Wikipedia talk:WikiProject Mathematics

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No new articles[edit]

At Wikipedia:WikiProject Mathematics/Current activity, we find no new articles since May 25. Jitse's bot, run by Jitse Niesen, which edits that page, has done so more recently, and mathbot, which, among other things, lists new articles, whose lists are used by Jitse's bot, has been active more recently. Are there no new articles? Michael Hardy (talk) 18:44, 31 May 2015 (UTC)

Are you looking at the same current activity that I am? Because I see 14 new articles on May 26 (starting with Alicia Dickenstein), 6 new articles on May 28, and a large number of new articles (possibly caused by moving some category involving tilework into the ones the bot lists) on May 29. —David Eppstein (talk) 19:17, 31 May 2015 (UTC)
Yes, there a many entries dated after May 25. A diff shows them. I see "This page was last modified on 31 May 2015" at the bottom of Wikipedia:WikiProject Mathematics/Current activity. If you se an older date then try to bypass your cache. PrimeHunter (talk) 19:26, 31 May 2015 (UTC)
The second article is not suitable I would say, as it duplicates content that is already in a much more readable form elsewhere in the encyclopedia. The first is certainly an encyclopedic topic, but the name "Loewner order" is not very standard. Most mathematicians would not attribute this to Loewner, just calling it the partial ordering of hermitian matrices. Sławomir Biały (talk) 19:51, 5 June 2015 (UTC)

I'm experiencing the same problem described by user Michael Hardy... Currently, the last date I can see on the "New articles:" section on the table is "5 Jun". But there were indeed mathematical articles created after 5 Jun (Yair Minsky (6 Jun) and Richard Canary (7 Jun) are proof of this). — Preceding unsigned comment added by 189.6.195.23 (talk) 13:24, 8 June 2015 (UTC)

The bot has been having problems on and off for a couple of months. See the last two sections of User talk:Jitse's bot. I've tried pinging and e-mailing Jitse Niesen but have had no response. I don't know if there's anything else that can be done, such as someone else take over maintaining them.--JohnBlackburnewordsdeeds 13:32, 8 June 2015 (UTC)

There are two bots involved, mathbot and Jitse's bot. But in this case, mathbot appears to be picking up the new articles; it's the updates to the current activity page by Jitse's bot that have gone missing. —David Eppstein (talk) 17:45, 8 June 2015 (UTC)
Jitse Niesen has not made any contributions since 10:54, 20 October 2014, so I am afraid that we must assume that he is unable or unwilling to participate further in the English Wikipedia. JRSpriggs (talk) 04:03, 9 June 2015 (UTC)
If Jitse Niesen has left us, does someone inherit his bot? Will the Mathematics Wikiproject collapse permanently if his bot dies? Michael Hardy (talk) 23:48, 10 June 2015 (UTC)
What does it take to run a bot? Do we or can we use a sever at the wikimedia foundation? It would be nice, long term, if we can rely on an institution instead of an individual editor. (Right now, we are in the post-apocalyptic world, I suppose.) -- Taku (talk) 23:14, 19 June 2015 (UTC)

Deletion sorting for Math articles?[edit]

Is there deletion sorting for mathematics-related articles or do they just end up under Wikipedia:WikiProject Deletion sorting/Science?

Anyway there are three articles at AfD about algorithms for voting systems, not sorted into anything technical:

Thanks for looking at these. StarryGrandma (talk) 23:05, 19 June 2015 (UTC)

Relations[edit]

Are Dependence relation and Dependency relation the same thing? WhatamIdoing (talk) 03:13, 22 June 2015 (UTC)

No. Completely different. And probably, both are not widely used. Boris Tsirelson (talk) 05:51, 22 June 2015 (UTC)

Rfd for Category of graded vector spaces[edit]

Hi there.

Over at Wikipedia:Redirects_for_discussion/Log/2015_June_20#Category_of_graded_vector_spaces this has been listed. I think it is redundant and perhaps harmful since it is not a Wikipedia catgegory but a redirect to an article: surely the grading/graduation is itself the way to categorise them so to categorise the grading would be some higher order function, which I'm sure is not intended here. (To categorise the categorisation, i.e. in formal logic of some kind, Bertie Russell turning in his grave).

I only have maths up to basic graduate degree level, and mostly on the engineering side of it rather than theory, so I'd appreciate your opinion on whether this is useful. Si Trew (talk) 07:22, 22 June 2015 (UTC) see my userpage on 3d slope formula here — Preceding undated comment added 00:34, 23 June 2015 (UTC)

What formula is this?[edit]

I am in the process of renaming two-letter filenames on Commons, to provide less ambiguous titles. Today I came across this one:

DFhosq.png

What is this equation? Or, more directly, what would be an appropriately unambiguous, but concise, name for this image file? Cheers! bd2412 T 19:55, 24 June 2015 (UTC)

A good question to the person that uploaded it. Boris Tsirelson (talk) 21:10, 24 June 2015 (UTC)
The person who uploaded it seems to be a ghost. They appeared on Commons a month ago, uploaded a dozen and a half images like this, and disappeared. Are these anything at all? bd2412 T 21:24, 24 June 2015 (UTC)
Perhaps it's time to exorcise the ghost? — Arthur Rubin (talk) 21:50, 24 June 2015 (UTC)
If these images are useful, we should keep and properly describe them. If they are not, they should be deleted. I don't have the background to determine whether these are at all meaningful. bd2412 T 22:19, 24 June 2015 (UTC)
These appear to have something to do with magnetism and perhaps magnetic flux. Equations are better written in the text and I don't mean to be harsh, but the illustrations are small enough that they probably aren't too useful. --Mark viking (talk) 22:55, 24 June 2015 (UTC)
It does not seem to be used anywhere. We should delete it. JRSpriggs (talk) 09:17, 25 June 2015 (UTC)

The Assayer[edit]

The book The Assayer by Galileo is one of the works that ushered in the scientific method as well as the method of indivisibles closely related to Galileo's atomism. Recently I added sourced material on this aspect of the book. Input would be appreciated. Tkuvho (talk) 07:36, 25 June 2015 (UTC)

Context: Tkuvho is engaged in a content-based edit war over the relevant material; he and User:William M. Connolley have both been blocked for 24 hours as a result. There are no obvious signs of consensus-forming. Probably, the input of some neutral editors would improve the situation. --JBL (talk) 13:12, 25 June 2015 (UTC)

Dualizing sheaf listed at Redirects for discussion[edit]

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An editor has asked for a discussion to address the redirect Dualizing sheaf. Please participate in the redirect discussion if you have not already done so. Ivanvector (talk) 14:48, 25 June 2015 (UTC)

Copyright Violation Detection - EranBot Project[edit]

A new copy-paste detection bot is now in general use on English Wikipedia. Come check it out at the EranBot reporting page. This bot utilizes the Turnitin software (ithenticate), unlike User:CorenSearchBot that relies on a web search API from Yahoo. It checks individual edits rather than just new articles. Please take 15 seconds to visit the EranBot reporting page and check a few of the flagged concerns. Comments welcome regarding potential improvements. These likely copyright violations can be searched by WikiProject categories. Use "control-f" to jump to your area of interest.--Lucas559 (talk) 22:25, 25 June 2015 (UTC)

Ceci N'est Pas Un Cercle[edit]

There is a silly argument going on between myself and two other editors at the new article real projective line about whether \mathbb{R}P^{1} "really" is a circle. At first, it was argued that it must be homeomorphic but not diffeomorphic to a circle, because the universal cover of S^{1} is S^{1}, and that of \mathbb{R}P^{1} is S^{1}, and the property of being one's own universal cover is a diffeomorphism invariant - fortunately this argument was dropped. Then it was argued that it may be topologically equivalent to a circle, but have a different geometric structure, but later it was accepted that the natural metric makes \mathbb{R}P^{1} isometric to a circle. Presently it is argued (I think) that there is some intermediate structure, stronger than the topological structure but weaker than the metric space structure, wherein cross-ratios of four points can be defined without reference to any distance function. I believe this is impossible; defining the cross-ratio (and proving that it is well-defined) requires using the metric. The reason this is significant is that I believe it is important to state clearly in the lede that the object is a circle, without reference to terminology that may confuse laymen, such as "homeomorphic," "isometric," or "birationally equivalent." This is the text I want:

In mathematics, the real projective line is a circle. It is a trivial example of a more general class of topological spaces known as projective spaces. The real projective line is formed from lines through the origin in two-dimensional space. One considers these lines to be the "points" of the real projective line, and the angle between them to be the "distance" between these "points." Formally, the lines through the origin form equivalence classes, allowing for the real projective line to be defined as a quotient space.

Having this context in mind may give the reader a better chance of understanding the technical details that follow. I think the importance of stating clearly that we are talking about nothing other than a complicated way to define a circle is shown by the talk page itself. Even a relatively mathematically-sophisticated reader might see "a space homeomorphic to a circle" and think that it has some other geometric structure, that it is a double cover of a circle, or whatever. This is what led a normally quite competent editor to the logical and factual fallacies in the "homeomorphic but not diffeomorphic" argument above; he was trying too hard to rationalize a wrong idea, when the truth was just too simple. On a related note, the article is also suffering from the idea that the group PSL_{2}(\mathbb{R}) is the "automorphism group" of the real projective line. I think that someone just made this up. It is now the central principle in the platform of the "not a circle" party. --Sammy1339 (talk) 13:49, 26 June 2015 (UTC)

For understanding the context of this post, I recommend to the reader to consult Talk:Real projective line § Is the projective line a circle?. I have nothing to add to my posts in this discussion, especially the last ones. D.Lazard (talk) 14:09, 26 June 2015 (UTC)
"Obviously" a projective line is not a circle (real or otherwise). There can be an isomorphism between the two depending on a category in the context; say, one is working in the category of topological spaces, but such an isomorphism is not the equality ("is"); a morphism ceases to make sense once you step out of the category. -- Taku (talk) 17:04, 26 June 2015 (UTC)
For example, saying "a projective line a twisted cubic curve" is at worst wrong or at best very misleading; you can't replace an isomorphism by an identity. -- Taku (talk) 17:22, 26 June 2015 (UTC)
But (correct me if I'm wrong) there's no category in which they are not isomorphic. --Sammy1339 (talk) 19:09, 26 June 2015 (UTC)
I don't know if it would ever occur to me to read the word "circle" as referring to an intrinsic abstract manifold, even one with a metric. To me the word implies an embedded circle, the set of all points in some larger (usually Euclidean) metric 2-manifold equidistant from a given point. Is there some natural way of identifying such an embedding space in the case of the real projective line? --Trovatore (talk) 19:16, 26 June 2015 (UTC)
Well, I think of "circle" as meaning an intrinsic manifold, but if you want to look at it that way, then yes, there is: take \mathbb{C}^{2} and form the complex projective line (Riemann sphere), and look at what happened to the two real axes. They became a great circle, formed by the real line and the point at infinity. --Sammy1339 (talk) 19:33, 26 June 2015 (UTC)
But this doesn't seem to be exactly inherent in the notion of the real projective line. I think this is the basic problem. The real projective line is intrinsic, whereas the circle is embedded. Therefore they are not the same. --Trovatore (talk) 19:40, 26 June 2015 (UTC)
So would it be appropriate to say it's an "abstract circle?" --Sammy1339 (talk) 19:42, 26 June 2015 (UTC)
Possibly. --Trovatore (talk) 19:43, 26 June 2015 (UTC)
Just so we understand each other though, is the Riemann sphere not a sphere? --Sammy1339 (talk) 19:47, 26 June 2015 (UTC)
No, for the same reason; in fact, our very own Riemann sphere doesn't say so in the first paragraph (it defines it as a one-point compactification of the complex plane, which is correct; in fact, even more correctly it uses the term "model"). Interestingly, complex projective line redirects to "Riemann sphere", which is probably ok. By analogy, should real projective line redirect to a "circle"? Am I the only one who thinks that's crazy? Having separate articles already suggests the two concepts (RP1, S1) are distinct. -- Taku (talk) 22:47, 26 June 2015 (UTC)
Of course the article Riemann sphere calls the Riemann sphere a sphere -- any time you have a construction "the [adjective] [noun]," you can expect the reader to understand that you are speaking of a kind of [noun] unless you say otherwise, and this does not require special mention. (In mathematics sometimes it is the case that an [adjective] [noun] is not actually a [noun], and in this situation one can expect to find somewhere an explanation of this situation, e.g., "The terminology is somewhat confusing: every topological manifold is a topological manifold with boundary, but not vice versa.")
I do not have strong feelings about the underlying debate, but I certainly would not have thought to criticise or correct someone who referred to RP^1 as a circle. --JBL (talk) 23:07, 26 June 2015 (UTC)
I should have phrased it differently. Is S^{2} with the spherical metric a sphere? --Sammy1339 (talk) 01:47, 27 June 2015 (UTC)

@Sammy : If one defines distance between two points on a circle to be the length of the chord between them, then that is topologically but not metrically equivalent to the circle intrinsic metric in which the distance is the arc length. Might that be the circle that is not isomorphic to the projective line, or is the chord-length metric a natural thing to use for that? As far as cross-ratios go, linear fractional transformations on the complex numbers take circles to other circles while changing distances but leaving cross-ratios intact. Therefore the function assigning cross-ratios to quadruples of points on the circle does not determine the function assigning distances between them. In that sense one can say that the cross-ratio function amounts to less structure than the metric but more than the topology. Michael Hardy (talk) 23:41, 26 June 2015 (UTC)

(Late response to original post.) To play devil's advocate: If RP^1 is a circle, then what is the radius of the circle? The average reader of Wikipedia thinks that circles have radii. They do not implicitly understand that you have omitted the words "smooth manifold diffeomorphic to". The one-point compactification construction suggests that the radius is infinite. The fact that the unit circle in R^2 double-covers RP^1 suggests that its radius is 1 / 2.
The average reader is not familiar with notions of space that lack notions of distance. And do we expect such readers to read this article? Or should this article expect that the reader is coming from some background in topology, algebraic geometry, etc.? Mgnbar (talk) 00:20, 27 June 2015 (UTC)
To put it another way: If RP^1 is just a circle, then why does it have any special name at all? (I have been asked such questions about Riemann spheres being "just" spheres.) Mgnbar (talk) 00:27, 27 June 2015 (UTC)
@Michael Hardy:@Mgnbar: There is a natural metric on the real projective line and it is the same as the metric of a circle with radius one-half. I explained this on the talk page. About why \mathbb{R}P^{1} has a name, it assuredly wouldn't, were it not for \mathbb{R}P^{n} - in fact I am having trouble finding sources that even talk about it in any detail, presumably because it is just a circle. --Sammy1339 (talk) 01:57, 27 June 2015 (UTC)
It is not "just" a circle. Topologically it is a circle, but it may differ in some other respects from what is normally called a circle. Michael Hardy (talk) 04:01, 27 June 2015 (UTC)
Under your metric, the real line does not isometrically embed into RP^1. So readers may be confused by statements about how RP^1 is just the real line with one point at infinity added. That's the point. There are several ways to think about projective spaces. Mgnbar (talk) 03:30, 27 June 2015 (UTC)
The euclidean real line cannot be isometrically imbedded in \mathbb{R}P^{1}. --Sammy1339 (talk) 03:56, 27 June 2015 (UTC)
I think that our disagreement comes from different viewpoints, which exist because RP^1 appears in various areas of mathematics. Your viewpoint seems to be differential geometry. I mentioned the real line because its topological embedding into RP^1 is an important example in topology (the one-point compactification). Your talk of metrics and circles seems beside the point to me, because in elementary algebraic geometry, which uses projective spaces heavily, there is often no mention of circles and metrics.
So maybe we should stick to precise (and verifiable) statements about how RP^1 is topologically a circle, can be endowed with a metric under which it is isometric to a Euclidean plane circle with radius 1/2, etc.? Mgnbar (talk) 12:35, 27 June 2015 (UTC)

I would also like to suggest that at some point someone makes an attempt to find sources supporting their position, rather than relying on appeals to pure reason only. (And that is the last from me, probably.) --JBL (talk) 01:15, 27 June 2015 (UTC)

@Joel B. Lewis: Yes, I share that concern. But we also have to use common sense and write the article in a way laypeople can understand. We're supposed to paraphrase sources, not copy from them. I am bothered by some of the uncited claims in the article though, particularly the stuff about the "automorphism group." --Sammy1339 (talk) 01:57, 27 June 2015 (UTC)
Yes, sources determine what we can and cannot write here. But keep in mind that different sources may use terms such as "circle" differently. In fact, a topology textbook and a geometry textbook may disagree on what that term means. And maybe neither of those books is written for this article's audience. Mgnbar (talk) 03:30, 27 June 2015 (UTC)
Contrary to what was indicated by Sammy above, the universal cover of \mathbb{R}P^{1} and of S^{1} (which are the same thing) is \mathbb{R}. Remember that a universal cover must be simply connected. JRSpriggs (talk) 11:00, 28 June 2015 (UTC)

Is Jitse's bot dead forever?[edit]

Jitse's bot hasn't updated the new articles list in almost two weeks. Four days ago I sent Jitse Niesen an email and I haven't heard anything. Will Wikipedia be forever dependent on one person in that way? How should we proceed? Michael Hardy (talk) 23:27, 26 June 2015 (UTC)

Actually I responded at the very top section #No_new_articles several days ago and got no response. I will try again here. What does it take to run the bot? Does it run on the wikimedia foundation's server? I found this page [1] but I'm not sure if is related. As for a long-term plan, I agree it would make sense if someone else can take over running the bot (it should be so much easier to taking over the task than starting over), as apparently Jitse is no longer active. -- Taku (talk) 00:17, 29 June 2015 (UTC)

Another terminology problem: what is a metric?[edit]

The word "metric" is used differently in (1) the context of a metric space, and (2) such context as "the metric of space-time".

A manifold with a metric tensor is called a pseudo-Riemannian manifold. (Quoted from "Metric (mathematics)#Important cases of generalized metrics".)
A special case of great importance to general relativity is a Lorentzian manifold, in which one dimension has a sign opposite to that of the rest. (Quoted from the lead of "Pseudo-Riemannian manifold".)

Thus, sometimes a space endowed with a metric is not a metric space. Regretfully, this confusing situation is not explained enough in our articles. See the ongoing dispute: Talk:Metric space#Questions to User:Verdana Bold about a recent attempt to emphasize the "more physical" usage of the word "metric". Indeed, that usage is notable and should be mentioned. However, this should be made carefully enough. Boris Tsirelson (talk) 17:35, 27 June 2015 (UTC)