# User talk:Tsirel

Welcome!

Hello, Tsirel, 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 ask your question and then place {{helpme}} after the question on your talk page. Again, welcome!  – Oleg Alexandrov (talk) 03:50, 21 March 2007 (UTC)

## Re: Large deviations ...

I replied on my talk page. Oleg Alexandrov (talk) 14:50, 23 March 2007 (UTC)

## Thanks

I forgot to say, thanks for the new Large deviations of Gaussian random functions. If at some point you want to get to know other people who contribute to math articles, our main discussion forum is Wikipedia talk:WikiProject Mathematics. Cheers, Oleg Alexandrov (talk) 03:43, 24 March 2007 (UTC)

## Subpages

I have a small note. You can also use subpages as sandboxes, if, for example, you want to work on many articles at the same time. For example, User:Tsirel/Sandbox, User:Tsirel/Article 1, User:Tsirel/Probability space, etc. Cheers, Oleg Alexandrov (talk) 11:14, 29 March 2007 (UTC)

Thanks, I do. It helps. Boris Tsirelson 15:08, 29 March 2007 (UTC)

## Question on the Wikipedia:WikiProject Physics talk page.

May I ask you to have a look at Wikipedia talk:WikiProject Physics#(Superquantum) non-locality and perhaps comment? --Pjacobi 17:36, 7 May 2007 (UTC)

OK, I did. Boris Tsirelson 12:30, 8 May 2007 (UTC)

## Typo redirect Schroeder-Bernstein theorem for measurable speces

Hello, this is a message from an automated bot. A tag has been placed on Schroeder-Bernstein theorem for measurable speces, by another Wikipedia user, requesting that it be speedily deleted from Wikipedia. The tag claims that it should be speedily deleted because Schroeder-Bernstein theorem for measurable speces is a redirect page resulting from an implausible typo (CSD R3).

To contest the tagging and request that administrators wait before possibly deleting Schroeder-Bernstein theorem for measurable speces, please affix the template {{hangon}} to the page, and put a note on its talk page. If the article has already been deleted, see the advice and instructions at WP:WMD. Feel free to contact the bot operator if you have any questions about this or any problems with this bot, bearing in mind that this bot is only informing you of the nomination for speedy deletion; it does not perform any nominations or deletions itself. To see the user who deleted the page, click here CSDWarnBot (talk) 19:10, 23 August 2008 (UTC)

No, it was myself, who wished it to be deleted.Boris Tsirelson (talk) 19:16, 23 August 2008 (UTC)

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## Re: list of probability topics

I replied on my talk page. Oleg Alexandrov (talk) 17:06, 2 December 2008 (UTC)

## Schramm–Loewner evolution maths rating

I have promoted the article to "Mid" based on your comment at Talk:Schramm–Loewner evolution. siℓℓy rabbit (talk) 20:25, 11 December 2008 (UTC)

Nice; thank you. Boris Tsirelson (talk) 21:57, 11 December 2008 (UTC)

## E(X^2)-E(X)^2

Privet Boris, It's mentioned in our preprint on arxiv. Katzmik (talk) 13:10, 25 December 2008 (UTC)

Archived: User:Tsirel/MHP#Monty Hall — 2009 Feb.

## Potential new section for Monty Hall problem

Archived: User:Tsirel/MHP#Monty Hall — 2009 Feb.

## Is this a valid unconditional proof of the Monty Hall Problem?

Archived: User:Tsirel/MHP#Monty Hall — 2009 Feb.

## Just One More Thing...

Archived: User:Tsirel/MHP#Monty Hall — 2009 Feb.

## Stability

Hello. I noticed you commented once on the Stability (probability). We have also the article on stable distributions. A merger has just been proposed, see the talk page. Your input would be welcome. ptrf (talk) 15:26, 20 February 2009 (UTC)

Yes, I did. Boris Tsirelson (talk) 18:45, 20 February 2009 (UTC)

Good work with that trial. Incidentally, it'd be neat to know how you thought the trial went. I can't see any major problems myself, but obviously, I know very little about your area of expertise, so it'd be great if you could just say "It all went to plan" or "I encountered a few problems but...". A minor, trivial thing, but you'd be surprised how many complaints only arise 6 months down the line when records have been lost ;) Anyhow, keep up the good work! - Jarry1250 (t, c) 17:30, 24 March 2009 (UTC)

It is very much appreciated. If it's OK with you I think I would prefer to issue another 7 day trial, rather than jump straight to approved. Would that be fine? - Jarry1250 (t, c) 19:44, 24 March 2009 (UTC)
No problem. Thank you for the compliment. The same to you (I mean, "keep up the good work"). Hopefully, my poor English does not disturb you too much :) Boris Tsirelson (talk) 19:52, 24 March 2009 (UTC)
Quite frankly, there are English people who speak much worse English than you (some of the crap on new page patrol!). Anyhow, you should find a trial materialising on that BRFA in the next 5 minutes. - Jarry1250 (t, c) 19:59, 24 March 2009 (UTC)

## WP:RFBOT

Your recent bot approvals request has been approved. Please see the request page for details. When the bot flag is set it will show up in this log. All the best, – Quadell (talk) 12:44, 8 April 2009 (UTC)

Nice; thank you. Boris Tsirelson (talk) 17:01, 8 April 2009 (UTC)

## Biography

Hello, I am interested to add your birth data in the He-wiki. david1955 (talk) 09:19, 4 April 2009 (UTC)

May 4, 1950; Leningrad. Boris Tsirelson (talk) 17:34, 4 April 2009 (UTC)
Thank you david1955 (talk) 18:32, 4 April 2009 (UTC)

Hi Tsirel I wanted to let you know that Wikipedia:Bots/Requests for approval/CataBotTsirel has been approved. Please visit the above link for more information. Thanks! BAGBot (talk) 12:45, 8 April 2009 (UTC)

Nice; thank you. Boris Tsirelson (talk) 16:49, 8 April 2009 (UTC)

In response to your comments in an AfD discussion on the "infamous principle of indifference", I've written some comments here. What do you think? (You can put your comments below mine on that page.) Michael Hardy (talk) 21:47, 9 May 2009 (UTC)

I did. Boris Tsirelson (talk) 06:58, 10 May 2009 (UTC)

## Disinformation from Israeli intelligence

... the underlying measurable space of any standard probability space is Radon (if its topology is chosen appropriately).

I'd say you were ignorant, but I'm not going to insult your intelligence. This type of thing does not help people who are trying to learn math on Wikipedia. Deepmath (talk) 05:53, 26 July 2009 (UTC)

1. Sorry, I know I hardly take hints and understand humor. Could you please be more explicit? What exactly is bad in that phrase? Is it wrong? Or rather true but unwanted in Wikipedia? Why?

2. Look closely at the history of that article. I did not add the phrase. Someone else wrote its first part, which was incorrect, and I have corrected it adding the second part.

3. Your word "disinformation" astonishes me. What is the reason for such crude word here? Is it a semi-personal attack (on the Israeli intelligence)? Boris Tsirelson (talk) 06:10, 26 July 2009 (UTC)

rABBI. Deepmath (talk) 06:16, 26 July 2009 (UTC)
It wouldn't be so bad if you hadn't also trashed the history of that article. Look at the history of the talk page, too. Deepmath (talk) 06:25, 26 July 2009 (UTC)
Now I am utterly puzzled. What do you mean? What else are my crimes? Boris Tsirelson (talk) 06:32, 26 July 2009 (UTC)

## Yehuda Leib Tsirelson

I discovered your great uncle after reading a responsum that cited a ר"י צירלזאהן. a (שו"ת חלקת יעקב חו"מ סיםן ל"ד) After cleaning up his page a little I clicked on some of the links and came upon you. Fascinating.--Danthecan (talk) 04:26, 25 August 2009 (UTC)

Nice. I see, you have some knowledge about the Rabbi. Boris Tsirelson (talk) 06:33, 25 August 2009 (UTC)

## Ending the Monty Hall problem Morgan Emphasis

Archived: User:Tsirel/MHP#Monty Hall — 2009 Dec.

## Proposed deletion of Catalog of articles in probability theory

The article Catalog of articles in probability theory has been proposed for deletion because of the following concern:

Non standard article, with non standard editing rules and techniques. Seems to fundamentally break several core policies. It is also self/wikipedia referential in the lead.

While all contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the {{dated prod}} notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the article to address the issues raised. Removing {{dated prod}} will stop the Proposed Deletion process, but other deletion processes exist. The Speedy Deletion process can result in deletion without discussion, and Articles for Deletion allows discussion to reach consensus for deletion. 22:13, 5 December 2009 (UTC)

## Articles for deletion nomination of Catalog of articles in probability theory

I have nominated Catalog of articles in probability theory, an article that you created, for deletion. I do not think that this article satisfies Wikipedia's criteria for inclusion, and have explained why at Wikipedia:Articles for deletion/Catalog of articles in probability theory. Your opinions on the matter are welcome at that same discussion page; also, you are welcome to edit the article to address these concerns. Thank you for your time.

## A deletion discussion

Polynomially reflexive space has been proposed for deletion. I suppose you are a pretty good person to ask about the notability of this topic. (The reason for proposal was lack of any references; I don't like this way of proceeding. There is now a reference. I would still like to know whether this is a good topic for the encyclopedia.) Charles Matthews (talk) 21:39, 15 February 2010 (UTC)

OK, I'll think a bit. Boris Tsirelson (talk) 05:19, 16 February 2010 (UTC)
I believe that the article should be (a) expanded and made less technical, and (b) merged to something broader.
I just did (a), to some extent.
About (b): maybe, into Polynomials on vector spaces? For now it is purely algebraic. However, the good Vector space article contains analytic sections; also "Polynomials on vector spaces" could do. Boris Tsirelson (talk) 14:02, 16 February 2010 (UTC)

## Probability theory,absolutely continuous

Hi, could we discuss your undoing my change to the article Probability theory? My opinion still stands, I did not understand your comment. Here is, again, my reasoning:

"The existence of a derivative almost everywhere is a properity of absolutely continuous functions, not its definition." Quiet photon (talk) 09:16, 3 March 2010 (UTC)

Well, if you insist, I shall not object to your change. On the other hand, the phrase "its derivative exists and integrating the derivative gives us the cdf back again" is one of several equivalent definitions of absolute continuity. True, it is not the definition given in "absolutely continuous". However, this definition is more relevant to "Probability theory". This is why I did not see anything wrong with the old phrase in the article. Boris Tsirelson (talk) 09:58, 3 March 2010 (UTC)
Thank you for your reply. I did not know these were equivalent definitions. Do you have any kind of reference for that, or can explain? I am somewhat new to the field of probability theory so I learn as I go, and point out difficulties I see on the way. Not knowing much about absolutely continuous functions bar the basic definition and basic properities the formulation in the article seems confusing to me, and the mentioning that the property only holds almost everywhere lacks completely. My edit was very rudementary in the hope, that somebody with experience in the field would take the time to improve this forumlation. Quiet photon (talk) 10:37, 3 March 2010 (UTC)
Maybe something should be done; I'll think. However, "Probability theory" is not the best place for technical details. We should look at such articles as Continuous probability distribution. Boris Tsirelson (talk) 11:24, 3 March 2010 (UTC)
Really, everything is already written in Absolute continuity. That is a rather good article, but maybe it can be made still better. Boris Tsirelson (talk) 20:15, 3 March 2010 (UTC)
I did, to some extent. Boris Tsirelson (talk) 21:50, 3 March 2010 (UTC)
Thank you for your great work, this article really helps now. In Probability theory one could still add that the derivative only exists almost everywhere. What do you think? Quiet photon (talk) 11:16, 5 March 2010 (UTC)
I am glad you like it. You are welcome to improve anything. But, once again, "Probability theory" is probably not a good place for technicalities; it should be a wide-scope overview. You may say that anyway it must be correct. Well, maybe a reasonable compromise exists. When needed, we put links to more special articles. Boris Tsirelson (talk) 12:40, 5 March 2010 (UTC)
Also, do you think an article about the relation of probability measures on $(\R,B)$, cumulative distribution functions and probability density functions could or should be written? Quiet photon (talk) 11:25, 5 March 2010 (UTC)
We already have Probability distribution; isn't it the right place for all that? Probably for now it does not satisfy you. It attracts, naturally, many non-mathematicians interested in applications rather than theory. But anyway, you can participate, improving it. Otherwise, I do not know, which title will you give to the new article. And note that it is not a good idea, to create a "parallel" article conforming to your taste; probably it will be called "content fork" and deleted (or merged to the existing article). Boris Tsirelson (talk) 12:40, 5 March 2010 (UTC)

## Codomain of a random variable: observation space?

The technical term "observation space" for codomain of a random variable was used by User:Winterfors on 14 Feb 2008 in Bayesian experimental design, then by User:3mta3 on 7 May 2009 in Probability distribution, by an anon on 26 Aug 2009 in Random variable, and by User:Stpasha on 27 Nov 2009 in Probability density function. Now User:WestwoodMatt and a `random passerby' are unhappy with it, see Talk:Probability distribution#Observation Space.

As far as I understand, the term is used mostly by non-mathematicians, and its use in such articles as random variable is a bit off-label. On the other hand, it could be rather convenient here. Maybe we should mention it, but use sparingly.

However, the very idea to define a random variable as a measurable map from a probability space to an arbitrary measurable space could be a WP:POV. Maybe some sources use such terminology, but not the mainstream. Checking four books, "Probability: theory and examples" by Richard Durrett, "Probability with martingales" by David Williams, "Theory of probability and random processes" by Leonid Koralov and Yakov Sinai, and "Measure theory and probability theory" by Krishna Athreya and Soumendra Lahiri, I observe in all the four cases that a random variable is a measurable map from a probability space to the real line. More general objects are called random vectors, random functions and, most generally, random elements (of a given measurable space).

Any opinions, please? Boris Tsirelson (talk) 16:36, 27 March 2010 (UTC)

My immediate reaction, then, is to do one of two things:
a) Find a way of rigorously defining "observation space" with the caveat that it is generally used as an imprecise concept;
b) Define "random variable" without using "observation space", and also indicate that it can be defined in two ways:
i) The "usual" way, that is, as a map to the real line;
ii) In a more general way that is rooted in measure space concepts, in which the image of the random variable is a more general measure space - and providing a link to the explanatory definition that specifies that a real line is an instance of a measure space, thus showing that the more specific is an instance of the more general. I see that's sort of already been done, but I believe it could be made more rigorous and precise.--WestwoodMatt (talk) 17:07, 27 March 2010 (UTC)
In the article on Bayesian experimental design, I used the term "observation space" in the sense "the set of all possible observations", which if you define the observation as a (conditional) random variable will be its codomain. In the context of Bayesian experimental design the alternative term "data space" is often used, but I prefer "observation space" since "data" is more ambiguous than "observation".
I think the term is appropriate in the article on Bayesian experimental design, but not in the articles Probability distribution, Random variable or Probability density function since these describe more general cases not necessarily relating to the probability of making a particluar observation.
-- Winterfors (talk) 18:31, 28 March 2010 (UTC)

## Per Enflo

Dear Professor Tsirelson,

Would you look at the recent edits at Per Enflo, many by a user named "EdStat" (whose has recently returned from a suspension for sock-puppetry). Many of EdStats comments use phrases from the discussion about the article on an applied statistician, Shlomo Sawilowsky. This editor has a history of attacking other editors as WikiWarriors and charging them (and perhaps me) with anti-semitism.

Also, in general, the article on Per Enflo could use review from a functional analyst, which I am not.

This is a waste of your time, of course, but you have identified yourself and made so many pro bono contributions, that I thought you could be helpful. Perhaps you could suggest another editor to help with the Per Enflo article.

Sincerely,Kiefer.Wolfowitz (talk) 14:26, 13 April 2010 (UTC)

Unfortunately, no, I am not a useful person for this case. First, I never participated in biographies (well, almost never; I did a bit for Chatterjee and some others, just because all mathematicians were asked to help urgently to save them from deletion); I have no idea what is usual and what is not when writing bio; and I am hardly interested in these things. Surely Per Enflo is quite notable; but I see that no one doubts it. Second, the first years of my academic career I dealt with Banach spaces indeed, but it was about 40 years ago, and since then I never returned to this topic. About suggesting another editor, you'd better write a note on the talk page of Wikiproject Mathematics. Sorry. Boris Tsirelson (talk) 15:13, 13 April 2010 (UTC)
This is perfectly understandable. You accomplished enough in your initial contributions that you have left BS space theorists wanting more! Cheers, Kiefer.Wolfowitz (talk) 17:21, 13 April 2010 (UTC)

## Peaceful Coexistence of the Monty Hall Problem Solutions

Hello Boris,

I have offered two versions of a 2-row table in support of the 'you always get the opposite if you switch' solution to the MHP.

Would you be kind enough to read this section only of the talk page, and offer your comments/criticisms of the table?

Thank you. Glkanter (talk) 10:57, 13 June 2010 (UTC)

No, sorry. To my amusement, a number of people like to spend (a large portion of) their life to MHP. What could I say to them? I do not belong to the club. Boris Tsirelson (talk) 14:50, 13 June 2010 (UTC)
I am glad I bring you amusement! I respect your decision, of course. But in answer to your question, you needn't say anything, beyond your criticism of the table in regards to probability.
Thanks. Glkanter (talk) 15:04, 13 June 2010 (UTC)
Aren't you at least a little bit curious? You know all about the professional controversies. I claim this 2 row table in support of 'you always get the opposite' ends them. Period. Forget the Wikipedia part. Don't you have a scientific curiosity? It's part of your curriculum, isn't it? Glkanter (talk) 06:36, 14 June 2010 (UTC)

## You are now a Reviewer

Hello. Your account has been granted the "reviewer" userright, allowing you to review other users' edits on certain flagged pages. Pending changes, also known as flagged protection, is currently undergoing a two-month trial scheduled to end 15 August 2010.

Reviewers can review edits made by users who are not autoconfirmed to articles placed under pending changes. Pending changes is applied to only a small number of articles, similarly to how semi-protection is applied but in a more controlled way for the trial. The list of articles with pending changes awaiting review is located at Special:OldReviewedPages.

When reviewing, edits should be accepted if they are not obvious vandalism or BLP violations, and not clearly problematic in light of the reason given for protection (see Wikipedia:Reviewing process). More detailed documentation and guidelines can be found here.

If you do not want this userright, you may ask any administrator to remove it for you at any time. Courcelles (talk) 01:29, 18 June 2010 (UTC)

I see, thanks. I'll try it. Boris Tsirelson (talk) 07:16, 18 June 2010 (UTC)

## Distortion problem

Hi Boris, Any chance you would be willing to have a look at the recent addition to Hilbert space on the so-called "distortion problem" (diff)? As it is presently written, the paragraph is clearly out of place. In fact, I'm skeptical that the distortion problem is high-profile enough to be mentioned in the main article on Hilbert spaces, but I'll defer to your judgment. Do you have any sage advice on what to do? Best, Sławomir Biały (talk) 19:24, 23 June 2010 (UTC)

Why skeptical? It is a bit advanced, yes, but it takes several lines of the long article, and it deserves its place, I believe. It is the tip of an iceberg, in fact. And, why "clearly out of place"? It is related to a large stream of research in Banach spaces theory. Boris Tsirelson (talk) 07:33, 24 June 2010 (UTC)
Thanks! I'm glad that you hold a different opinion. Allow me to clarify my own. I'm not opposed to including research-level content in the article, but it needs to be written in a way that readers can understand and appreciate its significance. Currently, the paragraph builds absolutely no context for the result that it quotes, and so seems "out of place" as it is currently written. Regarding the large stream of research that this is clearly a part of, if we could somehow emphasize that aspect of things, I think it would be an improvement. Indeed, this is part of the reason that I thought you should be consulted on the matter. But I'm out of my element when it comes to such things: I don't really get anything out of the articles cited. Sławomir Biały (talk) 12:32, 24 June 2010 (UTC)
I see. Then maybe move that staff into a new stub article and let it grow there in an indefinite future. Boris Tsirelson (talk) 16:35, 24 June 2010 (UTC)

## Svante Janson

Hi Boris. I saw that you'd cited a paper by Svante Janson, for whom an article was created this week. I've tried to add secondary references. Perhaps you could help with a photo, either your own or from Allan Gut, etc.? (It's possible the page could be nominated for DYK, but this would have to be done quickly.) Of course, your comments and corrections would be valuable. Best regards, Kiefer.Wolfowitz (talk) 16:33, 2 July 2010 (UTC)

No, sorry, I do not know him personally. But if you just want a photo, probably you could send an email to Janson. Boris Tsirelson (talk) 18:42, 3 July 2010 (UTC)

## Reference

You are probably better placed than me to find a reference for this. Stephen B Streater (talk) 07:28, 29 July 2010 (UTC)

I did; please look. Boris Tsirelson (talk) 08:48, 29 July 2010 (UTC)
Thanks. Stephen B Streater (talk) 19:49, 29 July 2010 (UTC)

## 170,000 words on a single talk page

I mean Talk:Monty Hall problem, archives 16-21. These 170,000 words were added during three months. Did you know?.. I wonder, is it a record?

In particular, the word "door" occurs 1888 times; "solution" 852 times; "probability" 789; "problem" 780; "conditional" 507; "2/3" 230.

Not sure whether this is WP record, but it is probably the most contested/debated math article. However imho it is likely to assume that various hot topic in the of social sciences/economics/philosophy/religion/politics/climate sciences. It was reported in the press that the German WP created a book length discussion page for some TV tower (mainly arguments about its exact name and categorization (view tower versus tv/broadcast tower). I think as far as neverending (and mostly unproductive) discussions are concerned there might be a large number of articles competing for the top.
regards--Kmhkmh (talk) 14:27, 8 September 2010 (UTC)
P.S.: We probably could ask somebody with toolserver access to run a query for the largest discussion pages or firectly file a request [1].--Kmhkmh (talk) 16:55, 8 September 2010 (UTC)
Great stuff! You may want to include results from the Arguments page and the Mediation page for the whole picture. Glkanter (talk) 15:22, 8 September 2010 (UTC)

## Sobolev space

Hi Boris, I visited recently the entry on Sobolev spaces which I did not liked very much for the choice of developing the theory on the unit circle (?!?) and on the ball (?!?). There is a new user that is doing a good job, motivating his choices: I wrote you since I saw that you criticized the contents of the entry in its talk page, and the new structure seems to be an improvement (or at least a standard treatment :D). Daniele.tampieri (talk) 13:40, 12 April 2011 (UTC)

Maybe. My understanding of this matter is so-so. I've visited it as a reader (rather than a potential contributor or critic). I did not found the needed detail, and wrote a remark. I have no opinion about the choice of developing the theory on the unit circle, is it good or bad. And now I do not need that space. --Boris Tsirelson (talk) 20:12, 12 April 2011 (UTC)

## Another mathematician for your collection

User:DoronZeilberger is Doron Zeilberger.  :-) Sławomir Biały (talk) 01:01, 5 January 2012 (UTC)

I see, thanks. Boris Tsirelson (talk) 06:29, 5 January 2012 (UTC)

## Greetings

Hi Boris, I saw your name within the editors of the new Springer Ecyclopaedia: well done, and good work! Daniele.tampieri (talk) 21:12, 8 January 2012 (UTC)

Thank you. Maybe that is the right wiki for me. Well, the name is not itself a good work, but hopefully my articles will be (and two already are?) useful for mathematicians. Others will find them too hard, alas. Boris Tsirelson (talk) 21:40, 8 January 2012 (UTC)

Hi. The article 'Mathematics' has a dead link that could not be repaired automatically. Can you help fix it?

• You added this in June 2010.
• The bot tested this link on 29 March, 31 March, 2 April, 10 April, 17 April and today, but it never worked.
• The bot checked The Wayback Machine and WebCite but couldn't find a suitable replacement.

This link is marked with {{Dead link}} in the article. Please take a look at that article and fix what you can. Thank you!

PS- you can opt-out of these notifications by adding {{Bots |deny=BlevintronBot}} to your user page or user talk page. BlevintronBot (talk) 15:44, 21 April 2012 (UTC)

Please disregard this message. My bot made a mistake in this case---the reference is fine. Sorry about the trouble. Blevintron (talk) 15:49, 21 April 2012 (UTC)
OK, I see what happens; no problem. Boris Tsirelson (talk) 20:34, 21 April 2012 (UTC)

## Bell and quaternions

Archived: User:Tsirel/Bell#Bell and quaternions.

## Formalized libraries coverage of probability theory

Thank you, Professor Tsirelson!

Would you happen to know the state of coverage of probability theory in the different proof assistants? Why is the Law of Large Numbers and Central Limit Theorem still blank in the top 100 list? Is there some major barrier to formalizing them? Yaniv256 (talk) 23:49, 23 July 2012 (UTC)

No, I do not expect any barrier. Probably, just because these people are less interested in measure and probability. But I saw some measure and probability on "Isabella". Some time ago I had the idea to make on it the Borel isomorphism between arbitrary uncountable Polish spaces, or something in this direction; but I did not. Boris Tsirelson (talk) 05:45, 24 July 2012 (UTC)

## External Links to formalized math

On another topic, I have been accused of breaking WP:ELNO points 1 and 13 by inserting the following link in the sigma-field external link section:

I worked quite a bit to get that piece of code to work and I really thought it could make a contribution. Would you care to state an opinion in the matter? Yaniv256 (talk) 01:24, 24 July 2012 (UTC)

About "point 1", I fail to understand the objection. Clearly, it is a "unique resource beyond what the article would contain if it became a featured article". But "point 13" is indeed a problem: "only indirectly related". Maybe that link would look better in an article devoted to Mizar. Boris Tsirelson (talk) 05:55, 24 July 2012 (UTC)

Hi Boris,

Sorry about the mess that is Join (sigma algebra), I will try to come back and fix it in the next few weeks or month or so. I have an unrelated question, about a topic in which I think you are a true expert. To be clear, let me be very simplistic about it, so as to be clear: I was thinking about taking the limit $N\to\infty$ of the sum $\mu_N(x) = \frac{1}{2^N}\sum_{k=0}^{2^N-1} \delta\left(x-\frac{2k+1}{2^{N+1}}\right)$ where $\delta$ is the traditional Dirac delta. In 'plain english', this puts a tiny little mass of measure at every dyadic rational. (I don't know if you like 'plain english' or the more precise formulas better). From what I can tell, this seems to be a valid measure on reals; it assigns a measure of exactly 1 on the unit interval. I convinced myself that, in the limit, this assigns exactly the same value to an interval (a,b) as the Lebesgue measure, that is, $\int_a^b\mu_\infty = b-a$ for $0\le a \le b \le 1$. My question to you: does this measure have a name? Have you seen it written up somewhere? Some formal discussion? Perhaps this is some standard textbook example; I really don't know.

Yes, each $\mu_N$ is a valid measure on reals. In the limit... well, now the question is, what kind of limit? If you mean weak convergence, then the limit is Lebesgue measure (and so, yes, this measure has a name! :-) ). But if you mean convergence in norm (variation) then this sequence does not converge (and in fact is not a Cauchy sequence, as you can easily check).
Indeed a sequence of discrete measures can converge weakly (but not in norm) to a continuous measure. For a continuous function the integrals converge, for discontinuous --- not (try Dirichlet function).
Here is an informal counterpart: a sequence of polygonal functions with derivative $\pm1$ (except for the edges) can converge to the zero function (uniform convergence is meant); but their total variations remain 1 and do not converge to 0. Does it mean that we may introduce a new kind of function, with all values 0 but variation 1? Well, we cannot do it within the pre-existent class of functions, but if needed we can invent another class of object (as "we" did when adapting the Dirac delta-function; note also the so-called rough path).
Boris Tsirelson (talk) 20:11, 13 August 2012 (UTC)

I stumbled upon it in a considerably more abstract setting at first, while considering measures on countably infinite Cartesian products, and weak convergence, and what-not. One certainly doesn't have to plonk down those delta's at exactly the locations given above; there's an (uncountably) infinite number of other similar measures that are dense in the reals, and give the same Lebesgue measure results. Really, the proper definition I had in mind is in terms of sigma algebras not delta functions, but, to keep this posting short, I resorted to the ugly notation above; I hope you see through it. And so there are a few other abstract tricks and questions that arise in the above. But before I got to far, I figured that this must somehow be 'well-known', and that you would be the one to know it. linas (talk) 17:44, 13 August 2012 (UTC)

On a related note: the construction that lead me to the above, also made me wonder about something else: so, for the sigma-algebra, the word 'sigma' is often taken as a synonym for "countably infinite". Have you ever seen or heard of a formulation of some crazy measure-theory like thing, where the sigma is replaced by "uncountably infinite"? That is, most/all the axioms of measure theory are kept, such as additivity or sigma-additivity, or promoted to an axiom about 'uncountable'-additivity, as appropriate? I've sketched out for myself a simple framework where such questions are clear, well-defined, and seem to make sense, but, before I got too far inventing crazy shit, wanted to make sure I wasn't re-inventing something... linas (talk) 17:56, 13 August 2012 (UTC)

This matter reminds me of k-complete Boolean algebras and their morphisms. Could be of some interest there, but not in probability theory, thus, beyond my expertise. Boris Tsirelson (talk) 20:19, 13 August 2012 (UTC)

## Invitation to comment at Monty Hall problem RfC

You are invited to comment on the following RfC:

Talk:Monty Hall problem#Conditional or Simple solutions for the Monty Hall problem?

--Guy Macon (talk) 22:14, 8 September 2012 (UTC)

Yes I did. Boris Tsirelson (talk) 07:14, 9 September 2012 (UTC)

## MHP

Archived: User:Tsirel/MHP#MHP.

## Other distributions for which uncorrelated implies independent?

Thanks for setting me straight on the n=1 binomial. Besides the Gaussian, are there any other distributions with the property that uncorrelated implies independent? Duoduoduo (talk) 17:17, 15 February 2013 (UTC)

First of all, the Gaussian case is not of the same kind as the two-valued case.
In the two-valued case, the two marginal (one-dim) distributions are restricted (required to be two-valued) but the joint (two-dim) distribution remains arbitrary (as far as it conforms to the given marginals).
In the Gaussian case, the joint distribution is restricted (required to be multinormal). Otherwise, if only marginals are Gaussian (but the two-dim distribution is not multinormal), these can be uncorrelated but dependent.
Thus we face two different properties rather than a single "property that uncorrelated implies independent". Which one do you like to consider?
Boris Tsirelson (talk) 15:38, 16 February 2013 (UTC)
Both types interest me -- are there other examples (or categories of examples) of each? Duoduoduo (talk) 22:30, 16 February 2013 (UTC)
For the first type (the two values) – definitely no. Only two random variables, only two values each one. Otherwise it does not hold. (But I doubt that it is published somewhere; maybe my Original Research...). Boris Tsirelson (talk) 06:41, 17 February 2013 (UTC)
For the second type (like Gaussian) – this happens rather often. Each time that we have a one-parameter family of 2-dim distributions, containing a product measure (that is, the independent case), whose parameter is the correlation (or a one-to-one function thereof). I could write down a lot of such families. However, (a) the only notable family I know is the Gaussian, and (b) all that is probably my Original Research... Boris Tsirelson (talk) 11:38, 17 February 2013 (UTC)
To help me get an understanding of how this works, could you give me a non-Gaussian example? Thanks. Duoduoduo (talk) 13:46, 17 February 2013 (UTC)
Here is one. Consider the intersection $Q_a$ of the square $[-1,1]\times[-1,1]$ and the strip $|x-y|\le 2a$; here $a\in(0,1]$ is a parameter. (Draw the picture!) Now, consider the uniform distribution on $Q_a$. For $a=1$ we have independence; for other a we have a positive correlation. If you like to have also negative correlations, think about another strip $|x+y|\le 2b.$ Boris Tsirelson (talk) 16:16, 17 February 2013 (UTC)
Thanks -- this will give me something good to think about! Duoduoduo (talk) 18:02, 17 February 2013 (UTC)
Yes... And here is a wider class of such families. Take two independent random variables X and Y with variance 1; otherwise, choose their distributions according to your taste. Now consider the joint distribution of random variables $X+aY$ and $aX+Y.$ For $a=0$ they are independent. Otherwise they are correlated: their covariance is 2a. Boris Tsirelson (talk) 18:42, 17 February 2013 (UTC)
Great, this one is much more intuitive to me. Duoduoduo (talk) 18:57, 17 February 2013 (UTC)

## Harmonic mean

Hi Tsirel! I request a feedback from you on the issue presented on User talk:Toolnut on the harmonic mean. I see that you are more wiki-active than Toolnut is these days. Thanks in advance.--MagnInd (talk) 21:38, 11 March 2013 (UTC)

What really is your question? Harmonic mean is less than arithmetic mean (see "Inequalities"). There is no functional relation between them. And no, the sum and the sum of reciprocals are not functionally related. Boris Tsirelson (talk) 22:01, 11 March 2013 (UTC)

The question was focused on the relation sum and the sum of reciprocals. I thought (initially) that knowing the sum of some variables one could calculate the sum of their reciprocals but I realize that is not possible because partial products of variables appear in calculating the sum of reciprocals.--MagnInd (talk) 23:17, 11 March 2013 (UTC)

## Tsirelson space

Thanks for your attention to this article! By the way, the article seems to have disappeared (at least to me) right now, although the corresponding Talk is still visible. Can you still see the article?

well, it came back! Bdmy (talk) 11:59, 16 April 2013 (UTC)

Also, I keep repeating that you solved a question of Banach, but I couldn't find it in Banach's book. Do you know more? With best regards, Bdmy (talk) 11:54, 16 April 2013 (UTC)

No, thank you for your, active, attention (my was passive)! I am glad it did not disappear forever. :-)
No, I did not see it in Banach's book (otherwise I probably would write so in 1974). Did you see attribution to Banach in some papers/books? Boris Tsirelson (talk) 13:43, 16 April 2013 (UTC)
Lindenstrauss-Tzafriri Classical Banach Spaces I, Sequence spaces, says on p. 95: "a long standing open problem going back to Banach's book". Well, "going back" is not like "Banach, p. xxx"! Bdmy (talk) 16:37, 16 April 2013 (UTC)
Puzzling indeed. Maybe erroneous. Boris Tsirelson (talk) 16:52, 16 April 2013 (UTC)

## Absolute determinism

Boris you wanted to discuss my disagreement with your remark,'[Absolute determinism] ruins science as whole, thus, Bell theorem (as any other scientific claim) loses any meaning and relevance'. As this is not particularly relevant to the Bell's theorem article I have brought it here.

One argument against what you say is that AD is outside the scope of physics, thus its truth or otherwise can have no effect on physics. It is like religion and belief in God. As I have heard it put, the two subjects are orthogonal.

Many respected physicists have believed on an all-powerful God and that everything that happens is his will. This has not reduced their enthusiasm for physics though. Believing in an omnipotent God does not ruin science it merely changes what scientists believe that they are doing from modelling nature to modelling God's world. Absolute determinism would mean that we are modelling the way things have been so far (and the way we expect them to be in the future) rather than nature itself. To a physicist, what is the difference? Martin Hogbin (talk) 15:30, 6 January 2014 (UTC)

Yes, I agree, AD itself makes no difference. (Also Richard agrees; he wrote that it does not matter whether the nature decides its coin tossing in real time or by a preexistent large table of (pseudo)random numbers.) The problem is not AD itself. The problem is, CONSPIRACY. As long as the seemingly independent events may be treated as independent for all practical purposes, philosophy and physics stay orthogonal indeed.
However, this "physically harmless" philosophy is also "physically useless": it provides no escape from the Bell problem. CONSPIRACY provides the escape. At a terrible price; the price is, unknowable nature. If I believe that the Red Sea was separated into two halves by God in blatant violation of all physical laws, I still can be reasonably sure that nothing like that will happen tomorrow in my laboratory when I'll measure a physical quantity. But if I believe that my seemingly free decision which quantity to measure is correlated with the measured particle, and the correlation is not at all small (it explains the difference between probabilities 0.75 and 0.853), then why will I go to my laboratory? Maybe I am destined (not necessarily by God; maybe just conspiracy of molecules that I naively assumed to be a noise) to measure my particle only when its mass is high, while in reality its mass changes all the time, and maybe another physicist is destined to measure it only when its is low. This is not a problem of the unknowable essence of things. This is a problem of observed phenomena. Boris Tsirelson (talk) 17:40, 6 January 2014 (UTC)
I do not understand your statement, 'However, this "physically harmless" philosophy is also "physically useless": it provides no escape from the Bell problem'. I agree that AD is physically useless, but I thought you had agreed that it is compatible with Bell's theorem. Are you still happy to say, in appropriate wording, that experimental verification of Bell's theorem does not disprove AD? Martin Hogbin (talk) 18:46, 6 January 2014 (UTC)
Strangely, we are in a loop. I emphasize all the time that there are (at least) two very different determinisms. Surely you remember. And here again I wrote "As long as the seemingly independent events may be treated as independent for all practical purposes". In other words: without CONSPIRACY. (Should I write this word in larger font?) In still other words: determinism that underlies (surely you remember, what). This "benign" determinism is "physically harmless" and "physically useless". The other "malignant" determinism is an escape from Bell problem. But is lethal for physics. Well, death really is an escape from cancer. Never say "determinism" without specifying which one, and things should become much more understandable. ("Absolute" is not enough; it still can exist in both forms.) In your words: "If words are used with one meaning ... but understood ... to have another ..." Boris Tsirelson (talk) 20:21, 6 January 2014 (UTC)
Sorry but I do not understand the distinction that you are now making. The AD that I am referring to has no free will and the future is absolutely fixed but physical measurements are exactly as we see them now. This AD may conspire (if that is the right word) to produce an experimental verification of Bell's theorem. What is the other kind of AD? Martin Hogbin (talk) 22:54, 6 January 2014 (UTC)
The other kind of AD is one that does not conspire (if that is the right word). Boris Tsirelson (talk) 06:26, 7 January 2014 (UTC)
Really, I started this discussion in the hope that you'll show me a controversial but interesting philosophy according to which physics could survive in a conspiratorial Universe. But now I doubt you have it. Boris Tsirelson (talk) 10:53, 7 January 2014 (UTC)
I do not think the word 'conspire' is a good one, it ascribes human emotions to the physical world. Nevertheless, let us agree to talk about what you have termed the 'malignant' AD which 'conspires' to produce the results that we actually observe. I am going to use the simple term AD (as Bell did) to refer to this.
Firstly do you agree that this philosophical belief is outside physics. It cannot possibly be tested experimentally because, by definition, it produces all experimental results? Martin Hogbin (talk) 11:03, 7 January 2014 (UTC)
Yes, I agree that it is not falsifiable. Boris Tsirelson (talk) 15:25, 7 January 2014 (UTC)
So now I return to my original answer. If it is not falsifiable then the truth or otherwise of AD cannot produce any detectable experimental results. Physics is exactly the same whether AD is true or not. As a physicist I am therefeore completely neutral about AD. It makes no difference to me. I do agree with Richard, though, that AD is of no interest to physics.
Philosophically speaking, you may find AD unpalatable, that is your free choice. Maybe your answer changes what physics is but, in my opinion, not by much. The question of AD has been around for millennia;best not think about it too much, but we must make exactly the point in the article that you do above; that AD is not falsified by Bell's theorem. Martin Hogbin (talk) 16:32, 7 January 2014 (UTC)
Here is your phrase from the article: "While this does not demonstrate QM is complete, one is forced to reject locality, realism, or to accept the philosophical position of absolute determinism in which there is no free will and the future is fixed." I agree with a different phrase: "...one is forced to reject locality, realism, or freedom" (these three short terms being explained in the next paragraph of the article). Rejection of freedom is not the same as acceptance of absolute determinism. AD is compatible with the "freedom" and with "non-freedom" just because it is compatible with every phenomenology. I explained in which sense AD is compatible with the "freedom" when I wrote about "benign" determinism. Thus, why at all to mention AD in the article? Where do you see in the article a claim against AD? The claim that any reasonable physical theory must be non-deterministic (not really from the article, but even if it were) is as compatible with AD as everything else. It is compatible with AD that the universe seems to physicists to be non-deterministic. As well as the opposite (and a lot of other options). Your logic is a double-edged sword, as Gill wrote in the edit summary of 11:22, 30 December 2013‎. Boris Tsirelson (talk) 17:12, 7 January 2014 (UTC)
Perhaps you are forgetting the reason that I want to add something about AD to the article. The point is that other people, elsewhere, claim that Bell's theorem disproves AD. You agree that that is not the case. Such a claim is absurd but it is often heard. I would simply like to make clear that what other people claim elsewhere is false. I want use the word 'determinism' not because I care about this word but because the dictionary definition would appear define the word to mean AD and the word is used by people who make these extravagant claims.
If you would like to restore the original wording but allow me to add somewhere else that Bell's theorem does not disprove AD (because nothing can) that is fine with me. I am not trying to make some complex philosophical point but just to dispel a commonly heard fallacy about Bell's theorem. Martin Hogbin (talk) 17:32, 7 January 2014 (UTC)
Well, but then we have a wiki problem: we have to cite some of these claims of these other people. Have you these? Google finds me some, but they do not seem to be solid enough: [2], [3] [4] Boris Tsirelson (talk) 18:00, 7 January 2014 (UTC)
I could support (in the article) a disclaimer like this: Bell theorem deals with classes of physical models rather than a single model; but it does not mean crossing the boundary between physical models of the nature and the nature itself. Philosophical problems concerning relations between the nature itself and its scientific models are a separate matter, not related to Bell theorem and therefore not touched in this article. Boris Tsirelson (talk) 18:08, 7 January 2014 (UTC)
There is no wiki problem. I have a perfectly good source for what I want to say. The language you use in your disclaimer is too complex to address the disinformation in the intentionally unreliable sources that you have found. We need to say something simple. It need not be long but it needs to make clear to the layman that what your unreliable sources say is nonsense. It may not be physics but it is an important piece of information for the general public.
I am afraid, Wikipedia is not a good place for effective polemic with bloggers. I am afraid, it will be very hard to find a formulation both clear to layman and correct, given the very subtle nature of the problem (too subtle even for many physicists, as Richard wrote). --Boris
As this discussion is directly about what to put in the article I suggest that we move back to the article talk page. Martin Hogbin (talk) 19:20, 7 January 2014 (UTC)
OK. Boris Tsirelson (talk) 20:15, 7 January 2014 (UTC)

## Math teaching

I've just listened to an interesting TV interview on the subject of teaching, and the many failures that students experience in the U.S. I bought the individual's book, and so far it looks extremely interesting. One of the claims that he made, backed up by statistics if he is an honest person, is that it's a little better to have only 15 students in a class rather than 30, but the difference is not really worth paying for. Having a good teacher for the 30 students will make an immense difference by comparison, and if you add one or two students to the teacher's class it won't degrade the experience for anybody. That discussion reminded me of taking calculus at Stanford in 1958-1959. In the first trimester there was a very kind lady who could do calculus problems so fast that the whole thing was over before I had begun to follow through the connection between the first and second things she had said. She would ask, "Does everybody understand?" The well-prepared students who sat in the first couple of rows all said or nodded yes. She would do another problem and another problem. I struggled and I thought I was stupid. The second trimester my room mate insisted that I should use bribery, extortion, or whatever was necessary to get into the class of Mr. Restrepo. I somehow lucked out and registered without resort to skulduggery. Prof. Restrepo was, I suspect, only a grad student working for his Ph.D. However, he was a brilliant teacher.

Mr. Restrepo never went fast. He had a little foreign accent, but enunciated clearly. In the course of one period he would write a sentence, say a little, write another sentence... By the end of the period he would have filled the blackboard with clearly written sentences and math, and by the end of the period I would understand why the calculations were being made. Frequently on Friday he would have five or ten minutes time left over at the end of the class period. So he would offer us one more problem. It would sound so horrible that I would anticipate spending the entire weekend to calculate an answer. Then he would show us how to do the problem in our heads.

The third trimester I could not make his schedule and my required courses work together, so I ended up taking Calc. 103 from the head of the math department. He was only "o.k."

In this century if anybody has a teacher like (surely he is by now) Dr. Restrepo, s/he should take a video camera to class, record every precious minute of the class, and post it on the Internet. I always looked for a Beginning Calculus book by this teacher. Nothing. When I was back at Stanford four years after I graduated I went to the math department. With some prodding they remembered that there had once been such an individual on their staff. "Where is he now?" "I think he went back to South America." Unfortunately although I must have heard it once or twice I have no memory of his first name. I have never tracked him down, much to my regret.

I don't suppose you have ever run across this gentleman. He would be in his 80s if some tragedy has not overtaken him.

Thanks.P0M (talk) 08:29, 14 March 2014 (UTC)

Long live to him. Boris Tsirelson (talk) 12:27, 14 March 2014 (UTC)