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Talk:Tangent bundle

You mean tangent bundle is a term used in auto mechanics, Michael Hardy? Phys

 * Not that I've ever heard of, but you can get from cars to tangent bundles in three easy steps: Automobile → differential → derivative → tangent bundle. Yes, I'm bored :) Fropuff 00:54, 2004 Mar 15 (UTC)

This is a very nice and modern description. Note that the purely algebraic description of curvature and especially its group theoretical invariance discussion leads via tangent bundling to examples of cosmoligical models, which general relativity needs for an global approach. Hannes Tilgner

Should have some import of sections, the hairy ball theorem, etc. Jake 22:07, 2 Jun 2005 (UTC)

discussion at Wikipedia talk:WikiProject Mathematics/related articles
This article is part of a series of closely related articles for which I would like to clarify the interrelations. Please contribute your ideas at Wikipedia talk:WikiProject Mathematics/related articles. --MarSch 14:08, 12 Jun 2005 (UTC)

Description in the introduction
Oleg, when I read your example I was led to visualize the tangent space as the subspace in the plane consisting of a line tangent to the given point on the circle. I do not know whether this is what you intended, but this does not strike me as a good way of looking at things. Instead, I think of a vector space attached to each smooth point, representing all possible tangent vectors to this point. I don't really think about the space being embedding in anything, which is perhaps why I was disturbed by this. I changed it to how I see things for now. Also, I thought the cylinder construction could be clarified... it seems vague right now. Thoughts? - Gauge 05:05, 19 September 2005 (UTC)

 * Hi Gauge. You are the differential geometry guy, so I will defer to you in everything in that region. Let me explain my motivation however. The reason I created that example, and the reason I still prefer it as originally stated, is because I found the tangent bundle page very hard to understand for anybody who is not proficient in differential geometry. That's why I have the silly example with tangent lines to the circle, lines which need to be rotated in 3D so that they don't intersect and so that they align smoothly, eventually having no choice than to settle into a cyllinder. I know this is not rigurous, but I have a question: can one at least intuitively think of the tangent bundle that way? Oleg Alexandrov 15:25, 19 September 2005 (UTC)

 * The tangent bundle to a circle is (isomorphic to) a cylinder, not just intuitively, but in actuality. Viz. $$TS^1=S^1 \times \mathbb{R}$$  (using the product topology, I suppose, if one wanted to get fancy.) linas 00:50, 20 September 2005 (UTC)

I caught the comment in the last edit; wanted to point out that locally, every tangent bundle is a simple product. That is, one can always find a subset $$U \subset M$$ where dim U = dim M = n, such that $$TU \simeq U \times \mathbb {R}^n$$ (for a real manifold, C for a complex manifold). (And that futhermore, a whole collection of these can be found so as to cover all of M. And when they intersect, the intersections are of dimension n as well). That's the whole point of charts: to flatten out the manifold into these rectangular bits. Its how the charts stitch together that makes the global topology of the thing non-trivial. This article should absitively posolutly, mention this. What I can't think of is a good simple example of a manifold with a non-trival tangent bundle; I guess mobius band doesn't really cut it. I'm also thinking it might be good to explain why the mobius band is not the tangent bundle to the circle. linas 04:05, 20 September 2005 (UTC)

Tangent bundles are a special type of fibre bundle (when the manifold is connected as required in the definition of a fibre bundle) with fibre homeomorphic to a tangent space of the manifold. Also, since we are considering the direct sum (i.e disjoint union), of the tangent spaces, each point has a neighbourhood U such that the direct sum of all tangent spaces on U is actually homeomorphic to the product space U X T. In fibre bundles, each point is required to have a neighbourhood whose preimage is homeomorphic to a product space so the example with the circle is not surprising.

You have raised a good point; I think that it should be mentioned in the article that the tangent bundle is a special type of fibre bundle.

Topology Expert (talk) 04:01, 28 August 2008 (UTC)

Err, well, tangent bundle to $$S^2$$, but you have to explain a whole pile of stuff, the whole "combing the hair" bit. Somewhere on WP, there's an article on combing the hair ... maybe in line bundle ? linas 04:18, 20 September 2005 (UTC)

 * Yes, every tangent bundle is locally a product, but not globally. About combing the hair, how about the hairy ball theorem? Oleg Alexandrov 04:23, 20 September 2005 (UTC)

 * Yep that's the one, but I see that article is less than illuminating as well. Sigh. Parts of WP are a mess. linas 04:25, 20 September 2005 (UTC)

To do
The state of this article was deplorable, so I rewrote it. Still to do: I may not get around to these soon, so I invite others to help. -- Fropuff 06:51, 20 September 2005 (UTC)
 * Expound upon the simplest nontrivial example, T(S2).
 * Comment on the conditions for the tangent bundle to be trivial (existence of a global frame) and the definition of parallizability.
 * Give the relationship between the tangent bundle of M and the frame bundle of M.
 * Mention functorality of the tangent bundle construction and the pushforward map.
 * The rewrite made the article much better, thanks! It is still not accessible for people not knowing anything at all about differential geometry, but that is to be expected in a sense, as this is not a trivial concept. Oleg Alexandrov 15:21, 20 September 2005 (UTC)

union
why don't you use \bigcup instead of \coprod for disjoint union I didn't do it myself, as I why would rather ask first (is this the right way to handle such a question?)

 * \coprod is the standard symbol for a disjoint union. See that article for reasons. -- Fropuff 19:48, 22 December 2005 (UTC)

 * The idea is tbat the tangent spaces at two different points of the manifold may contain the same tangent vector. In this case, it has to be included twice in the tangent bundle, once as a tangent vector at the first point and once as a tangent vector at the second point. -- Jitse Niesen (talk) 22:10, 22 December 2005 (UTC)

Disputed statement
MarSch, Is there any particular reason why you removed this statement from the tangent bundle article?

 * When this happens the tangent bundle is said to be trivial. Just as manifolds are locally modelled on Euclidean space, tangent bundles are locally modelled on M × Rn.

-- Fropuff 15:31, 18 January 2006 (UTC)

 * Yes.
 * 1) "when this happens" is misleading/ambiguous.
 * 2) TM does NOT locally look like M x R^n.
 * --MarSch 12:19, 19 January 2006 (UTC)

Depends on what you mean by "locally looks like". Certainly, small patches of TM look like small patches of M × Rn. I think this is sufficiently useful intuition to include in the article. -- Fropuff 20:19, 19 January 2006 (UTC)

 * Of course small regions on the tangent bundle look like small regions on M × Rn; that's how the charts are defined. So agree with Fropuff. Oleg Alexandrov (talk) 21:11, 19 January 2006 (UTC)

 * Agree with Oleg and Fropuff. This is a standard way to introduce trivial bundles versus arbitrary bundles; see Milnor and Stasheff, for example. There they speak of "local triviality", which can be made precise. - Gauge 21:40, 20 January 2006 (UTC)

Examples
It's taking me a while to figure all of this bundle business out. Suppose I have an idealized particle somewhere in space. Its position can be modeled by a point in an affine space. Is it correct then that its complete state (position and velocity) represents a point in (member of the) tangent bundle of that affine space? Similarly, would a bound vector (a vector with a defined tail position as well as direction and magnitude) really be a member of a vector bundle? —Ben FrantzDale 06:20, 28 January 2007 (UTC)

 * Yes and yes. -- Fropuff 16:27, 28 January 2007 (UTC)

 * Great. Thanks. —Ben FrantzDale 21:46, 28 January 2007 (UTC)

It seems weird in the "Examples" section that it says that "The tangent bundle of the circle is also trivial and isomorphic to $S^1\times R$." Given the definition of trivial previously, that is redundant (and hence confusing, because the reader might think that he has misremembered the definition of trivial.) Thomaso (talk) 16:05, 13 February 2013 (UTC)

There is no Canonical Vector Field
Upon opening this article I was shocked to see that it claims the existence of a canonical vector field living on TM. There is no such thing. You can try write it down in a particular coordinate system (see the current article) but it is *not* a well defined (i.e. coordinate independent) geometrical object. For a reference, see Burke p. 93. I recommend just deleting this section, though I didn't want to just do it before giving people an explanation. Milez 00:26, 16 September 2007 (UTC)
 * There seem to be a misunderstanding. Even if the canonical vector field V is not as well known as the canonical 1-form on the cotangent bundle, there definitely is a canonical vector field on every tangent bundle. This is sometimes called the Liouville vector field or the radial vector field. I don't have Burke so I can not check his exact claim. Does he maybe say there there is no canonical vector field on M? In any case, I added one reference that uses V to characterize the tangent bundle. Essentially, V can be characterized using 4 axioms, and if a manifold has a vector field satisfying these axioms, then the manifold is a tangent bundle and the vector field is the canonical vector field on it. Haseldon 06:15, 20 September 2007 (UTC)
 * Burke's Applied Differential Geometry only says that (using coordinates as in the article)
 * $$ \sum_i v_i \frac{\partial}{\partial x_i} $$
 * is not a coordinate-independent vector field. -- Jitse Niesen (talk) 07:17, 20 September 2007 (UTC)

 * There seems to be some confusion resulting from Burke's claim. The expression that Jitse Niesen wrote above is not a coordinate expression for the canonical vector field V of TM. Additionally, I have just reverted an erroneous "correction" which somebody made to the page using the above expression. The correct expression is
 * $$ V = \sum_i v^i \frac{\partial}{\partial v^i}. $$
 * I recommend ignoring Burke's book, as it simply confuses matters. Leo C Stein (talk) 21:16, 6 October 2017 (UTC)

 * Ok, my bad. I actually just misread the old entry due to the notation (I was thinking that the y's were coordinates on the underlying manifold). I totally agree that the quantity appearing on the current page is a well defined geometric quantity. Also, thanks for the info - I came to this page in the first place to learn more about the Liouville field. Milez 18:14, 21 September 2007 (UTC)

 * IMO the so-called canonical vector field would be better described if you avoided local coordinates. See double tangent bundle for how to do this. Rybu (talk) 05:11, 10 September 2008 (UTC)

 * The canonical vector field lurks in several articles with this same precise meaning, and I would like to point out that it is not in any way special to the tangent bundle. Namely, for any vector bundle (E,p,M) one can define the canonical vector field V as the infinitesimal generator of the Lie-group action
 * $$ \mathbb R\times (E\setminus 0) \to (E\setminus 0) \quad ; \quad (t,v)\mapsto e^tv $$
 * on the slit vector bundle (E/0,p|E/0,M), which is obtained from (E,p,M) by removing the zero section. IMO this construction should be moved into the article on vector bundles. Lapasotka (talk) 09:58, 4 March 2010 (UTC)

Higher order Tangent bundle deleted by TopologyExpert
TopologyExpert deleted the higher order tangent bundle section saying it was completely incorrect. What exactly do you see as incorrect, because it looks largely correct to me and the people who created it. The article clearly states the tangent bundle is an object that exists for a smooth manifold, moreover, later in the article it clearly states that the tangent bundle is itself a smooth manifold, so the concept of the tangent bundle of the tangent bundle is perfectly well-defined. The bit about the tensor is a little uninformative but it was otherwise totally on the mark. So what do you perceive as totally wrong? Rybu (talk) 04:24, 3 October 2008 (UTC)

 * I brought higher order tangent bundles back. I moved them ahead of the canonical vector field on the tangent bundle since the double tangent bundle is needed to make sense of that section.  I also added a "role" section where it's explained that the point of the tangent bundle is to serve as domain and range for the derivative of a smooth map of manifolds. Rybu (talk) 03:28, 4 October 2008 (UTC)

 * Yes, it is true that the total space of the tangent bundle of a smooth manifold is a smooth manifold. I deleted that section because at the time there were no reasons as to why these 'higher order tangent bundles' are of interest. Also, the section claimed (wrongly) that higher order tangent bundles are like 'higher order derivatives' which is meaningless. Of course, higher order derivatives of a smooth function between smooth manifolds can be induced on higher order tangent bundles. But the section is good know so I have no intentions of removing it again.

Topology Expert (talk) 03:34, 9 October 2008 (UTC)

Request to clarify intro and intro figure
The intro, in my view, is frustratingly opaque, possibly for want of a few very minor stepping stones. I'll try to point out some sticky points.

First, could someone please annotate the initial "TM = ..." definition a bit more thoroughly? Specifically:

-- What is TM? Is that two separate symbols, with T and M having individual meanings, or a single combined symbol denoting "entire tangent space for manifold M". And if so, where does tangent bundle appear in this algebra? Or does TM mean "tangent bundle"?

 * "TM" denotes the tangent bundle of the manifold M (in a vague sense, one could view T as an "operator" sending a manifold to its tangent bundle, "analogous" to the "operator" D sending x to its differential "Dx"). The tangent space of a manifold at a particular point is denoted by "TxM", where the point in question is x. -- PS T  01:54, 9 December 2009 (UTC)

 * Thanks, that was useful. So "T" = "Tangent bundle of". And overall the algebra is saying that the tangent bundle of the entire manifold (eg: circle) comprises the disjoint union set of the tangent bundles at each individual point on the manifold. Gwideman (talk) 03:47, 9 December 2009 (UTC)

-- What the heck is that upside-down pi? How would a reader go about looking it up? I looked at the disjoint union link and didn't find it there. Or is this expression intended to introduce and define upside-down pi?

 * The "upside-down pi" (although one usually does not refer to it in that manner)

serves to write the tangent bundle as the disjoint union of its tangent spaces (as a set). This means that an element of the tangent bundle is in one and only one tangent space (indeed, it is a tangent vector to the manifold at some point). Topologically, however, the tangent bundle is not necessarily the disjoint union of its tangent spaces (that is, its topology is not necessarily the "disjoint union topology") (do not worry about understanding this, if you do not wish to; it is not necessary). -- PS T  02:00, 9 December 2009 (UTC)
 * Don't worry, I don't understand the distinction being made here :-). But as a consolation it would be helpful to know how one does refer to the upside-down pi symbol. Gwideman (talk) 03:47, 9 December 2009 (UTC)
 * One usually refers to the "upside-down pi" as a disjoint union. Sorry for not mentioning that. -- PS T  10:49, 9 December 2009 (UTC)

OK, now moving on to the informal circle example, which could be the way into this topic for those stumped by upside-down pis. Though the example has a plain english description, the description doesn't relate the figure to the introduction.

Perhaps the correspondence is as follows: -- The blue circle is the manifold (as the caption notes.)

 * Correct. -- PS T  02:21, 9 December 2009 (UTC)

-- The red lines in the top figure are the tangents at a few example points around the circle, and the concept extends to the complete set of tangents at every point around the circle.

 * Clarification: Each red line is the tangent space of the circle at a particular point (and not merely a tangent vector). The totality of all such red lines is the tangent bundle.
 * Got it. In this case one of these tangent spaces is one dimensional, occupying the same space as the infinite-line tangent. Hence containing all possible tangent vectors for that point on the manifold.Gwideman (talk) 03:47, 9 December 2009 (UTC)

-- Murky: Is each red line the "tangent space at x" described in the intro? Ie: in this instance, the tangent space is 1-D? Or is each red line actually the edge view of a tangent plane?

 * Since the circle is one-dimensional (locally it "looks like a curved line segment"), the tangent bundle only encompasses one-dimensional tangent spaces (that is tangent lines). If it were a sphere instead of a circle, one would consider two-dimensional tangent spaces (that is, tangent planes). The top of the image shows the tangent bundle horizontal to the circle. However, since one aspect of mathematics is the development of different views of particular phenomena, one seeks for another view of the tangent bundle which is simpler. The bottom part of the image, that is the totality of all red lines pointing vertically, shows the tangent bundle as an infinite cylinder (a far simpler description than the top part of the image). -- PS T  02:21, 9 December 2009 (UTC)
 * OK, got the one-D part. But here's where I come off the rails. What makes it OK to regard each tangent space as equivalent to a one-D space in a completely different direction? (Because apparently I was wrong about the cross operation, below.) Gwideman (talk) 03:47, 9 December 2009 (UTC)
 * I would just like to say that Lie groups are parallelizable but that would not be right ;). Before you read what follows, just note that profound mathematicians such as John Milnor, Raoul Bott and co. have done major work in trying to determine which spheres (in higher dimensions) have tangent bundles that can be represented in the "vertical manner" that is done for the circle (so you are not the only one who is trying to figure that out (seriously, it was a tough problem; people eventually determined that the circle (one-dimensional sphere), the three-dimensional sphere and the seven-dimensional sphere are the only ones)). Intuitively, the circle is "uniform" in that given any two points on the circle, there is a smooth map carrying one point to the other (rotation does this, for example). Therefore, the tangent spaces of the circle "free-flow" in that they spread around the circle in a "circle-like manner" (cylindrical) (the fact that there is a smooth map carrying one point of the circle to any other implies that the map induces a linear isomorphism of tangent spaces at the respective points, more precisely). In particular, one can arrange the tangent bundle in a vertical manner, while essentially retaining its internal structure. If you did not understand that which I have said at first glance, don't worry too much. This particular point is not too important in a first look at tangent bundles (but when you gain more experience, you will see that this is indeed trivial ;)). -- PS T  11:07, 9 December 2009 (UTC)

-- Taking each of the red line tangents, and substituting a line that's perpendicular to the plane of the circle corresponds (I'm assuming) to the cross (X) operation in the third part of the TM= expression, and results in the lower figure. This produces lines that are non-overlapping but together form a smooth surface (here a cylinder).

 * The "cross" (see below) serves to represent an element of the tangent bundle (which is of course a set) as an ordered pair; it can be uniquely described by knowing the tangent space to which the element belongs. Equivalently, one must know the point to which the tangent space is associated, as well as the particular element of the tangent space considered (that is, the particular tangent vector). Any element of the tangent bundle can be described as (x, v), therefore, where x is in the manifold and v is some vector in the tangent space at x. -- PS T  02:21, 9 December 2009 (UTC)

-- Murky: What kind of operation is this cross? It doesn't seem to be ordinary vector cross product, because U{x} doesn't seem to be a vector, but rather a set. (The figure caption describes this as "considering and joining", so maybe cross is the "considering" operator.)

 * See cartesian product. -- PS T  02:21, 9 December 2009 (UTC)

 * Ah-hah. OK, so cross (cartesian product) here just assembles the x points with the v vectors to make a set whose members are (x,v). So cross does not explain (in the example) the move from tangent lines/spaces to lines/spaces arranged perpendicular to the plane of the circle. (As I noted above.) Gwideman (talk) 03:47, 9 December 2009 (UTC)
 * Quick clarification: The cartesian product represents elements of the tangent bundle as rdered pairs; the first "coordinate" represents the point at which one is considering the tangent space, and the second "coordinate" represents the particular tangent vector within the tangent space. For instance, if I was considering an element of the tangent bundle of the circle, I would have to consider which "red line" the element is in (according to the image); so I would have to know which point the red line is tangent to, as well as the corresponding vector on the red line. These two pieces of information would describe the element of the tangent bundle uniquely. If I just said "unit vector", I would not be able to determine the particular element of the tangent bundle since each and every red line has a unit vector; to determine the element uniquely, I would have to know which red line to choose. Likewise, if I only knew the red line to which an element of the tangent bundle belongs, I would not be able to determine the element since there are "many" vectors on the red line; I would have to know which vector to choose (in addition to the given red line). -- PS T  10:47, 9 December 2009 (UTC)

Clearly at this point I don't understand this subject enough to make complete sense of it, but perhaps my description will allow someone to troubleshoot. Gwideman (talk) 14:39, 8 December 2009 (UTC)

 * Your comments are much appreciated for they show that the lead could be explained in a simpler fashion. However, this subject is usually referred to as differential topology (or differential geometry); one must usually have a background of point-set topology and linear algebra to appreciate it. I am not saying that you do not have the background to appreciate the subject, but rather that a complete acquiantance with these subjects aids one in appreciating differential topology. Hope this helps (note that I have responded to your points in detail above). -- PS T  02:21, 9 December 2009 (UTC)
 * Thanks for your patient explanations. I feel pretty close to a light-bulb moment on this one, with the remaining mystery being the jump from tangent vector spaces to a bunch of vector spaces conveniently arrange all parallel to each other. Gwideman (talk) 03:47, 9 December 2009 (UTC)
 * No problem - I am happy to help. If you are interested in furthur questions about tangent bundles (or any other math-related topic, for that matter), a good place to visit would be Reference Desk/Mathematics. Cheers, -- PS T  11:09, 9 December 2009 (UTC)

-- It seems to me that the first equation in this article is a bit odd, particularly the last expression. First of all, is $$\{x\}$$ supposed to refer to the set of all $$x\in M$$, or simply to the set containing only the single point $$x$$? If the former, then there is no need for union symbol since this is already part of the definition of the Cartesian product, and also in that cast we could just refer to $$x\in M$$ as simply $$M$$ (since we're only defining a space rather than elements of that space). If the latter, why not just refer to $$x$$ rather than $$\{x\}$$? It would seem to me that the clearest way to define the tangent bundle would be just $$TM \equiv \coprod_{x\in M} T_x M = \{ (x,v) \mid x \in M, v \in T_x M \}$$ similar to on Wolfram.

Also isn't it true that each $$T_x M$$ is mathematically just $$\mathbb{R}^n$$, and is only unique in its interpretation/significance? Given thats the case, wouldn't it also be correct to identify $$T_x M$$ as $$M \times \mathbb{R}^n$$? Somebody please me know if I'm going astray here since I'm new to differential geometry. AnIsometry (talk) 11:25, 21 December 2009 (UTC)

Request for clarification, cont'd
The previous section was very helpful in clarifying some problems. Here are a few items that the discussion has prompted:

1. The upside-down pi symbol is used here to stand for "disjoint union". However, the disjoint union article, which this article references, uses the \bigsqcup, not the coproduct symbol \coprod. I think it would help to change to the bigsqcup, unless coproduct is intended. (A previous talk section "union" suggested the plain bigcup symbol, which the other article would argue against, though I do see bigcup used that way in many other web sources.)

2. Footnote note 1 is a bit mangled on the way to almost explaining a point I'm about to make below. I think the phrase "align them in a plane perpendicular plane" doesn't make sense. Possibly it should be "align them perpendicular to the plane of the circle".

3. From the "Request for clarification" discussion of the last few days, and my finally understanding the notation of the "TM=..." algebra, I think I see where the intro got me way off track, and how the intro could be improved.

Not understanding the notation, I tried to make it make sense as a statement of how to calculate the arrangement of the tangent bundles in space. I.e.: if we were to apply that algebra somehow to the circle example, it would "calculate" the answer: a set of "vertically" arranged 1-D spaces. Instead, I now see that the algebra is merely a statement of the requirements: a set of vector spaces, one vector space for each point on the manifold, with each vector space disjoint from the others (and make them collectively contiguous and smooth? -- though I don't see that in the requirements). The actual solution -- 1-D vector spaces perpendicular to the circle's plane, and arranged around the circle so as to form a cylinder -- was devised by separate thinking not shown here, and is "the answer" because it satisfies the requirements.

Now, if I'm right about this, it would be helpful for the intro to point this out: That having stated "Tangent bundle" in terms of requirements, we are looking for solutions for those requirements, not calculating the shape of the tangent bundle.

Thanks again for the discussion Gwideman (talk) 12:54, 9 December 2009 (UTC)

Canonical vector field: tangent space is naturally a product
Clearly, "the tangent space of a vector space W is naturally a product, $$TW \cong W \times W$$" should read "the tangent bundle of a vector space...", which raises the question why we can apply this product structure to the tangent bundle $$T(T_x M)$$ at each point. How do we get $$T(T_x M)$$ from $$T(TM)$$? Also, is it obvious that the given "informal" definition gives a coordinate-independent vector field? If not, what is the point of this lengthy explanation? Doesn't the map $$(x, v) \mapsto (x, v, 0, v)$$ given below achieve the same less cryptically? I would also like to see an explanation of the phrase "splitting the map via". Theowoll (talk) 00:07, 12 March 2018 (UTC)

title: Talk:Tangent bundle


text:
Tetrad

Tetrad ('group of 4') or tetrade may refer to:

 * Tetrad (area), an area 2 km x 2 km square
 * Tetrad (astronomy), four total lunar eclipses within two years
 * Tetrad (chromosomal formation)
 * Tetrad (general relativity), or frame field
 * Tetrad formalism, an approach to general relativity
 * Tetrad (geometry puzzle), a set of four simply connected disjoint planar regions in the plane
 * Tetrad (meiosis), the four cells produced by meiotic cell division
 * Tetrad (music), a set of four notes
 * Tetrad (chord), a series of four notes
 * Tetrad (symbol), or tetractys, a triangular figure of ten points arranged in four rows, and mystical symbol
 * Medical tetrad, a group of four signs or symptoms which characterise a specific medical condition
 * Nibble, or tetrade, a 4-bit group
 * a tuple of length 4
 * Tetrad Islands, in the Antarctic

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Tetrad


text:
Musical similarity

The notion of musical similarity is particularly complex because there are numerous dimensions of similarity. If similarity takes place between different fragments from one musical piece, a musical similarity implies a repetition of the first occurring fragment. As well, eventually, the similarity does not occur by direct repetition, but by presenting in two (or more) set of relations, some common values or patterns. Objective musical similarity can be based on musical features such as:

Pitched parameters
 * Pitch interval similarity
 * Melodic similarity
 * Modulation pattern similarity
 * Timbral similarity

Non-pitched parameters
 * Metrical structure similarity
 * Rhythmic pattern similarity
 * Section structure similarity

Semiotic parameters
 * Modality structure similarity
 * Extensional similarity
 * Intensional similarity

Nevertheless, similarity can be based also on less objective features such as musical genre, personal history, social context (e.g. music from the 1960s), and a priori knowledge.

Similarity is relevant also in music information retrieval. Finally, musical similarity can be extended to the comparison between musical gestures in performance and composition.

Applications
Automatic methods of musical similarity detection based on data mining and co-occurrence analysis has been developed in order to classify music titles for electronic music distribution.

title: Musical similarity


text:
Naraku

Naraku may refer to:

 * Naraku, Iran, a village in Bushehr Province, Iran
 * Naraka, one of the underworlds of Buddhism
 * Naraku (奈落), a character in InuYasha
 * Ninja Slayer's ninja spirit, from Ninja Slayer
 * Naraku from Senran Kagura video game franchise

title: Naraku


text:
St Bernard Pass

St Bernard Pass may refer to:

 * Great St Bernard Pass crosses the Valais Alps between Martigny, Switzerland and Aosta, Italy
 * Little St Bernard Pass lies between Mont Blanc and the Graian Alps, connecting Bourg St Maurice, France to Courmayeur, Italy

title: St Bernard Pass


text:
1966 in Afghanistan

The following lists events that happened during 1966 in Afghanistan.

Thanks largely to the intelligent use made of the aid given by the U.S.S.R., the United States, West Germany, Britain, China, and the World Bank, the internal economy of the country made good progress.

The first five-year plan, which began in 1956, aimed at encouraging agriculture, especially irrigation. Experience showed, however, that progress in these spheres could only be partially achieved as long as internal communications remained primitive and the natural resources of the country were largely unexplored. As a result, the major effort was diverted to the construction of roads and airports, and to the systematic investigation of sources of water supply and of mineral wealth.

During the course of the second five-year plan, conditions became favourable on many economic front. Promising deposits of natural gas and of iron ore were discovered; the power available for industrial use increased dramatically; and the extension of irrigation led to substantially increased agricultural production.

In Afghanistan, as in many other underdeveloped countries, however, this rapid success led to the emergence of new problems, unforeseen in the original planning: inflation of prices, difficulties over foreign exchange, and an unhealthy reliance on large-scale external aid for the easing of current domestic shortages. The indications are that the third five-year plan will aim mainly at consolidating what has already been achieved rather than at any new major advances.

Incumbents

 * Monarch - Mohammed Zahir Shah
 * Prime Minister - Mohammad Hashim Maiwandwal

January 1966
The break with the past represented by the new democratic constitution inaugurated in 1965 is further underlined by the appointment of a woman, Kubra Noorzai, to the cabinet as Minister of Public Health. Under the new constitution, women can both vote and stand as candidates, and in September 1965, four were returned to the new National Assembly. Even so, Miss Noorzai's elevation to cabinet rank is regarded as a striking illustration of the determination of King Mohammad Zahir Shah and of the government headed by Mohammad Hashim Maiwandwal to bring the country into line with modern ideas on the political and social status of women.

April 4–8, 1966
Cordiality with the People's Republic of China is cemented by a visit to Kabul by President Liu Shaoqi and Marshal Chen Yi. Afghanistan maintains its traditional policy of friendliness without involvement, its relations with Communist and non-Communist countries being equally cordial. The former friction with Pakistan has also ceased.

End of 1966
The first parliament created under the new democratic constitution adjourns for the winter recess. Its relations with the Maiwandwal cabinet were close and cordial, and it gave full support to the government's efforts to achieve national financial stability. Drastic cuts were made in government expenditure and, due to an agreement with the International Monetary Fund, the country is able to face with confidence the completion of the second five-year plan and the beginning in May 1967 of the third five-year plan.

title: 1966 in Afghanistan


text:
Sepak takraw

Sepak takraw, or Sepaktakraw, also called  buka ball, kick volleyball or foot volleyball, is a team sport. It is played with a ball made of rattan or synthetic plastic between two teams of two to four players on a court resembling a badminton court. It is similar to volleyball and footvolley in its use of a rattan ball and players using only their feet, knees, shoulders, chest and head to touch the ball. Sepak Takraw is often referred to as a mixture of volleyball, due to its use of a net, and association football, as players use their feet.

The sport's modern version was introduced, developed and standardized in 1960 when officials from Malaysia, Singapore, Thailand and Myanmar met in Kuala Lumpur to agree on a name and standard rules for it. It was previously known as Sepak Raga Jaring, and was first exhibited in Penang in 1945. It was introduced in the 1965 Southeast Asian Games in Kuala Lumpur as a medal event. Sepak Takraw is considered Malaysia's national sport.

Sepak takraw is governed internationally by the International Sepaktakraw Federation (ISTAF), formed in 1988, which is responsible for major international tournaments including the ISTAF SuperSeries (ISS) and ISTAF World Cup (IWC), Malaysia's Khir Johari Cup, and Thailand's King Cup.

Sepak takraw resembles native sports known as Sepak Raga in Brunei, Indonesia, Malaysia, and Singapore; Takraw and Rago/Raga in Indonesia; Sipa in the Philippines; Chinlone in Myanmar; Takraw in Thailand; Kataw in Laos; and Sek Dai in Cambodia. It is also claimed to be related to Cuju in China, Cau May in Vietnam, Jegichagi in Korea and Kemari in Japan.

Etymology
The word sepak is Malay (Jawi: سيڨق) for kick while the word takraw is of Thai (Thai: ตะกร้อ) origin, translated as muzzle or woven rattan ball. "Sepak Takraw" quite literally means "to kick a rattan ball". The choice of this name for the sport was essentially a compromise between Malaysia and Thailand in Kuala Lumpur in 1960.

In the past, it was called "Sepak Raga Jaring" in Malaysia, after the term "Jaring", meaning net in Malay, was added to the traditional "Sepak Raga" game when it was created by Hamid Mydin in Penang in 1945. In Thailand, it is simply known by its original name of "Takraw". Internationally, only the term "Sepak Takraw" is used to refer to the modern sport.

Predecessors
Sepak Takraw may have been introduced to Southeast Asia by the Chinese, who were inspired by the traditional game Cuju, an ancient military exercise where soldiers play to keep a leather ball filled with feathers airborne by kicking it back and forth between two or more people. As the game evolved, the feather-stuffed ball was replaced by an air-filled ball with a two-layered hull. Cuju is also considered by the International Football Association (FIFA) as the origin of football as a sport.

In Myanmar, Sepak Takraw is known as "chinlone". Chinlone has played a prominent role in Myanmar for about 1,500 years. Its style is performance-based because it was first created as a demonstrative activity to entertain Burmese royalty. Chinlone is heavily influenced by traditional Burmese martial arts and dance.

In Malaysia, the first recorded instance of Sepak Takraw, with balls made of woven strips of rattan, was in the Malacca Sultanate (present-day Malaysia) in the 15th century, according to an ancient Malay manuscript, "Sejarah Melayu" (Malay Annals). The Malay Annals described an incident involving Raja Muhammad, a son of Sultan Mansur Shah, who was accidentally hit with a rattan ball by Tun Besar, the son of Bendahara Tun Perak, in a Sepak Raga game. The ball hit Raja Muhammad's headgear and knocked it to the ground. Angered, Raja Muhammad immediately stabbed and killed Tun Besar, leading to some of Tun Besar's kinsmen wanting to kill Raja Muhammad in retaliation. However, Bendahara Tun Perak managed to restrain them from an act of treason by saying that he would no longer accept Raja Muhammad as the Sultan's heir. Sultan Mansur Shah ordered his son out of Malacca and had him installed as the ruler of neighbouring Pahang.

In Thailand, there is evidence that the Thai played Sepak Takraw during the reign of King Naresuan (1590–1605) of Ayutthaya Kingdom. A French historian, François Henri Turpin, wrote about how the Siamese played the game of Takraw to stay in shape. Murals at Bangkok's Wat Phra Kaeo, built in 1785, depict the Hindu god Hanuman playing Sepak Takraw in a ring with a troop of monkeys. The game was played in a circle for hundreds of years, until modern Sepak Takraw began taking shape in Thailand sometime during the early 1740s. In 1929, the Siam Sports Association drafted the first rules for Takraw competition. Four years later, the association introduced the volleyball-style net and held the first public contest. Within just a few years, Takraw was introduced to the curriculum in Siamese schools. The game became such a cherished local custom that another exhibition of volleyball-style Takraw was held to celebrate the kingdom's first constitution in 1933, the year after Thailand abolished absolute monarchy.

In Indonesia, Sepak Takraw is also known as Sepak Raga. In Sulawesi, the traditional Bugis football game is called "Raga" (the player is called "Pa'Raga"). Men play the "Raga" circle in a group, where the ball is passed from one to the other, and the man who kicks the highest ball is the winner. "Raga" is also played for fun by demonstrating several tricks, such as kicking the ball and placing it on the player's head with the handle of the tengkolok bugis (Bugis headgear similar to a Malay tanjak).

In the Philippines, the sport is related to a native game called "sipà" (or "sipà salama" among Muslim Filipinos), and along with traditional martial arts, survived Spanish colonization. It is a popular sport played by children in Philippines, and was the Philippine national sport until it was replaced by Arnis in 2009. Sepak Takraw is included in Philippine's elementary and high school curriculum.

Origins of the modern sport
In the beginning, Sepak Takraw was not meant to be competitive, but was a casual game with an emphasis on physical activity. The game acted as an exercise to improve dexterity and loosen the limbs after long periods of sitting, standing or working. However, the modern version of Sepak Takraw began taking shape sometime during the 1940s. In 1935 in Seremban, Sepak Raga was first played on a badminton court over the net with players on two opposing sides, amid celebrations of the Silver Jubilee of George V. The event is the earliest example of modern sport rules being used for Sepak Raga, turning it into a competitive sport. Badminton was a preferred sport for the British, whereas Sepak Raga was mainly played by the Malays. Since the diversion sport was first played amid the Jubilee festivity, it was known as "Sepak Raga Jubilee" (Jubilee Sepak Raga).

It is likely that the sport had gained popularity in Negeri Sembilan, and spread to various states of Malaya (now West Malaysia). In the years following World War II up to the mid-20th century, "Sepak Raga Jubilee" was played in rural villages and towns throughout Malaya. Though Malaysia is a multiracial country, Sepak Takraw is mainly popular among the Malay community. The new sport then spread to Penang. The popularization of present-day Sepak Takraw is, for the most part, attributed to three people from Jalan Patani, Penang. In February 1945, a net and tenets like badminton were presented by Hamid Mydin, accompanied by local Sepak Raga sportsmen, Mohamad Abdul Rahman and Syed Yaacob to demonstrate Mydin's new variation of "Sepak Raga Jaring" (Net Sepak Raga). The new version was preferred due to quicker pace, distinctive styles of kicking and the higher standard of athleticism that it demanded. It is considered the pioneer version of modern Sepak Takraw and remains one of the dominant competitive forms.

The first properly organized Sepak Takraw competition was held at a Swim Club in Penang on May 16, 1945. Three teams from Malay populated localities in Penang were among those that competed for the Nyak Din Nyak Sham Trophy. The sport spread rapidly through the remainder of Malaya. From Penang, "Sepak Raga Jaring" spread to Alor Setar in Kedah, to Kampung Baru in Kuala Lumpur and then to Singapore. By 1960, the variation was well known in many Malayan schools that had badminton courts. The sport was frequently played by football players because of the similarities in skills required for both sports. Several Sepak Raga associations formed in various Malayan states.

About the same time, similar developments occurred in Thailand. In 1929, the Siam Sports Association drafted the first rules for the Takraw competition. Four years later, the association introduced the volleyball-style net and held the first public contest. Within just a few years, Takraw was added to the curriculum in Siamese schools. The game became such a cherished local custom that another exhibition of volleyball-style Takraw was staged to celebrate the kingdom's first constitution in 1933, the year after Thailand abolished its absolute monarchy.

Standardization
The determination and perseverance of Penang's Sepak Takraw pioneers led to the founding of the "Jawatankuasa Penaja Sepak Raga Pulau Pinang" (Penang Sepak Raga Sponsors' Committee) on 25 March 1956 at Dewan UMNO Pulau Pinang. On 28 January 1960, the committee negotiated with representatives from Selangor, Negeri Sembilan, Kedah and Singapore at Bangunan Persatuan Melayu Pulau Pinang on the founding of "Jawatankuasa Penaja Perseketuan Sepak Raga Jaring Malaya" (Malayan Sepak Raga Jaring Sponsors' Committee), a national organization. The initial rules and regulations of the sport were enacted and compiled in writing on 15 April 1960 at Sultan Sulaiman Club in Kuala Lumpur.

On 25 June 1960, the Malayan Sepak Raga Federation (now renamed Malaysian Sepak Takraw Association (PSM)) was established at a meeting held in Balai Rakyat, Jalan Patani, Penang. The ceremony was officiated by the Chief Minister of Penang, Wong Pow Nee. During the meeting, representatives of Kedah, Selangor, Negeri Sembilan and Penang had unanimously appointed Khir Johari as its first President. Hamid Mydin was also recognized as the creator and founder of Sepak Takraw by the federation at that meeting. The Sepak Raga rules compiled on 15 April in Kuala Lumpur were also ratified by the Malayan Sepak Raga Federation on this day.

Later that year, representatives from Malaya, Singapore, Myanmar and Thailand met in Kuala Lumpur to standardize the guidelines for the sport. After intense debate, they came to a consensus that the sport would be officially called "Sepak Takraw". Thus, a game of Sepak Takraw that witnesses acrobatic movements by athletes was officially introduced at the international level. In Malaya, an inter-state competition known as "Khir Johari Gold Cup" was organized at Stadium Negara, Kuala Lumpur from 27 to 28 December 1962 to further advance the sport. Penang, where Sepak Raga Jaring originated, would become the primary holder of the tournament. By that point, "Sepak Raga Jaring" was quite popular in Malaya, and is now regarded as Malaysia's national sport.

Global game
In 1965, the Asian Sepaktakraw Federation (ASTAF) was formed. Its first task was to translate the Sepak Takraw rules into English, facilitating the first worldwide competition, the Southeast Asian Peninsular Games (SEAP Games) (now Southeast Asian Games (SEA Games)) held in Kuala Lumpur. It was still confusingly known as "Sepak Raga". From the fourth SEAP Games in 1967, the term "Sepak Takraw" become the established name.

In the 1970 Asian Games at Bangkok, Sepak Takraw was introduced as a demonstration sport by Malaysian and Thai teams.

In 1975, the Kedah's Sepak Takraw team visited Germany in conjunction with The Sports Press Feast 1975 to play Sepak Takraw as a demonstration.

In 1977, Penang's Sepak Takraw team participated in North Malaysian Week in Adelaide, Australia.

In 1979, ASTAF for the first time held a conference in Jakarta in conjunction with the SEA Games and reviewed the Sepak Takraw laws submitted by the Malaysian Sepak Takraw Association. The ASTAF technical committee also held its second meeting in Singapore in the same year for the same purpose.

In 1980, the Malaysian Sepak Takraw team played several Sepak Takraw games in China, South Korea and Hong Kong, an outstanding achievement in the history of Sepak Takraw towards introducing the sport to East Asian countries.

In 1982, the woven synthetic ball was introduced to replace woven rattan ball in Thailand.

In 1988, the International Sepaktakraw Federation (ISTAF) was formed by members of the Asian Sepaktakraw Federation (ASTAF). It was recognised as the international governing body for the sport by the Olympic Movement in 1990.

In 1990, Sepak Takraw was included as a medal sport at the Asian Games in Beijing.

In 1997, the first women's championship was held in Thailand.

In 1998, Sepak Takraw was introduced as a demonstration event in the Commonwealth Games held in Kuala Lumpur.

In 2011, the inaugural edition of Sepak Takraw's flagship tournament, the ISTAF World Cup, was staged in Kuala Lumpur, Malaysia. The ISTAF SuperSeries, a new series of elite tournaments was also launched in Bangkok.

There are more than 30 countries with national Sepak Takraw organizations, with representatives in the International Sepaktakraw Federation (ISTAF) overseeing the sport.

Competition
International play is now governed by ISTAF. Major competitions for the sport such as the ISTAF SuperSeries, the ISTAF World Cup and the King's Cup World Championships are held every year.

Sepak Takraw is now a regular sport event in the Asian Games and the Southeast Asian Games, with Thailand having won the most medals for the event.

Asian Games
Sepak Takraw has been a sport at the Asian Games since 1990 with Thailand securing the highest number of gold medals.

Canada
The Lao people first brought Sepak Takraw into Canada when they immigrated as refugees in the 1970s. But the game began gaining exposure outside the Laotian communities when a Saskatchewan teacher, Richard (Rick) Engel, who was introduced to Sepak Takraw while living in Asia, included it in Asian Sport, Education & Culture (ASEC) International's School Presentation Program. Sepak Takraw was so well received by schools that it became part of ASEC's mandate to help introduce, promote and organize the sport across the country. In May 1998, after introducing many schools to the sport, and in concert with experienced players, ASEC International organised the first Canadian inter-provincial tournament with men's, boys' and girls' teams. By the end of 1998, Engel was sent to Bangkok, Thailand to film at the 14th King's Cup Sepak Takraw World Championships – the footage of which was used to produce a widely used instructional Sepak Takraw video/DVD, called Sepak Takraw – Just for Kicks.

On 11 December 1998, the Sepak Takraw Association of Canada (STAC) was incorporated to organise and govern the sport nationally. Its office was set up in Regina, Saskatchewan, where there were experienced players and organizational support, sharing resources and office space of the already established ASEC International, a committee which has now become Sepak Takraw Saskatchewan Inc. The first annual Canadian Open Sepak Takraw Championships (a national and international tournament event) were held in May 1999 in Regina, and have over the years attracted teams from across Canada, the United States, Japan, Malaysia and China. That same year Canada also attended its first International Sepaktakraw Federation (ISTAF) Congress and was accepted as member of ISTAF. In 2000, Rick Engel, Perry Senko and Brydon Blacklaws played for Team Canada and earned a silver medal in the entry level division of the King's Cup World Sepak Takraw Championships in Thailand. Another major milestone was achieved on 3 December 2000, when STAC and the sport of Sepak Takraw became an official class E Member of the Canadian Olympic Committee.

Canada has since contributed much to the development of Sepak Takraw worldwide, with Engel authoring three instructional books and helping produce five DVDs about the sport, while STAC did the publishing. The most notable of these books is Sepak Takraw 101 - The Complete Coaching/Instructional Manual for Sepak Takraw (Kick Volleyball), the third edition of which has also been translated into Indonesian and published in Indonesia through a government education project. Engel has since introduced the sport and conducted Sepak Takraw skills clinics in schools and sessions at physical education teachers' conferences all over Canada, the US and Europe.

Japan
A Japanese team played at the 1990 Asian Games in Beijing. While as of 2010 there are no professional teams in Japan, university-level teams have been established at Asia University, Chiba University, Keio University, and Waseda University.

Philippines
Sepak Takraw is also known as "Sipa" in the Philippines. The Philippine Sepak Takraw team competes internationally. Among veteran players still in the lineup are Jason Huerta, Reyjay Ortuste, Mark Joseph Gonzales, Josefina Maat, Des Oltor, Ronsted Cabayeron and Sara Catain.

United States
The earliest accounts of organized Takraw in the United States involve a group of students from Northrop University (Greg St. Pierre, Thomas Gong, Joel "big bird" Nelson, and Mark Kimitsuka) in 1986 in Inglewood, California, learning about and playing the sport in Los Angeles. In the early 80s, Southeast Asians held soccer tournaments with Takraw events in Wisconsin, Michigan, Minnesota and California, especially within the Lao, Hmong and Thai communities. Malaysian students attending the university often enjoyed playing the sport on a court atop the dormitory cafeteria. They taught a handful of curious American students how to play, which in turn inspired Malaysia Airlines to sponsor a US team from the university to attend the National Tournament in Kuala Lumpur in November 1987. The Northrop team played in a bracket of international new teams with Korea, Sri Lanka, and Australia. The US team beat Sri Lanka and Australia to bring home the gold.

The Los Angeles Asian community and Northrop's team had already established a Takraw community in and around the city. Kurt Sonderegger moved to Los Angeles, founded the United States Takraw Association, and started a business that sold plastic Takraw balls. In 1989, he was sent an invitation from the International Sepaktakraw Federation, and along with a few of the Northrop group, travelled to represent the United States in the World Championships.

The team was well beaten but the Takraw world celebrated the participation of non-Asian teams in the World Championships.

Rules and regulations
Measurements of courts and equipment often vary among tournaments and organisations that operate from a recreational to a competitive level; international competitive rules and regulations are used in this section. There are two types of event categories: the regu and the doubles regu. The regu category is played by three players on each team while the doubles regu is played by two players on each team.

Expressions
Takraw is the Thai word for the hand-woven rattan ball originally used in the game. Therefore, the game is essentially "kick ball". The concept of Footvolley originates from Thai Takraw pronounced (Tha-Graw). It is also sometimes incorrectly referred to by foreigners as "Shaolin Soccer"; however, it is an ancient game mainly enjoyed between Thailand and Laos.

Court
Sepak Takraw is played on court a similar to badminton's double sized court.

The court has an area of 13.4 x free from all obstacles up to the height of 8 m measured from the floor surface (sand and grass court not advisable). The width of the lines bounding the court should not be more than 4 cm measured and drawn inwards from the edge of the court measurements. All the boundary lines should be drawn at least 3.0 m away from all obstacles. The center line of 2 cm should be drawn equally dividing the right and left court.

Where the center line meets the sidelines, quarter circles shall be drawn, on either side, from the sideline to the center line with a radius of 0.9 m measured and drawn outwards from the edge of the 0.9 m radius.

The service circle of 0.3 m radius shall be drawn on the left and on the right court, the center of which is 2.45 m from the back line of the court and 3.05 m from the sidelines, the 0.04 m line shall be measured and drawn outward from the edge of the 0.3 m radius.

Net
The net should be made of fine ordinary cord or nylon with 6 cm to 8 cm mesh, similar to a volleyball net.

The net should be 0.7 m in width and not shorter than 6.10 m in length, taped at 0.05 m from tape double at the top and sideline, called boundary tape.

The net should be edged with 0.05 m tape double at the top and the bottom of the net supported by a fine ordinary cord or nylon cord that runs through the tape and strain over and flush with the top of the posts. The top of the net shall be 1.52 m (1.42 m for women) in height from the center and 1.55 m (1.45 m for women) at the posts.In Myanmar they now used at least 1.82m or 2.43m depend on the situation as the standard height is too short and can kick in easily.

Ball
The Sepak Takraw ball should be spherical, made of synthetic fibre or one woven layer.

Sepak Takraw balls without synthetic rubber covering must have 12 holes and 20 intersections, must have a circumference measuring from 42 to(-) for men or from 43 to(-) for women, with a weight that ranges from 170 to(-) for men or from 150 to(-) for women.

The ball can be any single or multi-color, but must not be in any color that would impair the performance of the players.

The Sepak Takraw ball can also be constructed of synthetic rubber or soft durable material for covering the ball, for the purpose of softening the impact of the ball on the player's body. The type of material and method used for constructing the ball or for covering the ball with rubber or soft durable covering must be approved by ISTAF before it can be used for any competition.

All world, international, and regional competitions sanctioned by International Sepaktakraw Federation, including but not limited to, the Olympic Games, World Games, Commonwealth Games, Asian Games and SEA Games, must be played with ISTAF approved Sepak Takraw balls.

Players
A match is played by two teams called 'regu', each consisting of three players. On some occasions, it can be played by only two players (doubles) or four players (quadrant) per team.

One of the players should be at the back; they are called a "Tekong" or are also known as the "Server". The other two players should be in front, one on the left and the other on the right. The player on the left is called a "feeder/setter/tosser" and the player on the right is called a "attacker/striker/killer".

Start of play and service
The side that must serve first should start the first set. The side that wins the first set should have the option of "Choosing Service".

The throw must be executed as soon as the referee calls the score. If either of the "Inside" players throws the ball before the referee calls the score, it must be re-thrown and a warning will be given to the thrower.

During the service, as soon as the Tekong kicks the ball, all the players are allowed to move about freely in their respective courts.

The service is valid if the ball passes over the net, whether it touches the net or not, and inside the boundary of the two net tapes and boundary lines of the opponent's court.

Serving side during service

 * The "Inside" player who is throwing to the server plays with the ball (throwing up the ball, bumping, passing to another "Inside" player etc.) after the call of score by the referee.
 * The "Inside" player lifts their feet or steps on the line or crosses over or touches the net while throwing the ball.
 * The Tekong jumps off the ground to execute the service.
 * The Tekong does not kick the ball on the service throw.
 * The ball touches a serving side player before crossing over to the opponents' court.
 * The ball goes over the net but falls outside the court.
 * The ball does not cross to the opponent side.
 * A player uses their hand or hands, or any other part of his arms to facilitate the execution of a kick even if the hand or arm does not directly touch the ball, but it touches other objects or surfaces instead when doing so.

Serving and receiving side during service

 * Creating distractions or noise or shouting at an opponent.

For both sides during the game

 * Any player who touches the ball on the opponent side.
 * Any part of player's body crosses over into opponent's court whether above or under the net except during the follow-through of the ball.
 * Playing the ball more than 3 times in succession.
 * The ball touching the arm
 * Stopping or holding the ball under the arm, between the legs or body.
 * Any part of the body or player's outfits e.g. shoes, jersey, head band etc., touches the net or the post or the referee's chairs or falls into the opponent's side.
 * The ball touches the ceiling, roof or the wall (any objects).

Scoring system
An official doubles or regu match is won by best of three sets (win 2 out of 3 sets), with each set being played up to 21 points.

A team event or group match is effectively three regu matches played back to back, using different players for each regu. The winner is determined by best of three regus (win 2 out of 3 regus), where a winner of each individual regu is determined by best of 3 sets, played up to 21 points per set.

In the last or third set a change of sides takes place when one team reaches 11 points.

When either serving or receiving side commits a fault, a point is awarded to the opponent side.

Serving: Teams alternate serving every three points, regardless of who wins the points. If a tie takes place at 21-21, each team alternates one serve each until a winner is determined.

Set: Each set is won by the side which scores 21 points with a minimum lead of two points to a ceiling of 25 points. In the event of a 21–21 tie, the set shall be won by the side which gets a lead of two points, or when a side reaches 25 points (whichever occurs first).

Match: A match is won by the team who has won two sets. A team event match is won by the team that wins two regus.

Ranking: In group stages of tournaments or team events (round robin) the ranking in a group is determined by: 1. Sum of match wins; a match win gives 1 point 2. Sum of set points 3. Points difference +/-

Competing countries
International play is now governed by ISTAF, the International Sepaktakraw Federation.

 * Southeast Asia
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 * South Asia
 * Oceania
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 * South Asia
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 * South Asia
 * Oceania
 * South Asia
 * Oceania
 * Oceania
 * Oceania
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 * Oceania
 * Oceania
 * Oceania

 * Americas
 * Europe
 * Africa
 * Europe
 * Africa
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 * Africa
 * Europe
 * Africa
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 * Middle East
 * East Asia
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In other media

 * The sport is mentioned in the fourth episode of the sixth season of the animated series Supa Strikas.
 * In the second episode of Nichijou, Mio Naganohara's mother fails to wake her daughter up for school because she went out to play Sepak Takraw with the neighborhood association.
 * The sport is played in the Let's Go Luna episode "Kick It Good".
 * Sepak Takraw was featured in the episode Temple Frogs from the Disney animated show Amphibia, where Sprig stumbles upon a match played at the Thai Temple.

title: Sepak takraw


text:
Talk:Ex-gay movement

Recent addition
Darwin Naz recently made a large addition to the article. I accept that the addition was made in good faith and indeed much of it looks helpful. Unfortunately, the addition was in some ways misleading. It also involves an improper synthesis of sources, as described at WP:SYNTH. The first part of the addition lists the main goals of the ex-gay movement, including "coordination with individuals and organizations, particularly opponents of gay and lesbian civil equality to influence public perception and public policy" among other things. It is cited to Ex-Gay Research, a scholarly book edited by Jack Drescher and Kenneth Zucker. The second part states that "These goals rest in the claim that sexual orientation is a choice and that change for homosexuals is possible through therapy and prayer", and it is cited to an article in The Atlantic, a non-scholarly popular magazine. The content cited to The Atlantic is misleading, since it is not in fact true that supporters of the ex-gay movement all view sexual orientation as a choice, and nor is it supported by the source provided. The material makes it look as though the popular Atlantic article discusses the goals of the ex-gay movement as described in the scholarly book Ex-Gay Research and shows that they "rest in the claim that sexual orientation is a choice", which is not the case. What the Atlantic article actually states about "choice" is that, "Ex-gay leaders traveled to churches and appeared on television news programs citing a litany of examples of happily married “former homosexuals” to demonstrate that sexual orientation is a choice and that change is possible." That statement does not support the claim that the goals of ex-gay movement as described in Ex-Gay Research "rest in the claim that sexual orientation is a choice and that change for homosexuals is possible through therapy and prayer". FreeKnowledgeCreator (talk) 00:21, 6 September 2018 (UTC)

Potential addition to "People who no longer support the ex-gay movement"
Gerald Davison is perhaps one of the first psychologists who practiced conversion therapy, and disavowed it in the early 1970's. He was also the President of the Association for Behavioral and Cognitive Therapies in the 1970's. There isn't much on his wikipedia page regarding this, however this | article here on USC's student blog feautures a lot of quotes from an interview he did. I'm sure there is a better secondary source covering his shift elsewhere, in a book or a journal. At the time they didn't technically call it "ex-gay", but should he be included? He also later supported removing homosexuality from the DSM. --Sxologist (talk) 10:25, 22 March 2020 (UTC)

"Transformational ministry" listed at Redirects for discussion
A discussion is taking place to address the redirect Transformational ministry. The discussion will occur at Redirects for discussion/Log/2020 October 27 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Hog Farm Bacon 23:20, 27 October 2020 (UTC)

Milo Yiannapolos
I think we should add Milo since he’s now ex gay Nlivataye (talk) 12:25, 31 May 2021 (UTC)
 * Merely identifying as "ex-gay" does not make one part of the movement; the people here encouraged folks to dehomosexualize themselves and/or offered training or counseling to do so. --Nat Gertler (talk) 12:54, 31 May 2021 (UTC)

Ex-gays without conversion therapy
You have repeatedly tried to insert this text:
 * There are also believers gathered in Christian organizations, such as Your Other Brothers or Voice of the Voiceless, who claim they have not been attracted to homosexuality since their new birth, without having recourse to a conversion therapy. They insist on the importance of welcoming and loving homosexuals, but believe that sexuality should be reserved for heterosexual marriage.

using this NBC source for "Voice of the Voiceless" claims and this Christian Post source on "Your Other Brothers". However, these sources do not actually support the statements that you make. The "Your Other Brothers" articles describe their writers not as being people who have not been attracted to homosexuality, but as "Christian men who experience same-sex attractions" -- no past tense there, nor any mention with regard to whether they've attempted conversion therapy. The Voiceless piece sites he president of the organization as claiming not to have undergone conversion therapy (as well as a couple other people who were not identified as members of the organization) but specifies that the organization has supported conversion therapy. It makes no statement about a stance regarding sex only being within marriage, nor on the importance of welcoming homosexuals. It makes no statement that the one identified member has not been attracted to homosexuality, much less that that is a defining aspect of the membership. There may be things to be said about these two groups, but not this text with these sources. As such, I am removing it (again). --Nat Gertler (talk) 00:56, 8 August 2021 (UTC)
 * And now you've reworked it and gotten rid of the "Your Other Brothers" material and included "Freedom March", which is the name of both an organization and of events they help organize (but are not sole backers of.) However, the NBC article mentions only the event, not the organizing group, which should not be assumed to include the same people. Neither source discusses them having "new birth" or being "born again" (which is not neutral-point-of-view language anyway.) The new text continues the claim about conversion therapy, when we still only have one person claiming that from Voiceless and the March group claiming only that most of them have not been through such therapy, not that it's a defining characteristic. As such, I am removing it (again). I suggest you discuss what you want to insert and find consensus for it before retrying. --Nat Gertler (talk) 03:18, 8 August 2021 (UTC)

 * Hello . Thank you for the comments. This contribution aims to highlight the fact that ex-gay Christians have not had recourse to conversion therapy. The new version talks about two things:

1 : https://www.nbcnews.com/feature/nbc-out/pulse-survivor-others-gather-celebrate-freedom-being-gay-n871651

Ruiz, who said he no longer identifies as gay and denied going to conversion therapy, promoted his decision to attend the event on Facebook.

Daren Mehl, president of Voice of the Voiceless, said he did not seek conversion therapy in his personal journey from homosexuality to heterosexuality. He said the decision was “not forced but a choice.”

https://www.christianpost.com/news/ex-lgbt-men-women-to-share-stories-of-transformation-at-2nd-freedom-march-in-washington-dc.html

The whole notion of "conversion therapy" is misleading, Byrd told CP, "because the majority of us has never experienced conversion therapy; our experiences were encounters with the Holy Spirit that changed our lives."

2 : https://www.nbcnews.com/feature/nbc-out/pulse-survivor-others-gather-celebrate-freedom-being-gay-n871651

“I don’t want to tell everyone it’s a ‘gay-to-straight’ thing because God is not calling me to that," Ruiz told NBC News. "I feel that I want to live in a life of purity. I feel that through loving Christ, he will walk me out of any situation. I love the LGBTQ community, I love my family. There’s no hate here, there’s love.”

Fredi and Paul Cleveland, pastors of Koinonia Congregation in Washington, came to the event to support those who had left their gay and transgender identities behind and also to support the message of love.

https://www.christianpost.com/news/ex-lgbt-men-women-to-share-stories-of-transformation-at-2nd-freedom-march-in-washington-dc.html

Through the Freedom Marches, we want to spread messages of love and acceptance for people who have shed their LGBTQ identity and show others that we do exist.

"None of us were ever forced to change or put in a camp; it was a decision that we made to follow after Jesus and His love."
 * Thanks for your help. --ServB1 (talk) 14:41, 18 August 2021 (UTC)
 * The version you just added has two sentences:
 * Some people say they are no longer gay since they became Christians, without going to conversion therapy.
 * They stress the importance of love for gay people, but believe they have the right to share their ex-gay stories.
 * Number 2 can be batted away quickly. It lists no sources, the claim it makes is not made in either of the prior two sources, and it seems to be putting up a bit of a straw man, as if there is some strong force telling these Americans that they don't have the right to tell their stories.
 * Number 1 has a number of problems. The first source used, the NBC one, does not have people saying they are no longer gay, it says that they no longer identify as gay or that they left their gay identity behind. I may not identify myself as a chubby guy, but that doesn't mean I don't still have that spare tire 'round my waist. Also, none of them say that it was "since becoming Christians", so they may well have been Christians before that. The second source does not have the lack of conversion therapy in multiple people being said in the voice of the Christian Post, our presumably reliable source. Rather, the Post is quoting a "[v]ocalist and Freedom March worship leader", who would not qualify as a reliable source on these other people.
 * As it makes no accurately-sourced statements, I am removing the new version. Given the number of go-rounds on this, I again suggest that you propose an addition here on the Talk page and find consensus before adding it to the page. --Nat Gertler (talk) 16:43, 18 August 2021 (UTC)
 * Hello . Thank you for the comments. The word identification was added and their willingness to share a message of love for LGBTQ people (cited several times in both articles). Thanks for your help. --ServB1 (talk) 17:22, 18 August 2021 (UTC)

"Kristin J. Tremba" listed at Redirects for discussion
An editor has identified a potential problem with the redirect Kristin J. Tremba and has thus listed it for discussion. This discussion will occur at Redirects for discussion/Log/2022 March 31 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Unbh (talk) 13:25, 31 March 2022 (UTC)

title: Talk:Ex-gay movement


text:
18th Street gang

The 18th Street Gang, also known as Calle 18, Barrio 18, Mara 18, or simply 18 in North America, is a multi-ethnic (largely Central American and Mexican) transnational criminal organization that started as a street gang in Los Angeles. It is one of the largest transnational criminal gangs in Los Angeles, with 30,000-50,000 members between the United States, Mexico, and Central America and is also allied with the Mexican Mafia, another US-based crime organization. A United States Department of Justice report featured the following statement regarding 18th Street and rival gang MS-13, "These two gangs have turned the Central American northern triangle into the area with the highest homicide rate in the world."

History
The 18th Street Gang was formed in the Rampart District of Los Angeles in the 1960s by Mexican-Americans and other immigrant youths who were not accepted into existing Hispanic gangs. They were originally part of Clanton 14 but wanted to make a separate "clique" called Clanton 18th Street and allow immigrants the opportunity to join. This proposal was rejected by the Clanton 14, which led to the formation of the 18th Street Gang. The two gangs have been bitter rivals ever since.

18th Street grew by expanding its membership to other nationalities and races, and it was among the first multiracial, multi-ethnic gangs in Los Angeles. In the beginning, they were made up largely of second-generation Hispanics. As the 18th Street Gang began to battle with more established Hispanic gangs, they began to recruit outside the Hispanic community. There are approximately two hundred separate, autonomous gangs operating under the same name within separate barrios in the San Fernando Valley; specifically, in North Hollywood, the San Gabriel Valley, South Bay, Riverside, East Los Angeles, South Los Angeles, Hollywood, Downtown Los Angeles, Northeast Los Angeles, Pico Union, Westlake, Koreatown, Inglewood, South Gate, Huntington Park, Maywood, Bellflower, Long Beach, Orange County, San Bernardino County, and Los Angeles' Westside or West LA, according to the latest figures from the NDIC. In the early 2000s, the Federal Bureau of Investigation initiated wide-scale raids against known and suspected gang members, netting hundreds of arrests across the country.

Central America
18th Street started as a Mexican American gang, but the gang also became Central American as it started to recruit more members of other ethnic groups. When Central American gang members were arrested in the United States, they were then deported back to Central America, where the gang arose not just in El Salvador, but also in Honduras and Guatemala, becoming one of the most violent gangs in the region. 18th Street later became a bitter rival of MS-13 as both gangs sought supremacy in Central America. Members of 18th Street are mainly Mexican, Salvadoran, Honduran, and Guatemalan, but the gang does have members from other parts of Central America. 18th Street influences have recently been spotted in Belize as well.

In El Salvador, a faction called the "Revolucionarios ("Revolutionaries") split off 18th Street in 2005, becoming rivals with the other members, who came to be known as the Sureños ("Southerners.")

Location
The majority of 18th Street cliques operate throughout Southern California, but are active in other states and internationally as well. Los Angeles members began migrating to other areas outside California and started to establish their own gangs. 18th Street gangs are active in 44 cities in 20 U.S. states, as well internationally reported in Australia, Canada, England, France, Germany, Lebanon, Peru, Mexico, Guatemala, Honduras, El Salvador, and Venezuela.

Organization
The organization of the 18th Street Gang differs from location to location. With the gang being spread so vastly nationally and internationally, it is difficult to have a universal organizational structure. The gang is organized in such a way that allows for leadership at every level. One common organizational structure seen used by Barrio 18 is as follows. At the very top are “palabreros” or “leaders,” a majority of these members are in prison, but still help run the gang by coordinating all criminal activities. “Palabreros” also exist outside of the prison and are known as “en la libre.” Lastly, there are civilians who are known as collaborators. They are not officially gang members, but they are responsible for helping the gang with small jobs, like obtaining intelligence, and moving or holding illicit goods. The 18th Street Gang also designates positions in their organizational structure in another way. In this structure, at the top are the leaders, known as the “toros,” meaning bull. Underneath each “toro” is a clica, which is led by a “homie.” Under each “homie” are the “soldados,” meaning soldiers. Outside of the prisons, Barrio 18 is organized into divisions based on territory called “canchas.” The gang is horizontal in structure, allowing for a more decentralized approach to things. Although, overall 18th Street Gang is not very organized compared to some other modern day gangs. Women were also able to join the gang, but were treated very poorly. The women that joined the gang had three ways to do so, first was an 18-second beating, second was sexual intercourse with multiple members, and the last option was being the girlfriend or wife of a member can potentially lead to membership over time. The women were expected to take on male-associated roles often involving violence, as well as playing more of a mother role by caring for children and taking care of the sick.

Culture
18th Street Gang members are required to abide by a strict set of rules. Failure to obey the word of a gang leader, or to show proper respect to a fellow gang member, may result in an 18-second beating, or even execution for more serious offenses. According to the FBI, some factions of the 18th Street Gang have developed a high level of sophistication and organization. 18th Street Gang members often identify themselves with the number 18 on their clothing and sporting clothing from sports teams such as the Duke Blue Devils, Los Angeles Clippers, Los Angeles Rams, Los Angeles Chargers, Los Angeles Dodgers, Los Angeles Lakers, Los Angeles Kings, and Las Vegas Raiders. 18th Street will use the symbols XV3, XVIII, X8, 666, 99, and 3-dots in their graffiti and tattoos. 18th Street colors are blue and black; blue is to represent and to pay tribute to The Mexican Mafia, and black is to represent the original color for the gang. The 18th Street Gang is occasionally referred to as the "Children's Army" because of its recruitment of elementary and middle-school aged youth. They also allow other ethnicities to join their ranks making the gang multi-ethnic. In El Salvador it is common for members of the gang to be tattooed on the face with a large "18". In many cases the tattoo covers the entire face.

In California, the majority of the 18th Street gang's members are illegal aliens from Mexico and Central America.

Pete Wingfield's 1975 single "Eighteen With a Bullet" is the official theme song of 18th Street.

Criminal activity
The most lucrative activity of the 18th Street gang is street-level distribution of cocaine and marijuana, and to a lesser extent, heroin and methamphetamine. The gang is also involved in auto theft, carjacking, drive-by shootings, extortion, identification fraud, robbery, assault and homicide.

Special Agent George Rodriguez of the federal Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF) described the 18th Street gang as "one of the most violent street gangs and one of the most prolific in the United States". Cars are stolen and homes are burgled by the gang routinely. On average, someone in Los Angeles County is assaulted or robbed by 18th Streeters every day. The gang has left a bloody trail at a pace three times that of many of the city's most active gangs. 18th Street is a well established gang that is involved in all areas of street-crime. Several 18th Street Gang members have reached a higher level of sophistication and organization in their illicit activities than other gangs. While their main source of income is street-level distribution of drugs, they also have been linked to murders, assaults, arson, copyright infringement, extortion, human trafficking, illegal immigration, kidnapping, prostitution, robbery, and weapons trafficking, as well as other crimes. 18th Street Gang has also been implicated in the high-profile kidnapping and murder of the 16-year-old brother of internationally renowned Honduran football player Wilson Palacios.

In 1998, Catarino Gonzalez was sentenced to life in prison after a jury convicted Gonzalez of first-degree murder for fatally shooting Officer Filbert Cuesta in the back of the head, while the officer was sitting in a patrol car.

Kingston, New York police arrested and jailed several young men on the charge that they abducted a victim, took him to nearby woods, and murdered him. They were held on federal murder and racketeering charges.

In 2019, an 18th Street gangster was fatally shot by a member of rival gang MS-13 in a Queens subway station.

In Guatemala City, many bus drivers have been killed by 18th Street Gang members that drove through the alleged territory of the gang. Bus drivers were often victims of robberies and extortion. In one particular case the bus owners refused to pay the gang; a few moments later, a young man, the son of one of Libertad's bus owners, was driving his bus along Route 4, which ran from the terminal down to the Universidad de San Carlos de Guatemala in the southern part of the city. As he passed through Zone 6, two men flagged down the bus. They boarded it and shot the driver in the head killing him instantly.

In film

 * , a 2008 documentary film by Christian Poveda.

title: 18th Street gang