User talk:Jakob.scholbach/Archives/2009/February

Featured topics

Hi. I just came across the following Wikipedia:Featured topics. There are currently no "featured" math topics, and it could be cool to have one. I'm not sure what you're planning on doing after Vector space, but I thought maybe you'd want to know about this featured topic thingy (or maybe you already knew). Sorry I haven't really helped yet with the featured article, I have been immensely busy, and I'm rather certain it will continue until I'm done with my PhD. Keep up the good great work! Cheers. RobHar (talk) 06:19, 4 February 2009 (UTC)

Yeah, I'm also a bit thrilled by the FT idea, but I didn't work in that direction in a proper sense.

I'm currently planning to let vector spaces rest a bit, bring matrix (math) to GA and possibly beyond, and maybe renominate vsp for FAC. It would be an idea to make Algebra a featured topic, but I don't know how seriously they take, e.g., "There is no obvious gap (missing or stub article) in the topic. " This would certainly kill all plans of doing a featured topic of a range that is that big. Jakob.scholbach (talk) 08:40, 4 February 2009 (UTC)

Yeah, I was thinking algebra as well, and indeed I found the clause you mention troublesome. It does seem like they have a way around that: something they call overview topics. A topic could be "Basic structures in algebra" like vector space, groups, rings... RobHar (talk) 09:06, 4 February 2009 (UTC)

OK. Anyway, it seems reasonable only with at least 2 or 3 more FA or GA... This is where you ${\frac {\text{sh}}{\text{c}}}{\text{ould}}$ :) come in. I know doing a PhD and WP in parallel is a lot, since I'm in the same position, but it is feasible to do both. Best, Jakob.scholbach (talk) 09:54, 4 February 2009 (UTC)

Greece Runestones

Dear Jakob, I wonder if you would like to have a look at your reasons for opposing and strike some points. I'm hesitant to add more sections because of the size of the article since it must be less than 100kb and it is already 85.--Berig (talk) 18:29, 7 February 2009 (UTC)

Sure. To do so, it would be helpful if you would actually reply to the points there (simply "Done", or reply why you don't want to do certain things). Jakob.scholbach (talk) 22:21, 7 February 2009 (UTC)

I have added a section on the special signs you wondered about and I have tried to make a more adequate lead now.--Berig (talk) 15:31, 8 February 2009 (UTC)

Vector space

I saw that you were looking for someone to read it. I don't qualify for the lack of knowledge, but I don't think in mathspeak, so maybe I'll have a crack at the lead and leave you a message here. Awickert (talk) 05:14, 9 February 2009 (UTC)

OK - just from giving it a skim, it seems to be on the dense and rigorous side to me. When I think of a vector space, I think of a set of vectors that define a n-dimensional space that consists of everything those vectors can reach. It's a much more tangible thing to me than a mathematical construct. So maybe something like this (which is rough, and I might be making mathematical terminology atrocities):

"A vector space is the set of all points in space that is accessible by combining multiples of the vectors that describe it."

And then maybe: "Its dimension is defined by the number of vectors in independent directions that constitute it; for example, three mutually perpendicular vectors define a three-dimensional rectangular coordinate system that is often used to describe the three observed spatial dimensions."

I don't know if the suggested sentences are any good, but I would suggest to ground it to the real world right away in some way and tell a reader what it can mean outside of just the formal mathematical definition.

Awickert (talk) 05:23, 9 February 2009 (UTC)

One other dubiously useful comment that could show you how a non-mathematician may use vector spaces as a construct for thinking: when solving problems with large numbers of unknowns and not enough constraints, I always think of the problem in terms of narrowing down an n-dimensional vector space and trying to get it down to a single point (i.e., use basic physics to constrain this, use this empirical relationship for that, can't constrain this axis but can set boundary conditions, etc. etc.). Awickert (talk) 05:27, 9 February 2009 (UTC)

Thank you for reviewing the article. I'm currently out of town, and have limited internet access. I will get back to you and your suggestions early next week. Thanks again. Jakob.scholbach (talk) 12:03, 10 February 2009 (UTC)

Sure - sorry for the stream-of-consciousness state of my comments. I'll be watching your talk page if you want to continue the conversation sometime. Awickert (talk) 17:00, 10 February 2009 (UTC)

I'm back now. Could we meet over at Talk:vector space to discuss things? Jakob.scholbach (talk) 21:38, 16 February 2009 (UTC)

OK Awickert (talk) 21:43, 16 February 2009 (UTC)

Alternative counter

I noticed on User talk:Interiot that you were experiencing the same problems with the edit counter as I was. I've located another edit counter that you may want to try. Best regards --Eustress (talk) 03:47, 20 February 2009 (UTC)

Thanks and a request

Thanks for signing up at Wikipedia:Peer review/volunteers and for your work doing reviews. It is now just over a year since the last peer review was archived with no repsonse after 14 (or more) days, something we all can be proud of. There is a new Peer review user box to track the backlog (peer reviews at least 4 days old with no substantial response), which can be found here. To include it on your user or talk page, please add {{Wikipedia:Peer review/PRbox}} . Thanks again, and keep up the good work, Ruhrfisch _><>°^° 04:31, 25 February 2009 (UTC)

Request by MACHerian

Jacob.scholbach Would you be kind enough to review the following article on my user talk page Thank you MACherian m.a.cherian@btinternet.com

On Gödel’s Conjecture Abstract: ‘Not (proved or disproved)’ does not exhaust all reference to ‘proved’, or ‘disproved’.

Gödel presents his Incompleteness Theorems as proof that in natural numbers, inductively (recursively) generated as a ‘denumerably infinite’ set large enough for his numbering procedure, there is no consistent and complete formalization of elementary arithmetic. His proof is conditional on the axioms of Principia Mathematica [PM], with the added axiom of infinity (in the form he wants it, viz. ‘there are exactly denumerably many individuals’), the axiom of choice, and Zermelo-Fraenkel-von Neumann axioms of set theory appended to the Peano Postulates. [Collected Works Vol.1, OUP 1986 p.124]. He says, "…all methods of proof used in mathematics today have been formalized in them, i.e. reduced to a few axioms and rules of inference. It may therefore be conjectured (Vermutung) that these axioms and rules of inference are also sufficient to decide all mathematical questions which can in any way at all be expressed formally in the systems concerned", (p.145). For his conjecture to hold he also needs to have shown that only valid formulae follow from the rule-following inferences he relies on of PM.

If ‘p’is taken as true, and ‘-p’ false, the logical and the formalist equivalence and truth of: |p| < = > |(- -p)| < = > |(p or -p)| < = >|-(p and -p)|, viz. the laws of double negation, excluded middle and non-contradiction follow. Any one statement taken as true implies implies the truth of any and all the others. Based on the same axioms and rules of inference, on which Gödel [p.145] claims that in a formally deductive system, an arithmetical statement cannot be 'proved or disproved', i.e. -(p or -p), and hence is undecidable from within that system; he could have added that it is also not |-(p and -p)| i.e. ‘proved and disproved'; and ‘-p’, i.e. ‘disproved’. ‘Not (proved or disproved)’ does not exhaust all reference to ‘proved’, or ‘disproved’.

The law of Double Negation is |-|-p| < = > |p|. There are only two ways about it, either p or else -p, viz. the law of the excluded middle |p or -p|. |-|-p| is another way of writing |p|, and |p or –p|. Against Gödel, it is only necessary to show that the law of excluded middle |p or -p| entails that of non-contradiction |-(p and –p)|. When only |p or -p| is true, |p and -p| is false, |-|p and -p| is true viz. the law of non-contradiction. Equivalent steps of deduction are used in PM. The equivalence of |p or -p| and |-|p and -p|, also follows by De Morgan’s Rules (included in the PM) starting from either side. MACherian

I'm afraid I'm incompetent in these matters. Also, please notice that many Wikipedians (including myself) are somewhat allergic w.r.t. requests that are unrelated to WP (like people putting external links to their fav. website etc.). Jakob.scholbach (talk) 13:56, 25 February 2009 (UTC)