User talk:Boris Tsirelson

Welcome!

Welcome to the Citizendium! We hope you will contribute boldly and well. Here are pointers for a quick start. You'll probably want to know how to get started as an author. Just look at CZ:Getting Started for other helpful "startup" links, and CZ:Home for the top menu of community pages. Be sure to stay abreast of events via the Citizendium-L (broadcast) mailing list (do join!) and the blog. Please also join the workgroup mailing list(s) that concern your particular interests. You can test out editing in the sandbox if you'd like. If you need help to get going, the forums is one option. That's also where we discuss policy and proposals. You can ask any constable for help, too. Me, for instance! Just put a note on their "talk" page. Again, welcome and have fun! Hayford Peirce 17:35, 16 June 2009 (UTC)

Welcome Aboard

I'm fairly new here myself, with maybe a weeks worth of edits under my belt. I just wanted to be the first (besides those pesky account creators) to welcome you to Citizendium.Drew R. Smith 20:07, 16 June 2009 (UTC)

Thank you! But do not expect me to deal with aquarium fish :-) Boris Tsirelson 20:13, 16 June 2009 (UTC)

As long as you don't expect me to deal with math ;-) Did you come from The Other Place™, or is this your first wiki experience?Drew R. Smith 20:27, 16 June 2009 (UTC)

If it is an euphemism for Wikipedia, then the answer is "yes"; thust visit (again) my home. Boris Tsirelson 20:34, 16 June 2009 (UTC)

Привет Борис, приятно Вас увидеть здесь. В случае проблем с местными процедурами или шаблонами, спросите у тех, кто на сайте (участники постараются быть вежливыми, обычно успешно), или прямо в Форуме. С улыбкой, --Daniel Mietchen 06:58, 17 June 2009 (UTC)

Thank you. However I wonder, is it polite enough to speak Russian here? Boris Tsirelson 08:17, 17 June 2009 (UTC)

My understanding is that as long as the content of the message can be understood by all concerned with it, you can use whatever language you like. --Daniel Mietchen 08:26, 17 June 2009 (UTC)

Hello, Boris. It is a pleasure to welcome you here. Aleksander Stos 13:30, 17 June 2009 (UTC)

Thank you. Boris Tsirelson 15:14, 17 June 2009 (UTC)

On doubts

Do you actually intend to do significant work on the article sometime in the next hour? If not, don't upload it, or not until you actually want to start working on it. We are not creating a mirror of Wikipedia here. If you merely want your brilliant work on Wikipedia to be reprinted in another, more credible source, then you must make up your mind: are you really going to maintain and develop the article here on the Citizendium or not? If not, stick with Wikipedia. (A quote from CZ:How to convert Wikipedia articles to Citizendium articles)

I am astonished. Even commercial scientific journals do not insist that a journal article must differ from its preprint in the arXiv. In order to differ from the archive it is sufficient for a journal to be more selective. Likewise, in order to differ from Wikipedia it is sufficient for Citizendium to be more selective.

Is it a decent goal, never mirror Wikipedia? Or rather jealousy? Maybe I shall indeed stick with Wikipedia.

Thanks for the feedback. I tried to rephrase that policy page, such that it makes more sense. Some noteworthy differences between Wikipedia entries and arxiv preprints include that the latter are written with a coherent narrative about original research by a few experts for other experts, with no or few hyperlinks to freely available explanations of concepts that provide the context for understanding. --Daniel Mietchen 08:52, 17 June 2009 (UTC)

Nice. This version sounds better for me. Now I feel astonished, however, that you just modify a policy. In Wikipedia, to modify a policy is quite a problem; a consensus must be reached between a lot of editors on the talk page before even a small change. Are you sure that others agree with your new formulation? Boris Tsirelson 09:23, 17 June 2009 (UTC)

I didn't modify the policy, just tried to distill it down onto that policy page from my experience of about one year at the site. The best way to get feedback on such issues are the forums, so I started a new thread there. --Daniel Mietchen 09:53, 17 June 2009 (UTC)

What I really had in mind are Wikipedia articles made by myself (with quite small changes by others), that are written with a coherent narrative (I hope so!), for instance [http://en.wikipedia.org/wiki/Non-Borel_set. And of course I would be ready to improve it here if some critique appears. But the policy required me to criticize myself as a precondition! Boris Tsirelson 09:29, 17 June 2009 (UTC)

This is covered at CZ:How to convert Wikipedia articles to Citizendium articles#Are you the main author of that Wikipedia article?. --Daniel Mietchen 09:53, 17 June 2009 (UTC)

I'd try to avoid mirroring Wikipedia, because I don't think it is realistic, as perhaps had been the original CZ intention, to be "WP but better". Instead, I believe CZ needs to develop its own identity, taking advantage of some of the different policies. We aren't going to have the sheer number of articles — the question then becomes "why are we here"? The multiple answers involve doing some complementary things.

For example, allowing expert opinion and what WP calls "original synthesis" can position CZ as a resource that contextualizes information in a way that WP cannot. The Related Articles subpage system provides more means of contextualizing.

While I once contributed substantially to WP, I do no longer, as I simply do not find it a congenial environment. Other people do. I'd rather have the environments be well differentiated.

While both have provisions for educational projects, we may be able to have a better Eduzendium service. Howard C. Berkowitz 15:21, 17 June 2009 (UTC)

For now I am not quite understanding it, since it seems to me, I would create basically the same article here if I would start here. Nothing specifically "wikipedianish". Well, in fact some of my WP articles do not fit here (as far as I understand); but others do. Why not? Boris Tsirelson 15:33, 17 June 2009 (UTC)

Let me answer by example. The article Wars of Vietnam, with a very large number of subarticles, probably could not have been written at Wikipedia. Indeed, a number of the subarticles could not have been, because they contain expert opinion that isn't necessarily in a reference that could be cited.

In like manner, we had a problem with a number of agenda-driven articles dealing with U.S. foreign policy, which, in fact, were imported from Wikipedia but before a subject matter expert could review them. The approach I used to put facts in context was to develop concepts in a top-down manner, from interrogation to intelligence interrogation, U.S. to intelligence interrogation, U.S., George W. Bush Administration. In many of these, I wrote as an expert, and, where appropriate, cited primary sources. I did not, as had a previous author, write about random prisoners and only cite allegations of impropriety. Ironically, I had much the same low opinion of the politicians involved, but I was able to stay reasonably objective.

It is my personal opinion that the WP tradition of writing articles on anything, and not ensuring they are linked to context, is flawed. Indeed, WP has expressed concern over "orphaned articles". I do not expect that articles on random subjects will eventually coalesce into a reasonable structure, unless some effort is taken. That may mean that subject matter experts guide by writing top-level articles, as well as advising on specific articles.

While it probably doesn't affect your subjects, another difference is that we do expect the first author of an article of a controversial subject to make some effort to present all sides. Some WP authors put up only their, in WP terms, POV, and expected others to balance it. Howard C. Berkowitz 15:43, 17 June 2009 (UTC)

All that is probably interesting, but quite far from my area of competence. In order to be specific, I'll create a text, you (I mean, "you all") will criticize it, and then hopefully I'll understand what is really the problem. Boris Tsirelson 18:18, 17 June 2009 (UTC)

Ah, someone should really write an article about the nuances among "you all", "y'all", and "all y'all." :-) Matt? Howard C. Berkowitz 18:25, 17 June 2009 (UTC)

Seriously, if you are primarily in mathematics, it's less likely that you will run into some of the conflicts as in other areas. Still, I'd hope that if you write about a specialized topic, there would also be a top-level article defining the area of mathematics. I'd also encourage your writing Related Articles subpages, which you can do even before the article is written -- it's a way to define work to be done. Howard C. Berkowitz 18:25, 17 June 2009 (UTC)

Since I was quite involved in discussing the policy you cited, let me add my 2 cents. To make it short: feel free to import your articles from WP. Many members did so; in particular Hayford, the constable who welcomed you (see e.g. his articles on tennis players). A special template ({WPauthor}) is used in this case.

My longer answer: As far as I can tell, our policy doesn't discourage import. For genuine authors rather the converse is true. The paragraph you cited at the beginning addresses the (once typical) issue of (perhaps serial) importing arbitrary articles with no intention to work on. Now, frankly, who needs yet another mirror of Wikipedia? This is not "jealousy"--there is just no "public interest" in creating such a thing.

The policy starts with "advantages of writing from scratch". I'd add one more. While mirroring is of no big interest, having two sources treating a subject from an (even slightly) different angle has many advantages to web users. And--for a "generic" article--writing from scratch seems to be the best way to achieve this. Serious reworking might be good as well.

If you import your article here, you may discover that here you are given more freedom to polish and develop it (...and get less feedback as for now). You're not presupposed to "criticize yourself"--rather invited to review your text with respect to the local style policies (this holds true for articles not coming from Wikipedia too!). In general, some style adjustments might be needed, esp e.g. in human sciences. But in maths this might be less of a problem. If it's OK, it's OK. Aleksander Stos 18:52, 17 June 2009 (UTC)

PS. I don't see what your articles "do not fit here". Probably, anything of mathematical interest can be easily adapted.

Welcome and more about uploading articles from Wikipedia

Boris, first let me welcome you most heartily. It is obvious that you have already rolled up your sleeves and are about ready to start writing/editing articles here.

I spent about 3 years or so on WP until I finally got fed up with all of the vandalism and, even worse, the revisions by inexperienced, young post-grads and others who considered themselves know-it-alls but who were not.

I have now been here on CZ for over a year and half. I never bothered to read the CZ article on how to convert WP articles. I have uploaded dozens of WP articles that I either created or contributed to heavily. But I first copied them to a personal sandbox here and then spent much time on re-writing/re-formatting/updating/correcting them before uploading them into CZ's namespace. I also moved the WP's "See also" section to CZ's subpage "Related Articles" and WP's "External links" section to CZ's "External Links" subpage. Then I also was quite careful to explain that WP had a similar article (and my role in the WP article) on the Talk page of the article that I had uploaded into the CZ namespace.

I echo the comments above about using the CZ forums to discuss new policy or initiative ideas. Also, when contemplating significant editing of existing articles written by others, it is "good form" here on CZ to first discuss your proposed editing thoroughly on the article's Talk page. Yes, I know that is the same as on Wikipedia ... but it actually works here on CZ and it did not work in WP.

I will also say that in my year and a half here, I have yet to see even one instance of vandalism in a CZ article. In WP, I spent about 1-2 hours every day cleaning up vandalism to articles I had written or trying to convince know-it-alls that their edits were not correct. There is also no incessant use of templates telling us to add references or "fact check"... expertise is trusted and valued here with or without a multitude references. Yes, I add many references to my articles but only where I feel they are needed.

Once again, welcome to CZ and I hope my comments are useful. Milton Beychok 18:26, 17 June 2009 (UTC)

An opposing view to Howard's

Hi, Boris, I've been here a little longer than Howard and have brought in a number of articles from WP, which I then generally expanded, rewrote, improved, polished, or worked on one way or another. I've also created my own new articles here. I understand Howard's point of view on the purpose of CZ, and how we should go about getting there, but I don't agree with it. If he, or anyone else, wants to write "top down" articles, or all-encompassing articles that then gather in a whole bunch of lesser articles, then fine, let them do it. I myself, however, write strictly what *I* want to write, in my own manner (within CZ conventions, of course), and if they're 100% stand-alone articles with no relationship whatsoever to some grand Unified Field Theory, then tant pis as our French friends say. Eventually, if enough people like me write enough articles about what *we* want to write about, then the Great Unifiers will come along and sweep them all together. And we'll have a Better Wikipedia. So my own personal advice to you is: Write just exactly what *you* want to write about and don't try to write about what Howard *wishes* you would write about. Let Howard and Milton and me and everyone else do what *we* want to do, and someday it will all come together. And don't worry about bringing in WP articles: bring 'em in, fix 'em, improve them, rewrite them, polish them, perfect them, and then we will have a much better article than the one in Wipipedia. So, above all, "to thy own self be true!" Hayford Peirce 19:04, 17 June 2009 (UTC)

And sign your articles, Hayford. :-) Howard C. Berkowitz 19:01, 17 June 2009 (UTC)

Thanks to all

Wow, I could not expect such an impressing, massive discussion here. Thanks to Daniel Mietchen, Howard C. Berkowitz, Aleksander Stos, Milton Beychok and Hayford Peirce. (Or did I forgot someone?!) Now I feel more convinced that I really should try, and then we all will see what comes out. Clearly, we all strive to the best and, as usual, choose different ways. I suppress my impulses to reply here and there, for two reasons. First, being a newbie here, I have too little idea what is right and what is wrong. Second, I'd better spend my time preparing an article. Your advices surely make my way shorter. Boris Tsirelson 19:38, 17 June 2009 (UTC)

Non-Borel set

It is created. Now please start to criticize/correct/improve me.

That short article answers a frequently asked but infrequently answered question: what about a constructive example of a non-Borel set? Boris Tsirelson 06:49, 19 June 2009 (UTC)

This is a decent article and I see no special issue to "criticize/correct". Of course, it may be developed in a normal wiki manner as any other article (e.g. I proposed a new wording but it has nothing to do with the previous discussion). Cheers! Aleksander Stos 10:41, 19 June 2009 (UTC)

One technical suggestion: here is a typical usage of the template

{{WPauthor|WP article "Non-Borel set", version of 23 Aug 2008, was used. I am its sole author.|Boris Tsirelson}}

If you agree, you may put it on the discussion page. Aleksander Stos 10:47, 19 June 2009 (UTC)

Nice. Yes, I did. Thanks, Boris Tsirelson 11:03, 19 June 2009 (UTC)

Hi!

Hi, Boris. I have taken a look and made some remarks. Peter Schmitt 00:13, 21 June 2009 (UTC)

I see. Thank you. Boris Tsirelson 04:45, 21 June 2009 (UTC)

Space

Boris, thanks for your corrections.

I just want to mention that I noticed your work on Space (mathematics) which is now a quite substantial article. I have not reacted until now because, unfortunately, I have not yet read it thoroughly. Probably it needs only some proof reading and polishing before it is ready for approval. But since it is a quite ambitious survey, I think that the title should be changed to reflect this (Abstract space?, I'm not yet sure.) and leave "Space (mathematics)" for a more basic introduction.

Peter Schmitt 22:40, 4 October 2009 (UTC)

Thank you for the high opinion; I am glade you like it.

About the title: as we know (and non-mathematicians maybe do not know), the word "space" in mathematics is mostly used in such combinations as "linear space", "topological space" etc. Thus, it is "abstract" by default. The other usage could be rather "Space (solid geometry)" or something like that? Boris Tsirelson 10:05, 5 October 2009 (UTC)

However, why discuss the article here? I copy the discussion to Talk:Space (mathematics) in order to continue there. Boris Tsirelson 19:14, 5 October 2009 (UTC)

Eventology

Boris, what is your opinion of Eventology? The author wrote some papers on it, for instance, this paper (in Russian). I don't read Russian—and I don't know if I knew the language whether I could make a judgment about its contents. I see references to very respectable Russian mathematicians. Is eventology a respected subfield of mathematics and worth an article in CZ? --Paul Wormer 07:37, 10 October 2009 (UTC)

OK, I am trying to use my Russian; please wait. Boris Tsirelson 16:34, 10 October 2009 (UTC)

See Talk:Eventology#Another_comment. Boris Tsirelson 18:52, 10 October 2009 (UTC)

Geometric series

Boris, I need a line of explanation, because I never gave any thought to the divergent case. You're saying that the sign of the series is undetermined for q ≤ −1?--Paul Wormer 08:41, 11 January 2010 (UTC)

Yes, and I just gave some explanation in the article. Take for instance (+1)+(-1)+(+1)+(-1)+...; the partial sums oscillate: 1,0,1,0,1,... For q<-1 they oscillate stronger. Boris Tsirelson 08:44, 11 January 2010 (UTC)

See also WP:Grandi's series and WP:Cesaro_summation. Boris Tsirelson 08:49, 11 January 2010 (UTC)

Mathematical nonsense

Boris, CZ is a wiki, be bold, improve or delete any math articles that are substandard (including those written by me). There is not much point in complaining on your user page, it is better that you address the responsible people: the math editors. Further, I get the impression that especially high-school math article are bad, is that your impression too?--Paul Wormer 15:57, 28 March 2010 (UTC)

Yes, I'll try to do something, but my abilities are scanty... thus I also call everyone to bother: "When I write outside my expertise, my intuition is not reliable enough, I should also consult some (text)books".

About high-school math: yes; but this is quite natural. For example, a plane (in the space). There is no problem to define a two-dim linear subspace of a given three-dim linear space. However, what to say to a man not ready to this level? How to define a plane to him (or her)? Really a problem! Maybe I'll try. I am sure that such article must contain several levels of complexity/accessibility. Boris Tsirelson 18:22, 28 March 2010 (UTC)

Boris, I fully agree that there are much too many poor and very poor articles and stubs here, often confusing.

In fact, when I first "found" CZ (about 10 months ago) 2 or 3 such pages were the reason to join. I wanted to correct them. Soon I saw how much there is to do. I have a very long (mental) to-do-list ...

I first saw parallel (geometry), plane (geometry), and surface (geometry) when recently pictures were added to them. I did not like them, either. In the meantime I have replaced surface (by a page acceptable, I hope, as a first information), but unfortunately I am slow when writing. Nevertheless, I could have written and improved more articles since then, but I often get distracted by general discussions on talk pages and in the forum, in particular, concerning the drafting of the Charter.

In fact, concerning most of the mathematics articles I am glad that they are hidden far down on the Google results.

By the way, the good articles on mathematical topics are mainly contributions by Paul (though written from a physicists point of view). He has been here longer than I am and is much more efficient ...

--Peter Schmitt 23:37, 28 March 2010 (UTC)

Plane

Boris, I wrote plane. Could you comment on it? I like to insert it into plane (geometry). --Paul Wormer 11:02, 30 March 2010 (UTC)

Yes, please, insert it. It is nice. If only the choice of letters could be better? But maybe not; I did not really try it. Boris Tsirelson 14:57, 30 March 2010 (UTC)

What do you mean by choice of letters? It is easy for me to change anything.--Paul Wormer 15:17, 30 March 2010 (UTC)

I mean for instance the vector a with the coordinates u,v,w and soon after that the vector f with the coordinates a,b,c. It is formally correct, but still a bit unpleasant. A good use of letters is the vector r with the coordinates x,y,z.

And by the way, the division of vector by number seems to me a somewhat informal style; in a more formal style it is

${\frac {1}{a}}\,\mathbf {a}$

(a number times a vector). Boris Tsirelson 16:12, 30 March 2010 (UTC)

[unindent]

I used initially a = (a_x, a_y, a_z) but Peter Schmitt didn't like it together with r = (x, y, z). How about r = (r_x, r_y, r_z)?

Now I see the problem... On one hand it is too expensive to reserve 3 more letters to each vector; and on the other hand, r=(x,y,z) is rather traditional and natural. As for me, we could make an exception for r. But if Peter disagrees... Well, maybe write initially r = (r_x, r_y, r_z) but afterward pass to r=(x,y,z), after a word of apology?

I will change the division (although it cannot hurt here because the product commutes).--Paul Wormer 16:50, 30 March 2010 (UTC)

Yes, it is only a matter of style (and tastes differ). Boris Tsirelson 17:27, 30 March 2010 (UTC)

Notation is a matter of style and taste, and it is often difficult to find a good and consistent choice. I only noticed the discrepancy between (a_x,a_y,a_z) with indices and (x,y,z), (a,b,c) without. I made comment but did not think about a "better" suggestion.

What about P=(x,y,z) (avoiding two x's: X,x) and n=(a,b,c) (it is a normal vector) and (a_0,b_0,c_0) (or similar) for the normed vector?

On Paul's page I suggested not to insert his part into yours. My reason: You wrote a non-technical introduction and I think it would be nice to keep it that way. His page could serve as a starting point for (elementary) analytic geometry in 3-space (and be properly linked, of course).

On the other hand, plane (geometry) could profit from drawings that illustrate the four ways to define a plane. (It were the current pictures that made me see the page. The crumpled picture does not fit here, and the drawing could be done better.)

What do you think? (It will not be lack of interest if I do not react for some time. I shall be offline for some days.) --Peter Schmitt 23:56, 30 March 2010 (UTC)

The crumpled picture is no more there.

Drawings would be good, of course, as I noted on the talk page there.

My "non-technical introduction" contains already three parts of different accessibility. It could contain more parts, of different accessibility/technicality. Or that could be another article. Both options are OK with me.

P=(x,y,z), and n=(a,b,c), and (a_0,b_0,c_0) for the normed vector, would be nice (if I do not miss some problem with them). Boris Tsirelson 05:39, 31 March 2010 (UTC)

[unindent]

I fixed the notation in the text (but not yet in the drawing) to be as close as possible to your wishes. In the drawing the point X will be P and vector a will be vector d. I kept vector r for position of P, but don't insist on it. With regard to notation I'm completely flexible. --Paul Wormer 07:51, 31 March 2010 (UTC)

Nice. I'd say, this text explains the equivalence between the "Definition via right angles (orthogonality)" and the "Definition via Cartesian coordinates" in the framework (of points, vectors and inner products) that is a less formal version of the "Modern approach". Boris Tsirelson 09:14, 31 March 2010 (UTC)

Yet another piece

Boris I wrote this new section. Could you comment on it? Thanks.--Paul Wormer 14:09, 31 March 2010 (UTC)

You are energetic! Well, you could mention near the start that these are three points not on a line. Also I note that this time you do not explain any equivalence but just formulate something in vector terms. I'd say it is about "a plane as a 2-dim affine subspace". You could also show that a point belongs to the plane if and only if it is an affine combination of A,B,C; that is, a linear combination with the sum of coefficients equal to 1. It is also related to barycentric coordinates. (Strangely it is written there that "it may be convenient to take $x_{0}+\cdots +x_{n}=1$ while I believe it is obligatory.) Boris Tsirelson 14:57, 31 March 2010 (UTC)

I'm not energetic, I'm retired and have CZ as one of my most time-consuming hobbies.

I added barycentric coordinates and think that the section is now ready to be inserted into plane (geometry), but maybe you have further suggestions? --Paul Wormer 08:46, 1 April 2010 (UTC)

Only that the first picture should be updated: the point P, not X. And the origin O is indeed outside the plane on the picture, but in principle it can also belong to the plane. That is, the theory holds for any plane, be it through the origin or not. Boris Tsirelson 09:46, 1 April 2010 (UTC)

Boris, clear the cache of your browser. It is P for some time already. I will change the wording about position of O.--Paul Wormer 10:23, 1 April 2010 (UTC)

Yes, now I see, it is P. Nice. Maybe I'll add to "my" sections some comments about "yours". Boris Tsirelson 11:19, 1 April 2010 (UTC)

Line

Encouraged with the success of "Plane" I clone it to "Line". Please look. Now it is probably your move... Boris Tsirelson 11:06, 2 April 2010 (UTC)

Editorship

It looks like Roger already made you a mathematics editor on May 3. David E. Volk 15:04, 5 May 2010 (UTC)

Indeed. Thanks anyway. Boris Tsirelson 16:43, 5 May 2010 (UTC)

Neighbourhood

Boris, thank you for nominating Neighbourhood (topology). I have reread it and made four minor copyedits. (If you agree, you have to update the version.) Perhaps a native speaker (for correct English) and a non-mathematician (for readability) should check it, too? --Peter Schmitt 09:43, 6 May 2010 (UTC)

Yes, I'll update the version. However, do you really prefer the red link to "Euclidean vector space" to a blue link "Euclidean space"?

About English and readability, I have no objections if it will happen, and on the other hand, my idea of approval is that it is not like journal publication (irreversible); it is just a stage. A reader can already not worry whether it is true or not. (Remaining English imperfections are not misleading, I believe.) And authors can (and should) work further on the draft as long as they can and wish. Boris Tsirelson 10:53, 6 May 2010 (UTC)

What do you mean by Euclidean vector space? A vector space with positive definite inner product? --Paul Wormer 11:03, 6 May 2010 (UTC)

Probably he does (sorry for answering instead); but anyway, it is all the same when defining balls and neighbourhoods. We usually do not bother do make such distinctions unless they really matter (which happens for example when considering the group of authomorphisis, that is, symmetries). Boris Tsirelson 11:13, 6 May 2010 (UTC)

I was not sure what to use to "explain" R^d. I first inserted "space of d-dimensional real vectors" (linking to vector space), then changed it to Euclidean vector space (yes, real inner product space, Euclidean as opposed to Hermitian), but Euclidean space is probably better, though actually a more abstract concept than a space of vectors. These are points where a mathematics article would profit from the opinion of non-mathematicians reading it -- but this probably will not happen, so we cannot wait for it. (I mentioned language only because we all -- you, Paul, Dmitrii, and I -- are non-natives. --Peter Schmitt 11:52, 6 May 2010 (UTC)

I have changed the link to "Euclidean space". --Peter Schmitt 12:34, 6 May 2010 (UTC)

Well, the version is updated.

A non-mathematician will hardly read these "${\mathcal {N}}(x)=\left\{U\mid (\exists n\in \mathbb {N} )B(x,n)\subset U\subset \mathbb {R} ^{d}\right\}$". But again, improvements (also of English) are welcome at all times, be it before of after approval; why make a peak of activity at the time of approval? (I know it is a tradition to do so, but I am not sure it is a good tradition.) Boris Tsirelson 13:13, 6 May 2010 (UTC)

For a non-mathematician (like myself) the notation is not so much the problem, but the highly abstract concepts. Whenever I come across concepts as "neighborhood", "open" and "closed" I sneakingly flee into metric space and imagine a ball of well-defined radius. --Paul Wormer 13:24, 6 May 2010 (UTC)

Also I deal mostly with metric spaces. However, a closed set may well be, say, the Cantor set or another fractal; not at all a closed "ball of well-defined radius". And the metric need not be Euclidean; thus a ball may well be what is usually called a cube, an octahedron, etc. Boris Tsirelson 13:49, 6 May 2010 (UTC)

I would say that most mathematicians use 2- or 3-dimensional objects to visualize mathematical concepts.

As to the formulas: I have tried to avoid them as far as possible for most of the article, but the examples, in particular the second one, would not make sense without them.

As to "peak of activity": It is always useful to reread something after some time has gone by. (And what would be a better opportunity?) The distance helps to see what one might have overlooked before. (A real peak according to tradition would be if suddenly a dozen of fellow citizens chimed in ...) --Peter Schmitt 14:08, 6 May 2010 (UTC)

I'd like such a "real peak according to tradition", but after approval, in order to move to version 2 not in fuss and bustle. Boris Tsirelson 14:20, 6 May 2010 (UTC)

Neighborhood (topology)

Congratulations Boris! Look forward to many many more. D. Matt Innis 01:24, 7 May 2010 (UTC)

Thank you! Yes, definitely, (many) more will follow soon. Boris Tsirelson 05:06, 7 May 2010 (UTC)

Cryptography

I note that you work in probability theory. Could you comment on Cryptography#Random_numbers or random number generator? That is a rather important topic in cryptographic work and I suspect our current text lacks theoretical rigour. Sandy Harris 02:25, 9 May 2010 (UTC)

No, sorry, I have nothing to add. I really work in probability theory, where (true) randomness is just postulated. I have only a slight idea of cryptography. Your texts cover, by far, everything that I could say. Boris Tsirelson 05:25, 9 May 2010 (UTC)

Article Approved

Congratulations, Boris, I have just Approved [1]! Hayford Peirce 21:43, 11 May 2010 (UTC)

Thank you! I feel I am a serial approver :-) Boris Tsirelson 04:46, 12 May 2010 (UTC)

Geometric sequence

Approved! Make me work harder ;-) D. Matt Innis 22:03, 14 May 2010 (UTC)

Thanks! Yes, as much as I can :-) Boris Tsirelson 17:42, 15 May 2010 (UTC)

Covariance

Another feather for your cap! D. Matt Innis 03:04, 19 May 2010 (UTC)

Thank you. I'll try more, but our reservoir is nearly depleted :-( Boris Tsirelson 04:45, 19 May 2010 (UTC)