Wikipedia talk:WikiProject Mathematics/Archive/2012/Mar

From d to d

An IP has been straightening out all the italic "d"s in dy/dx at fundamental theorem of calculus. I had the impression the consensus in an earlier discussion was otherwise. Tkuvho (talk) 14:04, 21 February 2012 (UTC)

I have undone those changes, in addition to making many other typographical fixes. Ozob (talk) 21:46, 21 February 2012 (UTC)

I don't think it was actually a consensus but more of an agreement that in general people shouldn't change whatever is being used in an article, nothing was put in MOSMATH about it though.--RDBury (talk) 23:15, 22 February 2012 (UTC)

This seems a sensible thing to at least make a note about in WP:MOSMATH. If there is general agreement about what to say. Perhaps under WP:MOSMATH#Notational conventions a bullet stating that since both notations are used in the literature, consistent use of either d or d within an article should not be modified? Opinions? — Quondum^☏✎ 08:27, 23 February 2012 (UTC)

Sounds like a good idea to me. Leonxlin (talk) 04:59, 28 February 2012 (UTC)

Agree. Paul August ☎ 13:25, 1 March 2012 (UTC)

False (logic), contradiction and principle of explosion

A help needed from experts in logic. I recently wrote a small article about the false (I complained about its absence since 2009, and nobody else made it), but I probably failed to explain a subtle difference between false and contradiction. We all understand the difference between logical truth and a theorem, and there should be the same on the dark side of the logic. So, it would be nice to clarify the terminology in "contradiction" and "principle of explosion". What is contradiction: an occurrence or use of the false in proofs? A proof-theoretical interpretation of the false distinguished for historical reasons from, say, truth-functional one? And what terminology ("false", "contradiction", both as synonyms, or distinction) to use in "principle of explosion"? Incnis Mrsi (talk) 18:37, 26 February 2012 (UTC)

I don't really think people understand the relationship between logical truth and theorems at all. All we can agree on with consensus is that they "are related." You should take a look at the history and talk pages of rule of inference, theorem, and logical truth. I recently made a description at Rules of inference,Theorems, and Arguments to address one of the issues which you bring up. In many cases we have popularly used or named theorems which are also rules of inference, and also argument forms, etcetera. So in some cases we have one and not the other. It's not consistent. Greg Bard (talk) 19:25, 26 February 2012 (UTC)

I think one of the main problems lies with the part about contradiction, especially this sentence: "Contradiction means that a statement is proven to be false". In my opinion, this is not correct. A contradiction is a statement that is false for any possible evaluation. That does not necessarily mean the same as "proven to be false". Take for example the sentence "People watch TV" opposed to "People watch TV and People don't watch TV"; the first one can be proven false, but it is not necessarily always false. However, the second sentence is always false because it is an inherent contradiction. So basically what I'm trying to say is that there is a difference between proven something to be false and having something that is always false (a contradiction). I think this contributes in great part to the confusion, as well as the sentences surrounding the one I mentioned. Other than that, I agree with the commenter above that the relationship between logical truth and theorems is probably not clear to everyone. Mythio (talk) 19:31, 26 February 2012 (UTC)

Some people try to convince me what the contradiction is not. But what the hell it is, indeed? Look at the history of False (logic) (edit | talk | history | links | watch | logs) and to its talk page. Initially it was a redirect to Logic. In mid-2009 I changed it to "contradiction" because I felt that it is the closest target of all articles. After a half year it was reverted; more exactly, a user changed it again to Logic, may be independently of the past history. Then I complained to WikiProject Logic about a bad redirect, to no avail. And now, when there is already a small article, no one can explain why "contradiction" was not a possible target for a redirect! Incnis Mrsi (talk) 20:31, 26 February 2012 (UTC)

Simply put a contradiction is a statement that is false in all possible interpretations. False is not the same as a contradiction, since something can be false in some cases and not in all. With this in mind, I hope its clearer why, imo, a redirect to contradiction is not the correct course of action. A possible solution could be Hans Adlers proposal in here. On another note, Its not clear to me what your aiming for with this article when reading your reply; what are you trying to make this article about? For instance the sentence you start with is "false is the opposite to logical truth". The argument could be made that this is incorrect, because reading the definition of logical truth on its page, the opposite would be a contradiction (and hence the article already exists). Could you clarify a bit further what you understand to be the concept of false perhaps? Mythio (talk) 20:56, 26 February 2012 (UTC)

I do not take Hans Adler's proposal seriously first because he eventually did not even attempt anything, and second, because he argued for a merger of all possible targets to Truth value, which is "not the correct course of action" for reasons mentioned in this discussion and also in the discussion just above (I had not so strong feeling yet in 2009). IMHO the logical truth article is a bit confusing in an ambiguity and lack of distinction between (the abstract) logical truth and a property of a statement to be necessary true. It explains in details, what means "necessary", but does not explain, what means "true". What I understand to be the concept of false? First, a proposition which is a priori opposite to the truth, such as "⊥" nullary connective in those versions of propositional calculus which have it. This is not exactly symmetric to "⊤", if we use only material conditional, conjunction and disjunction. We easily can (re)define "⊤" as p→p but cannot define "⊥" if we have not a negation yet. Second, the false as a truth value, which is different from the truth, and which is always assigned to "⊥". Incnis Mrsi (talk) 22:23, 26 February 2012 (UTC)

Perhaps something should be said about how classical logic can get away with treating all non-truths as equivalent to each other? JRSpriggs (talk) 10:27, 27 February 2012 (UTC)

I think the best answer is simply to delete false (logic), given that it's ambiguous between the truth value "false" and the notion of "logical falsehood" (that is, logically necessary falsehood, which is very close to if not the same as contradiction). If it were actually a useful link, I suppose you could set up a disambig page, but I do not understand what is the rationale for having such a link at all. False (logic) is an unlikely search term and a bad internal link; having it around seems to do nothing but encourage overlinking. There is rarely if ever going to be any good reason to link the word false at all. --Trovatore (talk) 03:39, 29 February 2012 (UTC)

I would strongly support keeping the article, which is linked from the dab page False. It logically covers the truth value and "⊥". There is plenty of material around to improve the article with. -- 202.124.75.236 (talk) 12:26, 1 March 2012 (UTC)

I support keeping the article. There is tautology which is the negation of a contradiction; there is theorem, but no nontheorem (which is not the same as the negation of a theorem, and could easily be an article of its own). I don't see why we can't have logical truth and logical falsehood. However False (logic) should be about the truth value, not about contradiction, and not about logical falsehood which are types of sentence or proposition. Greg Bard (talk) 21:35, 1 March 2012 (UTC)

Serif/sans-serif for math expressions in running text

I could put this on the talk page of trivial module but we all seem to be here and it might come up in the other articles, so here goes: Quondam's latest change involved using the {{math}} template to boldface some zeroes. Personally I do not feel this is an improvement. (I concede that my feeling on this may be influenced by the fact that I loathe that template in general, mostly for its imposition of serif fonts in running sans-serif text rather than for the boldface). I would prefer to remove that part of Quondam's edit, while keeping the copyedits. Thoughts? --Trovatore (talk) 19:07, 27 February 2012 (UTC)

AFAIK the template does not bold anything. The intent is consistency of the font of the symbols (including numerals) throughout the text (as distinct from stand-alone lines) within each article. This is a reasonable forum to discuss the idea of a more uniform serif/sans-serif choice or guideline for symbols/math globally across math articles. Replacing {{math}} with {{nowrap}} is easy if consensus is for a sans-serif font. I find the serif font aids interpretation by visually distinguishing math and text without the formatting problems of the <math> tags, but I'll be happy to go with consensus. — Quondum^☏✎ 14:54, 28 February 2012 (UTC)

I prefer serif to sans-serif for math expressions, so I am in favor of {{math}} but at this point I think that changing over to it is somewhat of a waste of effort. What we should be doing instead is pushing harder to get MathJax support made more standard in Wikipedia, relative to its current experimental status, and then using <math>. —David Eppstein (talk) 17:14, 28 February 2012 (UTC)

In isolation serif is better. It's the mixture of serif with sans-serif that I object to. If {{math}} continues with serif, then it should be used only displayed, the same as <math>. --Trovatore (talk) 19:17, 28 February 2012 (UTC)

It is just imitating what <math> does with TeX. The target is to use Tex eventually but at the moment the results can be ghastly inline. If you're really worried by this then you should stick in some private css that ensures {{math}} uses a non-serif font. In the long term you'll need to ensure that Mathjax has some option to do the same sort of thing because many more things will use TeX when it works inline okay. Dmcq (talk) 00:08, 29 February 2012 (UTC)

In my view one of the things that's "ghastly" about inline TeX in the current implementation is the serif/sans mixing. It's not as bad as the mixed sizes, but it's still pretty bad. MathJax is still useful even if we use it only displayed, because it just renders so much better than PNGs. --Trovatore (talk) 00:55, 29 February 2012 (UTC)

I've just started running with MathJax enabled and I'm very happy with its inline capabilities though I'll be using the math template for a while because of problems with the current PNGs and how long I know it will b before it is generally supported. You really do need to have a way of setting the font selected by MathJax and the math template if you want to avoid serif fonts inline. What you want will never be the general default so you'll need an option. Dmcq (talk) 01:12, 29 February 2012 (UTC)

It's not for me. Mixing serif and sans looks bad. We shouldn't do it, for anyone. --Trovatore (talk) 01:16, 29 February 2012 (UTC)

I happen to like it mixed like that. It makes the math variables more clearly variables rather than one-letter words. —David Eppstein (talk) 02:10, 29 February 2012 (UTC)

You know, that might be OK if the typefaces were somehow designed together, like a serif version and a sans version of the same typeface. But I have never actually heard of such a font, and in my estimation the ones that actually render look awkwardly jammed together. The overall effect is something like one of those stereotypical ransom notes with letters cut out of magazines — not so extreme, of course, but along those lines. To me it comes across as distracting and unprofessional.

While there are advantages of serif fonts in mathematics, I think it's worth noting that the Beamer class uses sans, and this has not impeded its widespread adoption. --Trovatore (talk) 02:36, 29 February 2012 (UTC)

Before the debate goes too far, I think it should be noted that this topic has been covered before (e.g. here), and it seems clear to me that consensus on this question will not emerge here. In particular, there is enough support for inline {{math}} use that no recommendation to the contrary will be accepted. I think the inadequacy of the fonts in the context of math and browsers should be addressed as a broader WP issue, not at the template level. So I think the only principles that will emerge are already in place:

• The original writers of an article are free to set their own style
• One may fix inconsistencies of format style in individual articles
• Don't switch the style of an entire article without consensus.

— Quondum^☏✎ 06:46, 29 February 2012 (UTC)

There are a bunch of people who really don't like it when two fonts that aren't extremely similar are used together. Some cry out in pain if they see a poster just using comic sans. For those people there needs to be facilities for changing the font in the math template, in MathML and when MathJax gets used. They are not going to get he default changed, the Tex font is accepted in professional maths books, and in the future there will be even more of it in the running text, so they have to just accept that and move on to what can be done to fix the situation as far as they're concerned. Dmcq (talk) 09:15, 29 February 2012 (UTC)

No, you're quite wrong here. Of course the TeX font is accepted in professional math books — they're written in that font! So it looks fine. It looks horrible when mixed with sans. Having the mixture as a default is unacceptable. --Trovatore (talk) 17:48, 29 February 2012 (UTC)

Do you or do you not accept that you're talking to the wrong people and the math template is the wrong target for doing anything about fixing what you want fixed? That in fact the math template is the easiest one for you to fix for your own use by setting your private css but if you don't engage with MathJax any effort with the math template will eventually be totally wasted? Dmcq (talk) 18:39, 29 February 2012 (UTC)

How am I talking to the wrong people? WikiProject Math is where standards for mathematical articles get discussed. My private use is entirely irrelevant here — I'm arguing to improve the professionalism of the display of our articles. --Trovatore (talk) 20:11, 29 February 2012 (UTC)

The people here have very little control over technical issues on Wikipedia such as the use of MathJax as a default. WP:VPT may be a better choice for that. —David Eppstein (talk) 20:32, 29 February 2012 (UTC)

But what we can discuss is whether it ought to be used inline. --Trovatore (talk) 20:34, 29 February 2012 (UTC)

You're not seriously suggesting we try banning all inline maths? Dmcq (talk) 22:16, 29 February 2012 (UTC)

Not a hard ban, no. But I am saying that if MathJax uses a distractingly different font from the rest of the article, we should try hard to avoid inline uses of it where reasonably feasible, and HTML may still be better than MathJax for unavoidable inlines. --Trovatore (talk) 22:46, 29 February 2012 (UTC)

I think we should avoid using the {{math}} template (and its cousins like {{var}}, etc.) This makes the code more difficult to edit by hand, and it is looking very likely that MathJax will give a much better solution very soon. I think it's time we start to deprecate html (and these funny templates). Sławomir Biały (talk) 11:48, 29 February 2012 (UTC)

The normal Tex to html or png converter could have been fixed ages ago to do most of the things {{math}} patches over like being able to put ≥ in the inline text without getting some png messing it up. $a\geq 0$ or a ≥ 0 anybody? How soon is soon when we couldn'r fix something like that in years? Dmcq (talk) 14:05, 29 February 2012 (UTC)

What might be worth developing in time for Mathjax is a special tool which would search for {{math}} templates and automate converting them to <math> format. That way we needn't deprecate anything for the moment and do a better job both now and eventually. Dmcq (talk) 14:13, 29 February 2012 (UTC)

Just to clear some illusions about MathJax... It too wil use a serif font, even when used inline. It uses webfonts for rendering, so it has the potential to clash with whatever font a user has set for running text. With regard to matching fonts, I know of only one that matches serif and sans-serif in design and size: DejaVu. I you already use DejaVu Sans as the default font, use this CSS to display formulae in {{math}} in a matching serif:

span.texhtml {
  font-family: 'DejaVu Serif', serif;
  font-size: 100%;
}

— Edokter (talk) — 16:47, 29 February 2012 (UTC)

See e.g. this edit for why sans-serif inline math is bad. If we can't distinguish the capital vowel I from the lowercase consonent l from the digit 1 from the vertical bar |, we have a problem. (In the font I use, the digit is clearly distinguishable from the other three, but obviously even that's not true for everyone.) —David Eppstein (talk) 21:47, 1 March 2012 (UTC)

Honestly I like serif better than sans in general. I wish Wikipedia as a whole were written in a serif font (see e.g. a recent discussion at talk:Iago). But the "ransom note" effect is real, and distracting, and detracts from our image of professionalism. The workaround for the issue you bring up is to strain to avoid using those letters as variables. --Trovatore (talk) 21:54, 1 March 2012 (UTC)

I think there are reasons that sans-serif tends to work better with screens than on paper which are very different media, something to do with interlacing and resolutions. MathJax does have some support for sans-serif fonts, but its limited to only the standard letter and numbers. If you look at many of the other symbols in maths $\sum \int \theta$ the fonts used have more in common with serif fonts: varying line widths and little serifs. Going completely over to sans wound end up with a very mixed typography within equations. Better to mix sans text with serif maths, at least those are used for completely different things.--Salix (talk): 01:31, 2 March 2012 (UTC)

I can buy that it may not be workable to make MathJax do sans. But in that case I think MathJax is not really a solution to the inline problem (so basically we still don't have, and may never have, a solution to the inline problem). And if that is the case, then we should continue to avoid inline mathematics to the extent feasible. --Trovatore (talk) 02:11, 2 March 2012 (UTC)

I'm pretty certain there's some straightforward way of getting the normal running text in Wikipedia to use any font you like so you could use a serif font for that if you like. I'm sure someone on the help desk could do that fairly easily. That would probably be quite an easy option to put in the appearance preferences for general use and might be quite popular. Dmcq (talk) 09:40, 2 March 2012 (UTC)

Please quit talking about what I would like for my personal use. That's entirely beside the point. My objection is to a problem that detracts from the professionalism of the appearance of our articles. --Trovatore (talk) 22:18, 2 March 2012 (UTC)

I think this suggests that some thought should be given to coordinating the default fonts (perhaps only for maths articles?) for the main text, {{math}}, <math> and MathJax, much as is done in professional texts. This would mean some override of the browser's default font choice for serif and sans-serif, and carries with it the pitfall that these may not be installed fonts for a large enough base. If serif is to be avoided due to display problems, and widely installed suitable matched serif and sans-serif fonts cannot be found, this problem is probably going to be around for longer than we'd like. — Quondum^☏✎ 13:12, 2 March 2012 (UTC)

It will only be people who are worried by this sort of thing who would set a preference and we can have a help page link in the preferences page we direct them to show them how to download fonts if they have problems. Fonts on the web have a good fallback facility so the main problem is if a font is used that has bad looking characters in it. Dmcq (talk) 23:27, 2 March 2012 (UTC)

The problem is a problem for everybody, not just for people who set preferences. I am completely opposed to shunting it off into preferences. --Trovatore (talk) 23:35, 2 March 2012 (UTC)

I concur with Travatore – in principle. But until we can identify suitable fonts for setting as the Wikipedia defaults with most browsers and typically available fonts, this does not seem achievable. Is there a suitable set of fonts typically available with all browsers that is suited? (DejaVu is not generally installed, and has other drawbacks IMO.) Alternately, is it necessary/desirable to remain with sans-serif in the body of the article, or could we switch to serif (for maths articles)? I personally like the serif/sans-serif contrast between math and text, but jarring discontinuity as would occur with badly mismatched fonts should preferably not occur in the typical default setup. — Quondum^☏✎ 07:49, 3 March 2012 (UTC)

See WP:Typography. There really is not much choice. When I created {{math}}, I took into account what most users would be seeing on screen, with default fonts installed, at default sizes, and tried to match up as best I can. It is impossible to take every deviation into account, presicely because teh lack of standards in web typography. What prevailed in my mind is the legibility of math, which suffers badly in a sans-serif font. — Edokter (talk) — 10:15, 3 March 2012 (UTC)

And thanks very much for that. I see the math template as having done a very good job of patching over some problems with the current TeX processing. It is irrelevant to the future though now that MathJax is fairly imminent. The question is about the differences between MathJax and the normal running text and I'm pretty certain I like the distinction whatever if someone else calls it unprofessional. As you say serif is preferred for maths and it matters more for maths as a wide range of symbols are used, they are not really letters π is just looks different from π as a maths symbol. We're not going to force the rest of the Wikipedia community to adopt serif fonts either. Typography is a matter of preference and such choices should be in preferences. Also it might be worth asking MathJax to allow preferences for fonts in their work too. If somebody wants Wikipedia in Comic Sans let them I say.Dmcq (talk) 11:09, 3 March 2012 (UTC)

What is a product?

A mathematician may say "I have proved that the following products are both equal to 5:

$\prod _{i\in A}x_{i},$

$\prod _{j=1}^{10^{90}}y_{j}.$

If they're both equal to the same number, and a product is the value that results from multiplying, and these are both equal to 5, then these are not two products, but one. Our article titled product (mathematics) says:

a product is the result of multiplying, or an expression that identifies factors to be multiplied.

The latter usage occurs in such expressions as the title of a book called Table of Integrals, Series, and Products or articles titled "Proof that a Product Considered by Schriemann Diverges to Zero". Yet it seems many sources say only that a product is the value of a multiplication operation. A non-logged-in user has been arguing on my talk page that we should therefore omit the "expression" characterization from the definition given in the article.

Opinions of this proposal? Michael Hardy (talk) 16:24, 1 March 2012 (UTC)

The duality of the meanings of terms such as "product" (and this obviously is not limited to product, but includes limit, etc) is one of the most active areas in math education. Certainly we should keep both meanings on the product page and avoid excessive formalism at all cost. Tkuvho (talk) 16:30, 1 March 2012 (UTC)

This is the usual intensional vs. extensional equality issue that appears everywhere. Is $\lim _{x\to 0}x/x$ the same as $\lim _{x\to 5}1$? Is $2\cdot 15$ the same product as $6\cdot 5$? The same issue arises with derivatives and integrals that have equal values, and with whether two groups are the same if they are isomorphic, and with many other objects. The real point is that when mathematicians say "equal" or "same" they can mean many things depending on context. Regarding products specifically, the current language looks good: sometimes the product is identified with its value, some time it is not. — Carl (CBM · talk) 16:31, 1 March 2012 (UTC)

One of the most active areas in maths education? Sheesh. So someone with maths skills has to both want and like to teach children but also be willing and able to put up with this sort of stuff being thrust at them as being the way to teach maths? Explains a few things. Dmcq (talk) 17:07, 1 March 2012 (UTC)

@Dmcq : I doubt that he was proposing to actually tell children about this stuff. Michael Hardy (talk) 22:52, 2 March 2012 (UTC)

Meriam Webster has both meanings: http://www.merriam-webster.com/dictionary/product . -- Jitse Niesen (talk) 17:14, 1 March 2012 (UTC)

Surely the non-ultra-formalist way of saying this would be "...are two expressions with the same value", or "two different formulations for what can be regarded as the same object"? -- The Anome (talk) 17:18, 1 March 2012 (UTC)

Both usages are important. It is counterproductive to favor one over the other. Rschwieb (talk) 17:45, 1 March 2012 (UTC)

This is a special case of the problem of making the proper distinction between an expression, a function, the value of a function for a given value of its argument and the evaluation of an expression. I would say, for the example given by Michal Hardy, "I have proved that the two following expressions both evaluate to 5". In other words, a product is an expression whose leading operator is a multiplication, and saying that two products are equal is an abuse of language and a shortcut for "when evaluating the functions and operators appearing in the two expressions, we get the same result". Thus I would suggest for the article product (mathematics):

"A product is an expression whose leftmost operator is a multiplication. By abuse of language product denotes also the result of the evaluation of the operations appearing in such an expression"

All of this is not WP:OR. I may not cite any math book for this, but it is the basis for any computerization of the mathematics and appears in some way in the manuals and tutorials of every computer algebra system, like Maple (software).

D.Lazard (talk) 18:42, 1 March 2012 (UTC)

Seconding Tkuvho and Rschwieb. D.Lazard, your proposed alternative, whatever its advantages, will do much to make the article unimpenetrable for many readers. (One possible confusion that it will create: it appears to assert that $x \cdot y + z$ is a product.) The current wording is clear, correct, easy to understand, and should be kept as-is. --Joel B. Lewis (talk) 19:37, 1 March 2012 (UTC)

"Unimpenetrable"? Maybe impenetrable? Rschwieb (talk) 20:13, 1 March 2012 (UTC)

Isn't it about the mathematical counterpart of "Sense and reference"? Boris Tsirelson (talk) 19:44, 1 March 2012 (UTC)

I agree that my formulation is not convenient for the level of the readers and that the current wording is convenient. About "leftmost" : "outmost" or "top" or something like that would be better. But the point is that we have to have this kind of things in mind when looking for the best formulation. Another example of today: The first sentence of discriminant was "the discriminant of a polynomial is an expression ..." which is incorrect. I have replaced this by "the discriminant of a polynomial is an element of the ring generated by its coefficients", which is correct but has been reverted as too technical. After discussing with the author of the reversion, the formulation is now "the resultant of a polynomial is a function of its coefficients", which is sufficiently correct (it is not a function, but the value of a function), easy to understand and contents more information that the previouus formulation. D.Lazard (talk) 20:47, 1 March 2012 (UTC)

I have to agree that that way of using the word "leftmost" will be---um------"unimpenetrable" to almost everyone. I understood it here only because of the context of this present discussion. And I think other aspects of that proposed opening sentence are objectionable on grounds almost as cogent as that. Michael Hardy (talk) 22:55, 2 March 2012 (UTC)

Hello to all,

I am that non-logged-in user (but I learned how to log-in now!) who asked the question from Michael.

First let talk about the difference between multiplication and product in Natural numbers (ℕ). Multiplication in ℕis a binary operation which is a function from ℕ×ℕ to ℕ, so it gets two Natural numbers as input and the result or output of this function is another Natural number. The mathematical symbol for multiplication function is ×, so in function notation we can write: ×(3,4)= 12. In infix notation we can put the operation (here ×) between two operands (here factors) and use the notation 3×4=12. But we know a function is a set of single valued ordered pairs. In this point of view multiplication is a set like ×={((1,1), 1), ((1,2), 2), …} and one of its elements is ((3,4), 12) and the output or value or result 12 associated with the pair (3,4).

By the present definition, product refers just to the result (and result can be a number or an expression like Meriam Webster but still refers just to the result). The difference between product and multiplication is like as the difference between element and set.

There is another close example. When you say the function f(x)=x² actually you omit two important parts, domain and codomain. This function is not one-to-one from ℝ toℝ but it is one-to-one from ℕ to ℕ, so you can omit the details if there is no ambiguity.

I agree both usages of the product are important, so it seems we need to change the definition of the product, but how? By inserting in Wikipedia? I think this is not a good idea because a divergence will appear between Wikipedia and other references. It is better to think for a better way. — Preceding unsigned comment added by Sohrab.Rahbar (talk • contribs) 03:09, 3 March 2012 (UTC)

I would find this more concerning if, in my entire life before now, I had encountered a single person who pressed the distinction. IMO, pressing the distinction is more confusing than not. Rschwieb (talk) 15:17, 3 March 2012 (UTC)

Yes. To repeat the key point (but with fewer strange coinages/typos than last time): there may be some technical subtlety in the rigorous definition of a product, but this subtlety has no business being brought up in the introduction of the article product (mathematics), which should be as widely accessible as possible. --Joel B. Lewis (talk) 01:22, 4 March 2012 (UTC)

Mathematical formulas in the lead section of an article

WP:MOSINTRO used to say "Mathematical equations and formulas should not be used except in mathematics articles." So in that state it wasn't really relevant to this project, since it was only about other articles. But in this edit a month ago, an editor (intending to broaden it to allow formulas in technical but non-mathematical articles such as Joule) changed it to instead say "Mathematical equations and formulas should only be used when absolutely necessary." Today this has led to an editor on golden ratio attempting to take all the math out of the lead section there, because math articles are no longer exempt and he didn't see why it was necessary. So anyway, this is just a heads up: discussion on the issue has started at Talk:Golden ratio for the specific editing concerns there, and Wikipedia talk:Manual of Style/Lead section for what the MOS should actually say about this. —David Eppstein (talk) 05:30, 2 March 2012 (UTC)

"in that state it wasn't really relevant to this project, since it was only about other articles"

Is that true? Are mathematical expressions in non-mathematics articles outside the scope of this project? Michael Hardy (talk) 03:18, 4 March 2012 (UTC)

List(s) of mathematics articles/topics

There was a request to rearrange the redirect Lists of mathematics articles. Right now it points at Lists of mathematics topics but the request was to use Lists of mathematics articles to hold List of mathematics articles instead. I opened a thread here to discuss the best way to handle those confusing names. — Carl (CBM · talk) 17:51, 4 March 2012 (UTC)

Wikipedia:Foundations of mathematics

I wrote an essay how to improve standards for articles about mathematical logic. I hope, some day it will become an official guideline. Thanks for your attention. Incnis Mrsi (talk) 07:23, 5 March 2012 (UTC)

Projective resolutions and free resolutions

Projective resolutions and free resolutions is a new article. Projective resolution and Free resolution redirect elsewhere. Should the redirects be altered or should some articles get merged or what? No other articles linked to the new article until a moment ago when I added a cross-reference. If it is not merged into other articles, then some things should link to it. Michael Hardy (talk) 17:31, 17 February 2012 (UTC)

Both redirects are to Projective module#Projective resolution. Thus the new article is useful. I'll redirect Projective resolution and Free resolution to the new article and move the new article to Projective resolution and free resolution. This will add a lot of links to the new article. D.Lazard (talk) 17:52, 17 February 2012 (UTC)

I like the idea of having pages dedicated to homological resolutions, but this page title leaves us in an awkward situation of where to place the flat and injective resolutions. Is four names too many for a page title? Rschwieb (talk) 18:48, 17 February 2012 (UTC)

For the moment Flat resolution and Injective resolution link to sections in Flat module and Injective module. By the way Flat module has a red link to Resolution of a module. I suggest, first, to add a "see also" section in Projective resolution, linked to Flat resolution and Injective resolution. A second step could be to expand Projective resolution and free resolution in order to move it to Resolution of a module. D.Lazard (talk) 20:14, 17 February 2012 (UTC)

I think a good name would be Resolution (homological algebra). This should cover projective (and thus free) resolutions, injective, flabby, flat, acyclic resolutions. The title "Projective resolution and free resolution" is too long and focussing on just these two resolutions is also awkward from a content-point of view. Jakob.scholbach (talk) 15:01, 21 February 2012 (UTC)

I agree that "Projective resolution and free resolution" is too long. But I am not sure that Resolution (homological algebra) is better than Resolution of a module. In fact, in ring and module theory, resolutions are frequently used independently of the consideration of any homology. This occurs especially in the computational theory of polynomial ideals, where the degrees which occurs in a minimal free resolution (Castelnuovo-Mumford regularity) are strongly related to the complexity of computing a Gröbner basis and to the Hilbert series. Most people interested in these questions do not know nothing of homological algebra and the name Resolution (homological algebra) could lead them to miss the page which is relevant to them. In any case, whichever name is chosen, the other should be a redirect. D.Lazard (talk) 16:00, 21 February 2012 (UTC)

I believe that Resolution of a module would be the right scope for this situation. The full blown categorical concept would probably best be tackled in its own article. Rschwieb (talk) 21:30, 21 February 2012 (UTC)

What about resolution (algebra)? I am concerned that resolution of a module is too restrictive a title, as it does not include resolutions in general abelian categories (such as categories of sheaves or categories of complexes of modules). Surely we need an article about those. Ozob (talk) 21:38, 21 February 2012 (UTC)

Well, that's a surprise. Resolution (algebra) already exists and is about just this topic. Ozob (talk) 21:40, 21 February 2012 (UTC)

Good catch, I suppose that'll be a better starting point for this material! Rschwieb (talk) 00:49, 22 February 2012 (UTC)

(unindent) I have tried my hand at resolution (algebra)--improve it if you can! Jakob.scholbach (talk) 14:10, 22 February 2012 (UTC)

Resolution (algebra) is looking pretty good. Earlier I sorted some redirects for consistency and weeded out a few circular redirects caused by the recent activity. (The resolution pages all point toward resolution, the dimension pages point toward the correct sections in injective, projective, and flat articles.) Rschwieb (talk) 02:54, 23 February 2012 (UTC)

One more thing: the article mentions projective resolutions are unique up to chain homotopy. I would guess the same can be said for injective and flat resolutions, but I'm not familiar enough with the subject matter to verify. Is this the case? Thanks. Rschwieb (talk) 14:24, 23 February 2012 (UTC)

I am not sure, but, as far I remember, this uniqueness is a consequence of the fact that one may pass from a projective module to another one by a chain of operations consisting in adding (direct sum) a projective module or removing a direct factor. This is certainly not true for flat modules and probably not for injective modules (I am not familiar with them). D.Lazard (talk) 18:29, 23 February 2012 (UTC)

OK then the answer is at least not obvious. I'll leave it as it is until someone certain comes along. Rschwieb (talk) 21:25, 23 February 2012 (UTC)

I have just noted that resolution (algebra) contains another important class of resolutions, which generalizes all the other ones. I have tried to clarify the corresponding section which was not understandable, even with some background in homological algebra. I hope that the result is better and mathematically correct. D.Lazard (talk) 11:50, 5 March 2012 (UTC)

Factor theorem at AfD

Factor theorem is up for deletion.  --Lambiam 02:44, 4 March 2012 (UTC)

Well, guess who has moved from categorizing articles to proposing them for deletion? Sławomir Biały (talk) 02:58, 4 March 2012 (UTC)

Your point being? Brad7777 (talk) 08:12, 4 March 2012 (UTC)

WP:POINT. Please do not use AfD in this fashion. Use the Talk pages of articles in egregious cases. Deletion nominations of articles that are clearly encyclopedic is misuse of the system. It is putting a gun to the head of the community, saying "work on this because I'm telling you to". It takes effort away from other efforts to improve the site. We all have our priorities, and we should respect the rights of others not to jump to attention to deal with them. Charles Matthews (talk) 12:50, 4 March 2012 (UTC)

Not to mention, you might want to follow the earlier advice of this same project: focus on content for awhile before you use semi-automatic tools like Twinkle and HotCat to categorize pages (and now to take them to AfD, apparently). The community opinion seems to have had zero effect on your disruptive behavior. Sławomir Biały (talk) 13:42, 4 March 2012 (UTC)

No I will not change my focus. You should notice my projects are beyond the scope of WP:MATH and not controlled by this community. If you disagree with something that I have done from the perspective of your project, then I am happy to discuss it and adapt to it as long as it is not nihilistic. Comments like "Well, guess who has moved from categorizing articles to proposing them for deletion?" are only for one purpose. My behaviour has only been disruptive once you have resorted to WP:SOAPBOX. Please if I make any further mistakes, could you point out the specific problem like Charles Matthews has done? Thanks Brad7777 (talk) 16:59, 4 March 2012 (UTC)

The specific problem is that you are using automated tools to do thousands of edits, some of which are problematic. I can give many examples of specific edits that are a problem. But this is missing the point. Stop using the tools. You've shown repeatedly that you can't be trusted with them. Sławomir Biały (talk) 11:39, 5 March 2012 (UTC)

According to my edit counter; out of the 5946 edits I have done, only 134 have been deleted. However, I will stop using the tools on political grounds. Brad7777 (talk) 13:52, 5 March 2012 (UTC)

We have a large backlog of articles tagged as unsourced, as does WP in general. In this case, as with many of them, the content falls under WP:CK, at least for mathematicians, and the article was created back when standards for new articles were rarely enforced. For articles created now I'd say strict enforcement of notability requirements is needed, we certainly don't want to add more to the backlog, but for established articles it isn't reasonable to expect that people will be cleaning up unreferenced tag in a timely manner. In any case WP:BEFORE has guidelines on how to cut down on spurious nominations, though in my experience no matter how hard to try to follow it you stand a good chance of being criticized for not following it whenever you do an AfD.--RDBury (talk) 12:01, 4 March 2012 (UTC)

Brad, if you continue in this fashion you stand a large chance of being blocked. CRGreathouse (t | c) 03:39, 5 March 2012 (UTC)

George Boole

This is one of our more interesting articles relating to the history of mathematics. I have been working it over to sort material, and remove some of the more obvious misunderstandings from old text. There are a couple of minor queries left on the Talk page. It could easily be 50% bigger, and as usual more inline referencing is needed (quite important here because Boole has been praised for the wrong things in the past).

Boole was famous in his own time for differential equations. His stuff looks like D-modules to me; that line of attack traces back to Thomas Gaskin and a notorious Tripos question (not as celebrated as the one which set the Stokes theorem, but that might be historical injustice in a way). Without OR rearing its ugly head, it appears that a better job of explaining what Boole actually did would be possible on the basis of some recent research papers that are still behind paywalls. Drop me a note if you come up with anything. Charles Matthews (talk) 13:04, 4 March 2012 (UTC)

Hi Charles,

do you know Boole's inequality for (what is now called) the Hilbert Stieltjes transform? If you wish, I can send you a reference to one of the modern surveys in the (EST) evening.

Sasha (talk) 18:24, 4 March 2012 (UTC)

e.g. the introduction and Ch. 7 of this book of Cima, Matheson, and Ross, or the survey of the same authors. Sasha (talk) 03:30, 5 March 2012 (UTC)

Similar remarks in more detail: a) Boole's work in analysis, in particular, the 1857 paper JSTOR 108643, deserves to be mentioned. It contains several interesting things, perhaps it's worthwhile reading it (or is there a good secondary source)? b) One of the results in this paper of Boole is an identity (see page 26 in the review linked above) for the measure of the set where

$\sum a_{i}/(x-b_{i})>\lambda$

c) This identity and its generalisations play an important role in the modern theory of Stieltjes transform (see again p.26): it is an identity for singular measures (pure point measures are essentially covered by Boole's argument), and an inequality for arbitrary measures.

Best, Sasha (talk) 15:06, 5 March 2012 (UTC)

Two pages to glance at, and a question

1. Algebraic structure is now less of an abomination (I hope.) I cut way back on universal algebra detail, and several examples that didn't really seem important. If there is some representative structure that isn't mentioned, I hope someone brings it up on the talk page.
2. I came across Quantum differential calculus and tagged it as needing attention. I have the vague feeling that there was probably an article covering this material already under a different name, (but can't find such an article). Please let me know if you find this is the case.
3. I would also like to edit the algebraic structure template to have less things. For one thing, I think it's kind of silly to put commutative ring and ring with unity on it. The template is certainly never going to contain every single algebraic structure in wikipedia, so I was hoping to put just the most representative things on it. Please let me know if I'm crossing some line with any edits. Rschwieb (talk) 20:48, 5 March 2012 (UTC)

Algebraic structure template

In reply to question 3 above regarding {{algebraic structures}}:

If abelian group is on there, then commutative ring should be too. The study of commutative rings is a huge discipline, and I don't see anything silly about having a link to it in the template. Personally I'd rather see the template expanded to include Unique factorization domain and Principal ideal domain and Euclidean domain, then the chain of inclusions on those pages could be replaced by the template.

Ideally the template would have collapsible sections along the same lines as {{calculus}}. We could have one big division for types of rings, one for groups, one for modules (including vector spaces and Lie algebras), and one for magma, semigroup, monoid (not sure of a good collective name for those three). I don't have the necessary template super-powers to make this happen myself. Is anyone else game? Jowa fan (talk) 23:47, 5 March 2012 (UTC)

I like the idea for collapsable sections with important types underneath. The reason I think having "ring" and "commutative ring" and "ring with unity" (I guess I should have objected to abelian group too) is because it looks to me like "car", "red car", "green car" on the same list. However the collapse tab to put commutative ring etc underneath ring would certainly make me happy by getting them off equal footing. Everyone interested should drop by Template_talk:Algebraic_structures to discuss. Rschwieb (talk) 02:05, 6 March 2012 (UTC)

Losing "ring with unity" wouldn't bother me at all. On the other hand, (noncommutative) ring theorists and people studying commutative rings seem to be doing two quite different sorts of things, so I believe it's worth keeping "commutative ring". (Imagine a world in which red cars really did go faster. Then it would make sense to have both "car" and "red car".) Jowa fan (talk) 06:58, 6 March 2012 (UTC)

The placement of articles on fields of mathematics into Category:Fields of mathematics

There are many articles on fields of mathematics, examples include algebra, geometry etc. There also exists a category Fields of mathematics. This category at the moment contains a few selected eponymous categories aswell a few articles related to the term "fields of mathematics". The category Fields of mathematics is a set category, i.e a category named after a class so I think it would be logical to include all articles that fit this class, i.e all fields of mathematics like algebra, geometry etc. I have brought this idea up before but as I was a new editor I was not able to explain it. I hope those who saw my previous effort now understand what I mean. I think not only this logical, it is also very practical for a user-browser of Wikipedia, particularly those with interests across the scope of mathematics, who do not necessarily want to have to dig deep through the subcats. Of course, this should't be done without consesus, so views? Brad7777 (talk) 20:29, 28 February 2012 (UTC)

So you would like to move more field categories here? There are about 20 subcats now, but it seems like that might go way up depending on what you are aiming to include. Do you have a concrete list of additions to that category or at least an estimate on how many things would go in? Rschwieb (talk) 14:09, 1 March 2012 (UTC)

I mean adding the articles to this category. These would not be taken from their current categories, they would have just an additional category Category:Fields of mathematics. There is an estimate on Glossary of areas of mathematics. Brad7777 (talk) 17:53, 1 March 2012 (UTC)

Sorry, I knew you just meant adding but since I never mess with categories I might have misspoke. The glossary appears to have hundreds of items, but I don't know if they should all go in. It would certainly seem logical to have areas of mathematics categorized under Fields of mathematics. Will anyone else contribute their 2 cents? Rschwieb (talk) 20:19, 1 March 2012 (UTC)

There may be a couple that do not belong there (or the glossary). I think it is also worth noting that many of the terms do infact link to the same article. Brad7777 (talk) 18:06, 4 March 2012 (UTC)

Important— does anybody disagree with this idea? Brad7777 (talk) 18:06, 4 March 2012 (UTC)

Current state seem to be about fine. It does mean Category:Mathematics is quite clean, the isn't a real need for article like Geometry to be in this category as they can easily be found in the category of the same name. Only minor point is I don't think Category:Trigonometry needs to be this high up the tree. --Salix (talk): 19:32, 4 March 2012 (UTC)

I'm not sure how it would make any difference to Category:Mathematics either way? I meant articles such as geometry and trigonometry be placed into Category:Fields of mathematics mainly for the reasons I stated above, but also for the point you have just demonstrated — which is to disagree with the subcats of this category. If all articles were placed in c:fields of mathematics it would not be such a problem for people finding specific fields of mathematics. The fact that people have different views of the heterarchy of mathematical disciplines and the direct subcats of c:fields of mathematics are unavoidably arbitrary means this category will be quite dynamic in terms of its structure, making it difficult to determine where a article on a field of mathematics will be. (Not all fields have eponymous categories to further complicate things for the user). Brad7777 (talk) 20:01, 4 March 2012 (UTC)

It certainly sounds plausible to put major fields of mathematics under Fields of math, but the list at glossary of mathematics is far too large. A minimalist subset could be transferred, but hundreds of subfields would be doomed to be outside of this structure. Trying to include them would face us with the intractable problem of sorting intermixed disciplines. Can one even call trigonometry a field?! Rschwieb (talk) 16:19, 5 March 2012 (UTC)

I can see how sorting the intermixed disciplines would be a problem, would m theory, statistical mechanics, econometrics or mathematical sociology for example be included? I would be inclined not to include these, my distinction would be they could not be classed as pure mathematics, but the problem I see with this distinction then is do we include the article applied mathematics or fuzzy mathematics? I could be using the term field incorrectly however, as i am unsure of its actual definition? Brad7777 (talk) 13:16, 6 March 2012 (UTC)

We still need a short list of proposals of what fields you think should move. As I glance at it, quite a few of the broad fields are already there, and I can't immediately see what's missing. A good place to start would be to pick a subset of first level areas on Mathematics_Subject_Classification. I will suggest a few additions for comment: commutative algebra, algebraic geometry, field theory, category theory, universal algebra, differential equations, functional analysis, differential geometry, algebraic topology, probability theory, statistics, numerical analysis, information theory, mathematical physics, game theory. Rschwieb (talk) 14:22, 6 March 2012 (UTC)

Conic sections template

A new template, Template:Conic sections was recently added to the articles on conic sections. I'm not convinced this is an improvement and if not whether it can be made into one by tweaking the template. My main objection is that previously the lead images in Ellipse were an ellipse and a rather nice photo of Saturn, but now the lead image has all the conic sections, which makes it a bit unclear what the article is about, and Saturn has been pushed down "below the fold". Is it just me and if not what should be done?--RDBury (talk) 03:33, 5 March 2012 (UTC)

No, it's not just you. The graphic in the template is quite nice (although a little misleading in the hyperbola case), but the template as a whole doesn't add much, and I'd rather see the specific images for "ellipse" coming before the generic picture of conic sections. Jowa fan (talk) 04:14, 5 March 2012 (UTC)

I don't like images in navigation templates at all. Often they distract from the purpose of the template, which is navigation, instead they become more a "look at me" device dominating the pages they are on. Particular egregious examples are {{Groups}} with a large Rubiks cube. Why not just have it as plain navigation template like {{Calculus}}.--Salix (talk): 13:21, 5 March 2012 (UTC)

I like this new image better than that of Saturn, but I find the "no images in templates" viewpoint most persuasive. Rschwieb (talk) 15:58, 5 March 2012 (UTC)

Images work in some infoboxes, Template:Taxobox is a good example. But in that one the image is a parameter so what you're looking at is what the article is about. I'm thinking that for now a navbox approach would actually work better for conics.--RDBury (talk) 21:52, 5 March 2012 (UTC)

I created the template to try to help tie the conics together more and to get a more consistent feel between the articles on the conic sections. I thought adding a simple image made in the same style to the template for each section would help achieve this. Do you think that removing the sub-pictures would make it better? Also even if it doesn't work for the individual sections would it not still be good for the general conic section article?

Once I get some more time I would like to help rewrite the articles to make them more complementary. I think that a template of some sort would help in achieving this goal. Any thoughts?

Phancy Physicist (talk) 04:45, 7 March 2012 (UTC)

I think navigation templates work a lot better in a wide format at the bottom of the article rather than in a narrow format at the top of the article. The top of the article is supposed to be where you're learning what the article's subject is, and instead you get distracted by this big flashy box telling you all of the other things that it isn't. —David Eppstein (talk) 05:24, 7 March 2012 (UTC)

MathJax update

I'm making good progress on integrating MathJax into the Math extension and hope to make it available as an experimental option shortly (it'll definitely be on an experimental wiki very soon!). Currently there are some problems with Chrome and with our JavaScript debug mode which I hope to resolve. list of all bug dependencies

After that it should be mostly testing to make sure things work, and then we'll see if we need to make fixes to upstream MathJax or additional customizations (eg custom latex commands that might not be translated yet). --brion (talk) 20:44, 5 March 2012 (UTC)

Thanks very much for your hard work on this feature, which as you know is something many of us have wanted for a long time. —Mark Dominus (talk) 19:18, 7 March 2012 (UTC)

You are welcome. :> Nageh (talk) 19:45, 7 March 2012 (UTC)

mathJax progress

On this page on bugzilla.wikimedia.org, we find this comment from Brion Vibber:

Getting closer! MathJax, once enabled in the extension, now is available as a third rendering mode (beyond PNG and 'leave as tex'), so won't interfere with other things when turned on.

It can then be opted-in by anybody who wants to help try it out while we continue poking at things...

Michael Hardy (talk) 00:30, 6 March 2012 (UTC)

OK, I just tried to set my preferences, and I find:

• Always render PNG
• Leave it as TeX (for text browsers)

But I see no third option. Michael Hardy (talk) 00:41, 6 March 2012 (UTC)

for 'now' I would guess it means what ever version of MW gets that patch. It does say 'Target Milestone 1.20mwf deployment' so that will be the next version if all goes to plan, due heaven knows when given that we're only days into 1.19.--JohnBlackburne^words_deeds 00:49, 6 March 2012 (UTC)

Well, it says "now is available". Michael Hardy (talk) 00:55, 6 March 2012 (UTC)

Available in the source code, not deployed. Nageh (talk) 01:00, 6 March 2012 (UTC)

And I just checked the test wiki and it's not there yet (if you have universal login it works there too so no need to register). That is probably the place to go to try it out first.--JohnBlackburne^words_deeds 01:14, 6 March 2012 (UTC)

My impression is that the English Wikipedia is usually the last or among the last to get the benefit of any changes to the mediawiki code, because we're so big and they want to find the bugs in smaller wikis first. —David Eppstein (talk) 02:05, 6 March 2012 (UTC)

The code needs a quick review before deployment to the 1.19 wikis; I think you guys are probably our best testers for math stuff so English Wikipedia will certainly be among those that get it soon. :) --brion (talk) 21:06, 7 March 2012 (UTC)

Quick review:

1. In wiki2jax.js, "\displaystyle" does not need curly braces as it does not take a parameter.
2. In ext.math.mathjax.enabler.js, the function call to TEX.Parse.Augment() can be removed in its entirety as MathJax 2.0 includes support for specifying the line spacing in newlines.
3. I assume you have uploaded also the output HTML-CSS jax's STIX font directory. In that case you should include "STIX" as one of the "availableFonts".
4. In texvc.js, quick-and-dirty support for color is not needed anymore as MathJax 2.0 includes an extension for the color command. See this diff.
5. In TeX-AMS-texvc_HTML.js, if you remove the hackish color support from above, you must include "color.js" as one of the preloaded "TeX" extensions since otherwise the \color macro will be interpreted wrongly (MathJax 1.0-style instead of TeX-style). Also, you must include "cancel.js", which will not be loaded automatically.

Cheers, Nageh (talk) 22:28, 7 March 2012 (UTC)

Category:Rules of inference and Category:Theorems in propositional logic

In principle, the former should contain only rules such as A ⊢ B, and the latter should not contain rules at all, only facts such as (axioms) ⊢ B. But after a mass addition of articles by Gregbard there is much confusion in the theorems' category. Modus ponens is not a propositional theorem by no means. Incnis Mrsi (talk) 12:49, 4 March 2012 (UTC)

Really? "by no means?" There are several sources naming "((P --> Q) & P) --> Q" as modus ponens. Every rule of inference (of prop logic) can be stated as a theorem of prop logic and vice versa. Although the rules produced would quickly become quite complex. that's why commonly you see about 19, with some extras that are often interchanged for others. Greg Bard (talk) 09:38, 5 March 2012 (UTC)

Nope. First, which "rule of inference (of prop logic)" corresponds to p → p, a trivial one, you can say? … well, to classical logic's (p → q) ∨ (q → p) and (p → q) ∨ p? No rule corresponds to these theorems. Second, you apparently cannot get rid of the confusion between a "rule of inference (of classical propositional calculus)" and a rule of inference as an abstract concept. BTW my new essay has a section about this. Incnis Mrsi (talk) 10:00, 5 March 2012 (UTC)

So you don't see that one can always construct a rule of inference out of a theorem of propositional logic. There are an infinite number of theorems, and so too with r.o.i.s but only a few have names. Modus ponens is the most famous. In the case of your examples, a formal system could have a rule (a metalogical statement) that "If "P" is written on a line of a proof, then you can write "P" on a subsequent line of the proof." corresponding to p → p This is a trivial rule which is probably not contained in hardly any logic ever published. Not every theorem is used as a rule of inference or as an axiom. For any that are named, some account should be given. Greg Bard (talk) 10:19, 5 March 2012 (UTC)

p → p would correspond to the rule I call "reiteration". See deduction theorem#Virtual rules of inference. JRSpriggs (talk) 10:42, 5 March 2012 (UTC)

I agree that the Bard is adding confusion, but A ⊢ B and ⊢ A → B are difficult to distinguish; only in cases where the latter makes no sense (i.e., modus ponens) should it not be considered a theorem. — Arthur Rubin (talk) 09:15, 5 March 2012 (UTC)

What is it that you are confused about? Greg Bard (talk) 09:38, 5 March 2012 (UTC) In response to your two formulas, the question is the difference between logic and metalogic. All of the ones on this list are theorems. Greg Bard (talk) 10:32, 5 March 2012 (UTC)

First, if they are theorems of propositional logic, then they are tautologies, which is the correct term, so that should be the category. In fact, the deduction theorem states that exactly all theorems of propositional logic are the tautologies. That being said, every rule of inference of the form

• $P_{1},P_{2},\cdots P_{n}\vdash Q$

is equivalent to the tautology/theorem

• $\vdash P_{1}\land P_{2}\land \cdots \land P_{n}\rightarrow Q$

(forward derivation: conditional proof; backward derivation: what most rational people call the rule of tautology, but some — editor — has managed to get another article at that name)

So the category is misnamed, at best. Modus ponens, in particular is worthless if written as $P\land (P\rightarrow Q)\rightarrow Q$, as you have to use modus ponens (rule) to obtain modus ponens (rule) from modus ponens (tautology).

— Arthur Rubin (talk) 16:28, 5 March 2012 (UTC)

Arthur, we are engaging in some civil discourse here, and again I have seen the same pattern. You throw words around in a way that is so careless, as to affect your credibility. All theorems are tautologies so calling tautologies theorems is "misnamed?" Obviously that is not true at all. The same objects are called both in different contexts. However, "tautologies" as a category will surely place these articles in more philosophy category trees than mathematics categories. Your suggestion is inconsistent with the form of subcats in category "mathematical theorems." So you basically have a lot of explaining to do on that suggestion. Secondly, you are completely incorrect in saying that the given theorem called "modus ponens" can't be derived without a modus ponens inference rule. It certainly can be derived in a formal system that does not also contain the modus ponens inference rule. I am a little surprised at that mistake Art. You should know better. Greg Bard (talk) 20:11, 5 March 2012 (UTC)

Comment While the last paragraph achieves its purpose of disagreement, it could have been better with less tongue-clucking and more concrete evidence. Overlooking this and pressing onward, can someone suggest the proper talk page for this discussion to continue, and maybe a short list of qualified editors to request comment from? Rschwieb (talk) 14:08, 6 March 2012 (UTC)

Say listen, Arthur said there was some "confusion" and being the decent, good faith editor that I am, I wanted to get to the bottom of it. It turns out there isn't any confusion. Just more rhetoric from Arthur. So, you should more appropriately direct your concern to Arthur vis-a-vis "clucking." I asked the question in innocent good faith, and it turns out, it's just Arthur's bad attitude AGAIN. Shame on you. Being as fair-minded as I am, I feel I have to say that I do think that the formulation that Arthur has provided concerning the deduction theorem is excellent, and should be included in both the theorem, and tautology article. Greg Bard (talk) 09:29, 7 March 2012 (UTC)

Let's suppose for now that we all appreciate what is going on, and move on with the evidence supporting each side. Rschwieb (talk) 13:50, 7 March 2012 (UTC)

There is a many-to-many correspondence between rules of inference ($P_{1},P_{2},\cdots ,P_{n}\vdash Q$) and theorems of the predicate calculus ($\vdash P_{1}\land P_{2}\land \cdots \land P_{n}\rightarrow Q$), and a one-to-one correspondance of the latter with tautologies ($\vDash P_{1}\land P_{2}\land \cdots \land P_{n}\rightarrow Q$).

For example, modus ponens is

• $P,P\rightarrow Q\vdash Q$

As a theorem, is it:

1. $P\land (P\rightarrow Q)\rightarrow Q$
2. $(P\rightarrow Q)\land P\rightarrow Q$
3. $P\rightarrow ((P\rightarrow Q)\rightarrow Q)$
4. $(P\rightarrow Q)\rightarrow (P\rightarrow Q)$

(Note theorem #4 is an instance of the the theorem $P\rightarrow P$, which, in turn, corresponds to the "rule" $P\vdash P$.)

For the reverse corresponance, if you use the first formulation, then

$P\land Q\rightarrow Q\land P$

corresponds to the rules

1. $P,Q\vdash Q\land P$
2. $P\land Q\vdash Q\land P$
3. $\vdash P\land Q\rightarrow Q\land P$

If you use the second formulation:

$P\rightarrow (Q\rightarrow P\land Q)$

corresponds to the rules

1. $P,Q\vdash P\land Q$
2. $P\vdash Q\rightarrow P\land Q$
3. $\vdash P\rightarrow (Q\rightarrow P\land Q)$

In any case, all rules of inference (of "standard" (non-intuitionistic) propositional logic) correspond to one or more theorems in propositional logic, and the reverse. Either there should be only one category, or only those "rules" which correspond to theorems which are used as theorems should be included in the "Theorems" category, and only those theorems which are actually used as rules should be included in the "Rules" category. — Arthur Rubin (talk) 15:43, 7 March 2012 (UTC)

Or we could go with Incnis Mrsi's approach; only those rules which are stated as rules should be in the "Rules" category, and only those theorems which are stated as theorems should be in the "Theorems" category.

In any case, the present duplication of categories is unacceptable. — Arthur Rubin (talk) 16:04, 7 March 2012 (UTC)

I was also hoping citations would surface to dispel philosophical qualms. Rschwieb (talk) 16:05, 7 March 2012 (UTC)

I admit to not being a philosopher. — Arthur Rubin (talk) 19:00, 7 March 2012 (UTC)

Arthur, I think you are forgetting how WP works. Certainly you, I, or any of the talented people here at WP:MATH can construct a r.o.i out of any theorems and vice-versa. However there really are only about 19 or so that are actually published as r.o.i. That is the standard. Whether or not the "rules of inference" category should also be a subccategory of "theorems of propositional logic" is something I am open-minded to, either way. However, just because Arthur doesn't like it, is no reason to move or delete either of those categories. Just because you aren't looking for r.o.i doesn't mean someone else isn't. Show some respect. If articles are removed from "theorems" then the "r.o.i." cat needs to be placed as a subcat of the "theorems" cat. I wouldn't prefer that. Greg Bard (talk) 21:02, 7 March 2012 (UTC)

"R.o.i." being part of "theorems" would be absurd. "Theorems" being part of "r.o.i." would not be absurd, as $\vdash P$ is a perfectly good rule of inference. Perhaps {{catseealso}} in both categories would be more appropriate. But perhaps I don't understand how Greg Bard's argument is consistent with Wikipedia policies and guidelines.

Still, I don't see why either my approach (in the related category if called, in the literature, a "r.o.i" or a "theorem", or both), or Incnis Mrsi's approach (in the related category if we call it an "r.o.i" or a "theorem", or both) wouldn't be consistent with WP:CAT, if the {{catseealso}}s are in place. See, for example, the following excerpt from WP:CAT:

• Articles should be categorized by the defining characteristics of the article topic.

— Arthur Rubin (talk) 23:24, 7 March 2012 (UTC)

Arthur, theorems as a subcat of r.o.i. is absurd. A rule of inference itself is a metalogical statement about a logical system. A theorem is a statement from within a logical system. So, you are precisely incorrect. The question is how are we to organize under category:logical expressions. All of these things that we are talking about are theorems of some system, and are used as rules of inference in some systems based on the fact that they are derived as theorems. So the way they should be organized under logical expressions is that some are in both r.o.i and theorems based on whether or not systems have been published expressing them as such. Like I said, I can see r.o.i under the theorems category or side by side with it under logical expressions, like it is now. I cannot see theorems under the r.o.i. category at all. Greg Bard (talk) 18:33, 9 March 2012 (UTC)

Actually your statement really is absurd. Rereading the first sentence of the last section — how can a metalogical statement be a "theorem". Any theorem (of the propositional calculus, anyway) $P$ constitutes a rule of inference $\vdash P$, while rules of substitution constitute theorems only by use of the rule of tautological equivalance from Rubin, probably called other things in other systems. However, I think side-by-side is better, with both trimmed significantly to those rules of inference actually used as rules of inference in reliable sources, and those theorems actually stated as theorems in reliable sources. — Arthur Rubin (talk) 06:10, 10 March 2012 (UTC)

Edits at Divisor function and Riemann hypothesis

A succession of anonymous/new editors have been editing divisor function and Riemann hypothesis, inserting what looks like a claim to have proved the result unconditionally, supported only by a preprint at vixra.org. More eyes on both articles would be welcome. —David Eppstein (talk) 16:06, 6 March 2012 (UTC)

For context, vixra.org is a version of arxiv.org that is specifically for cranks. From their website: "ViXra.org is an e-print archive set up as an alternative to the popular arXiv.org service owned by Cornell University. It has been founded by scientists who find they are unable to submit their articles to arXiv.org because of Cornell University's policy of endorsements and moderation designed to filter out e-prints that they consider inappropriate. ViXra is an open repository for new scientific articles. It does not endorse e-prints accepted on its website, neither does it review them against criteria such as correctness or author's credentials." Sławomir Biały (talk) 16:40, 6 March 2012 (UTC)

Its still ongoing. Someone should protect Riemann hypothesis at least. Sławomir Biały (talk) 00:52, 7 March 2012 (UTC)

Anyone want to work through the pages with references from Vixra (http://en.wikipedia.org/w/index.php?title=Special:LinkSearch&limit=500&offset=0&target=http%3A%2F%2Fvixra.org) to see whether they make sense in their respective articles? I'm leaning toward no in most of the ones that I looked at.Naraht (talk) 15:07, 7 March 2012 (UTC)

It's not up to us on Wikipedia to referee papers, if somebody wants to do that and thinks there actually is something there worth bothering about then of course you could say here even though officially this isn't a forum, but it still couldn't go into the article until it was peer reviewed outside of Wikipedia. Dmcq (talk) 15:28, 7 March 2012 (UTC)

I glanced them over, and they don't really make sense. Even if they did make sense, they don't appear to contain any new deep mathematical ideas (in contradistinction to many of the supposed proofs of these big theorems that at least have the superficial appearance of great depth). There is zero chance that this approach will show anything like what the author claims, even if cleaned up and made readable. Of course, I make my standard offer to the author: I will read and provide detailed feedback for $1000 (US), payable in advance. Sławomir Biały (talk) 15:44, 7 March 2012 (UTC)

If vixra authors were unable to place their texts on the arxiv, they are unlikely to get published in reputable venues, which would seem to argue against their inclusion at wiki. Tkuvho (talk) 13:13, 9 March 2012 (UTC)

Strong and weak (logic)

I am not familiar with English terminology, but something like it certainly should exist. A proposition is strong if it entails many other propositions. The proposition P is stronger than Q if P├ Q (provability/deducibility partial order relation) or P ⊧ Q (semantic partial order relation). Also, it may be generalized to theories. A theory is stronger if it has more theorems that another, which uses the same formal language. For example, classical propositional calculus is stronger than intuitionistic one, and an inconsistent theory is the strongest possible.

I could use titles strong and weak (logic) or strong and weak propositions, which is better? Also, which sources should I search for definitions? Incnis Mrsi (talk) 06:50, 9 March 2012 (UTC)

Is there really enough to say about that to justify creating an article? — Carl (CBM · talk) 11:26, 9 March 2012 (UTC)

Imagine a text:

“ Wizzle's theorem has a stronger antecedent and hence is weaker than Woozle's theorem. But Wizzle's theorem admits a generalization to bobjects in Poozle's spaces which cannot be obtained as a consequence of Woozle's theorem. Pizzle's conjecture for Poozle's spaces was stronger than both Wizzle's and Woozle's theorems, but Squizzle recently built a counterexample to it (and also to generalized Woozle's theorem) in a foo-dimensional Poozle's space. At Winnie-the-Pooh symposium it was discussed that in foo-dimensional case some weakened version of Woozle's theorem may be true, which is not equivalent to Wizzle's theorem. But for all known bobjects the corresponding statement is a really a consequence of either the foo-dimensional Wizzle's theorem or this theorem in some degenerate space. ”

Happily we have logical equivalence, but how do you propose to link "weaker", "stronger" and "weakened"? Or should I explain this inline? Incnis Mrsi (talk) 13:14, 9 March 2012 (UTC)

Wikipedia articles should not be written merely to document jargon. I'm pretty sure all the content of what you propose to write is covered elsewhere. So basically I don't think you should do this at all. --Trovatore (talk) 01:38, 10 March 2012 (UTC)

I think your definition (P is stronger than Q if P├ Q) suggests that entailment is the underlying concept (although that article is a mess). -- 202.124.74.200 (talk) 01:34, 10 March 2012 (UTC)

Merging localization of a ring to localization of a module (or other way)

Do we really need two separate articles for a basically one single topic: localization in commutative algebra (or algebraic geometry)? For one thing, the constructions are the same. For another, it's simpler to have one article to discuss basic facts like local property. For example, "noetherian" is not local property. But if localization of a module has a section on local property, it probably should have a mention of this. -- Taku (talk) 15:14, 10 March 2012 (UTC)

My experience tells me that such mergers often result in disastrous articles. It would be better to start a new article like localization (algebra), and gradually merge/rewrite these articles into that one on an equitable basis. But at the moment, having two decent articles on similar topics is probably better than having one article with an uneven, confusing, and inconsistent merger. Sławomir Biały (talk) 16:04, 10 March 2012 (UTC)

Right (especially, "experience" part). I for one cannot promise to deliver coherency. -- Taku (talk) 17:17, 10 March 2012 (UTC)

Ah, I actually just completed the merger: localization (algebra). It differs very little from the existing ones. I forgot to say in the above, but I think an important example of the localization of a module is that of localization of an ideal and I think it seems easier to add discussion on it to this new article. -- Taku (talk) 18:05, 10 March 2012 (UTC)

Mathematical fallacy

If anyone is looking for a fun diversion, bringing mathematical fallacy into decent shape looks like a project with collaboration potential. See my comment at Talk:Mathematical fallacy. Sławomir Biały (talk) 00:36, 11 March 2012 (UTC)

Conventions for ordinals

I'm currently in a discussion (see my talk page) with another editor on the meaning of the phrase "the first 5 Fibonacci numbers". My interpretation is 1, 1, 2, 3, 5, but the other editor, based on conventions used in computer languages such as C and Python, thinks it would be 0, 1, 1, 2, 3. The other interpretation has some merit in that most authors start the sequence with 0, so it comes down to whether you consider 0 the 0th number or the 1st number in the sequence. My preferred solution is to avoid the issue altogether my rewording the phrase, but we've been back and forth several times now so I thought it was time to raise the issue in a larger forum.--RDBury (talk) 14:45, 7 March 2012 (UTC)

I don't think there's any ambiguity in the phrase "the first 5". If the sequence starts with element #0, then "the first 5" elements are elements 0, 1, 2, 3, and 4. If the sequence starts with element #1, then "the first 5" elements are elements 1, 2, 3, 4, and 5. But even if you consider element #0 "the 0th element", the phrase "the first 5" means elements 0–4, not elements 1–5. —Mark Dominus (talk) 15:49, 7 March 2012 (UTC)

Agree completely: "first five" does not mean "six" regardless of indexing conventions. Also, even if the indexing starts with 0, it could be that F(0) = 0 or F(0) = 1, the choice of index does not determine the choice of initial conditions for the recurrence. Any prticular formulas will depend on both an indexing convention and a choice of initial conditions. — Carl (CBM · talk) 15:56, 7 March 2012 (UTC)

I think that it is more clear in general to just say "From F(1) to F(n)" or "From F(0) to F(n-1)", because then the reader knows exactly what is intended. Under zero-based numbering F(0) is both the zeroth and first element of the sequence. — Carl (CBM · talk) 16:24, 7 March 2012 (UTC)

The phrase is ambiguous, otherwise the issue would not have come up. The way the article was worded it said "The sum of the first n Fibonacci numbers is the (n + 2)nd Fibonacci number minus 1." This triggered a "correction" by the other editor which I then reverted and the resulting discussion is mostly on how the phrase should be interpreted. The two interpretations give different results for "the sum of the first 5 numbers", 12 in one case and 7 in the other, and only one interpretation makes the statement correct.--RDBury (talk) 16:40, 7 March 2012 (UTC)

Whether "first five" works there does not depend on whether the first one is called F(0) or F(1), it depends on whether the first one is equal to 0 or equal to 1, in other words it depends on the initial condition of the recurrence, because it is a property of the actual sequence, not a property of the numbering of the sequence. Based on the formula in the article, and assuming F(0) = 0 as the article does, it would work to phrase that sentence in the article as "the sum of the Fibonnacci numbers F(1) through F(n)" thus avoiding the entire issue. — Carl (CBM · talk) 16:48, 7 March 2012 (UTC)

I think the notation used in the article is pretty much universal, otherwise we seem to be in agreement. I rephrased it in the article as "[The] sum of the first Fibonacci numbers up to the nth is equal to the n+2nd Fibonacci number minus 1."--RDBury (talk) 17:28, 7 March 2012 (UTC)

I agree that the quoted statement is true, but if the indexing begins at 0 then it does not match up with the formula $\sum _{i=1}^{n}F_{i}=F_{n+2}-1$ that is just below it in the article. With zero-based numbering, $F_0$ is the first (and zeroth) number, and when read literally the formula states that the sum of the second through $n+1$st numbers is equal to one less than the $n+3$rd number. — Carl (CBM · talk) 18:50, 7 March 2012 (UTC)

I am the "other editor", and there is one thing I do not understand. The mathematical formula says "sum from i = 0 to i = n". The text should just say the same, is all I meant. If somehow it is more clear that the text says "the sum from i = 1 to i = n", then it should be the mathematical formula that should be changed to say the same. The problem is not one of counting from zero or from one. The text and the formula should simply be consistent with each other. Is there an editorial agreement about that? Olivier Danvy (talk) 18:58, 7 March 2012 (UTC)

Let's link to the section being discussed: Fibonacci_number#Combinatorial_identities. I agree that there's a lot of potential for confusion. To my mind, if we have a sequence beginning F₀, F₁, F₂,..., then F₀ is the first element, F₁ the second element and so on. But it's liable to be interpreted differently by different people. What is the reason for writing out all the formulae in words as well as in symbols? Perhaps the nineteenth-century charm of the prose style is enjoyable, but in this case it causes more trouble that it's worth. Why not just delete all the verbal descriptions, and then there's no argument about the meaning of nth? Jowa fan (talk) 23:57, 7 March 2012 (UTC)

Going back to the original question, the sequence "1, 1, 2, 3, 5" is more aesthetically pleasing than "0, 1, 1, 2, 3". The former captures more of the essence of how the F. numbers actually look. You say to people: "What sequence goes 1, 1, 2, 3, 5 ..." and they're far more likely to say "Of yes, Fibonacci numbers", but "0, 1, 1, 2, 3" just isn't so obviously recognisable as a signature.

In my mind the mathematical pedantry is obscuring the message. If you *must* be accurate, say "Fib nos. F1 to F5 are 1, 1, 2, 3, 5" which bypasses the whole fussy question. --Matt Westwood 06:04, 8 March 2012 (UTC)

I agree with this, I think this is where the fundamental difficulty in resolving this issue comes from. The top of the article defines F₀ to be 0 and F₁ to be 1. But then the identities in the combinatorial identities section start summing from F₁, which isn't the first Fibonacci number according to the definition at the top at all! Therefore the sentence "the sum of the first Fibonacci numbers up to the nth" (which would be F₀ + F₁ + F₂ + ... + F_n-1) clashes with what the formula says, because the formula starts at i=1. This problem exists for several of the combinatorial identities. A radical way to solve the problem would be to chose a different definition at the beginning of the article. That's quite radical though. The other option would be to be explicit and write "summing the numbers F₀, F₁, F_n gives F_n+1-1". Leaving it as it is feels extremely unsatisfying to me, because it is muddled, inconsistent and wrong. Cfbolz (talk) 15:23, 13 March 2012 (UTC)

Work might start on Outline of algebraic structures

After I felt like Algebraic structures was in recovery, I reexamined restoring the outline version to usefulness. It has many problems, some of which might have been caused by the whole outline/list fiasco. I've proposed some changes on the talk page, and I hope a few other WP:Math members are willing to check it out from time to time. Among the recommendations: organize it more like Algebraic structure, include a section on the usual order of learning things in intro, decrease total number of mentioned structures, remove example list. I'm awaiting response from WP:Outlines concerning if they want to help. Rschwieb (talk) 14:23, 12 March 2012 (UTC)

'New' math rendering options

Check your preferences: with MW 1.9 the math rendering options are down to two: always PNG and display TeX. See the RfC here: [1]. Renders some of the Math MOS redundant, such as MOS:MATH#Forcing output to be an image and MOS:MATH#Very simple formulae. Probably the whole section needs rewriting.JohnBlackburne^words_deeds 02:19, 1 March 2012 (UTC)

You mean MW 1.19 which has just been rolled out. PrimeHunter (talk) 03:00, 1 March 2012 (UTC)

That's really really stupid if it means what I think it means. Anything like that should have been delayed until MathJax or another way of displaying stuff properly inline had been implemented properly. Dmcq (talk) 13:02, 1 March 2012 (UTC)

Yep it is what I thought. I was testing MathJax so I didn't see it before. Luckily or unluckily people seem to have tried avoiding <math> inline in lots of places so the effect isn't as bad as it might be. I really do think it would be a good idea to have a conversion tool to help change {{math}} uses to <math> when MathJax comes along, this latest business is going to force even more instances of <math> to be turned into {{math}} to avoid the ugliness of the inline PNGs. Dmcq (talk) 13:17, 1 March 2012 (UTC)

At some point soon (i.e. maybe during 2012), mathJax should become the default for everyone. Developers are working on it. Does this latest roll-out have anything to do with progress in that direction? Michael Hardy (talk) 16:17, 1 March 2012 (UTC)

The big problem now is the baseline problem with $x^{a}$ being positioned too low. Brion said he was going to investigate this in the RfC, but it looks like it hasn't happened.--Salix (talk): 16:59, 1 March 2012 (UTC)

The relevant bugs are the following:

• Bug 31406 - Set $wgMathUseMathJax = true on Wikimedia wikis
  • This depends on/blocks other bugs
• Bug 32694 - Use baseline shift when positioning inline math PNGs

Helder 17:18, 1 March 2012 (UTC)

I've now responded to the former bug, it looks like MathJax might be just round the corner.--Salix (talk): 18:38, 1 March 2012 (UTC)

---

Apparently I missed something with MathJax. Does anybody use it to browse articles in English Wikipedia and is it really functioning? Incnis Mrsi (talk) 17:44, 17 March 2012 (UTC)

User:Nageh/mathJax is a ready-to-use solution. Turn off the rump of WP:texvc and use this script. Incnis Mrsi (talk) 19:06, 18 March 2012 (UTC)

Iteration of mathematical curves

The new article titled Iteration of mathematical curves is at best currently a mess, and possibly a violation of WP:OR. Further opinions? Michael Hardy (talk) 15:31, 11 March 2012 (UTC)

There's also Jasinski Flower, by the same editor (who is probably Andrzej Jasinski). Sławomir Biały (talk) 15:45, 11 March 2012 (UTC)

Having looked at them I've put a prod on them as non notable and probably self promotion. Dmcq (talk) 20:33, 11 March 2012 (UTC)

A number of times laterly I've seen "non" used like this as if it were a separate word rather than a prefix. Have schools stopped teaching that there is such a thing as a prefix? Michael Hardy (talk) 15:52, 13 March 2012 (UTC)

The other day a young news reporter caught my attention with the awkward phrase "...want to be able to not be concerned..." Rschwieb (talk) 01:05, 14 March 2012 (UTC)

It is a phrase I only use on Wikipedia but it seems to be a fairly standard phrase here which is why I used it, there's even a redirect WP:Non-notable Dmcq (talk) 01:22, 14 March 2012 (UTC)

Michael was objecting not to non-notable but rather to non notable. --Trovatore (talk) 01:47, 14 March 2012 (UTC)

Well that's just un acceptable. Are you il literate or some thing? (This post is just to annoy Michael Hardy.)  :-D Sławomir Biały (talk) 11:24, 14 March 2012 (UTC)

Your non sense is un necessary and in appropriate, Slawomir! :) User:Rschwieb|Rschwieb]] (talk) 13:58, 14 March 2012 (UTC)[[

This does highlight the messy state of out articles on curves. We have

• Curve
• Plane curve - a stub
• Algebraic curve
• Differential geometry of curves
• List of curves
• Gallery of curves

all of which overlap somewhat, none of which are particularly complete. What sees to be missing is an article on parametric curve the closest there being Parametric equation.--Salix (talk): 08:04, 14 March 2012 (UTC)

Would some one like to talk to the author of that Iteration of mathematical curves and Jasinski Flower? I am pretty certain they are OR but I don't really feel I'm the right person to try sand get them to move it to somewhere better or workon what Wikipedia does. They've put an effort into it and there's some talent and I'm more of a putter downer. Dmcq (talk) 22:44, 16 March 2012 (UTC)

Segal–Shale–Weil distribution and Metaplectomorphism

Boodlepounce believes these articles are nonsense. Can anyone at the project refute Boodlepounce's assessment by verification from reliable sources? Boodlepounce (talk) 21:33, 15 March 2012 (UTC)

Although Boodlepounce definitely raises a valid point, Boodlepounce might be taken more seriously at first blush if it referred to itself in the first person. Bad Boodle! Sławomir Biały (talk) 23:14, 15 March 2012 (UTC)

Currently they may deserve {{context}}. Segal–Shale–Weil distribution certainly does not deserve deletion. Charles Matthews (talk) 10:56, 19 March 2012 (UTC)

Wikipedia:Categories for discussion/Log/2012 March 19#Category:Matrices

A discussion on disambiguation. Please have a look. Charles Matthews (talk) 10:53, 19 March 2012 (UTC)

One proposal suggests renaming all categories that have a dab page, which would just waste time and memory. We would have groups (mathematics), fields (mathematics), idiocy (Wikipedia category discussions), etc.

The combination of fatuous bluster and sloth in these discussions is unmatched in Wikipedia: One should not expect that the category experts have taken any time to read the articles or their ledes.  Kiefer.Wolfowitz 12:10, 19 March 2012 (UTC)

Articles needing expert attention

In their infinite wisdom a number of editors have decided it would be a good idea to delete {{expert-subject}}. This means Category:Mathematics articles needing expert attention will soon be empty. Is anyone interested in preserving this list of articles somewhere (or taking the template to WP:DRV)? —Ruud 13:10, 9 March 2012 (UTC)

I would appeal the deletion. I don't see consensus for deletion in the discussion contrary to what the closing admin claims. Frankly, this is one of the templates I think are useful. This is not just about notifying editors but also about warning readers about problematic content and inviting potential expert readers to contribute. Nageh (talk) 13:17, 9 March 2012 (UTC)

It seems useful to me too. Let me know where to write if an appeal forms. Rschwieb (talk) 16:00, 9 March 2012 (UTC)

I've opened a deletion review at Wikipedia:Deletion review#Template:Expert-subject. —Ruud 16:43, 9 March 2012 (UTC)

The closing statement did say "after adding 'attention=yes' or equivalent parameter in the corresponding WikiProject banner". This may well be a good thing to do to {{maths rating}}. Maybe an {{expert-mathematics}} template might be a workable solution. The big problem is that few other projects monitor these, so there is a case for a project specific template. Curiously there is a big discrepancy between Category:Mathematics articles needing expert attention with 158 articles and Wikipedia:Pages needing attention/Mathematics/Lists#Articles needing expert attention with only 34 articles.--Salix (talk): 18:35, 9 March 2012 (UTC)

The issue noted in the last sentence is now fixed. -- Jitse Niesen (talk) 15:50, 10 March 2012 (UTC)

I've created a mathematics specific version {{expert-maths}} as an experiment. It has an additional reason parameter to indicate what the problem is.--Salix (talk): 22:06, 10 March 2012 (UTC)

Do you suggest to start moving articles there from {{expert-subject}}? Sasha (talk) 22:25, 10 March 2012 (UTC)

Its too early for that as the Deletion review is still pending. So I'm just gauging opinion at the moment. The main question is whether we want something to appear in the main article space as this template does or talk namespace as adding a parameter to the project banner would do.--Salix (talk): 22:56, 10 March 2012 (UTC)

I note that the deletion review closed with a "relist" decision, but the template was never relisted. Is it necessary to start another deletion review? -- 202.124.75.161 (talk) 06:42, 18 March 2012 (UTC)

{{expert-subject}} has been relisted for TfD discussion. Nageh (talk) 10:08, 20 March 2012 (UTC)

Lebesgue integration

There is a problem with the picture of „intuitive explanation“. Which one is better/„not too false“? a,b or c? In my opinion a) is the worst one, but it is back in the article.

a)

b)

c)

--Svebert (talk) 22:10, 18 March 2012 (UTC)

Well, (b) is clearly wrong by any measure. Where is the simple function s (from the definition of the Lebesgue integral) that is $\leq f$ in this picture? This image appears to represent an upper Darboux sum for the Riemann integral of f. The image (c) is probably marginally better than (a), although both convey the same basic idea. Sławomir Biały (talk) 22:33, 18 March 2012 (UTC)

Pls. see p. 146 of [2]. I don't get your comment with „where are the simple functions in figure b)“...Figure a) is totally misleading.--Svebert (talk) 23:04, 18 March 2012 (UTC)

Sorry, I can't see the page you just linked. I was referring to the definition in our article Lebesgue integral, which is quite standard. There is nothing about (b) that seems to be correct from this point of view. Sławomir Biały (talk) 23:26, 18 March 2012 (UTC)

Lebesgue partitioned the y-axis, not the x-axis. Michael Hardy (talk) 23:18, 18 March 2012 (UTC)

Here is the reference again: Bernd Siegfried Walter Schröder (12 November 2007). Mathematical analysis: a concise introduction. John Wiley & Sons. p. 146. ISBN 978-0-470-10796-6. Retrieved 19 March 2012.. You are right, Lebesgue partitioned the y-axis and Riemann the x-axis. But what figure a) shows definitively doesn't happen in Lebesgue integration. The Lebesgue integral is defined as follows:

$\phi =\sum _{i}\alpha _{i}\chi _{A_{i}}$

$\int _{\Omega }\phi {\mbox{d}}\mu =\sum _{i}\alpha _{i}\mu (A_{i})$

here $\phi$ is the simple function, which is essentially a sum of characeristic functions on some sets $A_{i},\,i=1\dots n$. These sets are parts of the x-axis in the shown pictures. The integral now, „looks up“ the bigness of every $A_{i}$ and scales it with the appropriate factor $\alpha _{i}$ of the simple function.

Please explain to me, where are horizontal slices shown in figure a) in the definition? Figure a) is totally misleading because it shows that some parts of the x-axis (some $A_{i}$) are added several times to obtain the integral. But in the definition every $A_{i}$ is considered exactly 1 time in the sum.

The idea of lebesgue integration is reflected much more precise with figure b) and c): One partitions the y-Axis in say N equal parts with length $\Delta y$. So one can assign for every such y-interval $y_{i}+\Delta y$ an interval on the x-axis (in general disjoint /scatterd). Each such interval on the x-axis is now one set $A_{i}$. The lebesgue integration now measures the bigness of every $A_{i}$ only one time and scales this bigness with the appropriate factor $\alpha _{i}=y_{i}$. In both figures b) and c) exactly this is shown. The measure of the sets $A_{i}$ are the x-axis parts of rectangles with same color.

This is what Henry Lebesgue said: Lebesgue integration is that what a careful businessman does. If he has to count his money than Riemann would just count the coins as they come: 1,1,4,4,5,4,3,1. The careful businessman would order the coins after there value: 3*1+3+3*4+5. (Here $\mu (A_{1})=3,\mu (A_{2}=0),\mu (A_{3})=3,\dots$).--Svebert (talk) 09:29, 19 March 2012 (UTC)

Here is another good reference: [3]--Svebert (talk) 10:36, 19 March 2012 (UTC)

The horizontal slices are the same horizontal slices that appear on page 146 of the reference you gave. Sławomir Biały (talk) 10:50, 19 March 2012 (UTC)

? except that there are also vertical slices and the sets $A_{k}$ are „scattered“...

I understand your point, that the lebesgue-figures of b)/c) can also be considered as figures for Riemann-integration with non-equidistant partition of the x-axis. But I think a figure for the intuitive explanation should be in 1D otherwise the figure is too complicated and I personally dont know a better explanation than b)/c) for 1D.

Back to lebesgue integration (I am talking only for 1D integrations in the following): The point of lebesgue integration is not that one partitions the y-axis instead of the x-axis, also it is a good starting point for the explanation. The point is, that the partitions can be scattered. They don't have to be intervals. Therefore an optimal picture should have huge oscillations (like the one of the wolfram-reference) to make clear that the partitions dont have to be connected.

Therefore figure a) misses this „scatterd partitions“ point. Also it is totally misleading and even wrong! For me the picture shows sets $A_{i}$ which are not pairwise disjoint (the sets $A_{i}$ are the projections of the slabs onto the x-axis). If you refer to definition 9.21 of the book-reference above, you read „Let $A_{1},\dots A_{n}$ be pairwise disjoint sets“. Also I dont understand what part of figure b) is wrong, could you please be more precise?--Svebert (talk) 11:20, 19 March 2012 (UTC)

The main with (b) is that it is based on an approximation of f from above rather than below, and so it has no connection with the definition of the Lebesgue integral, which uses approximations from below. As for the emphasis on the sets $A_{i}$, I agree that it could be made clearer in the image (although none of the images really does this well). Even so, the Lebesgue integral of a nonnegative function can be defined by

$\int f=\lim _{n\to \infty }2^{-n}\sum _{k=1}^{\infty }\mu \{x|f(x)\geq k2^{-n}\}$

which is what (a) illustrates directly. Sławomir Biały (talk) 11:53, 19 March 2012 (UTC)

I have to agree with User:Svebert that the horizontal bars in a) are misleading. I've never seen this horizontal slice picture used to describe Lebesgue integration (or if I did, I promptly discarded it). It does not seem to embody the simple function approximation. I think c) is patently superior to a). It incorporates the partition of the y-axis using dotted lines instead of solid. Diagram a) looks like the beginnings of a "washer" approximation of volume of a revolutionary solid to me. Rschwieb (talk) 13:47, 19 March 2012 (UTC)

The horizontal slicing is actually a very common way of explaining the Lebesgue integral. It even appears in the reference Svebert gave. In addition, it is described in the Folland text referenced in the article. More references to this perspective are available upon request. Sławomir Biały (talk) 14:03, 19 March 2012 (UTC)

I noticed your comment that it appeared in that reference, but I do want to throw its commonality into question. I guess the question for weighing if it should be included is "how high is the percentage of texts using the horizontal bar picture?". The estimated range right now is too broad: "quite common" to "never seen it used". Rschwieb (talk) 15:02, 19 March 2012 (UTC)

Well, I think the relevant sample is "how many textbooks attempt to illustrate the Lebesgue integral with a picture"? Of this sample, we can start to ask which of them do it by dividing the range, and which do it by some other means. Sławomir Biały (talk) 15:07, 19 March 2012 (UTC)

Presumably the correct measure of commonality is its proportion (not frequency) among texts using an illustration, but other than that I have no idea how what you wrote is different from what I wrote. And I really do mean it to be constrained to "how many use the picture", since we all agree on the definition of the Lebesgue integral but we disagree on the effectiveness of picture a). So there's no mistake, I want to say that we should be comparing the relative proportions of both type a) and type c) illustrations to measure their commonality. Rschwieb (talk) 20:01, 19 March 2012 (UTC)

I agree that figure b) has the problem that it doesnt obey $\phi \leq f$. I will fix that. But I totally disagree that the reference I gave use the „slab-picture“. Both references which I posted above explain lebesgue integration with figures like b)/c). Of course without the flaw that in b) $f>\phi$.--Svebert (talk) 20:29, 19 March 2012 (UTC)

@Slawomir: Pls show me a reference except Folland which uses the „slab-figure“ (I cant access the Folland-reference). Thanks.--Svebert (talk) 20:29, 19 March 2012 (UTC)

The figure (b) has now been substantially improved, especially with the addition of the horizontal rulings. While I don't think it adequately conveys the fundamental difference between the Riemann and Lebesgue integrals, I think it should be given by itself as an independent illustration of the "simple function" definition of the Lebesgue integral. Could this be separated from the Riemann integral?

One doesn't actually need to know anything about simple functions to have an intuitive grasp of the meaning of the Lebesgue integral, and this probably points to an overall fault in our article. Probably the simplest definition I know for a nonnegative measurable function f, the Lebesgue integral is simply

$\int f:=\int _{0}^{\infty }f^{*}(t)\,dt$

where

$f^{*}(t)=\mu \{x|f(x)>t\}$

and the integral on the right is an ordinary (improper) Riemann integral. The idea implicit here is that, intuitively speaking, we can rearrange the function values by sliding all of the horizontal slabs to the left in the picture (a). You'll note that this integral agrees with the limit in my earlier comment

$\int f=\lim _{n\to \infty }2^{-n}\sum _{k=1}^{\infty }\mu \{x|f(x)\geq k2^{-n}\}$

--Sławomir Biały (talk) 23:18, 19 March 2012 (UTC)

Looks like b) is much improved now! I like it better now than the other two. It also has the added benefit of having more variety (it's more than just a hill.) Rschwieb (talk) 13:10, 20 March 2012 (UTC)

Sorry Slawomir, but I dont understand your comments. It took me 10 minutes to understand the "nearly circular" definition of $f^{*}(t)=\mu \{x|f(x)>t\}$.

I still dont understand what this weird f* function has to do with the defintion of the lebesgue-integral (except that both include the measure $\mu$ of a set). I only see that the function rotates x und y axis for a box-like function. And that for a tent-like function f, f* is linearly going down. And that in those two examples the integral of f and of f* from 0 to infinity are the same. I dont understand what this has to do with the slabs and the lebesgue integration.

Perhaps I am just not smart enough, however, i am not a mathematician.

We are talking about the "intuitive explanation" of lebesgue integration, not that kind of explanation what only experts understand. This slab-picture is not intuitive because i still cant put the definition of the lebesgue integral together with this horizontal-slab-picture (and i really thought about it a long time). Additionally I gave 2 references which do not show your "totally obscure" horizonztal explanation. As I said the Folland reference is not accessible for me. Pls show me a book on google-books which explains this horizontal-slab-picture to me. --Svebert (talk) 19:42, 20 March 2012 (UTC)

I think this approach is described in Lieb and Loos. I don't know about availability on Google books. Sławomir Biały (talk) 19:57, 20 March 2012 (UTC)

As for the connection with the slab figure, $f^{*}(t)dt$ is the area contained in an infinitesimal slab at level t. Sławomir Biały (talk) 21:40, 20 March 2012 (UTC)

Thanks for the reference! I found your explanation (except for the figure, but the formulae etc.) here: Elliott H. Lieb; Michael Loss (2001). Analysis. American Mathematical Soc. ISBN 978-0-8218-2783-3. Retrieved 21 March 2012. on page 12.

ok, now I see, that they define the lebesgue integral without simple functions and with your weird f* function.

$(*)\int _{\Omega }f(x)\mu (\mathrm {d} x):=\int _{0}^{\infty }f^{*}(t)\mathrm {d} t$.

where the right-hand side is a normal riemannian integral.

Now I realized, that the lebesgue integration article really lags clear definitions. If one knows the definitions for i) simple functions, ii) non-negative functions and iii) "all" functions, then one knows where to look at in the article. But otherwise it is totally unclear where one finds the definitions of the lebesgue integral in the article.

Every time I talked about showing a picture for the intuitive explanation for the lebesgue integral I had only the definition for the case i) in mind. Slawomir, you had all the time the case ii) in mind.

Slowly I can understand what you are talking about, Slawomir. And after sketching f and f* again, I finally see that f*(t)dt corresponds to a red slab in figure a).

I summarize: After hours of overthinking the figures and definitions and with your comments I got the connection between figure a) and lebesgue integration.

But there is the huge problem, that nobody (except people who already dissolved the riddle of fgure a) with support of other books and good comments of slawomir) can understand the connection between the figure a) and the lebesgue integration. 1. the article doesnt make clear to which defintion the figure refers (I thought all the time on i) and than there is no chance to work it out). 2. The steps you gave to me to understand the pciture are missing in the article.

Proposal: Rewriting the Integration and Intuitive interpretation part. The Integration-part has to be rewritten so that we have three paragraphs with clear definitions for the cases i), ii), iii). The intuitive part must clearly refer to either case i) or case ii) with the appropriate figure and enough text and formulae to understand the figures.

I still prefer figure b). But I must agree that figure a) is not wrong, but is totally useless without a deliberated explanation. Although I think figure b) is more common and much more easy to understand than figure a)

Off topic: Why are here so less people discussing with us???? I thougt the en:wp has much much more authors than de:wp and on the mathematics-portal there we have discussions with much more authors. Is here anywhere a better place (more authors) to discuss these math problems???--Svebert (talk) 11:14, 21 March 2012 (UTC)

to me the picture a) and the definition of Sławomir seem the most natural. However, as Svebert points out, this definition is not well-explained in the article. So the problem is with the article and not with the picture.

It would be nice to explain in the article why the formula (*) above (Svebert -- sorry for redacting your comment) is true for the Riemann integral (by Fubini theorem), and then that the RHS is defined in a much more general setting. Sasha (talk) 17:02, 21 March 2012 (UTC)

Yes, that seems like a very good suggestion. Sławomir Biały (talk) 20:53, 21 March 2012 (UTC)

Disambiguation needed - Conjugation

I have been working through all the pages that have links to the disambiguation page Conjugation, but I have been unable to resolve those listed here. I am hoping that an expert from this project will be able to fix these. Thanks. Trace identity, SL2(R), David Spiegelhalter, Complete group. Derek Andrews (talk) 16:42, 19 March 2012 (UTC)

Only David Spiegelhalter is left. --Joel B. Lewis (talk) 18:19, 19 March 2012 (UTC)

the last one barbarously resolved (by myself) using the Gordian Knot method. Sasha (talk) 16:48, 21 March 2012 (UTC)

Helmholtz decomposition is wrong

Dear members of world mathematical community!

The Fundamental theorem of vector calculus, (Helmholtz decomposition) states that any sufficiently smooth, rapidly decaying vector field in three dimensions ${\mathbf {F} }$ can be constructed with the sum of an irrotational (curl-free) vector field and a solenoidal (divergence-free) vector field (scalar potential $\varphi$ and a vector potential ${\mathbf {A} }$)

${\mathbf {F} }=-\operatorname {grad} \psi +\operatorname {rot} {\mathbf {A} }\Rightarrow {\mathbf {F} }=\operatorname {grad} \varphi +\operatorname {rot} {\mathbf {A} }$ (1*)

However, the gradient of scalar function does not form the vector field. As well known from textbook [1, p. 15] « … under co-ordinate change the gradient of function transforms differently from a vector »: hence the theory requiring (1) must be false. The next unpleasant things we can see for such well-known classical rules. In mathematics and physics the rot (or curl) is an operation which takes the vector field ${\mathbf {A} }$ and produces another vector field $\operatorname {rot} {\mathbf {A} }$ . However it is well-known that $\operatorname {rot} {\mathbf {A} }$ is an Antisymmetric Tensor . Therefore under co-ordinate change the tensor $\operatorname {rot} {\mathbf {A} }$ transforms differently from a true vector. For elimination of these contradictions the Fundamental theorem of vector calculus can be written as follows:

${\vec {F}}=\operatorname {grad} \varphi +\operatorname {rot} \operatorname {rot} {\vec {A}}$. (2*)

This formula completely corresponds to transformed Navier–Stokes equations(NSE) for incompressible fluids ($\operatorname {div} {\dot {\vec {u}}}=0$)

$\rho {\vec {F}}-\operatorname {grad} p+\mu \nabla ^{2}{\dot {\vec {u}}}=\rho {\ddot {\vec {u}}}\Rightarrow \rho ({\vec {F}}-{\ddot {\vec {u}}})=\operatorname {grad} p+\operatorname {rotrot} \mu {\dot {\vec {u}}}.$ (3*)

Here,

${\vec {F}}={\vec {F}}_{1}+{\vec {F}}_{2}+\cdots$ vectors sum of a given, externally applied forces (e.g. gravity ${\vec {F}}_{1}$ , magnetic ${\vec {F}}_{2}$ and other), $p$- pressure (scalar function), ${\dot {\vec {u}}}$- velocity vector, ${\ddot {\vec {u}}}=d{\dot {\vec {u}}}/dt$ - acceleration vector, $\rho$ - density (const), $\mu$ - viscosity (const), $\nabla ^{2}$ - Laplace operator.

Equations (3) and (2) are consistent. Hence there is no reason to say that the theory requiring (2) must be false. As we can see from NSE the sum - $\operatorname {grad} p+\mu \nabla ^{2}{\dot {\vec {u}}}=-(\operatorname {grad} p+\operatorname {rotrot} \mu {\dot {\vec {u}}})$ forms the vector field.

Note that we will receive the formula (2) also after similar transformation of the Navier–Stokes for a compressible fluid and after transformation of the Lame equations for an elastic media.

From this brief note follows that Helmholtz decomposition is wrong and demands major revision. This follows from comparison of two articles in Wikipedia (http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations and http://en.wikipedia.org/wiki/Helmholtz_decomposition ).

Therefore let's try to formulate the text for editing of this article: http://en.wikipedia.org/wiki/Helmholtz_decomposition .

1.B. A.; Fomenko, A. T.; Novikov, Sergeĭ Petrovich (1992). Modern Geometry--methods and Applications: The geometry of surfaces, transformation groups, and fields] (2nd ed.) . Springer. (p. 15).ISBN 0387976639.

--Alexandr (talk) 18:35, 7 February 2012 (UTC)

Do you have counterexamples to Wiles' proof of Fermat's last theorem, too? Tkuvho (talk) 18:49, 7 February 2012 (UTC)

To Continuum-paradoxes: Your argument against the Helmholtz decomposition assumes that the decomposition must be invariant under coordinate transformations. However, the decomposition theorem does not claim that the decomposition is so invariant. So your argument fails.

In any case, you must provide a reliable secondary source for any such "fact" which you wish to include in Wikipedia. Your original research is not acceptable. See WP:NOR. JRSpriggs (talk) 07:39, 8 February 2012 (UTC)

On one hand, Alexandr is right (and should not be asked for "counterexamples to Wiles' proof of Fermat's last theorem, too"). The gradient of a function is a covector rather than vector, of course. On the other hand, working in a Euclidean (rather than just linear) space it is possible, and quite usual, to treat its dual space as (another copy of) the same space (see Linear functional#Dual vectors and bilinear forms). Or, in terms of transformations (if you prefer this old language): only orthogonal transformations are relevant. Boris Tsirelson (talk) 08:52, 8 February 2012 (UTC)

Fomenko et al is certainly a standard reference. This is all the more reason that I find their discussion of gradients bizarre in the extreme. The exterior derivative df is the usual notation and terminology for the associated covector. The gradient of a function is almost always taken to be the vector, exploiting the usual identifications as mentioned by Boris. I don't think we need to relate to Fomenko's odd choice of terminology. Tkuvho (talk) 09:14, 8 February 2012 (UTC)

The vector potential in the invariant version of the Helmholtz decomposition is a pseudovector. However most sources do not make this distinction, so I don't think our article should either. If someone is bothered by it, then we can add a remark about it somewhere. Sławomir Biały (talk) 12:33, 8 February 2012 (UTC)

However Fomenko does make a distinction and if people are going to go on to deal with manifolds it seems a good idea so I think a note at the very least is called for. Personally I don't like pseudovectors as it strikes me as a kludge or not quite figured out half way to there kind of idea. Dmcq (talk) 13:13, 8 February 2012 (UTC)

On a manifold, it's the Hodge decomposition (which is invariant by design). The boundary conditions are different. Those for the Helmholtz decomposition only really make sense in Euclidean space. Sławomir Biały (talk) 13:31, 8 February 2012 (UTC)

In quantum mechanics when they have CP violated do they talk about that in terms of pseudovectors or what do they call it when things don't look the same in a mirror thanks? Dmcq (talk) 18:23, 8 February 2012 (UTC)

Chirality? Sławomir Biały (talk) 22:07, 11 February 2012 (UTC)

To Continuum-paradoxes: In my previous comment above, I should have said that the Helmholtz decomposition is invariant under the group of translations and rotations ($\mathbf {R} ^{3}\rtimes SO(3)\,$), but not under more general curvilinear coordinate transformations. In the smaller group, there is no difference between the behavior of contravariant vectors (what some call vectors) such as the rate of flow of a fluid and the behavior of covariant vectors (what some call covectors) such as the gradient of temperature, nor between ordinary vectors and axial vectors. JRSpriggs (talk) 11:26, 10 February 2012 (UTC)

It's the other way around: vectors are covariant (go in the same direction), covectors are contravariant (go in the opposite direction). Thus, you push forward a tangent vector, but pull back a differential form. Tkuvho (talk) 20:11, 11 February 2012 (UTC)

I see that the page you referenced says otherwise. There is a problem of terminology here. Tkuvho (talk) 20:14, 11 February 2012 (UTC)

It's an unfortunate abuse of language that I have at various times tried to minimize on Wikipedia: referring to vectors as "contravariant" and covectors as "covariant". What is in fact the case is that the components of a vector in a coordinate system are contravariant and those of a covector are covariant. So it is infinitely preferable to talk about whether the components of some quantity are covariant or contravariant than whether the something itself is. Sławomir Biały (talk) 22:07, 11 February 2012 (UTC)

How would that work in abstact index notation? One is no longer allowed to say whether a tensor is covariant or contravariant? Or do we only talk about covariance and contravariance of "placeholders"? Tkuvho (talk) 12:49, 12 February 2012 (UTC)

Well, it's not really meaningful to talk about covariance and contravariance of abstract tensors. The co/contravariance refers to the behavior under what physicists call passive diffeomorphisms, whereas tensors themselves are actually invariant. In an abstract index setting, I think it's common to refer to the indices themselves as covariant or contravariant. But this is also an abuse of language that should probably be minimized. Sławomir Biały (talk) 13:05, 12 February 2012 (UTC)

This is not how the term is used in category theory. See contravariant functor. Here I am using the term "category theory" in a very loose sense. This usage of "contravariant" and "covariant" has certainly "permeated the fabric of modern mathematics", to quote Carl. Tkuvho (talk) 13:28, 12 February 2012 (UTC)

Actually, it is precisely the same notion as that in category theory, provided that a vector or a covector is defined to be a functor that associates a list of numbers to a frame, where both frames and lists of numbers carry the structure of a GL(n)-torsor. But it is not the same in the category of manifolds and mappings between them. However, I much rather prefer to think of the vector as existing independently of how it is described in coordinates (that is invariant under passive diffeomorphism), so calling a vector "contravariant" because of how its components transform seems to put the cart before the horse. Sławomir Biały (talk) 13:36, 12 February 2012 (UTC)

I agree, it is best not to think of it in terms of coordinates. Thus, if you think of a differential 1-form intrinsically as an assignment of an element of T* at every point, then a diffeomorphism will result in a pullback of the differential form. Therefore differential forms are contravariant according to the definition found at contravariant functor. Tkuvho (talk) 13:41, 12 February 2012 (UTC)

Yes, I agree with this. My point is that it depends on what category you are working in. Some define a tensor as an equivariant function from the frame bundle to a representation of GL(n). The GL(n) action gives morphisms on the frame bundle, and linear maps define morphisms of the representation. From this point of view, a vector is definitely a contravariant functor. If, on the other hand, you consider a vector as a functor on a category of manifolds whose morphisms are local diffeomorphisms, then it is covariant. This is why I find it to be an abuse to call the vector itself contravariant: what we are really talking about is its representation in terms of GL(n) torsors. Sławomir Biały (talk) 13:55, 12 February 2012 (UTC)

Well, I think that you two are dealing in pointless abstractions. I am all for using coordinates and indices which represent numbers designating specific directions in spacetime (the local tangent space). In physics, they begin with equations for each component separately and only later realize that these components can be combined into something like a matrix (i.e. tensors). Thus, to my mind, a tensor is its components as a function of: the event, the choice of coordinate system, and the values of the indices. JRSpriggs (talk) 20:26, 12 February 2012 (UTC)

So, for you a vector is contravariant, period. Things are not necessarily so absolute for the rest of the world, though. It cannot hurt to insist on referring that components transform contravariantly or covariantly, accordingly. Most reliable sources do this already. Sławomir Biały (talk) 22:05, 12 February 2012 (UTC)

Dear Participants of discussion!

Many thanks for your professional comments. Please, pay attention to addition in my message (Notation 1). However I ask (if it is possible) not talk this problem outside of rectangular Cartesian co-ordinates. It can be made later (after consensus for rectangular Cartesian co-ordinates). I ask to apply only short phrase without difficultly translated words. Remember that your comments are reading all over the world by means of computer translators.

Notation 1.

The vector fields cannot be constructed out of scalar fields using the gradient operator. Therefore so-called Laplacian field is not a true vector field. Thus, the requirements $\operatorname {rot} {\dot {\vec {u}}}=0,\operatorname {div} {\dot {\vec {u}}}=0$ are inconsistent for true vector fields.

This result confirms the proof about impossibility of irrotational velocity field in this old university textbook [4]p. 100-101. 2. Other unpleasant things we can see for many well-known classical equations in Wikipedia. For example the Euler equations (fluid dynamics) can be written as follows

$-\operatorname {grad} p=\rho (\operatorname {div} {\ddot {\vec {u}}}-{\vec {F}})$

Note that such equations have no sense as exact vector equations because $\operatorname {grad} p$ is not the true vector.

Here Helmholtz_decomposition we can read: “This theorem is of great importance in electrostatics, since Maxwell's equations for the electric and magnetic fields in the static case are of exactly this type.[2]” Thus Maxwell's equations have no sense as exact vector equations. We can to continue a list of similar incorrect mathematical physics equations in Wikipedia.

--Alexandr (talk) 12:05, 14 February 2012 (UTC)

You seem to be very confused. The gradient is defined as a vector (see, for instance, Borisenko and Taparov "Vector and tensor analysis with applications"). There is no problem with the equations you have listed. Sławomir Biały (talk) 12:58, 14 February 2012 (UTC)

I see that Covariance and contravariance of vectors states that the gradient is covariant. Is this consistent with the approach you developed above? Tkuvho (talk) 13:46, 14 February 2012 (UTC)

No. That should probably be clarified somehow. It's true that the partials transform covariantly, but these are the components of the differential. The gradient involves the inverse metric tensor. Sławomir Biały (talk) 14:02, 14 February 2012 (UTC)

It may be a good idea to make a note of it at Talk:Covariance and contravariance of vectors. Tkuvho (talk) 12:33, 15 February 2012 (UTC)

It probably doesn't help matters that in applied mathematics, people talk about "covariant components" and "contravariant components" of a given vector. This could be a big source of the OPs original confusion. Sławomir Biały (talk) 12:59, 15 February 2012 (UTC)

To Sławomir Biały. I have formulated my conclusion on the basis of this university textbook; 1.B. A.; Fomenko, A. T.; Novikov, Sergeĭ Petrovich (1992). Modern Geometry--methods and Applications: The geometry of surfaces, transformation groups, and fields] (2nd ed.) . Springer. (p. 15).ISBN 0387976639. Authors of this textbook – authoritative mathematicians: http://www.mathnet.ru/php/person.phtml?&personid=8368&option_lang=eng http://www.mathnet.ru/php/person.phtml?option_lang=eng&personid=4537 http://www.mathnet.ru/php/person.phtml?option_lang=eng&personid=21899 As well known from this textbook « … under co-ordinate change the gradient of function transforms differently from a vector ». Therefore the gradient of scalar function does not form the vector field. Thus, your objections «You seem to be very confused…. » concern first of all these authors.

I can present other and newer arguments that gradient of scalar function does not form the vector field.

--Alexandr (talk) 11:38, 17 February 2012 (UTC)

You should consult other books. What Fomenko et al define is usually called the differential. The gradient is usually defined to be the vector obtained from the differential by applying the inverse metric. See for instance Definition 2.3.9 of Abraham, Marsden, Raitu "Manifolds, Tensor Analysis, and Applications". Basically any book on tensor analysis agrees with me. Look at James Simmonds "A Brief on Tensor Analysis" (Springer UTM); Arfken and Weber "Mathematical methods for physicists", Chapter 2. Even in any calculus textbook you will see the definition that the gradient of a function is the vector whose magnitude is the greatest rate of change of the function and whose direction is the direction in which that rate of change occurs. (Under this definition, the gradient will transform as a vector.) Sławomir Biały (talk) 12:11, 17 February 2012 (UTC)

The gradient is the list of the coefficients of the differential of the function. The differential is a linear form, and thus, by definition of the dual vector space, is an element of the dual of the working space. A basis of this working space being chosen, the gradient is thus the vector of the coefficients of the differential on the dual basis (the members of the dual basis are the linear forms which send a basis vector to 1 and the others to 0). This being stated, to know if the gradient is a vector field depends on which definition of a vector field you choose (the definition in vector field is ambiguous): If a vector field is a function of the working space into its associated vector space, then the gradient is not a vector field for this definition. If a vector field is a function of the working space into an arbitrary vector space, then the gradient is a vector field for this definition. Whichever definition is chosen, the metric of the working space (dotproduct) induces an isomorphism between the working vector space and its dual. But this isomorphism may not be considered as an identification. This is the reason of the distinction between vectors and covectors, which are both vectors but in different spaces. — D.Lazard (talk) 14:49, 17 February 2012 (UTC)

No, the gradient is a vector, not a covector. The differential is the covector you describe. The gradient is the vector whose inner product with another vector is the differential of the function applied to the vector. This is the definition of the gradient. It is not in the dual space. The gradient has no meaning without a metric. (See also symplectic gradient for the symplectic version of this idea.) Sławomir Biały (talk) 16:06, 17 February 2012 (UTC)

I do not agree with you. You may be right if you consider only the usage of the gradient in physics. In the study of the functions of several variables, and in particular in optimization, the gradient is defined and used independently of any metrics, like in a sentence like the gradient is null at the local extrema of a differentiable function. The covector property of the gradient is clear in the conjugate gradient method, because the direction of the minimum of a quadratic function is not the gradient but its conjugate direction. D.Lazard (talk) 16:52, 17 February 2012 (UTC)

Gradient descent is a good example of what I mean. If it makes sense to "move in the direction of the gradient" then the gradient is a vector. One cannot move in the direction of a covector. Sławomir Biały (talk) 17:14, 17 February 2012 (UTC)

Dear Participants of discussion!

The assumption “vector fields can be constructed out of scalar fields using the gradient operator and so-called Laplacian field is a true vector field” is 100 years old. This assumption have many “Strict proofs”, covered in hundreds of textbooks, and taught each year to many thousands of students. It is difficult to believe that all “Strict proofs” are wrong. Therefore has changed nothing after edition in 1979 of the textbook Modern Geometry in which it is written '« … under co-ordinate change the gradient of function transforms differently from a vector » The convincing counterexample is necessary. Such counterexample I bring to your attention. This counterexample kills mentioned “Strict proofs”. I will specify a source of this counterexample later.

Counterexample. As we well know the divergence of any vector field on Euclidean space is a scalar field. Therefore as an example let's calculate the divergence of an acceleration vector $\operatorname {div} {\ddot {\vec {u}}}$ . The acceleration vector components can be written as

${\ddot {u}}_{i}={\frac {d{\dot {u}}_{i}}{dt}}={\frac {\partial {\dot {u}}_{i}}{\partial t}}+{\dot {u}}_{x}{\frac {\partial {\dot {u}}_{i}}{\partial x}}+{\dot {u}}_{y}{\frac {\partial {\dot {u}}_{i}}{\partial y}}+{\dot {u}}_{z}{\frac {\partial {\dot {u}}_{i}}{\partial z}},(i=x,y,z)$

After taking an operator div we have

$\operatorname {div} {\ddot {\vec {u}}}={\frac {\partial {\ddot {u}}_{x}}{\partial x}}+{\frac {\partial {\ddot {u}}_{y}}{\partial y}}+{\frac {\partial {\ddot {u}}_{z}}{\partial z}}={\frac {\partial }{\partial t}}\operatorname {div} {\dot {\vec {u}}}+{\dot {u}}_{x}{\frac {\partial }{\partial x}}\operatorname {div} {\dot {\vec {u}}}+{\dot {u}}_{y}{\frac {\partial }{\partial y}}\operatorname {div} {\dot {\vec {u}}}+{\dot {u}}_{z}{\frac {\partial }{\partial z}}\operatorname {div} {\dot {\vec {u}}}+{}$

${}+\left[{\left({\frac {\partial {\dot {u}}_{x}}{\partial x}}\right)^{2}+\left({\frac {\partial {\dot {u}}_{y}}{\partial y}}\right)^{2}+\left({\frac {\partial {\dot {u}}_{z}}{\partial z}}\right)^{2}+2\left({{\frac {\partial {\dot {u}}_{x}}{\partial y}}{\frac {\partial {\dot {u}}_{y}}{\partial x}}+{\frac {\partial {\dot {u}}_{y}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial y}}+{\frac {\partial {\dot {u}}_{x}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial x}}}\right)}\right]$ (1)

As we can see this formula can be written as

$\operatorname {div} {\ddot {\vec {u}}}={\frac {d}{dt}}\operatorname {div} {\dot {\vec {u}}}+(\operatorname {div} {\dot {\vec {u}}})^{2}$ (2)

if and only if such equality is true

$\left({\frac {\partial {\dot {u}}_{x}}{\partial x}}\right)^{2}+\left({\frac {\partial {\dot {u}}_{y}}{\partial y}}\right)^{2}+\left({\frac {\partial {\dot {u}}_{z}}{\partial z}}\right)^{2}+2\left({{\frac {\partial {\dot {u}}_{x}}{\partial y}}{\frac {\partial {\dot {u}}_{y}}{\partial x}}+{\frac {\partial {\dot {u}}_{y}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial y}}+{\frac {\partial {\dot {u}}_{x}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial x}}}\right)=(\operatorname {div} {\dot {\vec {u}}})^{2}$ (3)

The realization of (3) require such equality:

${\frac {\partial {\dot {u}}_{x}}{\partial y}}{\frac {\partial {\dot {u}}_{y}}{\partial x}}+{\frac {\partial {\dot {u}}_{y}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial y}}+{\frac {\partial {\dot {u}}_{x}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial x}}={\frac {\partial {\dot {u}}_{x}}{\partial x}}{\frac {\partial {\dot {u}}_{y}}{\partial y}}+{\frac {\partial {\dot {u}}_{y}}{\partial y}}{\frac {\partial {\dot {u}}_{z}}{\partial z}}+{\frac {\partial {\dot {u}}_{x}}{\partial x}}{\frac {\partial {\dot {u}}_{z}}{\partial z}}$ (4)

Note that equality (3) can make sense only for $\operatorname {rot} {\dot {\vec {u}}}\neq 0$ In the case $\operatorname {rot} {\dot {\vec {u}}}=0$ all terms in brackets of (3) are positive and $\operatorname {div} {\dot {\vec {u}}}=0$ is impossible. Thus the requirements $\operatorname {rot} {\dot {\vec {u}}}=0,\operatorname {div} {\dot {\vec {u}}}=0$ for vector field are inconsistent. As we well know ${\dot {\vec {u}}}=\operatorname {grad} \varphi ,_{}\nabla ^{2}\varphi =0$ , if $\operatorname {rot} {\dot {\vec {u}}}=0,\operatorname {div} {\dot {\vec {u}}}=0$. Therefore the vector fields cannot be constructed out of scalar fields using the gradient operator and so-called Laplacian field is not a true vector field.

--Alexandr (talk) 12:20, 27 February 2012 (UTC)

If this counterexample were true, it would be a counterexample to the chain rule, having nothing to do with the covariance and contravariance of vectors. Since this is clearly ridiculous, you must have made a mistake. Your error seems to be in going from (1) to (2). Sławomir Biały (talk) 13:25, 27 February 2012 (UTC)

Dear Sławomir Biały !

I hope, that your doubts will disappear after consideration of these well-known analogies which You can see in textbooks:

$\operatorname {div} {\mathbf {\vec {u}} }=\varepsilon _{\operatorname {o} }={\frac {1}{\delta V}}d(\delta V)$

$\operatorname {div} {\dot {\vec {u}}}={\dot {\varepsilon }}_{\operatorname {o} }={\frac {1}{\delta V}}{\frac {d(\delta V)}{dt}}$ (5)

Here, $\delta V$ - infinitesimal volume, $\varepsilon _{\operatorname {o} }$ - volume deformation, ${\mathbf {\vec {u}} }$ - infinitesimal displacement vector ( ${\vec {u}}$ - any displacement vector), ${\dot {\varepsilon }}_{o}$ -velocity of volume deformation. By analogy, the acceleration divergence $\operatorname {div} {\ddot {\vec {u}}}$ probably can be written as ( ${\ddot {\varepsilon }}_{\operatorname {o} }$ - acceleration of volume deformation)

$\operatorname {div} {\ddot {\vec {u}}}={\ddot {\varepsilon }}_{\operatorname {o} }={\frac {1}{\delta V}}{\frac {d^{2}(\delta V)}{dt^{2}}}$ (6)

It is only a hypothesis on the basis of obvious analogy. The acceleration of volume deformation can be transform so

${\ddot {\varepsilon }}_{o}={\frac {1}{\delta V}}{\frac {d^{2}(\delta V)}{dt^{2}}}={\frac {1}{\delta V}}{\frac {d}{dt}}\left({{\frac {\delta V}{\delta V}}{\frac {d(\delta V)}{dt}}}\right)={\frac {1}{\delta V}}{\frac {d}{dt}}\left({\delta V\operatorname {div} {\dot {\vec {u}}}}\right)=$ $={\frac {d}{dt}}\operatorname {div} {\dot {\vec {u}}}+\operatorname {div} {\dot {\vec {u}}}{\frac {d(\delta V)}{\delta Vdt}}={\frac {d}{dt}}\operatorname {div} {\dot {\vec {u}}}+(\operatorname {div} {\dot {\vec {u}}})^{2}$. (7)

As you can see this equality is exact. Therefore our hypothesis is correct if (4) are satisfied and, for example, such additional conditions are satisfied

${\frac {\partial {\dot {u}}_{x}}{\partial x}}{\frac {\partial {\dot {u}}_{y}}{\partial y}}={\frac {\partial {\dot {u}}_{x}}{\partial y}}{\frac {\partial {\dot {u}}_{y}}{\partial x}},{\frac {\partial {\dot {u}}_{x}}{\partial x}}{\frac {\partial {\dot {u}}_{z}}{\partial z}}={\frac {\partial {\dot {u}}_{x}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial x}},{\frac {\partial {\dot {u}}_{y}}{\partial y}}{\frac {\partial {\dot {u}}_{z}}{\partial z}}={\frac {\partial {\dot {u}}_{y}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial y}}$ (8)

These equalities satisfy (4). Therefore in this case formula (1) can be written as (2) also. I will specify a source of this counterexample later.

--Alexandr (talk) 17:31, 11 March 2012 (UTC)

Well, I'm seeing a few fundamental errors in this. The first one is in equation (5). But the bottom line is that even if you did have a counterexample that would turn mathematics on its head, it's offtopic for the encyclopedia. We can only report what reliable sources say (and do so in proportion to their relative weight). So, if you can get your counterexample published in a top mathematics journal, and it is discussed by mainstream vector calculus textbooks, then (and only then) can we report on it here. For better or worse, those are the rules. Sławomir Biały (talk) 20:10, 11 March 2012 (UTC)

Dear Sławomir Biały ! You have written:

1. «Well, I'm seeing a few fundamental errors in this. The first one is in equation (5)».

However equation (5) follows from comparison of the continuity equation

${\frac {1}{\rho }}{\frac {d\rho }{dt}}+\operatorname {div} {\dot {\vec {u}}}=0$ (9)

and conservation of mass law

${\frac {d(\delta m)}{dt}}={\frac {d(\rho \delta V)}{dt}}=\delta V{\frac {d\rho }{dt}}+\rho {\frac {d(\delta V)}{dt}}=0\Rightarrow {\frac {d\rho }{\rho dt}}=-{\frac {d(\delta V)}{\delta Vdt}}$ (10)

Therefore

${\frac {d(\delta V)}{\delta Vdt}}=\operatorname {div} {\dot {\vec {u}}}$

Where you see first fundamental error?

2.«But the bottom line is that even if you did have a counterexample that would turn mathematics on its head, it's offtopic for the encyclopedia…».

This problem we will discuss later.

--Alexandr (talk) 11:44, 23 March 2012 (UTC)

You haven't correctly taken a time derivative in going from the first equation in (5) to the second, or in going from the second equation of (5) to equation (6), etc. But as I said, this discussion is pointless. It's also not our job to point out errors in your calculations. But be assured, you are making errors. The way to understand these things would be to enroll in a class on vector calculus and discuss your findings with the professor. While I've already said more than is usual for me, my standard offer in evaluating such claims is $1000 (US), payable in advance, if you would like me to seriously engage your purported counterexample and identify the mistakes. Sławomir Biały (talk) 12:36, 23 March 2012 (UTC)

Much ado about differing differential vs gradient conventions. What the hell is going on? — Kallikanzarid^talk 14:32, 25 March 2012 (UTC)

Well, Alexandr above claims to have found a counterexample to the chain rule, having nothing whatsoever to do with different conventions (although he doesn't seem to realize this). Sławomir Biały (talk) 18:26, 25 March 2012 (UTC)

Dear Sławomir Biały !

Thanks for your comments!

1.“You haven't correctly taken a time derivative in going from the first equation in (5) to the second” The going from first equation in (5) to the second carried out differently. I wrote above ${\mathbf {\vec {u}} }$ - infinitesimal displacement vector ( ${\vec {u}}$ - any displacement vector). As you can see we have different vectors. Therefore the time derivative is pointless.

2.“or in going from the second equation of (5) to equation (6)”

The second equation of (5) and equation (6) obtained independently.

However this discussion is from other field (continuum mechanics).

Very important comment:

“Alexandr above claims to have found a counterexample to the chain rule”

The velocity vector of Cartesian 3-space ${\dot {\vec {u}}}={\dot {\vec {u}}}(x,y,z,t)$ for a fix time $t={\bar {t}}$ can be represented as ${\dot {\vec {u}}}={\dot {\vec {u}}}(\varsigma )$ , $\varsigma =\varsigma (x,y,z)$ . This representation is well known as a vector function of scalar argument (or vector-valued function). Then according to chain rule [Vygodsky M.J. (1977) Manual on Higher Mathematics (12th edition). http://eqworld.ipmnet.ru/ru/library/books/Vygodskij1977ru.djvu (Russian). ASIN: B001U5VF9O (English)]

${\frac {\partial {\dot {\vec {u}}}}{\partial x_{i}}}={\frac {\partial {\dot {\vec {u}}}}{\partial \varsigma }}{\frac {\partial \varsigma }{\partial x_{i}}},(x_{i}=x,y,z)$ . (11)

Formulas (11) can be written explicitly concerning ${\frac {\partial {\dot {\vec {u}}}}{\partial \varsigma }}$. Therefore this common factor can be eliminated. As a result we have

${\frac {\partial {\dot {\vec {u}}}}{\partial x_{i}}}={\frac {\partial {\dot {\vec {u}}}}{\partial x_{j}}}{\frac {\frac {\partial \varsigma }{\partial x_{i}}}{\frac {\partial \varsigma }{\partial x_{j}}}}$ (12)

In component form formulas (12) look like

${\frac {\partial {\dot {u}}_{x}}{\partial x_{i}}}={\frac {\partial {\dot {u}}_{x}}{\partial x_{j}}}{\frac {\frac {\partial \varsigma }{\partial x_{i}}}{\frac {\partial \varsigma }{\partial x_{j}}}},{\frac {\partial {\dot {u}}_{y}}{\partial x_{i}}}={\frac {\partial {\dot {u}}_{y}}{\partial x_{j}}}{\frac {\frac {\partial \varsigma }{\partial x_{i}}}{\frac {\partial \varsigma }{\partial x_{j}}}},{\frac {\partial {\dot {u}}_{z}}{\partial x_{i}}}={\frac {\partial {\dot {u}}_{z}}{\partial x_{j}}}{\frac {\frac {\partial \varsigma }{\partial x_{i}}}{\frac {\partial \varsigma }{\partial x_{j}}}}$ (13)

Relations (13) can be written explicitly concerning ${\frac {\frac {\partial \varsigma }{\partial x_{i}}}{\frac {\partial \varsigma }{\partial x_{j}}}}$. Therefore this common factor can be eliminated. Thus

${\frac {\partial {\dot {u}}_{x}}{\partial x_{i}}}{\frac {\partial {\dot {u}}_{y}}{\partial x_{j}}}={\frac {\partial {\dot {u}}_{x}}{\partial x_{j}}}{\frac {\partial {\dot {u}}_{y}}{\partial x_{i}}},_{}{\frac {\partial {\dot {u}}_{x}}{\partial x_{i}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{j}}}={\frac {\partial {\dot {u}}_{x}}{\partial x_{j}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{i}}},_{}{\frac {\partial {\dot {u}}_{y}}{\partial x_{i}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{j}}}={\frac {\partial {\dot {u}}_{y}}{\partial x_{j}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{i}}}$ .

We have the same result (8) !!!!!!!!! As we can see our conjecture about (8) is true. This conjecture has appeared after such transformation of counterexample (1)

$\operatorname {div} {\ddot {\vec {u}}}={\frac {d}{dt}}\operatorname {div} {\dot {\vec {u}}}+(\operatorname {div} {\dot {\vec {u}}})^{2}-$ $-2\left[{\left({{\frac {\partial {\dot {u}}_{x}}{\partial x_{i}}}{\frac {\partial {\dot {u}}_{y}}{\partial x_{j}}}-{\frac {\partial {\dot {u}}_{x}}{\partial x_{j}}}{\frac {\partial {\dot {u}}_{y}}{\partial x_{i}}}}\right)+\left({{\frac {\partial {\dot {u}}_{x}}{\partial x_{i}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{j}}}-{\frac {\partial {\dot {u}}_{x}}{\partial x_{j}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{i}}}}\right)+\left({{\frac {\partial {\dot {u}}_{y}}{\partial x_{i}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{j}}}-{\frac {\partial {\dot {u}}_{y}}{\partial x_{j}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{i}}}}\right)}\right]$ (14)

--Alexandr (talk) 19:31, 10 April 2012 (UTC)

Tau (2π)

What do folks here think about the article Tau (2π)? Recall the AfD last year. In that AfD, the sources presented were news items in the mainstream press. Consensus seemed to be that an article could be spun out from those sources. But now I'm concerned that many of the works cited in that article are not reliable, but rather various wacky "manifestos" pushing the τ concept. Furthermore, parts of the article are not cited at all. What should be done? Sławomir Biały (talk) 11:46, 13 March 2012 (UTC)

If it is an article about the number, then it should be moved to 2π (mathematical constant) because this name is the most recognizable and at least not more ambiguous than "Tau". Also, because this τ-notation is much less known than the π-notation, all formulas should be presented in two ways: with "τ" and with "2π". Incnis Mrsi (talk) 12:08, 13 March 2012 (UTC)

If the use of the "new number" cannot be sourced in reliable publications, the page should go to AfD. Tkuvho (talk) 13:45, 13 March 2012 (UTC)

I propose to rename the page Tau (2π) against pi (π) debate and to insert at the beginning of the lead something like "The constant π = 3,14159... is widely used in many scientific and engineering areas, including mathematics, physics, astronomy, electrical engineering, signal processing, ... It has been proposed to replace π by τ = 2π and a debate has followed, in which none of the international scientific organizations has been involved and which has not been echoed in any major scientific publication. This page presents the rationales which have been developed in this debate". Per wp:BRD, I'll do these changes immediately. This is not incompatible with AfD. D.Lazard (talk) 14:00, 13 March 2012 (UTC)

P.S.: I have modified the lead, but I am unable to move to a title containing Greek letters. Thus it is moved to Tau against pi debate. D.Lazard (talk) 14:34, 13 March 2012 (UTC)

Instead of wasting time with an AfD, I suggest we simply redirect this to pi and include a brief note there that at least one person supports replacing pi by tau=2π. Tkuvho (talk) 15:59, 13 March 2012 (UTC)

What "new number"? What "replacing π by"? There is a lot of sources about the "2π" constant and its importance (for example, as a conversion factor from turn (geometry) to radian). These are less sources which propose a special symbol for this constant. But if one tried to compose an article focused on these proposals, he would have to write about the number, eh? So, it will be either an article about the number or not an article. I repeat: the article has to be moved just to 2π (mathematical constant), without mentioning of any controversies in the title (because "2π" is recognizable, but "Tau against pi debate" is not). Mentioning this τ-notation in the article itself, as well as links from "τ" and "turn (geometry)" will be enough. Incnis Mrsi (talk) 08:30, 14 March 2012 (UTC)

Some pretty good arguments have been put forward for tau and the subject did gain international press. Hence an AfD is ridiculous, the proposed "debate" title doesn't cover the article and the attempt to shove it down various users throats has been thwarted (no consensus). The subject was allready deemed notable and WP:NPOV demands we give it a fair treatment instead of trying to bury it in another article. Hence I strongly oppose the suggestions made here. Kleuske (talk) 10:09, 14 March 2012 (UTC)

The symbol τ isn't used in favor of 2π in any scientific sources. What do the news items actually say about it? That's what the article should be based on. Sławomir Biały (talk) 10:37, 14 March 2012 (UTC)

Yeah, here's some wacky college called MIT – and who's ever heard of them – that apparently considered tau notable enough to center their new student admissions announcements around it. Yes, tau is very new. Extremely new. So consider how remarkable it is that a year and a half after it first appeared, that MIT did this. How about a little patience here, instead of destroying people's work? If you're wrong, you'll just have to recreate the page, and soon. If you're right that tau isn't going to go anywhere, you'll get your chance to kill off the page soon enough. Joseph Lindenberg (talk) 11:04, 14 March 2012 (UTC)

I'm not sure if your being serious about that MIT link, but there is no way that can be used as a scholarly reliable source in an encyclopedia article. Sławomir Biały (talk) 11:14, 14 March 2012 (UTC)

No, I'm not suggesting citing it in the article. But it should make you ask yourself if you aren't being hasty, given that this article already exists. Ask yourself what conversations must be going on at MIT for them to use something like that. Given that creating the article was OK'd less than a year ago, I don't see why today on Pi Day, you're suddenly determined to kill it. Joseph Lindenberg (talk) 11:53, 14 March 2012 (UTC)

I've cleared out at least the most blatant original research at that article. There is more, but it is going to require looking at sources. However, there seems to be a complete lack of reliable sources on this subject. I'm looking at the AfD debate, and there were a few news items mentioning tau, but pretty thin on details. Here are the "reliable" sources mentioned at the AfD: [5], [6], [7], broadcast, article,

• • Eoin O'Carroll (March 14, 2011). "Pi Day: Why we celebrate 3.14..." The Christian Science Monitor.
  • Elizabeth Landau (March 14, 2011). "La constante matemática pi tiene un rival: tau" (in Spanish). CNN México.
  • Michiel Hendryckx (June 30, 2011). "Weg met 3,14159265... ?". De Standaard (in Dutch).
  • Jacob Aron (January 8, 2011). "Michael Hartl: It's time to kill off pi". The New Scientist. 209 (2794): 23. doi:10.1016/S0262-4079(11)60036-5.

I've looked through most of these, and it really doesn't seem like enough to base an article on. The only other reliably published source is Palais's op-ed in the Math Intelligencer http://www.math.utah.edu/%7Epalais/pi.pdf (and I think op-eds can only be used as primary sources for the opinions of their authors). If there really is nothing else, then this will be a very short article indeed. Sławomir Biały (talk) 11:11, 14 March 2012 (UTC)

AFAIK there's no requirement that sources be "scholarly", just reliable. If there is such a requirement, we can delete quite a lot of articles, thus making maintaining the encyclopedia a lot easier. So please, where do i find that guideline? Kleuske (talk) 11:29, 14 March 2012 (UTC)

Did I make that argument anywhere? Or are you just creating a straw-man? Please, just find any reliable sources for the subject. What the article will look like should be dictated by those. Sławomir Biały (talk) 11:40, 14 March 2012 (UTC)

P.S. I could have made that argument, and been on solid footing per WP:SCHOLARSHIP and WP:NEWSORG. While there is no absolute requirement that sources be scholarly, on scientific subjects they should be. If the article is about the constant, then scholarly sources are needed. If it's just about the cultural phenomenon, then news items might pass muster. But the article simply can't use news items to justify its existence (as a piece about the cultural phenomenon) only then to document the purported "scientific" notion (sourced to various blogs, etc.). That's original research. Sławomir Biały (talk) 11:48, 14 March 2012 (UTC)

The idea of basing such an article on a "cultural phenomenon" is interesting, but since we are discussing this at WPM, the discussion needs to focus on its scientific merits. Regardless of an outcome of a future AfD, we should be able to reach a consensus whether such an article can stand as a scientific piece. If we agree that it can't, this does not necessarily predetermine the outcome of an AfD, but it does clarify this particular issue. Tkuvho (talk) 11:54, 14 March 2012 (UTC)

It's clear that there is no merit for a scientific article on the subject, given the lack of scientific sources. The only reliable sources are various fluff news items about "tau day" and suchlike, documenting a cultural phenomenon rather than a legitimate scientific debate. The article needs to be rewritten based on those sources. Sławomir Biały (talk) 11:59, 14 March 2012 (UTC)

This is clear to the two of us, but other editors seem to have expressed themselves otherwise. Do we all agree that there is no meric for a mathematical/scientific piece? Tkuvho (talk) 12:04, 14 March 2012 (UTC)

After looking at the available reliable sources, they seem for the most part to be about "tau day", rather than documenting the constant itself or any supposed debate about it in a serious way. Any thoughts about rewriting the article to be about tau day instead from these sources, and then moving it to tau day? Sławomir Biały (talk) 12:07, 14 March 2012 (UTC)

You're going to have an article about Tau Day but no article about tau? Joseph Lindenberg (talk) 12:14, 14 March 2012 (UTC)

If there is a consensus that we are talking about a cultural rather than scientific phenomenon, then tau day may be more appropriate. Tkuvho (talk) 12:17, 14 March 2012 (UTC)

A day in honor of the number that shall not be named. Uh huh. Joseph Lindenberg (talk) 12:24, 14 March 2012 (UTC)

I appreciate your sense of humor. Note however what while we don't have an article on dry, we do have one on dry humor. Tkuvho (talk) 12:42, 14 March 2012 (UTC)

Yeah, encyclopedias don't usually have many articles about adjectives. Nouns, on the other hand... Joseph Lindenberg (talk) 13:02, 14 March 2012 (UTC)

There seem to be reliable sources about the day, but not the constant. So, yeah. Sławomir Biały (talk) 12:28, 14 March 2012 (UTC)

In [[Talk: Tau (2π)], I have started a discussion to move to tau versus pi debate. It seems a better title for the cultural phenomenon. D.Lazard (talk) 12:34, 14 March 2012 (UTC)

Can't wait to see what MIT and its applicants think of Wikipedia when at 6:28 pm today, they discover tau no longer exists. If tau doesn't exist, "tau time" doesn't exist, so I guess all those applicants to MIT will just never find out if they got in. Yeah, I'm making jokes, and I know the opinions of the smartest high school seniors in the country aren't relevant here, but if you read through the comments, there's an awful lot of support for tau. It's one thing to delay allowing an article to be created. Removing one on a subject that's gotten this popular this fast and is accelerating, well... Tell ya what. Try something. Go to google and type "pi is". Just "pi is". See what the first autocomplete choice is. Joseph Lindenberg (talk) 12:53, 14 March 2012 (UTC)

Do you really think that an humoristic blog is the official position of MIT? D.Lazard (talk) 13:00, 14 March 2012 (UTC)

Do you think MIT takes its reputation so lightly that they'd email that out to every single applying freshman and their parents, and actually alter the time when they post the notices online, if there were just one or two crackpots in the basement of the math building who supported tau? Would the Dean of Admissions approve being portrayed as appeasing a few crackpots? Or do they realize this could be taking off quickly, and it would be best for MIT's reputation to get on early, even if only half-way. I realize it isn't an official statement of MIT's position. But they're moving in the opposite direction of what you're proposing. Joseph Lindenberg (talk) 13:28, 14 March 2012 (UTC)

Then your second to last sentence is an admission of the uselessness of that page. Let's pretend for a moment that the opinions of one well-reputed school should influence WP. Under that assumption, we have to remember that even the "smartest" people are allowed to have some silly opinion that you should pay no heed to (one example, Jeremy Silman: excellent chess author, and also a proponent of astrology.) These sort of opinions are especially endemic to young people, who can get overexcited about things they perceive as new. MIT, is of course interested in getting young people excited so naturally this sort of thing makes a good impression on students. Rschwieb (talk) 13:39, 14 March 2012 (UTC)

I dont see what relevance the MIT comic has to the continued discussion. It has already been agreed that it is not a reliable source. Sławomir Biały (talk) 13:44, 14 March 2012 (UTC)

My point is it's a clear indication of the growing legitimacy of tau. Again, I'm not saying to cite it in an article, but maybe you should postpone this action. Joseph Lindenberg (talk) 14:12, 14 March 2012 (UTC)

Do you really think the Dean of Admissions at MIT would allow himself to be portrayed as supporting astrology? Has MIT ever said they changed their notification date because it was a bad day astrologically? Showing him wearing cut-off suit pants and skateboarding is how they appealed to the young people. Their parents won't see any harm in that. But if you're paying $40,000 tuition to send your kid there for a first-class sci/tech/math education, you're not going to want to see anything that even looks like them endorsing crackpot science/math. And MIT knows it. And MIT employs public relations experts to make sure that never happens. That cartoon wasn't just some random doodling by a secretary who then sent it out for giggles. That kind of thing gets scrutinized very carefully before being sent out. There's a lot of money at stake in their reputation. Joseph Lindenberg (talk) 14:07, 14 March 2012 (UTC)

I am not sure about "random doodling for giggles" but I think is is possible that questionable material would be used in such a situation to "liven up" a presentation so as to attract, as you put it, the $40,000 etc. Tkuvho (talk) 14:21, 14 March 2012 (UTC)

These seem to be blogs by various alumni. They in no way represent anything approaching an official position of the university (or the dean of admissions for that matter). Sławomir Biały (talk) 14:25, 14 March 2012 (UTC)

Uh, no. That was the official email sent out to all applicants notifying them when the decision would be posted. An individual alumnus couldn't change the time MIT posts those decisions to 6:28pm. Joseph Lindenberg (talk) 14:33, 14 March 2012 (UTC)

Oh, if you're saying that because at mitadmissions.org it says for more information, see this guest blog entry, that's a joke. The supposed guest is Sir Nigel Blogberry. He's based on Sir Nigel Archibald Thornberry, who was apparently a kids' TV character when these applicants were kids. You can be sure MIT had to pay for the rights to use it. Like I said, this wasn't some casually put together thing. Joseph Lindenberg (talk) 14:45, 14 March 2012 (UTC)

Because the thing that marketers know attracts teenage kids most isn't sex, alcohol, sports, or gee-whiz technology. It's multiplying a math constant by 2. Joseph Lindenberg (talk) 14:28, 14 March 2012 (UTC)

I just checked the "contributions" of User:Joseph Lindenberg. They started last summer, number in the hundreds, and focus exclusively on the Tau article. Under the circumstances, it is unlikely we will be able to change User:Joseph Lindenberg's mind about the usefulness of the page. I do want to encourage User:Joseph Lindenberg to diversify his contributions to wiki. Tkuvho (talk) 14:46, 14 March 2012 (UTC)

Thanks for the info: that explains a lot. Rschwieb (talk) 16:02, 14 March 2012 (UTC)

yeah... It's also ad hominem _and_ you still have to convince the creator of the article. To wit, yours truly. Wanna have a look at *my* track record? (hint, check three language projects) Kleuske (talk) 17:26, 18 March 2012 (UTC)

Kleuske, I'm not keeping track of who is taking what position here (and really I'm not even sure what's in dispute), but no, no one has to "convince the creator of the article", not in principle anyway. I don't want to come across too aggressive on that, because we strive for collegiality, but having started an article does not give you any special privileges with regard to it. See WP:OWN. There are arguably some limited exceptions regarding things like variety of English used (see WP:RETAIN), and maybe some similar issues like citation style, basically things that don't affect the article much but that people get exercised about anyway. --Trovatore (talk) 20:05, 18 March 2012 (UTC)

Varieties of English and such things are not what i'm concerned about and i know about WP:OWN. Nevertheless, the project is based on concensus, which is absent. Given the date on which the assault on the article was launched (pi-day), i cannot help suspecting a lot of WP:POINT in the debate. Kleuske (talk) 20:29, 18 March 2012 (UTC)

If you want a consensus, you should avoid words like assault, cease to "suspect a lot" other editors and to qualify their edits of "madness". The point is that the previous version of the article was mainly WP:OR and that it did not respected the rules WP:undue and WP:GEVAL. In particular, I read in WP:undue: "If a viewpoint is held by an extremely small (or vastly limited) minority, it does not belong in Wikipedia regardless of whether it is true or not and regardless of whether you can prove it or not, except perhaps in some ancillary article. Keep in mind that, in determining proper weight, we consider a viewpoint's prevalence in reliable sources, not its prevalence among Wikipedia editors or the general public." As there is no reliable source supporting tau against pi, this not only justifies the new version of the article but would be a valid reason to delete it. D.Lazard (talk) 21:28, 18 March 2012 (UTC)

I honestly don't understand the argument about reliable sources that's been raised time and again in this debate. While many of the documents referred in the article are indeed in the form of manifestoes, videos, web pages, and such, I believe that we can agree that they do come from fairly established mathematicians and educators. I don't think it's fair to call them unreliable. You might argue about them being primary sources, but for that there is also plenty of third-party coverage of the Tau concept. I think that the severe amputation that has been done to the article was a disservice to Wikipedia, and the insistence on deletion even more so. --Waldir ^talk 19:30, 19 March 2012 (UTC)

@Waldir: No "established mathematicians" have used tau in their work (beyond the manifestos and youtubes), contrary to your claim. Your comments are therefore WP:POV. Tkuvho (talk) 08:57, 23 March 2012 (UTC)

Merge proposal

I am planning to merge tau (2π) into turn (geometry) since the tau article is a WP:POVFORK of the turn article. Any thoughts on this? Sławomir Biały (talk) 10:51, 22 March 2012 (UTC)

This could be done. But, at talk:tau (2π), there is a move request for renaming the page "The tau movement". The two proposals seem to be not compatible. IMO the discussion of Sławomir's merge proposal should be delayed after the closing of the move request. D.Lazard (talk) 11:07, 22 March 2012 (UTC)

That move proposal seems to be dead on arrival. In any event, as I said, we need to get clarity on what the article is actually about. If it's about the mathematical constant, then it should be merged to turn (geometry), because in that case these articles are about the same thing. If it's about the "movement" (a dubious term for a couple of random dudes who think a turn should be given the symbol τ), then the question is whether that movement is notable enough for its own article. I would say "no". There seems to be a lack of serious sources that address the so-called "movement". Press coverage about "tau day" could be used in an article about tau day (perhaps), but these human-interest stories are clearly insufficient to document any kind of "movement". Sławomir Biały (talk) 11:15, 22 March 2012 (UTC)

The move proposal has the great advantage to separate clearly the math questions from the non math one. If the move is done, keeping or deleting the article will be only a question of the real existence of such a movement and of the notability of tau supporters, and the debate will not be polluted by opinions on the math constants. If the move is rejected, I support the merge. However, merging now will induce to mix math and non math questions in the discussion and, probably, prevent a clear conclusion of the discussion. D.Lazard (talk) 12:16, 22 March 2012 (UTC)

Just a caution: though I agree that the "tau movement" is not notable, and possibly even that "tau" is also not notable enough to justify an article of its own, there is a gulf of semantic (and probably formal) difference between the constant tau and the geometric concept "turn" (or cycle, revolution or whatever), notwithstanding their connection/relationship in the geometric context when choosing the (very natural, but not inevitable) units of radians. The suggested merge therefore seems inappropriate; I would have thought a merge of tau (2π) as a section in the article pi would have been more appropriate (possibly not stressing the symbol τ, but rather that 2π is natural and is more prevalent constant than π is). Imagine the reaction of mathematicians to renaming the article pi to halfcycle. — Quondum^☏✎ 12:38, 22 March 2012 (UTC)

Whatever your belief about the meaning of "turn" in geometry, the article turn (geometry) is about the constant 2π. We should not have two articles about the same constant. We can debate what the final target should be, e.g., 2π. But it's clear that these articles should get merged. Sławomir Biały (talk) 12:43, 22 March 2012 (UTC)

I which case a merge may be appropriate, but definitely not under the disambiguator "(geometry)", and not under a geometric term such as "turn". A merge of both to something like tau (mathematical constant) would then make sense if you do not think they should both be merged into pi. — Quondum^☏✎ 12:49, 22 March 2012 (UTC)

I agree that the names are bad. But I think tau (mathematical constant) emphasizes a fairly uncommon usage of the symbol τ in mathematics (see Talk: tau (2π) for discussion on this very point). I think twice pi would be the most common and NPOV article title. Sławomir Biały (talk) 12:51, 22 March 2012 (UTC)

On the contrary, I believe that is a reason to make sure the article turn (geometry) is about the geometric concept, and tau (2π) is about the number. If the contents of "turn (geometry)" currently focus on the constant 2π, that needs to be fixed (and relevant content moved to "tau (2π)"). --Waldir ^talk 14:50, 22 March 2012 (UTC)

This tau-madness continues for some reason incogitable to me. Turn (geometry) is a unit of angle, and 2π is a number. Who does not understand the difference? If one suppose that 2π is the same as turn, then 1 is the same as radian and π/2 is the same as right angle, isn't it a crap? There is only one natural topic for an article, the number 2π, but Sławomir Biały invents some unnatural things for more than a week. Incnis Mrsi (talk) 12:55, 22 March 2012 (UTC)

This is evidently an old debate and I'm new to it, so I don't want to stick my neck out, although it is clear Sławomir is not confusing terms in the post above. I will simply add my support for a name centred on the constant 2π (i.e. not tau or turn, but maybe twice pi or similar). — Quondum^☏✎ 14:15, 22 March 2012 (UTC)

I agree with Incnis Mrsi, and franky, I can't think of a better name than "tau (2π)" for the article. It's concise, precise, unambiguous and intuitive. All the proposals for merge or renaming I've seen would IMO only harm the title in one of these dimensions, and make it harder to find for those interested in the topic. I can't see any benefit in doing so. --Waldir ^talk 14:50, 22 March 2012 (UTC)

the distinction between number and geometry seems artificial. Besides, the manifesto of Palais already appears at turn (geometry). "Tau" is best redirected there. It is senseless to have two pages on the same subject. Tkuvho (talk) 15:02, 22 March 2012 (UTC)

(@Incnis Mrsi) I hadn't appreciated this distinction until you just now pointed it out. So, you suggest moving it to 2π, as has already been attempted? That seems reasonable, and would then possibly have adequate scope for an article. Sławomir Biały (talk) 15:38, 22 March 2012 (UTC)

Just like mathematicians have adopted Pi as a shorthand notation for 3.14... (which happened many years after it began being used), the proponents of 6.28... have agreed on Tau for the same reason. Since there is no opposition among proponents of 6.28... as a circle constant to the use of Tau (quite the contrary), it seems natural to use that in the title of the article just like pi does. --Waldir ^talk 15:56, 22 March 2012 (UTC)

Agreed. Everyone who doesn't call it 2π calls it tau now, including Bob Palais. Furthermore, notice something interesting in the two MIT blog posts (here and here), including the many discussion comments, and the Boston Globe article quoting MIT's Dean of Admissions. NOBODY EVER MENTIONED Michael Hartl or Bob Palais. Seriously, go and look. Tau is no longer the name proposed by Michael Hartl, etc. It's the name many people are using to refer to the number. They're not arguing over whether 6.28... should be called tau. They're arguing over whether tau should be used instead of pi in education. Even people who hate that idea are using the name tau like it's already the accepted name. Joseph Lindenberg (talk) 16:21, 22 March 2012 (UTC)

And just because something doesn't (yet) appear in math journals and textbooks doesn't mean it's not a legitimate term. Wikipedia has a page titled "fortnight". It's supposedly a unit of time, but you never see it in any physics journal or textbook. Does that mean we should AfD it, or move it to a subsection under "day"? Joseph Lindenberg (talk) 16:31, 22 March 2012 (UTC)

Joseph, you seem to be laboring under the mistaken notion that the "tau" thing is opposed by people who "hate the idea" that "tau should be used instead of pi in education". This is a conspiracy theory of yours. Please try to internalize the fact that the reason people at WPM are sceptical about the "tau revolution" is because it is not notable. Tkuvho (talk) 16:52, 22 March 2012 (UTC)

Hear, hear! Rschwieb (talk) 17:23, 22 March 2012 (UTC)

Maybe I am indeed mistaken about the motivations of some of the people involved here at Wikipedia. There are definitely people who explicitly say they "hate" the idea of switching to tau. But I increasingly realize some of the people here at Wikipedia may just be sticklers about their footnotes. I search for discussions of this topic online, and I'm constantly seeing people in favor of tau. Most just recently heard about it. I read through the comments by those MIT applicants. I read some of the 5,800 comments on Vi Hart's video, which has surpassed 800,000 views. There's a lot of evidence out there of a lot of people coming to favor tau. Unfortunately, there is a time lag before the appearance of the footnotable sources. Maybe the difference is you guys aren't watching this issue as closely as I am. That's not a criticism. I'm just trying to explain how we have such different views. But this is why I keep urging a little patience. I see something growing rapidly. Can't we table this for a few months? I have no intention of spending years defending this page if I'm wrong. Joseph Lindenberg (talk) 18:03, 22 March 2012 (UTC)

Invest some of your energy into studying WP:CRYSTAL. Tkuvho (talk) 18:23, 22 March 2012 (UTC)

You will notice that I've never written any of my predictions into the article text itself. Joseph Lindenberg (talk) 18:29, 22 March 2012 (UTC)

Thought: No! Turn is an angle. One turn or full rotation is 360 degrees, 400 gradians, 2π radians, or τ radians. Tau is not a turn. Tau is a number, the number of radians in one turn. 1/4 turn is τ/4 radians, is π/2 radians. π is a number, NOT a derived unit that means "half a turn". If Tau should redirect to turn, it follows that 360, 400, and 2π should also redirect to turn, which would be absurd. (Currently, 2π redirects to Tau (2π), as it should.) The proposed merge would be a sloppy a conflation. A876 (talk) 18:25, 22 March 2012 (UTC)

Note: Tau is interesting, and has its merits, but this section (Merge proposal) IS NOT THE PLACE TO DISCUSS that question. Please discuss it elsewhere; in fact (uncommon request), Editors: please Cut your own off-topic comments mistakenly posted here, and Paste them someplace else. A876 (talk) 18:25, 22 March 2012 (UTC)

Tkuvho and Rschwieb, if A876 is serious, you've got my permission to move the whole subtree of our discussion to tau's talk page. Joseph Lindenberg (talk) 20:26, 22 March 2012 (UTC)

I actually consider a turn to be a unit of angular measurement, just like degrees and radians are. But whether it's an angle or an angular unit, that's clearly very different from being a number. Joseph Lindenberg (talk) 18:37, 22 March 2012 (UTC)

• Oppose – the fact that there are tau radians in a turn is not a good reason to merge tau and turn, and more than you would merge 360 (number) and Turn. Dicklyon (talk) 05:52, 23 March 2012 (UTC)

RfC

I have started started an RfC. Please comment. Sławomir Biały (talk) 18:55, 25 March 2012 (UTC)

history of algebra or history of calculus?

An IP insists on adding material on the history of algebra in the history of calculus page of calculus, claiming in the latest revert that there is "no need to discuss" the addition. see here. Tkuvho (talk) 13:40, 15 March 2012 (UTC)

There's been a couple of people who stick in those the Arabs discovered everything or puffing things up to unreasonable proportions and they keep having to be pruned back, they do it to whole swathes of Wikipedia not just maths. Dmcq (talk) 13:57, 15 March 2012 (UTC)

The material being re-added may be appropriate at the history of algebra page. That's a subject of a separate discussion. But here it seems to hinge on the play on words on the term "calculus". Tkuvho (talk) 14:03, 15 March 2012 (UTC)

It may be a mistake, or confusion between "calculus" and "calculation". The IP seems to be French-speaking: he or she added a French source. Many French-speaking people make this mistake when trying to speak English, probably because en:calculus reads like latin "calculus" (="calculation" or "computation" = fr:calcul). en:calculus = fr:analyse (mathématiques) --El Caro (talk) 16:53, 15 March 2012 (UTC)

The French words for "calculation" and for "calculus" are both "calcul". RobHar (talk) 02:34, 26 March 2012 (UTC)

The two IPs involved trace back to Pakistan, using the geolocate tool. Rschwieb (talk) 22:45, 15 March 2012 (UTC)

Simple Wikipedia needs help with mathematics...

Hello all,

Simple English Wikipedia is one of the smaller Wikipedia projects; it tries to explain topics using simpler language. The big challenge there is to not sacrifice accuracy while explaining the topic at hand. Today, I extended the System of linear equations article there; I added the information that such systems are commonly represented and solved using matrices. I also added a section describing the general process of solving such systems, and links to common methods. The problem I found was that most of these (even the common ones, like Gaussian elimination or Cramer's rule) do not have articles there. We are a small community, and none of us has a background in mathematics. I am aware that there may be some concurrency between English and Simple English, and that in the minds of some people Simple English Wikipedia has a bad reputation. We would therefore look forward to any topic-specific help you could provide. --Eptalon (talk) 12:05, 24 March 2012 (UTC)

Nice article, but combining accuracy with clarity is something we struggle with in the mathematics community. Hopefully we can put our clear-speaking caps on and lend a hand, although some articles probably can never be put in simple terms. -- 202.124.73.23 (talk) 14:03, 24 March 2012 (UTC)

Merge help needed - Inertia tensor of triangle

Should Inertia tensor of triangle merge to List of moment of inertia tensors? Please comment at Talk:Inertia tensor of triangle#Merge proposal. I'd also appreciate if someone in this project could actually complete the merger (assuming the wiki community supports it, of course) since I don't know the math here. Thanks, D O N D E groovily Talk to me 12:32, 25 March 2012 (UTC)

restricted randomization

Restricted randomization has been nominated for deletion. Here's the discussion: Wikipedia:Articles_for_deletion/Restricted_randomization.

Apparently everyone has ALREADY forgotten that in 2002 probably 10% of Wikipedia articles were just copied from either the US Geographic Names Data Base or a federal agency web site on telecommunications. An article would say,

In telecommunications, the Atlantic Ocean is an ocean bounded on the east by Europe and Africa and on the west by the Americas, across which the transatlantic cable was laid.

It was crazy, but the policy was that we were to work on and improve them. Now this article is nominated for deletion only because its initial version is copied from a (non-copyrighted) federal government web site. The article needs work, but it's nowhere near as bad as lots of others that survive. Michael Hardy (talk) 17:50, 25 March 2012 (UTC)

This article is actually our only article on split-plot designs! Clearly it needs improvement. Michael Hardy (talk) 18:26, 26 March 2012 (UTC)

The question needs to be asked: why exactly is this article not considered a copyright violation? The original site [8] doesn't have a clearly visible copyright notice, but I also can't see any explicit waiver of copyright or any statement giving permission for the content to be reproduced elsewhere. (I agree that we should have an article on this topic; I just want to understand this issues fully before I comment at the deletion discussion.) Jowa fan (talk) 06:57, 27 March 2012 (UTC)

Works created by U.S. Federal Government employees (as part of their employment) cannot be copyrighted, under U.S. copyright law. No copyright, no copyvio. —David Eppstein (talk) 07:07, 27 March 2012 (UTC)

There used to be a specific template for NIST:

 This article incorporates public domain material from the National Institute of Standards and Technology

(I had the same question, a couple years ago, regarding Optimal design, for which the NIST material too closely followed Montgomery's textbook, which too closely followed Box & Draper's textbook, which too closely followed Box's article on alphabetic optimality, which too closely followed Box....)  Kiefer.Wolfowitz 07:08, 27 March 2012 (UTC)

Haha, with the internet today you can easily find many examples of what people might call plagiarism today.--Milowent • ^hasspoken 12:15, 27 March 2012 (UTC)

When you see an apparent case of plagiarism, please investigate it before deleting our text. Sometimes it is the other site plagiarizing us. For example, see Talk:Axiom of choice#Plagiarism?. JRSpriggs (talk) 13:04, 27 March 2012 (UTC)

Category:Featured articles on Mathematics Portal

As a result of this CfD discussion, 37 articles have Category:Featured articles on Mathematics Portal on their talk page. That's fine, but it is awkward how the category is stuck at the bottom of the page, where it will inevitably cause confusion to those adding comments in the last section. For example, click "edit" for the last section at Talk:Golden ratio and see that if you were adding a new comment, you should insert it above the "Category" line. Perhaps the category should be included as an option in {{Maths rating}}? Johnuniq (talk) 11:32, 27 March 2012 (UTC)

{{maths rating}} does not support portal pages; it's just for articles. But we could make a different template for these talk pages, like {{FA on Math Portal}}, that could be put at the top and which would categorize the articles. I'd be happy to do that if people want it, I think that the bare category at the bottom is indeed a problem. — Carl (CBM · talk) 15:26, 27 March 2012 (UTC)

But all the pages in Category:Featured articles on Mathematics Portal are standard articles which already have the template, an extra field would be easy enough to implement. Alternatively it is only a convention that categories need to be at the bottom of the page. It might be easier just to move these to the header.--Salix (talk): 16:35, 27 March 2012 (UTC)

I misunderstood, and thought these were portal pages. Since they're articles, I'm neutral between using the math rating template or a new one, or moving the category up (although I fear that some misguided bot will get confused in the third case and move it back to the bottom). — Carl (CBM · talk) 16:40, 27 March 2012 (UTC)

Yes bots might be a problem. I've now added a "portal" field to {{maths rating}}. Just add {{maths rating| ... | portal=true}} to place it in the category. I'm not entirely sure of the purpose of the category.--Salix (talk): 08:20, 28 March 2012 (UTC)

class="texhtml" (used by template: math)

Should we make fonts in class="texhtml" look similar to ones used by user:Nageh/mathJax? Currently an article intermixing <math> and {{math}} formatting, e.g. Quaternions and spatial rotation, looks patchy. The letter x shows an especially ugly contrast between the (default browser) "italic" and cursive fonts used in both texvc PNGs and mathJax. Incnis Mrsi (talk) 07:55, 27 March 2012 (UTC)

No. In fact, the STIX fonts, used by the MathML renderer (and supported also by the HTML/CSS renderer once MathJax is available as an official Wikipedia/MediaWiki option), match quite well with the {{math}} template font. Since even the STIX and TeX fonts have different font faces hard-coding any font values is not a good idea. However, you can always specify a custom font family using CSS code in your common.css file. Btw, I noticed a discussion on the MathJax user mailing list, suggesting that a future release may support the selection between serif and sans-serif fonts, which may address objections previously raised regarding the clash between maths fonts and surrounding text fonts. Nageh (talk) 13:55, 27 March 2012 (UTC)

I think that we should wait to see what happens with a site-wide mathjax rollout before we worry about these things. The {{math}} template is not widely used, and is mentioned but not encouraged WP:MOSMATH. Once mathjax is enabled, I expect we will be able to merge {{math}} and <math>, eliminating the issue. — Carl (CBM · talk) 15:24, 27 March 2012 (UTC)

It would be very nice to have the option to specify the fonts to MathJax, I like a strong distinction between maths and text but others find the distinction very jarring and want to be able to join both into sentences. I don't think we need worry too much about the {{math}} template, I believe that soon and at long last we will have good rendering of inline <math> and be able to phase the math template out. Dmcq (talk) 16:45, 27 March 2012 (UTC)

These reasonings of Nageh and Dmcq sound good, but have actually nothing to do with the problem: which formatting guidelines ought en.WP to follow today. For example, see the recent clash in Robinson arithmetic. CBM, probably with some followers, tries to eradicate {{math}}, arguing that pre-existing raw wiki markup is better. When MathJax finally came, there will be no consensus again on how to implement it in such cases, and conflicts will erupt yet another time. CBM and Dmcq speak about merger of {{math}} and <math> like such a decision were already taken. But when en.WP will have a good <math>, numerous compatibility problems with HTML formatting will preclude the conversion to <math> in many cases, and such a move will be not so easy as one could imagine. Incnis Mrsi (talk) 10:32, 30 March 2012 (UTC)

Unlike with {{math}} and <math>, when we have MathJax available as the default for readers, I will support using MathJax alone for both inline and displayed formulas. I find the appearance of MathJax on other sites, such as mathoverflow.net, to be perfectly acceptable, and I'm willing to live with the change to the current HTML math to get its benefits. On the other hand I don't see any strong benefits to the {{math}} template as it is currently formatted, although some disagree. In my LaTeX documents the math is not typically in a larger, different font, so that seems quite strange to me on Wikipedia. But I am not trying to eradicate {{math}}; for example if someone starts a new article they are welcome to use any style they want. — Carl (CBM · talk) 10:50, 30 March 2012 (UTC)

What means "any strong benefits"? We may dispute the comparison of {{math}} to various <math> implementation (such as unclickable PNG/texvc and client-side resource consuming MathJax), but {{math}} has at least one advantage over a raw wiki code: it explicitly labels an expression as mathematical and hence protects it from various automated and semi-automated stupid changes. Incnis Mrsi (talk) 11:05, 30 March 2012 (UTC)

I'd be happy to search for {{math}} and replace it with <math> and redo the formulae in the articles I watch when MathJax comes along so I see the math template as being a good marker that way. Dmcq (talk) 12:01, 30 March 2012 (UTC)

Original work

Dear mathematicians,

A contributor has put a theorem of his own in an article (Expander graph). He exhibits formulas that are not referenced in any academic source. Despite what he's saying, it requires much more than "routine calculations" to reach his result.

There was an interpretation mistake of one of the sources that led to a mistake in his formulas. This mistake stayed in the article during one year and a half. I did not succeed in convincing him that was the very illustration of the dangers of doing original work.

He "fixed" the formulas, but I'm still not perfectly convinced that the new version is correct. And no one can tell, since the result is not in the sources.

I also had him to remove a definition that was not in the sources (this time with success).

I would your need help to let him understand that, if something is not in the sources, it has nothing to do on wikipedia.

Discussion is here: Talk:Expander graph#"Original research" template.

Thanks in advance, --MathsPoetry (talk) 07:45, 28 March 2012 (UTC)

If the result is not published it should be swiftly removed regardless of correctness. Tkuvho (talk) 08:52, 28 March 2012 (UTC)

Ditto, and you can depend on support here if you remove questionable unsourced material and OR. Rschwieb (talk) 13:28, 28 March 2012 (UTC)

The question is whether it is indeed original research, as claimed above, or whether it is just a change of notation and routine calculations, which are allowed. I'm not sure myself, even after reading the source. -- Jitse Niesen (talk) 14:05, 28 March 2012 (UTC)

Tkuvho & Rschwieb, please have a look at the disputed paragraph; I am not sure you will retain your opinion after that. Sasha (talk) 14:28, 28 March 2012 (UTC)

I imagine what I wrote above was slightly misread, as I didn't make any comment on whether the material was OR or not. My opinion that OR should be deleted won't change. I am completely unaware if the content in dispute is OR or not, that is for someone familiar with the material to decide. Rschwieb (talk) 15:53, 28 March 2012 (UTC)

thanks for the clarification. Obviously, I agree with your opinion. Sasha (talk) 16:07, 28 March 2012 (UTC)

This seems to be a borderline case. On the face of it, it is a routine calculation, as long as you understand the different notations involved. However, the original editor did make an error that lost a factor of ${\sqrt {2}}$ (since corrected) so maybe its not quite as routine as it appears. Gandalf61 (talk) 14:38, 28 March 2012 (UTC)

There should be no question that this is not OR. MathsPoetry is obviously having a positive effect on the article, but I don't understand the particular focus on removing (rather than correcting) what is an immediate corollary of the cited work. The fact that a factor of 2 got lost in changing notations is not important at all, and putting the word "wrong" in boldface doesn't make it more so. --Joel B. Lewis (talk) 14:55, 28 March 2012 (UTC)

There are two points to it. First, I don't think it's an "immediate corrolary". I am not even sure his result is correct. Second, I don't think it's up to us to derive new corollaries from existing work.

Some background information: I'm no English speaker (sorry if my written English is suboptimal), and I am the guy who wrote the French article on expander graphs.

As a sidenote, I don't agree that losing a factor of 2 is not important: wrong math formulas have been online during one year and a half, due to that mistake.

Thanks to all for your kind advice on this. --MathsPoetry (talk) 16:25, 28 March 2012 (UTC)

I realize the subject is quite technical, so I have provided an outline of the proof of my contradictor on Talk:Expander graph#Ylloh's proof. This should enable you to judge whether it is an immediate corollary or not. I tried to make the presentation as neutral as possible, and I only did my remarks about possible problems after the demonstration. Best, --MathsPoetry (talk) 18:06, 28 March 2012 (UTC)