User talk:Trovatore/Archive03

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This archive page covers approximately the dates between 12 February 2006 and 4 December 2006.

Post replies to the main talk page, copying or summarizing the section you are replying to if necessary.

I will add new archivals to User talk:Trovatore/Archive04. (See Wikipedia:How to archive a talk page.) Thank you. Trovatore 07:27, 15 January 2007 (UTC)


Re: Footnote/MathML bug[edit]

Hi Trov, I've replied to you comment on my talk page. Paul August 23:18, 12 February 2006 (UTC)

Saw it, thanks. If I see the bug again (and it's reasonably convenient) I'll grab the HTML source in case there's some developer who'd be willing to take a look at it. Do you know who I might send it to? --Trovatore 23:21, 12 February 2006 (UTC)
Not really. Paul August 23:35, 12 February 2006 (UTC)
I'd be interested in the HTML source. I think it might be related to bug 3504, but it's only a wild guess, and it wouldn't explain why you see the bug only intermittently. -- Jitse Niesen (talk) 01:31, 13 February 2006 (UTC)


I should have asked for a pizza along with the explanation of omega-completeness. :) --moof 06:38, 14 February 2006 (UTC)

Combined set theory[edit]

Hi Trovatore. Have you taken a look at combined set theory? I've proposed it for deletion as original research, based on the authors comments at talk:combined set theory. If you think there is anything worth saving there, please remove the "PROD" tag. Thanks — Paul August 15:01, 22 February 2006 (UTC)

Looks like a straightforward application of the NOR policy to me; I've noted before that in the math project we tend to be a little tolerant of minor OR (observations arrived at by routine methods, when they clarify issues in the article) but we can hardly allow an entire article on unpublished research. Once published it might well be an interesting subject for an article, though I haven't read deeply enough to really know if there's any there there. --Trovatore 16:11, 22 February 2006 (UTC)

Yes that's what I figured, thanks for taking a look. Paul August 20:15, 22 February 2006 (UTC)

twin prime conjecture[edit]

Now on my watchlist. Dmharvey 03:18, 3 March 2006 (UTC)

Thanks. --Trovatore 03:25, 3 March 2006 (UTC)
Now on mine too. :) Oleg Alexandrov (talk) 03:37, 3 March 2006 (UTC)

Good work[edit]

Congratulations on the quick and excellent job of completing the article on Renato Caccioppoli initiated by me! --R.Sabbatini 10:37, 4 March 2006 (UTC)

Thanks! --Trovatore 16:50, 4 March 2006 (UTC)


I think we both know what the pronunciation is but it's the phonetic transliteration that's the problem. When I read "keenAWtoh" I hear a strong New York accent! We need an accent-free version, otherwise I think it is misleading for non-Americans. Could you do an IPA version? (I'm not confident enough with IPA vowels.) Nick 18:57, 5 March 2006 (UTC)

Most of the IPA symbols show up as boxes for me. I wish we'd move to Kirshenbaum, in which I'd write it "ki 'nOt to". --Trovatore 19:02, 5 March 2006 (UTC)

mathematical induction[edit]

this just doesn't strike me as an encyclopedia article. It would be a good sort of observation to include in a textbook, maybe for a discrete math course. --Trovatore 06:55, 6 March 2006 (UTC)

Here's an exercise for you:

0 is not a sum of fewer than 0 numbers each of which is smaller than 0;
1 is not a sum of fewer than 1 numbers each of which is smaller than 1;
2 is not a sum of fewer than 2 numbers each of which is smaller than 2;
3 IS a sum of fewer than 3 numbers each of which is smaller than 3;
generally, n IS a sum of fewer than n numbers each of which is smaller than n, for n ≥ 3.

Comment on the relevance to this article. The numbers 0, 1, and 2 correspond to the three forms. Michael Hardy 21:54, 6 March 2006 (UTC)

And this has what to do with whether this is a suitable topic for an encyclopedia article?
Come on, Michael, we all know you've written many many good articles. This isn't one of them. The case division doesn't even have any precise meaning that I can see (for example, you can always re-index to make n=0 the "substantial" case, assuming we agree on what a "substantial" case is). It's a didactic observation worth communicating to students; that doesn't make it encyclopedic. --Trovatore

No, you can't reindex that way, in the relevant sense. There is an obvious sense in which it is trivial to reindex that way, but that is not the relevant sense. To see why not, look carefully at the newly added example concerning the triangle inequality. If you're confusing the trivial sense in which you can reindex, with the actually relevant sense in which you cannot, then you haven't understood what this is about yet. But I think the recent edits, leaving the article no longer a stub, should make it clear. Michael Hardy 23:34, 6 March 2006 (UTC)

Oh. One other remark:
n = 0

The former is generally considered good style and is followed by TeX, but in non-TeX notation it requires conscious attention. (But ignore this remark until after you've digested my other comments.) Michael Hardy 23:35, 6 March 2006 (UTC)

...and now I've added Polya's famous proof that there is no horse of a different color. In some senses, that is the Platonic form of this idea. Michael Hardy 00:10, 7 March 2006 (UTC)

Three forms of mathematical induction[edit]

This article was intended to be comprehensible to all mathematicians.

It was not intended to teach mathematical induction. It was not intended to explain what mathematical induction is, nor how to use it.

What I see is (mostly) a bunch of non-mathematicians looking at the stub form in which the article appeared when it was nominated from deletion, and seeing that

  • It was not comprehensible to ordinary non-mathematicians who know what mathematical induction is, and
  • The article titled mathematical induction is comprehensible to ordinary non-mathematicians, even those who know --- say --- secondary-school algebra, but have never heard of mathematical induction.

And so I have now expanded the article far beyond the stub stage, including

  • Substantial expansion and organization of the introductory section.
  • Two examples of part of the article that is probably hardest to understand to those who haven't seen these ideas.
  • An prefatory statement right at the top, saying that this article is NOT the appropriate place to try to learn what mathematical induction is or how to use it, with a link to the appropriate article for that. It explains that you need to know mathematical induction before you can read this article.

Therefore, I invite those who voted to delete before I did these recent de-stubbing edits, to reconsider their votes in light of the current form of the article.

(Nothing like nomination for deletion to get you to work on a long-neglected stub article!) Michael Hardy 23:30, 6 March 2006 (UTC)

  • Michael, I'm afraid I'm still not all that convinced. I see what you're getting at now, but some things come to mind:
  1. You seem to be claiming, implicitly, that it's rare to have a proof by induction in which the base case and the induction step are both nontrivial, and where the first does not reduce to the second. That's probably true, if you're willing to work hard enough to do the reduction, but then it turns into a Scholastic argument about whether the idea of the base case is "the same" as the idea of the induction step.
  2. I suspect that the reason you're having the nontrivial case show up when you have two prior steps is that you're using binary functions. If you were proving something analogous about ternary functions, wouldn't it show up only after you have three prior steps? The whole thing reminds me a little of the "threeness" idea of Charles Sanders Pierce. --Trovatore 02:38, 7 March 2006 (UTC)

binary and ternary[edit]

I suspect that the reason you're having the nontrivial case show up when you have two prior steps is that you're using binary functions. If you were proving something analogous about ternary functions, wouldn't it show up only after you have three prior steps?

Can you do better than to merely suspect? How about an example of such a case involving ternary functions?

The identity relation has an inherently binary character: if any two horses are of the same color, then all horses are of the same color. The addition and multiplication operations have an inherently binary character: if we can find the sum of any two numbers, then we can find the sum of any finite number of numbers. In both cases, breaking a set of n members into a union of fewer than n sets of size smaller than n is involved. That won't work if n = 2, so that is the basic case in induction arguments of this form.; we cannot reach the number 2 from below.

Does anything have an inherently ternary character? Here's an attempt: A set A is linearly ordered by a relation "<" if and only if every subset B of A such that |B| = 3 is linearly ordered by that relation. Now are there any corresponding induction proofs? Michael Hardy 23:02, 14 March 2006 (UTC)

Hmm, I'm not sure. Part of the problem is that the characterization above isn't quite right in general (doesn't work if A has cardinality 1 or 2)
But it's this attempted divination of the "inherent character" of the base case that makes me uneasy with the whole argument. Whether natural-seeming definitions say something sensible in trivial cases is, I think, largely a matter of luck. In some cases, like your example with partitions, it does. In others, like whether 1 is a prime number, it doesn't (the most natural definitions make 1 a prime, but that just doesn't work right). That's why I'd like you to give a precise characterization of what you're talking about, and preferably find someone who's written about it. --Trovatore 23:18, 14 March 2006 (UTC)

Trashing my introduction to "large countable ordinals"[edit]

I do not appreciate your trashing of my introduction to "large countable ordinals". Granted that it was not polished yet and your added material is good. But you took out some important information. Also I think that there should be a section header before the introductory material to make it easier to edit it without having to edit the entire article. JRSpriggs 03:59, 16 March 2006 (UTC)

Please read WP:LEAD. Which important facts did I take out? They can always be re-added. --Trovatore 04:17, 16 March 2006 (UTC)
I already repaired the introductions to large countable ordinals and ordinal arithmetic. Please do not delete anything from them again without discussing it first. JRSpriggs 04:26, 16 March 2006 (UTC)
JRSpriggs, your wording is a bit too strong I think. I am sure you and Trov can reach a reasonable agreement without getting to "trash" things and arguing "whose" article that is. Oleg Alexandrov (talk) 16:00, 16 March 2006 (UTC)

Now that I have had a day to cool off, I have tried to address Trovatore's concerns. Please let me know whether you like the new beginnings of the articles. I got angry because he seemed to come out of nowhere to make a lot of changes all at once while admitting that he had not even read the article carefully. Also he delete my links back to the main article "ordinal number" and other links without seeming to care about the effort I took to create them. JRSpriggs 08:05, 17 March 2006 (UTC)

Thank you for the good things that you added to these articles. I now feel that I over-reacted to a minor inconsideration, and I should not have yelled at you. Please feel free to delete these comments and forget the whole thing. JRSpriggs 12:34, 19 March 2006 (UTC)
Hi, Mike! I'm a Lloydie who decided to poke around your page a little bit after I saw your flag. Just so you'll know, I got a little bit crosswise with JRSpriggs when I first started working on Wikipedia, but now we talk to each other quite cordially almost all the time.
Have a great day! ;^> DavidCBryant 11:19, 13 January 2007 (UTC)
To David: I assume that you are talking about Mathematical induction#Infinite descent and Talk:Mathematical induction#Who is JRSpriggs? (which I found by going over your early contributions). Frankly, I had forgotten all about that. It seemed insignificant to me. I am sorry if it upset you. As for this section and my dispute with Trovatore, it occurred ten months ago when I had just started working on Wikipedia and just three files occupied my entire attention. So when he changed one of them unexpectedly, I over-reacted. I was trying to write something about ordinals and he modified it because of considerations related to cardinals which felt like an invasion from another part of mathematics. Also I did not understand how Wikipedia works generally then. Actually, I was hoping that Trovatore would eventually delete (or at least archive) this section of his talk page, because I now feel embarrassed by it. JRSpriggs 04:41, 15 January 2007 (UTC)

another thing for you to vote on[edit]

Could you please vote at Wikipedia:Articles_for_deletion/Proof_that_22_over_7_exceeds_π?

Some people are actually saying any article devoted to a partiucalar mathematical proof is non-encyclopedic and should be deleted! Or that all articles primarily for mathematicians, that the general reader will not understand, should be deleted. Michael Hardy 00:13, 17 March 2006 (UTC)


Don't you hate that particular phenonema? (; Sorry, I couldn't resist.--Lacatosias 09:01, 17 March 2006 (UTC)

Image copyright problem with Image:NetscapeNewsOops.jpg[edit]

Thanks for uploading :Image:NetscapeNewsOops.jpg. The image has been identified as not specifying the copyright status of the image, which is required by Wikipedia's policy on images. If you don't indicate the copyright status of the image on the image's description page, using an appropriate copyright tag, it may be deleted some time in the next seven days. If you have uploaded other images, please verify that you have provided copyright information for them as well.

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Bogdanov Affair[edit]

Hi Trovatore,

You asked an excellent question on the talk page of the "Bogdanov affair" article. I try to answer here because I cannot do it on the talk page of the article : the Arbcom banned me from Wikipedia, even for the talk page.

The Arbcom banned all people involved in an "edition war" about the Bogdanov affair. For them, "entangled" just means that we had already argued about this affair on several fora (Usenet and Web) before we "arrived" on Wikipedia. The worst problem is that after this strong decision, they changed it : they "saved" 2 editors, who were 2 detractors of the Bogdanovs. One of them, rbj, had violently insulted them on the talk page of the article, without getting any reproach from the administrators who took part to the article... And then, he was "nominated" by the Arbcom to be able to write a NPOV article on these people he had insulted ! As I protested against this unfairness on the talk page, the Arbcom decided to extend the ban to the discussion pages...

Of course the article is the less NPOV you can imagine : they even removed the external links to three sites about the Bogdanovs (including mine) without explanation, surely because they gave a good image of them. Since we are banned, we cannot neither put them back, nor protest against this new censorship on the talk page. I will write soon an article about this "affair Wikipedia" on my site (, one of the sites whose link they censored).

Thank you and bravo, anyways, for having asked this question : I was surprised that nobody reacted to this argument of the Arbcom.


Winning strategy[edit]

Trovatore - I moved the article to that category because it seemed more similar to mathematical analysis of games like chess and nim, rather than game theory in economics. I understood that to basically be the distinction between our categories "game theory" and "combinatorial game theory". If you think it belongs in the other category, that's cool. I'm just trying to keep things organized... :) --best, kevin [kzollman][talk] 04:18, 28 March 2006 (UTC)

I don't know whether it belongs in category:game theory either, but combinatorial game theory seems too specific for the article. --Trovatore 04:19, 28 March 2006 (UTC)
I agree, there are several articles along these lines that don't really fit in with game theory as studied in economics, philosophy, and biology nor do they fit into combinatorial game theory. Perhaps a new category mathematical game theory? I don't like the name, since it implies other types of game theory is not mathematical. Got any ideas? --best, kevin [kzollman][talk] 04:29, 28 March 2006 (UTC)

So there seem to be four classes of games that need to be taken into account, with some overlap between classes and possibly some common features I'm not capturing:

  1. Games as in economics: Mostly not of perfect information, finite length, used instrumentally in studying other things.
  2. Games that game players play (chess, etc): Some perfect information, some not. Finite length. Played as ends in themselves.
  3. Games of the sort I'm interested in: Mostly infinite length, mostly perfect information, used instrumentally.
  4. Combinatorial game theory: Perfect information, finite length, very specific winning condition (last player with a legal move wins), used both instrumentally and as ends in themselves. This term is very specific to the work of John Horton Conway and those who have followed up on it.

Now I think winning strategy was aimed at all four sorts of games, which is why I wouldn't put it in category:combinatorial game theory; it's not specific to the Conway theory. Because of its generality I found it inadapt for the determinacy article, and put my own definition of winning strategy there.

Anyway, just some thoughts; I don't have a good answer at the moment. Which of these four classes do see as part of "mathematical game theory"? --Trovatore 13:00, 28 March 2006 (UTC)

I was thinking less about a division that was a nice cleavage of the topic, but rather a division based on which types of academics work on those. 1 is studied widely (econ, bio, philo, polisci, etc.) and known to most people as game theory. 2-4 are studied primarily by mathematicians whose interest is in them as mathematical objects, not as tools for empirical study. Could you say more about how winning strategy applies to 1? The thing that led me to move it was its reference to "winning" which is a term not oft used in type 1. --best, kevin [kzollman][talk] 18:09, 28 March 2006 (UTC)

Do you have any suggested articles to work on?[edit]

Oleg said that you might be able to suggest articles in the area of ordinal numbers or cardinal numbers which need work. Or topics for which new articles should be written. Do you have any suggestions? JRSpriggs 07:01, 30 March 2006 (UTC)

A lot of the articles linked from list of large cardinal properties could use a lot of work; many of them are just bare definitions and could use background, context, and applications. There doesn't seem to be an admissible ordinal article, or one on the singular cardinal hypothesis. --Trovatore 16:14, 30 March 2006 (UTC)
Another general suggestion: Look on Wikipedia:Requested articles/Mathematics#Logic for articles people have requested, and at Category:Mathematical logic stubs for articles needing serious expansion. --Trovatore 18:38, 30 March 2006 (UTC)
Thanks for the information. JRSpriggs 04:15, 31 March 2006 (UTC)
P.S. Your user-talk page is on my watch list. So you do not need to put a message on my user-talk page when you reply to one of my messages here. JRSpriggs 04:40, 31 March 2006 (UTC)

I have added a lot of material to the article Constructible universe. Please proof-read it or give me comments on it. JRSpriggs 09:21, 15 April 2006 (UTC)

Juan Rico[edit]

No, he wasn't Argentine, his mom was killed in BA, but the family spoke Tagalog at home, so were almost certainly of Filippino descent. Given who wrote the book, characters speaking Anglic in public (not English, but close), and other character's names, I think we can assume that he and his family lived in North America, probably the former US. MilesVorkosigan 18:46, 10 April 2006 (UTC)

Well, but who says it's about descent? I gather that there was a single world political structure so it may not make sense to talk about "citizenship" per se, but in that case if they lived in North America they were North Americans (just as a US citizen who moves to California is a Californian). --Trovatore 18:49, 10 April 2006 (UTC)

Mexican mathematicians[edit]

Hi Mike. I can give you some names of people who are or were both mathematicians at UNAM and notable in some way or another. I would probably be unable to provide more than stubs, though, and I would not be able to do so in the near future; I am about to leave town, and the semester is winding down. Off the top of my head, I can suggest Alberto Barajas and Graciela Salicrup (both now deceased); Emilio Lluis Riera (the first Ph.D. given in the new Campus in Ciudad Universitaria); and Jose Antonio de la Pe~a, one of the top people in representations of algebras (you can get a biographical sketch in English by going to, clicking on his name, and then on the "Curriculum" link that appears in the window). Magidin 19:48, 11 April 2006 (UTC)

Golden ratio[edit]

To start, I thought: If Schroeppel claimed this, it has to be true. Then I remembered having noticed something like

This is basically immediate from the closed-form expressions for and . So all you need now is some n such that and are both even. LambiamTalk 00:15, 12 April 2006 (UTC)

Donald A. Martin[edit]

Hey do, Mike. Concerning Tony Martin's article, it could do with a few things such as date of birth, background, and explaining Martin's Axiom in layman's terms. Otherwise, nice work! Fergananim 19:46, 19 April 2006 (UTC)

So unfortunately I'm missing some of that information. I think he was born in '42, because his sixtieth birthday celebration was held in '02, but birthdays aren't always celebrated on the exact year, so that's not for sure. He hails from West Virginia but I don't have a source for that. Explaining MA in layman's terms? Have at it; better you than me. I suppose some aspects of it could be explained to non-set-theorist mathematicians, but better than that I can't see.
One thing that would be interesting to mention, but that I'm not sure just how to source and work into the article, is that he doesn't have a PhD. He got an offer before he'd finished his dissertation, and just never bothered to jump through the hoops. My guess would be he's the only living US mathematician of similar fame to be in that position. --Trovatore 23:14, 19 April 2006 (UTC)

Re. Falsifiability and Math[edit]

Your point is indeed Imre Lakatos' position on the matter, and is obvious only to mathematicians and their friends, which was why I asked CSTAR first. I happen to think the point can be said far less obtusely than it currently is in that article. Very much appreciate your reply...Kenosis 13:42, 20 April 2006 (UTC)

Forza Italia[edit]

Hi! The reason for emptying is that I had added a new Category:Members of Forza Italia to several members of that party which were not included to Category:Forza Italia politicians. Furthermore, the new cat. is consistent with other about Italian parties (i.e.: Members of the Italian Communist Party, Members of the Italian Liberal Party etc.) —The preceding unsigned comment was added by Attilios (talkcontribs) 16:45, 22 April 2006 (UTC)

You're still not supposed to empty a cat on your own initiative. You should list it on categories for deletion. Another possibility is to make Category:Forza Italia politicians a subcat of Category:Members of Forza Italia (then articles that appear in the former should not appear in the latter).
A note on wikimarkup: When you want a link to a category, as opposed to adding a page to a category, put a colon before the word "category". [[:Category:Members of Forza Italia]] gives a link; [[Category:Members of Forza Italia]] makes my talk page part of the category. --Trovatore 16:50, 22 April 2006 (UTC)
OK, thanks. The sole thing is: "You are supposed to" is not such a nice expression to use, at least with me here. Attilios 17:07, 22 April 2006 (UTC)
Well, I thought maybe you weren't familiar with the accepted procedures. Looking through your contributions I see you've been very energetic contributing to articles, but I don't see much activity in Wikipedia space, which is where the procedural stuff gets done. I didn't make this up; this really is the accepted procedure. See Wikipedia:Categories for deletion for details. --Trovatore 17:10, 22 April 2006 (UTC)
OK. Now we have in the same article Berlusconi listed as Member of Forza Italia and Forza Italia politician, simply because you're sticking on paper procedures instead of consistence of the encyclopedical content. I did a mistake, ok. But now? Why had a mistake to another? Let me know. Attilios
Because maybe someone will object to the change. Not me; I don't really care. But someone could. You should undo the mistake by listing the category on Wikipedia:Categories for deletion. --Trovatore 18:40, 22 April 2006 (UTC)

Merci for ze caring :D[edit]

"boink" is a word I accidentally misused once...and to a woman, too. ;) --VKokielov 17:23, 26 April 2006 (UTC)


I did not "Know" that that photo was of a porn actress. My point, I think was not to imply that I have never "studied" such copyrighted photo's of women. When I was younger I was too familiar... my point was that there should be some way of protecting our kids from viewing sexually explicit stuff that adults may indulge in. Free speech on the internet is essential and I don't believe in censorship! I just am concerned about what kids can view on a safe free encyclopedia like Wikipedia. Let Bomis serve up Porn if they want to, but let Wiki be more family oriented. I'm sure its founder (Wales)would agree!--merlinus 14:25, 27 April 2006 (UTC)

Saints Wikiproject[edit]

I noted that you have been contributing to articles about saints. I invite you to join the WikiProject Saints. You can sign up on the page and add the following userbox to your user page.

Gloriole.svg This user is a member of the Saints WikiProject.

I also invite you to join the discussion on prayers and infoboxes here: Prayers_are_NPOV.

Thanks! --evrik 16:57, 28 April 2006 (UTC)

Please be objective[edit]

President Milosevic was called Sloba,not Slobo.......Only Croats and Muslims call him Slobo.....If you want to be part of it,please stay objective,and dont call him insulting names.Thank youDzoni 00:32, 29 April 2006 (UTC)


You're right about Prodi. Sorry :-)--Stephen 17:12, 2 May 2006 (UTC)

Hi, It's Merlinus[edit]

It wasn't Vandalism to my own User Page. I was trying to make a link and I messed up and left a message saying so. Is my signer properly signing? -- 19:27, 2 May 2006 (UTC)? I think I restored my TALK page alright? Could you take a look? I have important things on there? I checked and I am properly signed on... I don't know why its not registering my name as Merlinus but just the numbers Could it be because my wife uses her own Wikipedia User Page? I don't want to reregister under another different name or anything?-- 19:31, 2 May 2006 (UTC)

Hm, I don't know why you're having the problem with your login. You might try the following: At the login page, check the box that says "remember me". Then, once logged in, clear your browser cache.
As to your pages: You now seem to have identical content in User:Merlinus and User:Merlinus/Recently read books. I doubt that's what you want. If you no longer want the latter page to exist, put the following line
       {{db|author request}}
at the top of the latter page, and someone will come along and delete it. --Trovatore 23:22, 2 May 2006 (UTC)
Oh, one more thing, about your talk page: You seem to have done a copy-and-paste from User talk:Merlinus/Recently read books to User talk:Merlinus. The problem with that is that the GFDL requires attribution for other people's work; this attribution is usually contained in the page history. User talk:Merlinus does not contain that history, so it could be judged a copyright violation. What you should probably do is:
  1. Copy anything you want to save from User talk:Merlinus to User talk:Merlinus/Recently read books, noting the authors in the edit summary.
  2. Get an admin to delete User talk:Merlinus.
  3. Move User talk:Merlinus/Recently read books to User talk:Merlinus.
Then the history will be preserved. --Trovatore 23:29, 2 May 2006 (UTC)

Khodorkovsky and martyrdom[edit]

Hi Heptor,

A while back I was looking at the article on Mikhail Khodorkovsky and saw a section called "An attempt at martyr creation", which was clearly tendentious. I changed it to the more neutral "Martyr?", with the question mark indicating that no position was being taken. I see you changed it back, claiming that the original was "more neutral". I think it's far less neutral; it's quite clearly anti-Khodorkovsky, whereas my version just asks a question. Maybe you can think of something better, but please don't change it back to the original POV version. --Trovatore 15:29, 2 May 2006 (UTC)

Hi Trovatore,
I'd say that "An attempt of martyr creation" is more neutral, but this is of course in the eye of the beholder. "A martyr to some" is fine though, do you agree? -- Heptor talk 10:01, 3 May 2006 (UTC)
It's alright. I can't imagine how you can think the "attempt" wording is more neutral, though. It directly accuses Khodorkovsky's supporters of trying to manipulate perceptions. --Trovatore 14:24, 3 May 2006 (UTC)


So what was the reason for your reversion?

-- PCE 01:57, 4 May 2006 (UTC)

The fact that what I reverted, was nonsense --Trovatore 02:56, 4 May 2006 (UTC)
Are you refering to Rucker's proof or to my refutation? -- PCE 03:39, 4 May 2006 (UTC)
Perhaps you could explain instead why the following is nonsense:
  1. Let x = 1.
  2. Square both sides: x2 = 1
  3. Subtract 1 from both sides: x2 – 1= 0
  4. Factor: (x+1)(x-1) = 0
  5. Divide both sides by (x-1): x+1 = 0
  6. Substitute the value of x: 1 + 1 = 0
  7. Conclusion: 2 = 0.
-- PCE 03:53, 5 May 2006 (UTC)
Yeah, I could. --Trovatore 03:54, 5 May 2006 (UTC)
Okay. Good to see you are up. Thought I had stumped you with the above question about Rucker's proof or my refutation. -- PCE 03:57, 5 May 2006 (UTC)
How about this: think of yourself as Gödel and answer the question as if you were him? -- PCE 15:55, 5 May 2006 (UTC)

Okay, let's go on to something else... assuming that Gödel's Incompleteness Theorem only applies to the natural numbers does that mean it applies only to base 10? --- PCE 22:50, 5 May 2006 (UTC)

This is a trivial question; if you really don't know the answer, then you need to spend a lot more time acquiring some basic background in logic and foundations of math before it will be a sensible use of time to discuss it with you. The other possibility is that you do know the answer, and are just trying to make trouble. Either way I don't see the point in responding further. --Trovatore 23:06, 5 May 2006 (UTC)
Well part of the reason for the success of a wiki is that it serves as an opportunity for nubees to learn from experts even if the experts only suggest an article to read. But when an expert is so rude and arrogant that he deletes an edit without even so much as a referral, much less an explanation as to why he performed the deletion, then that expert is not conducive to donations of a finacial kind. Comprenda? -- PCE 23:33, 5 May 2006 (UTC)
So you're holding Trov responsible for your unwillingness to make a monetary donation to the Wikimedia Foundation, because he didn't give you a reference to show that Gödel's incompleteness theorem is not dependent on the radix used to denote the natural numbers? What is this, extortion? -lethe talk + 00:56, 6 May 2006 (UTC)

User_talk:Paul_August#Your_revertion..._G.C3.B6del_Incompleteness_Theorem -lethe talk + 02:10, 4 May 2006 (UTC) seems like a troll to me. Do not feed the trolls. JRSpriggs 05:28, 6 May 2006 (UTC)
JRSpriggs seems like an ostracist to me. -- PCE 13:41, 6 May 2006 (UTC)

Wrongful and malicious deletion of talk pages on your part...[edit]

When you deleted the talk topic: "PCE's doubts" you deleted the following commentary and other valuable points of discussion which although may not be of any value to you may be of value to others, if for no other reason than the amount of work and effort others have poured into them.

See falsifiability for a crucial difference between the laws of physics and theorems in mathematics. The laws of physics are not "proved" in the same way that mathematical theorems are.
Gödel's theorem applies, in the original version, to "Principia Mathematica", but there are many generalizations that apply to other axiomatic systems (such as ZFC) or other formal constructs (such as Turing machines). I am not sure where the borderline between Theoretical/Pure Mathematics and Applied Mathematics is precisely, but it seems clear that Gödel's theorem is a theorem of pure mathematics.
Aleph4 16:54, 6 May 2006 (UTC)

How about next time before you delete any discussion in which you are not an immediate participant reframe from such deletion until you have advised the actual participants what you intend to do. If you can not do that then how about surrendering your status as a fellow Wikipedian or start making a few financial contributions to help pay the bills.

-- PCE 20:50, 8 May 2006 (UTC)

I didn't delete it. I moved it to a new "arguments" subpage. --Trovatore 20:53, 8 May 2006 (UTC)
I agree that moving the discussion to a subpage was a good idea, for the reason that Trovatore gave: Please reserve this page for discussions about improving the *article*.
Really, such discussions should not be held on Wikipedia at all -- this is an encyclopedia, not a chat forum, nor a math class. But sometimes it is hard to resist. --Aleph4 21:54, 8 May 2006 (UTC)
Okay. My apologies. The whole concept of a wiki is new to me since I have only recently begun to participate regularly in newsgroups (chat forums). I am now in the process of learning wiki protocols. Thanks for your head's up and for your reply. Again my apologies. -- PCE 17:36, 10 May 2006 (UTC)

reconsider adminship?[edit]

I am aware that you've previously turned down a nomination for adminship. I think you're a very valuable contributor and would make a useful addition to our phalanx of math admins. Adminship should probably be a matter of course for editors who've been productive and noncontroversial here as long as you. If you think you could manage to mostly ignore the addition of a few extra buttons to your wikipedia interface without having more time sucked up by the project than is already, I'd be happy to nominate you again (as would many others I'm sure). If nothing else, it might be expedient for dealing with new appearances of WAREL puppets. -lethe talk + 10:04, 11 May 2006 (UTC)

PS did you take your username from the opera? -lethe talk + 10:05, 11 May 2006 (UTC)
A troubadour with a rollback button, now that's will be intersting. Oleg Alexandrov (talk) 15:53, 11 May 2006 (UTC)

Well, not just now; thanks, Lethe and Oleg. I've got a lot of things to think about right now, moving and changing jobs. BTW I don't know that particular opera per se; I like the name "Trovatore" because I'm an Italophile and like to sing. --Trovatore 02:59, 12 May 2006 (UTC)

It's the opera that the famous Chorus of the Anvils is from. If operas are your thing, that's a good one. -lethe talk + 11:46, 12 May 2006 (UTC)

Romano Prodi[edit]

I copied your request for protection from WP:AN/I to WP:RPP, where you're likely to get a quicker response. AmiDaniel (talk) 23:34, 13 May 2006 (UTC)

Thanks. --Trovatore 00:25, 14 May 2006 (UTC)


I understand, but the problem is that semiprotection isn't intended to prevent anons from editing content. Only to prevent them from vandalizing. At its heart, this is a content dispute between two anon users, so semiprotection doesn't apply. Hopefully this will encourage them to come to the talk page and discuss things. If that doesn't work quickly, I'll remove the protection. · Katefan0 (scribble)/poll 21:02, 15 May 2006 (UTC)

OK, I understand; this is probably consonant with current policy. In my opinion the policy should be changed; anons should be allowed to make non-controversial edits, but once things become disputed, they should have to log in if they want to continue. It's frustrating to try to discuss things with ghosts. --Trovatore 21:08, 15 May 2006 (UTC)
There is a guideline that sorta says as much; Wikipedia:Accountability. But of course, it's just a guideline, not an official policy. You may find it useful to try to guide the two anons to this page, though. Sometimes it's enough to convince people to sign up for accounts. · Katefan0 (scribble)/poll 23:27, 15 May 2006 (UTC)

Crazy Mathematicians[edit]

I am fascinated by the trajedies of some modern mathematicians - Cantor, Godel, Kacynski. I believe I sat next to Kacynski in the back of a Berkely classroom one day years ago. He was the assistant Professor auditing another's class; I was the flake flunking out.

I was encouraged to see your recent post on the Georg Cantor discussion page - encouraged to beseige you with a Cantor question: What was Cantor's motive in using the Hebrew alphabet? I can see three plausabile answers...... Clarity - He wanted something not to be confused with all the other, mostly Greek, symbols. Homage - He WAS proud of his heritage and desired to acknowledge it. Ego - mentioned in my Cantor page post - He wanted to emphazisize the drama and significance of his theory by using one of the oldest alphabets, even older than Greek. Any clues about his motivations? --Therealhrw 17:45, 23 May 2006 (UTC)

I'd just be speculating, and I'm not really very good at history. --Trovatore 17:54, 23 May 2006 (UTC)

Cantor's diagonal argument[edit]

Given a sequence of objections to Cantor's diagonal argument, can we construct an objection not in the sequence? -Dan 15:27, 24 May 2006 (UTC)

Hmmm that depends. Can every objection be written as a finite list of symbols from a finite alphabet? Dmharvey 16:43, 24 May 2006 (UTC)
Some are potentially infinite, I think you realize that. -Dan 18:40, 24 May 2006 (UTC)

I apologize if I have annoyed you with my off-topic talk page ramblings. Incidentally if the posts immediately above this was also an issue, I assure you it was meant in fun. Cheers, -Dan 20:59, 26 May 2006 (UTC)

No, no problem; I have no objection to general chattiness. I just think the discussion on that page is getting kind of long, and something should probably be done about it to reclaim the page for its intended purpose. But I wasn't annoyed, and no apology is necessary. --Trovatore 22:29, 26 May 2006 (UTC)

Inaccessible cardinal axiom[edit]

Not sure this is a standard name. Personally I wouldn't give it a name but would just call it "there exists a proper class of inaccessibles". The hierarchy of axioms is too finely divided to give every axiom a name (hard enough just keeping track of the large-cardinal properties). Anyway I've never heard this usage among set theorists. --Trovatore 03:33, 27 May 2006 (UTC)

You know, I was just about to post a comment on User talk:JRSpriggs and ask him to comment on the actual usage of this axiom, but you'll do just as well. Anyway, I just read an informal paper which admitted that the axiom is not often used, and was arguing that it ought to be used. Actually, he's talking about the universe axiom' with that name, not the name inaccessible cardinal axiom. I can't comment on how much those names are used. Let me change the language a little and see how you like it. -lethe talk + 03:41, 27 May 2006 (UTC)
I don't think it's so much "seldom used" as seldom called that. It's really a very weak axiom as these things go. I suppose it's adequate for category theorists who want only to talk about Grothendieck universes–provided all they want to prove in those universes, orthogonally to the Grothendieck–universe stuff itself, is what can be proved in ZFC. But what if you want more large–cardinal strength in the universes than that?
The axiom of the form "there is a proper class of blank" that's currently of the most interest, I think, is the immensely stronger proposition "there is a proper class of Woodin cardinals". That's because that's about the minimum you need to make Ω-logic work sensibly.
But of course that's off-topic in an article about inaccessibles, whereas the axiom you mention is not. And the axiom is true, of course. I'm just not sure it has enough separate importance to give it a highfalutin name; it's just a not-so-distinguished point in a very long and finely-divided hierarchy. --Trovatore 03:57, 27 May 2006 (UTC)
Well, I understood that Grothendieck gave it a name, and I think that would be good enough, even if in modern set theory it's not very interesting. I'll admit that the paper wasn't crystal clear on that. Maybe Grothendieck only named the universe axiom and not the inaccessible cardinal axiom. In any case, do you have a suggestion? Excise the name altogether? But then what will we name the section header? -lethe talk + 04:15, 27 May 2006 (UTC)
How about "A proper class of inaccessibles"? --Trovatore 04:30, 27 May 2006 (UTC)

Re "New try at first para"[edit]

Trov: can you say if my lastest suggestion for a new first paragraph at Talk: mathematics is acceptable to you? I'm trying to generate a consensus there. Thanks Paul August 18:49, 31 May 2006 (UTC) (P.S. nice new article on Suslin ;-)

Large cardinal property[edit]

Please check the new version of the first paragraph of Large cardinal property to make sure that it is correct. JRSpriggs 05:01, 8 June 2006 (UTC)

Well, it's not worse than it was. On rereading it I'm a little concerned that it gives too much of an impression that this is an exact definition of large cardinal property (even though this is explicitly disclaimed later in the section). BTW I changed the all-caps to italics. --Trovatore 22:21, 8 June 2006 (UTC)
Thanks for checking it. I felt that the old version was not as clear as it could be. I agree that the definition is not exact, but I do not see any better way of saying that than it already does. JRSpriggs 04:55, 10 June 2006 (UTC)

Arithmetical and Borel hierarchies[edit]

I edited Arithmetical hierarchy this morning. I saw in the talk that you were thinking of it in terms of classes of reals. I think that that meaning should go in the article Borel hierarchy which I am hoping to get to soon. —The preceding unsigned comment was added by CMummert (talkcontribs) 12:59, June 13, 2006.

Hi Carl,
I think the sets-of-reals meaning belongs in arithmetical hierarchy. It's the lightface counterpart to the Borel hierarchy, and it really is the same idea as for the sets of naturals. Just a little awkward to word. --Trovatore 13:28, 13 June 2006 (UTC)
I agree that they are the same underlying idea. My hesitation is that the lightface Borel hierarchy (sets of reals) goes up to omega^{CK}_1 but the arithmetical hierarchy (sets of naturals) only goes to omega, so you can't count quantifiers in the lightface Borel hierarchy. My conception of the AH is closely tied to Post's theorem and counting quantifiers. I would appreciate your thoughts on how to arrange things, and I'll hold off the BH article for a while to think about it. (I apologize for forgetting to sign my previous comment.) CMummert 13:57, 13 June 2006 (UTC)
I edited analytical hierarchy. What do you think of the general layout? Would a similar approach satisfy you for arithmetical hierarchy? CMummert 15:17, 13 June 2006 (UTC)

"If" in definitions[edit]

I did not see any contribution from you to the discussion about this topic which I initiated at Wikipedia_talk:WikiProject_Mathematics. However, since you are one of those who has changed "iff" to "if" in definitions, I would like to know what your justification is. I explained my position in the subsection I just added, Wikipedia_talk:WikiProject_Mathematics#Using a conditional rather than a biconditional in a definition is wrong. JRSpriggs 04:03, 20 June 2006 (UTC)

Since I still find "if" offensive and you still find "if and only if" offensive, I am wondering whether we could agree on some third usage which is tolerable to both of us? For example, "means" or "is defined as". Would either of them be acceptable to you? JRSpriggs 05:25, 22 June 2006 (UTC)
Heh, JRS and Trov trying to decide the fate of the world. :) As far as I am aware, 'if' is the standard, and I don't think anything can be done about it. :) Oleg Alexandrov (talk) 16:02, 22 June 2006 (UTC)

Possible covariance matrices[edit]

What are the restrictions on what matrices can be covariance matrices? I guess the matrix has to be symmetric; is any symmetric matrix a possible covariance matrix? --Trovatore 23:11, 19 June 2006 (UTC)

I've now made the answer to this question into a new section in the article titled covariance matrix. The answer is that a matrix is a covariance matrix of a vector whose components are real-valued random variables if and only if it is a nonnegative-definite symmtric matrix with real entries. The proof involves a simple application of the finite-dimensional case of the spectral theorem. Michael Hardy 17:14, 22 June 2006 (UTC)

I notice that your question, "is any symmetric matrix a possible covariance matrix?", is the easy part. That some such matrices are NOT covariance matrices follows quickly from one of the identities. But a point of rhetoric: Your question, "is any symmetric matrix a possible covariance matrix?" is ambiguous. It could mean "is there any symmetric matrix that is a possible covariance matrix?" or it could mean "is every symmetric matrix a possible covariance matrix?". Michael Hardy 17:17, 22 June 2006 (UTC)

Thermodynamic temperature and absolute zero[edit]

Discussion moved to talk:thermodynamic temperature; please continue there. --Trovatore 15:45, 12 July 2006 (UTC)


Hi, I assume that you are not (talk · contribs), so I took the liberty of reverting his/her edit to your page. If you have indeed become a native de/it speaker overnight, please accept my apologies. --Aleph4 09:55, 3 August 2006 (UTC)

Photon in the box[edit]

Il Trovatore, please sto restoring this section. This section is a disaster, it talks about entities long abandoned in SR (rest/relativistic mass), it has no experimental foundation, it has no references, it is contradicted by other articles in the same page, it looks like someone's pet college exercise and is not conform to wiki's definition. Please remove it and stop reverting it, it is an embarassmentAti3414 00:32, 8 August 2006 (UTC)

Relativistic mass, rest mass[edit]

If you want to hang on these outdated concepts, fine. If you want to use them as a means of propping up an even more ridiculous concept, the "photon in a box" exercise picked off the John Baez FAQ, this is fine too. If you want to apply the concepts to calculating the "mass" of a system of photons, fine with me as well. This is what makes wiki a joke when it comes to the relativity chapter. Ati3414 00:32, 8 August 2006 (UTC)



Sorry if you didn't like the definition I was used to, it's just the only one to which I was exposed. I am wondering what you mean when you say it's "useful" to keep it your way; they seem, to me, equivalent, and I just saw my version as being simpler. I probably haven't seen or worked with as much with logic as you have, so I was wondering if you could enlighten me. Also could you recommend a book or two? thanks, --Bernard the Varanid 01:08, 8 August 2006 (UTC)

oh, also I should probably revert the similar change I made to List of first-order theories. I'll go do that now...--Bernard the Varanid 01:10, 8 August 2006 (UTC)

Actually, on reflection I'm not so sure. I thought I remembered that constant symbols didn't make the Ehrenfeucht–Fraïssé game any more complicated, but function symbols did. But I'd have to think it through again and see if I was really right about that. --Trovatore 01:13, 8 August 2006 (UTC)

"excessive" wikilinks[edit]

I fail to see the utility of removing wikilinks. --Michael C. Price talk 20:03, 9 August 2006 (UTC)

It's policy that you shouldn't link to the same article twice. In practice I think it's fine to repeat a link if the first link was much earlier in the article, to save people from scrolling up (see WP:SENSE and WP:IAR), but repeated identical links in the same short section are distracting and ugly. --Trovatore 20:08, 9 August 2006 (UTC)

Stop reverting[edit]

If you don't understand what you are dealing with then leave it alone, you are reverting back in antiscientific,antiquated POVs. Stick to your math, leave physics alone Ati3414 04:08, 10 August 2006 (UTC)

Create arguments page at Photon[edit]

Would you please create an arguments subpage at Talk:Photon and perhaps also Talk:Mass in special relativity as you did at Talk:Gödel's incompleteness theorems, and move all the back and forth with Ati3414 there. JRSpriggs 10:44, 13 August 2006 (UTC)

Hmm, that thought had occurred to me, but the problem is that the material is not so cleanly separated. All the stuff about exercises and thought experiments should go into "Arguments", but it's interleaved with opinions about what should appear on the article page, which (tiresome as some of those opinions are) actually do belong on the talk page. In the Gödel case it was easier; there were whole sections that had dropped any pretense of being editorial. But if you feel like wading through it, go for it. There's nothing technically hard about it. --Trovatore 18:03, 13 August 2006 (UTC)

How about a normal archiving then? The point is that the talk pages are much too long now. JRSpriggs 05:10, 14 August 2006 (UTC)

Nice "sonnet"[edit]

On my page, all things are sonnets
No matter their number or phonics,
I love them all, from half rhymes to triplets, }
And anacoluthon will fit it. }
So thanks I will extend to each of the wits }
And laurels I profer with the right extended
And, for the left, pray don't inspect it.

(Nice use of the polysyllable, there....reminded me of TSE's "polyphiloprogenitive, the sapient sutlers of the Lord." Geogre 02:27, 17 August 2006 (UTC)

The form, as you may know, is a double dactyl, and the hexasyllabic word is one of the requirements. Notwithstanding my favorite example, by Piet Hein, breaks that rule. I won't break his copyright, but I don't mind telling you who will: Go to this site and search for the word "grook".
I once won a (notional, but Totally Official) sheep with one of these. Search for "Michael Ray Oliver" and "xerolocality". (Yes, I figured out later it should have been "xerilocality", but the officials didn't notice at the time.) --Trovatore 04:08, 17 August 2006 (UTC)

Stop move of "Ordinal number"[edit]

User:Salix alba is planning to move Ordinal number to another name. Please stop him. JRSpriggs 03:49, 4 September 2006 (UTC)

Infinity and User:[edit]

I am all over this one! HighInBC 03:48, 13 September 2006 (UTC)

12 / 0 = 0, says school division chart[edit]

If evidence is found that there actually are schools which have sunk so low as to use this chart, it just might be worth a mention. -- Meni Rosenfeld (talk) 18:46, 2 August 2006 (UTC)
It's actually highly educational. It's a good early lesson that grownups don't always know what they're talking about, and just because you see something on a laminated chart doesn't make it true. --Trovatore 18:50, 2 August 2006 (UTC)

I looked at that web page, and I can't see anything on the chart that says 12/0 = 0. It's too small to read. How do you know it's there? Michael Hardy 20:29, 4 August 2006 (UTC)

Save the image to disk, and blow it up in ImageMagick or Eye-of-gnome or whatever you use. --Trovatore 20:50, 4 August 2006 (UTC)

Can you shed any light on how to do that? I looked at the html code for that page. I find various gif and jpg files, but none that appears to be that particular image. Michael Hardy 21:38, 19 September 2006 (UTC)

Well, it's browser-dependent, but in Mozilla I just right-click it, and choose "Save image as..." --Trovatore 21:41, 19 September 2006 (UTC)

Oh... right-clicking. I'm not used to that. Thanks. Michael Hardy 21:52, 19 September 2006 (UTC)

Observable Universe Comments[edit]

Trovatore, your comments on my talk page (we should henceforth use the talk page on the Observable Universe article) concluded with "...There is likely a planet somewhere whose observable universe does not even include the Earth, so it obviously can't be the same as Earth's observable universe." This statement is true of billions of planets because electromagnetic radiation follows the inverse-square law. There exist objects in the observable universe sufficiently far from each other that the inverse-square law kills any radiation one observer might detect from the other observer. By your definition then, there are billions of planets that would be "outside of the observable universe." But the observable universe is not defined by observers that live on Earth but rather upon the maximum possible physical size the universe could be, based upon inflation models. Thus, the observable universe does indeed include billions of star systems that technically can't "see" each other but which still exist within the same observable universe. If, as the article contends, scientists mean "observable universe" when they say "universe" then we cannot define the observable universe as that space excluding observers that cannot see each other's radiation. Within the current experimentally-supported (i.e. WMAP, et. al.) cosmological models the observable universe is the universe and anything existing outside of our own space-time is irrelevant (physically, that is). For these reasons primarily I originally deleted the "ball-shaped region surrounding the Earth" comment in the intro back in June. Until we find a source that supports this claim of a preferential reference frame it would not make sense to go back to that definition. The current intro. para. on the O.U. page now reflects, with proper verifiable citations, the scientific definition of an observable universe without reference to a particular observer. I am happy to discuss your take on these ideas from your mathematical background. Perhaps we can find a way to improve the article further together. Cheers, Astrobayes 19:32, 25 September 2006 (UTC)

There is no upper limit to "the physical size of the observable universe, based upon inflation models". It may well be infinite. Take a look at the responses to my questions at Wikipedia talk:WikiProject Physics, particularly those of Chris Hillman and JRSpriggs.
As for the inverse square law, that has nothing to do with it. I'm not talking about whether the intensity of light would be too low to be observed, but whether the light could get there at all, given that it can't follow a spacelike path --Trovatore 19:56, 25 September 2006 (UTC)
There is in fact an upper limit on the size of the universe and the sources I cited, which you deleted, again, explain this in very understandable terms. Three times now you have reverted a section that I put in, deleted its citations, and kept the same wording each edit - without citations to support what you've written. I have done a search to verify the edit you've made and I can not verify what you've edited with any source. According to the Wikipedia policy on verifiable sources, what you've written is therefore in dispute. Even if you can make a compelling personal case for why what you've put in the article might make sense, Wikipedia forbids original research, so there is therefore a burden on the editor (you) to cite references for what you've edited. I am therefore asking you, again, to kindly cite these sources because I'm exhausted at this debate and I'm ready to submit this article for arbitration. Again, the introductory paragraph in this article is not supported by any resource that I can find, be it scholarly article, periodical, or peer-reviewed journal. As it stands now it is physically confusing. In addition to this I would remind you that there is a three-revert rule in general here. So, neither you nor I can make another revert on this article until this matter is settled. Post your sources from where you obtained the phrase "ball-shaped region surrounding the observer." After an extensive search I find none that support such a definition of observable universe. You are stretching the limits of good faith here and I think it is time we get some arbitration on this article. Astrobayes 22:04, 25 September 2006 (UTC)
As to the first source: I'd need a ScienceDirect password to get it; it's possible that I can do this through one of my university logins but I'm not going to try right now (I'm at work). Please quote the exact text that you think supports your case.
As to the second: It flatly contradicts you. Note the second paragraph of the introduction: is certainly possible that the Universe extends infinitely in each spatial direction...
So there is, in fact, no upper limit imposed on the size of the (whole) universe by anything in current knowledge. --Trovatore 22:19, 25 September 2006 (UTC)
FWIW I'm with Trovatore on this. There is no limitation on the possible size of the universe, which may be either finite or infinite. Astrobayes is making a number of other strange claims, such as the observable universe forming a ball shaped region implying a special reference frame: it doesn't imply anything of the sort: it is consequence of the shape of the future and past light cones. --Michael C. Price talk 01:18, 26 September 2006 (UTC)
This is the problem... this "discussion" has become so entrenched in semantics and mathematics that my original edit I made to that article, the sources I cited, and the explanation I gave back in June (which have several times been deleted) are nothing like the statement in the preceeding paragraph. First and foremost, I am a physicist by education and training. And I am not attempting to make any strange claims. My problem with the original article was the statement, "...a ball-shaped region surrounding the Earth..." and my point was quite simply that we can define an observable universe without any mention of Earth, and there are strong arguments against an infinite universe in light of current observations. Period. And these are not my words; one great resource of many is to consult Misner, Thorne, and Wheeler's text on Gravitation, Chapter 27, pp.701+. The "Earth" bit has been removed from the article and I can live with that now. But my problem was always with putting the Earth as somehow important to define the reference frame for the observable universe, when doing so is not necessary; my problem was never with the spherical nature of the observable universe; in fact, relativity says it must be so. Since Wikipedia is an encyclopedia, for non-specialists, I was trying to stay away from technical arguments and all of the convoluted mathematics that subsequent discussions on this topic centered upon. Read the chapter I just cited in the M.T.W. text. You'll see that there are convincing physics arguments for having a universe with a finite radius. I appreciate that Trovatore and others are very skilled mathematicians. But a Ph.D. in set theory does not a physicist make. And I was simply trying to put aside all of my fancy education (we would all do well to do this when editing these articles) and instead read the article from a perspective of a curious youngster who had read a little on astronomy and physics in their local library. When I saw the "...region surrounding the Earth..." bit, my physics alarm went off. "This sounds like the celestial sphere," I said. Who cares where Earth is in all of this? If I were a youngster reading this in their local library I would be inclinded to ask, "Is not the observable universe the observable universe regardless whether we're in Andromeda, on Earth, or near Alpha Centauri?" So, I dug up some resources to help me answer that question, cited them, and they were promptly deleted (a good WP editor would have, instead of deleting them, moved them to the external links references, but that's another issue).
I am also a scientist and I do concede that as we relax our assumptions on any model, our results can change. Perhaps the universe is indeed infinite (doing so presents some problems with energy, but see the M.T.W. text reference above). But since the article is on the observable universe, anything that can not be observed (read: any universe we make up in our heads that may or may not exist outside of the observable universe). is as irrelevant as choosing a particular point of observation and saying that the view from there is somehow special. Again, my problem was always with the "Earth at the center" bit, not the sphericity of the observable universe. With the "Earth" bit taken out of the article, I'm happy and I'll let the rest of it go. I would also like to say that both Trovatore and I have reached our revert limit on the article. Any further edits on that particular section by anyone else can not be reverted by either Trovatore or me, Astrobayes, as doing so would really be in poor trust of WP policy. Cheers, Astrobayes 17:59, 26 September 2006 (UTC)
You posed the question: "Is not the observable universe the observable universe regardless whether we're in Andromeda, on Earth, or near Alpha Centauri?". The answer is no. PS I am a physicist not a mathematican. Reading MTW pg 750 I note the sentence "But today's view of cosmology, as dominated by Einstein's boundary condition of closure (k= +1) and his belief in , need not be accepted on faith forever"..."Observational cosmology will ultimately confirm or destroy them". Observation has already rejected one of these two articles of faith. Now take the argument back to the appropriate talk page. --Michael C. Price talk 18:25, 26 September 2006 (UTC)

Navigational boxes[edit]

"Oh bother" (well, somethign stronger). I was completely unaware of this - thanks for drawing this to my attention. I've started a discussion on it over at Wikipedia:WikiProject Mathematics. Tompw 15:13, 9 October 2006 (UTC)

Re: Markup in section headers[edit]

Sorry about that... I didn't realize it broke clickability. -- Moondigger 00:32, 17 October 2006 (UTC)

"a monarchy is never a republic"[edit]

er, that would be decidedly wrong. the presence of an executive heading one branch of a government occurs under a constitutional monarchy, such as what England, then Great Britain, had following the Revolution of 1688-89. reverted. Stevewk 15:28, 19 October 2006 (UTC)

  • hey, you're being ignorant. i buried my stuff in a footnote. ok, i'll have the Wiki guys step in. Stevewk 21:25, 19 October 2006 (UTC)

Image copyright problem with Image:NiceBobKitty.jpg[edit]

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don't replace HTML by unicode[edit]

please, could you stop making edits just to replace HTML to unicode, like in this edit ? on several pages it is explicitely mentioned that this should not be done. — MFH:Talk 23:29, 20 October 2006 (UTC)

Markup should never be used in section headers (though simple wikilinks, that is with no colon at the start, are OK). This is because the edit summaries reflect the markup, and when you click on them, you don't get sent to the correct anchor. So I will continue to remove markup from section headers. --Trovatore 23:38, 20 October 2006 (UTC)

Cardinalites and models[edit]

Cardinality is an inherent and absolute property of each set (if the set exists). If two models disagree on cardinality of the same set, then at least one of the models is deficient (e.g. countable model of real numbers according to the Skolem-Lowenheim theorem, which does not satisfy the Least-upper-bound axiom). Leocat 18:36, 21 October 2006 (UTC)

Which is relevant how to what I said? This is what I wrote:
so what you wrote at continuum hypothesis is kind of a natural mistake, but still wrong. I'm guessing you're thinking of CH as saying "there is no set of reals of cardinality strictly between that of the naturals and that of the reals", and so you'd think if you have more sets of reals, then you have more chance to find such a set.
What you're missing is that the smaller model and the larger one may not agree on whether a given set of reals has the same cardinality as R. Given a fixed set of reals X that's in both models, it's the larger model that might have a bijection between X and R, when the smaller one doesn't.
It actually works in exactly the opposite direction from what you might have thought. If N and M are two transitive models of ZFC both containing all the reals, with N contained in M, then if N satisfies CH, then M must also satisfy CH. But the reverse is not true. --Trovatore 06:48, 20 October 2006 (UTC)
Now, in the above case, obviously N is "deficient" (if it disagrees with M about CH). N fails to have a witness that the cardinality of the reals is ; that witness shows up in M. And in that case, CH is really true. But that doesn't falsify anything I said. --Trovatore 18:50, 21 October 2006 (UTC)
But what if CH is false? Then the richer model may have a witness to < continuum. (By the way, the Freiling's axiom of symmetry looks pretty convincing to me. What do you think about it?) Leocat 19:20, 21 October 2006 (UTC)

What do you mean by a witness that CH is false? I can imagine a witness that CH is true -- a well-ordering of the real numbers together with injections from each of its proper initial segments into the natural numbers. But what would your witness be? JRSpriggs 09:59, 22 October 2006 (UTC)

A construction (or at least a proof of existence) of a set whose cardinality is strictly between and continuum would be such a witness. This has been the problem in the research on CH so far, not establishing the cardinality of a set. Therefore it is natural to consider models containing certain subsets of R and enough functions to establish their cardinality. Leocat 17:03, 23 October 2006 (UTC)

Leocat, you still don't seem to have come to terms with the fact that "having cardinality between and the continuum" is not a property that's preserved upwards from a smaller model to a bigger one. The reason is that the larger model may have a bijection between the set in question and the continuum, that the smaller model lacks.
Whereas the property "being a bijection between and the continuum" is preserved upwards, between models that have the same reals. (It's not obvious, but is true, that if they have the same reals, then they also have the same ). --Trovatore 17:27, 23 October 2006 (UTC)
You should realize that your model may fail to establish "having cardinality between and the continuum", but having such cardinality is an absolute property of a set - either it has it, or it does not.
So you need a model that is rich enough to let you establish either existence of a set with such a cardinality, or a contradiction caused by the assumption that such a set exists.
You keep mentioning models that do not let you establish certain bijections, while this has not been the problem in the history of research on CH.
You have not answered my question about Freiling's axiom of symmetry. Leocat 14:27, 24 October 2006 (UTC)
  1. "Either the set has it, or it does not", in the sense that every mathematical proposition is either true or false, yes. But that doesn't help in this context. It's not an "absolute property" in the usual technical meaning of "absolute", which is that different models (restricted to a context-dependent collection of such models) agree on the property.
  2. Models do not "establish" anything, in the usual sense of the word "establish". Propositions are true or false in models; they are established (that is, proven), or refuted, in theories. Your use of language is a bit sloppy here. You need to distinguish carefully between syntax (theories) and semantics (models).
  3. Research on CH has moved on a bit from what you may know about it. Yes, the early work was about trying out various kinds of definable sets -- open sets, perfect sets, Borel sets -- and seeing if they could be of intermediate cardinality. Basically the answer to all those questions is "no" -- all sets "like that", in a sense I won't get into now, are either countable or have the cardinality of the continuum. That doesn't really help much in trying to figure out whether a radically undefinable set might have intermediate cardinality.
  4. Freiling's argument is interesting, but not convincing to me personally. Things like probabilities and measures don't work well with arbitrary, non-definable sets; Banach-Tarski is a good example of this. In fact Freiling admits that it's an argument not just against CH, but also against AC; since AC is obviously true in the full universe of sets, there must be something wrong with the argument in that context. --Trovatore 16:03, 24 October 2006 (UTC)
Would you enlighten me why Freiling's argument is an argument against AC? Leocat 18:18, 24 October 2006 (UTC)
I don't actually remember that (assuming I actually knew it at one point). But you can look up Freiling's article in the JSL, or one of the famous Penelope Maddy papers, "Believing the Axioms, I" and "Believing the Axioms, II". --Trovatore 05:32, 25 October 2006 (UTC)

measurable functions not closed under composition[edit]

Hi Trovatore, nice to meet you. Thanks for your thoughtful answer to my HelpDesk question on measureomorphisms last month. (Unfortunately it's out of reach now, the page has only more recent questions) I just put a comment on talk page of Measurable function, and hope it's ok I referenced what you said. Now I'm honestly wondering if they are actually closed under comp., but I've experienced many times apparently obvious reasoning blown away by something tricky when set or measure theory is involved. Regards,Rich 10:12, 4 November 2006 (UTC)

Kolmogorov complexity[edit]

Could you please have a look at that article. I am particularly concerned about the recently inserted picture of the Mandelbrot set. See my remark on the talk page. Although models of computation over the reals have been developed (e.g. by Smale, Shub, Blum and others) Kolomogorov complexity as dealt in this article concerns objects which are explictly encoded by finite bitstrings (Remark: what an encoding is for elements of a class of objects, is itself not entirely trivial. I think of an encoding as analogous to a chart on manifold; here two charts φ ψ are equivalent iff the overlap function φ ψ-1 belongs to some computational class such as PT.) In any case, I don't see how one can consider a class subsets of the plane large enough to include the Mandelbrot set as being encoded by finite bitstrings. I am aware that some very special classes iteratively defined fractals can be encoded by finite bitsrings, but it's not clear to me how that applies here.

In any case, I am very tried of the endless argumentation on WP.--CSTAR 18:33, 4 November 2006 (UTC)

Probability-based strategy AfD[edit]

Just a note to let you know that I have nominated the article you have edited, or expressed interest in, for deletion. See Wikipedia:Articles for deletion/Probability-based strategy Pete.Hurd 05:29, 7 November 2006 (UTC)

12/0 = 0, bis[edit]

Since you participated in the discussion at talk:division by zero about the chart being sold by an (allegedly) educational publisher that says that 1/0 = 0, 2/0 = 0, etc., perhaps it will interest you to know that at this web site where the chart is sold, the publisher now solicits opinions of the product. You can go there and tell them what you think. Michael Hardy 20:58, 9 November 2006 (UTC)

Thanks, Michael --Trovatore 21:01, 9 November 2006 (UTC)

About Category:Redirects from alternate names[edit]

Hi, Mike. Concerning the message you left me I will not recreate this category. By the way, you hold a PhD in mathematics, mathematics is one of my favourite subjects. I was very glad to know that Wikipedia has about 15 000 articles about mathematics which is more than the articles in Mathworld.

--Meno25 17:35, 10 November 2006 (UTC)

Thanks, Meno. Are you getting your degree in math?

--Trovatore 04:59, 11 November 2006 (UTC)

  • Sure I will try, but in Egypt where I live, I am still young for this.

--Meno25 02:29, 14 November 2006 (UTC)

Winning strategy[edit]

Do you have a citation from a game theory text that this is within the scope of game theory rather than combinatorial game theory? I checked the usual suspects (Osborne & Rubinstein, Gibbons, Tirole & Fudenberg) and can't find it. ~ trialsanderrors 19:46, 14 November 2006 (UTC)

I have no idea. It's a bit of a problematic article. It already existed when I started working on determinacy, and it was interfering with the more technical definition (though of the same idea) that I wanted to make there. But it's definitely not combinatorial game theory. Maybe it's not ordinary game theory either. I think it's more "theory of real-world two-player perfect-information games". --Trovatore 20:15, 14 November 2006 (UTC)
Ok, I brought it up at User talk:Trialsanderrors/SCIENCE#Test case: Winning strategy. ~ trialsanderrors 20:33, 14 November 2006 (UTC)
The article appears to me to be correct. It is just stated in a more general and less mathematical way than in Determinacy. Also, I do not think that it is limited to two-person games nor to perfect-information games. JRSpriggs 09:53, 15 November 2006 (UTC)
Yeah, there's nothing really wrong with the article; it just doesn't fit neatly into the larger scheme of things. In what context is it trying to explain winning strategies? Barnaby Dawson wrote it, I think, to support axiom of determinacy, but it isn't well-suited for that purpose in my opinion. The first time a person sees this notion, if it's described in terms of real-world board games like chess, he's likely to be thinking too much of algorithmic strategies.
Charles Matthews did some rewriting of the article under the assumption that it was about real-world games (he's a rather well-known go player, I think) and it didn't really fit with the way strategies are usually described in determinacy theory. So I put a definition inline in determinacy, possibly too terse, but more narrowly tailored to the subject, and put the pseudo-dabline at the top of winning strategy. I don't know what the best global solution is. --Trovatore 17:20, 15 November 2006 (UTC)
Why not just make winning strategy into a disambiguation page? This solution appears to have worked for random number, another article that was vaguely related to many topics but not really about any one of them. CMummert 17:31, 15 November 2006 (UTC)

Re: Hydrogen carbonate[edit]

As I mentioned in my reference desk post, which I assume you already saw, I would like to see sources for this usage you propose. Though I can easily find references to hydrogen chloride, hydrogen sulfate, hydrogen phosphate, and so on referring to the compounds, I cannot find any reference to hydrogen carbonate referring to H2CO3, nor does it match what I was taught (I was a chemistry major back in college). I did not mean to imply that I thought the term was logical or preferable. — Knowledge Seeker 06:36, 17 November 2006 (UTC)

Romano Prodi[edit]

Just to let you note that an IP address has put back the infamous KGB allegations sections. Curiously, it is one of the same IP addresses as before. --Angelo 17:54, 17 November 2006 (UTC)

Just a quick not imploring you not to revert again, I don't want to see you being blocked for a 3RR. Kind Regards - Heligoland | Talk | Contribs 16:58, 22 November 2006 (UTC)
Thanks for the note. Actually I could revert another time without violating the letter of the law, but I won't today. Others can take it up. To tell the truth I'd be less inclined to fight the addition of the material if it had been added by someone with an established username under which he continued to edit. For most purposes we can say anon editors are equal to those who give their names, but when it comes to controversial edits, I don't think we should be forced to give equal weight to ghosts. --Trovatore 17:07, 22 November 2006 (UTC)
According to Wikipedia:Biographies of living persons, the WP:3RR does not apply to removing unverified derogatory claims about a living person. "In cases where the information is derogatory and poorly sourced or unsourced, this kind of edit is an exception to the three-revert rule." JRSpriggs 07:02, 23 November 2006 (UTC)

Ultrafilter explained through hyperreal numbers as a motivating example[edit]

I am sorry if I have spoiled the Ultrafilter article. I thought my contribution to serve as a good motivating example. Shall I begin to amend it, or shall I revert it entirely (e.g. because of being out-of-place etc.)? Thank You for Your attention. Physis 16:39, 19 November 2006 (UTC)

Hm? Why do you think you've spoiled it? In one edit summary I said I hadn't read it yet, which I still haven't. I probably shouldn't even have mentioned that. --Trovatore 18:35, 19 November 2006 (UTC)
Thank You for the quick answer! Best wishes, Physis 19:22, 19 November 2006 (UTC)

von Neumann[edit]

Care to explain why the lowercase tag is innapropriate to articles that begin with "von Neumann"? None of the articles use "Von Neumann" in the body of the text. - Stormwatch 15:30, 24 November 2006 (UTC)

The WP capitalization convention is to start article titles with a capital letter. In a few cases this does violence to the meaning of the phrase. A good example is e (mathematical constant). It is rendered "E" in the article title, but the constant is never called "E", and if that were used in print, people simply would not understand what you mean.
There is no such problem with "von Neumann". Von Neumann's name does sometimes use a capital "V", namely when it starts a sentence (as, for example, in this sentence). So it's not true to say that the title is incorrect; since the V is the first letter of the title, by WP capitalization conventions, the capital V is correct. --Trovatore 19:01, 24 November 2006 (UTC)
So you couldn't move omega-consistent theory because you didn't want to go through a simple formality, and instead I had to go through the trouble ;) I hope you feel a bit guilty now, and that you'll willing to give #Reconsider adminship? another thought. I assume you finished your moving house, so: would you accept a nomination to become administrator? Per favore? -- Jitse Niesen (talk) 08:46, 25 November 2006 (UTC)

Wikipedia:Articles for deletion/Alexander Litvinenko assassination[edit]

May I suggest that you speedily close Wikipedia:Articles for deletion/Alexander Litvinenko assassination. This article has thousands of edits in its edit history, so deleting is not an option. You are of course free to revert the move and split, if you feel so (or suggest it). -- Petri Krohn 02:05, 4 December 2006 (UTC)

The article in now on Main page, so this is urgent. --Petri Krohn 02:16, 4 December 2006 (UTC)
I misapprehended what had happened, for which I apologize. But IMHO you shouldn't have moved in the first place; you should have created a new article to move the content. The edit history belongs with the bio, not with the article about the poisoning, and there's now no easy and clean way to get things back to where they should be. --Trovatore 06:51, 4 December 2006 (UTC)
Actually it now seems to be back where it should be. And by the histories, this happened hours ago, whereas it didn't seem to be true when I checked half an hour ago. I really don't understand quite what has happened here. --Trovatore 07:10, 4 December 2006 (UTC)