User talk:Arcfrk/Archive3

I'll reply sometime soon in detail to your request to summarize my remarks in my San Diego talk last week. For the moment, let me say omly that there are two rather contrary problems in writing the history of mathematics: (1) Taking anecdotes and second-hand reports for truth. This is a particular problem in mathematics, because it has its own internal logic, and mathematicians tend to write what they feel *ought* to have happened, whereas history is almost always more erratic and illogical. (2) Getting lost in the trees instead of making an attempt to give an overview. In my opinion, thsi is frequent among professional historians, who bend over backwards not to commit error #1.

In reply to one of your questions - I do know several professional historians, and I am just now in the process of discussing Wikipedia with some of them.--Bill Casselman (talk) 02:33, 13 January 2008 (UTC)[reply]

Howdy, I wanted to expand the example a bit, but didn't want to mess up your perspective.

Could you point out explicitly the ${\displaystyle \rho _{n}^{D}}$ in the example? In some sense the symmetric and antisymmetric parts are very clear (the "Schur functors" in Fulton-Harris seem quite natural), but then considering the tensor product formula seems almost misleading in this case purely because the ${\displaystyle \pi _{k}^{D}}$ are one dimensional. I think your current text is fine for those comfortable with the subject, but may be helpful to a larger audience with the main elements made explicit. I believe the current version implicitly names the ${\displaystyle \rho _{k}^{D}}$ as ${\displaystyle S^{2}\mathbb {C} ^{n}}$ and ${\displaystyle \wedge ^{2}\mathbf {C} ^{n}}$, and then explicitly names the ${\displaystyle \pi _{k}^{D}}$ in the text below.

Do you think the decomposition of ${\displaystyle \mathbb {C} ^{n}\otimes \mathbb {C} ^{n}\otimes \mathbb {C} ^{n}}$ would be helpful? This would force the tensor product into view, but might also confuse since the dimension two representation of S₃ appears twice, I believe. JackSchmidt (talk) 23:01, 18 January 2008 (UTC)[reply]

(reply to post)

I moved the not-simple parts of Schur's lemma to after the tie-in to group rings. The Lam reference can still apply to the first paragraph, but is mostly useful for all the related concepts which are now in the last paragraph.

For Schur–Weyl duality, I agree that n=2, all k would be a much better contrast than all n, k=3. JackSchmidt (talk) 06:11, 21 January 2008 (UTC)[reply]

I've had another go at Schur's lemma, trying to separate the essentials from the extras. Somehow, I couldn't find a proper place the "absolutely simple" stuff. It probably belongs to

absolutely irreducible, not this article. But feel free to further tweak the article. Arcfrk (talk) 07:11, 21 January 2008 (UTC)[reply

]

Your edit is much better overall. Also thank you for including the "converse is not true" part. The absolutely simple part is meant to tie into the previous comment that the endomorphism ring is as small as possible. Schur's lemma says the ring is well behaved if it is irreducible, but it is only best-behaved when it is irreducible even after tensoring. I think I found a place for it, and I included two explicit examples for the converse failing. I hope the second one is clear enough; modules don't have nice names, but this one is called "4 / 1" and has the same property that the image of an endomorphism is either the entire module or zero, because the only nonzero proper submodule is the one dimensional module and the four dimensional simple module has no quotient isomorphic to it. JackSchmidt (talk) 07:39, 21 January 2008 (UTC)[reply]

Hi Arcfrk,
I read the correction you operated on the manifold entry where you removed the wikilink point that I created.

(cur) (last) 07:38, 26 January 2008 Arcfrk (Talk | contribs) m (52,873 bytes) (rv meaningless wikilink) (undo)

In my talk I had also the following message from Silly rabbit (talk) :

Excessive wikilinking

Hi, Just so you know, the Wikipedia

make links that are relevant to the context. I have noticed that many of your recent contributions to Wikipedia are creating wikilinks to isolated words which are irrelevant to the context of the article. For example, at manifold, you linked point rather than to the correct point (geometry). It is important, when wikilinking, to consider not just if the word can be linked, but if it should be linked, and if so how. I would ask that in the future you please exercise more discretion in your choice of words to link. Regards, Silly rabbit (talk) 12:45, 26 January 2008 (UTC)[reply

]

4 (Four) meaningful coincidences during these days

Now if you don't mind I would like you to take part of the train of thought that took me insert a wikilink on the word point.
I have experienced a total of 4 (four) meaningful coincidences (

(one coincidence today).
I am very impressed and scared at the same time because I don't understand what is going on exactly...
I saw you have a barnstar on your profile for your "outstanding comments made in the discussion on Hilbert space and how to make the intro more accessible".
I know all this could sound odd to you but maybe you could explain me or try to explain me what is going on from a scientific or epistemologic point of view using mathematics...or maybe even psychology because I am the one that wrote the italian wikipedia article on the political crisis: Crisi Politica italiana 2008 as you can check from the history page.
. I don't even remember when was last time I have experienced a significant coincidence before...
On the synchronicity entry (english wikipedia) I added in the "See also section" the link to Hilbert Space...
I was thinking to add synchronicity in the "See also section" of Hilbert Space but then I thought about contacting you before and listen to your opinion first.
Thanks for your time.
Maurice Carbonaro (talk) 18:45, 27 January 2008 (UTC)[reply]

Hi, and thanks for your comments at

]

MathWorld Mersenne links

The links in [1] were to different MathWorld articles. They both seem relevant to me. PrimeHunter (talk) 17:36, 15 February 2008 (UTC)[reply]

Oops! Sorry, I didn't realize that. Arcfrk (talk) 00:50, 16 February 2008 (UTC)[reply]

I've created a single header for MathWorld links to avoid repeating this kind of error. By the way, what do you make out of two links to papers on representations of Mersenne numbers by quadratic forms? Aren't they getting a bit undue weight? Arcfrk (talk) 01:00, 16 February 2008 (UTC)[reply]

Yes. I think the one-page Reix paper should go. It was added in [2]. PrimeHunter (talk) 01:55, 16 February 2008 (UTC)[reply]

You've done good with the page splits. I replied briefly on my talk page. Sorry not to have time to say more! Geometry guy 20:31, 17 February 2008 (UTC)[reply]

I get your point, but the phrase "infinitely many uncountable choices" leaves a bit of ambiguity regarding the nature of the axiom required. I think "uncountably many choices" is not too technical, but you disagree. Is there anyone who looks up Banach Tarski paradox who does not understand "uncountably infinite"?Likebox (talk) 23:16, 18 February 2008 (UTC)[reply]

Yes, to your last question! Many people do (have you ever looked at Wapner's book?) Anything you may put in one sentence will leave ambiguity, no matter how carefully you construct that sentence. If you really want to talk about the axioms, insert uncountability below, where forms of AC needed for BT paradox to be true are discussed. Personally, I think that AC is a red herring, because the heart of the paradox (and of its proof) is the decomposition of the free group described in the article. Just to give you another example: most results about manifolds are valid only under the very restrictive assumption that their topology is second countable. It may even be argued that anyone seriously needing manifolds should be able to understand what it means. But would it be a good idea to insert this disclaimer in the first paragraph (or even the lead) of the article "Manifold"? Arcfrk (talk) 23:31, 18 February 2008 (UTC)[reply]

I see your concern, and it is a fair one. I put a wikilink in the article to try to adress it, so that uncountable is defined in the link. Let me tell you my central concern--- the Banach Tarski paradox is a theorem which is false in the mathematical universe that most people imagine. In this universe the real numbers are a measurable set. It is important to clue people in that this "theorem" is not like the theorem that there are infinitely many primes. It is just a set theoretic bit of fantasy that does no harm.

I think I said it in a lay accessible way--- the theorem requires an "uncountable number of arbitrary choices" gets the flavor across without being too technical. I might be wrong about that, of course, but I think you are selling the readers of the article short.Likebox (talk) 03:09, 19 February 2008 (UTC)[reply]

Now, when you're talking about manifolds, I think second countability is automatically assumed by mathematicians and most people, so that there is no discrepancy. By the way, to assume that there is no countable basis for the topology of some manifolds is also a harmless bit of set theoretic fantasy.Likebox (talk) 03:10, 19 February 2008 (UTC)[reply]

Well, what mathematical universe that most people imagine is highly debatable (are they professional mathematicians? do most people even know what "measurable" means?), but it's not germane to our task. You have failed to make a case that isolated technical details, such as the variety of AC needed for the paradox to hold, should go into the first paragraph. I've moved it down a bit, to the discussion of the set theory involved in the proof/validity, where it fits more naturally. Your comment that "this article sells the readers short" is off the mark: there is a fairly extensive description of AC and philosophical issues, right in the lead, just not in the first few sentences. Arcfrk (talk) 02:18, 20 February 2008 (UTC)[reply]

I like your rewrite and I don't care where the concern is adressed. I can tell you, though, that in the mathematical universe that nearly everyone imagines, including professional mathematicians, it is possible to pick a real number between 0 and 1 at random uniformly. This is a flat out contradiction with BT. I am happy with the article, again, but I wanted to say that this type of theorem makes many students very uncomfortable because it just "feels" false, and there's no way to fix the feeling that it is false because it's just conventionally true not true in any verifiable way. You can alternatively take as an axiom that you can pick a real number between 0 and 1 uniformly randomly.Likebox (talk) 02:42, 20 February 2008 (UTC)[reply]

Hi Arcfrk,

Regarding the Differential equation page, I think the statement which I removed is trying to be helpful, but only is so to someone versed in the field. I tried to write an example based upon how DEs are important in the real world (not in the mathematical sense, no mathematician needs to be told how important calculus can be!) such as that using projectile motion instead, but didn't have the references to back it up, nor to do so eloquently in a few short sentences. I may try again soon, so if you wish to make a comment, that would be great. User A1 (talk) 11:27, 21 February 2008 (UTC)[reply]

Yes, I understand your concern. I'll take a look at your example in a little bit. That article suffers from the lack of explanations, it's a skeleton without flesh, so to speak, so expansion in this direction would be very helpful. Arcfrk (talk) 18:21, 21 February 2008 (UTC)[reply]

Another editor has added the {{

]

Howdy, I didn't see a quick fix. I was thinking make

height (ring theory), but perhaps a new article would be better? JackSchmidt (talk) 21:56, 6 March 2008 (UTC)[reply

]

I wrote a ridiculous stub for

minimal prime (commutative algebra) and converted the redirect into a disambig page. The stub could absolutely use work. JackSchmidt (talk) 22:14, 6 March 2008 (UTC)[reply

]

It's a good start. I didn't see anything ridiculuous about it, eventually, it will get expanded. I am temporarily very busy, but you seem to be managing very well by yourself! Arcfrk (talk) 22:12, 7 March 2008 (UTC)[reply]

Actually, Fermat never announced or claimed that all Fermat numbers were prime. He very explicitly said he was guessing/conjecturing they were, as opposed to his claims of proof in both letters and his marginal notes. Each time Fermat explicitly claimed he could prove or he had proven something, it has turned out to be a true statement. He did not always guess correctly, however, but his incorrect guesses were given as "theorems" or claims, just as guesses or conjectures. Magidin (talk) 03:44, 14 March 2008 (UTC)[reply]

That seems a bit surprising to me, although I cannot claim any expertise, since I have a very vague recollection of Fermat's writings, which, moreover, I read in translation. The traditional view is that Fermat made many unproved claims, especially of number-theoretic nature, including the one about Fermat primes (false) and representations of prime numbers as sums of two squares (correct). It is hard to discern the difference between "he claimed he could prove" and "he was guessing", since he supplied preciously few proofs of his statements. (One of the best known exceptions is his ingeneous proof of the case n = 4 of the FLT by infinite descent.)

What are the "true statements" that you have refered to? Have you looked at Fermat's actual wording? What is the difference in the language he used for the claims that turned out to be true versus the claims that turned out to be false? In the case of the "truly marvelous proof of this proposition", for example, he does not say "Theorema", yet this may be a terminological nuance open to interpretation. Arcfrk (talk) 04:21, 14 March 2008 (UTC)[reply]

As I understand it, in most cases, Fermat issued challenges; in others, he wrote saying he had proof. In those circumstances, he was claiming proof. For the case of Fermat numbers, as I understand it, what he did was prove that for a power of two plus one to be a prime, the exponent itself must be a power of two; observed that the first five were prime, and then stated that he believed they would all be prime, which is different from saying I have a proof that all are prime, or I have discovered they are all prime, etc. There has always been a difference understood between a mathematician saying "I believe this is true" and "I can prove this is true." That all Fermat numbers are prime is always described as a conjecture of Fermat that was proven to be false, not as a claimed theorem that was proven to be false. In any case, it would seem Arthur Rubin agrees with your wording in the article. Magidin (talk) 14:12, 14 March 2008 (UTC)[reply]

Hello. I don't understand the following sentence, which you added to monkey saddle (great name, by the way): "The monkey saddle will have a local maximum along certain planes, but it won't be a local minimum along others — just a point of inflection." The intersection of the monkey saddle with the plane y = kx is the curve ${\displaystyle z=(1-3k^{2})x^{3}}$, which has an inflection point at the origin (excluding the degenerate case ${\displaystyle 1-3k^{2}=0}$). Would it be possible to reformulate the sentence so that I can understand what's meant? -- Jitse Niesen (talk) 15:41, 21 March 2008 (UTC)[reply]

It had already been there when I edited the article, I'll take another look at it tomorrow. The language of that article is quite ambiguous — that's why I got involved — and it frequently confuses the function z(x,y) with its graph. Arcfrk (talk) 22:44, 21 March 2008 (UTC)[reply]

Oops, I should have checked the history more carefully before accusing you of making mistakes. Sorry about that. -- Jitse Niesen (talk) 23:37, 21 March 2008 (UTC)[reply]

Hah! You owe me at least one administrator-assisted page move, now! This monkey business turns out to be quite profitable, after all. Arcfrk (talk) 20:50, 22 March 2008 (UTC)[reply]

Hey good work on the gaussian curvature article. I want to get that article up to a higher level of quality but I'm not sure what other content we should add. Jhausauer (talk) 22:07, 23 March 2008 (UTC)[reply]

Thank you for your kind words! One thing conspicuosly missing is the definition of Gaussian curvature based on the Gauss map. Total curvature and A. D. Alexandrov's approach to geometry of nonregular surfaces with positive curvature should, perhaps, also be explained. Gauss–Bonnet section is rather terse: it should also mention the case of a polygon on a surface, not just the closed surface case. Further directions include sections on surfaces with (non-constant) positive and negative curvature. Examples include work of Hadamard and Morse on the geodesics for surfaces with K < 0 (cf. "Hadamard's dynamical system") and the Weyl problem for K > 0. Some of this material is already on wikipedia, so it can be just linked at first. These are just some thoughts that occur naturally. Arcfrk (talk) 22:28, 23 March 2008 (UTC)[reply]

You said: "Not sure what you mean by "this format is all wrong" (since, whether you like it or not, it is widely used at various dab pages) or by "discussion still occurs" (I only see reverts occurring, with no discussion), but you should at least be aware of the fact that in the version to which you have mechanically reverted, much of the content is wrong. Arcfrk (talk) 03:40, 24 March 2008 (UTC)"[reply]

I have again reverted, and provided an actual sample in my edit summary. Please share your thoughts on the talk page. Lord Sesshomaru (talk • edits) 03:48, 24 March 2008 (UTC)[reply]

I have taken this as awkward. Is it a complement or something else? Please respond on your talk page (I have watchlisted it). Lord Sesshomaru (talk • edits) 04:00, 24 March 2008 (UTC)[reply]

Hi Arcfrk,

I have been thinking about the issue of Lecture Notes in Mathematics and here are my thoughts:

• Generating the URL to chapters and or titles in the series seems nearly impossible as there is no apparent pattern between one URL and another.
• Template:LNM is not currently being used. Its content could be:

#REDIRECT[[:Template:Cite book]]

and it would act exactly like the {{cite book}} template. However, Special:WhatLinksHere/Template:LNM could be monitored by a bot which could fill in the details.

« D. Trebbien (talk) 03:05 2008 March 27 (UTC)

Thank you for looking into it! Yes, you are right: the does not seem to be a way to link directly to a particular volume, I didn't realize that.

• The best thing to do may be to just to create a template named "Template:LectNotesMath" (or a similar title) that would html link to the main page of the series itself and include a wikilink to the article "Lecture Notes in Mathematics" (it doesn't exist, but I can start it). This may further pipe into/invoke the book citation template, as you have suggested.
• I didn't quite understand the bot part: do you think that a bot can be asked to maintain a database with the html or doi links to the actual volumes? Best, Arcfrk (talk) 03:33, 28 March 2008 (UTC)[reply]

• Sorry. I missed the notification of your replies on my watchlist. Anyway, your idea of starting Lecture Notes in Mathematics is probably the best solution here.

The reasoning is similar to why I started

Proceedings of the Steklov Institute of Mathematics

; ie, rather than trying to describe the journals in the citation, I created another page and linked to it in the true spirit of wikilinking :).

Cheers. « D. Trebbien (talk) 16:01 2008 April 12 (UTC)

It would be nice to have you participate in the discussions about the function article. The changes that have been made recently are, mostly, cosmetic (diff). The main issues I see here - lack of organization, especially - were already present before, just not as well highlighted. — Carl (

]

Thank you for the invitation, Carl. Yes, I realize that polemic sentences such as "yet we are not satisfied" have been there for a long time, but maybe we can use the opportunity and streamline the whole definition section. Unfortunately, I will not be able to do anything in the next three days, but I'll take a close look at the article and the talk page after that. Arcfrk (talk) 19:42, 31 March 2008 (UTC)[reply]