have a split article as well? It's just the radio adaptation already has a large separate section with cast lists, etc, as well as a slightly confusing fanboyish "differences from the novel" section. It might be nice for this article to be mainly about the novel. Any thoughts? Bob talk 00:12, 12 March 2011 (UTC)

 * Ok, fair enough. If theres's enough material then the split for the radio and tv adaptations are justified.--Chnt (talk) 13:12, 7 April 2011 (UTC)

I decided not to split the radio version off after all, but I did trim it down a little bit to remove the "list of differences". Luckily, the TV version has been commissioned for three more episodes. Bob talk 13:54, 7 April 2011 (UTC)

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The Monk and the Rock Painting
When trotting down to where Reg has left his time machine, the monk notices some ancient rock painting, obviously done ages ago by a primitive tribe. The monk spends some time reflecting on this2A02:C7F:5205:C00:90EB:9BE1:16DD:AB56 (talk) 19:51, 6 July 2020 (UTC). To me it seems there must be some significance, but what?2A02:C7F:5205:C00:90EB:9BE1:16DD:AB56 (talk) 19:50, 6 July 2020 (UTC)

Removal of "Inconsistencies" section.
I'd like to propose the removal of the final section, "Inconsistencies with ending". Douglas himself may not have been able to remember, but the plot does make sense, even if it is mildly convoluted.

The alien ghost was experiencing long periods of forgetfulness, and had to give the knowledge of how to get back to his ship, and fix it, to Coleridge, who wrote it into the second part of "Kubla Khan".

Using the time machine so that Dirk could interrupt Coleridge, thereby becoming the real-life person from porlock, the second part of the poem was forgotten, causing that information to be lost, and preventing the ghost from possessing Wenton-Weakes in the first place, and thus saving humanity.

The time machine stopped working because BT fixed the phone lines, and apparently it's impossible for both the time machine and the phones to work simultaneously. (Or, Chronotis was lying, and simply disabled it.) David G (talk) 07:19, 2 March 2024 (UTC)

 * I have now done so. David G (talk) 00:10, 25 March 2024 (UTC)


text:
James "Bubber" Miley

James Wesley "Bubber" Miley (April 3, 1903 – May 20, 1932) was an American early jazz trumpet and cornet player, specializing in the use of the plunger mute.

Early life (1903–1923)
Miley was born in Aiken, South Carolina, United States, into a musical family. At the age of six, he and his family moved to New York City where, as a child, he occasionally sang for money on the streets, and later, at the age of 14, studied to play the trombone and cornet.

In 1920, after having served in the Navy for 18 months, he joined a jazz formation named the Carolina Five, and remained a member for the next three years, playing small clubs and boat rides all around New York City. After leaving the band at the age of 19, Miley briefly toured the Southern States with a show titled The Sunny South, and then joined Mamie Smith's Jazz Hounds, replacing trumpeter Johnny Dunn. They regularly performed in clubs around New York City and Chicago. While touring in Chicago, he heard King Oliver's Creole Jazz Band playing and was captivated by Oliver's use of mutes. Soon Miley found his own voice by combining the straight and plunger mute with a growling sound.

Duke Ellington years (1923–1929)
Miley's talent and unique style were soon noticed in New York's jazz scene by Duke Ellington who wanted him to jump in for trumpeter Arthur Whetsel. According to saxophonist Otto Hardwick, Ellington's band members had to shanghai Miley into joining them for his first performance, at the Hollywood on Broadway in 1923. At the time, Ellington's Washingtonians were formally led by Elmer Snowden, but Ellington, who factually had already been running the formation, also took over its official leadership a few months later.

Miley's collaboration with Ellington has secured his place in jazz history. Early Ellington hits, such as "Black and Tan Fantasy", "Doin' the Voom Voom", "East St. Louis Toodle-Oo", "The Mooche", and "Creole Love Call", prominently featured Miley's solo work and were thematically inspired by his melodic ideas, which he, in turn, often borrowed from Baptist hymns sung in his church, such as Stephen Adams' "Holy City". With fellow band member, trombonist Joe "Tricky Sam" Nanton, Miley developed the "wah-wah" sound that characterized Ellington's early "jungle music" style. Many jazz critics consider Miley's musical contributions to be integral to Ellington's early success during the time they performed in the Kentucky Club and Cotton Club.

In 1924, while working with Ellington, Miley also recorded "Down In The Mouth Blues" and "Lenox Avenue Shuffle", as a duo named The Texas Blues Destroyers, with Alvin Ray on reed organ. They managed to trick three different record companies into recording the same two songs, both composed by Ray.

In interviews, former co-musicians such as Ellington, Nanton, Hardwick, and Harry Carney spoke fondly of Bubber Miley's carefree character and joie de vivre, exemplified in numerous anecdotes. On the other hand, they also mention his unreliability, and problems with alcohol abuse. Miley's lifestyle eventually led to his breaking up with Ellington's band in 1929, but his influence on the Duke Ellington Orchestra lasted far longer. His legacy lived on in trumpeters such as Cootie Williams and later Ray Nance, who both were able to adopt Miley's style when required.

Final years (1929–1932)
After leaving Ellington's orchestra in 1929, Miley joined Noble Sissle's Orchestra for a one-month tour to Paris, France. After returning to New York, he recorded with groups led by King Oliver, Jelly Roll Morton, Hoagy Carmichael, Zutty Singleton and with Leo Reisman's society dance band. Miley also performed live with Reisman, albeit being the only African American in Reisman's all-white formation, either dressed in an usher's uniform and off the bandstand, or hidden from view by a screen. In 1930, he recorded six songs for Victor Records under the name Bubber Miley and his Mileage Makers, a formation of thirteen musicians including clarinetist Buster Bailey.

Miley's alcoholism terminally affected his life. On May 20, 1932, at the age of 29, he died of tuberculosis, on Welfare Island, now Roosevelt Island, in New York City. Miley lived just a little longer than his contemporary, jazz cornetist Bix Beiderbecke, whose life was also cut short due to alcohol abuse.

title: James "Bubber" Miley


text:
User:Muriel Gottrop~enwiki

pt:Usuário:Muriel Gottropnl:Gebruiker:Muriel Gottrop

I am a wikipedian since February 2003. I contributed a lot for wiki-en in the past, now you can find me at wiki-pt. Beijinhos e abraços e dentadinhas nos cachaços.

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I am not currently in the mood for producing anymore of these. If somebody wishes to do so, here is my recipe: draw the thing in a drawing program, i use Corel (it can be fastidious, but is a relaxing thing to do: no thoughts whatsoever garanteed for a couple of hours, better than meditation); export the thing to a *.png or a *.jpeg format (beware with the size of the file); upload to wikipedia and dont forget to add it to the list.
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Watch for reincarnations
Rosario Poidimani

You deserved this barnstar long ago, Muriel
I can't believe nobody has given you a barnstar in all the time you've been here! For all the work you've done for Wikipedia, I award you this barnstar. I assure you, you won't be forgotten. To keep up with you from now on, I guess we'll all have to learn Portuguese! :-) David Cannon 02:04, 16 Jul 2004 (UTC)

One just doesn't cut it for Muriel

I award this second barnstar because I don't think a single one quite covers your vast accomplishments on the 'pedia, particularly on Roman-related topics. Not to mention I've also found you one of the most pleasant users on here to deal with :) Enjoy your retirement, you've easily earned it. Tchau! Sarge Baldy 01:49, Aug 29, 2004 (UTC)

You need another one...
I've look at your edits especially the family trees, they are really awesome. Your contributions are of really really high standards... I just can't believe you retired... squash 10:38, Sep 18, 2004 (UTC)

title: User:Muriel Gottrop~enwiki