Wikipedia talk:WikiProject Mathematics/Archive/2009/Sep

To hyphenate or not to hyphenate...that is the question
Trend change: Henry Delforn (talk) 19:34, 23 August 2009 (UTC)
 * Ghits (all times): "noncommutative" exclude: "non-commutative" = about 2,200,000
 * Ghits (all times): "non-commutative" exclude: "noncommutative" = about 5,440,000
 * Ghits (past 1 yr): "noncommutative" exclude: "non-commutative" = about 330,000
 * Ghits (past 1 yr): "non-commutative" exclude: "noncommutative" = about 181,000


 * Short answer: it is a matter of taste, so follow the style of the first main contributor in any given article.


 * Slightly longer answer: the trend to remove hyphens over time is common in general and in mathematics in particular. When a new combination is introduced, a hyphen is often used so that readers recognise the familiar constituents more easily. However, a hyphen is only really needed if the reader would be led up a mini-garden path without it. I've introduced at least one new term with a hyphen myself, and regretted it (fixing it in subsequent papers) because the hyphen was unnecessary. So if you want to persuade other editors to use noncommutative, instead of non-commutative, then you have a good chance of success in the long run. If you want to argue the other way, you are batting on a sticky wicket. Geometry guy 20:17, 23 August 2009 (UTC)


 * Agree with G'guy. Love his cricket metaphors --Robin (talk) 00:54, 24 August 2009 (UTC).
 * yeah, i agree with G'guy G-guy Gguy too. Henry Delforn (talk) 15:02, 25 August 2009 (UTC)
 * Yeah, it's a matter of taste and consistancy is the key. For what it's worth: I much prefer the hyphenated non-commutative. I find it easier to read.  Dr Dec  ( Talk )    15:56, 31 August 2009 (UTC)

215
Why is there a redirect here?--Sandrobt (talk) 01:04, 31 August 2009 (UTC)


 * 215 is an article about the year and not about the number. 215 (number) redirects to 210 (number) because the latter includes mention of the numbers from 211 to 219. There are a large number of such redirects for numbers which don't have their own article. Often the target covers an interval of 100. For example, 668 (number) redirects to 600 (number) which mentions 601 to 699. PrimeHunter (talk) 01:41, 31 August 2009 (UTC)


 * Ah, OK, sorry I wasn't paying so much attention to the article itself, I was too surprised by the redirect. Thanks,--Sandrobt (talk) 03:41, 31 August 2009 (UTC)


 * 215 is the smallest uninteresting number in Wikipedia and so doesn't deserve its own page. Dmcq (talk) 08:12, 31 August 2009 (UTC)

Category:Euclid
Category:Euclid clearly needs attention. At present, it seems to be a mish-mash of things having the term "Euclidean" in them, irrespective of whether these were actually due to Euclid or in some historically significant way connected up with Euclid. (I mean, apart from the fact that, for instance, a Euclidean ball is a ball in a Euclidean space.) Sławomir Biały (talk) 18:22, 31 August 2009 (UTC)

Truth tables
I am teaching an "introduction to proofs" course for undergraduate prospective math majors this semester, and just recently I have presented truth tables. It is always nice to provide a source for more background information for those who are interested (the course text doesn't say much), so I looked at truth tables.

The first sentence in the overview (the first section following the lead) is:


 * The pattern of reasoning that the truth table tabulates was Frege's, Peirce's, and Schröder's by 1880.

It doesn't even sound as though it was written by a native English speaker. The second sentence:


 * The tables have been prominent in literature since 1920 (Lukasiewicz, Post, Wittgenstein)" (Quine, 39).

After three readings, I think this is a quotation from page 39 of Quine's book, with a missing introductory quotation mark. Note that the prominence in the literature is being demonstated by a citation rather than by directly citing the literature in which it appeared. How circuitous.

And so forth. No way would I want my students to read this article. Can anyone help? Plclark (talk) 19:07, 31 August 2009 (UTC)

Equiareal map
What shall we do with the article titled equiareal map? The facts are:
 * Most links to the topic are not links to that article, but rather link to a section of a different article titled 2 &times; 2 real matrices.
 * Links to equiareal map come from
 * talk pages like this one;
 * lists;
 * redirects;
 * a disambiguation page;
 * and, finally, the 2 &times; 2 real matrices article.
 * The topic is important in cartography, where it's mentioned in many Wikipedia articles under the term equal-area.

So the incoming links are treating the section of 2 &times; 2 real matrices as the main thing, even though that article currently refers to equiareal map as the "main article". Michael Hardy (talk) 21:15, 31 August 2009 (UTC)


 * More food for thought: The article volume-preserving is currently a redirect to Measure-preserving dynamical system. While this redirect is not entirely offbase, there is definitely room for an article volume preserving map (or measure preserving map) covering the general notion, equi-areal maps then being a special case.


 * I question whether 2 &times; 2 real matrices is the ideal place to give details on equi-areal transformations. Surely the correct place for such a discussion is in the more specific article SL(2,R).  Moreover, the exposition should be simplified considerably.  One doesn't need to invoke differential forms (which not every reader will be comfortable with).  Instead, as I'm sure you are aware, the only essential fact required is that the area of a region under a linear mapping scales by the determinant of the map.  Sławomir Biały (talk) 23:05, 31 August 2009 (UTC)

Mathematicians must not be identified

 * In complex analysis, a branch of mathematics, a Bergman space is a function space of holomorphic functions in a domain D of the complex plane that are sufficiently well-behaved at the boundary that they are absolutely integrable.

In "nowiki" mode, the above looks like this:
 * In complex analysis, a branch of mathematics, a Bergman space is a function space of holomorphic functions in a domain D of the complex plane that are sufficiently well-behaved at the boundary that they are absolutely integrable.
 * In complex analysis, a branch of mathematics, a Bergman space is a function space of holomorphic functions in a domain D of the complex plane that are sufficiently well-behaved at the boundary that they are absolutely integrable.

Same thing with Bergman kernel. I added the commented-out part. I see this a lot. When I can, I actually fill in this information. Am I the only one who does this? Michael Hardy (talk) 03:43, 1 September 2009 (UTC)


 * I also add the information when it occurs to me to do so. However, both of the "Bergman" articles were my own.  I'm terribly sorry.  I suppose I was primarily interested in getting the mathematical details, and the subsidiary issue of linking to the mathematician didn't occur to me.  Again, I apologize.  Sławomir Biały (talk) 03:51, 1 September 2009 (UTC)

"Recent changes" links removed from MathTopicTOC
After making the nomination for Articles for deletion/List of mathematics articles (J-L), and being informed that that article was necessary to the proper functioning of the "recent changes" links in MathTopicTOC, declared that such links were inappropriate in article space and removed them from the template. I have no strong opinion on whether this was the right thing to do but others may. Discussion taken here rather than in the AfD (where it's inappropriately off-topic) or the template talk page (where nobody will see it). —David Eppstein (talk) 07:06, 2 September 2009 (UTC)
 * I've copied the contentious row "Recent changes" to a Wikiproject page, and included it atop the WikiProject_Mathematics/Current_activity, which appears the proper place to centralize that kind of information. This should be a reasonable compromise. The letter-range lists themselves could be easily copied to the Wikiproject space, but that looks unnecessary, as the discussion on those lists seem headed for a "keep". These range-lists are merely transcluding the letter-indexed lists like Index of mathematics articles (J) updated by User:Mathbot -- this latter type of Math article lists are thankfully not proposed for deletion. Pcap ping  14:14, 2 September 2009 (UTC)

Hundreds of "Removed articles" listed under Current activity?
A recent daily update of WP:WPM/CA (the Current activity subpage) lists hundreds of mathematics articles in the "Removed articles" row. Why did this occur? Is this a result of some kind of change in categorization, the recent issues with Template:MathTopicTOC or what? —Preceding unsigned comment added by Classicalecon (talk • contribs) 13:15, 3 September 2009 (UTC)


 * This could be related, or it could be unrelated, but it seems that pages such as List_of_mathematics_articles_(C) were moved to Index_of_mathematics_articles_(C), even though Mathbot will be updating the former location, not the latter. I will go through and do the history merges sometime this week, back to the locations that are being actively updated. &mdash; Carl (CBM · talk) 13:38, 3 September 2009 (UTC)
 * It looks like User:Cybercobra needs to be slapped with a WP:TROUT for those moves. Perhaps, somebody could add a template to the talk pages of those lists/indexes saying "do not move, a bot expects to find this page under this name?" Pcap ping  13:44, 3 September 2009 (UTC)
 * Or you could just make them move:sysop. Pcap ping  13:46, 3 September 2009 (UTC)


 * FWIW, Jordan algebra came back onto the list today, but most of the other articles did not. I would assume there was some change in a category that affect Mathbot's decision on whether an article was a math article or not, but I don't see the pattern. JackSchmidt (talk) 14:50, 3 September 2009 (UTC)

My current hypothesis is that the articles which were removed had been manually added over time, and thus the bot did not automatically include them when it recreated the lists from scratch after they were moved. I have merged all the histories and restored the largest version of each page. I hope this will fix things; the logs may still be strange through the next update. &mdash; Carl (CBM · talk) 15:31, 3 September 2009 (UTC)
 * Not only has the current activity update gone nuts and listed large numbers of existing articles, it failed to list at least one new article, Albertson conjecture. —David Eppstein (talk) 02:56, 4 September 2009 (UTC)
 * It may take a couple cycles for everything to work through. The bot did find Albertson conjecture but this was lost as part of my cleanup of the page moves. In short, I restored the versions from Sep. 1 to restore all the manually added article. I expect the bot will find the new articles from Sep 2. again tomorrow. If not, we may need to go through and add them by hand. Of course, I may misunderstand how Mathbot works, since I am not familiar with its code. &mdash; Carl (CBM · talk) 10:12, 4 September 2009 (UTC)
 * The bot did pick up Albetson conjecture today . &mdash; Carl (CBM · talk) 11:54, 4 September 2009 (UTC)

Visual Detection of Imaginary Roots in a Parabola
I came across this article - it looks rather like an academic paper and the editor notes that: "Plotting the imaginary roots using empty circle in the Cartesian coordinate system is something new I am proposing. Over time, this method may be accepted as an alternate way of plotting imaginary roots.". I know pretty much nothing about the subject so I was wondering if someone could take a look and see if it is original research or a valid article or something else? (As an aside, if it is an article, is there a more specific category than Category:Geometry that I could use?) Thanks -- &#9735;  Kateshortforbob talk &#9732;  14:43, 29 August 2009 (UTC)
 * As it stands it reads like a textbook, and the last paragraph should probably be removed as OR. Maybe the bit about finding imaginary roots visually could be merged into quadratic equation or quadratic function as a new section? I don't think any of the verification is needed, and the introduction is covered in the quadratic articles. I have no idea how to do a merge though, or even if it is appropriate in this case as there are no references.Acb314 (talk) 15:03, 29 August 2009 (UTC)

imaginary intersections are a very interesting topic, and not just lines and parabolas have them, lines and circles have them as well. To be frank, I am shocked that there is not article on the topic of imaginary intersections, maybe I am missing something? This article on imaginary intersections of lines and parabolas is a good start. There are some good citations on the subject starting at least from Hamilton's elements in 1865.TeamQuaternion (talk) 04:06, 30 August 2009 (UTC)


 * Circular points at infinity exists. Charles Matthews (talk) 21:02, 5 September 2009 (UTC)


 * That is an excellent suggestion for treating this topic in a more encyclopedic manner. Sławomir Biały (talk) 12:22, 30 August 2009 (UTC)


 * Is this the stuff at Conic sections? I always thought the business about the two imaginary points of intersection of circles was good. Dmcq (talk) 13:10, 30 August 2009 (UTC)


 * Yes. A good reference on this is Dan Pedoe's "Geometry: A comprehensive course", where he draws upon both the projective algebraic view and classical methods.  Sławomir Biały (talk) 14:14, 30 August 2009 (UTC)


 * Article reads like OR, and lack of sources bears this out. A proposed deletion was contested, so I have now nominated the article at AfD. Gandalf61 (talk) 09:54, 3 September 2009 (UTC)


 * An I completely forgot I posted this slightly belated "thanks" to everyone for looking at this one! -- &#9735;  Kateshortforbob talk &#9732;  13:33, 5 September 2009 (UTC)

A proposal to change WP:SYNT
Somebody made a proposal to change WP:SYNT. While the practical relevance of the change proposed is rather insignficant on how Math articles are written in practice here, in theory it does impact it. Proposal and discussion. Pcap ping  16:56, 5 September 2009 (UTC)


 * Probably off-topic, but I cannot resist... That discussion reminds me of the following. Being in Soviet Union (SU), I was once dealing with a huge table of statistical data about SU. I was informed that these data are not secret (and therefore may be mentioned in my article), however, any result of their processing is secret (just by definition) and therefore not publishable. It was exciting to see several non-secret numbers whose sum is secret! Boris Tsirelson (talk) 18:33, 5 September 2009 (UTC)
 * The catch is that the logic and concepts used in most non-Math/Science articles are "fuzzy". Even with math sources, you can draw the wrong conclusion in a syllogism like "A=>B, B=>C therefore A=>C" if you get the first two from different sources that use the same terminology or notations for different concepts (you only get a syntactically correct syllogism). For instance, see what happened on Talk:Entropy Pcap ping  18:49, 5 September 2009 (UTC)
 * I see... Nothing very impressive there. Yes, the life of a wiki-physicist is probably harder than ours. Anyway, it seems to me that we have a lot of right math in Wikipedia (mixed with some garbage) because we do allow SYNT. Prohibiting it we throw away the garbage AND most of the right math. Is it better for Wikipedia? (Recall "IgnoreAllRules...) (On the other hand, I understand that political articles really need different attitude that ours.) Boris Tsirelson (talk) 20:11, 5 September 2009 (UTC)
 * This is a tricky topic. I used to think that very modest forms of OR were more acceptable in math articles than elsewhere, given that anyone can check the proof. I don't really think that anymore, based on experience, though I've certainly done it myself.
 * It is true that on occasion it's convenient to be able to give a specific example of something, very much in the style that the authors of the sources would have done if called on to do it, and maybe what I advocate for that is not so much explicitly legalizing it, as turning a blind eye to it when it seems prudent. If someone calls you on it, though, you just have to say they caught you speeding.
 * My experience is that OR-by-synthesis is a real problem in math articles, particularly in cases where philosophical interpretation is at issue. --Trovatore (talk) 20:25, 5 September 2009 (UTC)

Let's not miss one point. OR is wrong if it is used to advance a thesis. It is mostly not wrong in mathematics itself, because we deal in truths which are not tendentious. Almost anything else (e.g. history, including history of mathematics) is an area in which any "thesis" is likely to be tendentious. Those discussions on SYNT tend to have the standing assumption that theses are advanced only because they do tend in some direction. Mathematicians have the benefit of true syllogisms. Tweaking the rules on OR doesn't sound good to me, anyway, but it should not be taken as limiting conclusions from axioms. (This may seem to be arguing against the well-established idea that people should prove their theorems elsewhere, not here. That wasn't the type of point I was trying to make, though. I was just trying to explain something usually left tacit.) Charles Matthews (talk) 20:38, 5 September 2009 (UTC)


 * Wikipedia has many drawbacks. However, after trying also Citizendium I suspect (with some grief) that maybe Wikipedia is the best of all possible wiki-worlds. Citizendium is much better, but... not possible. Is it at all possible to make Wikipedia really better? Boris Tsirelson (talk) 20:48, 5 September 2009 (UTC)
 * Nobody is proposing to get rid of SYNT (on the policy page discussion page anyway). The minor tweaking proposed appears good to me because the original/current formulation is confusing upon close reading. The opening sentence&mdash;the defintion practically&mdash;does not actually imply the stronger requirement asked of the first "A, B, C" example in order to be declared synthesis free. This is probably not the worst contradictory or confusing statement in a policy/guideline (let alone between policies/guidelines), but it seems easy enough to fix were it not for social reasons. Pcap ping  21:33, 5 September 2009 (UTC)
 * See Wikipedia_talk:No_original_research for the actual proposal. The discussion above it is rather meandering. Pcap ping  21:36, 5 September 2009 (UTC)
 * Is the difference between the two formulations of any practical importance for math in Wikipedia? Boris Tsirelson (talk) 21:51, 5 September 2009 (UTC)
 * Like I wrote in the first message of this thread, the practical relvance is nearly nil given the practices here, e.g. preferring general references rather than (overusing) inline citations. I did not expect my post to entail this much discussion. Pcap ping  22:44, 5 September 2009 (UTC)

Huh??
Does anyone know what happened with this edit? From the LONG list of allegedly new articles there's no clear way to tell which ones may be actually new articles without clicking on every one of them individually and examining their histories. Nobody can reasonable spare the hours that that would take. Michael Hardy (talk) 17:27, 5 September 2009 (UTC)
 * Isn't this to be expected after the bot removed a whole slew of articles earlier? See"" Pcap ping  18:08, 5 September 2009 (UTC)
 * Not unless one actually knows about that. That's why I was asking. Michael Hardy (talk) 01:33, 6 September 2009 (UTC)

HTML symbols versus TeX?
Small query... A number of edits were recently made to the Carleson's theorem article which I started, mainly changing the typesetting of simple expressions in TeX to HTML equivalents. This improved the appearance of the article significantly, removing lots of inconsistent spacing and sizing. However, I'm a little confused/concerned about compatibility issues. Mathematical_symbols states that the symbols given there should "work in most browsers", but WP:MOSMATH suggests (under "Special symbols") a preference for being conservative with the use of HTML symbols because of compatibility issues (stating one of the symbols from the "Mathematical symbols" article as an example). Does anybody have any concrete information on compatibility and established norms for symbols? Apologies if this is a newbie question... :-) Tcnuk (talk) 08:40, 2 September 2009 (UTC)


 * Essentially everyone is able to correctly see symbols that have named HTML entities, such as &amp;isin; (&isin;). The most frequent complaints are about symbols that have to be entered directly by Unicode number, or copied and pasted from a chart of symbols. For example, at the moment my browser only shows about half the symbols at Unicode Mathematical Operators.


 * But what WP:MOSMATH was trying to say there is that one should avoid the mindless use of symbols as a substitute for English words, because English will be easier for many people to read. So, instead of saying "We see that $$x \in 6\mathbb{Z}$$ and thus $$3|x$$", you could say "We see that x is in $$6\mathbb{Z}$$ and thus 3 divides x". This is a separate issue from the technical ability of a browser to render the symbols. &mdash; Carl (CBM · talk) 10:55, 2 September 2009 (UTC)


 * Thanks for the reply. Your link to the Unicode Mathematical Operators (shouldn't that be "Unicode mathematical operators"?) makes the point quite well, as I too can only see about half those symbols on my work machine, and it does make sense that most browsers should be able to cope with symbols with named HTML entities (though I do wonder what point in HTML's history these were introduced and hence how "new" a browser needs to be to understand them).


 * I had wondered whether WP:MOSMATH was trying to say that the symbols were best avoided for reader comprehension, rather than compatibility, but with the wording as it was, it definitely seemed more like the interpretation I gave (to me). I'd suggest editing it for clarity, but I can see that you've already done that and it's much more obvious now.  Thanks. :-) Tcnuk (talk) 12:17, 2 September 2009 (UTC)


 * Named HTML entities such as &amp;isin; have been around for a very long time, at least since the HTML 4.0 standard in 1999. I believe they were all chosen to be in the Adobe Symbol font, so that even at the time they would be supported by most computers and printers. &mdash; Carl (CBM · talk) 13:01, 2 September 2009 (UTC)

For me it's not a concern about "mindless use of symbols as substitutes for words"; it's about the fact that TeX fails to match the size of the surrounding text, being four times as big, and is too high or too low and does not align with either text or punctuation, and in some cases a period, comma, or parenthesis following it actually appears at the beginning of the next line. Michael Hardy (talk) 12:54, 2 September 2009 (UTC)


 * That would be a concern about using TeX for simple symbols. The concern I was responding to is that an inline symbol such as &#x2272; (typed "&amp;#x2272;") may not be visible to a significant number of readers. On the other hand, symbols such as &le; ("&amp;le;") are probably viewable by almost everyone with a graphical browser. The MOS was making two points: (1) avoid uncommon symbols such as &#x2272; inline; and (2) remember that not everyone knows mathematical notation, so articles may be more accessible if they use English when it does not get in the way. I hope my rephrasing of the MOS text makes it more clear that these are separate issues. &mdash; Carl (CBM · talk) 13:01, 2 September 2009 (UTC)

I am a bit confused about one of Carl's comments above, and maybe someone could clarify for me. I recall a months back (January?), User:Bob_K was having trouble viewing several articles because of sepcial mathematical symbols. But all of the symbols in question were HTML entities. (I think convolution, and set theory operations were the case.) He was using a version of Internet explorer, and when I tried this out on my XP machine at home I did indeed have the same problem. After that he added special character templates to a few articles like Hilbert transform and Set (mathematics). Now I admit that named entities have been around a long time, but I think (some versions of) IE doesn't necessarily support them anyways. And your computer doesn't need to be so out of date to have such a version. Does IE really support these symbols? I don't use it often enough to be sure. Thenub314 (talk) 11:52, 9 September 2009 (UTC)

PS. Part of our conversation is still on his talk page: User_talk:Bob_K. Thenub314 (talk) 11:56, 9 September 2009 (UTC)


 * IE does support them, but older versions of IE sometimes have font problems (see Unicode_and_HTML). Bob says he was able to view everything once he changed his display font from Times New Roman to Lucida. But he did not say what versions of Windows and IE he was using. The necessary fonts are installed by default on Windows XP. One thing that would probably be helpful is a rewrite of Help:Special characters. &mdash; Carl (CBM · talk) 13:24, 9 September 2009 (UTC)

I'm late to the party. For reference, I see correctly rendered every single symbol from Unicode Mathematical Operators at least since Fedora 9 (and possibly before that), as well as those from Unicode and HTML. But then, I always install almost all optional fonts. Pcap ping  15:35, 9 September 2009 (UTC)

Really strange fork
Is the section Diffusion MRI really encyclopedic? Anyway, it seems a lengthy and unnecessary fork of material on tensors. Sławomir Biały (talk) 02:33, 3 September 2009 (UTC)
 * Hmmm, tricky one—clearly he's an expert in the field, and I've no doubt there's useful material in there. How best to politely suggest that it might be more appropriate at WikiBooks or Wikiversity? Or rewritten in a more encyclopedic tone? (less WP:HOWTO, without the WP:self-references to wikipedia…) Qwfp (talk) 02:59, 3 September 2009 (UTC)
 * First, it's not a WP:HOWTO, since it doesn't describe how to do anything. Rather it follows WP:MTAA and explains how tensor math is applied in that particular field of (biomedical) engineering. Surely, the introductory style in that section is a little verbose, but then we have polymorphism in object-oriented programming, which is an even more "dumbed down" example of an intro. Pcap ping  12:29, 3 September 2009 (UTC)
 * At the very least, the tone is inappropriate. Apart from the references to other Wikipedia articles, it is entirely written in the first person. decltype (talk) 12:35, 3 September 2009 (UTC)
 * I removed the self-references since that was quick. If you don't like the tone sofixit or tag it with tone. Pcap ping  12:59, 3 September 2009 (UTC)

(e/c) My issue is mostly with the fact that it seems to duplicate material that should probably properly be elsewhere. The author even went so far as to include links to this article as an alternative treatment of tensors in all of the pages Tensor, Classical treatment of tensors, Intermediate treatment of tensors, and Tensor (intrinsic definition) (see these diffs:, , , ). The material was therefore presented as a strange kind of WP:POVFORK from the very beginning. Anyway, I don't think there is an urgent need to remove the material (although the section title will need to be changed, per WP:HOWTO), but readers should not be directed here as though it were an article about tensors. Sławomir Biały (talk) 12:41, 3 September 2009 (UTC)
 * Changing the section title was trivial, so I've done it. Pcap ping  13:01, 3 September 2009 (UTC)
 * By the way, there is no guideline or policy that prohibits the magic words "how it works" or similar constructs in the section title. Your link to WP:HOWTO describes no such restriction, and neither does WP:NOTHOWTO. Pcap ping  13:03, 3 September 2009 (UTC)
 * As for Sławomir's call for NO MORE TENSOR ARTICLES, PLEASE!, I agree that including this article as alternative explanation in math articles is inappropriate. Pcap ping  13:09, 3 September 2009 (UTC)
 * Yes, I meant WP:NOTHOWTO. While such titles are not specifically proscribed, in this case it does seem rather to flaut the guidelines. Sławomir Biały (talk) 15:30, 3 September 2009 (UTC)
 * My apologies for ever mentioning WP:HOWTO. Yes, I meant WP:NOTHOWTO too, but Pohta ce-am pohtit is right that is wasn't relevant. I made the mistake of editing during a rare spell of insomnia. I'll remember the advice of my favourite wikipedia essay in future. Qwfp (talk) 16:48, 3 September 2009 (UTC)
 * No worries. Pcap ping  17:02, 3 September 2009 (UTC)
 * Sławomir, I think the confusion here is due to the appearance of the word "how" in both English idioms. "How-to" articles/sections are indeed prohibited as they would normally contain instructions or steps how to achieve something. "How it works" is a fairly informal idiom, but often found even in academic papers or books normally entailing a fairly detailed description of something of interest, e.g. "Understanding DNA: the molecule & how it works", "Privatization of social security: How it works and why it matters". We have quite a few "how it works" sections in articles  here, and there's noting wrong with that. Pcap  ping  17:02, 3 September 2009 (UTC)
 * I don't think so. Part of the reason that HOWTOs are proscribed is that they are rarely ever encyclopedic in tone.  The purpose of an encyclopedia is, after all, to inform rather than instruct, and to do so in an appropriate WP:TONE.  The title that you are defending is not, in this editor's judgement, consistent with that aim.  Whatever. Sławomir Biały (talk) 17:57, 3 September 2009 (UTC)

Thanks for the suggestions. I first would say that although I have worked with multivariate statistics and tensor principles for more than 30 years, I found each of the Wikipedia mathematical articles completely impenetrable. My concern in this article is to consider the audience. Not only patients for whom a DTI study has been ordered, but also imaging technologists, neuroscientists, insurance companies looking to make decisions about authorizations, and neurologists, radiologists and (yes) neurosurgeons. As a group, doctors are definitely not mathematicians. My objective was to provide an explanation of tensors that linked the accessible level of math, the visual physical concept of the ellipsoid (physicians are generally very good with spatial object visualization as opposed to math) and the steps of the imaging processing. If you remove the discussion, then the reader is left not knowing what in the world a "tensor" actually is. If a mathematician reads my section they may be horrified by the simplicity and lack of formality. However, an encyclopedia cannot consider that it has just one kind of audience. The formal tensor treatments may be fine for mathematics graduate students but I can assure they are totally useless and impenetrable for a neurologists or family practitioner who just wants to have a clear enough idea about it to be able to explain it to patients and insurance company reviewers. I will certainly work on rewording it to get rid of the pronouns. I do feel very strongly that this is an appropriate amount of material and an appropriate level of discussion. Also, patients who want to know about DTI images and go to your mathematical tensor articles will be totally baffled. You don't need to send these people to some other Wiki, they expect to find this material in Wikipedia. All of the mathematical articles totally fail to cover any of the relevant material about tensors as it applies to DTI. You could modify or add to those articles to include a section for the non-mathematician. However, the only really large group of non-specialist, non-mathematical readers who are interested in tensors are those concerned with DTI MRI scans. Therefore, I think the best place for the DTI oriented tensor explanation is in the DTI article.(Afiller (talk) 05:36, 4 September 2009 (UTC))


 * Really, a problem! Here is another instance of the same problem: "As far as I can see, mathematicians understand the physical language very well—although they often don't like it because they find it too verbose—but the converse is not true, many physicists and practically all chemists do not know advanced mathematical terminology." A talk in Citizendium Trying to keep our control over math we mathematicians can become aggressive toward others. Boris Tsirelson (talk) 06:28, 4 September 2009 (UTC)

It is more clear to me that the material needs a copy edit, than that the copy edit needs to be in the direction of the general tensor articles. After all this is only matrices anyway, when it comes down to it. In other words, it is a writing issue. Charles Matthews (talk) 20:50, 5 September 2009 (UTC)

Please - no copy editing by mathematicians though. Your principal tensor site gets three or four visits per day - aside from editors. This site draws 300 to 400 visitors per day because it is a good article. It should not read like a mathematics page. It is written for patients and physicians and not for mathematicians. I can write technical material I assure you. The trick is to take mystifyingly complex ideas and re-render them as easily conceptualized elements that are widely accessible. I know you'll just say I'm biased, but the existing tensor articles are each a horrible mess for readability and communication. Why not focus first on copy editing them. They are basically failures as they read right now because they are only understandable by professors of mathematics. Remember, this is an encyclopedia that has very very popular articles about Britney Spears. It is not a professional encyclopedic treatment of complex spartan mathematical listings. If you have a mathematician copy edit the Britney Spears article it will be replaced in a day. If Charles Matthews has some good suggestions about what the copy editing needs are, I will certainly see if I can get there, but this is no problem article. It is very successful and effective. One of the writers above allows that I am an "expert." There may be some debate, but my invention with some use of tensors is already saving thousands of lives and will intimately impact millions into the future. Why not stop all the DTI imaging and just tell the patients to work a bit with matrices until they feel better? Apologies in advance for the argumentative tone, but what is it that you guys are so worked up about here? As an aside, I certainly agree with Charles Matthews that this just barely has to do with tensors - but tensors are involved to some extent. This section points that out - no tensor analysis needed. Historically, we called this "diffusion anisotropy imaging" and it was Peter Basser who helped create and promote the idea that this was some sort of incredibly complex mathematical methodology - not correct in 1992, not correct now. The basic test is that to develop the method, it had to be so simple that even a brain surgeon could do it. I know that most scientists and - certainly most mathematicians - will consider surgeons to be not very bright, (compared to a mathematician at least) but that is just a burden we have to bear. (Afiller (talk) 06:05, 6 September 2009 (UTC))
 * Yes, you are biased; and that phrasing suggests that you're violating WP:OWN, and should not edit the article; especially if the concepts in the section originated with you. I don't think I could copyedit the article, but removal of the section is more in keeping with Wikipedia policies and guidelines than the present phrasing.  Perhaps it would be better to note  that the diffusion in a given direction can be represented by a quadratic form or perhaps a definite form (not obvious to me, but there may be reasons explained earlier in the article), and noting the relevant characteristics of the quadratic form.
 * We've already banned Carl Hewitt and his students from editing his articles in Wikipedia for WP:COI violations; I would rather than hadn't happened, and I'd rather you weren't banned for being unable to edit other than emphasizing your contributions to the field.
 * I may not edit those articles where I am the expert, but I may edit articles where I am expert. If you cannot see the difference, perhaps Wikipedia is not for you.  — Arthur Rubin  (talk) 07:34, 6 September 2009 (UTC)


 * COI is an advisory guideline, and the Hewitt case was under WP:AUTO - let's keep that straight. I'm sympathetic with the need to have good exposition; but that does not over-ride either basic content policy (articles must conform to NPOV and in particular are not to "sell" anything), and also WP:OWN (it is simply not acceptable to say "mathematicians keep off"). There is obviously an issue about "bedside manner" in any article relating to clinical medicine in any way. I don't accept, though, that I would be an inappropriate editor of this or any other article. Charles Matthews (talk) 08:19, 6 September 2009 (UTC)
 * I agree that User:Afiller wrote an introduction at an appropriate level for the intended audience of that article, so it should be kept (there); of course, it could be improved. WP:MTAA allows such introductions, and we have others in Category:introductions. But, please cease the "mathematicians keep off" rhetoric; many editors that participate here are quite capable of editing a variety of topics, without making them impenetrable. If you think some edits introduce too much jargon or explanations that are unnecessary at the level of that article, dispute them individually without chastising the contributor. Pcap ping  14:31, 6 September 2009 (UTC)
 * I did not see participants in this wikiproject accuse of WP:COI User:Martin Davis after Martin Davis was "allowed" to edit Hilbert's tenth problem... So, this strikes me as a double standard. I can give you further examples of mathematicians that even engaged in WP:AUTObiographical endeavors here, although I'd rather not. Besides Magnetic_resonance_neurography and Diffusion_MRI lay out in the open the COI. Do we have that kind of tag on the cult articles that User:jossi has edited here for years, and created much negative publicity for Wikipedia in the press?? Heck, jossi was even an administrator, and his blocks caused some scientists to cease editing Wikipedia for good, e.g. Dr Zak, who contributed to the featured status of Aldol reaction&mdash;an article included in the comparison between Wikipedia and Britannica. Did I mention User:Henk Barendregt (i.e. Henk Barendregt) recently fixed an error in the lead of the lambda calculus article (which still has more errors left in the body)? Pcap ping  15:05, 6 September 2009 (UTC)
 * Having said all that, I do not contest that sometimes people add their own work to Wikipedia inappropriately, even when it is published. But this doesn't seem to be the case here, at least not in that section describing the mathematical background; I don't have the expertise to comment on MRI and related articles at large... Pcap ping  15:39, 6 September 2009 (UTC)
 * I apologize for the WP:COI accusation; perhaps I'm too sensitive, but I don't feel comfortable editing complex relationships involving the axiom of choice where my parents are/were the expert.
 * However, the last time I checked, the exposition, although at the appropriate level, and not obviously wrong, was not sourced (or at least, not referenced). Under the circumstances, that requires further investigation; we may not include comments as to what characteristics of the tensors are important, especially since &lambda;3 is not the quantity "graphed" as described in the detailed section above.  — Arthur Rubin  (talk) 15:50, 6 September 2009 (UTC)
 * Introducing COI considerations when inappropriate (i.e. when the encyclopedia is seeing the benefit of any expertise) is not good, and basically disruptive. Please just stop all that. The COI guideline was put together for a reason (I was one of the people involved) and the major concern for me was and is that those coming from outside may have no idea at all what it would be like to endure an edit war exacerbated by having a stake in the subject. I have gone in and done some work on the article. Apart from a few issues with the first person plural that might take thought to sort out, there is nothing so terrible that issues can't be discussed on the Talk page there. Charles Matthews (talk) 19:48, 6 September 2009 (UTC)

The COI issue has been covered at some length so I won't repeat it here. I do apologize for saying "no mathematicians" and I meant it more in humor. My poke in the ribs on this is not exactly a "ban." My concern is that if the tensor section in the Diffusion MRI article was made to look like the tensor discussions in the mathematical articles, then it wouldn't serve the people I felt were the audience. The edits from Charles Matthews are excellent. In the discussion for this article I point out how complex COI can be. A popular competing claim for early steps in the use of tensors in Diffusion MRI comes from Peter Basser, but he is a senior program director at NIH and so is responsible for doling out the grants to most of the scientists in the field. When Basser's story is championed in a signed article, isn't the scientist looking out for his next grant in order to keep funded, produce papers and get that next academic promotion - maybe there will be an invite to give a plenary lecture, etc. In academia, we understand that all scientists publish about work they themselves have done and upon which their livelihood depends. In most cases, this is obvious to the reader. When interests of the writer exist that may not be obvious to the reader, then they should be declared as I have done. Wikipedia - unlike academia - encourages anonymity and that sets up a terrible potential for untraceable COI. All that being said - relevant to the material here, explaining the mathematical basis is not an area to worry about conflicts as far as I can see. This is particularly the case because I'm not really an advocate of the ellipsoid model. Nowhere do I mention the anti-symmetric dyadic tensor model I've been publishing about - most of the publications in the field (there are about 4,000 peer reviewed articles) orient towards the ellipsoid tensor model. I'm all in favor of the point made about re-explaining the mathematical basis and there are thousands of scientists trying to develop new and better methods of processing diffusion anisotropy MRI data. I'm focused on research on the biophysics and data capture. Diffusion MRI and "DTI" are the work of thousands over the past 15 years, and Arthur Rubin's suggestion to "ban" me isn't very civil. This article is almost entirely about the collective work in this field. I have written some major portions because no one had bothered to in the past and because I like writing to teach - as I have done in other books I have written (such as "Do Your Really Need Back Surgery"). I understand how difficult it is to be successful with the entire project of Wikipedia. I'd like to be helpful, but would not want to be harmful to wikipedia. If you just delete the entire article, you will have to find someone to write again from scratch. If you think there is a punitive value in deleting the tensor explanation then I am truly baffled at what you are trying to accomplish other than wielding authority. I certainly agree (and have said elsewhere) that - if you can't take the heat you should stay out of the blogosphere - and that applies equally well to Wikipedia. (Afiller (talk) 04:57, 7 September 2009 (UTC))
 * Just a quick comment: mathematicians are probably less aware that in other areas of academia authorship is easily diluted. This is a sort of tradition in many fields, where it's far more common (than in math) to see a grad student's adviser, a lab director, a senior faculty on someone's tenure committee, or even a grant giver being listed as authors when their intellectual contribution to a result/paper was insignificant. My WP:OR thesis is that this tends to happen in proportion to the financial resources needed to obtain results in a given field. Pcap ping  09:33, 7 September 2009 (UTC)

Duplicate articles
So, I came across List of mathematics articles (A-C) and its ilk, and they are evidently used exclusively for recent changes tracking by this wikiproject using Mathbot. I asked Mathbot's author, and he told me to ask here. So: is there any reason (besides the bot's current settings; the author could change them easily) these pages could/should not be moved to a subpage of this wikiproject? They are complete orphans, they duplicate the single-letter articles, and they are solely used internally. I just don't understand why these are in mainspace. --Cyber cobra (talk) 22:39, 5 September 2009 (UTC)


 * See also Articles for deletion/List of mathematics articles (J-L). CRGreathouse (t | c) 01:06, 6 September 2009 (UTC)

...and hyphens
List of mathematics articles (0-9) has been moved a number of times, and in some of its incarnations had an ndash rather than a hyphen. Our usual conventions say an ndash is correct. So why isn't that used? There may be some sort of dispute about whether to say "list" or "index", but I would think it would be obvious that the ndash is correct.

Likewise List of mathematics articles (A-C), etc., should have ndashes rather than hyphens, regardless of whether they're called "lists" or "indexes". Michael Hardy (talk) 01:31, 6 September 2009 (UTC)


 * I don't have any strong opinion about the hyphens, but please coordinate any renaming with User:Mathbot, so that the correct pages are updated and nobody needs to do any history merges. &mdash; Carl (CBM · talk) 02:54, 6 September 2009 (UTC)

Requested move
A requested move discussion for the pages has been started @ Talk:List of mathematics articles (A-C). --Cyber cobra (talk) 04:31, 9 September 2009 (UTC)

Articles for deletion/Visual Detection of Imaginary Roots in a Parabola
That discussion is currently full of inclusionist/deletionist rhetoric - does anybody feel up to the task of getting it back on track before Thursday morning? Either presenting a reliable source or a fresh voice explaining why the topic is not notable would be nice. - 2/0 (cont.) 03:04, 6 September 2009 (UTC)


 * See previous discussion under Visual Detection of Imaginary Roots in a Parabola above. Note that the article has now been moved to Graphical methods of finding polynomial roots and its original contents have been moved to its talk page. In the interval since the previous discussion and the article's AfD nomination, the title, topic and contents of the article have all been completely changed. Gandalf61 (talk) 11:08, 6 September 2009 (UTC)

The current name of the AfD discussion is Articles for deletion/Graphical methods of finding polynomial roots.

The article got drastically rewritten in such a way that its original topic was no longer there. I then restored the original topic without all the kindergarten-level algebra text material and with a correctly drawn graph, within the article's new larger context.

In view of the citing of the book titled Visual Complex Analysis, of which it is said that it goes through similar material with more complicated functions, I think the article can evolve into something worthwhile. Michael Hardy (talk) 21:39, 6 September 2009 (UTC)


 * Your re-write of the original topic is certainly much better in style than the original text. However, as far as I can tell, Colonel Warden's citing of Needham's Visual Complex Analysis at Talk:Graphical methods of finding polynomial roots was entirely bogus. It is an excellent book, but I can see no mention of this method of locating complex roots of quadratics. Also, the method does not generalise to higher order polynomials - how would you apply it to locating the complex roots of $$y=x^3+1$$, for example ? Gandalf61 (talk) 22:00, 6 September 2009 (UTC)
 * While I don't have a sufficient interest in this topic to delve in it, I'll point out that the book has "limited preview" on google books, meaning you can read most of it,, so issues surrounding what's in it should be easy to sort out. Pcap ping  23:18, 6 September 2009 (UTC)

I've looked at the "limited preview", and it does appear that "Colonel Warden" was confused. It seems quite plausible that the topic could be treated in that book. But that's not a reason to cite it.

Now let's imagine an analytic function of a complex variable, that takes real values for real arguments, and suppose in some neighborhood of a real number a it's approximately [(x &minus; a)2 + (a small positive number)], where "small" means by comparison to its deviation from that parabola. The proposed method should give reasonable approximations to the non-real roots, and with some work one should be able to say something precise instead of saying "reasonable".

But of course that won't work for something like x3 + x. Michael Hardy (talk) 02:23, 7 September 2009 (UTC)

Free paparazzi pictures
Does everyone here condone the picture we have on Grigori Perelman? It certainly wasn't there a year ago when I last looked at that article. I'm sure the picture has a free license and what not, but do we condone the use of a picture likely taken without the subject's knowledge, and not in the best of circumstances&mdash;he looks like bum in that one&mdash;as the main picture in biographical articles? Pcap ping  16:16, 7 September 2009 (UTC)
 * On closer look, the picture was taken by "author unidentified" (in Russian), so I've nominated it for deletion since it couldn't possibly have a free license under those circumstances. Pcap ping  16:43, 7 September 2009 (UTC)


 * You have a point, but (in the general context) yes, we are reduced to using photos that are less than ideal, unless people who are the subjects of articles have put an approved pic into the public domain or at least under some free license. That is certainly what we would like them to do. If they can't, won't, or don't care then we have a selection of not-so-good options ("Fair use", scrape the bottom of the barrel, or just do without entirely). Charles Matthews (talk) 18:40, 7 September 2009 (UTC)
 * Perelman is still alive, so Wikipedia's policies (at least as they are currently interpreted and enforced) don't allow us to use a non-freely-licensed image even when such use would be legal fair use. —David Eppstein (talk) 18:58, 7 September 2009 (UTC)


 * Pcap realized already that this was an image on commons, so it had to be nominated for deletion there. Independently I asked a commons admin about it, who agreed it was a clear copyright violation: the source was a deep link to a newspaper site, where the front page has a restrictive copyright notice. Commons only accepts free images.


 * David Eppstein is correct that, because Perelman is alive and (presumably) could be encountered in public, we can't use a non-free image in the infobox of his article. So we can't upload the image here just to use it on his article. &mdash; Carl (CBM · talk) 19:51, 7 September 2009 (UTC)
 * There are exceptions to that, in cases where a free-use image is extremely unlikely to be obtained even if the subject is alive. For example, people in countries where photos of living people are difficult to obtain for religious reasons (I believe Saudi Arabia is one), photos of people incarcerated for life in countries where access to prisons is difficult, etc. -- Avi (talk) 14:18, 8 September 2009 (UTC)
 * Still, I believe there should be limits to that kind of pictures. I don't think WP:NOTCENSORED was meant to mean "I can post any embarrassing picture of someone on his/her Wikipedia biography because it's verifiably true and a free picture." Pcap ping  14:31, 8 September 2009 (UTC)
 * Pictures of living people are covered by WP:BLP, so unless the "uncomfortable" picture is of a situation which is in-and-of itself notable and has its own article, in which the picture is posted, it should be removed and replaced with a neutral one (I have not seen any of the pictures in question for what it is worth). -- Avi (talk) 18:57, 8 September 2009 (UTC)

Hilbert space for GA
I've nominated Hilbert space for good article status. Follow the links at Talk:Hilbert space. Sławomir Biały (talk) 20:23, 7 September 2009 (UTC)

Beta function disambiguation.
Looking for feedback at talk:Beta_function. Thanks. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 02:31, 9 September 2009 (UTC)

Digit grouping style (notice of discussion)
In case anyone is interested, a discussion about digit grouping styles is taking place at Village Pump (policy), related to this question: "On Wikipedia, should the selection of digit grouping styles depend upon regional and topical conventions used in the English language?" Please refer to that page for details and discussion. TheFeds 04:01, 9 September 2009 (UTC)

Requested move
There is a discussion at Talk:List of mathematics articles (A-C) regarding moving these pages to userspace. Oleg Alexandrov (talk) 17:16, 9 September 2009 (UTC)

Math Genealogy
Why do we have two different templates Template:MathGenealogy and Template:Mathgenealogy? --Robin (talk) 18:32, 4 September 2009 (UTC)
 * Good question. The latter has no documentation and far fewer transclusions. Unfortunately it appears to have a slightly different syntax, so I don't think it would work to simply redirect it to the former. Perhaps Mathgenealogy should be labelled with Tdeprecated? Template syntax ( etc.) is not my strong point so I won't attempt that myself as 70-odd mathematicians might get labelled as deprecated instead. Qwfp (talk) 19:35, 4 September 2009 (UTC)
 * I wonder if it would be possible to rewrite the MathGenealogy template so that it also handles the syntax from the other one (I think the only difference is that the lowercase one wants name= instead of title=)? If so we could fix the inconsistency with a redirect. But my expertise in programming templates is quite limited. —David Eppstein (talk) 21:06, 4 September 2009 (UTC)
 * Now done. MathGenealogy accepts the name= parameter and redirect to MathGenealogy. --Salix (talk): 08:16, 6 September 2009 (UTC)
 * Just noticed that you did this. Thanks Salix. --Robin (talk) 14:29, 13 September 2009 (UTC)

An issue at Field extension and more
I've had an issue with user PST at Field extension and I've reverted his edit twice so I'm raising my issue here (it has also been discussed by me and him at User talk:RobHar). He wants to say that the fact that ring homomorphisms between fields are necessarily injective is a consequence of Schur's lemma, which in some sense it is, but that's complete overkill. It's just because fields have no non-trivial ideals. In the same edit he replaces "ring homomorphism" with "non-zero ring homomorphism" though on wikipedia ring homomorphisms are assumed to be unital, and hence automatically non-zero.

An additional problem is his edit at Talk:Banach manifold where he raised the math rating importance of that article from "low" to "top". His reason is that manifolds are top importance and manifolds are special cases of Banach manifolds, hence Banach manifolds are top importance. This is of course an inappropriate use of transitivity, but I fear I will not be able to convince him of that myself. RobHar (talk) 11:26, 7 September 2009 (UTC)


 * It may be worth it for an uninvolved party to have a chat with PST about math priorities. He posted a request for help at User talk:Geometry guy just over a week ago, but G'guy was busy in real life at the time, and didn't reply at length.  Someone else (not me) should probably discuss this with him at his talk page.  I've made an edit to Field extension that will hopefully resolve the dispute.  It doesn't really hurt to say the additional word non-zero.  At best, those for whom "ring homomorphism" means "unital ring homomorphism" will see it as redundant.  Otherwise, it avoids potential confusion.  But you are correct that Schur's lemma is definitely overkill.  If there were a way to bring in Schur's lemma as a side note, then I would support it.  But I don't see a way to do that, since the remark is already somewhat peripheral to the topic of the article.  Sławomir Biały (talk) 12:43, 7 September 2009 (UTC)
 * (ec) I will only comment briefly on terminology. Assuming that Wikipedia is a book, and thus that one article's terminology necessarily entails something in another is a bit of a stretch given how most people use this resource: they don't read some "chapters" in order here; they may simply know from somewhere else what "ring homomorphism" is, which may not be exactly the same as defined on Wikipedia, so a little extra precision like "(non-zero) ring homomorphism" can't hurt in other articles when the non-zero qualification matters in that context. Pcap  ping  12:46, 7 September 2009 (UTC)


 * About the terminoloy: we have conventions in the mathematics articles on wikipedia. These conventions are meant to be useful for both readers and editors.  It is true that articles should not be written in a way that assumes readers have mastered all the conventions, but it is possible to inform/remind readers of conventions in a way that reinforces them, not undercuts them.  In this case, it would be appropriate to remind the readers that a homomorphism of rings is assumed to take 1 to 1.


 * Regarding the Schur's Lemma, PST claims in User talk:RobHar that the statement that a field homomorphism is injective is "the "classical form" of Shur's lemma presented in some textbooks" and "Perhaps you are right that mentioning Shur's lemma is "overkill", but many textbooks and the literature do so in the same situation". What are these sources?  For that matter, could someone indulge me and explain exactly how the injectivity of field homomorphisms follows from the fact that the endomorphism ring of a simple module is a division ring?  Plclark (talk) 19:20, 7 September 2009 (UTC)


 * Because every field is a simple module over itself. &mdash; Carl (CBM · talk) 19:33, 7 September 2009 (UTC)


 * Right, this is equivalent to saying that it has no nontrivial ideals. If you know this, you know that any homomorphism into a nonzero ring must be injective, and conversely.  But listen carefully to my question: how does the fact follow from the fact -- i.e., the implication -- that the endomorphism ring of a simple module is a division ring?  Does it make sense that to say that A follows from A implies B?  Plclark (talk) 19:53, 7 September 2009 (UTC)


 * It seems that we are talking at cross purposes. To reset the conversation, I'll just suggest that the issue here is that, in the specific situation at hand, several definitions that would ordinarily be different all specialize to express the same bare fact of reality about fields. Whether one views this fact to be "primarily" about nontrivial ideals, or a consequence of Schur's lemma, or a fact about simplicity of modules, etc., will depend on individual taste. &mdash; Carl (CBM · talk) 20:17, 7 September 2009 (UTC)


 * Are we? I'm asking for an explanation of why the fact that a homomorphism of fields is necessarily injective follows from Schur's Lemma.  To be more direct, I am saying that I see no direct logical implication here.  (How are you using the conclusion of Schur's Lemma, that some endomorphism ring is a division ring?  Where is the endomorphism?)  Whether one mathematical statement implies another should not depend on individual taste.  To be more wikipedian about it and return to my first point above, PST claimed that this implication is found in "many textbooks and in the literature".  I have in the past taken time to try to persuade PST that this sort of statement -- I claim that support for my position exists in the literature (but I will not tell ou where) -- is not only unhelpful but antithetical to the wikipedian way.  I am concerned that this is happening again.  Can you put my concerns to rest with a reference? Plclark (talk) 20:44, 7 September 2009 (UTC)


 * (Moreover, I don't understand how a definition can express a fact. Your statement is therefore quite confusing to me.) Plclark (talk) 20:48, 7 September 2009 (UTC)


 * It does seem like you need to know there are no nontrivial ideals to even apply Schur's lemma to this situation (to know that the field is an irreducible module over itself). RobHar (talk) 00:37, 8 September 2009 (UTC)

I did not know that my edit at field extension or my edit at Talk:Banach manifold would create a conflict and I am sorry if it did. However, I do not understand why it is absolutely necessary that a mention of Shur's lemma should be removed because of an opinion that it is overkill - a name was merely given to a particular (rather simple) result. Altough I can understand how people might feel that this is unnecessary, I do not think that it is worth to discuss this issue to any great depth so in effect I will not revert that statement again.

With regards to Talk:Banach manifold, I feel that priority ratings unnecessarily seem to classify research as being "low importance", "mid importance" or "high importance". After reading the appropriate policy page (WP:WikiProject Mathematics/Wikipedia 1.0/Importance), I observed the statement: "However, it does not assess the importance of the article as it is currently written, but the potential value of having a high quality article on the topic. This is usually closely tied to how important the subject is, and consequently, importance levels are often described in terms of the importance of the subject rather than the article." In some sense, this compares to asserting that "Mathematical research on a field should be determined by priority; the potential value of someone researching the theory of manifolds is greater than that of researching Banach manifolds." Of course, this is my interpretation if Wikipedia believes that some articles should be given more attention that others according to priority. Do we really want to convey that Banach manifolds are apparently "low priority" because they do not have applications in string theory (for instance) unlike Euclidean manifolds (actually they do - or a subclass at least)? In effect, I do not understand why the logical deduction that Euclidean manifolds constitute a subclass of Banach manifolds implies that they have the same importance, is flawed. This is just my opinion so in effect there may well be a good reason but at present, I am unable to see it (as another instance of "priority ratings" - ). As someone mentioned above, I consulted Geometry Guy regarding this issue, and I feel that it should be considered.

If I understand correctly, Plclark asserts that Shur's lemma does not apply to ring homomorphisms between distinct fields whereas it does apply to ring endomorphisms. As such, this criticizm is perfecly appropriate - I did not state that this was so. I did state, however, that in the literature this is sometimes stated as a "generalized Shur's lemma" in a vague sense. At the time, I did not feel that this point needed evidence as it was not at the heart of the debate. The source I had in mind, upon closer check, does not in fact have the precise statement I asserted and so I apologize for stating that this is used in the literature (I could not find other instances of this, either).

I think that this discussion has reminded me that one should edit articles which are apparently unheard of by mathematicians (because of their specialization). Articles on well-known topics appear to be defended from constructive edits. Possibly, it is better if someone does not know which articles you edit (or at least has no clue about the topic) so that no conflict arises. -- PS T  01:00, 8 September 2009 (UTC)


 * A general rule of thumb is that about 1% of articles should be "top" priority (which would be about 230 articles right now; we are right on target). This does not leave room for every interesting article to be top priority. The thing to keep in mind is that the priorities are not meant to measure how worthwhile a topic is. They are only meant to measure how crucial that topic is to a mathematics encyclopedia. Clearly Addition is of higher priority than Group ring, in the sense that not even an abridged encyclopedia could do without the former, but one could make a reasonably decent general encyclopedia such as Britannica without having an article on the latter. &mdash; Carl (CBM · talk) 01:40, 8 September 2009 (UTC)
 * Thanks. I think that I appreciate your explanation of priority ratings better than those which I have already seen. Earlier, my main concern was the idea that certain mathematical concepts were more important than others (which by extension, in some sense, implies that researchers of one mathematical concept should be given more credit than those of another). -- PS T  09:48, 8 September 2009 (UTC)

I resent the implication that PST is making that my actions prevented "constructive edits" from being made. PST has also accused me on my talk page of not handling this matter in an "ideal" fashion because I immediately reverted his original edit. He seems to suggest I should have waited or something. I simply followed wiki's consensus-building process by removing an edit that I didn't agreed with. PST proceeded to reinsert his edit two more times without seeking consensus first. I feel I've done exactly what wikipedia suggests, and I feel that PST has made two baseless accusations. RobHar (talk) 15:18, 8 September 2009 (UTC)
 * I interpret the way in which the edit war progressed differently. In my view, the fact that you reverted my first edit was not a problem since you had a differing view to me. However, at this point, the war became a conflict of opinion, and not merely "right and wrong" edits. Apparently, other editors share the same opinion with you and thus your revert remains. This is not the first time that I have encountered such an "opinion-based" dispute where someone has had a differing opinion to me. Nevertheless, the path of the dispute has never gone in the same direction as the dispute between you and I; after I reverted someone else's edit (or vice-versa), we stopped edit-warring there and discussed what should be done. Sometimes I agreed that the other person's edit was more appropriate than mine and sometimes the other person agreed that my edit was more appropriate than his/hers. Almost always, this is how I have come to consensus and I never regret that the other editor has "prevailed" over me (or vice-versa), because I eventually agree with him/her. Never has more than one revert occurred at any particular instance in the edit war. The fact that this is the first instance that this has happened here in a long time (with me involved), suggests to me that something is different here. In effect, I am still yet to understand why you (first) reverted before discussing with me and waiting for my reply (you argue with the exact same reasoning on your talk page - "My subsequent revert was because you didn't attempt to reach any sort of consensus before reinserting your edit. You made a comment on my talk page but didn't even bother to wait for me to reply."). In effect, I believe that the "reverter" should attempt to come to consensus rather than the "original editor" (edits made with the intention of improving the encyclopedia should be given a higher priority than reverts of such edits) so that Wikipedia progresses. In that case, I might have changed my mind and agreed with you resulting in an end to the conflict - User:Sławomir Biały and I had a similar dispute at Nakayama's lemma but Sławomir did not revert before he convinced me of his view, and I agreed. When I said that "your handling of the matter was not ideal" I meant this in comparison with my previous experience. I also feel that you proceeded to this page knowing that you will almost certainly be supported. I am not "accusing" you as such, but noting that this dispute has ensured that I will not edit articles in field theory for a while which I think (and now know) will result in your revert. In most cases, Wikipedia appears to be a better place when one person improves an article to a significant extent and not a collection of people (how many people have significantly contributed (50 edits +) to a particular math featured article on WP?). Although I am not in favor of this idea, it appears to be the truth. Since you have put more effort in improving the article field extension, I respect that. -- PS T  01:51, 9 September 2009 (UTC)


 * I'll say it again, my behaviour is perfectly within the accepted practices of wikipedia. I saw an edit that in my opinion was wrong/bad (and frankly a vast majority of decisions about edits are matters of opinion, even if the statements inserted are true they may not be notable; furthermore, you've since said you were wrong about your initial interpretation of your source). So I undid the edit, thus returning the article to its previous consensus. It is then your burden to convince me, or bring in other people to convince, that your edit is good and obtain consensus for it (a process that normally occurs on the article talk page, not the reverters talk page. Your use of the reverters talk page is unconventional and personalizes the discussion in an unnecessary fashion). For example, sometimes someone makes an edit that's wrong, someone reverts, and then the person thinks about it and sees that the revert was appropriate. If people on Wikipedia had to explain everything on the first revert, the encyclopedia-building process would take much longer. Perhaps other people in the math project behave differently from me, or perhaps they behave differently when it comes to you. I know I do. This was not the first time I've been unhappy about your edits, but I usually let it go because I've seen you get into long drawn out discussions (like this one) with other editors, forcing them and all the others who inevitably get involved to spend all sorts of time reiterating the ways in which you are wrong. And I don't have the patience for that. This time, I thought your edit at Field extension was absurd, and figured I should intervene. I also figured it shouldn't be too hard to convince you your edit was inappropriate. I was wrong about that.
 * I'm unclear about your point when you say that I "proceeded to this page knowing that you will almost certainly be supported". Your behaviour forced me to come here. The guideline WP:3RR prevented me from reverting you again. You may believe that your (incorrect) edit should have remained in the encyclopedia until it was determined that it is good (a sort of "good" until proven "not good"), but this is not the way wikipedia works, and should not be the wikipedia works. Your reinsertion of your edit multiple times indicated to me that my simple powers of persuasion were not going to be enough so I came here. Of course I knew I would get support here as your edit was absurd (which is why I reverted it in the first place). If you had just taken a bit of time to consider my point of view, as opposed to simply reinserting your edit each time, things would not have come to this.
 * From following many pages and seeing your edits, I can see you are clearly very passionate about wikipedia and that you put a lot of effort into it. I do not want to scare you away from editing. Don't avoid editing articles on field theory because of me (my watchlist is much more vast than that anyway), but instead simply realize the way the process of editing works at wikipedia. Someone can revert your edits, and then you have to obtain consensus, preferably with them, but if that doesn't work, then in a bigger forum. Don't assume you're right and they're wrong. RobHar (talk) 11:03, 9 September 2009 (UTC)
 * I would reply to your above comment but I do not think that further argument is appropriate. Nevertheless, I disagree with some of your points and some of the accusations that you have made about me. Although this dispute no longer has worth, I will still remember it while undertaking future edits for the good and the bad aspects. -- PS T  01:57, 10 September 2009 (UTC)

Proposal to link WP:MTAA from WP:NOT PAPERS
I find the current version of WP:NOT PAPERS both reductive, containing some redundancy, and rather poorly explained (in particular the ban on "academic language" at dictum 7). It also fails to defer to the guideline where the finer points of those issues are discussed. I've made a proposal to address these shortcomings. Actually, I had already implemented it, but I've been reverted by someone insisting that I "get consensus", although that editor had to comments on the substance of my edits. So, this notice is an attempt to get the interested parties to form a consensus. Pcap ping  16:13, 8 September 2009 (UTC)
 * WP:NOT is policy - what we aim to achieve; WP:MTAA is a guideline - suggestions on how to achieve it. Policy does not defer to guidelines, and should not. Septentrionalis PMAnderson 23:12, 12 September 2009 (UTC)
 * For practical purposes many policies do just that. In the matter at hand, WP:NOT PAPERS already does that at dictum 7, where it defers to WP:UCN. Pcap ping  22:50, 13 September 2009 (UTC)

Envelope article
I have some doubts about example 2 which was added to the article yesterday. Don't get me wrong: it is a very nice piece of mathematics. But I think it might be a bit out of place in the article as it stands. The idea of an envelope is a simple one from differential geometry. When people talk about envelopes they are, by and large, talking about the envelopes of families of smooth submanifolds. This new addition seems very algebraic (e.g. it uses a special case of the Hölder inequality) and topological, and a little out of place. Could some people please take a look and see what they think. I think it should be removed. Maybe a new article or a new section could be added to deal with envelopes from a non-differential geometry point of view. As it stands, everything in the article, except the new example, is about simple differential geometry. Dr Dec ( Talk )    15:25, 10 September 2009 (UTC)


 * The argument that we should not explore the different aspects of a topic in an article, rather than that we should, sits rather oddly with WP:NPOV. It is not "out of place" to extend the range of examples in this way; the question would be whether it was giving attention to some aspect that is not at all representative. Charles Matthews (talk) 12:06, 13 September 2009 (UTC)
 * But that's why I said "it might be a bit out of place in the article as it stands" and that "Maybe a new article or a new section could be added to deal with envelopes from a non-differential geometry point of view." I didn't just say: let's delete it!  Dr Dec  ( Talk )    20:50, 13 September 2009 (UTC) p.s. it is very out of place to introduce an example of that nature without any motivation or background whatsoever. I have been in contact with the example's editor and we are in agreement that some work needs to be done.   Dr Dec  ( Talk )    20:56, 13 September 2009 (UTC)


 * The usual strategy for something like that is to discuss the main topic first, and include the secondary topic lower in the article. For example, the article on the Euclidean algorithm starts with the usual description of the algorithm for finding the GCD of two integers, but lower down it discusses how a similar algorithm can be applied to real numbers to obtain continued fraction expansions.


 * I completely agree that our articles should include these more esoteric concepts, presented in a way that all significant aspects of the topic are covered in proportion to their coverage in the literature. &mdash; Carl (CBM · talk) 14:42, 13 September 2009 (UTC)


 * So you think that "a new section could be added to deal with envelopes from a non-differential geometry point of view."?  Dr Dec  ( Talk )    20:52, 13 September 2009 (UTC)


 * I'm no expert on envelopes, so I can't say for sure. It may be that example 2 is just written in a way that differs from how things are normally presented, in which case the solution would be to rephrase example 2 so that it is more in agreement with the literature. Only if there is nontrivial (if minor) interest in envelopes outside differential geometry would it be worthwhile to add a new section. &mdash; Carl (CBM · talk) 21:13, 13 September 2009 (UTC)

Russell's paradox
We might need some collaboration at Russell's paradox. Some of you may know that Will Bailey, User:Wvbailey, is a thoughtful, careful, and hard-working contributor. However he has a tendency towards what to my taste is an overly "historical" focus, and a tendency to overvalue primary sources, as opposed to the secondary ones from which we are supposed primarily (oh the irony!) work.

He has recently made some well-researched changes, but ones that in my estimation impair the readability of the article and muddle its focus, which (just to reveal my biases) in my opinion should be primarily on the way that the paradox refutes Frege's attempt to reduce sets to logic. There is no question of any edit war here, at least not from Will; his good faith is unquestioned, and I'm certain we can work through this, but some further eyes might spot something helpful. --Trovatore (talk) 20:47, 13 September 2009 (UTC)

Detailed history sections based on primary sources
In general, for history articles here it is not acceptable to directly use primary texts to write an article. Several heated conflicts have occurred on this wiki when some editors tried to promote their own historical interpretations of ancient texts. More recently, I've seen a number of Mathematics articles that have fairly detailed history sections essentially written directly from reprints of the original papers, typically 19th century and early 20th century papers. Examples include, but are not limited to Function_(mathematics), and Algorithm#History. I am a bit surprised, because at least for some of these topics, detailed historical accounts have been published. For instance I've added one to Algorithm. Clearly, writing about the history of mathematics is a little different than other types of history. So, I have to ask here: to what extent do we wish to condone such practices? Should we add something to the Math MOS about it? Pcap ping  13:19, 5 September 2009 (UTC)


 * In many cases for ther more specialized topics, the later papers on the topic (despite being "primary" for whatever results are included in those later sources) will also include a history of the subject that can be used as a secondary source. In fact, probably that's where most of our histories are drawn from. But the temptation is high to just copy all the citations from that history and not mention where the history itself was drawn from. —David Eppstein (talk) 14:36, 5 September 2009 (UTC)


 * To step a bit back from this, I think it is often helpful to include references to the primary sources, whatever their vintage. This is no substitute for having good secondary sourcing as well, and specific claims like "Cauchy was the first mathematician to consider..." should also be referenced to reliable secondary sources.  But I think this is already covered by existing policies like WP:V and WP:OR, and doesn't need to be covered further in a manual of style page (which would be misplaced, since this is a core policy issue rather than a stylistic one).  At any rate, I just wanted to say that we shouldn't discourage inclusion of references to primary sources in history mathematical articles.  Rather we should emphasize the need for including secondary sources in addition to the primary sources. Sławomir Biały (talk) 17:10, 5 September 2009 (UTC)


 * I'd also like to comment that the history section at Function (mathematics) does, in the footnotes, appear to include at least some detailed references to secondary sources. So this would not appear to be an especially good example of an article whose history section is entirely based on primary sources.  Some parts of the history do appear to rely on more primary source material than others. Sławomir Biały (talk) 17:21, 5 September 2009 (UTC)


 * The need to use both primary literature and secondary sources is very well put. The section on "Attribution" in the scientific citation guidelines describes one of the more common areas where references to primary literature are useful: when we are describing breakthroughs, new concepts, and eponyms. &mdash; Carl (CBM · talk) 14:36, 13 September 2009 (UTC)

The history in function is derived primarily from van Heijenoort 1967. And van Heijenoort always prefaces his articles with excellent commentary, either written by him or by another scholar e.g. Quine. And he, like Martin Davis's The Undecidable, often had access to the authors themselves (e.g. Goedel, Russell). In the assembly of these "sourcebooks", these minds went through a huge amount of literature, condensed it, and then presented their "best pieces" (together with their commentary and analysis); you can see this in their extensive bibliographies. A lot of this sort of research is similar to what a wiki contributor has to do in the case of a biography -- read a lot of sources and connect the dots. True, sometimes we get lucky and find a huge trove of primary stuff e.g. Goedel's nachlass as compiled and sorted by (and commented on) by Dawson. But it's almost always a case of reading something in a secondary source and then going hunting into the original to verify the secondary source. My experience has been that the original author always says it best; précis and other condensing usually butchers the original. Bill Wvbailey (talk) 04:08, 14 September 2009 (UTC)

I'd also like to add that quite often "primary" sources themselves serve as "secondary" sources of background info with respect to issues being treated by the author. In other words, the "primary" source is actually behaving, in part, as a review of a (more-)primary source. In exactly the same way, any good review article or book is always "primary" (in its extension) but can be "secondary" (in its intension); this has always been a problem with criticism in fiction and art -- do you just review the art on the page (the extension) without regard to the author's intension (e.g. his infered state-of-mind based on his biography, his prior works, his own comments re his work etc)? For a good example of what I'm talking about see Zermelo's (1908) A new proof of the possibility of a well-ordering section b. Objection concerning nonpredicative defintion (van Heijenoort 1967:190-191) wherein Zermelo lambastes Poincaré with regards to Poincare's (1905, 1906, 1906a) dismissal of Cantor's set theory and with regards to Poincare's opinions re impredicativity (1906, p. 307). Here the page numbers in parentheses are in the original Zermelo, and they refer to the "primary" sources i.e. Poincare; van Heijenoort in his bibliography also cites them fully for the curious. I hope what I'm saying here makes sense. Bill Wvbailey (talk) 16:16, 16 September 2009 (UTC)

Church-Turing thesis as "unsolved problem"
(This is a cross-post from WP:COMPSCI believed to be of interest here as well, please reply there).

We have a box in that article that proclaims, rather idiosyncratically, that it is an unsolved problem. Of course, the actual (claimed) problem is to "formalize" it so it can be "proved". Even this appears to me to be an idiosyncratic view of a few authors, as most state that the thesis is not something that can be proved because in general one needs to "quantify" over all computational models (I can give citations if anybody doubts me). So, it's somewhat questionable to have it included in Unsolved problems in computer science as well, given that most authors do not believe it to be something of a provable nature. So, the box appearing in the CTT article reflects a minority POV in my view. Any other opinions? Pcap ping  23:04, 13 September 2009 (UTC)
 * For what it's worth I agree. See my post at Talk:Unsolved problems in computer science dated August 2006 (!) Staecker (talk) 01:08, 14 September 2009 (UTC)

There are actually 4 different viewpoints on the Church-Turing thesis (CTT) in the literature: So you can see that just calling CTT an "open problem" is not very helpful when there are several mutually-contradictory positions all of which state that it is not an open problem. &mdash; Carl (CBM · talk) 01:26, 14 September 2009 (UTC)
 * 1) CTT cannot be proved or disproved, and is just an informal thesis. This is the most common viewpoint in introductory undergraduate textbooks.
 * 2) CTT has already been proven beyond all reasonable doubt. See e.g. page 11ff of Robert Soare, "Computability and Recursion". This is a viewpoint relatively common among recursion theorists.
 * 3) CTT has not yet been proved, but might someday be proved if we come up with a set of axioms with which to formalize computation. This is the line of research currently being pursued by Gurevich and Blass.
 * 4) CTT has already been disproved. This is the line maintained by several in the hypercomputation community. See e.g. Burgin's Super-recursive algorithms.
 * My viewpoint is that CTT is a hypothesis about the behavior of the universe rather than a mathematical statement, and that therefore it cannot be proven or disproven mathematically, rather, like any other hypothesis in physics, it is subject to experimental validation. How does that fit into your quadripartite division of the literature? —David Eppstein (talk) 01:55, 14 September 2009 (UTC)


 * (ec) Well, 1 and 2 are not really contradictory, because they use a different meaning of "proved". The meaning of 2 is like saying the theory of evolution is proved, i.e. it has not been contradicted by anything. So, these two points can be reconciled without invoking some not-so-real controversy. Actually, S. Barry Cooper assumes 2 in his book after a certain point, after making clear it's an assumption. His book is aimed at undergraduates (IIRC) so the view is not that uncommon these days even at that level.
 * Point 3 is indeed a radical departure from the above two. But so far it's been the focus of few, too few to label the formalization of CTT as a major open problem for computer science; see also, this comment on WT:COMPSCI by User:Miym).
 * As for 4, surely there are theoretical constructs (oracle machine etc.) that can do that; as explained in super-recursive algorithms, the trouble is the redefinition of algorithm/effective method by these researchers. As David Deutsch puts it (in relation to his Church-Turing-Deutsch principle), there's something inherently physical about CTT; actually Roger Penrose also formulated a physical version of CTT as the "Turing principle". B. Jack Copeland goes to some length to emphasize that no physical formulation of CTT is directly attributable to Church or Turing, thus the physical version needs a different name. So, in this (CTD) sense, the hypercomputer guys are almost certainly talking about non-physically realizable computers. If say, real computers could be built, then P=NP could also be "proved" in sense that real computers can solve NP-complete problems in polynomial time, and what not. Pcap ping  02:21, 14 September 2009 (UTC)
 * N.B.: Soare also makes this distinction between physical process and mechanical procedure on page 13 of the paper CBM linked above. Pcap ping  02:59, 14 September 2009 (UTC)
 * Also, our article on CTT suffers from similar problems with Russell's paradox, as explained in the section right above this. Some edits from knowledgeable editors would not hurt. Pcap ping  02:21, 14 September 2009 (UTC)

The Church–Turing thesis is not a mathematical proposition, and so is not susceptible of mathematical proof. I'm not sure I'd call it a philosophical premise either. Certainly one can imagine universal assent to a surprising counterexample. It seems to live in some very lonely place in any of our ways of organizing what we think about. Michael Hardy (talk) 04:01, 14 September 2009 (UTC)


 * Yeah, it's hard to figure out exactly what sort of proposition it is. I definitely don't agree with David Eppstein &mdash; whatever it is, it's not directly a claim about the physical world, at least not in the obvious sense of "there is no physical realization of deterministic computation that exceeds the power of a Turing machine".  Proof:  There is no physical realization of deterministic computation of any sort; any machine will occasionally do the "wrong" thing.  Alternative proof:  Suppose the physical universe is finite, and thus only finite computations can ever be completed.  Would we say that therefore CT is true because all finite computations can be modeled by a TM?  Surely not.
 * So whatever CT is, it's not about physical realizations, but about idealizations of some sort. I suppose it's imaginable that one could phrase it as "there is no natural idealization of physical processes that would allow modeling a machine that performs computation exceeding the power of a Turing machine", but this seems to me to go beyond a claim about the physical world, to cover natural idealizations, whatever they might be, of as-yet-unknown physics. --Trovatore (talk) 05:57, 14 September 2009 (UTC)
 * Um, the "only finite computations" bit is a little unclear, I guess. Make it "there are only finitely many possible inputs and outputs, and therefore every computable function can be modeled as a finite lookup table". --Trovatore (talk) 06:15, 14 September 2009 (UTC)
 * While it's not directly physical, I think physical evidence is potentially relevant. Just as an actual modern computer is evidence that Turing-computable functions are effectively computable, an actual machine which could plausibly be claimed to be a de-idealized version of a Turing-machine-with-halting-oracle would constitute evidence against Turing's thesis. Algebraist 18:25, 14 September 2009 (UTC)
 * That's a fair point. --Trovatore (talk) 20:06, 14 September 2009 (UTC)
 * Well, Dershowitz and Gurevich claim they have actually proved CTT starting from their axioms on page 306. So, it's silly to list CTT, or even the formalization thereof, as an open problem based on the very paper that claims to have formalized it and proved it. Pcap  ping  06:27, 14 September 2009 (UTC)

Re Pohta: I was simply listing the viewpoints that can actually be found in the literature, without offering my own opinion about which of them is correct. I could certainly argue in favor and against all four positions, but that doesn't help anything. As I said, position 1 is the most popular in undergraduate textbooks and position 2 has significant popularity among researchers in recursion theory. &mdash; Carl (CBM · talk) 10:20, 14 September 2009 (UTC)
 * No quarrels with presenting that spectrum of opinion in the CTT article, but to include CTT (or even the formalization thereof) in the list of major CS open problems appears to me (and a few other editors here and in Talk:Unsolved problems in computer science) to be disregarding WP:NPOV, in particular WP:VALID. Pcap ping  16:14, 14 September 2009 (UTC)

My wording of the now-deleted "unsolved problem", with its verifiable sources, is not an instance of me violating NPOV. But I can understand people's confusion in thinking that I, evil ole Bill, am claiming that Dershowitz and Gurevich have indeed succesfully axiomitized the problem. Not a chance! I suspect D and G are all wet. But D and G's claim is in the literature and has to be dealt with; my invoking them was just adding another verifiable source re evidence that efforts of axiomatize (or "formalize" if you will) is still in play as an academic "issue". A quick survey of the history of this article shows that this "unsolved problem" was in the list long before I ever came to wikipedia. It wasn't me pushing a POV -- it was there in the article, then it was gone, then (as I recall) I reinserted it (together with very good sourcing) based on my reading of Goedel's comment to Church. For disbelievers that this issue is not current see CBM's find here: http://www.phil.cam.ac.uk/teaching_staff/Smith/godelbook/other/CTT.pdf. Here Smith reviews articles that discuss as "formalizing" the CTT. Bill Wvbailey (talk) 15:33, 16 September 2009 (UTC)

No "oriented matroid"
I just found out we have no article titled oriented matroid.

I'd have immediately created it if I weren't too confused about the definition to do so. Michael Hardy (talk) 04:03, 14 September 2009 (UTC)


 * This is an example of a topic where Wikipedia can profitably save time by creating a brief stub and then directing the reader to an expositional article for details. Not ideal, but better than a redlink. I think editors should do more of this. It is a quick way of expanding Wikipedia until someone gets round to doing a proper article. Charvest (talk) 08:18, 14 September 2009 (UTC)

Search box for archives?
If anyone knows how add that to the talk archives here, please do so. I spent a little trying to find how that's done but I couldn't find any clear instructions. Pcap ping  03:28, 15 September 2009 (UTC)
 * EmilJ added it ot the top of the page, then I integrated it into the archives list on the right side of the page. &mdash; Carl (CBM · talk) 12:10, 15 September 2009 (UTC)
 * Well, it does not appear to be working, e.g. typing "Hilbert" in the box returns this; I doubt the word "Hilbert" was never used in these archives. From what I've seen on other pages, there needs to be some code that tells a certain bot to index these pages... Pcap ping  15:10, 15 September 2009 (UTC)


 * Fixed, it should work now. I also tried to redesign the archive box in a horizontal layout, so that the search box does not have to be so narrow. — Emil J. 15:24, 15 September 2009 (UTC)
 * If you are going to make the archive list file so complicated, then you are going to have to assume responsibility for maintaining it. Specifically, when the end of the year is reached, you should add links for 2010. JRSpriggs (talk) 08:34, 16 September 2009 (UTC)
 * ??? If anything, the list is simpler than it was before (except maybe for addition of the inputbox code at the end, which is however constant). — Emil J. 10:19, 16 September 2009 (UTC)
 * Adding a new year appears to be a simple matter of copying and pasting a row with the appropriate change in the year number... Pcap ping  17:52, 16 September 2009 (UTC)

Boolean algebra (dab)
Should this really be a dab? I suspect the average person looking for this would be rather confused. We have:
 * Boolean algebra (structure)
 * Boolean algebra (logic)
 * Boolean algebras canonically defined
 * Boolean algebra (introduction)

The "(introduction)" article clearly belongs to Category:Introductions, and is well justified, but I don't even know which article serves as main article for introduction purposes... Also, it's unclear to me how Boolean algebra (logic) differs from Boolean logic.

I could echo what Sławomir wrote above (vis-a-vis tensor articles) along the lines "no more boolean algebra articles, please!". Well, don't get me wrong, I think we don't need more repetitive articles, rather than no more articles on topics in this area. Opinions on reorganizing this in any way? Pcap ping  22:57, 17 September 2009 (UTC)
 * I think semilattice is good example how a concept that can be defined in two "paradigms", algebraically and in order theory, can be structured. There are more options for boolean algebra as explained in Boolean algebras canonically defined. Perhaps that article should be the main article, with Boolean algebra (structure) and Boolean ring serving as a sub-articles, while Boolean algebra (introduction) can serve as intro. Boolean algebra (logic)/Boolean logic are applications/special cases methinks. As for the relationship between the latter two, I suppose Boolean logic should be the intro article for Boolean algebra (logic), which contains more advanced concepts like soundness and completeness, but I doubt we really need two articles on boolean logic just because of that. Pcap ping  23:32, 17 September 2009 (UTC)
 * We also have Two-element Boolean algebra/Boolean domain, which appear no different to me than Boolean algebra (logic)/Boolean logic. Pcap ping  23:40, 17 September 2009 (UTC)
 * Actually, they're not the same. The two-element Boolean algebra is a structure, not a calculus. --Trovatore (talk) 23:48, 17 September 2009 (UTC)
 * (ec)I would be sharply opposed to basing everything on the rather idiosyncratic Boolean algebras canonically defined, which really ought to be merged into Boolean algebra (structure). Probably Boolean ring should also be merged there.
 * I think there are two basic, and quite different, things people are looking for under the name Boolean algebra. One is where "Boolean algebra" is understood as a count noun; this is the intent of Boolean algebra (structure), and all the count-noun occurrences should be merged there, with the most common approach used as the introduction (a Tarskian structure with two binary functions ^ and v and one unary function &not;), and the others (ring, category-theory) ones explained deeper in the body.
 * The other basic thing has "Boolean algebra" understood as a mass noun; a means of manipulating propositional formulas. This side of the question is more complicated, because there is a reasonable amount to say from a technical perspective, but if you say all of that you completely lose all the people looking for Venn diagrams and how to do library searches.  So although it's not ideal in general, the mass-noun side probably needs more than one article, at different levels of technicality. --Trovatore (talk) 23:47, 17 September 2009 (UTC)


 * As to your question about how Boolean algebra (logic) differs from Boolean logic, that's a bit of history. Boolean logic is (or at some point was) largely the work of User:StuRat, who intended it as a "non-PhD-level" article (he didn't seem to understand that the distinction between the mass-noun and count-noun uses is not merely one of the level of difficulty of the treatment &mdash; eventually he accepted that he had to work with that distinction but I'm not sure he ever quite bought it).  Vaughan (I think it was) at some point decided to upgrade Boolean logic to be a more mathematical treatment of the mass-noun sense of the word; this was unacceptable to StuRat, who felt, probably correctly, that the article was now inaccessible to the original target audience.  So if I remember correctly, which I may not, the new content went to Boolean algebra (logic).
 * The correct thing to do would be to merge StuRat's content with the "introduction" article. Then perhaps Boolean logic should redirect to Boolean algebra (logic), or vice versa. --Trovatore (talk) 00:15, 18 September 2009 (UTC)

New article help
Hi, I've just come across A New Interpretation of Odd Magic Squares in the Lo Shu format and can't make head or tail of it. Is it WP:OR? If so, can someone WP:AFD it? cheers, Rd232 talk 01:19, 19 September 2009 (UTC)
 * The broad topic appears legit; see Magic_square. As for the details, I have no idea; there sole reference is a bit shady. Better ask on the talk page of the main article. Pcap ping  10:11, 19 September 2009 (UTC)
 * The method appears trivial, and only works for 3x3 squares. Given that general methods exist, I've prodded it. Pcap ping  11:14, 19 September 2009 (UTC)


 * Agree with prod. The article does not explain its general method, but the examples given in one of its external links here show that the method is the second variation on the Siamese method as decribed at Siamese method. So nothing new here - it is a content fork with some numerology thrown in for good measure. Gandalf61 (talk) 11:36, 19 September 2009 (UTC)

Envelope (mathematics)
Third set of eyes are needed at envelope (mathematics). Sławomir Biały (talk) 15:11, 21 September 2009 (UTC)

Page-copy vandalism
New article Wiart's triangle seems to be a straight cut-and-paste copy of Pascal's triangle with "Pascal" replaced by "Wiart" in a few places. It would appear to be a likely candidate for speedy deletion, but this type of page-copy vandalism doesn't quite seem to fit any of the WP:CSD criteria. On the other hand, prodding and waiting 7 days for deletion seems an unnecessary delay. What is the appropriate course of action ? Gandalf61 (talk) 11:37, 23 September 2009 (UTC)
 * A bold editor would replace the new article with a redirect to the original. Johnuniq (talk) 12:09, 23 September 2009 (UTC)
 * Is Wiart's triangle a valid synonym? Pcap ping  12:11, 23 September 2009 (UTC)
 * No hits in google books or scholar, so I've tagged it as blatant hoax. Pcap ping  12:13, 23 September 2009 (UTC)

I deleted the article. &mdash; Carl (CBM · talk) 12:22, 23 September 2009 (UTC)


 * Thank you. Gandalf61 (talk) 14:10, 23 September 2009 (UTC)

Schwarz integral formula is an orphan
There are no links to Schwarz integral formula from the article space, except from a list. Please help. Michael Hardy (talk) 18:25, 24 September 2009 (UTC)

Template for deletion
Template:Linear algebra references has been nominated for deletion. The discussion page is Templates for deletion. Jim (talk) 03:57, 25 September 2009 (UTC)

Formal language (logic) on AFD
I have nominated Formal language (logic) for deletion. The discussion page is Articles for deletion/Formal language (logic). &mdash; Carl (CBM · talk) 00:39, 18 September 2009 (UTC)
 * In a similar vein, someone interested in math logic may want to take a look at more articles that share similar issues:


 * Deductive system vs. proof calculus
 * Syntax (logic), Formation rule and Well-formed formula
 * Formal proof (claims that natural deduction is a generalization of "proof")
 * Pcap ping  06:12, 18 September 2009 (UTC)


 * It does appear to me that we need a position paper, i.e. essay, setting out principles such as Encyclopedic axiomatic mergism. A snappier term would be welcome. But judging by tensors, boolean algebras, formal languages alone, there seem to be some general issues to cover:


 * Topic sentences start us off with definitions, not "ways to think about X";
 * Pedagogy is a valid area of discussion, but what X is cannot be determined by "in courses X is often introduced as";
 * Mergism should be taken as subordinate to summary style, in that proper structuring of subtopics in an area requires a central article, off which specialised articles hang, rather than a menu of articles;
 * Proponents of POV forks are really arguing for a longer menu, rather than properly applying the core principles of encyclopedia-building.


 * Whatever you make of my formulations, I do think recent discussion suggests that these ideas need to be put together in a coherent discussion. Charles Matthews (talk) 09:22, 18 September 2009 (UTC)


 * Well, concerning myself with the nature of "stuff" rather than mere terminological distinctions, or differences between similar treatments is one of the first lessons I've learned editing here. Some separate articles like boolean ring vs. boolean lattice or Presentation of a monoid vs. string rewriting system or abstract rewriting system vs. State transition system may sometimes be justified based on focus even if size alone isn't an issue, but even then connections need to be stated explicitly. Obscuring connections by narrowly writing articles from few/one source[s], like we witnessed in the logic articles at hand here, is bad and non-encyclopedic practice. A guideline should definitely help some confused newbies... Pcap  ping  09:49, 18 September 2009 (UTC)

Result

 * Result was delete; could someone change the 100+ references to formal language (logic) in articlespace back to formal language? I can't run AWB on this computer, as IE is comprimized.  — Arthur Rubin  (talk) 07:19, 25 September 2009 (UTC)


 * I was willing to fix some by hand, but "what links here" does not seem to work properly for that article, perhaps due to parentheses in the name. It lists over 500 articles here, and the few I checked don't even link to the deleted article. I'm confused... Pcap ping  10:32, 25 September 2009 (UTC)


 * Edit Template:logic first. I just now created a redirect to solve the immediate problem. If someone else removes the links, let me know and I'll delete the redirect again. &mdash; Carl (CBM · talk) 10:35, 25 September 2009 (UTC)
 * Done. That cut down the number to 51 articles that were linked with AWB during the AfD, and which I and CBM did not reverse right then. Pcap ping  10:58, 25 September 2009 (UTC)

metalogic = metamathematics
I managed to find a source that explicitly says this, see Talk:Metalogic. So, I'm proposing a merge of those articles. Pcap ping  09:36, 18 September 2009 (UTC)

Rayleigh's method of dimensional analysis
Rayleigh's method of dimensional analysis could use a couple minutes of work to clean it up. I know 0 about the subject and have not been able to get a good enough grasp of it through google. Thanks for any assistance.Cptnono (talk) 02:53, 25 September 2009 (UTC)
 * Isn't it all covered under dimensional analysis? I'd have thought this was a candidate for deletion. Why particularly the 'Rayleigh' in the title? And by the way shouldn't the Rayleigh number be mentioned in the dimensional analysis article as one of the most famous uses? Dmcq (talk) 06:45, 25 September 2009 (UTC)

I've cleaned it up. I put some proper initial context words in the first sentence, added some links from the article to some others, brought the style (mostly) into line with Wikipedia conventions, and added some links to the article from other articles. Michael Hardy (talk) 19:56, 25 September 2009 (UTC)
 * To Dmcq: ??? :)
 * To M Hardy, thanks for the quick clean up.Cptnono (talk) 20:47, 25 September 2009 (UTC)

The article in its present form is not all that clear. I don't know whether it's really dealing with something that doesn't belong in the main dimensional analysis article. Michael Hardy (talk) 16:58, 26 September 2009 (UTC)

Hannan Binth Hashim
See Hannan Binth Hashim. Hoax? Non-notable instance of some journalist being stupid? Michael Hardy (talk) 19:08, 25 September 2009 (UTC)
 * From a quick read, it looks like both - a non-notable instance of a journalist taking in a host. I'll ProD it. --Paul Carpenter (talk) 19:54, 25 September 2009 (UTC)

Collaboration of the month - inactive?
I was thinking of ways to get myself more involved in Wikipedia again - specifically the maths topics. I was surpised to find that the Collaboration of the Month page was marked as inactive. Would there be interest in reviving it? --Paul Carpenter (talk) 16:26, 25 September 2009 (UTC)


 * Yes. But in the past there has (apparently) been a mismatch between the nominations of topics, and topics on which people have wanted to work. Something structural probably needs to be done to alleviate the passive-voice and wishlist aspects of simply having a popularity contest. Charles Matthews (talk) 20:19, 25 September 2009 (UTC)


 * I don't think there are enough active editors of mathematics articles to make Collaboration of the month worthwhile. People just work on articles they want to when they can. Charvest (talk) 20:22, 25 September 2009 (UTC)


 * Fair enough, I'll be watching the page in-case it fires up again. Maybe I'll take a look at the structure of it all sometime. Thanks. --Paul Carpenter (talk) 10:17, 27 September 2009 (UTC)

d'Alembert's formula
I believe there is a non-sense in the derivation of the formulae: umu.eta = u(x + ct)*(x - ct) = u(x2 - (ct)2) which is NOT the same as utt - c2uxx —Preceding unsigned comment added by 93.3.252.129   (talk • contribs)  27 September 2009
 * I've put this comment back and I'm not sure why you deleted it. Thanks for bringing this fairly messy article to our attention. I'm going to take a look at it. If you want to retract your comments that's all well and good but please avoid removing content from talk pages while it's still relevant.
 * I repeat my invitation for you to join Wikipedia properly.
 * --Paul Carpenter (talk) 15:03, 27 September 2009 (UTC)