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pi: 9th Top-priority FA article for project

The pi article has been nominated for Featured Article status. If successful, this will be the ninth Top-priority FA article for the Mathematics project. Editors familiar with the FA criteria are welcome to provide input at Misplaced Pages:Featured article candidates/Pi/archive1. --Noleander (talk) 12:33, 15 May 2012 (UTC)

The pi article mentions the series:
π = 3 + 4 2 × 3 × 4 − 4 4 × 5 × 6 + 4 6 × 7 × 8 − 4 8 × 9 × 10 + ⋅ ⋯ {\displaystyle \pi ={3}+{\frac {4}{2\times 3\times 4}}-{\frac {4}{4\times 5\times 6}}+{\frac {4}{6\times 7\times 8}}-{\frac {4}{8\times 9\times 10}}+\cdot \cdots }
A reviewer at FAC asked what the origin of this series is (who, when). Does anyone have a reliable source that identifies the origin of this series? Sources are available that define the series, so that is not a problem: it is the origin that is needed. Thanks in advance. --Noleander (talk) 20:01, 15 May 2012 (UTC)
I notice a lot of references to Eric Weistein's website, including the reference for this series. I wouldn't consider him a reliable source on anything. It's probably worth trying to find a better source. Sławomir Biały (talk) 20:12, 15 May 2012 (UTC)
Weisstein is used as a source only for "motherhood" factoids: formulae that are represented in hundreds of math texts (e.g. definition of polar coordinates). I don't mind changing those cites to hardbound math books, but I'm pretty certain that there was consensus within the Math project that Weisstein is a valid RS for simple or basic math-related facts. Is that not true? Of course, Weisstein should not be used as a source for contentious or complex material. --Noleander (talk) 20:22, 15 May 2012 (UTC)
If MathWorld is not an acceptable RS for basic math facts, I have at hand A guide-book to mathematics by Bronshteĭn and Semendiaev (H. Deutsch, 1971). Any objection to using that for area of a circle, etc? --Noleander (talk) 20:40, 15 May 2012 (UTC)
... also, just to clarify, the issue here is not the validity of the series (it is documented in many RSs) but rather: does any editor here know of additional detail about the origin of that series, so that additional detail could be incorporated into the article? At the moment, the article does not contain any statement about the origin of that series. --Noleander (talk) 20:24, 15 May 2012 (UTC)
All right, I think we are in good shape now: user:RJHall found a source for the above mentioned series. And, following the sage advice of user Sławomir Biały, I'm eliminating the use of MathWorld as a source in the article (just a couple more to go). So, no more help needed on this issue. --Noleander (talk) 22:56, 15 May 2012 (UTC)

Hello everyone! I would appreciate if a few people could lend their expertise over at the nomination page, even if it is just to confirm that one little section is not a piece of nonsense. I am just concerned about the little things, the off emphasis here, the obscure odd fact inserted there, that have a way of getting into even (or especially?) meticulously-researched articles, and that bespeak inexpertness. For example, detailed discussions of π's relationship to the Mandelbrot set fractal and the sinuosity of a meandering river (which are above my head) appear in the middle of other content, like a discussion of Euler's identity (the importance of which even I can understand) or the Fourier transform (which I have at least heard of). It just strikes me as a little fishy, though for all I know the article is perfectly well balanced. Which is why I'm asking for some help. Thanks! Leonxlin (talk) 19:33, 31 May 2012 (UTC)

Pi has passed its nomination! Leonxlin (talk) 01:27, 6 June 2012 (UTC)

Original research classification of magic cubes

The Pantriagdiag magic cube (AfD discussion) article is currently listed for deletion. Other articles in the same vein are diagonal magic cube, pantriagonal magic cube, pandiagonal magic cube, and perfect magic cube. I observe that we seem to have a bit of a problem with magic cube classification. I refer you to the second sentence of magic cube classes, whose boldface is in the article itself:

This new system is more precise in defining magic cubes.

The new system, it turns out, is the invention of Harvey Heinz (talk · contribs), who put up his new system on two sets of WWW pages and in a self-published book (Harvey D. Heinz Publishing), and who came to Misplaced Pages and wrote all of these "-agonal" articles, the magic cube classes article, and also the perfect magic cube#An alternative definition section of the perfect magic cube article. Misplaced Pages seems to be presenting an acknowledged idiosyncratic and novel classification of this subject.

Uncle G (talk) 15:09, 22 May 2012 (UTC)

List of scientific constants named after people

The list of scientific constants named after people includes a section on mathematical constants. The mathematical and physical parts should each be a hundred times as long as it is. Work on it. Michael Hardy (talk) 22:17, 22 May 2012 (UTC)

Template:WikiProject Mathematics

I would like to resurrect Template:WikiProject Mathematics. It is no longer used. Template:Maths rating is used instead. I think it is nice to be consistent with other wikiprojects. Makes the housekeeping easier. Is there WP-wide guidelines on this sort of thing? -- Alan Liefting (talk - contribs)

There is no wiki-wide guideline. There was a recent discussion in March that resulted in the current name being kept.
There aren't actually any housekeeping problems with the current name. On the other hand, unlike other projects, we do not need to tag articles just to say they are related to math; the name "maths rating" emphasizes that the purpose of the template is rating information. — Carl (CBM · talk) 01:59, 23 May 2012 (UTC)
Hmmm. This makes it a little harder for editors who work across all WikiProjects. From the discussion it looks like I am not the only one who has run into this little glitch. -- Alan Liefting (talk - contribs) 02:14, 23 May 2012 (UTC)
In general, if you don't deal much with mathematics articles and aren't comfortable assessing them, there's no reason why you need to worry about the {{maths rating}} template at all, you can just ignore it. — Carl (CBM · talk) 02:18, 23 May 2012 (UTC)

Category template deletion

Misplaced Pages:Templates_for_discussion/Log/2012_May_23#Template:Category-Logic.2Fheader

I wonder what you guys think about this template deletion at Category:Logic. Greg Bard (talk) 01:18, 24 May 2012 (UTC)

I see it has provoked Misplaced Pages:Village pump (policy)#Competition for the worst Misplaced Pages page - be in to win!. Personally I was just ignoring the deletion talk as I have a bit of a laissez faire attitude unless things really cause trouble and also I think that business is rather unfair about the template. Dmcq (talk) 18:17, 25 May 2012 (UTC)

Power spectrum estimation

Our coverage of power spectrum estimation (spectral density estimation) seems very weak, with very little bringing together or contrasting the different methods, or giving historical perspective. Indeed, most articles looking for a signal processing treatment of the subject appear to have been being redirected to spectrum analyzer, about a hardware box with very little discussion of algorithms usually used in pure-software methods.

In particular, there is very little discussion of all-poles versus all-zeros methods. There appears to be nothing at all about John Parker Burg or the Burg algorithm. We have quite a detailed article on the Levinson recursion, but nothing to say that this is perhaps its most important application. Linear predictive coding appears to exist in a silo of its own, without even a link to ARMA modelling; while in turn the article on ARMA models doesn't appear to mention power spectrum estimation at all. Autoregressive model is a bit better, but doesn't give any sense how a pure AR fit is likely to compare to other fits.

It probably doesn't help that spectral analysis goes to a dab page, and the top link spectrum analysis that probably ought to be merged into spectroscopy.

This is very poor. Given the importance of this topic in signal processing and applications, we ought to be able to match at minimum the level of discussion in Numerical Recipes at least. But at the moment we're way short. Anybody out there willing to step up to the plate? Jheald (talk) 09:23, 26 May 2012 (UTC)

Cross-posted to WT:WPSTATS, WT:PHYSICS Jheald (talk) 09:29, 26 May 2012 (UTC)
Discussion moved to Talk:Spectral density estimation#Coverage. --TSchwenn (talk) 17:12, 26 May 2012 (UTC)

Content fork in Finitely generated projective module

The page Finitely generated projective module has been created recently. IMO, this is a redundant content fork and this page has to be merged into Projective module. I have started a discussion in Talk:Finitely generated projective module and the author of the article disagrees. Please comment there. D.Lazard (talk) 13:04, 27 May 2012 (UTC) — (Links corrected after reading next post. D.Lazard (talk) 14:13, 27 May 2012 (UTC) )

I think you mean Finitely generated projective module. --Zundark (talk) 13:52, 27 May 2012 (UTC)
OOPS. You are right. Such a long title is, may be, another reason to merge. D.Lazard (talk) 14:13, 27 May 2012 (UTC)
Actually the precise term would be "finitely generated projective module over a commutative ring possibly without unity" (sorry, couldn't resist) The exclusion of unity is useful in allowing a commutative Banach algebra, as I understand. I think the subject suffers from a lack of catchy name. -- Taku (talk) 15:54, 30 May 2012 (UTC)

"Parity of zero" should be the gold standard for math articles

Parity of zero explains why zero is even in an easy-to-read format that I just don't see in other articles, namely Riemann hypothesis. 68.173.113.106 (talk) 21:08, 28 May 2012 (UTC)

So you think our articles should go on for pages and pages about trivialities rather than even attempting to explain anything complicated. That's useful to hear (really!) but I suspect not everyone would agree. —David Eppstein (talk) 22:34, 28 May 2012 (UTC)
And the Degrees of evenness section should be launched directly into the sun.Naraht (talk) 02:15, 29 May 2012 (UTC)
I don't think that the article is a useful model for this project. Its contents are not really about mathematics but rather math education; the math is trivial and the pedagogy complex. CRGreathouse (t | c) 04:03, 29 May 2012 (UTC)
There's inherent difficulties in the Riemann hypothesis that are absent in Parity of zero. One would really need to compare articles of about comparable difficulty I think. That was like comparing quantum mechanics to Newton's laws of motion. Dmcq (talk) 08:45, 29 May 2012 (UTC)
Completely agree. The main contributors to parity of zero have done an excellent job, but it is not too hard to write simply about simple subjects. It is much harder to write simply about complex subjects. Gandalf61 (talk) 08:58, 29 May 2012 (UTC)
I see. Maybe we could start a campaign to improve the readability of certain math articles, starting with moderate-readability articles, then working our way up to the really confusing ones. The main reason why I never read them is because they're that confuzzling. 68.173.113.106 (talk) 00:31, 9 June 2012 (UTC)
Well, you know, the subject itself is confusing. Good writing can certainly help (or maybe better stated, bad writing can hurt), but there is no way to make advanced mathematics understandable without some serious effort on the reader's part. Still, absolutely, writing them better is a good thing. --Trovatore (talk) 01:39, 9 June 2012 (UTC)

maclaurin

The following footnote at Colin Maclaurin is sourced at a personal page at the university of rochester:

"Neither Newton nor Leibniz – The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala". MAT 314. Canisius College. Retrieved 2006-07-09."

I wonder if it is the optimal source for the information. Tkuvho (talk) 08:20, 29 May 2012 (UTC)

It is a powerpoint and a book or article would be better. But to be frank I was pleasantly surprised by its quality. It might be I've come across too many people pushing the evidence way past where it should go when bigging up their countries contributions.. Dmcq (talk) 09:00, 29 May 2012 (UTC)
In any case, it is not clear which assertion is sourced from this course. In fact I can not understand the paragraph referring to this source, especially the sentence "At the time, Maclaurin was unaware and published his work in Methodus incrementorum directa et inversa, Maclaurin series which are Taylor series expanded around 0, and are not attributed to Maclaurin due to the past discoveries, ...". Can someone understand this? D.Lazard (talk) 09:17, 29 May 2012 (UTC)
My guess would be that the footnote is only used for the assertion that some form of Maclaurin series was known to the Kerala school. There is another reference for this assertion in Taylor series which points to an article by Dani; that might be a better one but I cannot access it. Regarding the sentence D.Lazard quotes, Methodus incrementorum directa et inversa was written by Taylor, so something has gone wrong there. I rewrote the paragraph using the article by Gradiner referred to, so hopefully it makes more sense now. -- Jitse Niesen (talk) 11:25, 29 May 2012 (UTC)

Bell's theorem

The article on Bell's theorem has been hijacked by crackpot Joy Christian and his cronies. Any attempt to remove references to Christian's discredited work (not published in any peer-reviewed journa, and shown o be fundamentally flawed by a long list of authorities in the fieldl) is immediately "undone" by Christian himself or his supporter Fred Diether. Conflict of Interest!

But if nobody cares about this article better to leave it to the crackpots. Richard Gill (talk) 18:31, 29 May 2012 (UTC)

Here's a silly question. If authorities have taken the trouble to point out the flaws in Christian's work--i.e. if Christian's work has received significant coverage in reliable sources--does that make it notable? I guess you're hoping that the answer is no, but the question does need to be asked. Jowa fan (talk) 03:18, 30 May 2012 (UTC)
It certainly can do okay or give it enough weight in an another article for inclusion I don't believe that is true in this case though. Dmcq (talk) 07:40, 30 May 2012 (UTC)
Generally, in an article about the crackpots, notability is the most relevant criterion. However, in an article about a mainstream scientific topic, we should not treat fringe views, as this often gives them equal WP:WEIGHT. The goal of an encyclopedia article on something like Bell's theorem is to give the reader a treatment of the subject as it is understood by the vast majority of standard, peer reviewed sources. Sławomir Biały (talk) 14:46, 30 May 2012 (UTC)
Thanks, Sławomir, I think that applies in this case. Jowa fan (talk) 00:10, 31 May 2012 (UTC)

Richard Gill called me “crackpot Joy Christian.” I wonder what his criterion of crackpot is. I let the readers judge for themselves. Here are my credentials: Dr. Joy Christian obtained his Ph.D. from Boston University in Foundations of Quantum Theory in 1991 under the supervision of the renowned philosopher and physicist Professor Abner Shimony (the “S” in Bell-CHSH-inequality). He then received a Research Fellowship from the Wolfson College of the University of Oxford, where he has remained affiliated both with the college and a number of departments of the university. He is an invited member of the prestigious Foundational Questions Institute (FQXi), and has been a Long Term Visitor of the Perimeter Institute for Theoretical Physics, Canada. He is well known for his contributions to the foundations of quantum and gravitational physics, including quantization of Newton-Cartan theory of gravity, generalization of Special Theory of Relativity to incorporate the objective passage of time, and elimination of non-locality from the foundations of quantum physics. A partial list of his publications can be found here: http://arxiv.org/find/all/1/au:+Christian_Joy/0/1/0/all/0/1 — Preceding unsigned comment added by 86.148.6.36 (talk) 22:03, 31 May 2012 (UTC)

As for the paper in question, "Disproof of Bell's Theorem", http://arxiv.org/pdf/1103.1879v1.pdf , is published in my peer-reviewed book, http://www.brownwalker.com/book.php?method=ISBN&book=1599425645, and is widely discussed on the Internet. My work has also been cited in several *published* articles, at least two of them in the Physical Review (not to mention its citations in some lesser known journals). I have given invited talks about my work on several occasions during the past five years. The book itself is only just published, and citations to it will undoubtedly follow in due course. On the other hand ALL of Richard Gill’s misguided, erroneous, and unpublished arguments against my work have been comprehensively debunked, many times over, not only by me but also by several other knowledgeable people on the FQXi blogs. I myself have given a systematic refutation of his misguided arguments in the following two papers: http://arxiv.org/abs/1203.2529 and http://arxiv.org/abs/1110.5876 -- Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk) 22:13, 31 May 2012 (UTC)

Whether or not you are a crackpot, your book is not peer-reviewed, and your result is not generally accepted. If discussed in peer-reviewed articles, it may be mentioned as a claimed disproof of Bell's Theorem. — Arthur Rubin (talk) 07:18, 1 June 2012 (UTC)

@Arthur Rubin: My book IS peer-reviewed. My work IS cited and discussed in Physical Review and other journals, and NOT as negatively as you are trying to suggest. You have no proof of what you are claiming. You are clearly biased.

On a different note, I urge the Misplaced Pages community to remove Richard Gill’s slanderous name claiming from his post above. As you can judge from my qualifications I listed above, his name calling has no justification whatsoever. -- Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk • contribs)

Your book IS NOT peer-reviewed. That would mean the publisher submitted it to your peers for review before publication. If it were reviewed in Phys.Rev., that would not constitute peer review; it might indicate notability, but not reliability.
As for Gil, he shouldn't have called you a crackpot. However, there are people much more established than you are who call you a crackpot, so I'm tempted to modify the places where you were called a crackpot to "so-called" crackpot. — Arthur Rubin (talk) 08:18, 1 June 2012 (UTC)

@Arthur Rubin: My book *IS* peer-reviewed. There are also people who call me a genius; so perhaps you should refer me as a “so-called genius.” -- Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk) 08:38, 1 June 2012 (UTC)

Nonsense. If your book was peer-reviewed, your publisher would have said so. And you need a cite that people call you a genius. — Arthur Rubin (talk) 08:40, 1 June 2012 (UTC)
Nonsense. My book *was* peer-reviewed, and my publisher does say so. I do not have to cite people who call me a genius. One can see that from my one-page paper itself: http://arxiv.org/abs/1103.1879 — Preceding unsigned comment added by 86.148.6.36 (talk) 09:18, 1 June 2012 (UTC)
From your one-page paper itself I see that indeed, your idea of what is stated by Bell theorem is far from that of Bell. Thus, treating you as the next genius after Bell, I'd rename your paper as follows: "Disproof of Christian strengthening of Bell theorem". Boris Tsirelson (talk) 11:33, 1 June 2012 (UTC) :-)

Boris, I respectfully disagree (if I understand you correctly). Bell claimed that no functions of the form A(a, L) = +/-1 and B(b, L) = +/-1 can reproduce correlations of the form E(a, b) = -a.b. “This is the theorem” (his exact words). What Bell did not realize is that this claim is true if and only if the co-domain of the functions A(a, L) and B(b, L) is NOT a unit parallelized 3-sphere, S^3. My one-page paper shows an explicit construction of the fact that when the co-domain of A(a, L) and B(b, L) is taken to be S^3, the correlations are inevitably E(a, b) = -a.b. I urge you to have a look at this longer paper to see my compete argument: http://arxiv.org/abs/1201.0775 . Thanks. -- Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk) 12:10, 1 June 2012 (UTC)

Ah, now I see, thank you for the clarification; I was not able to understand your text "as is", but now I know what did you really mean. Well, then we agree: “This is the theorem” was said by Bell about (+/-)-valued functions. For vector-valued functions, this is exactly what I called "Christian strengthening of Bell theorem"; and it is wrong, of course, so you are able to disprove it, of course. But in fact, for vector-valued functions it was "disproved" by Bell himself, in the same (historic) article; by doing this he showed that quantum spin measurements can indeed violate Bell inequality. Boris Tsirelson (talk) 13:24, 1 June 2012 (UTC)
I am afraid you still haven’t understood what I have shown. The functions A(a, L) and B(b, L) both Bell and I are postulating for measurement results are (+/-)-valued functions only, but the co-domain I am using is S^3 instead of the real line. In other words, A(a, L) and B(b, L) for me are maps of the form +/- 1 = A(a, L) = R^3 x H maps to S^3, where H is the hidden variable space. So A(a, L) and B(b, L) in my model are pure binary numbers, +1 or -1. They are not vector-valued, although they have been constructed out of a product of two bivectors. The difference is in the co-domain of these functions only, not in the actual values of A and B, which are still scalars, +1 or -1. Note that scalars, +1 and -1, are as much a part of the 3-sphere as the bivectors are. – Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk) 14:20, 1 June 2012 (UTC)
Yes, I haven’t understood. Yes, the two-point space {-1,+1} can be treated as embedded into the sphere (as a pair of opposite points), but this embedding does not change their correlation.
Anyway, the discussion becomes too specific for this page. If you like, we can continue it on my (or your) talk page. Boris Tsirelson (talk) 15:05, 1 June 2012 (UTC)
I have added some explanation of my model on your talk page. -- Joy Christian

Whatever the outcome of this discussion, it is clear that we should not cite Joy Christian's self-published work (WP:SELFPUB). There has been a long tradition of criticism of Bell's theorem from the fringes of physics. If mention of this is to be included in the article, it should be sourced to a reliable secondary source documenting such criticism and the replies of the scientific mainstream (WP:NPOV,WP:PSTS). Otherwise, including criticisms sourced to the primary literature is considered to be original research, and is forbidden by Misplaced Pages policy. Sławomir Biały (talk) 13:51, 1 June 2012 (UTC)

MathJax issue

Tracked in Phabricator
Task T38059

I'm not sure if this is a known issue, but there seem to be some inconsistencies in the way the Wikimedia parser processes TeX and MathJax. Consider <math>a<b</math>:

a < b {\displaystyle a<b}

versus <math>a\lt b</math>

Failed to parse (unknown function "\lt"): {\displaystyle a\lt b}

If MathJax is enabled, the first equation does not display correctly but the second one does. If "Render as PNG" is enabled the first equation displays correctly, and the second generates a parse error "Failed to parse (unknown function\lt)". This seems to be quite bad, since half of users will see one or the other of the two errors! Sławomir Biały (talk) 14:19, 31 May 2012 (UTC)

Now after writing this, the first equation seems to dispay correctly. Strange. Sławomir Biały (talk) 14:20, 31 May 2012 (UTC)
Perhaps related to this bug , though I don't see exactly how that would cause it.--JohnBlackburnedeeds 14:35, 31 May 2012 (UTC)
Yep. The first problem is bug 36059. Helder 15:12, 31 May 2012 (UTC)

In light of the fact that MathJax is "still experimental", I don't think the preferences page should also say that it is "recommended for most browsers". These two directives seem to be incongruous. Sławomir Biały (talk) 16:39, 31 May 2012 (UTC)

Obviously, this is the wrong place to complain about it (and that fixing this bug, pointed out even before the release, has been described as not being of a high priority). Just in case you missed it, the perceived editor-developer divide is being debated for a while now. Nageh (talk) 17:02, 31 May 2012 (UTC)
I don't want to join a fight particularly. It seems like this recommendation would be a trivial thing to change in the next update. Sławomir Biały (talk) 17:39, 31 May 2012 (UTC)
Worth bearing in mind that the "math" tags are not handled well by MathJax - they're deprecated. If you want to use MathJax then go the whole way. Then you can use dollar signs as delims or backslash-openround, backslash-closeround instead. But dollar delims IMO make more sense because they're not as fiddly to type as backslash-openround, backslash-closeround. --Matt Westwood 07:34, 3 June 2012 (UTC)

Bell's Theorem (bis)

Comments on Talk:Bell's_theorem#Seeking_consensus_to_exclude_the_disproof_of_Bell.27s_theorem will be appreciated. Thanks. History2007 (talk) 00:42, 1 June 2012 (UTC)

  • As a brief aside, I just wanted to say that the whole episode is a bit amazing and embarassing, and I'm sad to see geometric algebra caught in the middle :( Rschwieb (talk) 01:18, 1 June 2012 (UTC)

I urge the Misplaced Pages community to remove Richard Gill’s slanderous name claiming from his post above. As you can judge from my qualifications I listed above, his name calling has no justification whatsoever. -- Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk) 06:13, 1 June 2012 (UTC)

Both of you, would you mind going and bothering Misplaced Pages talk:WikiProject Physics instead? I don't know what we have to do with the matter. --Trovatore (talk) 08:42, 1 June 2012 (UTC)
It is a physics result, but it is mainly based on simple maths and logic rather than needing any great understanding of physics. I see the notification here as being reasonable. The 'discussion' should definitely be at the articles talk page though. Dmcq (talk) 08:48, 2 June 2012 (UTC)

betterexplained?

I don't recall http://betterexplained.com/archives/ being discussed in this space so I would like to raise the issue of whether this is a reliable source. Also, would it be appropriate to cite it in a footnote in the lede of an article. Tkuvho (talk) 07:29, 1 June 2012 (UTC)

A similar question with regard to http://plato.stanford.edu/ In this latter case, there are some serious factual errors. The chronic problem with these websites is that they are by no means peer reviewed. The peer review process certainly does not eliminate all errors, but its absence does not help, either. Tkuvho (talk) 07:33, 1 June 2012 (UTC)
We use many non peer reviewed sources such as textbooks and Stanford's Encyclopedia of Philosophy is comparable to that and hence a reliable source.
As far as betterexplained.com is concerned I wouldn't regard that as a reliable source and it's beyond me why you even would want to compare that to Stanford's Encyclopedia of Philosophy. They have hardly anything in common other than being available online.--Kmhkmh (talk) 09:12, 2 June 2012 (UTC)

Shouryya Ray on AfD

See Misplaced Pages:Articles for deletion/Shouryya Ray.

Is this person notable?

Are the news media's claims about him true or merely sensationalist exaggerations that help sell newspapers?

Opine at the page linked to above. Michael Hardy (talk) 16:45, 3 June 2012 (UTC)

Lester Dubins

I was surprised that we had no article on Lester Dubins. I've just created one. It needs further work, both within the article itself and in other articles that ought to link to it. Michael Hardy (talk) 17:31, 3 June 2012 (UTC)

Poincare's definition of manifold

I added Poincare's original definition of a differentiable manifold at Manifold#Poincar.C3.A9.27s_original_definition. Poincare defined a manifold as a subset of euclidean space which is locally a graph (see details there). This definition is arguably more accessible to a general reader than the more abstract definition involving atlases, charts, and transition functions. The lede could profit from focusing on the subset-of-R^n definition instead of the abstract definition. However, another editor feels that the reader does not need the crutch of Euclidean space to understand the concept of a manifold, and my changes to the lede were repeatedly reverted. Which definition should the lede be based on? Tkuvho (talk) 11:37, 4 June 2012 (UTC)

Having the historical definition in a section on history makes sense, but for example that definition makes it quite hard to see that the graph of the absolute value function, as a subset of R 2 {\displaystyle \mathbb {R} ^{2}} is a manifold (not differentiable at 0), or the unit circle as a subset of R 2 {\displaystyle \mathbb {R} ^{2}} (not locally a graph).
A similar thing happens with the concept of function; the historical definitions were simultaneously more limited in some ways and more broad in other ways than the modern definition, so we can't start the article with them. — Carl (CBM · talk) 12:09, 4 June 2012 (UTC)
I for one have serious difficulty understanding what is meant by the wording. Use of the term "graph" in place of "function" confuses. Also the implication that every manifold is globally embeddable in a Euclidean space should not be implicit in the (modern) definition, even if this is (nontrivially) provable. So, no, not Poincaré's definition in the lead. — Quondum 12:35, 4 June 2012 (UTC)
The lede as it currently stands (i.e. using a map on the surface of the earth as an example) is utterly perfect. My vote is: leave it like it currently is - non-mathematicians will be able to access it admirably from there. --Matt Westwood 13:38, 4 June 2012 (UTC)
@Carl: the graph of the absolute value function is not really relevant as it is not a smooth manifold (actually as an abstract Riemannian manifold it is perfectly differentiable at 0 also). The circle is indeed locally a graph, either over the x-axis or over the y-axis. As Whitney proved, the two definitions are exactly equivalent. This means that the atlas definition is only different from Poicare's definition in that it is harder to follow. It is neither more limited nor more broad.
@Quondum: y=f(x) is a function; the set of points (x,y) satisfying y=f(x) is its graph in the plane. I think most calculus students are more comfortable with the notion of a graph of a function than with transition functions between charts.
@WestwoodMatt: The current lede does not really tell you what a manifold is. Note that the abstract definition ends up using differentiable functions in the end, as well: the transition functions have to be differentiable functions. The only difference is the abolition of intuition in the abstract definition, according to Arnold. Tkuvho (talk) 13:45, 4 June 2012 (UTC)
A circle is not locally a graph, there's no neighborhood of the 3 o'clock point around which the curve passes the vertical line test. It could be that you mean that the circle is the image of the real line under a suitable embedding, but that is not what "is the graph" means, because the circle is not the graph of that embedding (the graph is at best a noncircular subset of R 3 {\displaystyle \mathbb {R} ^{3}} ). Whitney's theorem is about embeddings of manifolds, but the embeddings are not generally graphs of functions. — Carl (CBM · talk) 19:08, 4 June 2012 (UTC)
In this setting, a graph means that there exists locally an affine coordinate system in which the manifold is a graph. Nevertheless, under the naive meaning of "graph" as it is used elsewhere in mathematics, it is clearly problematic to say this. Sławomir Biały (talk) 19:36, 4 June 2012 (UTC)
@Carl: you are correct that Whitney's theorem is about embeddings of manifolds. Indeed embeddings are locally graphs of functions by the implicit function theorem (that's the content of the implicit function theorem). Tkuvho (talk) 14:27, 5 June 2012 (UTC)
Sławomir Biały already mentioned what you seem to be ignoring, which is that you are not talking about things that are locally graphs of functions in the usual sense of the term. The "original definition" of a manifold is not going to be more enlightening if it requires readers to apply unusual or field-specific definitions to the terms it uses. As it is usually considered, the implicit function theorem doesn't apply to the side points of the unit circle, because a certain matrix isn't invertible at those points. In fact they use this as an example in implicit function theorem. — Carl (CBM · talk) 02:21, 6 June 2012 (UTC)
Carl, what you seem to be ignoring that our page implicit function theorem is only a special case of a more general implicit function theorem applicable to any smooth submanifold or regular parametrisation thereof. Thus, whenever the gradient of the defining expression is nonzero, the implicit function theorem applies. I explained this in terms of your example, namely the circle, at Manifold#Poincar.C3.A9.27s_original_definition. I usually defer to your judgments when it comes to issues of mathematical logic. Have some common sense to acknowledge that this is not a field you are an expert in, and that your original opposition was based on a misconception. No "unusual or field-specific definitions" here. Tkuvho (talk) 11:27, 7 June 2012 (UTC)
I am quite happy to believe that the way you're using the terminology is common in the area. I'm simply saying that it is not as clear to people outside the area as one might think. — Carl (CBM · talk) 11:44, 7 June 2012 (UTC)

I do not like the definition through graphs of functions, because it is less intuitive (at least for me) and it uses implicitly the implicit function theorem, which is far of being trivial (it is needed to show that a circle, defined as usual by its implicit equation, is a manifold). On the other hand, I do not like either the use of "scale" in the first sentence of the graph, because it appears in neither formal definition. Thus, I propose for the first sentence: "In mathematics (specifically in geometry and topology), a manifold is a mathematical object that, near each point of it, looks like Euclidean space". This has the advantage to be very close to the definition by charts (except that nothing is said on the transition maps, which are needed only for technical reasons). In fact the definition by charts and atlas is simply a formalization of this informal definition. D.Lazard (talk) 16:12, 4 June 2012 (UTC)

@D.Lazard: Thanks for your input. I respect your sentiment in "not liking" the implicit function theorem. However, this theorem is standard for an advanced calculus course. The lede shouldn't be an occasion for pleasing the personal tastes of this or that editor, but rather dictated by the goal of greatest possible accessibility. Certainly the chart definition is an indispensible technical tool, but again the goal of the lede is not necessarily to provide technical tools. Rather, it is to give the reader an idea of the subject matter of the page. Tkuvho (talk) 16:22, 4 June 2012 (UTC)
@Tkuvho: I agree with you that the lead should "dictated by the goal of greatest possible accessibility". But it should, in a non technical formulation, be as close as possible as the technical definition. I "like" the implicit function theorem, what I do not like is to use it implicitly where it is not really relevant. IMO, the "greatest possible accessibility" implies to use only mathematical notions which are unavoidable for given an idea of the subject. Here "near every point" is unavoidable because neighborhoods appear in every definition. On the other hand, "scale" is not needed. The definition through graphs involves a (at least partial) choice of coordinates, which is also not needed. D.Lazard (talk) 16:57, 4 June 2012 (UTC)
I didn't put the "scale" in. Feel free to delete it. As far as choice of coordinates is concerned, it is unnecessary. One can use a coordinate plane in the ambient R^n without the need to choose new coordinates. Tkuvho (talk) 14:30, 5 June 2012 (UTC)

I don't really think the lead is perfect at present. In fact, it seems to be worse than the version from three years ago. I'd like to discuss possibly bringing back this earlier revision of the lead. In any event, I don't think it is a good idea to emphasize Poincare's original definition of manifold. Not many sources do this, and at least the motivational examples section of the article would need to be rewritten from this point of view. Sławomir Biały (talk) 16:37, 4 June 2012 (UTC)

The current version of the lede expects the reader to know what a homeomorphism is, what a topological space is, and what a neighborhood is. Is this more accessible than the graph of a function? Tkuvho (talk) 11:30, 6 June 2012 (UTC)
I think you are arguing that "graph of a function" would be easier to understand for people outside the area. I do know what a manifold is, but I don't find the "graph" explanation clearer even for one-dimensional manifolds, and it's much harder for me to visualize a 3-dimensional manifold as a graph of a function than as something locally homeomorphic to R 3 {\displaystyle \mathbb {R} ^{3}} . (And either way we have to know what a neighborhood is, because it's "locally a graph of a function".) — Carl (CBM · talk) 11:44, 7 June 2012 (UTC)

May I point out that this whole discussion should be taking place at talk:manifold, not here.TR 12:28, 7 June 2012 (UTC)

Some/several MathJax-Formulae are not displayed (correctly)

Tracked in Phabricator
Task T38059

Hello

Did I do something wrong/incomplete? I use Firefox 12.0 (enabled Java & Javascript) on Linux as my browser but sometimes/often mathematical formulae are not or are wrongly displayed. E. g. in the page in the table-style of all these matrices there appears a literal "amp;" for the column separator, or in section "Classification", subsection "Elliptic transforms" the formula "0 \le \mbox{tr}^2\mathfrak{H} < 4.\," is not interpreted at all - it is displayed rawly! (This is the first formula in this article , several follow, but the formulae before seem to be displayed correctly). Thanks in advance for any useful help. Achim1999 (talk) 14:22, 5 June 2012 (UTC)

This is a known bug in the software. Any equation with <, > or & in will not work with the current MathJax. It has been patched in the source so it should not be too long until it that is rolled out. For now you can use User:Nageh/mathJax which is a working implementation of MathJax.--Salix (talk): 15:33, 5 June 2012 (UTC)
Thank you very much. Now I "only" have problems to create my "custom skin file", but I will try. :-)
Achim1999 (talk) 16:16, 5 June 2012 (UTC)
Well it seems to work, the fiel must be named "vector.js" not "skin.js".
At least the rendering is now better and my described errors has gone. The new mistake I observed is: the fraction lines are unusually thick and what is very bad, are too short. So, certain formulae like in the subsection "Determining the fixed points" of the Moebius transformation article become unreadable. A further bug in MathJax, I guess. :-/ Achim1999 (talk) 16:28, 5 June 2012 (UTC)
Thats odd, Moebius transformation#Determining the fixed points looks fine for me. It could be a browser related bug, which browser are you using? You might want to bring this up at User talk:Nageh/mathJax.--Salix (talk): 16:52, 5 June 2012 (UTC)
Yepp, I'm afraid you are right. As I wrote at the beginning of this section, I used Firefox 12.0 under Ubuntu (at work). Now I'm logged into another system (my private) running Gentoo & Firefox 3.6.17. The same section now looks okay. Here fraction(line)s are displayed fine. :-/ Achim1999 (talk) 17:53, 5 June 2012 (UTC)
If its a browser bug it might be worth discussing it with the MathJax people . That would help them sort it out for anyone else who gets the same problem.--Salix (talk): 21:59, 5 June 2012 (UTC)

List of scientific constants named after people

The List of scientific constants named after people may not be notable, according to a recent tag put at the top of the article. Apparently what is needed is a literature citation showing that the topic of scientific concepts named after people has received attention from the authors of refereed publications. Michael Hardy (talk) 02:49, 9 June 2012 (UTC)