User talk:Silly rabbit/Archive 6

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Equations circumcircle

Dear Silly rabbit,

I'm not sure if this is a proper way to contact you, by I unfortunately don't know of any other. Right now I'm writing on a thesis where I will use the equation regarding the cartesian coordinates you posted in the article dealing with the circumcircle (http://en.wikipedia.org/wiki/Circumscribed_circle). I'm refering to the section headlined be "Using the cross and dot product".

Could you please tell me, where you found that relationship? I will need to quote in my thesis.

If you read this and want to reply, could you please send me an email to michaelkauth@web.de?

Thank you very much in advance,

Best regards,

Michael —Preceding unsigned comment added by 81.136.81.206 (talk) 11:09, 29 February 2008 (UTC)

Hi, I just moved it from the page circle. However, it follows from the section Circumcircle#Circumcircle equations using the determinant, which was there before I even touched the article (although I did do a bit to make it more intelligible). The result is a classical one, just expressed in terms of dot and cross products rather than the more traditional lengths and angles. See for instance formula 1.55 in

• Coxeter, H.S.M. (1969). "Chapter 1". Introduction to geometry. Wiley. pp. pp. 12-13. {{cite book}}: |pages= has extra text (help)

Best of luck, Silly rabbit (talk) 14:43, 29 February 2008 (UTC)

I'll see if I can find any better references, too. Silly rabbit (talk) 14:47, 29 February 2008 (UTC)

About External Links

Hi Silly Rabbit, I'm new to Wikipedia. I've just received your message that my external links are not considered to be within the guidelines. Sorry, for the hassle, I'll be more careful next time. Thanks.

Category:Vectors

Hello again, nice category creation. I'm surprised it didn't already exist. I noticed you reverted my addition of Vector bundle. Thanks for that; I agree it's not a good fit. I'd be grateful if you could review my other additions to the category. Also, do you have any detailed inclusion criteria in mind, expanding upon the category description? I'm asking here on your talk page rather than on the category talk page to avoid prodding category denialists into immediately putting the category up for deletion WP:CfD for allegedly being too broad or ill-defined. Perhaps you could reply here to keep it all in one place. Pretty tidy burrow you've got here on your talk page. - Neparis (talk) 01:33, 25 February 2008 (UTC)

Re my talk page. Freshly archived! I was planning on going on vacation, since I nearly blew my top the other day. But I seem to have calmed down a bit since then. Cheers, Silly rabbit (talk) 01:41, 25 February 2008 (UTC)

(copying here) Did I revert? If so, I certainly didn't mean to.  :-0 Silly rabbit (talk) 01:39, 25 February 2008 (UTC)

I see. No I didn't revert. I just saw that you added vector bundle to the category and popped over to have a look. It occurred to me that I didn't entirely agree with the first sentence of the article, so I changed the word "geometric" to "topological." Perhaps the point is arguable one way or the other, but I think of vector bundles as more topological, and then the stuff one adds to them (e.g., a metric, distribution, etc.) as geometric. Cheers, Silly rabbit (talk) 01:57, 25 February 2008 (UTC)

That's odd. Maybe it was a browser cache issue, or more likely my eyes are falling apart. - Neparis (talk) 02:36, 25 February 2008 (UTC)

(copying here) Cleary the category is needed, but I'm not really sure where to draw the line for inclusion. My first thought is that Wikipedia has a number of definitions of a vector which aren't all related by some category or another. So I added vector (spatial), row vector, column vector, vector space, and other sundry possiblities. Then you populated the category with some other definition-related articles, and some other interesting selections like Poynting vector. I guess an inclusion-criterion might be various definitions of vectors and vector-like objects, and particular vectors that are of importance to mathematics and physics. Perahps this is too broad? Cheers, Silly rabbit (talk) 01:46, 25 February 2008 (UTC)

Sorry, my brain doesn't cope very well with conversation being split between my talk page and yours, so I'm copying all your comments here to maintain the threading order.

A few thoughts on what to include: I added Vector calculus as a subcat because there were far too many subpages to include directly, and I thought about adding Linear algebra too as a supercat, but didn't because that would cause a number of articles, such as null vector and dimension (vector space), to be in both a category and its subcat, which infringes WP:CAT#Some_general_guidelines (point 3) and I anticipated potential controversy if I were to try resolving the problem by removing null vector etc from Linear algebra.

I suppose there are probably hundreds more math articles related to vectors that could be added. Should it include really esoteric articles such as vector superfield and Killing vector field? Should it exclude articles on properties, such as orthonormality? Should it exclude constructions that use vectors, such as the Gram–Schmidt process?? There may be something to be said for keeping the focus of the category on elementary and definition-related articles. Perhaps I have already added too much to the category? It was a nice and simple category when you started it, and that might be much more useful to lay readers, who could be confused and put off by seeing a huge category filled with lots of obscure article names, and very few basic articles. - Neparis (talk) 02:36, 25 February 2008 (UTC)

Yes, there is a clear danger of the category filling up with all manner of obscure articles. Maybe it should be limited to concepts which are as close to the fundamentals as possible. Silly rabbit (talk) 03:31, 25 February 2008 (UTC)

Hi, apologies for leaving the conversation unfinished; I was intending to return to it, but I see it has now been archived — my fault for taking too long to reflect. As you say, maybe the scope of the category could be limited to definition-oriented articles, though perhaps there is no clear line between articles that are definition oriented, and those that are not. Also, I think the category guidelines would require a change of category name to match the new scope, e.g. "Category:Vectors (definitions)". Alternatively, perhaps the category should be left to grow by consensus, within the limits of WP:CAT. - Neparis (talk) 23:46, 2 March 2008 (UTC)

Sorry, I got a bit carried away with the archiving. I was considering going off on a break again, but then got dragged back in by a variety of things. I have taken the thread out of the archives and put it here. Regards, Silly rabbit (talk) 00:23, 3 March 2008 (UTC)

No problem. Sorry you went to the trouble of dragging the whole thing out of the archives; I was actually thinking we had probably concluded the discussion! I'm happy to continue it though if you have any further thoughts. - Neparis (talk) 03:44, 6 March 2008 (UTC)

Dear Silly Rabbit

Your sobriquet immediately brought to mind the Thai rabbit that, like Chicken Little, thinks The Sky Is Falling (fable). Upon looking up this link, I found the chicken was originally a hare, and that the story originates from the Jataka Tales of Buddhist Indian folklore. So, whether or not you are a Buddhist, you outrank the silly chicken! BTW, disaster really is imminent. Pawyilee (talk) 09:33, 5 March 2008 (UTC)

Very interesting. Most westerners seem to associate my handle with a breakfast food. Silly rabbit (talk) 11:23, 5 March 2008 (UTC)

Dear Silly Rabbit

Why did you remove the text that I added to the article on Heterosexuality, giving link to a page on wikipedia. Both the text and the page have been created after discussing them at the LGBT talk page on Homosexuality. And, on the page on "Non-western concepts of male sexuality", I have provided 20 references from published papers from around the world -- including from western and non-western sources. This is certainly not original research.

Can you be more careful before you delete things like that? (Masculinity (talk) 16:01, 6 March 2008 (UTC))

Because you didn't cite any sources. See WP:REDFLAG. You have also tried to add this same content to a great many other pages, over the objections of almost every other editor around. Please obtain WP:CONSENSUS to add before you do so. Silly rabbit (talk) 16:08, 6 March 2008 (UTC)

first of all who are you and how do you have authority to block me for fixing factual errors, offensive statements, and gross misrepresentations from Wikipedia? —Preceding unsigned comment added by 12.181.61.147 (talk) 20:33, 7 March 2008 (UTC)

3RR warning?

I didn't revert anyone, you reverted my edits without discussion. Please see WP:CCC and please discuss (see my entry on talk page and my edit summaries) before reverting again. WNDL42 (talk) 22:52, 7 March 2008 (UTC)

For your consideration: "A small group of editors can reach a consensual decision, but when the article gains wider attention, others may then disagree. The original group should not block further change on grounds that they already have made a decision. No one person, and no (limited) group of people, can unilaterally declare that community consensus is fixed and determined." WNDL42 (talk) 22:57, 7 March 2008 (UTC)

7RR warning

You currently appear to be engaged in an edit war according to the reverts you have made on Pseudoscience. Note that the three-revert rule prohibits making more than three reversions in a content dispute within a 24 hour period. Additionally, users who perform a large number of reversions in content disputes may be blocked for edit warring, even if they do not technically violate the three-revert rule. If you continue, you may be blocked from editing. Please do not repeatedly revert edits, but use the talk page to work towards wording and content that gains a consensus among editors. If necessary, pursue dispute resolution. --USER:Silly rabbit, You are being warned for 7RR and gaming the system.

Silly Rabbit, when you reverted seven edits in a single edit here, you provide evidence that you are gaming the system to evade WP:3RR. Of the seven edits you reverted in that "single" revert, you have only discussed one issue on the talk page. Also, making false claims of consensus (see WP:CCC) as a means of justifying your reverts is also an example of gaming. Please undo your seven reverts here and return to the discussion. WNDL42 (talk) 13:55, 8 March 2008 (UTC)

You have, how shall we say, a rather idiosyncratic view of the rules. If you think you are right, then perhaps you should report me. Then we'll get this straightened out forthwith. Silly rabbit (talk) 14:12, 8 March 2008 (UTC)

Golden section

I'm not crazy about the title I gave to the Category, but it is extremely necesary to tie all the works studied due to their Phy proportions. In a couple of hours I'll have a significant list. Then again Wikipedia is way too slow right now. But trust me, the proposal will be interesting.--20-dude (talk) 03:41, 8 March 2008 (UTC)

Mmmh, didn't like the name you proposed either. But agreed, the name I choosed sucks harder. I'm not too worried about that, we will move it as soon as we come up with a better name. Meanwhile you can move it to your proposed name if you want, I don't mind.

I agree, it looks weird that I didn't start with the parthenon and the Gioconda, and the most famous examples. My bad.

--20-dude (talk) 08:07, 8 March 2008 (UTC)

Muhammad (PBUH) page

I realize that the editors want to keep the images on the Muhammad (PBUH) page, so I simply added to the comment of one of those pictures saying that it is forbidden in islam to portray the prophet, however, the editors have agreed to keep these images on this page. I hope the editors do not have a problem with this —Preceding unsigned comment added by Waisgai (talk • contribs) 03:38, 9 March 2008 (UTC)

Not all forms of Islam proscribe depictions of the prophet. At any rate, this too has been discussed and rejected at Talk:Muhammad/Images. Silly rabbit (talk) 03:41, 9 March 2008 (UTC)

so

Misner et al are wrong? I don't think so...--kiddo (talk) 04:40, 10 March 2008 (UTC)

Look my friend, it is late for me, but I expect tomorrow continue this exchange of words, ok? Besides, i would like to see some credentials from u, 'cuz it is very easy to be an incognit-sniper,... Juan --189.162.39.98 (talk) 04:56, 10 March 2008 (UTC)

Barnstar

		The E=mc² Barnstar
		To Silly Rabbit, for all round excellence in your many contributions throughout Wikipedia, but especially to science and math articles. Thank you! - Neparis (talk) 04:03, 11 March 2008 (UTC)

Thanks! Silly rabbit (talk) 13:54, 11 March 2008 (UTC)

Barnstar

		The Red Barnstar
		Yu have been awarded this because your username is awesome 207.80.141.11 (talk) 16:47, 12 March 2008 (UTC)

Hey thanks. It looks like something from Communism: the Red star. silly rabbit (talk) 02:22, 13 March 2008 (UTC)

Integrability conditions for differential systems

Please, let us not get into a wrangle about this. The accessibility condition is superfluous for the point being made, and in any case, is incorrect. Please believe me, I do know what I am talking about, since it is my specialty. You can check my web page if you doubt my qualifications. If you wish to discuss it further, please do so by e-mailing me at: rphysicist@gmail.com and I will be happy to provide more detailed explanations. But for the moment, please do not do any further edits of this article unless they are truly necessary, and you are sure they are correct. Thank you. R_Physicist (talk) 17:50, 18 March 2008 (UTC)

I didn't mean to sound condescending, I just wanted to assure you that I do know what I am talking about, since it belongs to my profession. Not everyone can have expertise in a given domain, and even though I have nothing against enthusiasts in maths who would like to make their own contributions to wikipedia, I find it wasteful, and tiresome to have to correct, and recorrect entries - about things that I am perfectly familiar with - erroneous notions that are introduced, and then re-introduced. The term contact form is perfectly fine, but is superfluous to making the point, that I presume you would like made in this example; namely that there exist Pfaffian systems that are not completely integrable. Introducing an object, or term, that has not appeared previously, just to show that you know of it, is of no help or use to the reader of the article. If you think that it is worthwhile discussing contact forms, and that this is pertinent to the article, please add a separate section lower down, in which this is correctly done, and add an example, if you wish, to illustrate it. But please, if you are trying to write about the mathematics, and none just make minor editorial corrections, please check first with someone who really knows the subject well, before making an addition.

I don't mean to suggest either that you should not edit this article further, or add to it; I would just like to ask you to be sure that what you are writing is actually correct, and to not alter a correction that has been made by someone who may, perhaps, know the subject somewhat better, since it his profession.

If you think about it, you will realize why the statement that you added, that one can reach any point in the first octant from any other point along an integral curve, is obviously incorrect. A wikipdia article, which some people might want to rely on as a source of information, is not the place to experiment with "facts" that you are unsure about. If you are unsure, please check with someone who knows the subject thoroughly before introducing such statements. R_Physicist (talk) 18:40, 18 March 2008 (UTC)

Reply

Thank you for the detailed response on my talk page. I realize that I may have initially over-reacted to your entreaty for me not to edit the article, and I apologize. I believe that the statement of accessibility is true (in the first octant). This is certainly true locally, by Darboux's theorem. Globally, it should also be true since there is a system of Darboux coordinates, say

$w={\frac {1}{2}}(xy+yz+zx),\quad u=x-y,\quad v=y-z$

in which the form is $\theta =dw+{\frac {1}{2}}(udv-vdu).$

Anyway, I suppose it's sort of irrelevant to the issue of whether this statement should be included or not. I do think it is important to mention that the form in the example has many integrals — in fact, sufficiently many (if you are willing to believe me) that any two points can be joined by an integral curve, at least locally. silly rabbit (talk) 19:33, 18 March 2008 (UTC)

Further reply regarding integral curves

The point is very simple, and can be explained in one sentence (and it has nothing to do with the Darboux theorem). No Pfaffian system whatsoever (except for the null one) can have integral curves that connect all pairs of points in any open region. For if this were the case, it would immediately imply that, at each point, the full tangent space was annihilated by the Pfaffian system, which can only happen if it is the null system. R_Physicist (talk) 02:30, 19 March 2008 (UTC)

At present, there are no issues to discuss.

Accessibility condition

I'm sorry to differ with you at Integrability conditions for differential systems. Perhaps you and I do not agree about what point, precisely, is being made by the example in question. In my mind, it is very relevant that the form in question should be a contact form, and I am uncertain why you are reluctant to point this out. Perhaps some further discussion needs to be added to the example in question. The restriction on the domain was selected, of course, precisely so that this would be true.

Also, I don't appreciate being told not to edit the article. It doesn't show much good faith in my own contributions here, which I stand by. I agree with your recent improvements of the article. I had originally written it as something that differential geometry articles such as Cartan connection, Maurer-Cartan form, and Connection form could link to for integrability conditions for connections. Of course, improvements are welcome. Condescention is not.

At any rate, I'm sure your expertise can improve many of the related articles here. If you need editorial advice, or help navigating, let me know. Cheers, silly rabbit (talk) 18:07, 18 March 2008 (UTC)

I didn't mean to sound condescending, I just wanted to assure you that I do know what I am talking about, since it belongs to my profession. Not everyone can have expertise in a given domain, and even though I have nothing against enthusiasts in maths who would like to make their own contributions to wikipedia, I find it wasteful, and tiresome, to have to correct, and recorrect entries - about things that I am perfectly familiar with - erroneous notions that are introduced, and then re-introduced. The term contact form is perfectly fine, but is superfluous to making the point, that I presume you would like made in this example; namely that there exist Pfaffian systems that are not completely integrable. Introducing an object, or term, that has not appeared previously, just to show that you know of it, is of no help or use to the reader of the article. If you think that it is worthwhile discussing contact forms, and that this is pertinent to the article, please add a separate section lower down, in which this is correctly done, and add an example, if you wish, to illustrate it. But please, if you are trying to write about the mathematics, and not just making minor editorial corrections, do check first with someone who really knows the subject well, before making an addition.

I don't mean to suggest either that you should not edit this article further, or add to it; I would just like to ask you to be sure that what you are writing is actually correct, and to not alter a correction that has been made by someone who may, perhaps, know the subject somewhat better, since it his profession.

If you think about it, you will realize why the statement that you added, that one can reach any point in the first octant from any other point along an integral curve, is obviously incorrect. A wikipdia article, which some people might want to rely on as a source of information, is not the place to experiment with "facts" that you are unsure about. If you are unsure, please check with someone who knows the subject thoroughly before introducing such statements. R_Physicist (talk) 18:46, 18 March 2008 (UTC)

Reply

Thank you for the detailed response on my talk page. I realize that I may have initially over-reacted to your entreaty for me not to edit the article, and I apologize. I believe that the statement of accessibility is true (in the first octant). This is certainly true locally, by Darboux's theorem. Globally, it should also be true since there is a system of Darboux coordinates, say

$w={\frac {1}{2}}(xy+yz+zx),\quad u=x-y,\quad v=y-z$

in which the form is $\theta =dw+{\frac {1}{2}}(udv-vdu).$

Anyway, I suppose it's sort of irrelevant to the issue of whether this statement should be included or not. I do think it is important to mention that the form in the example has many integrals — in fact, sufficiently many (if you are willing to believe me) that any two points can be joined by an integral curve, at least locally. silly rabbit (talk) 19:33, 18 March 2008 (UTC)

Further reply regarding integral curves

The point is very simple, and can be explained in one sentence (and it has nothing to do with the Darboux theorem). No Pfaffian system whatsoever (except for the null one) can have integral curves that connect all pairs of points in any open region. For if this were the case, it would immediately imply that, at each point, the full tangent space was annihilated by the Pfaffian system, which can only happen if it is the null system. R_Physicist (talk) 02:28, 19 March 2008 (UTC)

There is a classic theorem along these lines. See, for instance, Bryant, Chern, Griffiths, Greene (they attribute it to Caratheodory). In any region where there exists a Darboux coordinate system for a contact form, any two pairs of points are joined by an integral curve. This is, apparently, at odds with what you are saying here.

The proof is only a few lines long. Consider the one-form

$\theta =dz+{\frac {1}{2}}(ydx-xdy).$

The point $(x_{0},y_{0},z_{0})$ is joined to $(x_{1},y_{1},z_{1})$ by the arc

$z(t)=z_{0}+{\frac {1}{2}}\int _{0}^{t}\left(x{\frac {dy}{dt}}-y{\frac {dx}{dt}}\right)dt$

where the xy component of the curve $(x(t),y(t))$ is selected so that the signed area formed by the curve and the line segment adjoining $(x_{0},y_{0})$ and $(x_{1},y_{1})$ is equal to the difference $z_{1}-z_{0}$. This is an integral curve for θ, and yet it connects two arbitrary points in R³. silly rabbit (talk) 02:50, 19 March 2008 (UTC)

Another (less trivial) example of this kind of behavior is the holonomy of a connection. If one has a principal connection on a bundle whose structural group has been reduced to the holonomy group of the connection (see Kobayashi and Nomizu, for instance), then any two points in the principal bundle are mutually accessible by an integral curve of the connection form (a horizontal lift). silly rabbit (talk) 03:18, 19 March 2008 (UTC)

Further reply 2 regarding integral curves

I see now that you know more about Frobenius integrability than I had thought from the wikipedia article revisions. The solution that you give however is not quite correct, since points having the same projection to the $x-y$ plane cannot be connected by such curves. However, it comes close to providing a countereaxmple to my explanation, since any other pairs of points can be connected by integral curves. (My "one sentence" explanation was indeed incorrect, since it assumed that being able to reach any neighboring point implied being able to leave the initial point in an arbitrary direction, which is clearly not the case.) The general case of horizontal lifts along curves, however, convinces me, and in fact I am embarrassed to admit that I have used this fact many times, but don't seem to have recognized it in this case. So, essentially: point conceded.

I do not quite see, however, why this requires reference to the Darboux theorem. In the version(s) I know, this just tells you that locally all symplectic structures (and all Poisson structures) are equivalent. (Which of course is a manifestation of Frobenius integrability, but this is not needed for understanding this example). You seem here to mean by it that all contact structures are locally equivalent, wihch perhaps is how Bryant et al formulate it.

In any case, for a reader consulting this article for an introductory summary, bringing in the notion of Darboux' theorem or contact structures just to explain this simple example does not seem necessary, or even helpful.

As a compromise, if you still feel that the example needs more elaboration, I would suggest perhaps just giving an integral expression for the "most general" integral curve, instead of just the one parameter family that I have given, while pointing out that these all leave the initial point tangentially to a (generally) two dimensional plane. The real point about Frobenius integrability, of course, is that the neighboring planes cannot be attached to form the tangent bundle to a surface. But that would require a more detailed explanation than such an article need include, and would start to sound more like a textbook. R_Physicist (talk) 04:22, 19 March 2008 (UTC)

Vector qua ordered set

For an example of “vector” defined simply as ordered set, see Discrete Mathematical Structures by Kolman, Busby, and Ross. It is simply inappropriate for you to think of yourself as so expert that you may simply delete a mathematical definition because you've not encountered it. —SlamDiego_←T 22:29, 26 March 2008 (UTC)

I find the tone of your message on my talk page to be totally inappropriate. You are, of course, free to disagree with my editorial judgement on whether a linearly ordered set should be called a vector. However, leaving a barbed response on my talk page is unnecessary.

The article vector gives a list of the main uses of the word "vector" in mathematics, followed, rather inexplicably, by a reference to a linearly ordered set. This is definitely not standard usage in most areas of mathematics. It may be that there is some small subset of mathematics which uses this terminology, but I for one need convincing before I allow an unreferenced and rather bizarre entry to occupy a list consisting of otherwise uncontroversial and commonplace definitions. (I mean, does someone call the real line a "vector"? Really?)

I will try to check the reference you have given. To save me the time, perhaps you could post a direct quote on my talk page defining a linearly ordered set to be a vector. silly rabbit (talk) 02:16, 27 March 2008 (UTC)

Someone who felt that his personal experience was thus definitive would of course find it inappropriate to be told not to summarily delete content based on that experience.

The presence of the other definitions in the article is no more explained than is that of the definition that you summarily deleted. Nor could most of those other definitions be said to be standard usage in most areas of mathematics. Conferences that tried to resolve the conflicts in definitions ended in disappointment. (See Cajori's A History of Mathematical Notations for mention of an attempt.)

You may insist that the definition is bizarre, but it is obviously a generalization of the notion of the vector as an ordered set of numbers. And computer science folk have been happy to take it up. For example, Java's Vector.class is named in the context of this conception. (And, ironically enough, a Vector cannot have primitive numeric types as its elements.)

As to what you will allow, I suggest that you reconsider your sense of entitlement here.

Although Kolman, Busby, and Ross define “vector” as an ordered set, without condition that the set be countable, I don't think that they ever apply that definition to uncountable sets. Nor have I elsewhere seen it applied to uncountable sets.

I'm not sure how a quotation would make your life easier, as you'll still want to get the book, find “vector” in its index, and so forth. (The page number and so forth will vary with the edition; they're on edition 5 or 6 now.) But I suppose that I can dig up an exact quote if you haven't first. —SlamDiego_←T 03:55, 27 March 2008 (UTC)