Talk:The Prisoner of Benda

Math formula
Does anybody knows the math formula used in the episode to solve the theorem ?--193.152.249.195 (talk) 17:35, 21 August 2010 (UTC)
 * It might be pointed out in the final sequence of mind switches, or it could just be gibberish. We probably won't have the actual theorem until DVD commentary comes out and Ken Keeler or David X. Cohen decide to talk about it/outline it or put it in as a feature.Luminum (talk) 18:30, 21 August 2010 (UTC)
 * The process of fixing every ones minds is a rather (to myself at least) trivial solution, proving it however is different. What is written on the board by Clyde appears to be the correct proof, I can write it out if it is needed for the page. Sixequalszero (talk) 10:17, 25 August 2010 (UTC)
 * The problem of including the formula is finding a way to do it in an encyclopedic manner and not in the manner of a fan page. At least I see that as the main hurdle. If all we have is "This is the proof of the theorem" then it is in the style of a fan page. If we describe the steps and meanings and importance of the theorem then we have an encyclopedia article, the question is do we have enough information to make it encyclopedic? and seeing as we don't even know the name of the theorem I would argue that the answer is "no". If I saw a lot more sourced text already in the article or if we get a DVD special feature about this then at that point I might agree it was time to put this into the article. Using a screenshot of the proof might be a better option, if we can do it in a Fair use compliant way. Stardust8212 13:18, 25 August 2010 (UTC)
 * Would the proof not be Fair use compliant because it would have to not be "a low resolution screenshot of a television episode"? Sixequalszero (talk) 03:03, 26 August 2010 (UTC)
 * I'd be worried about the resolution but also showing that "Non-free content is used only if its presence would significantly increase readers' understanding of the topic, and its omission would be detrimental to that understanding." Do we need the theorem to understand what happens in the episode? It would be a hard argument to make if challenged. Once again, I think if there was really a full paragraph of discussion about the theorem it would be easy to say "We need to include the theorem" but the amount of discussion on it we have now hasn't reached that point. Stardust8212 13:10, 26 August 2010 (UTC)
 * Agreed. The theorem really only needs to be mentioned in detail if it's discussed in something else that highlights why the theorem's particular aspects are interesting.  Only, it's not necessary to understand the events of the episode, otherwise, the episode would have gone into detail about it, rather than just showing a one-second screen shot.  More than not, the nitty gritty is probably going to come in a way that would fill the "Production" section, if Keeler describes how he went about determining the theorem.Luminum (talk) 18:37, 26 August 2010 (UTC)
 * I do hope Keeler talks about this in the eventual DVD release, it would benefit this article and it would help with the other article I want to write. Stardust8212 19:34, 26 August 2010 (UTC)
 * First, let pi be some K-cycle on [n] = {1 ... n} WLOG write


 * pi =
 * (1 2 ... k k+1 ... n
 * 2 3 ... 1 k+1 ... n)


 * Let  represent the transposition that switches the contents of a and b.
 * By hypothesis, pi is generated by DISTINCT switches on [n].


 * Introduce two "new bodies" {x, y} and write
 * pi' =
 * (1 2 ... k k+1 ... n x y
 * 2 3 ... 1 k+1 ... n x y)


 * For any 1=1,...k let delta be the (L-to-R) series of switches


 * delta = ( ...) ( ...) () ()
 * Note each switch exchanges an element of [n] with one of {x,y}, so they're all distinct from the switches with [n] that generated pi, and also from . By routine verification,
 * Note each switch exchanges an element of [n] with one of {x,y}, so they're all distinct from the switches with [n] that generated pi, and also from . By routine verification,


 * pi'delta =
 * (1 2 ... n x y
 * 1 2 ... n y x) ie, delta inverts the K-cycle and leaves x and y switched (without performing ).


 * NOW let pi be an ARBITRARY permutation on [n]; it consists of disjoint (nontrivial) cycles, and each can be inverted as above in sequence, after which x and y can be switched if necessary via {x,y}, as was desired.


 * As is written on the board by Clyde Sixequalszero (talk) 03:03, 26 August 2010 (UTC)

Rather than include the screenshot, why not use the Wikipedia math symbols? Andrevan@ 01:33, 11 September 2010 (UTC)

Math theorm name
what is the specific name of the formula? I've gone through various journals and can't seem to find any citations to Keeler's work in this particular area. Is it perhaps something based on "partial derangement" / "Rencontres numbers"? —Preceding unsigned comment added by 203.42.22.146 (talk) 21:01, 23 August 2010 (UTC)
 * Though he created and proved the theorem, there's no literature on him actually publishing the theorem. I guess we'll have to wait and see if he did or not.  Otherwise, it could have just been written but never formalized.Luminum (talk) 21:04, 23 August 2010 (UTC)

Limitation
I thought the limitation of the professor's machine was actually that it couldn't be used on the same pair of bodies, not the same pair of minds. 198.70.193.2 (talk) 16:18, 24 August 2010 (UTC)
 * This is correct.
 * Quote The Professor "I'd be back in my body, but then you and Bender would be switched, and the Amy and Bender's bodies can't trade minds again since they just did."


 * Let A, B and P be Amy, Bender and the Professor, and b, m, body and mind. Then the switching occurs between,
 * [AP]b [AP]m  (Amy and Professor switch Amy and Professor's minds)
 * [AB]b [BP]m  (Amy and Bender's bodies switch Benders and Professor's minds)
 * Proposed:
 * [BP]b [AP]m  (Bender and Professor's bodies switch Amy and Professor's minds)
 * Restrained:
 * [AB]b [AB]m  (Amy and Bender's bodies switch Amy and Bender's minds)


 * Amy and Bender's minds have not been paired up before, however their bodies have, being the restriction stopping them from switching minds again.
 * Sixequalszero (talk) 08:57, 25 August 2010 (UTC)

Is this really a theorem?
This article needs to be NPOV with respect to the question of whether Keeler's math is actually proving anything. It seems to me to be more of a joke; the math seems like nothing more than a restatement of the inductive hypothesis. Andrevan@ 21:35, 10 September 2010 (UTC)
 * The cited source material seems pretty clear on the point, at least to me. From The American Physical Society "In an APS News exclusive, Cohen reveals for the first time that in the 10th episohttp://www.nbcphiladelphia.com/entertainment/television/Futurama-Hits-the-Century-Mark-101908483.htmlde of the upcoming season, tentatively entitled “The Prisoner of Benda,” a theorem based on group theory was specifically written (and proven!) by staffer/PhD mathematician Ken Keeler to explain a plot twist." If you have another source that discusses the origins of Keeler's theorem I would love to add that info to the article but for now I think what the article says very closely reflects the source materials available. Stardust8212 22:02, 10 September 2010 (UTC)
 * The source material doesn't address whether Keeler's theorem is actually a theorem as defined by the scientific community. While I think the second description under "Production" is OK because it attributes the name theorem to Cohen, I think the sentence in the lead that reads: "The issue of how each crew member can be restored to their correct body given the limitation of the switching device is solved in the episode by a mathematical theorem penned and proven by Keeler, a PhD mathematician, that was based on group theory." is too authoritative. Andrevan@ 23:41, 10 September 2010 (UTC)
 * I think Cohen and Keeler are versed enough in mathematics to use the correct term. Of course, we won't know for certain with a level of authority until Keeler or Cohen address the subject, probably on DVD commentary.  In the meantime, feel free to look at the actual "theorem" to determine if it meets the definition compared to that of mathematical induction: Luminum (talk) 00:58, 11 September 2010 (UTC)
 * I don't think it's a question of whether they know what a theorem is, but whether they were joking or not when they referred to it as one. I did have a look at the theorem but I don't really think it's proving anything significant. It appears to represent the body-switching solution used in the episode -- but it's simply a solution to the problem, not a new theorem in mathematics. This is my interpretation and therefore original research; but I don't think we should call it a theorem, nor do I really think added "reportedly" fixes the issue since it now sounds like there's some doubt that Keeler wrote it, not that it might not necessarily be a theorem. Andrevan@ 01:30, 11 September 2010 (UTC)
 * Looking at this further, it's not a WP:POV issue, it's a Verifiability issue. I completely agree that it is somewhat dubious to claim that it is a theorem when only Cohen and (I assume) Keeler stated it and no one else has corroborated that statement by analyzing the theorem themselves.  But it doesn't appear to be a joke, especially when APS nor any other of the many reliable sources promoting the idea has taken it as such.  I can't think why Cohen would say that when speaking to the APS, which is all about serious mathematics and physics, nor why he wouldn't correct his statement after seeing how much buzz it generated positing it as fact.  Regardless, under WP:V, we include it because the statement has been verified, whether or not we think or know it to be true (in this case, the burden of evidence is in favor of it being a fact--Cohen and Keeler say it, reliable and notable sources reiterate it).  Like you've mentioned, the challenge to the statement's truth must likewise be supported by those kinds of sources.  The problem, obviously, is that none of these reliable sources know enough about it to fact check the statement.  There's no POV to dispute here, since we're not debating a value judgment or perspective.  We're debating whether or not the statement is true and can be verified.  If the statement is challenged, this assumes that either 1) Cohen/Keeler were joking, 2)Cohen/Keeler are wrong, or 3)Cohen/Keeler are lying.  At present, I don't see any evidence to believe 1 or 3.  The only candidate is 2, but can we assume Cohen and Keeler are qualified and reliable enough for that not to be the case.  It's a difficult issue to handle, since I get the concern, but also note the verifiability of the issue.  I'd only see a reason if I knew enough about mathematics to know for certaint hat what's portrayed is definitively not a theorem at all.Luminum (talk) 02:53, 11 September 2010 (UTC)
 * I don't think the APS is promoting the idea that it is a theorem at all; they are merely reporting what Cohen said, which is exactly what we should do. "A mathematical work used in this episode was described by Cohen in an interview with the APS as a new mathematical theorem." is much better than "Keeler proved a new theorem in this episode." The reliable sources that picked up the story are merely repeating what the APS said Cohen said. An interview is a reliable source for notability, but cannot be used for the truth of what is said in the interview. (Like hearsay).Andrevan@ 04:35, 11 September 2010 (UTC)
 * It's a bit awkward, but I think it works. Go for it. :)Luminum (talk) 05:03, 11 September 2010 (UTC)

Futurama theorem merge into this article
Please see Talk:Futurama theorem. Andrevan@ 22:52, 1 April 2011 (UTC)

Rewriting the proof
I noticed a few people changed the proof to make it clearer. Unfortunately, this is not the appropriate venue for such reduction; the proof as written is taken directly from the Futurama episode screenshot, and anything further is original work. Andrevan@ 06:47, 12 April 2011 (UTC)
 * I disagree with this sentiment. It's common for encyclopedia articles to include a description or paraphrase of a source rather than a direct copy.  In fact, giving a verbatim copy of the screenshot raises some uncomfortable questions about copyright.  I see nothing wrong with rewriting the proof using conventional mathematical notation and terminology. Jowa fan (talk) 04:33, 13 April 2011 (UTC)
 * To reduce mathematics is not the same as to paraphrase. The changes made were conceptual and not simply semantic; this constitutes original research; please note that Wikipedia has its own set of policy and guidelines on this topic which may differ from a general encyclopedia (which would be unlikely to include an article about this anyway). If we are choosing to be paranoid about copyright, we should not include a "proof" section at all; I think it's fine on copyright grounds to reproduce the text of the proof in the same way we can show a low-res image like The_Prisoner_of_Benda.png. Andrevan@ 04:43, 13 April 2011 (UTC)
 * I've restored the edit to the proof. It was conceptually identical, but had some much-needed copyediting and notational adjustments so that it agreed with the standard mathematical notation for such things (as used in cycle (mathematics) and transposition (mathematics)).  This is well within the limits of what is considered acceptable under original research policy.
 * I would actually suggest reducing the proof further, if the main idea of the proof can be conveyed more simply without giving formal details. For instance, just doing an example of reverting a 3-cycle to the identity would already illustrate the main feature of the proof, and it might be clearer just to do this case.  Often it's better in mathematical writing in an encyclopedia, rather than writing a formal proof, just to say enough about the proof that an interested reader gets the main idea.   Sławomir Biały  (talk) 11:36, 13 April 2011 (UTC)
 * I've removed the proof altogether while we discuss this (which is proper under the policy on removing unsourced statements). Discuss, don't revert. Your inclusion of the "strategy" of the proof and the reference to cycles shows that you do not understand the policy on synthesis. It is not proper to combine knowledge of mathematics, or the Cut-the-Knot version, with what is written in the screenshot, this is synthesis. We can only report exactly what the sources say and nothing more. I suggest you take any further examination of simplicity in mathematics to Infosphere or another website; our policy does not allow for this kind of restatement. While you may make claims regarding the similarity of what you wrote to the original source, this is not obvious to the lay reader, and this is an article on a TV show, not a mathematical concept. Andrevan@ 02:55, 14 April 2011 (UTC)
 * I agree with Jowa fan and Sławomir Biały. It is common practice in Wikipedia mathematics articles to summarise or paraphrase published proofs - in fact, I would say this is more common than quoting a proof verbatim from a textbook. Summarising a published proof does not breach WP:NOR or WP:SYNTHESIS because it does not change the conclusion of the published proof - it simply rephrases and clarifies the route to that conclusion. Indeed, we have whole articles that summarise and explain particularly notable proofs - see Euclid's theorem, Wiles' proof of Fermat's Last Theorem and Solution of the Poincaré conjecture for examples. Inserting an original and unpublished idea for a new proof would breach WP:NOR, but that is not the case here. Gandalf61 (talk) 09:31, 14 April 2011 (UTC)
 * Perhaps this merger was a bad idea, then. I see it is now being used as a pretext for controlling the mathematical content of the article, which was something that I was explicitly against in the merge discussion.  In any event, my edit to the proof is no more original research than, say, giving a plot summary.  I suggest that the proof be restored.  There is no consensus to remove it, and the consensus is clearly that it was not original research.
 * Let me emphasize that the proof is the same as Keeler's, maybe not word-for-word identical, but it's the same proof. It's not a synthesis of the two proofs or anything like that, as you've claimed.  Strange, since at a different time you also claimed that the observation at the beginning of the proof was "just a restatement" of Keeler's proof... not sure how you're now claiming that's synthesis.  The references to cycles were already in Keeler's proof.  So how can that possibly be synthesis? This is not going to be controversial among editors that are able to read and understand the two versions of the proof.   Sławomir Biały  (talk) 13:00, 14 April 2011 (UTC)
 * First of all, you're revert warring. Second of all, this is an issue not of consensus but of references and sourcing. The proof has no references and therefore can be removed at any time. Find a reference for it if you want to put it back. See WP:BURDEN (which supports removing the disputed material and not adding it back without appropriate referencing). Wikipedia does not distinguish between "editors able to understand" and lay editors. All changes must be reflected directly and explicitly in the sources. WP:NOR is very clear about this, and the material you're changing is different enough. Whether the proof ought to be included at all is a different question. Andrevan@ 14:13, 14 April 2011 (UTC)

You referenced only the first sentence of the proof, not the disputed "strategy" sentence or any of the lines you changed in the mathematics. I propose we replace the proof with a screenshot of the blackboard from the episode to sidestep the issue. Part of the problem is that, if we "improve" the proof from the episode, it may appear as though we are giving the "improved' proof to Ken Keeler, when in fact he wrote no such thing. This article is about a TV episode, not about a mathematical proof. Andrevan@ 14:27, 14 April 2011 (UTC)
 * I disagree with the proposal to replace the proof with a screenshot. Also, you seem to be the only one disputing the summary, and that seems to be a tendentious disputation anyway since you earlier admitted it was "basically just a restatement". Essentially the same proof, but with a more detailed computational step, appears at CTK. So I've referenced that as well.  Sławomir Biały  (talk) 14:37, 14 April 2011 (UTC)


 * I'm not sure which earlier comment of mine you're referring to. Anyway, there is a problem here because the proof is not really a proof, it's a screenshot from a TV show. Therefore the mathematical significance ascribed to it is dubious, the CTK source nonwithstanding. If we change the proof in such a way to make it seem more mathematically correct, we risk ascribing that correctness to the TV show. Also, please note that consensus is not a voting or majority game, and well reasoned concerns even from a single editor still carry weight that cannot be negated by simply bringing in more editors who disagree. Andrevan@ 14:45, 14 April 2011 (UTC)


 * Andrevan - not sure if you were being serious when you added a "citation needed" tag to the phrase "any permutation is a product of disjoint cycles", since this is a bit like asking for a citation for 1+1=2. But, in case you have not come across this before, the relevant Wikipedia article is cycle notation. And if you object to having a mathematical proof in an article about a TV episode, well, we could always go back to putting the theorem and proof in a separate article ... Gandalf61 (talk) 14:42, 14 April 2011 (UTC)


 * If this is so obvious, it should be very easy to cite it to an external page. You can't cite another Wikipedia article, that's just basic. (Also, interestingly, cycle notation has no referenced and a citation needed tag of its own.) Citation needed applies to the entire statement -- "the strategy for the proof is to..." Find me an external reference that explains what the strategy for the proof is and why. Andrevan@ 14:45, 14 April 2011 (UTC)
 * Umm... Reading the proof maybe? That is the proof strategy. Look, this is no different that giving a plot summary.  It's normally enough to reference the work itself.  Sławomir Biały  (talk) 14:48, 14 April 2011 (UTC)


 * It's completely different. I've started an RFC on this below. Andrevan@ 14:52, 14 April 2011 (UTC)

Is the proof overly detailed and difficult to reference?
There is a dispute over the mathematical proof in the Production section. Several editors are "improving" the proof by simplifying its mathematical content and adding explanatory phrases about the "strategy" of the proof which do not appear in the sources. I argue that the proof should be removed and replaced with a direct screenshot of the episode it appears in, to avoid issues of original research synthesis and undue weight being given to a dubiously mathematical part of this episode. Andrevan@ 14:52, 14 April 2011 (UTC)
 * comment. When you merged the articles, which never had any consensus, I voiced my concern that the theorem deserved a detailed treatment. It seems, however, that the Andrevan is unwilling to work constructively with other editors to make that possible, and maybe mathematical content is not suitable for an article on a work of fiction. I suggest that the theorem be split back out into a separate article. Sławomir Biały  (talk) 14:59, 14 April 2011 (UTC)


 * The theorem is not a theorem. It's a single frame screenshot from this television show which showed up in Cut-the-Knot, presumably because the author of CTK is a fan. Regardless, this is not the issue in question here. You can start another discussion about the merger below, but let's discuss one thing at a time. If this RFC determines that we can't include the proof at all, it will be a tough sell to unmerge it. Andrevan@ 15:02, 14 April 2011 (UTC)

This diff is a basic example of the synthesis problem. The result of Bhattacharya's theorem is combined with the proof material to support a synthetic statement that the strategy of the proof is so-and-so. This is original synthesis, although it may seem trivial to a mathematician, it is nonetheless not found directly and explicitly in any source material. Andrevan@ 15:06, 14 April 2011 (UTC)
 * There has long been consensus among editors familiar with writing technical material that giving faithful summaries of derivation included in the sources is perfectly acceptable. I agree that the citation provided wasn't useful, probably because Gandalf didn't see what the problem was. Indeed, this sentence that you object to is the sort of thing that must routinely be done when we summarize the sources. We could cite CTK again, but I don't think that would placate you. 166.137.140.247 (talk) 15:15, 14 April 2011 (UTC) Sławomir Biały  (talk) 17:43, 14 April 2011 (UTC)
 * This is your 2nd contribution ever, so I assume you are someone else, care to identify yourself? Andrevan@ 15:32, 14 April 2011 (UTC)
 * Andrevan - I really can't believe you are serious here. You demanded a source, I provided a Wikipedia article, you demanded an external source, I provided an external source, you say giving an external source is synthesis. WTF ? Gandalf61 (talk) 15:17, 14 April 2011 (UTC)
 * Do you know what I mean when I say synthesis? It's using A, Bhattacharya's theorem, and B, the Keeler "theorem" from Futurama, to support a third assertion, C, that the strategy of the proof consists of so-and-so technique. You may state A and you may state B, but you cannot use the combination to prove C. That's what original research is in the context of Wikipedia. Andrevan@ 15:22, 14 April 2011 (UTC)
 * Okay, I see what the problem is. We have been assuming a level of mathematical knowledge and maturity that you do not have. So let me explain this slowly. The proof of the Futurama theorem depends on the fact that any permutation can be expressed as the product of disjoint cycles; the strategy of that proof is to show that something can be done for a single cycle, and then to extend this to any product of disjoint cycles, which therefore covers any and all permutations. Neither Keeler nor Bogomolny saw the need to prove or provide a source in their proofs for this decomposition into disjoint cycles, as it is something that is more-or-less self evident, and is proved in any elementary abstract algebra textbook anyway. But you demanded a source for this, so I pulled the first of many examples from such textbooks, at random. Mathematical proofs build on previous results, and the "synthesis" here, if there is any, was done by Keeler and by Bogomolny - although I doubt they would claim any great credit for this, as it is an obvious and simple approach. Gandalf61 (talk) 15:41, 14 April 2011 (UTC)
 * It really doesn't matter how much math I understand. This is an article about a television show. Of course Keeler and Bogomolny didn't provide sources, because they weren't writing on Wikipedia, where the source requirement holds (it does not apply to CTK or Futurama). You say that "The proof of the Futurama theorem depends on the fact that any permutation can be expressed as the product of disjoint cycles; the strategy of that proof is to show that something can be done for a single cycle, and then to extend this to any product of disjoint cycles, which therefore covers any and all permutations." I don't see this written explicitly anywhere. Note that I am not challenging the elementary definitions of the mathematics, but that Keeler used this strategy or idea when writing the proof. Andrevan@ 16:12, 14 April 2011 (UTC)
 * To a mathematician the strategy is obvious from reading the proof (either Keeler's proof or Bogomolny's proof). Actually, Bogomolny spells it out on the CTK page: "Every permutation is representable as a product of disjoint cycles. Using this property, the proof of the theorem reduces to separately treating individual cycles". Summarising the proof strategy in the article does not alter the proof, but does make it clearer for the general reader. By refusing to acknowledge this you are heading very rapidly into WP:IDIDNTHEARTHAT territory. Gandalf61 (talk) 18:49, 14 April 2011 (UTC)
 * That seems valid; nobody has mentioned that before. I've edited the article to include a paraphrase of that statement. Andrevan@ 22:33, 14 April 2011 (UTC)


 * Andrevan - perhaps you can clarify what you mean by "dubiously mathematical" above ? Do you think the theorem is not true ? Do you think the proof is incorrect ? Do you think that some part of the mathematics is incorrect ? Gandalf61 (talk) 15:17, 14 April 2011 (UTC)
 * It doesn't matter whether I think it's correct, it's whether there are sources to support a claim. The so-called theorem is not really a theorem, it has never been published or peer reviewed, and it hasn't been analyzed by mathematicians in any published forum. It appeared in Futurama, a television show, and then again in Cut-the-Knot. This is not sufficient to establish notability or veracity as a mathematical theorem. Andrevan@ 15:24, 14 April 2011 (UTC)
 * Actually depending on the exact nature of the theorem, cut-the-knot might be good enough for the veracity (see WP:SPS, cut-the-knot is award winning website published by an expert). Being mentioned on this website might not be enough to establish the notability for the theorem to get its own article, but it is good enough to be mentioned in another article where it might be an interesting info to readers (wikipedia is not paper and the article in question is not overly long either).--Kmhkmh (talk) 16:46, 14 April 2011 (UTC)
 * I haven't disputed the usability of CTK as a source. My issue is when we go beyond what CTK says to claim that the "Futurama theorem and puzzle," as CTK calls it, is more than an entertaining side note and constitutes a result in the field of mathematics worthy of note. Andrevan@ 16:53, 14 April 2011 (UTC)
 * Where exactly do we claim that? We claim it is a (funny) math tidbit of the interest to some readers, that's at least how I understand it. We are not describing it as textbook or research theorem nor does it have its own article, so i don't quite understand from where you get your notion of "serious result in the field of math worthy of note". Note that we even allow plenty of "funny tidbits" or recreational math topics to have their own articles on occasion (if it surfaces in several publicatons or gets picked by a well known author).--Kmhkmh (talk) 17:25, 14 April 2011 (UTC)
 * Gandalf61 and Slawomir Bialy have both claimed that the "theorem" deserves its own article. Andrevan@ 17:29, 14 April 2011 (UTC)
 * That would be a separate issue (if such an article was to be created). As I said above we allow recreational math topics in general, whether this theorem currently would qualify for that based on cut-the-knot alone might be questionable though.--Kmhkmh (talk) 17:40, 14 April 2011 (UTC)
 * That's reasonable. Andrevan@ 23:13, 14 April 2011 (UTC)

I am responding to the RFC. I don't see any original research in the current article. Minor repharasing of a proof is not original research any more than paraphrasing a sentences from a history book would be original research. Moreover, even if we cite something, if we do not also paraphrase it into our own words then we run the risk of plagiarism. This is true both for history articles and mathematical articles. &mdash; Carl (CBM · talk) 02:16, 15 April 2011 (UTC)


 * Well, thanks for responding. I think what we have here is more than minor rephrasing in the way we might substitute synonyms, it's more like reporting a slightly abridged sequence of events because of a theory you have of how the pieces fit together. I certainly agree with the general principle that rephrasing well-understood mathematical truths in a way generally agreed upon to preserve the full meaning of the original is acceptable. In this case, the judgments we are making about the original message and the modification to it are "improving" the meaning to be more like a proof that some editors have seen in a textbook before. Andrevan@ 00:46, 16 April 2011 (UTC)


 * Taking one person's proof and rephrasing it to look more like a standard textbook proof would also not be original research, any more than taking a fact from a newspaper article and rephrasing it to sound more like an encyclopedia article would be. The OR policy does not require that we have to merely copy sentences from sources with citations at the end; we are encouraged to do source-based research, which means reading sources, understanding them, and then conveying the same ideas in our own words. We would be free, in a history article, to abridge and completely reword a paragraph from a source that we paraphrase; we are not limited to replacing synonyms. &mdash; Carl (CBM · talk) 00:55, 16 April 2011 (UTC)


 * Yes, but a proof is not the same as a paragraph. When you remove pieces from a proof, the structure of the arguments and the way they affect each other change, whereas in a paragraph it's a severable sequence. Proofs are self-contained imperatives like computer programs or strict formal logic and proceed hierarchically. History articles are generally narratives, declarative sequences which are easily separated. Andrevan@ 01:04, 16 April 2011 (UTC)


 * That argument doesn't work from either side. It's true that we have to be careful when we write a proof, but we have to be equally careful when writing history. And the sort of proof we are talking about here is a natural-language proof, not a formal proof that a computer can generate. Proof prose is not unique in some special way from other prose, and there are not stricter rules that apply to proofs than to other writing. &mdash; Carl (CBM · talk) 17:51, 17 April 2011 (UTC)

Summary of proof that accurately reflects the sources
Andrevan has repeatedly challenged that "The strategy of proof is to prove it first for a cycle, and then use the fact that an arbitrary permutation is a product of disjoint cycles" is not an accurate summary if the proof given in either source. If not, I enjoin him to suggest an alternative that does accurately reflect those sources, or I will remove the citation needed tag. Sławomir Biały (talk) 15:43, 14 April 2011 (UTC)
 * That's not how citation needed tags work. In fact, I could just remove that entire sentence instead of adding the tag, but I did that as a show of good faith. The tag will remain until the statement is sufficiently sourced. The BURDEN is on you to show me that the proof even has a "strategy." I see nowhere any coverage of a strategy being used in the construction of the proof. Andrevan@ 16:00, 14 April 2011 (UTC)
 * I and others have asserted that the summary faithfully reflects the contents of the proof (either proof, I'm fact). Do you contest this assessment?  If so, please explain why it is not an accurate summary.  Sławomir Biały  (talk) 16:11, 14 April 2011 (UTC)
 * I am not even discussing whether the summary is faithful or not. Accuracy is completely irrelevant, the question is verifiability. I am claiming that it goes beyond what is directly and explicitly written in the sources, and it consists of a synthesis of several different sources to produce a new result. WP:NOR is quite clear about this being unusable. Andrevan@ 16:14, 14 April 2011 (UTC)
 * You didn't answer my question. Sławomir Biały  (talk) 16:22, 14 April 2011 (UTC)
 * I explained why your question was irrelevant to the article. Wikipedia editors never rule on truth, only verifiability. Andrevan@ 16:29, 14 April 2011 (UTC)
 * @andrevan: Frankly, I think this sounds a bit like wikilawyering. "Accuracy is completely irrelevant" is complete misleading attitude for writing an encyclopedia. Verifiability is WP's essential tool to assure accuracy. So we shouldn't confuse goal and tool here. With a correct (and undisputed) content, it is not always necessary that it is "directly and explicitly" stated in the source in a literal sense, otherwise intelligible writing can become almost impossible. The content needs to be close enough to the cited sources that at least somebody with domain knowledge can verify it easily (=verfiability). You may argue against Sławomir Biały's version for other reasons, simly because you (personally) prefer a different description, you disagree which level of detail is appropriate, but those are separate issues regarding disagreements between authors that have nothing to do with OR (or "citation needed").--Kmhkmh (talk) 16:36, 14 April 2011 (UTC)
 * I have no idea what you mean by wikilawyering in this case, but I did get a 170 on my LSAT. The "directly and explicitly" isn't my invention, that's what the policy says. Here are some quotes from WP:NOR: Best practice is to research the most reliable sources on the topic and summarize what they say in your own words, with each statement in the article attributable to a source that makes that statement explicitly. ... Even with well-sourced material, if you use it out of context, or to advance a position not directly and explicitly supported by the source, you are engaging in original research. ... Do not combine material from multiple sources to reach or imply a conclusion not explicitly stated by any of the sources. ... The threshold for inclusion in Wikipedia is verifiability, not truth. These are the grounds on which I dispute the text. Andrevan@ 16:41, 14 April 2011 (UTC)
 * Wikilawyering and as I tried to explain above your misreading the intent of the policy here with regard to article (and possibly in particular math topics in general)--Kmhkmh (talk) 17:16, 14 April 2011 (UTC)
 * I've read that page. However, I don't see how my arguments misconstrue the intent of the quotes I just posted. Also, this is not a math topic, but a television show topic. Andrevan@ 17:18, 14 April 2011 (UTC)
 * It is a recreational math topic within a TV article and it based on recreational/educational math source (cut-the-knot). And why I think you misread the intent of the policy I tried to explain the first posting above. I don't know how to make that any clearer.--Kmhkmh (talk) 17:30, 14 April 2011 (UTC)
 * You stated 'it is not always necessary that it is "directly and explicitly" stated in the source in a literal sense.' I think you are wrong about that. Andrevan@ 17:31, 14 April 2011 (UTC)
 * As I said intelligible writing requires that and after all having an accurate and readable encyclopedia is our primary goal and the policy you cite is the primary tool to achieve that goal and to settle disputes about accuracy between authors. But as with any tool, you shouldn't use it for the tool's sake but for the goal and if it hampers the goal (writing an accurate and readable article) then don't apply it (literally). We do even have an explicit rule (tool) for that as well btw. : WP:IAR. Here this means require verifiability of the WP content through the sources by somebody with domain knowledge at least, but do not require a literal copy of the wording in the source or the same level of detail.--Kmhkmh (talk) 17:56, 14 April 2011 (UTC)
 * I love IAR, but in this case I don't see the argument. Also, I disagree as to the domain knowledge aspect; this should be verifiable by a lay reader. Andrevan@ 22:51, 14 April 2011 (UTC)
 * This is an unsupported opinion. There is no requirement in any policy that things need to be verifiable to a lay-reader.  Indeed, if that were the case, we should have considerably fewer articles on "encyclopedic" topics like the sciences.  In fact, after reflection, that seems to be a big part of the problem with your attitude towards the current article.   Sławomir Biały  (talk) 00:12, 15 April 2011 (UTC)
 * Verifiability of all articles by lay readers (or all readers) is not a sensible requirement, in fact it is practical impossibility regarding the current scope of WP. Articles on advanced topics do require domain knowledge to understand them, there is no way around that. And you cannot create an intelligible article by just patching literally or minimally paraphrased quotes from sources together (no way around that either), just to allow any lay reader a "pattern matching". Such "pattern verifiable" articles are not really in the interest of authors or readers. Authors would often be blocked in writing intelligible on the subject and they would have the burden of providing additional "literal sources" for various wordings and summaries. In short we would get unhappy authors and badly written articles. The reader has the benefit of a "pattern verifiable" article, but he has lost his primary motivation to consult WP in the first place, namely finding an intelligible well written article on the subject he is interested in. In short this interpretation of verifiability (always verifiable by anyone independent of any domain knowledge, always an explicit literal "copy" of the source) and the concerned WP policies gets us nowhere.--Kmhkmh (talk) 05:07, 15 April 2011 (UTC)
 * Wikipedia does not, to my knowledge, distinguish at all between lay and expert readers. I believe this is a misunderstanding you have as mathematicians or whatever you guys are. Personally I've taken more advanced math courses than the average person, but I am not an expert in the field. However, I possess the tools necessary to verify that a statement in Wikipedia agrees with a source. Therefore the verifiability test is general -- the reader need only be literate and possess a modicum of understanding, not a true expert. Contrary to what you say, it's pretty easy to piece together a well-sourced article only using explicitly sourced paraphrased statements that are verifiable by lay readers on topics which are legitimate results in the mathematical field. The problem is that The Prisoner of Benda and the so-called theorem is very poorly sourced, so you guys are grasping at straws to make sense of what we have. The solution is not to synthesize or simplify but to stick closely to the sources and limit ourselves in constructing a lengthy exposition about this poorly-sourced topic. Andrevan@ 07:38, 15 April 2011 (UTC)
 * Please note that I didn't talk of true experts, but I was talking of the need for (some) domain knowledge and I made no comment whatsoever whether you personally have that domain knowledge or not. As far as the content in question here is concerned, you obviously don't need to be mathematician you verify it (just some limited abstract algebra knowledge). Whether some domain knowledge is sufficient or whether you may need to be "true expert" depends on how advanced the topic is and what the phrase "true expert" means in detail. Contrary to your notion it is not always pretty easy to use explicitly paraphrased statement only, moreover such a patchwork leads bad often unintelligible writing, which is something we do not want. There is also not reason to limit ourselves to awkward lengty but literally expositions. Summarizing, selecting, reformulating things, restating the content of sources in an more accessible manner is part of the basic work of any WP authors (or any encyclopedic authors for that matter).--Kmhkmh (talk) 15:46, 15 April 2011 (UTC)

But my question is about verifiability. Are we accurately reflecting the sources? If you don't answer, I'm removing the tag. One had enough of your tendentious arguments. Sławomir Biały (talk) 16:40, 14 April 2011 (UTC)
 * The answer is no, we are not reflecting what the sources say. However, even if I did not answer, you would not be within the bounds of reasonable editing to make an ultimatum like that. And please review the definition of tendentious editing, which in no way reflects upon our discussion here. Andrevan@ 16:41, 14 April 2011 (UTC)
 * Interesting. How would you summarize the proof instead?  I've read both versions, and that seems to me to be what they do. They prove it for a cycle and then use the cycle decomposition to prove it in general. Do you contest this?  Why? At a minimum you need to give a reason for insisting in a fact tag that other editors see as already directly supported by the source. Otherwise it should be removed, yes.  Sławomir Biały  (talk) 17:05, 14 April 2011 (UTC)
 * I am not making any comment on whether the summary is sufficient from a truth perspective. I am claiming that the proposed summary is not verifiable. The summary is an interpretation not explicitly stated in the sources and thus is original work. Especially given that this is a television article and not, say, Taylor's theorem or another legitimate math article, it is not for us to make judgments, as you are, regarding what the theorems do or say beyond the superficial, especially when those judgments require specialized mathematical knowledge that you are using for synthetic purposes. This is a Futurama article, not a theorem. If it were actually a mathematical theorem that appeared in textbooks, it would be very easy to source a summary like the one you're proposing, since many authors would probably have written similar summaries. In this case, it is nearly impossible to find a true mathematical reference. Andrevan@ 17:08, 14 April 2011 (UTC)
 * No, you're going to need to support the answer you gave above, directly.   Sławomir Biały  (talk) 17:15, 14 April 2011 (UTC)
 * That is support for my answer. The question is not, Is this summary true? It's, Is this summary verifiable? I do not believe it's possible to summarize the proof in a way that is reflected in the sources, which is why I think the proof and summary should be removed and replaced with a screenshot. Andrevan@ 17:16, 14 April 2011 (UTC)
 * So proofs can't be summarized in encyclopedia articles? Is that what you're saying? Sławomir Biały  (talk) 17:33, 14 April 2011 (UTC)
 * Not at all. I am saying that any summary must be based on something explictly mentioned in a source. Andrevan@ 22:37, 14 April 2011 (UTC)
 * A screenshot of what exactly (copyrightissues!?)?. Are And why do consider that an either or scenario. I don't quite see why the article can't have an illustrative screenshot (or graphic) and a textual summary (verifiably based on the cut-the-knot).--Kmhkmh (talk) 17:35, 14 April 2011 (UTC)
 * It's fine on copyright grounds to reproduce the text of the proof in the same way we can show a low-res image like The_Prisoner_of_Benda.png. You're right that it's not an either or scenario, the reason why I think it's preferable is the issue of "editing" the proof itself. Andrevan@ 22:25, 14 April 2011 (UTC)

Dubious
I've added a dubious tag to indicate that there is an ongoing discussion on the talk page as to whether your citation is sufficient. This is not exactly the correct tag -- really it's citation needed, since my doubts are that the source says what you claim it says and not whether it is actually factual, but since you insist on removing the citation needed tag, this is probably better. Andrevan@ 17:24, 14 April 2011 (UTC)
 * I've changed the wording so that it is an even more straightforward descriptive statement about the proof as it appears in either source. That's trivially verifiable. Time to remove the tag? Sławomir Biały  (talk) 17:38, 14 April 2011 (UTC)
 * I have removed the dubious and citation needed tags. Andrevan, you are editing tendentiously; see WP:TE. Ozob (talk) 22:27, 14 April 2011 (UTC)
 * That page refers to "characteristics of problem editors." Simply being repetitive does not constitute a violation of policy, and I think it's obvious I am not a "problem editor" (and, similarly, those with whom I am arguing are not "problem editors"). Andrevan@ 22:50, 14 April 2011 (UTC)
 * I've rephrased the statement to "The proof reduces to treating individual cycles separately, since all permutations can also be represented as a product of disjoint cycles", which as Gandalf mentions above, is mentioned explicitly in CTK. Andrevan@ 22:33, 14 April 2011 (UTC)

Difference between proof in TV screenshot and proof here
The original proof is as follows:

First let $&pi;$ be some $k$-cycle on [$n$]= { $1 ... n$ } WLOG [without loss of generality] write:
 * $$\pi =\begin{pmatrix}

1 & 2 & ... & k & k+1 & ... & n \\ 2 & 3 & ... & 1 & k+1 & ... & n \end{pmatrix}.$$

Let 〈$a,b$〉 represent the transposition that switches the contents of $a$ and $b$. By hypothesis $&pi;$ is generated by DISTINCT switches on [$n$]. Introduce two "new bodies" $x$ and $y$, and write:
 * $$\pi^* =\begin{pmatrix}

1 & 2 & ... & k & k+1 & ... & n & x & y\\ 2 & 3 & ... & 1 & k+1 & ... & n & x & y \end{pmatrix}.$$

For any $i &isin; {1 ... k-1}$ let $&sigma;$ be the (l-to-r) series of switches:
 * $$\sigma = ( \langle x,1  \rangle  \langle x,2  \rangle ...  \langle x,i \rangle ) ( \langle y,i+1  \rangle  \langle y,i+2  \rangle ...  \langle y,k  \rangle ) ( \langle x,i+1  \rangle ) ( \langle y,1  \rangle ).$$

Note each switch exchanges an element of [$n$] with one of 〈$x,y$〉 so they are all distinct from the switches within [$n$] that generated π and also from 〈$x,y$〉. By routine verification:
 * $$\pi^* \sigma=\begin{pmatrix}

1 & 2 & ... & n & x & y \\ 1 & 2 & ... & n & y & x \end{pmatrix}.$$

I.e., $&sigma;$ reverts the $k$-cycle and leaves $x$ and $y$ switched (without performing 〈$x,y$〉).

NOW let $&pi;$ be an ARBITRARY permutation on [$n$]. It consists of disjoint (nontrivial) cycles and each can be inverted as above in sequence after which $x$ and $y$ can be switched if necessary via 〈$x,y$〉, as was desired.

To what extent does our current version expand on the original? Andrevan@ 22:35, 14 April 2011 (UTC)


 * There's some monkeying with the parentheses in the 3rd step. In the original, there are parentheses from (x 1) to (x i) and in this version there aren't. Also, the word "permutation" is used in the new version, and not in the original. The new version is also missing some things like the all caps ARBITRARY and the (l-to-r)... My concern is that if we allow the proof to diverge from the version displayed in the TV show, we will open the door to original research. Andrevan@ 22:45, 14 April 2011 (UTC)


 * As it currently stands, there is no original research in the proof. The proof has been tweaked to bring it in line with our house style (notation and terminology), and I have made some copyedits.  In addition, I removed the assertion that the &pi; is a product of disjoint transpositions, since this is not relevant to the version of the proof that we have stated (and in particular the "by hypothesis" makes no sense at all).  The parentheses, too, were unnecessary, serving only to group the terms (but in the proper notation, additional parentheses look awkward, so think of this also as a cosmetic change.) Since you don't apparently have enough subject knowledge to assess this point, you'll just have to trust those editors that do on this point: there is no original research involved in making adjustments like these.  (Please refer to Kmh's post in an earlier thread on just this point.)   Sławomir Biały  (talk) 23:54, 14 April 2011 (UTC)


 * I would like to repost something that I said once elsewhere:
 * I think that most of the concern on this topic amounts to a concern about the meaning of the phrase "original research". WP:NOR says that original research is material not originally published by reliable sources. But what counts as material? A very strict reading could argue that every sentence original to Wikipedia represents an original thought, and therefore counts as original research or synthesis. A slight rephrasing of a reliable source's sentence might change the original emphasis or alter some shade of meaning, and the only way to ensure that Wikipedia's sentences are totally devoid of original content is to copy them straight from something else, that is, to commit a copyvio.


 * WP:NOR goes on to say that copyvios are prohibited, and that "Articles should be written in your own words while substantially retaining the meaning of the source material." Because this permits slight shifts in meaning, it allows slight amounts of original research. What is not permitted, and what the policy spends most of its time discussing, might be called original ideas. If I have a brilliant new idea for a revolutionary new theory, I can't go straight to Wikipedia. But brilliant expository prose is always welcome here (as far as WP:NOR is concerned; there are other restrictions).
 * Here our issue is again, "What counts as original research?" As before, I do not think that "any deviation from the sources" is a sensible answer. Ozob (talk) 00:03, 15 April 2011 (UTC)
 * I agree, unfortunately this seems to be a misunderstand/misreading of policies that's creeping in quite often. It is not the first that I'm seeing or having such discussions (the most recent being the "fall out" of the arbcom's preliminary ruling on the MHP case).--Kmhkmh (talk) 05:14, 15 April 2011 (UTC)

These are the things I have problems with. "I removed the assertion that the &pi; is a product of disjoint transpositions, since this is not relevant to the version of the proof that we have stated (and in particular the "by hypothesis" makes no sense at all)" This is clearly not simply a cosmetic change, it's a conceptual change to the original message as it appeared in Futurama. Ken Keeler meant something when he said "by hypothesis," and even though you may not be able to tell what he meant in the context of your mathematical knowledge, this gives the reader several pieces of information: 1) Ken Keeler is not a real mathematician and his proof is in some sense a joke, based on the reaction that real mathematicians get when they read the proof ("let's fix this so it makes sense"). 2) The proof as it appeared on Futurama included such language. What we're doing here is synthesizing Keeler's proof as it appeared on Futurama with the CTK version of the proof. We need to cite one or the other, not both. Andrevan@ 07:30, 15 April 2011 (UTC)
 * Ok from where do you get the notion, that Keeler is not a "real" mathematician. According to his WP biography at least, he started math in Harvard and has a PhD in applied math.--Kmhkmh (talk) 15:55, 15 April 2011 (UTC)
 * A fancy degree does not a mathematician make. Keeler has never published as far as I know, and although I am sure he wrote a dissertation to get that PhD, many students do the same every year without becoming mathematicians. He's a TV writer, which is awesome and I'm all for smart people creating the entertainment I consume, but that does not mean he is notable as a mathematician. Perhaps you could say he is an amateur mathematician, but I think when we call someone a mathematician it connotes professionalism of some kind, like a scientist.

Andrevan@ 00:12, 16 April 2011 (UTC)
 * This is getting somewhat ridiculous and apparently you are confusing the profession/occupation with being a notible persona in that field. Your claimed above Keeler was about Keeler not neing a (real) mathematician and not not being a notable mathematician. The term mathematician does not include not only people who working in mathematics "right now", it does of course also entail people who have retired or switched careers (applies to Keeler). In the broadest sense you could even argue it includes anybody that received (and graduated) a university education in mathematics and definitely includes somebody having PhD level degree in the subject (applies to Keeler as well). In any case he has learned and practiced enough math in his career to understand a topic like this "theorem" to the very last detail, so insinuating he might not really know what he was talking about (aka "just TV writer") is completely without grounds.--Kmhkmh (talk) 02:37, 16 April 2011 (UTC)
 * This is a side point and semantic. Keeler has not achieved notability as a mathematician, therefore, for the purposes of his Wikipedia entry, or related coverage, his expertise has not been established in mathematics. Andrevan@ 03:36, 16 April 2011 (UTC)
 * The phrase "by hypothesis" in Keeler's proof obviously means that by the conditions of the body swap scenario, the permutation &pi; must have been reached by a sequence of distinct transpositions i.e. once the transposition (1 2) has been used once, it cannot be used again. Sławomir Biały's point is that this is, in fact, a redundant condition because (a) any permutation can be expressed as a product of distinct transpositions so the set of permutations that can be reached by the "body swap" method is the whole of Sn and (b) the method outlined in the proof allows any permutation in Sn to be reversed anyway. Once again, this is all totally obvious on even a cursory reading of the proof, and it is becoming more and more difficult to AGF when you continue to hang your objections on such trivial points. Gandalf61 (talk) 08:55, 15 April 2011 (UTC)


 * I wonder if Andrevan's point of view is motivated by the use of multiple sources. The article mentions both the original Futurama episode and a page at Cut-the-Knot, therefore it looks as though the revised proof might be a synthesis of two different sources.  It seems to me that if the Futurama episode were readily available online or in most research libraries, then the Cut-the-Knot reference would be redundant: everything in the article could be sourced from the episode itself.  But since a citation to the episode wouldn't be easily verifiable, someone has linked to Cut-the-Knot as a substitute.  The underlying content is the same in either case. Jowa fan (talk) 11:40, 15 April 2011 (UTC)


 * That may be "totally obvious" to you, but it clearly required thought and analysis, even if that comes very easily to you. This thought and analysis is going beyond the source material and this constitutes an "original idea" as Ozob refers to above. This is more than paraphrasing, you are simplifying using the tools of mathematical thought. Andrevan@ 09:08, 15 April 2011 (UTC)


 * I disagree: It is a paraphrase. Anyone who can understand the original proof can understand what is written in the article with no difficulty, and vice versa. This is because they are the same in every detail; they differ only in the words they use to express those details.  If a source were to describe a man as "portly" and we were to call him "stout", would that be original research?  No.  Well, neither is this. Ozob (talk) 11:12, 15 April 2011 (UTC)


 * I agree that the use of the word "obvious" is not helpful in this context. However, the main point here is the question of original research.  An encyclopedia is more than a copy-and-paste compilation of sources.  Editors necessarily make choices about what to include and how to present and organise the material.  Such choices may certainly involve some degree of originality.  However, they do not constitute research.  This point has already been made many times above.  There is no "synthesis" going on here.  The content of this page, and of the page at Cut-the-Knot, are already implicit in Keeler's proof.  In my opinion it's time to apply some common sense, accept that edits here are consistent with the principle of avoiding original research, and be a bit less bureaucratic about this whole issue. Jowa fan (talk) 11:31, 15 April 2011 (UTC)


 * The key word used here is "implicit." As Wikipedia's many policy pages clearly state repeatedly and not with a wink or a nudge, direct and explicit reporting of sources is the way Wikipedia articles are written. We may report that source X said Y, but to take Y and change the meaning to make it less "wrong" or conform with normative thought is original work. We can certainly paraphrase, but the interpretation of Keeler's work should tend to the original. "I removed the assertion that the &pi; is a product of disjoint transpositions, since this is not relevant to the version of the proof that we have stated (and in particular the "by hypothesis" makes no sense at all)" Your judge of the relevance seems to be based on a very narrow foundation which originates in a mathematical model that you hold internally about what Keeler meant when he wrote this, combined with how Cut-the-Knot portrayed what Keeler wrote. These need to be separated and labeled appropriately. Andrevan@ 00:21, 16 April 2011 (UTC)


 * Andrevan, I now understand that what you're saying is in line with the written form of Wikipedia's various policies. However, that's not the way it's done on the various mathematics pages, and it hasn't been done exactly that way for a long time.  Applying these standards strictly would simply be an impossible burden.  In mathematics there exists a broad consensus on what "original research" means, and according to that consensus, paraphrasing a proof is not original research.  Once more: WP:BURO.  You made an RFC above, and someone has responded consistently with the viewpoint that everyone else is promoting here.  Please try to consider this matter in a broader context. If your argument were pursued to its logical conclusion, many hundredes of mathematics articles on Wikipedia would have to be thrown away.  It would be a very sad day if that happened. Jowa fan (talk) 00:44, 16 April 2011 (UTC)


 * I'll let you have the mathematics articles because I am motivated irrationally by your appeal to emotion (although it sounds like you just told me that the math editors have an original research cabal), but then give me this TV show article, which should conform to the stricter standard of the rules that we keep here in the consumer entertainment articles. In the same way that you can invoke "the way it's done" on mathematics pages, please refer to "the way it's done" with fan pages about popular media, which are strict with regards to sourcing. Andrevan@ 00:57, 16 April 2011 (UTC)
 * As far as I can tell the proof here is sourced, however, or at least could be, depending on your taste for paraphrasing from Cut-the-knot. I'll point out that you explicitly asked for the theorem to be merged to this article on Talk:Futurama theorem, which is why the theorem is stated here now. It seems to me that at least the statement of the theorem is completely encyclopedic, as the outcome of the episode rests on it. The value of the proof is more doubtful for encyclopedic purposes but it isn't original research in any case. &mdash; Carl (CBM · talk) 01:10, 16 April 2011 (UTC)

A proof
this is, in fact, a redundant condition because (a) any permutation can be expressed as a product of distinct transpositions so the set of permutations that can be reached by the "body swap" method is the whole of Sn and (b) the method outlined in the proof allows any permutation in Sn'' to be reversed anyway. '' - this, to me, is an original proof which you are making to justify the improvement to Keeler's proof. "Once again, this is all totally obvious on even a cursory reading." This is actually not obvious, which I take to mean naively trivial, or by naked eye examination. What you're doing is taking A, the principle "any permutation can be expressed as a product of distinct transpositions" which comes from, probably among others, Bhattacharya as referenced above, and B, that there exists a set of permutations that can be reached by the "body swap" method, which, according to Keeler, a set size of S+2 will always allow for a "shift" reversal. This is syllogistic - A and B = C. We may report source X said A, source Y said B, but we can't report C and then source it to X + Y. Because you guys have internalized A since you work with a lot of proofs, you've completely missed the fact that Keeler's proof is basically a masked presentation of a very simple, already long-discovered mathematical proof which should not be credited to him. Therefore we can report what he did actually say, and reference the Cut-the-Knot treatment, but we cannot combine them and claim this constitutes a result worthy of publication -- even if it did, because that's original research. Andrevan@ 00:24, 16 April 2011 (UTC)
 * I have seen no evidence that Keeler's result is a long-discovered mathematical result that should not be credited to him. &mdash; Carl (CBM · talk) 00:57, 16 April 2011 (UTC)
 * Not his final conclusion about S+2, but the earlier parts of the proof that were removed in the new version by Slawomir Bialy, as Gandalf pointed out above, are actually I believe he called a basic discovery in abstract algebra, and cited his textbook by a gentleman named Bhattarchya. Andrevan@ 01:01, 16 April 2011 (UTC)
 * "Parts of the proof" are not the result, however; that term refers to the final conclusion, the theorem that is being proved. Using some other known result in the middle of a proof does not make the final theorem unoriginal. Does our article actually claim that the result is worthy of publication? &mdash; Carl (CBM · talk) 01:06, 16 April 2011 (UTC)
 * Keeler sent a message with the original screenshot. What Gandalf, Slawomir, and the CTK source have done is unpack Keeler's message using CTK's assumptions about what he meant, when in fact it's not at all clear that Keeler's so-called theorem was anything other than a triviality written in mathematical language for the purposes of the joke in the episode. To resolve this ambiguity we should report the sequence, like you might a multiple source sequence in a history article. First, Keeler said X (the original proof -- it's pretty short and it wouldn't be plagiaristic any more than quoting or sampling or other fair uses are). Then, CTK said Y. The leap from X to Y constitutes original interpretation, just as if we had an Israeli source that called the 1967 War a necessity and an inevitability shouldn't be combined with a source from a Palestinian refugee that condemned an undue intrusion. Andrevan@ 01:13, 16 April 2011 (UTC)
 * If CTK says that's what was meant, why would we doubt them, unless we had some other source that said they were wrong? It's not as if there is some ongoing dispute about what theorem was proved. Similarly, if we have two newspaper stories on the same incident, we don't assume that the second one is really reporting on a slightly different incident. The OR and V policies allow us to combine multiple newspaper accounts of the same incident to make a seamless summary of events, and similarly we can use the CTK article to report on the same theorem that was proved on the show, we don't have to assume they are actually different theorems. &mdash; Carl (CBM · talk) 01:23, 16 April 2011 (UTC)
 * We could report exactly what the CTK source says. What we're doing now is substantially reporting what Keeler said, but editing it to conform with what CTK said. It's almost as though we took the first newspaper article and corrected differences between that and the second article selectively, and then reported the entire thing cited to both/neither. Andrevan@ 01:47, 16 April 2011 (UTC)
 * That is how source-based research works. We can use one source for the main stuff, and another source for some details that were not emphasized by the main source. We do this all the time; look at the section Inception in today's featured article. Presumably that article does not violate the OR policy. &mdash; Carl (CBM · talk) 01:53, 16 April 2011 (UTC)
 * That makes very clear which sentence is cited to which source. What we have here can't be cited particularly to CTK, or the episode. Andrevan@ 01:56, 16 April 2011 (UTC)
 * If we were to put a footnote after each sentence, which parts could not be cited to either source? &mdash; Carl (CBM · talk) 01:57, 16 April 2011 (UTC)
 * "Let σ be the permutation obtained as the composition" is an original construction. More importantly, though, what is omitted from the original changes its meaning. Andrevan@ 03:41, 16 April 2011 (UTC)
 * This is getting really silly. The proof introduces the symbol "σ" and gives a definition for that symbol.  In the original (going by the screenshot linked above) the definition is introduced by the phrase "let σ be the (L-to-R) series of switches", whereas we now have "let σ be the permutation obtained as the composition".  One is a paraphrase of the other.  The meaning is identical: both sentences are slightly more elegant ways of saying "we're going to use the symbol σ to represent the stuff that you'll see on the next line of this proof".  OK, there's a tiny ambiguity there: algebraists don't always agree on whether permutations should be multiplied from left to right or from right to left, so the "(L-to-R)" bit perhaps shouldn't have been omitted (although it's possible for a mathematically sophisticated reader to deduce it from the context).  I'll edit the page now to remove the ambiguity.  But this is hair-splitting of the pettiest sort. Jowa fan (talk) 08:50, 16 April 2011 (UTC) ETA: I thought the preceding sentence left no doubt as to my opinion, but there seems to be a certain lack of  common sense in this discussion.  The addition or removal of "left to right" does not in any way change the meaning.  It could possibly make a small difference to the readability of the proof.  My decision to make this change does not in any way constitute an admission that other edits could be described as original research.Jowa fan (talk) 12:48, 16 April 2011 (UTC)
 * This proves my point better than anything I could say would. Andrevan@ 11:23, 16 April 2011 (UTC)
 * Original wording (if that is what you mean by "original construction") is not on its own original research. If your concern was that the term "left to right" wasn't included, you could just say that. But the idea that we need to avoid any possible microscopic change in meaning by just directly quoting each source we use is at odds with the actual OR policy. &mdash; Carl (CBM · talk) 11:32, 16 April 2011 (UTC)
 * This is an example of why we should stick closely to what the sources say. When I say "construction" I mean something more advanced and impactful than simply rewording a substantially similar idea. Rephrasing is fine, but modification of meaning is problematic. I wasn't really pointing to that modification in particular, but it's a discrepancy that crept in when we started editing the proof. Copyediting the proof doesn't actually accomplish anything productive that I can see in this case, but it opens the door to this kind of change. The point is that math is a very specific kind of language with a very narrow set of meanings, and it's extremely easy to introduce ambiguity unintentionally when you start editing the proof. This is why we should instead hew closely to interpretations offered by the sources. One question that I've not seen anyone answer is what's the improvement gained in the edited version of the proof, which is indeed quite similar except for any unintentional modifications that might occur, such as this and perhaps others. Andrevan@ 11:39, 16 April 2011 (UTC)
 * Well I've been saying all along that it was an improvement, by using standard notation and terminology (so we can unambiguously link to articles that clarify the content of the proof), elinating all-caps from your version of the proof (which we should obviously avoid in an encyclopedia article, if possible), and eliminating a phrase from your version that makes no sense in the context of how the theorem was stated. So, to break this down: standard notation/terminology, encyclopedic writing style, elimination of nonsense. These seem like clear improvements. But, I'm not goon to argue tooth-and-claw with you over every inch of it: it's obviously a waste of my time to do so.   Sławomir Biały  (talk) 12:00, 16 April 2011 (UTC)


 * I understand that it is possible to introduce ambiguity in math, but the one at hand (not saying "left to right" explicitly) is exactly like an article saying "Miami" instead of "Miami, Ohio" in a context where the "Ohio" is already clear. Sure, we can go back and add "Ohio" if someone wants, but it's not a "problem", it's a trivial change. Our standard practice on Wikipedia is to reword proofs to make them sound better in our editorial judgment. You might as well ask why we reword any sources, since every rewording can cause small variations in meaning. Why not just make articles long sequences of direct quotes? That would be absurd. The idea of Wikipedia is that we rewrite things in our own words, including proofs. &mdash; Carl (CBM · talk) 12:03, 16 April 2011 (UTC)

The "elimination of nonsense" is what I have an issue with. The method used to determine what is "nonsense" is insufficiently transparent, and relies on information not used to reference the article. Andrevan@ 00:07, 17 April 2011 (UTC)
 * In the context of the theorem as stated in the article "by hypothesis" does not makes sense since nowhere is such a hypothesis made, nor is it relevant that the original cycle is a product of disjoint transpositions.  Removing this does not change the proof in any meaningful way: it just adapts it to the mode of exposition in the article. You may argue (as you have done with little success) that this is original research, but I think you'll have a tough time arguing that removing a phrase that really made no sense as it stood was anything but an improvement to the prose.  Sławomir Biały  (talk) 03:03, 17 April 2011 (UTC)
 * It makes sense to me, I think; there's an implied comma after "hypothesis." "By hypothesis, π is generated by DISTINCT switches on [n]." So basically he's hypothesizing that π is generated by distinct switches, and in the step later where he says "Note each switch exchanges an element of [n] with one of 〈x,y〉 so they are all distinct from the switches within [n] that generated π and also from 〈x,y〉," he's basically testing and proving that earlier hypothesis. I think the redundant writing that your edits have removed, e.g. "if necessary...as desired" is a statement in and of itself, a mockery of the way mathematical proofs are written, is part of the message that Keeler is sending - remember, he's a comedy writer first and foremost. I think he's satirizing as he writes the proof. We're editing out the irony. Andrevan@ 08:54, 17 April 2011 (UTC)
 * Andrevan - once again, you are wrong. "By hypothesis" means in accordance with the conditions of the body swap scenario, which says that no pair of bodies may swap brains more than once. In a general product of transpositions, the same transposition may appear more than once. However, when we represent a sequence of body swaps as the product of transpositions, by hypothesis, a transposition may not appear more than once in this product. This has been explained to you before. Gandalf61 (talk) 10:09, 17 April 2011 (UTC)
 * The issue is that, in the version of the theorem we state, there is no hypothesis that the permutation (or the cycle, for that matter) be represented as a product of distinct transpositions.  Sławomir Biały  (talk) 10:15, 17 April 2011 (UTC)
 * ... because any permutation in Sn can be expressed as a product of distinct transpositions, so the condition does not actually restrict the permutations that can represent the end state of a sequence of body swaps - any permutation in Sn is reachable anyway. See my post above. The "hypothesis" phrase is more or less redundant, but I don't mind whether we leave it in or take it out. What I am trying to correct is Andrevan's absurd and fictitious claim that it is some subtle form of irony (obviously so subtle that no-one apart from Andrevan gets it). Gandalf61 (talk) 10:27, 17 April 2011 (UTC)

What are the different "versions" of the theorem? How did we decide to state the one we state? Andrevan@ 10:35, 17 April 2011 (UTC)
 * There aren't "different versions". The theorem as we have stated it contains no hypothesis of the kind you think it does. It's from the CTK source. Sławomir Biały  (talk) 12:53, 17 April 2011 (UTC)
 * You wrote "in the version of the theorem we state, there is no hypothesis." The version with the hypothesis is Keeler's, versus the CTK version? Andrevan@ 23:06, 17 April 2011 (UTC)
 * I believe one of the previous posts contained a typo: "the version of the theorem that we state" should have been "the version of the proof that we give". The words "by hypothesis" appeared in the screenshot of the proof.  There is only one version of the theorem that I am aware of.  I don't see how it's constructive to pursue this further. Jowa fan (talk) 02:40, 18 April 2011 (UTC)
 * The use of the word version necessarily implies the existence of another version, does it not? Or were we just talking about Slawomir Bialy's edited version versus the original? Andrevan@ 02:54, 18 April 2011 (UTC)
 * Drop the "different versions" argument, please. What I mean to say is the following. The words "by hypothesis" make sense only in the setting of the original "body swap" scenario. Not in the context of proving this theorem, since it doesn't hypothesize that &pi; is a product of distinct transpositions. This would be a true statement, but not as a hypothesis of the theorem, and anyway not relevant to the theorem or its proof either.  Sławomir Biały  (talk) 11:13, 18 April 2011 (UTC)
 * Why doesn't the body swap scenario apply to our version here? Andrevan@ 11:59, 18 April 2011 (UTC)
 * Because the theorem doesn't say anything about the original permutation being represented as a body swap (i.e., product of distinct transpositions). It applies to any permutation, regardless of how it happens to arise. That is, the body swap isn't part of the hypothesis of the theorem.  Certainly the theorem applies to the body swap scenario, where the original permutation came about by distinct transpositions, but it's ostensibly more general than that because it doesn't assume this as an additional (and, after all, unnecessary) hypothesis.  Got it?  Sławomir Biały  (talk) 13:20, 18 April 2011 (UTC)

Current version of proof 2011-4-15
The current version of the proof (permanent link) reads fine to me. Is there still any concern with the sourcing of the actual text in that permanent link? &mdash; Carl (CBM · talk) 01:00, 16 April 2011 (UTC)
 * The entire thing is different than the one on this page, and the modifications represent a synthesis with the CTK source. Andrevan@ 01:01, 16 April 2011 (UTC)
 * What is "the one on this page"? &mdash; Carl (CBM · talk) 01:02, 16 April 2011 (UTC)
 * , which I also posted on this Talk page several sections above. I found the actual screenshot on Google Images here: . Andrevan@ 01:07, 16 April 2011 (UTC)
 * Surely you're not arguing that changing "ARBITRARY" to "arbitrary", or writing out "Without loss of generality" instead of "WLOG", is original research. For my benefit, could you list the actual differences in the two proofs that you are worried about? &mdash; Carl (CBM · talk) 01:11, 16 April 2011 (UTC)
 * The assertion that the π is a product of disjoint transpositions, "by hypothesis," and the parentheses if I'm not mistaken, which could be an error in the original proof. There's also a bit of wording about distinctness. The original proof and the restatement are practically the same length, so the idea that we would modify it is surprising to begin with. Andrevan@ 01:14, 16 April 2011 (UTC)
 * If we removed the added sentence, what else that is actually in the current article? I am looking for specifics, because you seem to be splititng hairs. The idea that we would copy material unchanged from a source without putting it in direct quotes would also be surprising - many people would call it plagiarism. We need to make sure that we have made an adequate paraphrase of the source in order to avoid that. That means that some things will not be phrased exactly as they are in the source (clearly). &mdash; Carl (CBM · talk) 01:25, 16 April 2011 (UTC)
 * I think we should put it in direct quotes, or state "The following appears verbatim in the episode" or whatever. What we're doing now is more of a copyright ambiguity because we're creating a derivative work of both the CTK and Keeler/Futurama sources and then crediting it to nobody in particular. Andrevan@ 01:46, 16 April 2011 (UTC)
 * That is the same thing we do if we write an article on a news event by combining two different newspaper stories. We need to credit the sources we use, and our claims need to be verifiable. But I don't see why we would need to quote just the episode version, any more than we would need to give direct quote fro just one newspaper instead of using multiple sources. It's not as if the CTK source is on a different topic; they both cover the same theorem. &mdash; Carl (CBM · talk) 01:48, 16 April 2011 (UTC)
 * But we couldn't blend two accounts with slight discrepancies by arbitrarily picking and choosing between the two to create a unified narrative as we saw fit. Andrevan@ 01:51, 16 April 2011 (UTC)
 * What source says there are discrepancies? I think that you are the only person arguing that there are. In fact we do routinely handle the sort of thing you are claiming is a "discrepancy", for example when we use multiple newspaper stories they often disagree in minor ways, but there is no OR problem in using them both. &mdash; Carl (CBM · talk) 01:54, 16 April 2011 (UTC)
 * I just showed you the discrepancies. The proof as a whole means something slightly different between the two versions. The argument is that the difference is "trivial" but all the people who think it is are mathematicians, or frequent contributors to math articles, and they aren't grasping the size of the difference. It's easy to "handle" a discrepancy by separating the sources and explaining one story and the other. The proof as we are showing here exists neither in CTK nor the original screenshot. It is substantially the original screenshot, and takes into account some of the assumptions and clarifications made by the CTK treatment. This is not a theorem - it hasn't been peer reviewed or analyzed broadly. If there were 5 or 10 sources all stating a slightly different yet overall consistent story, it might make sense to take the story as "true," but here we have 2 sources. A primary source, the screenshot, which should be adhered to as primary sources generally are, and a single secondary treatment which should also be treated in isolation since there aren't several corroborating interpretations. Andrevan@ 02:02, 16 April 2011 (UTC)
 * (&larr;) The OR policy makes no mention of "several corroborating interpretations". We have no reason to think that the two accounts are actually "different" in any significant way. At the moment I think you are the only one who thinks the difference is nontrivial, but this seems to be based on your own expert knowledge rather than on anything the sources say. The account of the inception of Me and Juliet does not exist in any of the sources in that article: it is a synthesis of those sources, but that sort of synthesis is permitted by the OR policy. The text here is not advancing any novel interpretation not present in the two sources, as far as I can see. &mdash; Carl (CBM · talk) 02:07, 16 April 2011 (UTC)


 * My point here is that the OR policy does allow us to blend several different sources into a coherent narrative. Today's featured article does it, and articles like this can do it. There is nothing special about proofs compared to musicals, so that we can use multiple sources to talk about a musical but can't use multiple sources to talk about the proof of a theorem. If there are things in the proof here that can't be sourced at all, that would be a problem, and we should fix it. But if the article uses several sources to present a proof that follows the same pattern as the published proofs we draw on, that is not original research, it's source-based research. &mdash; Carl (CBM · talk) 02:13, 16 April 2011 (UTC)


 * My point is that the original proof had ambiguities, or mistakes, or perhaps they were jokes. We have to rely on secondary sources to interpret what the original meant, but the text we are reproducing here is something original which takes the secondary interpretation and combines it with the original piece. Andrevan@ 03:42, 16 April 2011 (UTC)


 * Andrevan - please take a step back for a moment and look at the big picture here:
 * You are in a minority of one on this issue. You have no support, and five or six experienced editors are all saying repeatedly and at length that they disagree with your interpretation of OR and your view that the two proofs are significantly different.
 * You are replying, often within minutes, to almost every post on this talk page - you are not letting a discussion develop.
 * You are repeating the same points over and over again, instead of listening to other editors and working towards consensus.
 * Almost all of your Wikipdia edits for the last week or more have been on this issue.
 * May I suggest that you take some time to read the excellent advice at WP:CALM, and also to consider whether your focus on this single issue has crosssed over from a strongly held point of view into an obsession. Perhaps you should think about taking a Wikibreak, or at least spending your on-Wiki time on other activities for a few days. Remember there are no angry mastadons here ! Gandalf61 (talk) 08:49, 16 April 2011 (UTC)
 * I have to respond quite a bit more since, as you mentioned, it's me against five or six experienced math editors. Although my points may seem repetitive, I think we've seen a progression in the discussion over time. In fact, Jowa fan just corrected a discrepancy between the two proofs which should offer considerable support for my concern that modifying the proof is a form of original research which can easily introduce discrepancies, however subtle. So while I welcome your advice in the spirit it is given, I am quite calm and actually rather enjoy on-wiki discussion such as this. Andrevan@ 11:26, 16 April 2011 (UTC)
 * This is a discrepancy of the "Constantinople/Istanbul" sort, not some serious departure from the source. Moreover, omitting something trivial is quite different than adding something completely new. If a source said "The Louvre is in Paris, the capital of France", and we just say "The Louvre is in Paris", we have not committed original research. Similarly, if we say "Miami, Ohio" even though the source only says "Miami", we are still not be committing original research. If a source explicitly says that some permutation is written in left-to-right order, and we don't say that, we are not committing original research or making any sort of variation in the proof worth mentioning on a talk page. This is the sort of thing that is completely within editorial discretion. &mdash; Carl (CBM · talk) 11:37, 16 April 2011 (UTC)
 * What if we offered a definition of the derivative, but instead of (f(x+h) - f(x))/h, we omitted any one letter, or several parentheses? Maybe we were pretty sure it was the same thing and we had learned in math class that it was OK to just knock off the h. I think this shows that there's a huge difference between omission in a sentence about Miami, and in a proof. Andrevan@ 11:44, 16 April 2011 (UTC)
 * In the present situation, it's more like we switched the h to an a, and said "the limit as a approaches 0" instead of "the limit as h goes to 0", and this led to complaints that we were distorting the meaning of the original source. None of the "changes" you have mentioned goes beyond that type of rewording or notational change. That sort of trivial rewording does not introduce any originality into the article. The issue of correctness is handled here just like in an article on Miami: the editors do their best to follow the sources and to be correct, and if something isn't right we can always fix it. The main thing you are complaining about, the sentence on every permutationbeing a disjoint product of cycles, is already in the version of the proof you are using as a reference : "let π be an ARBITRARY permutation on [n]. It consists of disjoint (nontrivial) cycles ..." &mdash; Carl (CBM · talk) 11:52, 16 April 2011 (UTC)
 * I believe you have misunderstood me. The proof stated that π consists of disjoint nontrivial cycles, but not that all permutations do (until the end). The proof basically hypothesizes that a given permutation will consist of disjoint cycles, then checks by examination that one does, then at the end states that any arbitrary permutation does. It's barely a proof really. Andrevan@ 08:59, 17 April 2011 (UTC)
 * Umm... I don't think you understand the theorem. Or its proof for that matter. The theorem is not about disjoint cycles, it's about representing permutations in terms of distinct (not disjoint) transpositions of a certain specific kind.  Sławomir Biały  (talk) 13:15, 17 April 2011 (UTC)

Regarding "the text we are reproducing here is something original which takes the secondary interpretation and combines it with the original piece" - that is fine with the OR policy. We can use both a newspaper story and a biography to describe the same event in someone's life. We can use both a chronological plot summary from a movie, and a article analyzing the plot, to talk about the plot of a movie. Today's featured article uses numerous sources to describe the same things. So it's true that the Wikipedia account will not have literally appeared anywhere before, because we are supposed to do original writing. Otherwise we would be limited to using one source for each article, or one source for each paragraph at the least. That is not the actual requirement, we are allowed to combine material from different sources to make our articles better. We just need to make sure that there are no ideas in our articles that weren't already in the sources. That's the case here; we are not pushing ideas here that are not in the sources. &mdash; Carl (CBM · talk) 11:52, 16 April 2011 (UTC)

User:Andrevan, you should know that a famous editor who aggressively pursued this line of "work" in Wikipedia was eventually banned. Tijfo098 (talk) 07:52, 17 April 2011 (UTC)


 * While that is certainly interesting reading, I don't think I'm going so far as to say that it's impossible to paraphrase without committing original research. In this very narrow case, we are changing subtle meaning in a mathematical proof that appeared on a comedy TV show. Most paraphrasing on Wikipedia is probably fine. Andrevan@ 08:56, 17 April 2011 (UTC)
 * User:Andrevan - there is no change of meaning. Five or six experienced editors have repeatedly told you this, but you are refusing to listen. No one agrees with your assertions. Your obsessive refusal to accept consensus here has become tendentious. As an admin, a bureaucrat and a mediator, you should hold yourself to a higher standard of behaviour than this on Wikipedia. Once again, with the best of intentions, I urge you to take an objective look at the hole that you are in, and stop digging . Gandalf61 (talk) 09:57, 17 April 2011 (UTC)
 * I fully agree. Andrevan, if you still believe that the article is presently objectionable, I suggest that you request outside help. Perhaps mediation?  (I know that you're a mediator, and I don't mean that sarcastically.  I just think that an outside perspective might help.)  Ozob (talk) 13:19, 17 April 2011 (UTC)
 * Mediation is not a good idea, since it requires other parties willing to continue this interminable discussion over petty hairsplitting. The consensus is already clear from the discussion here. If a wider consensus is desired, then another RfC may be in order instead. Sławomir Biały  (talk) 13:45, 17 April 2011 (UTC)
 * I can't see an RfC changing anyone's minds at this point. In fact, I don't think that there are any points worth discussing, because I'm convinced that the current situation is a misunderstanding and nothing more.  I don't know a sure way of clearing that misunderstanding.  Since these talk page discussions don't seem to have helped, I think mediation is a reasonable next step.  Ozob (talk) 21:08, 17 April 2011 (UTC)
 * It doesn't seem like the argument is worth continuing to me. I just don't have the stamina. Who, then, would participate in the proposed mediation? Sławomir Biały  (talk) 21:51, 17 April 2011 (UTC)


 * I don't think mediation is necessary. Consensus supports the current version. Andrevan@ 22:59, 17 April 2011 (UTC)

This is a television article
This is a television article not a maths proof, this is a minor and trival aspect of the episode. Having a proof in the middle of this article give WP:UNDUE to some thing that is basically an Easter egg for maths fans Gnevin (talk) 22:50, 28 June 2011 (UTC)
 * It's both the basis for this episode's plot and production section, and a major part of the notability of this episode.  X  eworlebi (talk) 23:09, 28 June 2011 (UTC)
 * I done a quick search and while there is coverage I don't think it's a major part of the notability. Every other ep has it's own article which is clearly where the notability of this article is derived from. This is not that important Gnevin (talk) 23:21, 28 June 2011 (UTC)
 * That's not how notability works, other articles exist yes, not all of them should. (WP:GNG, WP:NOTINHERITED) This episode in specific received quite a bit of coverage because of the theorem, significantly contributing to why this episode is notable and other run-of-the-mill episodes aren't.  X  eworlebi (talk) 23:29, 28 June 2011 (UTC)
 * Where? I can't find it . Some mention the theorem and its coverage but proving it is overkill  Gnevin (talk) 23:57, 28 June 2011 (UTC)
 * I don't see proving it as overkill. This is both a TV episode article and the article on the theorem, because the article on the theorem was merged here. As I said in that merge discussion, I don't have any objection to the merge, but the theorem and its proof should certainly be included on Wikipedia. This is the apparently the location where we cover them at the moment. &mdash; Carl (CBM · talk) 00:04, 29 June 2011 (UTC)
 * "This is a television article"??? Where is the policy/guideline saying that an article listed in category X is not allowed to include content relating to subject Y? Jowa fan (talk) 00:34, 29 June 2011 (UTC)
 * Most of the rest of this talk page is taken up with a lengthy discussion of the proof in this article. Consensus was that a short summary of the proof was appropriate content. When you see a can with "Worms" written on it, it's usually best not to open it. Gandalf61 (talk) 08:24, 29 June 2011 (UTC)
 * On wiki be are encouraged to open cans but fair enough the consensus is that this is notable and improves the article Gnevin (talk) 13:12, 30 June 2011 (UTC)

Just something small I noticed
At about 13:55, Bender, in reaction to seeing his new wife as emperor, says "Hello baby." It bears an uncanny resemblance to the sound of the first lyric in the song Good Enough by Van Halen on the album 5150. I'd add it to the Cultural References section, but I have no source, as it is my own discovery (and I'm not even positive that was their intention). — Preceding unsigned comment added by 72.222.217.231 (talk) 06:15, 2 January 2013 (UTC)

Why left-to-right?
Why does the proof state that sigma is to be composited left to right? The only way I see that pi*sigma equals the id with x,y switch is by reading sigma right-to-left. The links to reverse polish notation did not help me. :( — Preceding unsigned comment added by 78.52.128.226 (talk) 00:54, 23 April 2013 (UTC)


 * The note about left-to-right has to do with conflicting conventions regarding how permutations (and composition of permutations) should be read: with one convention, $$\sigma$$ ends up as the wanted permutation, whereas with the other convention it ends up as the inverse of what is wanted (squaring the cycle instead of undoing it). Isolated arguments involving permutations can be troublesome because as a reader you never know which convention the author applied. In this case, the article text has two further problems:
 * 1. The link to Polish notation is nonsense — this has nothing to do with that.
 * 2. The phrase 'left-to-right' is of no help, as the matter of which convention it describes would itself require a convention.
 * The actual issue is whether composition of permutations satisfies $$(\rho\sigma)(j) = \rho\bigl( \sigma(j) \bigr)$$ or $$(\rho\sigma)(j) = \sigma\bigl( \rho(j) \bigr)$$. 78.79.230.106 (talk) 12:04, 5 November 2020 (UTC)

Nothing new. Why is Keeler getting credit for this?
This problem is probably known by some other name, and has existed for some time. At minimum, Stargate SG-1 had an episode revolving around that plot device in 1999. http://stargate.wikia.com/wiki/Holiday 68.197.227.39 (talk) 04:22, 7 September 2013 (UTC)

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Stargate S2E17
It seems to me that the body-switching problem was already presented (but only solved in a simple case) in a Stargate SG-1 episode (S2E17, Holiday) wouldn't it be fair to mention it? 2601:648:8601:93A0:6587:C3CE:584:3723 (talk) 23:23, 21 November 2022 (UTC)