User talk:AxelBoldt

Please add new comments at the bottom. I will reply on this page. If I wrote something on your talk page, please reply there. The idea is to make quoting easy and keep conversations in their logical order.

Older talk can be found in User_talk:AxelBoldt/Archive.

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Hi Axel: I am trying to find out who originated the page for the Goedel's incompleteness theorem. My interpretation of its History page suggested to me that it was User:Maveric149, but he said he thought it might be you.

I am thinking about making a change to what appears to be something that has been there since the beginning of that page, and if you are the originator, I would like to first ask your opinion about this. I find that the notation under the proof sketch to be a little awry. In particular, for example, the notation G(F) should be G(F(x)). I don't want to go into a lot of detail here if you are not the right person, so I would appreciate it if you would clarifiy that for me first.

Best wishes, User:BuzzB Apr 3, 2003

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Hello Axel,

Thank you for correcting the PMBOK entry.

I'm looking for volunteers to develop a GNU Free Documentation License Project Management Standard (just like the PMBOK, but possibly better). What do you think about it? User:Mkoval Apr 3, 2003.

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Hi Axel:

Thank you for your reply to my previous message. It is not my intention to be predantic, but I think my proposed changes make the sketch slightly easier to understand. In addition to notational changes, and the adding of some clarifying text, I changed "proven" and "unproven" to "proved" and "unproved" because I could not find "unproven" in my dictionary. I will reply on your opinion about whether my proposed changes are useful before making them. My proposed revision is below. I have underlined my changes to highlight them.

By the way, I am currently working on a short paper which reconsiders the incompleteness theorem in the context of a three valued system where the three truth vlaues may be interpreted as TRUE, FALSE, and PARADOX. I wonder if you might be interested in reading it.

Proof sketch for the first theorem

The main problem in fleshing out the above mentioned proof idea is the following: in order to construct a statement p that is equivalent to "p cannot be proven", p would have to somehow contain a reference to p, which could easily end in an infinite regress. Gödel's ingenious trick, which was later used by Alan Turing to solve the Entscheidungsproblem, will be described below.

First of all, every formula or statement that can be formulated in our system gets a unique number, called its Gödel number . This is done in such a way that it is easy to mechanically convert back and forth between formulas and Gödel numbers. Because our system is strong enough to reason about numbers, it is now also possible to reason about formulas.

A formula F(x) that contains exactly one free variable x is called a statement form. As soon as x is replaced by a specific number, the statement form turns into a bona fide statement, and it then is either provable in the system, or not. Statement forms themselves are not statements and therefore cannot be proved or disproved. But every statement form F(x) has a Gödel number which we will denote by G(F). The choice of the free variable used in the form F(x) is not relevant to the assignment of the Gödel number G(F).

By carefully analyzing the axioms and rules of the system, one can then write down a statement form P(x) which embodies the idea that x is the Gödel number of a statement which can be proven in our system. Formally: P(x) can proved if and only if x is the Gödel number of a statement that can be proved. (While this is good enough for this proof sketch, it is technically not completely accurate. See Gödel's paper for the problem and Rosser's paper for the resolution. The key word is "omega-consistency".)

Now comes the trick: a statement form F(x) is called self-unprovable if ~P(F(G(F))), i.e. the form F applied to its own Gödel number, is not provable. This concept can be defined formally, and therefore we can construct a statement form SU(y) which embodies the concept: SU(y) is provable if and only if y is the Gödel number of a self-unprovable statement form. That is, y = G(F) for some particular form F(x), and ~P(F(G(F))). Then define the statement p = SU(G(SU)). This is the statement p that was mentioned above.

Intuitively, we are now asking the question: "Is the property of being self-unprovable itself self-unprovable?" This is very reminiscent of the Barber paradox: the barber who shaves precisely those people who don't shave themselves, does he shave himself?

If p were provable, then SU(G(SU)) would be true, and by definition of SU, that would make y = G(SU) the Gödel number of a self-unprovable statement form, hence SU would be self-unprovable, which by definition of self-unprovable means that SU(G(SU)) is not provable, but this was our p: p is not provable. This contradiction shows that p cannot be provable.

If the negation of p were provable, then, assuming our system to be consistent, p cannot also be provable, i.e. SU(G(SU)) is not provable, and by definition of SU this means that y = G(SU) is not the Gödel number of a self-unprovable form, which implies that SU is not self-unprovable. By definition of self-unprovable, we conclude that SU(G(SU)) is provable, hence p is provable. Again a contradiction. This one shows that the negation of p cannot be provable either.

Best wishes, User:BuzzB

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Hi Alex:

I uploaded a revision in which I accepted your suggestion to leave the text with G(F) rather than G(F(x)), but I added some explanatory text.

I just printed out a copy of the Goedel proof from the web page reference, but I haven't had time to re-read it yet. Off hand, I tend to agree that the "only if" should be removed. I'm not sure I get the connection with inconsistancy, although if there is a connection then of course every statement would be provable.

Regarding my paper on a three valued interpretation, it is a work in progress. I don't expect to have a complete draft for a while yet, but if you would like me to send yoi a sketch of what I have in mind, I would be happy to do that.

Best wishes, BuzzB

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Hi Alex:

I think your edit to the proof sketch is a very good improvement.

I finally got my personal web site up. There is a link on my User page. I would appreciate any comments you would care to make about anything I have there. When I complete a draft of the paper on a three valued re-intepretation of the Goedel theorem, I will post it there.

Best wishes, BuzzB

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Many of your math entries (I was reading the one on the Open mapping theorem) can't be understood unless one is already studying that field of mathematics, or a similar topic. Could you define some of the terms that you use in the article? LittleDan

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Re: Persuasion Technology. A bizzarre, rambling document. I tried paring it down to make it clearer some months back. Not that fuzzy thinking is much improved by fixing grammar. I had hoped the author would take the hint to de-ramble it. Instead, the author immediately restored the original text verbatim without comment. So I put the NPOV dispute at the top and watched. If the author is now banned, perhaps you will fair better. User:Williamv1138:Williamv1138[?]

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Axel, I am writing to you because you have been active in Wikipedia for a long time. I have been in an edit war with JTDIRL and 172 on the China page, and I think there is both a need for some intervention, and an intervention that is not based on any argument about China, but rather about Wikipedia conventions, especially NPOV and naming conventions. I wrote to Mav who made a very brief and in my opinion constructive comment on the talk page a couple of days ago, although nothing has come of it. I have thought of asking some others, but you are one of the most experienced people here. And, as I said, I think what is most needed now is some explicit discussion of Wikipedia conventions.

To fully gradp the debate behind the edit war you would have to read a lot. Minimally, I would suggest reading the entire Talk: China (Archive 3) and Talk: China[?] pages (which I know is a lot to ask of someone who may not be so interested. As a party to the dispute and biased, I don't want to misrepresent it, but I will try to sum it up.

The question is, how to identify the Chinese (specifically, PRC) state. The article identified the state as communist. I checked the Chinese Constitution which states that it is a socialist state; an official Chinese website states that it is not a communist state. JTDIRL and 172 responded that all political scientists identify China as a communist state and that we should go by what Western scholars do. I talked to a few colleagues of mine -- a sociologist, two anthropologitsts, and a political scientist. They told me that many political scientists used to label China a communist state but that they are moving away from that designation, considering it inaccurate and meaningless; that many political scientists and most other scholars identify China as a socialist state, although some qualify it as "late" or "post" socialist. Now JTDIRL claims that it doesn't matter what political scientists say, that what ought to be presented is a "formal encyclopædic definition."

Now, I never heard of this phrase and doubt that it should be the basis of our deciding how to identify any state, as what we are trying to do is, arguably, devise a formal encyclopedic definition. I think he means we should call it a communist state because other encyclopedias do. I still think we ought to call it something that reflects the current state of scholarship.

But I hope you can see why I think this is a matter of clarifying general wikipedia conventions or norms, and not just a debate over China. And I hope you understand why I have turned to you.

I am not asking anyone to say "SLR is right and JTDIRL is wrong." I am asking the community, such as it is, to discuss the conventions and clarify them as they may apply to the case.

If you do not feel comfortable doing this, but understand why I bring it up, could you post this on the listserve for discussion? Either way, I appreciate your reading this far! Slrubenstein

Thanks for trusting me with this -- I don't want to get involved however. I'll post it on wikien-l (/pipermail/wikien-l/). AxelBoldt 04:45 Apr 25, 2003 (UTC)

Thanks -- I understand, and appreciate it, Slrubenstein

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Hi, From the page history I see that you're a main contibutor to the Euler pseudoprime page, I'd be in favour of moving the page and have given my reasons on Talk:Euler pseudoprime. I thought you may like to comment. Cheers -- Ams80 11:50 May 8, 2003 (UTC)

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TeX Etymology

Why is it called TeX? Surely the name of such a useful tool must have a significance, doesn't it? This information would interest the reader. I Googled a bit and couldn't find out anything. --Menchi 19:30 May 13, 2003 (UTC)

I don't know the etymology, but I agree it would be interesting to know. It's possible that "TeX" is just a variation on "text" though, with fancy letters and pronunciation. I would think that Knuth gave his reasons in the TeX book. AxelBoldt 20:46 May 13, 2003 (UTC)

Found it. Have included in the article. --Menchi 20:15 May 15, 2003 (UTC)

Nice. I noticed that you use font=symbol for tecne. It would be better if you used the greek HTML characters directly (wikipedia:How to edit a page), since the symbol font only works on Windows. Cheers, AxelBoldt 20:39 15 May 2003 (UTC)

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Hi Axel. One of your references in the linked article refers specifically to Columba livia, and it seem improbable that the other items refer to a different species (although it's a long time since I had to study F X Skinner) so I've moved it to Rock Dove. If I've got it wrong, please move it back. If you think it should be in both articles anyway, please make it clear it's Feral Pigeon in the group article. thanks jimfbleak 17:25 May 15, 2003 (UTC)

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Hi Axel!
Thanks for noticing I hadn't named the painter (Renoir) in the Impressionism article. I can't believe I did that!
Adrian Pingstone 15:48 16 May 2003 (UTC)

Axel, I'm no maths guru, but I confess to some suspicion of User:Stupidmoron's contributions so soon after the other nonsense, now deleted. Mind running an eye over them? Tannin 13:43 20 May 2003 (UTC)

Thanks Axel. That's good to know. Tannin

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Hi there - you had a slight factual error in the resignation of Otto von Bismarck. He was actually dismissed by the Kaiser, rather than as a result of the gains of rival political parties as you suggest. Dare I be cheeky and ask for the W1 you have offered for factual errors? - David Stewart 09:06 21 May 2003 (UTC)

Great, thanks. W1 is on its way. AxelBoldt 19:12 21 May 2003 (UTC)

Many thanks! - David Stewart 01:31 22 May 2003 (UTC)

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Axel,

I just noticed that you posted a question a month ago to my talk page about my additions to the quaternion entry. ... I've written up a response there. Steven G. Johnson (Jun 9 2003)

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Axel, I put a new proposal for naming of symbolic logic. Definetely you know more about math and give me comments if you don't mind. Cheers! -- Taku 15:31 31 May 2003 (UTC)

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Hi, found this (http://art-bin.com/art/medhistorypix/omedicalimages) on one of the blogs I frequent, and thought you might know what to do with it, if anything. Koyaanis Qatsi

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Hello Axel, I fixed a couple of minor factual errors on Otto von Bismarck. Since that's listed on User:AxelBoldt, does that earn me the Wikipedia:WikiMoney you pledged? :-) -- djmutex 10:50 4 Jun 2003 (UTC)

Sure, thanks! AxelBoldt 18:04 4 Jun 2003 (UTC)

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Hi, Axel,
I'm no mathemetician, but you are, so I come hat-in-hand asking for a favour. The constellation of contributions at neutrosophy, neutrosophic set, Florentin Smarandache, outer-art, the contributions of new user "Lit-sci" (/w/wiki.phtml?title=Special:Contributions&target=Lit-sci), the contributions of 64.106.24.51, which maps to University of New Mexico Gallup Branch (/w/wiki.phtml?title=Special:Contributions&target=64.106.24.51), and of 64.106.24.53, of that same institution (/w/wiki.phtml?title=Special:Contributions&target=64.106.24.53) lead me to suspect we're being scammed into covering a fairly idiosyncratic concept as though it were generally accepted. Is this something more than say 50 people have heard of/found useful? I'd be interested in your comments. -- Someone else 20:49 4 Jun 2003 (UTC)

On the contrary, I thank you for having the knowledge and inclination to set it all in its proper context! -- Someone else 23:12 5 Jun 2003 (UTC)

Thanks for that Axel - I had ever confidence somebody knowledgeable would come along and fix it eventually :) Martin

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Very nice work on Gertrude Stein, which I hope was more enjoyable than the equally-appreciated-though-undoubtedly-more-gruelling grunt work you've been doing on the Smarandistas. -- Someone else 23:52 9 Jun 2003 (UTC)

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Hi, could you take a look at DXM when you get a chance? I tried to correct the formatting and convert fragments to sentences, but I left parts of it alone because I didn't know how to change them, being generally unversed in the subject. Thanks. Koyaanis Qatsi 05:39 12 Jun 2003 (UTC)

DXM looks much better now, thanks. Glad you liked the wikien missive; Eclecticology has given me an idea--maybe with some practice I could be a comedy writer. ;-) Koyaanis Qatsi 20:57 12 Jun 2003 (UTC)

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Would you mind explaining your changes to limit (mathematics)? Pizza Puzzle

yes but from "division-by-zero" you cut:

• In cases where substitution results in 0 / 0, a limit probably exists; in other cases (such as 17 / 0) a limit is less likely. For instance; if f(x) = x³ + 1 / x - 1; then, if one substitutes 1 for x, one will obtain 2 / 0; the limit of f(x) (as x approaches 1) does not exist, as f(x) is unbounded
  • this should be rewritten to state, "the numerator is 0" rathern than " 0 / 0" but I do not think it should be cut. Pizza Puzzle

• and (x² - 6x) / x involved a notably different technique than (x³ - 1) / (x - 1) , which I argue to be just as "nice" of a technique

• and, yes, the absolute value definition duplicates a paragraph further down in the formal section, but it does so informally which makes it far more useful for the neophyte reader Pizza Puzzle

The statement "In cases where substitution results in 0 / 0, a limit probably exists; in other cases (such as 17 / 0) a limit is less likely." is simply false: 0/0 may or may not exist and 17/0 never exists. We have examples of both cases.

The technique for the two example functions is the same: use algebra to rewrite your function until you can plug in c. AxelBoldt 21:25 18 Jun 2003 (UTC)

You also deleted the section on one-sided limits. Pizza Puzzle

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1.b4 (Your move!) You also deleted (at product rule):

• Development of this rule is credited to Leibniz; who demonstrated that (x + dx)(y + dy) - xy = x(dy) + y(dx); as (dx)(dy) is "negligible".
  • As sources I offer The History of Mathematics by Burton and Calculus of a Single Variable: Early Transcendental Functions (3rd Edition) by Edwards, Hostetler, and Larson

Is this not true?

Oh yes, I meant to put that into a history section, maybe with a little bit more information, then I forgot about it.

Also, I am of the understanding that this is the Product Rule; not merely a product rule. Pizza Puzzle

Yes, but in the math arena we decided a while ago to use lower case throughout, for instance Fermat's last theorem. I agree it's a bit strange. 1. ... c6. AxelBoldt 15:27 19 Jun 2003 (UTC)

If everyone agrees its "strange" (I havent heard anybody actually support it) why continue to do it?

Well, some math books use the lower case style, and there's a general tendency to use lower case in titles, because in article texts people are much more likely to write "product rule" than "Product Rule".

Doesn't f(x) = (x² - 1) / (x - 1); have a discontinuity?

No: the function is continuous at each point of its domain, which doesn't include 1.

1.b4 c6 2.c4 Pizza Puzzle

2.... d5 AxelBoldt 04:18 21 Jun 2003 (UTC)

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Yes, f(x) is continuous at each point of its domain; but, the function has a discontinuity at x = 1; thus, the domain of f(x) is all real numbers except x = 1. Or so I understand...

1.b4 c6 2.c4 d5 3.e3 Pizza Puzzle

The Wikipedia articles on the laws of non-contradiction are not as clear as they could be. Would you mind taking a look at the articles on Law of excluded middle and Law of non-contradiction? I was wondering if we could give an example showing how the these are similar, and how they are diferent; Functionally, when are they practically identical? What examples can best show us the differences between what these laws? RK 00:28 28 Jun 2003 (UTC)

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moin Axel! sorry für die späte antwort.. ganz ehrlich habe ich den artikel de:Walletjes damals (in meiner newbie-zeit bei wikipedia) ganz aus dem kopf heraus geschrieben. ich bin mir wirklich nicht mehr ganz sicher woher ich diese info hatte, ich denke das kam von einem freund der ein paar jahre in amsterdam wohnte.. (zu meiner schande habe ich damals auch nicht wirklich nach-recherchiert). wenn du dich da besser auskennst ändere es bitte! gruß! pit 16:38 2 Jul 2003 (UTC)