User talk:Geometry guy/Archive 1

Welcome!

Hello, Geometry guy, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are some pages that you might find helpful:

I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes (~~~~); this will automatically produce your name and the date. If you need help, check out Wikipedia:Questions, ask me on my talk page, or place {{helpme}} on your talk page and ask your question there. Again, welcome! Oleg Alexandrov (talk) 16:17, 7 February 2007 (UTC)[reply]

Thanks Oleg ;)

Math Wikiproject

Just wanted to let you know that the central place for math discussion on Wikipedia is Wikipedia talk:WikiProject Mathematics, in case you ever want to join discussions there or start any. Cheers, Oleg Alexandrov (talk)

Thanks Oleg :) Geometry guy 15:59, 10 February 2007 (UTC)[reply]

Pushforward and pullback

Hello all: I just relinked about fifty pages to pushforward, which has now been disambiguated. If I made a mistake for any of these, my apologies! Geometry guy 22:20, 11 February 2007 (UTC)[reply]

I also relinked a few pullback pages. Same apology applies! Geometry guy 00:12, 12 February 2007 (UTC)[reply]

let me second Oleg's welcome. thanks for your contributions. there was a short note in the vector bundle article about the present discussion being restricted to finite dimensional fibers. it was removed sometime ago. perhaps it is sensible to include the non-finite dimensional case. Mct mht 00:22, 12 February 2007 (UTC)[reply]

It could be worth mentioning. But over a finite dimensional base, or an infinite dimensional base? Geometry guy 00:58, 13 February 2007 (UTC)[reply]

Thanks for all you work on the pullback and pushforward pages! These are in much better shape now then they were. FYI: I've updated the commutative diagram on the pushforward page to match your new notation (you may have to refresh your cache before you see the changes). -- Fropuff 01:15, 12 February 2007 (UTC)[reply]

Thanks - I was hoping you would do that ;) Of course, I don't insist on my choice, but the notation is now at least fairly consistent over the articles tangent space, tangent bundle, pushforward (differential) and pullback (differential geometry), which is surely a desirable feature whatever notation is used. Geometry guy 11:45, 12 February 2007 (UTC)[reply]

Connection (vector bundle)

I've rolled out connection (vector bundle). Have a look. Feel free to butcher it if you want to. We can probably remove a good deal of overlapping material from the connection form page. -- Fropuff 07:13, 16 February 2007 (UTC)[reply]

Looks good! I will make some edits when I get time. So far only one notational issue springs to mind: for the exterior covariant derivative and curvature, I think it's better to superscript the connection, but I don't insist on it. Geometry guy 08:49, 16 February 2007 (UTC)[reply]

Now made some fairly minor edits - hopefully without any butchery - but I did them individually so they can be reverted fairly easily. Geometry guy 21:30, 1 March 2007 (UTC)[reply]

Welcome and suggestion

Hi Geometry guy,

Welcome to Wikipedia! I like what you're doing for the coordinate-system articles, a few of which I started rather hastily when I first joined. But may I offer some advice? Our audience here is not necessarily mathematics graduate students and professors, but rather lay-people who may have little or no training beyond basic calculus. Also, there may some professionals in other fields such as engineering and physics who may use a different nomenclature. Since we're writing encyclopedia articles and not review articles, I'd advise being cautious in using "scary" nomenclature (e.g., "submanifold" and "1-form") early in the article; I've at least tried to warm up the reader a little before hitting them with the most technical language. ;) Please accept this as friendly and kindly meant advice from a fellow lover of geometry, Willow 20:57, 19 February 2007 (UTC) (Geometry girl?)[reply]

Hello and thanks for the welcome and comments. Welcome to my fledgling user page. I agree entirely with your advice: I just wanted to get the terminology clear first. Anyway, I've reordered the article to make it more accessible to lay-people and those from other fields. But perhaps these people shouldn't be hit with D-dimensions either ;) so the rewrite starts in 3 dimensions, and proceeds to other dimensions later. Perhaps the article now needs to be renamed again! Anyway, let me know what you think, either here, or on the talk page for the article, or both. Geometry guy 21:57, 19 February 2007 (UTC)[reply]

Upright d for derivatives and differentials?

From User talk:86.11.118.108

Please do not do mass changes in Wikipedia articles replacing italic d with roman d in math notation. This was discussed before, and italic d is preferred. If you want to raise this topic again, please do so at Wikipedia talk:WikiProject Mathematics. Thanks. Oleg Alexandrov (talk) 03:36, 23 March 2007 (UTC)[reply]

I think Oleg is being a bit hard on you here: your edits were clearly in good faith and it takes a while to get into the spirit of wikipedia. Why not get an account and join the discussion? Geometry guy 11:16, 23 March 2007 (UTC)[reply]

Thank you!

Hi - no, he was right, because I am new and I didn't read up on policy. I have posted my thoughts on the discussion page, and I do take responsibility for the unsolicited edits; after all, I'd be quite annoyed if someone modified to their liking something I had worked hard on without even an explanation!

Thanks for the the support though; do see my explanation on the talk:Integral page - I think on Wikipedia in the mathematics markup there is a lot to be gained from the Roman d. I never knew I would be so passionate about formatting as I have become!!! I will create an account, and I hope to be more constructive in future.

Thank you very much for the support!

Simon

And here I am with the account, and I shall hereby stop spamming your talk page. Thanks once again. Psymun 19:37, 24 March 2007 (UTC)[reply]

Welcome to wikipedia and congratulations on getting an account! Talk is not spam, but is encouraged: it helps us users work together rather than against each other. I've copied your talk from the anonymous page over here too. Wikipedia, especially in maths, is generally a nice and friendly place, but you sometimes have to take the rough with the smooth, even in calculus! Geometry guy 20:05, 24 March 2007 (UTC)[reply]

Plücker (and Grassmann) coordinates

Hello again, and thank you for providing a voice of reason in a chicken-or-egg type discussion. It was very frustrating to run into someone who denies the facts and twists the meanings to promote a pet point of view. Plücker embedding should definitely be written, but given the sensibilities, I won't do it myself. Arcfrk 21:08, 27 March 2007 (UTC)[reply]

You are very welcome. I share your frustration that a fundamental article like Plücker coordinates is overwhelmed by details coming from a computer graphics perspective, but these things sort themselves out in the long run, through forks and subarticles. (Let me remind you of Derivative, where I hope some progress is being made - the article is no longer at least, one third devoted to notation.) But, as I am fond of saying (especially to myself, as a reminder when I stray), wikipedia is an encyclopedia, not a math textbook, and I guess from what you have said before that you like to emphasise the same thing. Anyway, please don't underestimate KSmrq, who is an experienced editor with (in my view, from what I have seen) a nice mixture of mathematical expertise and a good idea of what an encyclopedic math article should be about. The comments on your page, even if they were written in a frustrated moment, contain some good advice. I actually prefer to post my area of expertise on my user page, as it helps me resist the temptation to argue from authority, rather than demonstrate my expertise through my knowledge of the facts (anyone can check my user page if they want to - in any case it proves nothing, which is one reason I like to stay anonymous, so my contribs are judged at face value). I hope you continue to have fun - it's an interesting place! Geometry guy 22:43, 27 March 2007 (UTC)[reply]

I saw that you've started an article on Plücker embedding, which was long overdue, and hope that it will develop smoothly! I actually looked at Category:Differential calculus per your suggestion, the two main articles there were indeed in messy state(s), and more than I could handle at the moment, so I didn't do anything about them. Thanks for your tip concerning posting the area of expertise on the user page, I haven't thought about it in those terms. My rationale had been not to post any identifying information, especially, since it's unnecessary for Wikipedia project; but I see how it could have its advantages. As for the experienced editor that you've mentioned, I had been quite impressed by his contributions, but after his conduct in Plücker coordinates discussion, he is off my list of reasonable people (as in: exercising one's reason in a proper manner; those with whom it makes sense to employ reasoning or argument). By the way, if you have time, can you, please, take a look at Abstract algebra#History and examples that I've written and tell me your opinion? Best, Arcfrk 01:30, 28 March 2007 (UTC)[reply]

Well it is a start. Thanks for looking at the calculus stuff: my main problem is that I have entered a strange world in which calculus is done either in one variable or in Banach spaces - a serious reality check is needed here! Anyway. please try not to rush to judgement with fellow editors: your comments can be quite provocative, generally in a positive way, but this doesn't always bring out the best in other editors. Meanwhile, I hope I will have a chance to look at the abstract algebra stuff soon. Geometry guy 01:49, 28 March 2007 (UTC)[reply]

Abstract algebra

(From above) ... By the way, if you have time, can you, please, take a look at Abstract algebra#History and examples that I've written and tell me your opinion? Best, Arcfrk 01:30, 28 March 2007 (UTC)[reply]

I had a quick click on your link. You've added an impressive amount of detailed content: possibly a case for a subarticle, but have a look at History of algebra, which is rather disconnected from the rest of wikipedia right now, and let me know what you think. Also, to be pedantic, footnotes go at the end of the page - I'll fix it for now. Geometry guy 02:13, 28 March 2007 (UTC)[reply]

I read History of algebra, it's an impressive piece of work. In fact, a secondary goal of mine was to fill the void it left concerning abstract algebra. But the primary question is, does the section that I added help to understand what abstract algebra is about? My concern is how to keep a balance between merely providing a list of topics and overwhelming the reader with explanations for which (s)he may be unprepared; in other words, is this section useful to non-algebraists? Arcfrk 05:20, 28 March 2007 (UTC)[reply]

I've read this in more detail now. You've added a lot of nice content here. I especially like the introductory paragraphs. As for your question, well the honest answer is "probably not". The intro does to some extent, but the group theory archetype rather overwhelms the reader with names of people and mathematical concepts, and might leave a non-algebraist wondering "if abstract groups are all permutation groups then what was the point of the abstraction?" However, the problem may be that this section is trying to do too much (another platitude of mine): it is hard to cover history, motivation and examples all at once as these themes get in the way of each other. Perhaps there should be a separate section on motivation? Alternatively, this article could defer to History of abstract algebra for all the names and dates, and concentrate instead on the themes. Also I wonder whether the example of attempts to prove Fermat's last theorem leading to rings, ideals and the ideal class group would be a good way in for the general reader?

Anyway, this is great start! Geometry guy 17:10, 28 March 2007 (UTC)[reply]

Thank you for looking at it! Yes, I was rightly worried that it's a bit too much too fast, but cowardly tried to silence my inner editor nonetheless. Some of the group theory related stuff can go into (non-existent) history of abstract algebra, but at the moment I don't have necessary time and resources to write a decent overview of the rest of the history. Probably, you are right that Fermat's last theorem is a better model for exposition of genesis of abstract algebra for more general audience. I'll get around to it in a while, and, please, let me know if you have any more ideas. Arcfrk 03:45, 29 March 2007 (UTC)[reply]

Math class

I added a few maths classifications to some articles I've been involved with. Rather than leave them as unclassified, I made an attempt to rate them myself. Please have a look (anyone) and change them if you want (I may not have been objective). The comment I have left is very bland in most cases, so please replace it with some more concrete suggestions for improvements. Geometry guy 09:35, 30 March 2007 (UTC)[reply]

Disambiguation for Mathieu group numbers

I saw your edits to M22, M23, and M24. I think your descriptions were the best anyone had come up with yet. I only made some stylistic changes to the entries (I removed periods and parentheses), but I otherwise left them unchanged. Thank you for the assistance. Dr. Submillimeter 15:00, 30 March 2007 (UTC)[reply]

Thanks, and sorry about the misplaced period! I also edited M11 and M12. The final form of the dab is not so important, but could you make sure it stays consistent across the five articles? Thanks. Geometry guy 15:05, 30 March 2007 (UTC)[reply]

I will do that. I am currently cruising through all disambiguation links between M1 and M110 to clean them up. Many of the pages violated multiple guidelines at MoS:DAB. Again, thank you for the explanation on the disambiguation pages.

As for Mathieu group, it at least looks like an effort to explain this concept in layman's terms. It's an improvement over the previous version of the article, although it is still tough to follow. Thank you for working on it. (If it makes you feel any better, I see the same problems with physics articles.) I leave it to you to decide on whether to remove the "technical" template. Dr. Submillimeter 19:37, 30 March 2007 (UTC)[reply]

Unfortunately, some articles are just inherently technical, so the best we can hope to do is provide the links to more basic articles in as coherent a way as possible. Anyway, I am not an expert on group theory. I expect an expert will remove the "technical" template at some point, but hopefully after improving the article further ;) Meanwhile your efforts on the M-article dabs are surely very worthwhile. Although to be really pedantic about MoS:DAB#Order of entries, it does give guidelines for ordering articles other than order of appearance in Google searches. Even as a UK guy, I'm not sure that UK motorways are particularly important encyclopaedic entries. I (for one) would certainly be happy if the Messier objects appeared high on the list! Geometry guy 19:51, 30 March 2007 (UTC)[reply]

PS. Don't forget MoS:DAB#Break rules - where appropriate of course...

Help with EB?

Hi Geometry guy,

Could I ask a favor of you? ... I'd appreciate it muchly! :) Geometry girl 21:07, 30 March 2007 (UTC)[reply]

Thank you Geometry girl, especially for your efforts to ask so nicely :). I am quite sad that I had to reply so harshly, but I was very honoured by your invitation, and felt I could only do this honour true justice by answering very honestly. Anyway, I have copied this talk over to your page, as it really belongs in your impressively broad domain, rather than my limited one. Geometry guy 23:52, 30 March 2007 (UTC)[reply]

Hmmm... I just read some of the discussions about EB (I deliberately made my review without reading them) and can see how the POV has arisen from a clamour to point out the failings and criticisms of EB. There is certainly space for an article on these criticisms, but they are given too much weight in the main article, particularly if (as some editors suggest) making EB into a Featured Article is intended demonstrate the neutrality of WP. Geometry guy 01:13, 31 March 2007 (UTC)[reply]

FYI

Hi Geometry guy, in case you didn't see it, I've directed a comment to you here. Regards, Paul August ☎ 21:07, 31 March 2007 (UTC)[reply]

Derivative

OK, thx. I actually had pretty good luck in the end with Edits in the end, though not at first. Similar to some of your experience, possibly. Best wishes. --Thomasmeeks 21:29, 1 April 2007 (UTC)[reply]

Linear Algebra intro

Here's what I think might make a better introduction to the linear algebra article. I've tried to give some more idea what the field is about (in my own view), to explain the key words a little bit (so hopefully it won't scare off all laymen), and to provide some idea of applications. Use it (with or without modifications) or disregard as you please. Good luck. GV, 1 april 2007. (User Special:Contributions/82.95.55.226)

"Linear algebra is the branch of mathematics concerned with the study of vector spaces (also called linear spaces) and linear maps (also called linear transformations). Like other algebraic structures, vector spaces are defined as sets of elements, with operations that yield elements of the same set - just like adding or multiplying numbers yield another number. For such a set to be called a vector space (and its elements, vectors) the operations have to obey certain rules, or axioms. From these axioms and further definitions many useful and interesting properties of vector spaces can be proved.

In particular, vector spaces can be mapped onto other vector spaces or themselves; meaning that there are functions that take one vector as argument, and that when applied to all vectors in a vector space yield a new set that once again obeys the axioms of a vector space. Such functions are called linear transformations and are computationally represented by matrices.

Vector spaces are a central theme in modern mathematics because many objects of mathematical study exhibit the structure of a vector space, e.g. Euclidean space, sets of functions, and n-tuples of (rational, real or complex) numbers. This explains the use of vectors in analytic geometry (readily generalizable to more than 3 dimensions), in solving systems of linear equations (and hence of partial differential equations), and in statistics. In the natural sciences and the social sciences nonlinear models are often approximated by linear ones in order to make use of the computational methods of linear algebra."

Thanks for your suggestions. The linear algebra article certainly needs some work, and your introduction is a distinct improvement. However, for my taste, it focuses too much on the axioms: linear algebra is about linearity, and this, the main article in Category:linear algebra, needs to convey this idea as informally as possible.

But why post your suggestion here, on the user page of some geometry guy, rather than at Talk:Linear algebra? Why not get an account and be bold?! You might like it here :) Geometry guy 12:31, 3 April 2007 (UTC)[reply]

Complaint

Dear Geometry guy, I am getting a bit tired and fed up with the insulting remarks you leave in your edit summaries when you edit my contributions. I'm referring in particular to the comment you left here, although your latest comment suggests you might be making a habit of it. Let me remind you to be civil to your fellow wikipedians and to stop making personal attacks such as calling me an "idiot", or telling me to "get it right the first time". Yes I make mistakes from time-to-time, but there is no need for these kinds of comments. What is worse, is that you do not seem to be so rude to other wikipedians, which makes me suspect you might be wikistalking me. Please stop. Geometry guy 08:46, 1 April 2007 (UTC)[reply]

Uncivil? Who is the one being uncivil here, leaving accusatory remarks on my talk page, suggesting I am breaking two policies and a guideline to wit?! I could get blocked for this. And your justification for this attack is just two diffs? I'm just doing my best to make wikipedia better, and I am fed up with having to correct the numerous typos, grammar mistakes and other errors that you make in your edits. Have you not heard of the preview button? How about proofreading your edit for a change? It is a wonder that I don't comment more often. I think I have been very restrained. Geometry guy 09:06, 1 April 2007 (UTC)[reply]

PS. And as for policy, have you never heard of assume good faith? Geometry guy 09:14, 1 April 2007 (UTC)[reply]

Talking to yourself on April Fools' Day?--Shtove 07:21, 19 April 2007 (UTC)[reply]

Huh?

Sorry if I am poking my nose into someone's family business, but do you by any chance suffer any form of split personality? Arcfrk 07:00, 6 April 2007 (UTC)[reply]

Well, yes and no! As for the preceding exchange, unfortunately I posted it three days later than I originally intended. I've fixed the dates artificially now so visitors get the idea ;) There is a serious point underlying this silliness, but nevermind about that... Geometry guy 12:25, 6 April 2007 (UTC)[reply]

Aaaaaah.--Shtove 07:21, 19 April 2007 (UTC)[reply]

Thank you, Geometry guy!

Hi Geometry guy,

Thank you very much for all your kindness and hard work, on the Encyclopædia Britannica and elsewhere. It was wonderful how you were able to pinpoint the difficulties and improve the article so much. I also really appreciate how you assumed good faith about me, even if I didn't deserve it; your faith and honesty helped me become a better person, which is all that we can hope for among ourselves, no? The fine draught of absinthe was medicinal indeed, despite the wormwood it held for me initially. I foresee that you have work on the EB still ahead of you, as do I, for which I thank you already. Please let me know if I can help you as you have helped me; in devoted friendship, Willow 11:19, 12 April 2007 (UTC)[reply]

P.S. Sorry that the image is not geometrical! ;)

Ah Geometry Girl, there is geometry in everything ;) It was a pleasure to help out at EB and thank you so much for adding some colour to my talk page! In your case I did not need to assume good faith: it is obvious from everything you do on WP! As for EB, I think it is in a very good state now: informative, comprehensive, balanced and encyclopedic. All thanks to one determined and energetic editrix, and a little encouragement from her many friends. Geometry guy 12:26, 12 April 2007 (UTC)[reply]

Hello Willow. I wonder if you might help out in one or two small ways. Here at maths we have a scheme called Mathematics collaboration of the week, which is not in good spirits at the moment. Our friend Cronholm has proposed Mathematical physics as a possible candidate, which I think is an excellent choice. Do you think you (and maybe A.N. Other) could support it? Meanwhile, the current collaboration is Theorem, but it is not in a good state right now. I'd like to help a bit - are you interested in joining in the fun? Geometry guy 23:53, 3 May 2007 (UTC)[reply]

Hi again, G! I'd be glad to help out, although I feel out of my depth. I have a vague notion of what physics and mathematics are, but I'm a little hazy about mathematical physics. Does it mean "mathematics that was developed to create theories of physics"? In my mind, I'm distinguishing it from physics-related mathematics, which I would imagine is mathematics that was inspired by or grew out of physical theories but then developed independently, kind of like the mathematics of torsion tensors and general connections arose from general relativity. Am I understanding that correctly? Willow 15:46, 4 May 2007 (UTC)[reply]

P.S. I'm going to visit my family soon, so I may not be able to reply soon. I have a sister graduating from college this weekend, and another sister from grad school in a few weeks. I'll try to write, but my family is a little old-fashioned and it might be difficult to get connected. Willow 15:46, 4 May 2007 (UTC)[reply]

Equipartition theorem

PS. Oh, I almost forgot! I've been working a bit on equipartition theorem. If you can spare a moment, any thoughts or suggestions you might have would be most welcome! :) Thanks, G-guy! Willow 22:37, 19 April 2007 (UTC)[reply]

I'll take a look at equipartition theorem when I have time, but it probably won't be until next week. Geometry guy 09:17, 20 April 2007 (UTC)[reply]

PS. Sorry to find that you were so low recently. I know the feeling! Geometry guy 10:35, 21 April 2007 (UTC)[reply]

Thank you once again for your wonderful edits to equipartition theorem, and, more personally, for your kind comment above, which I only just noticed. The right honourable lady appreciates your great help and insights into things beyond her own vision, and the graceful gentility with which they are uniformly delivered. :) Willow 14:25, 23 April 2007 (UTC)[reply]

You are most welcome, and thank you for the kind comments. Among these edits, I suggested a restructuring of the article, which you may not like, since it moves the history down past the general formulation. Anyway, I won't be offended if you change the order back! There is even an argument for putting the history at the end of the article in this case... Geometry guy 16:38, 23 April 2007 (UTC)[reply]

Here there be dragons... ;) I've been flayed a few times (luckily, dragons can shed their skins) over not putting the History section first; I think there's a policy somewhere about it, although I keep forgetting where. :( Still, I think we might get away with it here; the history seems quite hard to explain unless you've introduced the theorem, don't you agree?

At first, I was concerned about putting the quantum effects at the very end, since the role that equipartition played in showing the need for quantum mechanics was pretty important. But now I see that it makes more sense, given that the applications are all classical. Oh, do you know where we can find a nice Figure illustrating the development of ergodicity; I remember seeing some kind of "breakdown of invariant tori" Poisson-mapping kind of image, but I'm not sure where and whether it were free. I'll add some other Figures for color and fun. Willow 17:10, 23 April 2007 (UTC)[reply]

Well the onus is on the flayer to find the policy or guideline: this may take some time ;) Anyway, I certainly agree that in this article (indeed most technical articles), the history has to come after the definitions: affine connection is a rare counterexample. I had two other motivations for putting the limitations at the end: first, it is a pity to explain what the theorem is not good for before explaining what it is good for; second, these sections branch out into a wider context, which is what the end of an article should do. The figures look good, but I'm afraid I have no idea where to find an ergodic theory picture. Geometry guy 17:52, 23 April 2007 (UTC)[reply]

I'm pleased to see that you simplified and shortened the lead - I was going to suggest that at some point. It is much better now! I have some reservations about the NASA neutron star picture: it grossly oversimplifies the structure of neutron stars (as it is currently understood) and uses misleading words like "solid" and "liquid". The latter is probably refering to the superfluid neutrons that arise at certain densities, but this is believed to happen close to the crust, rather than deep in the interior, if I have understood correctly. Can you find a better picture? Geometry guy 11:54, 27 April 2007 (UTC)[reply]

Good luck with the FA, Geometry (and Physics) Girl! As you predicted, the issue of the history section soon arose. I'm still not in favour of starting with it, but I did have another thought: move some of the examples up, and the general formulation down. As geometers, we both know that the best way to understand a concept is with an example, right? ;) The kind of reordering I have in mind would be:

Basic formulation and applications
History
General formulation and further applications

The first set of examples would correspond roughly to the current "Basic applications" section, taking care to ensure that the discussions all use the quadratic point of view rather than the general point of view. It is just an idea, and maybe not a good one, but people seem to like the infinite beer glass example... Geometry guy 11:32, 29 April 2007 (UTC)[reply]

I feel a bit like the Eminence grise here: I leave a comment and, remarkably, Equipartition theorem changes accordingly! I realised too late that my latest suggestion had the disadvantage that that the sedimentation example is not quadratic, but you found a nice way around that. Still, I can see scope for further restructuring, e.g., to explain a specific heat example before the history, to reduce repetition around the application to ideal gases, and to avoid using the general form of the theorem before stating it. But, maybe I should pull down my shadowy hood and enter the fray! Geometry guy 18:04, 30 April 2007 (UTC)[reply]

PS. Nice to see you at Affine connection!

Votre visite me ferait grand plaisir, Votre Eminence; vous etes toujours bien venu chez nous. Je vous en prie, entrez et de votre propre vouloir, comme il dut un si grande Seigneur anglais. ;) Restez chez nous et editez avec une liberte (et j'espere contentment) plusplarfaite.

Forgive me for not having replied right away to your wonderful suggestions, which as you see I tried to bring to life. But I'm happy to see that you're diving in yourself now, as befits the Englishman: "once more into the breech, dear friends, once more; in peace, nothing so becomes a man — as editing Wikipedia." Wait, is that how it goes? ;) Willow 22:47, 30 April 2007 (UTC)[reply]

Umm, you missed the rather crucial line "Or close the wall up with our English dead." I'm dead for now, but tomorrow I will try to imitate the action of a tiger. Geometry guy 23:15, 30 April 2007 (UTC)[reply]

Well, I wouldn't want to stray into discourtesy or morbid thoughts; I couldn't ask such a high price of you for fixing up equipartition. ;) Besides, I conked out long before you did, the result of overly enthusiastic gardening. ;) Thanks for all your manifold improvements to equipartition! Speaking of manifolds, may I tinker a bit with affine connection? Although I'm not very good about it in my own articles, I think we ought to be more gentle with the reader there, starting with flowers before flours, ramping up gradually to the terribly twisted torsion tensor. ;) Although I'd intended to start in on making knitting into a Featured Article, this might be a fun diversion for a while, if you'll be patient with my limitations. :) Willow 15:27, 1 May 2007 (UTC)[reply]

Yes, blood was summoned and sinews were stiffened, but I still haven't fixed the problem that the article uses the general form of the theorem before stating it, so there is more to be done. I also think there is a confusion in one or two places between coupled oscillators and normal modes, which are not the same thing, and I wonder if the SHO section could be reorganised to put the application to crystals up-front.

P.S. I might have to revert to "bottle" of beer, because the equipartition theorem requires that equilibrium has been established, which could take weeks. I wouldn't want the beer in the glass to go flat! :)

I think after these hard days of editing and/or gardening, the beer going flat would not be the most serious problem affecting the experiment. (More seriously, I also switched from bottle to glass 'cos most of the bottles I know are coloured, so you can't see the haze very well - although, now I come to think of it, we could ask Corona to sponsor a product placement.) Geometry guy 16:07, 1 May 2007 (UTC)[reply]

Phew, I think that a beer (even in a bottle ;) would be most welcome. I've enjoyed a lot working on Equipartition, and I hope you did too, though we both had to face some nightmares: for you, differential forms, for me {{fact}}. I'm horrified I added such a tag, but am glad you fixed it easily. Geometry guy 22:37, 3 May 2007 (UTC)[reply]

I think you mentioned a Weizen? I hope you like it! :)

Dear G-guy,

PLease don't worry about adding the {{fact}} tag. I'm grateful; I would be rightfully ashamed if we coasted into FA-land with a substandard article. As the saying goes, seats in Valhalla should not be cheap. ;) We should recruit Awadewit and others to review the article; I suspect that they'll bring a good perspective to the article and help us to gauge how intelligible the writing is.

Someday, I may also conquer my irrational fear of differential forms; how tough can they be? ;) From dribs and drabs in random books, I sort of get the torsion tensor now, so maybe it won't be so hard to cross over into that promised land. Willow 15:34, 4 May 2007 (UTC)[reply]

Thanks for the beer! What a great present, just in time to celebrate the FA, although yet again, I didn't vote in time. Congratulations! Geometry guy 14:04, 5 May 2007 (UTC)[reply]

Affine connection

PS. Although I'm not sure I will like the taste of my own medicine, if you do stop by and would like something to do in a spare moment, take a look at Derivative or Affine connection, into both of which I have put quite a lot of work recently, but I am not sure what to do with them now. The latter, in particular, is rather advanced maths! Geometry guy 19:40, 15 April 2007 (UTC)[reply]

Hey Geometry guy,

I just discovered your postscript, I'm sorry about not responding earlier! The lead of affine connection looks good, although I'll need to read it more closely tonight. I've never understood all that, but now's my chance and what better teacher? :) I can already tell that I'll have difficulties with some of it, though, since I'm scared to death of differential forms and wedge products. I'm sure that it'll all appear trivial someday, but now... I didn't read the article carefully, but maybe you could derive the connection by embedding the manifold in a really high dimensional Euclidean space, translating the vector/tensor as in a normal Euclidean space, and then projecting back into the manifold? That's how I would do it, if I were an angel and could move things about in n dimensions. ;) But perhaps I have too conservative an imagination? I bet there's many ways of doing it! Willow 22:37, 19 April 2007 (UTC)[reply]

Well, straight away you spotted the main thing that I would like to add to the article (leaving me impressed, yet again)! At the moment, the construction of an affine connection by embedding a manifold in Euclidean space is limited to the example of the 2-sphere in 3-dimensional space (7.1). I would like to explain the construction in general, giving the 2-sphere as an example. Geometry guy 09:17, 20 April 2007 (UTC)[reply]

(Copied from above.) Speaking of manifolds, may I tinker a bit with affine connection? Although I'm not very good about it in my own articles, I think we ought to be more gentle with the reader there, starting with flowers before flours, ramping up gradually to the terribly twisted torsion tensor. ;) Although I'd intended to start in on making knitting into a Featured Article, this might be a fun diversion for a while, if you'll be patient with my limitations. :) Willow 15:27, 1 May 2007 (UTC)[reply]

I'm very glad you would like to work on affine connection. As for limitations, well if you'll be epsilon, I will be your delta ;) It is fun working on an article with you, and hopefully it will also inspire me to make the improvements I mentioned before. Geometry guy 16:04, 1 May 2007 (UTC)[reply]

Ah, I've just been looking at your sandbox, and I realise that there is something I should mention. This subject has two origins and two points of view, which might be called the French and the Italian, since the former is represented by Darboux and Cartan, the latter by Ricci and Levi-Civita. The French school developed the geometry, the Italian school the tensor calculus (although Bianchi contributed to both). In some sense, the Italian school "won" because they provided hands-on tools for Einstein to use in his theory of general relativity. The geometric point of view then became a minority interest for over half a century.

Why do I mention this? Well, there already exists an article — covariant derivative (perhaps misleadingly named) — which develops the notion of an affine connection from the tensor calculus point of view, although it still needs a lot of work. One of the main reasons I contributed to affine connection was that the most recent previous edits had put it on a collision course with covariant derivative and a merger was suggested (see the talk page and history of affine connection). Consequently, in my rewrite of the article, I took the point of view that readers might already have met the covariant derivative point of view, and so I tried to introduce them to Cartan's geometric point of view with that in mind.

Affine connection could certainly be made much more accessible, and I'm sure your input will be invaluable, but at first sight, it seems to me that many of the ideas you are developing fit better as (much needed) improvements to the covariant derivative article. I would be happy to join in an effort to improve both articles, but would be sad if the contrast between them was lost. I hope you see where I am coming from here. Geometry guy 02:04, 2 May 2007 (UTC)[reply]

PS. I've seen your sandbox is aimed at several articles. I just wanted to mention that another article where you/we could really make a difference is connection (mathematics) which is the lead article in the whole connections category. Geometry guy 02:20, 2 May 2007 (UTC)[reply]

Bonjour Votre Eminence! :D

Thanks for putting everything in context for me! I'm still just getting my feet wet, so I'll need a while before things come into focus. I barely understand the Levi-Civita approach now, although I'm beginning to intuit the torsional thing. However, a hundred different narratives and metaphors are already crowding in my brain to explain it to lay-people: "Once upon a time, there were two cousins, Sophie and Anaïs, who loved each other dearly but lived far, far apart..." Perhaps if the Italian school won out, we should call them "Sophia and Anna"? ;) Once I learn a little more, I'll look over the other articles that you mention and try to see how they fit together.

Can you recommend any good books on the French approach? I've heard of Cartan, but know nothing of his work. I've heard likewise of Darboux, but only remember him from the differential geometry of 3-D curves that I tried to pick up a while ago. It's a beautiful subject; I always wanted to learn more to help me understand my sewing, especially the proper shaping of princess seams. I like their long graceful look, but I have trouble designing such seams from scratch, except by smoothing darts and gores. Please be patient with your benighted Willow 10:57, 2 May 2007 (UTC)[reply]

In reply, I should probably ask you to be patient with the whole connections category ;) since it is still in rather a mess, although it has much improved recently thanks to the efforts of User:Fropuff and User:Silly rabbit. As for references, I guess even with your fondness for French, you might not want to tackle Darboux's multivolume Leçons ;) but the book of Sharpe (cited in affine connection) is quite good. Geometry guy 12:04, 2 May 2007 (UTC)[reply]

Thanks, I'll try to find Sharpe near me. I'll confess, though, that I'm getting a little discouraged. Sometimes I think I understand it, but other times I feel like I'm just fooling myself. There are so many ways of getting to an answer, and most of the books want to do it differently than my pen does. :( Willow 21:33, 2 May 2007 (UTC)[reply]

Please don't be discouraged! The problem with this stuff is that everyone wants to do it differently. In half a day you already managed to produce a better formulation than the covariant derivative article does! Trust your pen; I'm sure there is a place for all of your thoughts. Geometry guy 22:21, 2 May 2007 (UTC)[reply]

Thanks for the encouragement, G-guy! I feel like a droopy flower that just got watered. :) It also helps that I think I may have a valid "angelic transport" derivation of parallel transport, although of course there's tons of tweaking and fleshing out to be done. I'll keep plugging away at getting the Big Picture (and the refs for equipartition!) Thanks for all your help, personal and thoughtful, Willow 22:39, 2 May 2007 (UTC)[reply]

Plücker coordinates

You added a comment to the talk page of Plücker coordinates saying

"The role of Plucker coordinates in computer graphics seems to have too much weight here."

That may be your opinion, but by putting it where you did you make it damned awkward to have a discussion about it, so I am removing it and bringing the discussion here for the moment. I scanned the article to see what could possibly have supported it, and found myself baffled. There is a brief mention in the intro, that "[t]hey have proved useful for computer graphics, …" and both "External links" happen to be computer graphics related; but I find nothing in the body of the article. Since I wrote (almost all of) the body of the article, and did so by transcribing material on Grassmann coordinates straight out of Hodge & Pedoe (1994), but specializing it for Plücker line coordinates, I know first-hand that your characterization is not supported by the genesis. Furthermore, robotics was using Plücker coordinates (Mason & Salisbury 1985) long before computer graphics (and continues to), and they are also discussed in contemporary works on Clifford/geometric algebras, and in computational geometry (Stolfi 1991). I happen to think many computer graphics discussions are amateurish, but others insisted on adding the two external links; I'd be satisfied to see them both removed. The use of Plücker coordinates for lines in 3D may be trivial and boring from the view of research mathematics, but it is hardly so for applications. I apologize for handling the case of Plücker coordinates while leaving the greater spread of Grassmann coordinates untouched, but I was tired of wading through index soup, and not ready to write that separate article. And, so far, no one else has written even a stub. --KSmrq^T 03:05, 15 April 2007 (UTC)[reply]

Thanks for removing it. You are right. The comment was not well thought out. Geometry guy 06:11, 15 April 2007 (UTC)[reply]

The tough part was finding the comment source! (That subpage inclusion mechanism strikes me as a spectacularly bad idea.) To get some good out of this, I'm removing the entire "External links" section, since I think those links actually detract from the article. The references section already cites better online material, such as Stolfi's work. And I don't say that just because User:Jorge Stolfi is a Wikipedian. ;-) --KSmrq^T 09:46, 15 April 2007 (UTC)[reply]

Sorry for any inconvenience and annoyance this caused. I was working through many articles in the geometry and topology field adding ratings and comments (mostly not mine) and made a mistake. I guess I get put off by the index soup that seems to go with this subject as well ;-)

Anyway, the reason for all this is that there is one very good thing about putting comments in subpages: it allows the automatic generation of the maths rating pages by field: see CMummert's proof of concept demonstration. This is so useful, in my view, that it outweighs the awkwardness of having a subpage. This is being discussed at Wikipedia talk:WikiProject Mathematics#Mathematics ratings and tables.

Meanwhile, I changed the rating and dated it - I think B class is more accurate. Feel free to replace with your own assessment and comments. Geometry guy 12:06, 15 April 2007 (UTC)[reply]

Explanation by 141.211... from Talk:Derivative

I think I should give you an explanation, because you haven't seen me before. (Before this, I've mostly stuck to advanced articles like spectral sequence and sheaf (mathematics)—I'm rather proud of those two—and my only serious foray into more elementary topics, Riemann integral, didn't elicit any response.) First, I take the commandment be bold very seriously, and if I want to change something then I change it. If you don't like it, you should be bold and change it yourself. With an article as good as this one I'm changing mainly the exposition, not the content, and that's something that can be tinkered with endlessly. Second, I like my anonymity, and I want to remain anonymous even among Wikipedians. I'm well-aware that you can see my IP address and that an account will bring privileges I don't have. I'm still not getting one. (I seem to be an Exopedian.) I hope that clears things up a little. 141.211.62.20 15:14, 18 April 2007 (UTC)[reply]

I did visit sheaf (mathematics) a while ago, and think you have reason to be proud! It is a nice piece of work, and the edits I made were all pretty minor. I didn't notice that you were a major contributor, though, so thanks for pointing it out! Geometry guy 16:26, 18 April 2007 (UTC)[reply]

Re anonymity. You can actually be more anonymous with a user name that without. A user name does not have to tie your to a real world identity. From your IP I can identify which university you're at, and even where you sit. The benefit to us with a user name is that we can link your edits together - ah that's an edit by Mr Secret he generally does good work and not confuse you with a vandal. The benefits to you are you get this thing called a watchlist where you can see the recent changes to articles which you have edited. You can also join Wikipedia:WikiProject Mathematics/Participants and discuss things at WT:WPM. Of course you are free to remain an IP if you wish.

Coupled with WP:BOLD is Wikipedia:Consensus and the need to discuss things on the talk pages. Luckily your edits have all been of high quality so there has been little need for it. --Salix alba (talk) 16:09, 18 April 2007 (UTC)[reply]

Yes, I know, that's the peculiar thing. I don't understand my desire to do this, but I don't want to have an identity. I want my edits to stand alone, just as edits, without anything to back them up. If they are good, then they'll be accepted, and if they're bad, then they won't be. In particular I want to avoid, "Oh, that edit's by Mr. Know-it-all, it must be good," because everyone makes mistakes. There is a story: Once Alexander Grothendieck and a collaborator were working together on a problem and they got stuck. The collaborator suggested trying a specific example, which required choosing a specific prime number p. Reportedly, Grothendieck said, "How about p = 57?" (You can find the full story by searching Google for "Grothendieck prime".)

Regarding the user talk page for that IP: I don't care who knows what school I'm at. Anyone can look that up. Regarding the revert of my changes to calculus, it seems like there's room for discussion on the right way of describing things, so I figured I'd wait until people's opinions had settled somewhat. 141.211.62.20 18:04, 18 April 2007 (UTC)[reply]

I was about to make the same point about anonymity. There is a bot that automatically puts the information about an IP address on anonymous IP talk pages. This has happened at 141.211.120.199. You may wish to remove this.

I also wanted to remark that it is harder to make bold edits to more elementary and evolved pages because there are many more Wikipedians (often without specialist mathematical expertise) who are watching them, reverting any changes which they consider to be vandalism, or even unhelpful. I think this happened to you at calculus, for example. Geometry guy 16:48, 18 April 2007 (UTC)[reply]

Manifold

Hello, I've added a couple of things to Manifold and left some comments at the talk page, can you, please, take a look? I know it's all part of your grand plan! Arcfrk 02:27, 19 April 2007 (UTC)[reply]

Mistake... maybe?

Take a look at your edit to the discussion page of calculus. You posted in the middle of the WP:M at the top of the page and messed up the box a little bit and you copied almost word for word what was said in the to do list box. Just letting you know. Cronholm144 00:31, 22 April 2007 (UTC)[reply]

Thanks. It is a template problem, which we are trying to fix. Geometry guy 05:01, 22 April 2007 (UTC)[reply]

The template problem is now fixed. Anyway, I wanted to sign and date the calculus maths rating with a comment (so that it appears here) and your "todo" comment was perfect. I hope you don't mind that I used it. Imitation is...! Geometry guy 12:14, 25 April 2007 (UTC)[reply]

Thanks and no problem about the copy, frankly I was worried that I had subconsciously copied you after staring at the talk page for too long. I couldn't be more pleased with the welcome I have received here and hope to continue to add constructively wherever I go. I think we are getting close on the article and this, being my first major contribution here, is a very exiting feeling. If you ever want my inexperienced eye on an article your working on don't hesitate to ask. I will always do my best to help. Cronholm144 05:55, 26 April 2007 (UTC)[reply]

VeblenBot's table

I updated the bot's source code to match your changes. The way the bot is implemented, it does not merge the new table into the page, it just overwrites the entire page with the new table (including the noinclude part). So any changes to that page need to be made to the bot source code rather than to the table page itself. CMummert · talk 17:47, 25 April 2007 (UTC)[reply]

I see, thanks! Would it make sense do to what you did with the per-field pages, i.e., generate the table on a subpage of User:VeblenBot, and transclude it from there? Geometry guy 18:10, 25 April 2007 (UTC)[reply]

Pedantry at the WikiProject Mathematics front page

Pedantry is always welcome! We must put our best foot forward on our project page, after all. If you want extreme pedantry, I would point out that typically there are no spaces surrounding an m-dash—just like in this sentence. Since you've started hanging around here, I've seen a lot of you doing lots of good things. Thanks for being helpful! VectorPosse 00:16, 26 April 2007 (UTC)[reply]

Oh dear, I have put such extra spaces around m-dashes all over the place (I guess I like it that way), but feel free to fix them! Thank you so much for stopping by and for your kind remarks. Geometry guy 00:28, 26 April 2007 (UTC)[reply]

Space around em dashes varies from publisher to publisher (often hair spaces are used). By the way, you should avoid editing other people's spelling in talk page comments - you can edit my spelling all you want, but some people are very touchy about it. [1] The math project page is fair game, though. CMummert · talk 00:44, 26 April 2007 (UTC)[reply]

Yes, I'm aware of that, but thanks for the link (although I have not so far been overwhelmed with enthusiasm by SMcCandlish's attitude and contributions). I normally only fix the kind of trivial typos that I myself make all the time, but I have been known to fix the occasional very old spelling error (you probably noticed me correcting "coppied" recently). I think if someone gets upset about it long after the event, I can take the flak! I always try to make such edits in good faith, and not in order to criticize the original editor. Geometry guy 01:09, 26 April 2007 (UTC)[reply]

I certainly don't mind if you fix my occasional dyslexia. :) And thanks to CMummert for the clarification about the m-dash. A hair space actually seems more elegant to me than no space at all, so I might start using that if I can figure out how to create a hair space. VectorPosse 03:05, 26 April 2007 (UTC)[reply]

Mathematicians

I added code to VeblenBot to make the mathematician table. I also made all of the other tables sortable while I was at it. Please let me know if I have left any mistakes. CMummert · talk 14:23, 30 April 2007 (UTC)[reply]

Very good, and thanks for shipping the table header formatting out into templates. This allowed me to make some of the columns unsortable. Since there is no point in sorting comments, I have also (tentatively) moved the field into the comments column in "Table row format long". This may be a bit of a crowded look, but the rowspan = 2 approach meant that neither the article title nor the field could be sorted.

In general, I think it is a good principle to let VeblenBot concentrate on producing the data and leave page layout and formatting decisions to the Wikipedia 1.0 pages and associated templates. Separating form and content completely however, would require some thought, and quite a bit of work!

I may temporarily revert the mathematicians page to its previous form, since there is extra information still there that we need to decide whether we want to use.

Finally, I think the bugbear of the Unassessed-Class has bitten again: Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Unassessed-Class_mathematics_articles is not detecting the many unassessed mathematician pages that there are now. Geometry guy 15:51, 30 April 2007 (UTC)[reply]

Thanks for pointing that problem out; I changed the unassessed-class handling again and now it appears to work correctly. The problem is that the category is Category:Unassessed mathematics articles instead of Category:Unassessed-Class mathematics articles and so I have to translate back and forth between the category name and the name of the quality grade. Also the category is empty most of the time and so it isn't obvious during testing that there is an error. CMummert · talk 16:48, 30 April 2007 (UTC)[reply]

The mathematicians page was much easier. If there are more changes I need to make for it, please let me know. I didn't know there was an unsortable option, but it makes sense to use it where you did. CMummert · talk 16:48, 30 April 2007 (UTC)[reply]

Yes the name of the Unassessed category is a real pain! Anyway, we're still not out of the water: VeblenBot is using the wrong header and row format templates for Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Unassessed-Class_mathematics_articles although perhaps this will sort itself out at the next auto-update. Geometry guy 17:03, 30 April 2007 (UTC)[reply]

No, I just had the wrong parameter. It was a one-line change to switch to the correct template. CMummert · talk 17:14, 30 April 2007 (UTC)[reply]

Theorem article

Hey there! I think you are right, for whatever reasons there is a lack of boldness in editing the Theorem article. Anyway, just a reminder to work on that article, as you instructed on the talk page :-). Whatever you can do to make it better would be great! Kier07 00:01, 4 May 2007 (UTC)[reply]

Many thanks for the reminder and encouragement! If you look at very recent edit history of this talk page, you will probably see that I am already gearing up for this, and also hoping to recruit a friend. Thanks again. Geometry guy 00:20, 4 May 2007 (UTC)[reply]

Equipartition

As a representative of the educated but not scientifically-trained masses (and an avid reader of popular science books), Willow asked me to look over the equipartition theorem article again for overly obscure language. As I wrote in my earlier peer review, I am not sure that this article is one that anyone will stumble on who doesn't have some mathematical and physical knowledge already (unlike, for example, natural selection), but I do believe that at least the lead of every article should make an attempt to be comprehensible by the non-specialist. I think that the lead for this article has improved, but, to me, the opening paragraph is overly specific (I am thinking here of for example, the average kinetic energy in the translational motion of a molecule should equal the average kinetic energy in its rotational motion). "Translation motion" and "rotational motion" may be obvious terms to physicists and mathematicians, but they were not to me (but perhaps that is just me). I would suggest that every attempt be made in the lead to explain equipartition in simple terms and leave the "meat" for the article. Unfortunately, I understood equipartition not from this article, but from my live-in physics expert who explained it to me after I read the article. There must be some way to convey the gist of equipartition to the non-specialist in this article - perhaps in a separate section? Awadewit ^Talk 20:04, 6 May 2007 (UTC)[reply]

Many thanks for looking again at this article. It isn't really "under my wing", as Willow suggested: I just made a lot of edits recently, partly (despite my profession) to simplify and reduce the math content. Anyway, I agree entirely with what you say, and essentially all of my edits have been intended to make the article less technical and more accessible. The lead is a bit more accessible now, but (as you say) there is still some way to go, despite the FA status. Do you mind if I copy your comment over to the article talk page? If I make some edits along the lines you have suggested, this might help other editors see where I am coming from. Geometry guy 21:08, 6 May 2007 (UTC)[reply]

Copy away - I am on an ongoing quest to make the science articles on wikipedia more accessible to the lay reader; often, I find that science articles, even basic articles such a physics, are written by editors who think that they are addressing broad audiences but the articles end up being written only for highly-educated audiences. By the way, I don't understand the "despite" in your comment - I thought mathematics was all about simplification and reduction. My live-in physics expert is one of those physics people who loves math and he is always trying to explain the wonder of math to me. Just the other day, he showed me some equation that encompassed the entirety of our understanding of electricity and magnetism in it to try and inspire me to learn more math (an ongoing project of his). Awadewit ^Talk 22:51, 6 May 2007 (UTC)[reply]

A worthy goal indeed! Any thoughts on Adenosine triphosphate or glycolysis? Despite the forbidding names, these are really quite fundamental things (where do we get our energy from?) that are both fascinating and worth knowing about, but I found the articles pretty hard going. The "despite" meant that you might expect a mathematician to add math content, but I am happy that you didn't. It sounds like you have a great physics friend: I suggest you get (if you don't have it already) the T-shirt with the caption "And God said 'dF=0 and d*F=j' and there was light" :) Geometry guy 23:14, 6 May 2007 (UTC)[reply]