User talk:AxelBoldt/Archive July 2001 - December 2004

Hi Axel. Thank you for your work in Wikipedia. in Magic square-sagrada familia magic square-I've seen in the copy of square of Sagrada familia (Subirachs) isn't correct. There is 1 14 15 4 in the first row. Is it possible : a matrix for 4 dimensions? --151.51.163.214 (talk) 19:26, 18 January 2015 (UTC) Nevio Brcic neviob@libero.it[reply]

Hi Axel. Sorry if you don't wat this here but I really wanted to compliment you on what you did on those pages above, especially on Goedel's Theorem. Very good work! -- JanHidders

Thanks for the kind words! I'm enjoying myself tremendously here and have learned a lot already :-) --Axel

Hello, I love your page. Yours is the first page I've read where I and the author are in complete agreement on almost everything. Remarkable. --KQ

Hey KQ, do you mean my home page?? Because I have never met anybody who is in almost complete agreement with that. --Axel

Yes, I do. Specifically, I was referring to politics.html, though the rest is interesting too. I disagree about the prostitution argument, though, simply because people could also give food away for free out of love or charity, though I do agree that prostitution should be legal. And I must admit to having violated a few of your rules on webdesigning.... --KQ

Regarding recycling (your home page): among green types, recycling is recognized as the least desirable choice of the reduce/reuse/recycle trio. Reduce being to reduce what you use, reuse being to use something for the same purpose more than once (standard plates vs. paper plates, for example), and recycle being, as you put it, "downcycling." I collect aluminum for recycling in my office, but I don't buy or bring aluminum cans to the office myself. --Belltower

Dear Axel,

Upon checking upon KQ comment, curiosity led me to your page, and then to http://math-www.uni-paderborn.de/~axel/politics.html You are a brainy guy! But your statement "Medical research is a tremendous waste of time and money" is just plain stunning! I never thought I would ever hear anything like this -- hence "stunning". I also want people in Niger to overcome illiteracy, overcome poverty, and have access to the Internet. However, it would be wiser to speak about wrong allocation of resources or wrong priorities. Calling the work of thousands of good people and geniuses a waste of time and money is very unjust. The same research that serves a rich guy in Miami today can lead to a cure for malaria tomorrow and save millions of lives (I hope you care).

For balance, I subscribe to your ideas of "kid simulating the universe", "marriage is outdated", "marrying into the developing world", and "let's have global government" (this is quite obvious to many and we will get there one day).

However, I found your views surprising, contradictory or plain erroneous in several places. To be sure, I would first need to know what are your basic beliefs because the call to "sit still and retire early" once again proves to me how astoundingly different people walk this planet. Of further disagreements: give passports to Kosovars (I agree but ... what about those who want to get back home, what about Slobodan and justice, what about the principle of not rewarding aggression?), no breeding (if brainy people stop breeding, all your calls to change will lay in ruin -- you know why!), few links in HTML (this is against wikipedia, against your own writings on wikipedia, and against the principle that it is less harm to make a hesitant guy hesitate than to deprive a resolute guy of a choice to be informed), war on advertising (let advertisers bleed their money down the drain, read Seth Godin!), bogus e-mail (not only you fool spammers but you mess up web traffic and search engines -- why pollute to resolve pollution), web overhyped (perhaps for guys who want to "sit still", my life goes through a new renascence thanks to this knowledge goldmine), comments on Peter Duesberg and his "science" (prompted me to write an entry on Duesberg -- follow the link), and last but not least ... lots of people/companies make pretty money on the net and this is only gonna grow!

I am sure you will want to know if except for "agree" or "disagree" I was inspired. Yes, this was all put in a way that tickles "creativity centers" (I won't list them due to your dislike of medical research). The best was the idea of swapping citizenship. I never thought of it. On the top of my head, it would not work (5 million of Sierra Leoneans waiting for 3 US vacancies), but I will leave it in my memory for further processing.

btw: Why do you want no development ("sit still, retire early")? If you sit still in stagnation, how will you contact the kid that runs this universe in a computer simulation? How old are you? If you are below 27.3, your future is bright :) -- Piotr Wozniak

Piotr, I'm glad if I stimulated you; some of the "radical" statements on that page are actually intended to do just that. For instance, the "medical research is a waste of time and money" statement is intended to shock you into realizing how appallingly partial we are when it comes to applying the fruits of that research. And the "sit and retire" recommendation is supposed to point to the fact that much of our so-called activity is actually detrimental.

I also should say that this page has been created over 6 years and that I myself don't agree with all of it anymore :-)

Cheers,

 --AxelBoldt

Aha! Still the "shock method" on medical research may backfire as one could be tempted to think "crackpot page" and click on close button in the browser. I was lucky to dig deeper :) - Is your age a secret? (btw: I am 40) There must be some page on the net which is the focus of those wanting a global government! We gotta find it and put a hand (or thumb) -- Piotr Wozniak

I'm 35 and planning my retirement. --Axel

Just think how many Wikipedia articles you could write once retired! :-) --Belltower

Believe it or not, that was exactly what I was thinking when I wrote the above sentence. --Axel

Looking at your entries in the recent changes, this would be different than now because...? ;-) --Belltower

Because classes start on Monday :-( --Axel

Actually, the problem with advertising isn't that they're wasting money, but that it actually does work! We aren't quite the rational creatures we would like to believe, so advertisers can convince us we need a V-8 engine, to spend thousands on a diamond that 99% of us couldn't tell from cubic zirconium, and (worse) they convince our kids that they absolutely must have various and sundry kitschy items. By bombarding us with images of beautiful people and scenes, it alters our perceptions of the world around us. If advertising were just a way to inform us about new and potentially useful products, that would be one thing. But it's another, far more harmful thing. -- Belltower

Hi Axel--I have neglected to welcome folks since the latest Slashdotting, but you're clearly one of the most active and a very valuable member of the crew. Thanks for joining us. --Larry Sanger

Hi, and thank you for letting me play here. Yes, I'm one of the Slashdotters, but now I like it here a lot better :-) Larry, I thought you may like this. --Axel

I'm glad to see the four color theorem. A few weeks back I was tagging merchandise in different colors to correspond to different sections; we had tags in three colors and that sometimes resulted in corners where two different sections were tagged the same color, which set me off wondering if it were possible to avoid the problem with only three colors, or if not, how many would have to be used. And what do you know, that's a problem which had been vexing people for over 100 years, and solved in 1977. I'm glad I didn't waste my time trying to reinvent the wheel. :-) --Koyaanis Qatsi

Yes, my April's fool page about Udo von Aachen can be removed. But perhaps it would be best to update it to be a page about the hoax. I have a feeling other people will be fooled and so it would be nice if they can turn to wikipedia for a debunking. --Jimbo Wales

Axel,

I just came across this email snippet between you and you and Denis Howe (the editor of FOLDOC). Any word on him wanting to merge FOLDOC with Wikipedia?

For now, and as my time permits, I'll be moving content over and editting as necessay. I mean, just compare our TeX article with his... So finally, I just wanted to thank you for your work in securing permission to use FOLDOC and also the History of computing material. It's really good stuff. -- Stephen Gilbert

My understanding is that Denis will work on his own wiki-like interface to Foldoc for now and will not join our project at this point. But he is happy to have us use his material. --AxelBoldt

Axel - thanks for the literate programming article - an area I'm starting to explore. I think just a couple of hours passed between my requesting the article and your contribution. --Claudine

Axel - could you have a look at Functional analysis? It's so incomprehensible (and I did some second and third-year college mathematics, though I'm certainly no expert) that I'm just about wondering whether it's actual mathematics or just some pseudoscience somebody's deliberately slipped into Wikipedia to test whether it would be detected . . . and even if it's not, it could use some serious revision to be comprehensible (at least at a hand-waving level if not at a technical level) by lesser mortals --Robert Merkel

Cool, you've just done so. It's now at least semi-readable . . .

Axel - You are spot on with the big mess over in tensors. It *is* a very messy topic because of the large amount of baggage in train. Hopefully, someone such as yourself can dig into the math part and make it slightly more accessible. Others (maybe me) can handle the engineering side of it. And by the way, one very well-respected, though now dated, continuum mechanics simply states a matrix is a tensor if it changes coordinates the way tensors are supposed to. I might add that this text is in current use as an entry level graduate text at berkeley civil eng. this semester... =) In its favor, the author uses 3 different notations in the book: indicial, index free, and gibbs dyadic (whoa!).

Axel - I've added a few examples to WikiProject Concepts. I'd be interested in knowing what you think about it, as a mathematician. Do you believe that it can help structure the encyclopedia? --Seb

Seb: frankly, I don't see the point of the wpc hierarchy. Every well-written encyclopedia article about a concept should include generalizations and specializations anyway, and most math articles do already. So you are basically building a concept hierarchy parallel to the one of Wikipedia, except yours has a more formalized format and less information. --AxelBoldt

Axel - So what you're saying, basically, is that you don't see how having access to a well-defined structure might make navigation or edition easier? --Seb

In fact, it may make navigation more difficult. Suppose someone wants to find out about formal languages. They type it into the search box, and two articles show up: Wikipedia's and Wpc's. Which one to pick? If they pick Wpc's, they learn that a formal language is a kind of set, involves strings, read the definition and learn about several kinds of formal languages. The same information, and much more, is also contained in Wikipedia's article. So how does Wpc help? I think it would be more useful to make sure that all Wikipedia articles about concepts correctly link to their generalizations and specializations. --AxelBoldt

Good edits on the GNU Free Documentation License page. --TheCunctator

Would you write a stub for space-time ? (It's more than a graph of motion space vs. time.)~ BF

good work with the de-messing up of theory of relativity--AN

Hey Axel, I really like your work, even (or especially!) when you clean up behind a mistake I made. Thanks! --Dmerrill

Axel, it seems to me a relative prime would be a better title than relatively prime. --Dmerrill

No, because "relatively prime" is an adjective, there is no such thing as a prime that is "relative". --AxelBoldt

Hey Axel... I see a tesseract article. Are there fifth dimensional objects too? Add one if you wish. We need to teach Larry there are more than 3 D's. ~BF

Sure there are fifth dimensional objects. There are also infinite dimensional objects. Every little electron in your body is described by an infinite dimensional object. There's also not just one infinity. There is a hierarchy of infinitely many different infinitudes. You can quote me on New Age :-) --AxelBoldt

--- Re "Spinoza": You wrote "redirect saves one click".

REDIRECT is only smart when we're sure there aren't any other "Spinozas" (or whatever) that people might be looking for. I'm not sure.

AxelBoldt, your web site is remarkably interesting. Please add entries on Linux Bliss and the Hitler/Vatican Konkordat to the Wikipedia.

Hello Axel, in re: your question about Leni Riefenstahl: yes, she did take pictures, and also take some footage, but she's expressed dissatisfaction with the footage and not released it to the public. Riefenstahl discusses it in The Wonderful Horrible Life of Leni Riefenstahl, which is a long but clever and fascinating documentary about just what it sounds as if it would be about. She did publish some of the photos in a book. --Koyaanis Qatsi

Dr. Bolt I went to your .de homepage. Isla Vista is nice isn't it ? I have a question. Hypothetically speaking, if we raised c to the c power c ^|c| would we have a number expressing light accelerating at light speed ? BF

No we wouldn't. Something "accelerating at light speed" doesn't make sense: speed has the units meters per second (or miles per hour), while acceleration has the units meters per second per second or miles per hour per hour: it tells you how much the speed changes per hour.

Yes, Isla Vista is fun. I particularly miss the drunken Mexicans who would give me a ride home to downtown SB late at night when I had missed the last bus. --AxelBoldt

Axel: a request. I can't really put this under Requested articles because I don't exactly know what I'm requesting :). In one of Feynman's books he writes about learning how to 'differentiate parameters under the integral sign', or something similar. You couldn't write an article on procedure for this if you've got any spare time.

Many thanks -- sodium.

Google search on knowledge quotations led to this page: http://home.earthlink.net/~anewhaus/Aphorknowledge.htm .

The actual, full quotation is:

Desire to know why, and how, curiosity; such as is in no living creature but man: so that man is distinguished, not only by his reason, but also by this singular passion from other animals; in whom the appetite of food, and other pleasures of sense, by predominance, take away the care of knowing causes; which is a lust of the mind, that by a perseverance of delight in the continual and indefatigable generation of knowledge, exceedeth the short vehemence of any carnal pleasure.

Leviathan, Part I, Chapter VI

--TheCunctator

Thanx for the "idiotic edits" smart man...

Well we need to put some order under computer science then. We got a non hierarchical list there, but in definitions seems that complexity theory is a subfield of theory of computation which is a subfield of computer science... Huh? Please answer back here without deleting it, possibly.

(I know it's hard 4 ya, but at least, try, thnx)

--little guru

I agree that computer science is a mess. If you want to clean it up, be my guest. Sorry for "idiotic", but it was deserved. --AxelBoldt

Dr. Bolt, are you familiar at all with http://www.stardrive.org Jack Sarfatti's physics work ? I'm on his scientific mailing list.. don't ask me how. And he uses math symbols and equations in the emails. He seems to have a prestigious group of cronies, since he was a student of Feynman in the 1970s. ~BF

Hi Axel. I'm using Opera 6.0 for Windows, and neither of your bookmarklets are working for me. :( --Stephen Gilbert

Does it do Javascript at all? Try making a bookmark with url

  javascript:alert('hello Stephen');

If that works, we can work from there :-) --AxelBoldt

Works fine, but only if I remove the final semi-colon. --Stephen Gilbert

Oh, that may already be the thing. Can you go on irc, on the #wikipedia channel on irc.openprojects.net? I think we'll figure it out faster that way. --AxelBoldt

Well, obviously I couldn't last night. :) I tried dropping the final semi-colons from both the Netscape and IE versions; no dice. I can probably IRC tonight. I'm in the Atlantic timezone (one hour behind Eastern). --Stephen Gilbert

Or maybe not. Probably the most direct thing to do would be to install Opera yourself so you could see what's up. However, I that's a bit of a hassle for you. Maybe there's an Opera-using, Javascript-savvy Wikipedian around... --Stephen Gilbert

Ok, I have an Opera version of the bookmarklet on http://math-www.uni-paderborn.de/~axel/bookmarklet.html. It doesn't do the selection thing since Opera doesn't seem to support the relevant Javascript method, but you can still type or paste in Wikipedia search terms and you'll get a new window with the results. --AxelBoldt

It works great. Does Javascript have a method to grab the contents of the clipboard? If so, it would be possible to highlight the term, hit CTRL-C, then hit the bookmarklet. --Stephen Gilbert

It's always a matter of which methods the browser exports to javascript. Javascript itself doesn't have any way to access the clipboard, or the selection, or a window. It's all provided by the browser, and different browsers provide different things. I doubt that Opera provides access to the clipboard, since access to the selection is more direct and not included in Opera. --AxelBoldt

Hi Axel, I find some of the articles you have written or contributed to ver y interesting. Unfortunately, I cannot understand them -- specifically, in the article on Goedel's theorum, and a linked article on a consistent and complete system of arithmatic, I do not understand

? x : ? (0 = x + 1)

and what follows. I am neither a philosopher nor a mathematician, but would like to read articles on these topics. If there is an article in Wikipedia on how to read this system of notation (including a box which I don't think copied in this cut and paste), could you insert links to it in these articles? If there isn't such an article, perhaps you or someone else could write one? I am sure others would be as grateful as I -- SR

I'm not sure about what you don't understand; since you referred to a box, that may mean that a certain mathematical symbol didn't render correctly in your browser, and then of course everything that follows will be incomprehensible as well. But the Goedel article Gödel's incompleteness theorem doesn't have any symbols. So let me know what specifically is unclear in that article.

Presburger arithmetic and First-order predicate calculus have indeed several symbols that some browsers don't understand: the quantifiers. The "for all" quantifier looks like an A on its head, and the "exists" quantifier looks like a mirror E. They are valid HTML 4.0 symbols, but unfortunately, that doesn't mean much. If you look at the source of the page, you should be able to figure out what the equations mean. --AxelBoldt

you were right -- thanks -- SR

FYI, the Netscape bookmark works great in Mozilla 0.9.6 on Windows. I'll test Moz 0.9.7 on Linux tonight at home. --Dmerrill

Great, I added that information to the page http://math-www.uni-paderborn.de/~axel/bookmarklet.html --AxelBoldt

Axel...thought you were going to help us out over at Vietnam War! ;) F. Lee Horn

Hi Axel. I've seen you're list of contributions and I'm very impressed. --Georg Muntingh

Hi Axel, I was thinking of emailing you this, but maybe this is a better place. Do you have a list of good books that really allows one to understand many topics in CS? For example, reading SICP, it is clear that I can't predict things. I know a bit about computers to the gate level, so it was not hard to understand Knuth's TAOCP. But with different computational models like lambda calculus, I have little idea of what is underneath.

Are there any such books I can read? I am not near an English-speaking university (I'm in Germany) but I can order books. I don't even mind if they're things like Spivak's calculus, if analysis is important to the field.

Thanks for any help, Tj

If you have read and understood Knuth's books, then you know more algorithms than most computer scientists. So if you are mainly interested in the theoretical concepts now, I'd recommend Hopcroft and Ullman, Introduction to Automata Theory, Languages, and Computation. Every university has that book. There is a German translation too, but I think it is buggy. --AxelBoldt

Hello Axel, please see talk:Goedels ontological proof for a justification of the see-also to Absolute Infinite (which should, and will, have an article) - also please ignore my intemperate comment on one of the edits - I am a great admirer of your excellent contributions on this and other subjects. -- The Anome

Hello Axel. I would like to commend your contributions herein this Free Encyclopedia. I was looking for this kind of stuff all over and I think that finally I have found. I've done a lot of same things as you have and I have decided to put my works here. -- XJamRastafire

Well, that's great. Welcome aboard! AxelBoldt

Axel, I did not replace sex education with a completely differet article. If you'll take the time to read it, you will see that it is indeed incremental.

Please do not revert someone's changes simply because you disagree. Follow SR's example and your own advice, and make incremental changes.

--Ed Poor

I did read the article. For example, why did you remove the definition of "sex education" in the first sentence and replace it with your nonsensical "Sex education is a controversial issue in public education"? Wouldn't it make sense to tell people first what sex education is? Obviously, you hadn't even looked at the definition, you simply pasted in your version. AxelBoldt

No, I am the originator of the article and was putting back what someone else had taken out. I know you and I are on opposite polar sides on marriage and other issues, but I'm convinced if we both agree to adhere to NPOV guidelines, we can contribute value to the Wikipedia. User:Ed Poor

Hi Axel, thanks for your time on my old pages. You probably noticed that i already listed them on "wikipedia pages to be deleted", but thanks anyway :) szopen

Hi Axel, I will try to be diplomatic and respectful of others, but I have a concern with regard to contributing to an encyclopedia where someone like Ed Poor continues to inject articles with his own judgements. His pages written from NPOV are hardly that. I have no problem with describing a subject and that linking from the subject commentaries on it pro or against, but I do have a problem with the main article being littered with judgements one way or the other. One need not pass judgements on homosexuals, sex education, etc to write out what the topic is. I also think that it is completely appropriate to provide a link to a commentary regarding the topic in question. Is this too much to ask for? I realize that I have just started to contribute and I very much like the idea of wikipedia, but I don't want to continue if this is to be turned into a forum for someone or some group trying to push their own agenda.

If you find an article which tries to push a particular point of view, just go in and edit it, clarifying that such and such is a point of view typically held by such and such group, and also explain the view of the others. This can work pretty well, check out for example abortion and scientology.

The most important thing is to be bold; if you honestly believe that your change improves the article, then make it, don't shy away because you are too modest to modify somebody else's writings. AxelBoldt

Good catch on gay-bashing. I gather if the assailant is unaware of or unconcerned with the sexual orientation of a homosexual victim, then the term does not apply. User:Ed Poor

Yeah, I like the page too - and it prompts me to ask you for a specific review

While "intellectual property rights" may not exist, "intellectual property law" sure does and so does "intellectual capital" - sort of. I would like a strict Randroid, a strict Stallmanite, and Baruch Lev himself to have a look at "intellectual capital" and see what else could or should be said.

My approach was to put the non-controversial notions of instructional capital (it's pretty clear atht instructions to do something are a means of production or protection) and individual capital (it's pretty clear that creativity produces something even if we can't say what), but the simplistic models that try to explain *HOW* they fit together seem to be increasingly messy.

If we can focus the controversy into the "intellectual capital" article then we can have relatively stable articles on the way instructions produce value, or individuals (separate from their instructions or intellectual process) contribute value. Which are micro-economic.

Alex, feel free to use my Wiki and recommend others to your "Wikipedia Discussion" page to cover downtime. It's a little late now, but it did seem like a good idea... --LDC

... and I should really put it on the Wikipediholic page. "I'm not a Wikipediholic, but if I'm cut off for half a day, I scramble to organize fellow Wikipedians on some other wiki." AxelBoldt

Alex, nothing personal, but I feel that certain redirects and changes have been ideologically motivated, whether you're aware of it or not, and raised the issue of 'ideological vandalism' on Talk:Vandalism In Progress

The word "vandalism" is unfortunate but as I understand it here it refers to all violations of Wiki meta guidelines.

We might want to discuss, here, what you believe about "intellectual property law", "viral licenses", "cognitive science of mathematics", as I believe you have some objections to these generalizations of more specific concepts like copyright/patent/trademark, copyleft, and 'mathematics as product of mind' respectively. You are far from the only persons who wants to keep these ideas in a neat clean box, but so far you are the only one stomping articles that offend your sense of them. I'd rather know what you believe about them so that we may come to some agreement and I can point you to the sources that I seem to think are well-known that you seem to think are unique or obscure.

Well, you are mistaken about a lot of things. First, I did not touch your intellectual property law article. Second, your viral license article was crap, and instead of fixing it, I redirected to a much better discussion of the topic, and pointed out its crappiness in Talk:. I happen to be a fan of viral licenses and have used them for many of my software projects; right now I'm contributing to this php wiki script which is GPL. Regarding philosophy of mathematics: your pet theory, while interesting, is just one of many, certainly not a majority position, and should be presented accordingly. Personally, I'm a Platonist, but fall back to formalism (Curryism) when challenged, because it is the easiest position to defend. I am convinced that any intelligence, whether embodied or not, whether in this universe or elsewhere, will always by necessity arrive at the number pi, the monster group, the normal distribution, the prime number theorem etc. Most working mathematicians believe the same. But working mathematicians have nothing of substance to say about the philosophy of mathematics, just like cooks should shut up when it comes to restaurant criticism. So I haven't written a word about philosophy of math yet. And finally regarding your accusations of bias in September 11 articles: you have shown your own blatant biases by scare quoting "terrorist", as if there were a serious debate about the terroristic qualities of the attacks. AxelBoldt

While I don't particularly take them seriously either, it happens that 24's "pet" theories actually do have a small following among a few serious academics. But then, there are still people who read Social Text and take it seriously too. I agree that we should avoid cluttering most of the rank-and-file articles on math with these ideas, but we probably should mention them in articles like "philosophy of mathematics" and "body philosopher" and "George Lakoff", etc. Just as we mention creationism in the main "evolution" articles, but not in every biology article. --LDC

Agreed, "most" articles should not mention philosophy of mathematics concerns at all. Extremely fundamental things like Euler's Identity, pi, monster group, etc., should mention specific issues raised and provide links, but not spend more than a paragraph on it. There are maybe a dozen such articles.

I didn't *write* an intellectual property law article, and if it was not Axel (maybe it was LDC) who broke down the intellectual property law link inappropriately into three separate links to copyright, patent, and trademark, then I apologize.

OK, I have some sense of Axel now. Let me try to equalize by responding and laying out my own weird ideas for you both, so you know what's "pet". I am not a Platonist except insofar as the cognitive systems of animals have common fractal geometry (which Turing studied in detail and tried to put limits on, especially neuron growth). I dont shift positions to one that is easier to defend when I am challenged - I let myself be argued against on the same grounds I have promoted/established. I therefore lose more, and learn more. The rest of this is strictly to Axel:

You're entitled to your belief that pi, monster group, normal distribution, prime number theorem, e, and (most controversially) i are divinely determined or just built into the universe or all universes or whatever.

You cannot even quote me properly. I do not hold any of those beliefs. AxelBoldt

Many friends of mine share them. But it has always been a key question in the philosophy of math whether or which of these basic ideas arises from a desire of humans for some convenient simple notation that doesn't violate their immediate constraints... F=MA is also convenient, but under certain constraints, wrong. I tend to look at math more like physics and expect that "i" in particular will be shown to be a notational convenience at some point. But that's idiosyncratic - I don't even know what George Lakoff thinks of it, I don't mention it, and I make no claim that it has anything to do with the longstanding claim of indigenous peoples that colonists simply look at the applicability of mathematics a different way.

Santa Fe Institute and many others are my source for significance of Euler's Identity, which when I found it was titled "the most remarkable formula in the world" and didn't mention the basic operations that the formula includes, only the constants, as if hte operations were somehow above creating the remarkability... I left it much more neutral than I found it, and will eventually satisfy you that Euler's Identity is central to any cognitive science of mathematics, or to proving that one cannot be made to exist.

Re: politics.

The debate is on the use of the word "terrorist" to mean anything at all. The British Broadcasting Corporation (BBC) categorically refuses to use it,

Google search for "site:bbc.co.uk terrorist" give 8410 hits. AxelBoldt

the BBC was always willing to quote people accusing each other of being "Terrorists", but as I understand their on-air policy, they won't let their anchors or staff journalists use that word except when reporting someone else's opinion, or clearly in context of some other party's definition. Anyway to see what they think officially, see

http://news.bbc.co.uk/hi/english/world/americas/newsid_1693000/1693876.stm

they do appear to have been more willing to use the word since 9/11, but also since that time there have been UN and US and EU agreements on what it means... so it's not taking a side to say that grousp claiming to hvae done things that qualify as terrorism by those definitions are "terrorists"... from the standards of the society they speak to, they are... and it isn't always denied - some groups revel in it. Which creates its own distortions. These other objections to it still stand:

if calling someone a "terrorist" makes it easier to attack their families or communities, the word may only be useful to escalate violent conflicts... and may have to be ignored by people seeking peace.

and given its subjective context and heavy overuse (would you want to see the entire Viet Nam War described as "terrorist attacks on the Vietnamese"?) I believe it must be avoided. But I covered that in the "talk" sections and also left alone your Sept.11 Terrorist Attack text, heavily biased as it was and with features that would surely trigger your wrath elsewhere (should I add a memoriam to the My Lai massacre, yesterday's casualties in Ramallah, all Native Americans killed by cholera?) - I let you encounter this yourself. Read http://indymedia.org to see a variety of different views of Sept.11th - or csmonitor.com or theguardian.co.uk if you want something from a major newspaper.

I scare quoted "terrorist" to imply that I don't believe the word has any meaning in the neutral point of view... but to respect the common usage. I would like to see this standard applied everywhere, for reasons more clearly defined in asymmetric warfare.

I accept your dislike of the viral_license article, and would have accepted any rewrite, but not the redirect, which seemed (unlike many such redirects) to not preserve the original text anywhere for there to be any debate on it.

It's preserved in the history of viral license, and I also included a link to it in my criticism on Talk:copyleft. AxelBoldt

thank you, that was considerate, and I hadn't noticed, so I apologize. Hopefully we are done not reading each other's references... I hope... ?

We seem to hold extreme and opposing points of view on "terrorist", on the underlying basis of mathematics' validity, and perhaps on pornography as well. That's interesting in itself, as I have encountered no other such stark conflicts. I am certain we can learn from each other if we adopt a joint protocol for dispute resolution... or we can simply do as we've been doing (you chopping out text and pretending topics don't exist that do, and I complain in "Talk" files and enlist political support and new writers, without any attempt to modify or update your articles on political topics) - the asymmetry may also teach us something.

I respect your intellect if not your assumptions. If nothing else, Sun Tzu applies, and I will make every effort to comprehend your point of view fully.

Warmest regards, 24

From user:DanKeshet

I don't know who to thank about the improved diff, but I find it absolutely fantabulous. I don't know how I ever lived without it. Thank you kindly. DanKeshet

You can thank me a little bit :-) and Geoffrey T. Dairiki <dairiki@dairiki.org> a lot. He wrote difflib.php for use in the excellent phpwiki, and I pulled it into our script. AxelBoldt

Thank you kindly, then! :)

Axel, I just found your comments on my talk page, and I responded to them there. -- Toby Bartels

Hi, I've been on a 0-length-article deletion binge over the past couple of days, and some of the only ones left are old user pages that I didn't want to get rid of without asking the owners first. Can I delete AxelBoldt/Searchscripttest, AxelBoldt/Test? I'm on the verge of getting the "stub articles" page to be actually useful, and getting these off of the list would help. Bryan Derksen, Sunday, April 21, 2002

Thanks for doing that. Sure, all subpages of AxelBoldt can be junked. I'll do it right now. AxelBoldt

I've another question for you on Talk:Depth of field, Axel. Koyaanis Qatsi

Axel, thank you not only for your positive feedback, but also for frequent factual and stylistic polishing of my contributions. --Bolek Bobcik

I responded to your question about what I've been doing to the "complete list" articles over on my own usertalk. Bryan Derksen

Hey, Axel, I just made the discussed change to Locally_compact, as well as adding a bunch of new stuff. No, don't bother to look — it's not there. My question to you is, if my browser crashes while I've been editing an article, and I successfully pressed Preview a bunch of times (but never pressed Submit, successfully or no), is there any way to retrieve that text? (Answer here or in my User_Talk:. — Toby Bartels, Tuesday, June 11, 2002

It is gone. I edit my (longer) articles in a text editor and always keep a local copy of everything. That way, one also has access to spell-checking, search-and-replace etc. AxelBoldt, Tuesday, June 11, 2002

Axel, in global warming talk I wrote:

Great job! Now the article flows in one continuous narrative, like something from Time magazine. I couldn't have done it better myself . . .

I stand by that compliment. Creating a continuous narrative is not something I'm good at (I'm still learning how to write a single paragraph that sticks together).

After reading your version and pondering it (through several cycles of read and ponder), I began to have some ideas of improving the opening paragraphs.

I still think we can help improve the article by editing each other's work. You will be better than I am at certain aspects of editing, and you will contribute ideas or knowledge that I do not have. I hope to return the favor, with your consent.

Ed Poor, Wednesday, June 12, 2002

Important note for all sysops: There is a bug in the administrative move feature that truncates the moved history and changes the edit times. Please do not use this feature until this bug is fixed. More information can be found in the talk of Brion VIBBER and maveric149. Thank you. --maveric149

Thanks for the clarification on Ohm's Law. Vicki Rosenzweig

Hey Axel, Do you have developer access? I was in Portland, got the email requesting a password change, complied & logged out. That was two days ago & I can't remember my password; I'd ask Jimbo but I know he's busy like always. Anyway, if you do, could you just reset it to something random and email my nupedia address? I tried to send a msg from the account but it just said the page was loading forever, and it never went through. Cheers, KQ

Eh, never mind, I've just sent Jimbo an email about it. Best, KQ

Axel, I made several changes to global warming and greenhouse gas. Please review these changes, vetting them both for NPOV and scientific acceptability. --Ed Poor 06:21 Jul 30, 2002 (PDT)

Ed, note that Axel is on vacation until August 11. I looked at these a little myself, but I'm a poor substitute for Axel. — Toby 11:39 Jul 30, 2002 (PDT)

Axel, when you get back, can you look at the new and improved Separation axiom? This is a completely redesigned version of the former Separation axioms, which means that your edits to the original have been lost as such, although I hope that your lessons have been incorporated. The intent behind the change is at Talk:Separation axioms. Other new pages growing out of this change are Kolmogorov space, the stub Preregular space, and the currently unwritten History of the separation axioms. (Also don't forget Ed's note above.) — Toby 01:39 Aug 7, 2002 (PDT)

I like the new Separation axiom page. I think it's good to separate out the historical morass from our adopted definitions and to present the axioms in increasing order of strength. The graphic looks a bit crappy though; maybe you can use anti-aliasing for the fonts? AxelBoldt

O, is that what that's for? Let me try it ... No, the resulting GIFs look completely identical to me. If you know more about converting images well than I do, then I'd be happy to email you a PostScript file (or even a TeX source). — Toby 02:42 Aug 12, 2002 (PDT)

Hey Axel, both "referred" and "refered" are correct, and Wikipeodia ;-) doesn't have a preference for US or UK spelling (just FYI... :-) -- Marj Tiefert 09:32 Aug 11, 2002 (PDT)

Bast! I didn't know there was a diference for that word and have "corrected" this many times myself to the "rr" spelling. BTW welcome back Axel! --mav

Hi everybody. My Oxford dictionary, which presumably lists both British and American spellings, doesn't give "refered", and, more importantly, neither does American_and_British_English_Differences. Marj, do you have a reference? AxelBoldt

My mistake - English just isn't consistent! referred is right, but both referable and referrable are right, as is reference of course! -- Marj Tiefert 19:54 Aug 11, 2002 (PDT)

Google - search for 'refered' (139,000 results); search for 'referred' (8,750,000 results). Nuff said.Mintguy

If we went by Google, we'd use "it's" for the possessive... Fowler says "referred". mea culpa on one of the "seperate" you fixed... ouch... -- Tarquin 16:04 Aug 11, 2002 (PDT)

I haven't seen a dictionary that, given a correct spelling, lists common incorrect spellings for the word, but such a dictionary can be manually simulated by performing Google searches (or indeed, using any other Web searching service). The Web is made up of yahoos (citation: http://www.yahoo.com). P.S.: This incorrect spelling is also enshrined on the Internet in the server environment variable HTTP_REFERER. That doesn't make it right either. David 16:27 Aug 11, 2002 (PDT)

If there's some suggestion that the spelling with one R is British, I can assure you it's not the case; I'm English, and all of my dictionaries only give a spelling with 2 Rs (maybe I don't have enough dictionaries, I don't know). We normally ADD extra letters, you know, not take them out. --Camembert

How about making all these spelling corrections minor edits?Ortolan88

A question for you: any idea if in another english speaking country the decimal comma is used instead of a decimal point? How about in Europe in general? I ask because in the article hipparchus they write a formula with a 2,5 meaning 2.5. I know in some places that would be correct, but this is supposed to be english. But I don't know if it is a language or country thing. Probably decimal point deserves an article.

I know that in Germany we use a comma instead of a decimal point; the French and the Spanish do the same; I don't know how it's done in England or Australia. Let's ask around! AxelBoldt

In Britain we use the decimal point, and a colon for 24-hour time (eg 20:00 for 8pm, not 20,00). Incidentally, the Internet has enshrined a misspelling: if you read web server logs, the site that a user has come from is called the "referer". This should be "referrer", but it got to be a standard before anyone could correct the speeling. Mswake 20:08 Aug 19, 2002 (PDT)

I just found a web site for Australian teachers saying that Australia uses decimal points and spaces to separate groups of three digits, not commas. The SI system also apparently uses spaces, not commas for that. However, I think it's safe to say that in an English encyclopedia, a comma instead of a decimal point is out of place. 199.17.238.92 11:51 Aug 20, 2002 (PDT)

Axel; there is a bit of a discussion going on at talk:Orders of magnitude about what is the most proper E notation to be used for scientific notation. If you have time I would very much like to know what your thoughts are on this. --mav

Axel, I added 3 or 4 paragraphs to global warming and moved 500 words to climate change. Please vet for POV; as Jacob says, we often can't see our biases. --Ed Poor

Axel, I'd like to read (or create) an article briefly describing the common, over-the-counter analgesics: aspirin, acetaminophen (Tylenol), Anacin (=aspirin+caffeine, ibuprofen (Advil, Motrin) -- maybe even including mild prescription drugs like Tylenol III (contains codeine). Would you be able to point me in the right direction? --Ed Poor

Well, I just educated myself about acetaminophen and I don't know much about the others. I used Google and E2. I found a very basic introduction at http://www.fhradio.org/fm/archives/1998/2152(FM).html AxelBoldt

Hi Axel! Sorry I took so long to respond to your question on my Talk page. I've been taking a little breather after the recent debate in the mailing list. You asked me about Auschwitz. Actually, Auschwitz was a collection of many camps, each of which had factories. I am writing off the top of my head right now, but if I remember correctly, Buna (the camp made famous by Elie Wiesel) specialized in rubber, other camps did everything from armaments to road building to tailoring. I will be at work and check out my sources on Tuesday and give you a more complete answer then. Hope this helps in the meanwhile. Danny

Yup, I'm aware of the various work camps with associated factories. What I was wondering specifically though was the type of work prisoners in Auschwitz II Birkenau had to do, since there was no factory attached. AxelBoldt

I did a few of the year in review pages. They're now done through 1000. ... It's not exceptionally interesting work. :-) --KQ 14:34 Sep 22, 2002 (UTC)

Mav mentioned that I might start adding interlanguage links to the German wikipedia. I started doing that around 1012. --KQ

Heh. Once the Polish Wikipedia has all year pages in place, we can go through again :-) Also, could you remove the parentheses around the centuries if you're at it? The decades and years don't have any parentheses either. AxelBoldt

If you could point out a page that's exactly how it should be, that would be great. I just want to make sure I understand before doing another couple hundred. :-) (I'm kind of slow on the uptake sometimes, and an example would be great).

Yes, I think the interlanguage links could stand to have a more efficient system somehow. --KQ 12:12 Sep 23, 2002 (UTC)

1301 is a pretty standard example. AxelBoldt

Theres a revised version of the Lambert-W graph, but Mathematica produced a really ugly subscript on $W_0(x)$, so its just $W(x)$ I'm afraid. (The text makes it clear which branch is being plotted -- User:GWO

Thanks for the spell fix of "Occurrence" in the elements articles. I updated the template with the correct spelling. --mav

Hey Axel; I've started a new thread over at Wikipedia talk:WikiProject Elements about a concept for nav bars and locator maps for the chemical elements (there is a prototype example at Lithium). Join in if you are interested. --mav

Somebody added their own proof to Fermats little theorem:Proofs. I'm clueless in this regard, so maybe you can take a look at it? --mav

I was just looking at that, and debating removing it by virtue of wikipedia not being a place for original research. But I delayed because I wanted to see what others more mathematically inclined thought. --KQ

I'll move the page for the proofs to a better title and I'll edit the proof a bit; it is correct but not original. I don't think that it can hurt to leave it in, along with some other more standard proofs. AxelBoldt 03:30 Oct 1, 2002 (UTC)

Hi Axel. I'm going to bed. You might want to keep an eye on the vandalism, looks like we're getting a few tonght. Have a good one.

Do you hand-compile the list of stuff u work on? User_talk:hfastedge

Yup. AxelBoldt

Axel

I was working my way systematically through the timeline pages and cleaning each one up to the standards. So I'm afraid I've already removed the Years: from most of the 6th century.

Along the way I've also cleaned up the layout for Decades, and made sure Events, Births, Deaths are in the right order and some other stuff.

So what do you think is the best approach, leave Years: in or continue to work through each of them and take them out?

(Later) Axel, never mind. I see the update to the Timeline standards. I'll add Years: back to the 6th century (no pun intended). Bernfarr

Yup, virtually all years right now have the "Years:" in, we just didn't update the timeline standards. So unless you want to edit 2500 or so year pages... :-) AxelBoldt 02:48 Oct 9, 2002 (UTC)

I wonder if you have been keeping an eye on the Aria Giovanni talk webpage. The situation there is out of control.

Matters have deteriorated to a highly abusive level over a website link. Of special concern is the general conduct and attitude of someone called NetEsq, who claims in his details to be a lawyer.

He has repeatedly abused anyone who opposed the idea of the website link with such tactics as net misettiquete ( eg the use of the word 'you' in capitals and bold to emphasise shouting), a poor grasp of history, the unrepentant use of such termsas Nazi, out of context quotes and attempted alienation ("only YOU opppose it").

Regardless of the rights and wrongs of his beliefs, it is very advisable to bring this most unruly and arrogant person into line.

Given that your name is on the list of persons who can ban users, I thought it advisable to bring this to your attention, before it leads to persons leaving the wikipedia - something likely to stroke Netesq's already aggressive ego.

Hi Axel - Just wanted to get a recommendation from you on a good book on Category theory. I'm an autodidact, and am unlikely to take a course in it.

Lots of the edits I've been doing lately seem to be covering topics which are "tweaked" for Abelian categories, but work just as well (with minor alterations) for groups. If I knew enough about category theory, I'd probably just change them to read "in the category of groups", but that's really just my "street" category theory talking - I'm really not qualified to make such an assertion.

Cheers - Chas zzz brown 00:10 Oct 27, 2002 (UTC)

I really like the book "Categories for the working mathematician" listed under category theory; it motivates things quite well, but is definitely not "bathtub reading material". The later chapters are quite esoteric and you can skip them; if you can make it to adjoint functors, you will know more about categories than most mathematicians. AxelBoldt 00:38 Oct 27, 2002 (UTC)

I suspect that the relevant matters largely have to do with the existence of kernels and cokernels, but I'm not sure exactly what is required. In the meantime, saying "Abelian categories and the catgory of groups" should cover most applications, even though it's surely not complete. If and when I figure it out, I'll put in more definitive phrasing in those articles (unless, of course, you beat me to it ^_^). And yes, Categories for the Working Mathematician by Saunders Mac Lane is a classic. It's a scandal that we have articles on neither the book nor the author ^_^. — Toby 15:45 Oct 31, 2002 (UTC)

Kernels and Cokernels are often only defined for preadditive categories, and the category of groups doesn't fit. It really seems to play a special role.

See Kernel (category theory) for what is needed. The category of groups has zero morphisms, although we typically don't call them "zero"; they are the trivial homomorphisms.

Does the category of monoids have cokernels? Our proof of the five lemma doesn't apply there. AxelBoldt 16:11 Oct 31, 2002 (UTC)

Monoids also have zero morphisms, so the concept of kernel makes sense for them. One might hope that kernels don't in fact exist there, but they do (the preimage of the identity as usual). However, there is a sense in which these kernels are not good enough; they lose information; you can't reconstruct the entire kernel pair (which measures the deviation from monomorphismness of a morphism) from the kernel in this category, as you can in preadditive categories or in the category of groups. This is why monoid theorists don't study the preimage of the identity but instead study the notion of kernel from universal algebra, which is really more analogous to the kernel pair than to the category-theoretic kernel.

So, there should be some condition that a category must satisfy for these sorts of lemmas to hold, and I think that it will be something about kernels and cokernels, but it must require more than their mere existence. I will try to figure it out, or look it up; my guess at this moment is:

The category has zero morphisms (necessary for the remaining conditions to make sense);
Kernels and cokernels always exist (in the category theoretic sense);
ker coker ker = ker, and coker ker coker = coker.

These are all true for Abelian categories and for the category of groups, but the last fails in the category of monoids.

— Toby 05:12 Nov 3, 2002 (UTC)

Hey, I just noticed something neat. Given an object A in a category with all kernels and cokernels, ker induces an order reversing function from Sub(A) to Quot(A), while coker goes the other way. Then the last axiom above states that this a Galois correspondence between posets. In this case, a subobject or quotient object is normal in the category-theoretic sense iff it's normal in the Galois-theoretic sense. Of course, both uses of the term "normal" ultimately derive from a basic example featuring normal subgroups, so it's really no coincidence. — Toby 05:21 Nov 3, 2002 (UTC)

Yes, that's nice. Maybe we should have an article which compares the various notions of "normal".

I'm still wondering whether the category of monoids has cokernels though. AxelBoldt 16:03 Nov 4, 2002 (UTC)

By bolding important words the article is much more useful. For instance in angle, many astronomy pages link to it and all that the reader wants is the part on astronomy.

you better come up with an explanation of what an ellipsoid is....Lir 19:50 Nov 9, 2002 (UTC)

Which Frederick William I are we talking about here? The one I know, the "Soldier King" of Prussia, lived from 1688 until 1740. AxelBoldt 04:47 Nov 14, 2002 (UTC)

Axel, the numbering was "reset" after Friedrich Wilhelm III the Duke of Prussia, proclaimed himself Friedrich Wilhelm I the King in Prussia in 1701. Friedrich Wilhelm I, der Grosse Kurfürst (the Great Elector)the duke of Prussia (1620-1688) is the one who managed to turn the Polish Province into independent Duchy in 1660.
I hope this is helpful, Axel, although I'm sure Helga could've explained it better. BTW, where is Helga? Is she OK? I kinda miss her in a unique sort of way.
Space Cadet

Howdy Axel:

I just created a WikiProject for math; aka Wikipedia:WikiProject Mathematics. I'd love to see any input comments, etc. you might have. Cheers. Chas zzz brown 23:59 Nov 17, 2002 (UTC)

Hey I've left a note for you on the Calculus with polynomials page regarding your alternative proof. [[User:Kidburla2002|Kidburla2002]]

Hello. I've just left you a query on the Simplex talk page. Basically I'm not sure what "in general position" means, and why it is better than "linearly independent", and I would be grateful for some clarification. :) -- Oliver Pereira 23:14 Nov 23, 2002 (UTC)

Axelboldt, please watch the global warming article and jump in if I make any mistakes -- which I'm sure to do, if only due to ignorance or carelessness. --Ed Poor

Two replies to you on my talk page, one on an old subject, one on a new. — Toby 16:34 Nov 28, 2002 (UTC)

Axel, did Fred Bauder ever explain why he thought all the phenomenon articles were needed? I also was wondering if they were really necessary. --Ryguasu 01:02 Dec 2, 2002 (UTC)

I haven't seen a reply. I think physical phenomenon should be merged with, and redirected to, physics. But maybe we should give him a bit more time. AxelBoldt 01:34 Dec 2, 2002 (UTC)

Fair enough, though I did find it a little ominous when he blanked his talk page with no reply to you. --Ryguasu 01:31 Dec 3, 2002 (UTC)

Would you please take a look at Talk:U.S. customary units? I'm getting confused between "a square piece of land 6 miles wide" and "a piece of land containing 36 square miles", or whatever a "section" is supposed to be. (Ah, how my problems seem to multiply...) --Ed Poor

Hi Axel, just wondering how did you draw the structure of acetylcholine? (ex. using which software etc.) -- Ktsquare

I used JChemPaint from http://jchempaint.sourceforge.net/. It's not very good; for instance it really doesn't want to display letters for carbon and hydrogen. Also, apparently it's impossible to typeset CH₃ with a proper subscript. I couldn't find anything better though. Let me know if you dig up anything. Maybe a straightforward vector drawing program would be better. AxelBoldt 01:54 Dec 17, 2002 (UTC)

here's a piece on a potentially promising shift in publishing in scientific journals. http://www.librarian.net if you need a NY Times login. :-) cheers, --KQ

Axel, you added the following to Occam's Razor:

Ockham himself used the principle to argue that God's existence cannot be deduced from reason alone.

Could you add a reference for this claim? See the discussion on Talk:Occam's Razor. Thanks. --Eloquence 15:04 Jan 3, 2003 (UTC)

Hi Axel. Could you give me a hand on Duration and its talk page? I'm having trouble communicating with a new user & I don't know enough about the subject to show by example. tx -- Tarquin 10:29 Jan 5, 2003 (UTC)

Axel, was it 142.177.97.215 that you said looked like our old friend 24? I've seen a couple of edits by this person and they do seem to be 24ish. Anyway, I've blocked the IP after I saw a horrible racial slur inputed by this IP on a talk page. It implied that the first Hispanic American in space stole the Challenger O-rings. --mav

This is what I have to say in edit wars under Internet troll. I hope you find it funny:

Trollish behavior in an article entitled Internet Troll could be a self referential joke with its roots in the philosophy of meta-mathematics. It might be a wikified joke, about looking up Internet troll in the dictionary and finding a picture of User:AxelBoldt.

I know nothing at all about you. I am a Canadain.

I'm going to wade through the entire talk in philosophy of mathematics and then I'll be able to separate the wheat from the chaff. I guess it is such a snakepit nobody has been able to summarise the arguement. It's clear as an unmuddied lake. Two16

David, I have a couple of questions regarding your last edit to Skene's glands. Basically, the article matched the given references better before your edit. Did you work off of some other reference? AxelBoldt 03:35 Jan 11, 2003 (UTC)

Feel free to discuss your questions directly with me by email if you like (wiki lets you do this by clicking a link). I used a variety of references obtained via Google, which I did not list in the article (I probably should have).

I have doubts about some of the information that was there before my changes and that you have restored. In particular, I believe that Skene's glands are not the same as the G-spot, and are not located there. However, stimulation of the G-spot can cause female ejaculation, which generates fluid from the Skene's glands (among other tissues).

By the way, your contributions to Wikipedia are impressive.

David 23:32 Jan 14, 2003 (UTC)

I got that information from the BBC and New Scientist story listed in the article. The other link given in the article contains a couple of drawing which seem to suggest that Skene's glands are located near the G spot. AxelBoldt 01:58 Jan 15, 2003 (UTC)

It looks like neither of us is expert enough to make authoritative statements about these topics. I guess any corrections to the article will have to wait until someone with real expertise participates. David 20:49 Jan 15, 2003 (UTC)

The "printable version" of a page displays the the URL correctly, so it isn't necessary to have long unattractive URLs in the online articles. And there are ways, described in the Wikipedia:Manual of Style to display URL's when they have intrinsic interest. Regards, Ortolan88

Just so you know the language list on the Main Page was in alphabetical order per language codes. Since the native forms of the languages are presented using native alphabets, it doesn't make much sense to order the language titles based our alphabet. But all the language codes are in our alphabet - therefore it makes sense to order them that way. Not a big deal though. --mav

The process of giving unique Goedel identifer to each grammatical expression in one axiomatic system ( one version of the foundations of mathematics, usually identified as principia mathematica.), is a reletively straight forward matter.

Grammatically true statements in their minimum form may be identified by hand or in software implementaion. They are expressed in a language of symbolic logic. Each term used in the symbolic logic is uniquely identified with a natural number.
Grammatically true statements are uniquely identified with a number through a mark-up procedure involving an member of the prime number sequence used as a power on each term of the expresion. The results of each operation are summed.
Following this procedure will produce uniquely identifiable positve number for each expression of sybolic logic.

Because it was a work of philosophy, in the field of meta-Matematics, the fact that the numbers become arbitraily huge after a few terms is irrelevant. For a philosopher, the fact that this can be done in any disipline that depends on symblic logic (including all fields of study in science that use mathematics.) Some statements have comparatively small number values.

I'm going to provide examples to Juuitchan. Two16

Somebody added URL to goedel. There are many. Try [1] its just a series of writer some of whom wrote books on the proof or wrote on the inplication of the proof. 1st quote is the worst quote. User:Two16

Oh, the story is like that: I first create Ring (mathematics) and redirect it to Ring (algebra), but later I discover that it is better if I do it the other way round. That's why I cannot simply use Move this page method, as I already create Ring (mathematics)!!! User:Wshun

Hi Axel. Thanks for cleaning up my tex badness on Floor function. As you can tell - I'm new at it. snoyes 17:34 Feb 18, 2003 (UTC)

Axel, It's a done deal on fetus and circulatory system. I didn't see much at all to change in the latter, but on fetus I did add a bit...the only crucial part is that it's the (breath induced) differing pressures in the atria that close the foramen ovale, creating an "adult" system, rather than the closure of the ductus, which can occur a bit later. Other than that, you done good<G>...please have a look at them to be sure I haven't inadvertantly obscured some of your clarity! -- Someone else 20:34 Feb 18, 2003 (UTC) P.S. also added more info onto Terms for anatomical location. They have to do with 3 dimensions (visualization of which is not my forte) and mathematics, so I have no question you'll be better able to formulate/present/incorporate them. -- Someone else 05:25 Feb 19, 2003 (UTC)

Anatomical position<G>. It's peculiar, but this may give an idea: Standing up, head and eyes forward, arms down, extending out from sides about 15 degrees, palms forward, thumbs pointing out. Dunno why, but that's it: it's not a very "natural" position. Makes the thumbs lateral, rather than anterior. A picture would be worth a thousand words, methinks, but I don't know of any non-copyright-encumbered ones. -- Someone else 05:46 Feb 19, 2003 (UTC)

Sorry to but in here, but I'm guessing the reason this is designated the natural position is because of pictures. The diagrams in my old EMT textbook are simple drawings of the human body intended to be unambiguous and two-dimensional, basically your average sketch with the major body parts at easily identifiable places -- the thumb isn't normally parallel with the other fingers, but the simplest drawings don't differentiate. It isn't intended to be the position the body naturally falls in, just a simple uniform diagram that people out in the field can easily picture and apply to the victim in question. Tuf-Kat

Axel, 142.177.*.* (a.k.a. 24) has returned to philosophy of mathematics, if you care to monitor his "progress". Chas zzz brown 18:52 Feb 21, 2003 (UTC)

&#36665 &#26643 (axle+bolt)-&#35918&#30505

Hi, Axel, ketone bodies looks good, the only thing I suggesed was spelling out Acetyl-CoA the first time you use it (which I did, revert it if you don't like it<G>). -- Someone else

You made an edit to homophobic hate speech which you described as "AIDS isn't fatal." It's not? - Montréalais

Hi, I've tidied up the Charles Babbage page. Arno 06:43 Mar 7, 2003 (UTC)

That wasn't by any chance you editing the St Bart's Hospital page (Hogarth etc) from an IP address was it? (If not, please ignore this!) :) Nevilley 08:30 Mar 12, 2003 (UTC)

Hi, Axel,
I can add at least the mechanisms of ethanol's disinfectant action, though not in any particular detail. Like most disinfectants, the higher the concentration and the longer something remains in it, the better it works. If I come across any good explanations of disinfection in general while reading, I'll try to remember that it might make a good article in itself. -- Someone else 22:25 Mar 24, 2003 (UTC)

Hi Axel. I saw your note on Mav's page and thought I would answer here. You are right. Auschwitz first opened in 1940, as a camp for Poles. In 1942 it became a death camp. I can check the date that the first transports arrived (March is reasonable) when I am at work tomorrow, with the 5-volume History of Auschwitz. Danny

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

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.

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

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

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

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

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

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. AxelBoldt 04:45 Apr 25, 2003 (UTC)

Thanks -- I understand, and appreciate it, Slrubenstein

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)

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)

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)

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

______

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)

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)

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)

Hi, found this on one of the blogs I frequent, and thought you might know what to do with it, if anything. Koyaanis Qatsi

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)

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", the contributions of 64.106.24.51, which maps to University of New Mexico Gallup Branch, and of 64.106.24.53, of that same institution 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

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)

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)

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

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)

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)

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)

I thought you might be interested in the opinion poll going on now at Talk:Clitoris. MB 18:08 9 Jul 2003 (UTC)

How about a making fun of Barnes & Noble? This page conflates cinema verite with Dziga Vertov's Kino Pravda as well as Robert J. Flaherty's heavily fictionalized work; it claims verite has no director (!? WTF) (Flaherty himself directed quite a lot--having an igloo made with a side cut away to allow enough light for him to shoot the end of Nanook of the North, and cutting in the footage of the family inside the partial igloo to make it look as if they had built shelter just in time to avoid a blizzard--and in an earlier scene insisting that Nanook et al. hunt with harpoons instead of rifles); the page also claims that cinema verite did not use a script, making its inclusion of Vertov doubly misleading--Vertov had planned quite a bit of Man with the Movie Camera, though he may not ever have written it out in script form. Also the "real life" B&N mentions on camera hinges on Vertov's two phrases "life caught unawares" and "life as it is," which are commonly confused for each other and actually mean two distinct things. In short, I would say the last two sentences of the B&N article can go without qualification; the previous two need serious qualification; and the rest is crap. Koyaanis Qatsi 02:21 15 Jul 2003 (UTC)

Axel, could you look over the most recent changes to Turing machine? Personally, I think the article is considerably less accessible and a less useful introduction since the introduction of the "mathematical formulation". --Robert Merkel 05:57, 7 Aug 2003 (UTC)

Hi Axel,

I like your bookmarklet for searching Wikipedia, but I want to adapt it for phrase search. I tried (for IE)

javascript:s=(document.frames.length?'':document.selection.createRange().text);for(i=0;i<document.frames.length;i++){if(s)break;s=document.frames[i].document.selection.createRange().text;}if(!s)void(s=prompt('Enter search terms for Wikipedia:',''));wikiw=window.open('http://wikipedia.com/'+(s?('wiki.phtml?search='+'"'+escape(s)+'"'):''));wikiw.focus()

i.e. putting the phrase in quotes, e.g. for "closed and reclaimed" I get

http://www.wikipedia.org/wiki.phtml?search=%22closed%2520and%2520reclaimed%22

which does not work; using the wikipedia search box one gets

http://www.wikipedia.org/w/wiki.phtml?search=%22closed+and+reclaimed%22

which gives the right result.

http://www.wikipedia.org/w/wiki.phtml?search=%22closed%20and%20reclaimed%22

works also.

Do you know I should change the bookmarklet?

Patrick 11:55, 8 Aug 2003 (UTC)

Hallo Axel. Mir sind einige Ungereimtheiten im Artikel zero divisor aufgefallen, die ich in der dortigen Diskussions-Seite dargelegt habe. Vielleicht hast du ja Zeit, den Artikel zu ueberarbeiten. -- SirJective 10:52, 12 Aug 2003 (UTC)

Danke, so gefällts mir. Auf die Sache mit den Produkten von Linksnullteilern hätte ich ja selbst kommen können! *g* Da ich seit diesem Artikel einen Account in dieser Wikipedia habe, kann ich kleine Sachen auch selbst ändern. Größere Probleme werden nach wie vor zur Diskussion gestellt. --SirJective 19:56, 29 Aug 2003 (UTC)

Hi Axel. I just saw your May 22 edit of the property table at Nitrous oxide. In the future could you please make a note of your opinions on the tables at Inorganic table information, and perhaps even edit the template table there? I'm trying to keep all the tables consistent, but it's a bit hard to watch all 40 of them for edits. Also, I note you have been adding CAS numbers. Do you think it would be a good idea to include them in the table, underneath the formula? -- Tim Starling 02:26, Aug 21, 2003 (UTC)

Did you get my email regarding an emergency developer contact list?

Axel, check out the new proposal at Talk:Ethics; this looks like it should fix things in regards to that article. Your thoughts? RK 22:21, 31 Aug 2003 (UTC)~

See . -- Tarquin 12:03, 11 Sep 2003 (UTC)

Circumcircle :-) (and the triangle image doesn't show in the triangle article -- just the link as text. I can't work out what's wrong with it Tarquin 15:01, 11 Sep 2003 (UTC)

Can you help me with something in math? I know this question is not wikipedia, but you're a math professor, so I though I could ask you. If I can't, that's OK. I'm trying to learn first-order predicate calculus from a book I got in my local library, and I understood most of it, but I just got stuck. Right now, they are proving that predicate calculus is complete, so they are working with tautologies in the process. I don't understand the difference between the truth of a statement and if it is a tautology. I don't know why they are reproving things like modus ponens with tautologies instead of proofs, and subsequently I don't understand these proofs (they are just in English, not in any formal mathematical statement). The tautology article doesn't offer much help and neither does MathWorld. Am I in over my head? LDan 01:52, 29 Sep 2003 (UTC)

There's a subtle difference between true statements about predicate calculus, and tautologies. The following is a true statement about predicate calculus:

Whenever p→q holds and p holds, then q holds as well.

This is not a statement within the predicate calculus, but it is a statement about the predicate calculus, a so-called meta statement. And it is a true meta statement, called the modus ponens. Now a tautology is a formula within predicate calculus, which holds no matter what the variables stand for. The following is a tautology within predicate calculus

((p→q)∧p)→q

This formula holds always, no matter what you replace p and q with. And obviously, this tautology is closely related with the above meta statement, almost identical (and also sometimes called the modus ponens). In the chapter you're reading, they are probably currently proving these tautologies, assuming the corresponding meta statements. If you don't know the difference, then these proofs may look pointless. AxelBoldt 10:43, 29 Sep 2003 (UTC)

Regarding your question on the heart-and-lung image on nl:, I have forwarded it to the user who uploaded the image. I can only hope he answers - I had sent him a message about another image a few days earlier, and not yet received answer although he has been around. Andre Engels 13:12, 15 Oct 2003 (UTC)

Only now I see I had placed it on his user page rather than his talk page, so maybe there will be an answer after all. Andre Engels 13:16, 15 Oct 2003 (UTC)

Thanks Andre. Whether he answers or not, the episode has already been very fruitful for me: I just found a wonderful wealth of public domain anatomy drawings at http://www.bartleby.com/107/ . Cheers, AxelBoldt 13:40, 15 Oct 2003 (UTC)

While Keating's conviction was overturned on technicalities, he spent 4 1/2 years in prison, and pleaded guilty in April 1999 to reduced charges [2] which would let him out of prison. I think there were also some new hearings, possibly even a new trial. So I do not consider your current presentation entirely accurate, but I will abstain from editing the article until a conclusion has been reached regarding the basics.—Eloquence 00:32, Oct 27, 2003 (UTC)

Everything is fully explained at Charles H. Keating Jr.. AxelBoldt 00:41, 27 Oct 2003 (UTC)

That article is good, but Mother Teresa should note that Keating spent 4 1/2 years in prison for the Savings & Loan scandal. "Turley's statements have never been proven" is POV -- would Turley agree with that? He would probably say that his statements have been proven, but that the proof was ignored by the higher court on grounds of a technicality. IMHO the whole sentence is redundant with the "overturned" part.—Eloquence 01:00, Oct 27, 2003 (UTC)

The "technicality" was that the jury never determined whether Keating intended to defraud the victims, and that is of course the whole thrust of Turley's statements. In the end, the 50 months Keating spent in federal prison were for a bankruptcy fraud only marginally related to and much smaller than the S&L scandal; his two convictions in that scandal were both overturned. AxelBoldt 02:08, 27 Oct 2003 (UTC)

For the claim "Turley's statements have never been proven", it does not matter what the jury has determined -- it matters which proof has been presented in the case against Keating.—Eloquence 02:23, Oct 27, 2003 (UTC)

Ok, how do you like it now? AxelBoldt 14:02, 27 Oct 2003 (UTC)

Much better, thank you (didn't know about the plane). BTW, Keating is also the producer of Perversion for Profit, a notorious propaganda film against porn ("This same type of rot and decay caused sixteen of the nineteen major civilizations to vanish from the earth. Magnificent Egypt, classical Greece, imperial Rome, all crumbled away. Not because of the strength of the aggressor, but because of moral decay from within.") Perhaps also of interest: "By 1960, Keating was testifying before the U.S. House of Representatives armed with, according to a Cincinnati Enquirer article, 'hundreds of books and magazines -- purchased at newsstands throughout the country -- describing and depicting a variety of perverse sexual activities' After Keating's testimony...the House subcommittee burned the mass of material." [3] —Eloquence 14:17, Oct 27, 2003 (UTC)~

What was wrong with my definition of homeomorphic on Planar graph? [4] seems to agrees with me... Dysprosia 02:02, 29 Oct 2003 (UTC)

Well, it wasn't a definition. If, given the graphs A and B, and B which is an expansion of A, it is often described that A is homeomorphic to B.

The statement is technically correct, but readers could very easily leave with the mistaken impression that this is the definition of homeomorphic. For example, the graphs

   * - * - * - * - *
       |
       *

and

   * - * - * - *
       |
       *
       |
       *

are homeomorphic, but neither is an expansion of the other. AxelBoldt 10:36, 29 Oct 2003 (UTC)

Thanks :) You see, I mistakenly assumed that an expansion and a homeomorphism between two graphs was the same thing... You wouldn't mind if I clarify the homeomorphism terminology, would you? Dysprosia 11:05, 29 Oct 2003 (UTC)

Not at all; maybe a homeomorphism (graph theory) is in order. AxelBoldt 11:15, 29 Oct 2003 (UTC)

Lungs[edit]

You ask a subtle question, grasshopper<G>. I, who cannot draw to save my life, drew you a diagram for this one. Have a look at Lung and let me know if my words and pictures have made the interplay between tidal volume and lung capacity more obscure, or less obscure...-- Someone else 17:00, 8 Nov 2003 (UTC)

Statue of Liberty[edit]

When I said the torch was open, I meant the crown. Sorry. I hope you won't discredit me forever! -- Mattworld 02:35, 12 Nov 2003 (UTC)

Well, I may grant you one last chance to redeem yourself, if you can find out the status of the torch balcony for me :-) AxelBoldt 14:16, 12 Nov 2003 (UTC)

Hi Axel. It was closed for a while, then opened before 9/11, then closed after the attack. (Just checked with security here. I am right by the ferry and we were closed too). Danny 19:37, 14 Nov 2003 (UTC)

Thanks! AxelBoldt 20:57, 14 Nov 2003 (UTC)

Pic Captions[edit]

Hi Axel, just a quick one to ask why "my" caption on Edith Piaf was changed to largish font? I think the larger font looks a little ugly because it's now very slightly larger than the text. I thought that the caption-text produced by the small command had been accepted as looking about right for captions?
Adrian Pingstone 09:53, 16 Nov 2003 (UTC)

Just another thought, have a look at Trainer and imagine how a longer caption would look in that large font!

Adrian Pingstone 10:03, 16 Nov 2003 (UTC)

I think small fonts are difficult to read, especially in italics fonts. Trainer is an example of a caption that has way too much information. AxelBoldt 14:17, 16 Nov 2003 (UTC)

Axel, regarding the two math questions you left on my talk page. The theorem about the dimensions of division algebras is usually stated for real division algebras. I suspect it's capable of some generalization, but I'm don't know for certain. Also, it does apply to fields -- the proper definition of dimension of a division algebra is its dimension as a vector space over its center, so fields always have dimension 1. I do know the most general statement, which is that the dimension of a division algebra is always a square.

Regarding Gelfand-Mazur, since Banach algebras are by definition associative, so trivially Gelfand-Mazur applies to associative algebras. I think Mazur's theorem, and the various generalizations and variants of Gelfand-Mazur that are sometimes also called the Gelfand-Mazur theorem all require associativity. Loren Rosen 22:44, 20 Nov 2003 (UTC)

Thanks, I added the bit about division algebra dimensions being square to division algebra. I also made a couple other changes on that page and on Banach algebra and normed division algebra all having to do with topics you seem to be knowledgable about, so please have a look if you like. AxelBoldt 19:32, 21 Nov 2003 (UTC)

The word is "controversially" [5]. Cheers, Cyan 03:06, 8 Dec 2003 (UTC)

WikiProject Programming languages[edit]

Would you be willing to join WikiProject Programming languages, I could really use your help. —Noldoaran (Talk) 03:56, Dec 17, 2003 (UTC)

Thanks, but to be honest I'm not too eager. AxelBoldt 11:52, 17 Dec 2003 (UTC)

Challenge Problems:

Use the algebra of dimension theory to derive both the Planck-Einstein Law (E = Planck constant times frequency) and the De Broglie Law (momentum times wavelength = Planck constant) from the photonic law (wavelength times frequency = constant). Answer: http://members.fortunecity.com/jonhays/dimalg.htm.)

Use dimensional algebra to derive D'Alembert's Principle from Newton's Second Law of Motion, and to derive both D'Alembert's Principle and Newton's Second Law of Motion from The Antitonic Principle. (Answer: http://members.fortunecity.com/jonhays/dalderive.htm.)jonhays 17:23, 19 Dec 2003 (UTC)

I've created a diagram of the human heart similar to the one you linked to on Wikipedia:Requested pictures. No labels or anything yet, but they'd be easy enough to add. I'd welcome suggestions for improvements in coloring and anatomical correctness! It's SVG, so I can modify it fairly easily. Would it help if I produced a series of images showing the heartbeat process? Leave a message on my talk page. -- Wapcaplet 20:02, 20 Dec 2003 (UTC)

I'll go ahead and add labels to the heart diagram, and work up a couple of shots showing the blood flow. I can upload the finished SVG in addition to the exported .png images, so others can modify it for non-English versions. -- Wapcaplet 16:32, 24 Dec 2003 (UTC)

Done. Check it out and let me know what you think. -- Wapcaplet 20:51, 24 Dec 2003 (UTC)

just want to say thanks for the many quality math articles you contributed. I enjoyed them extremely. Xah P0lyglut 14:08, 2004 Jan 7 (UTC)

Axel, could I ask you to look at my latest remark under Talk:Marquis de Sade and see if you & I can get consensus? I don't think we are very far apart at this point, if at all. -- Jmabel 23:27, 9 Jan 2004 (UTC) TNX, looks like we now agree. --Jmabel 06:56, 11 Jan 2004 (UTC)

Neither \begin{eqnarray*}...\end{eqnarray*} nor \begin{align*}...\end{align*} are possible to use inside an equation. Does an alignment markup exists, that can be used inside $$ $$ ? (it'd be simple to add out-of-$$ markup to texvc, I'm just trying not overcomplicate the matter from the users' perspective).

For other stuff, see the recent wikitech post. Taw 23:24, 19 Jan 2004 (UTC)

Contradiction in ordinal number article[edit]

Hello Axel.

The article ordinal number contains statements that seem to contratict each other."Ordinals which don't have an immediate predecessor can always be written as a limit of smaller ordinals" contradicts "no sequence of elements in ω1 has the element ω1 as its limit". I have two month ago written this on the talk page, but noone answered yet. Do you know enough about ordinals to help me with this? --SirJective 16:21, 1 Feb 2004 (UTC)

Answer on talk:ordinal number. AxelBoldt 16:14, 2 Feb 2004 (UTC)

Royal Library book thief[edit]

In case you missed an answer, please look at http://da.wikipedia.org/wiki/Wikipedia:Landsbybr%F8nden#Royal_Library_book_thief --Christian 14:28, 9 Feb 2004 (UTC)

Thanks! AxelBoldt 14:58, 9 Feb 2004 (UTC)

Review request[edit]

Hi. I wrote a couple paragraphs in standard deviation, on interpretation and application. Would you mind looking it over and improving a bit? I've tried but it still feels incomplete and clunky to me. Isomorphic 09:03, 10 Feb 2004 (UTC)

I thought the paragraph was good; I changed only one little thing: we don't usually reject a hypothesis if our measurements are only one standard deviation away from the prediction; more commonly a 95% rule is used, which roughly corresponds to two standard deviations if we assume normally distributed measurement errors. AxelBoldt 02:38, 11 Feb 2004 (UTC)

Re:Linking captions[edit]

Sorry, but (right now) wiki does not support linking captions in pictures like that. The preference is that you discuss the picture in the article, and link relavent people/places/thingss from there. →Raul654 18:21, Feb 12, 2004 (UTC)

Random Praise[edit]

I just wanted to say that the stuff you've written about Group Theory is the best I've been able to find on the web, and it's more comprehensible than I remember my professor being when I took "Intro to Group Theory" a while back. I wish all my professors could lecture like you write! D0SBoots 00:03, 15 Feb 2004 (UTC)

Thanks! When I cover a topic on Wikipedia, I do try to produce the best stuff available on the web -- else, what would be the point? We would just be wasting our readers' time. Most of the group theory material wasn't written by me however, but by User:Chas_zzz_brown who produced excellent work but unfortunately seems to have left the project. Cheers, AxelBoldt 00:46, 15 Feb 2004 (UTC)

Hi, your search bookmarklet listed at Wikipedia:Searching#Bookmarklets doesn't work with Mozilla. I think you need to change wiki.phtml?search= to /w/wiki.phtml?search=. Angela . 04:08, Feb 16, 2004 (UTC)

Yes, thanks, will do :-) AxelBoldt 14:11, 16 Feb 2004 (UTC)

Hi. Unifying conjecture is listed on VfD by Charles Matthews, who says it's basically nonsense. I'm inclined to agree, but some have expressed a discomfort at relying on the opinion of one expert. Could you take a look and give another expert opinion? Thanks, Isomorphic 21:54, 23 Feb 2004 (UTC)

Hi. I just wrote an article on the short term Fourier transform. Aside from accuracy errors, I would like it if you could help with the relationship to the uncertainty principle, which I have seen connected in various articles online, with conflicting explanations. you were involved in a conversation on the uncertainty talk page, and I figured you would know about the relationship, or could help me find more, accurate, information to write it myself.

Thanks, Omegatron

Here's what I think I know about this: quantum mechanics postulates that the state of a system is described by a vector in a Hilbert space, and an observable (a variable like position or momentum) is modeled by an operator on that space. Given such a state and an observable, i.e. a vector and an operator, one can compute the probability distribution of the outcomes of measurements of that variable. Now from these postulates, one can prove purely formally that an uncertainty principle holds: it relates the product of the uncertainties of two variables to the commutator of the corresponding operators. All this doesn't need Fourier transforms.

Now, this uncertainty principle is completely general; the traditional uncertainty principle however is concerned with particular variables: position and momentum. Position is modeled by the operator "multiplication with x" and momentum by the operator "-i d/dx" (both are operators on the Hilbert space of square integrable functions f(x)). Now it turns out that the Fourier transform of -i df/dx is 2 π s F(s) (if F(s) is the Fourier transform of f(x)). From this, and the fact that the Fourier transform is invertible and compatible with the inner product in L², one derives that the probability distribution of the momentum variable is the Fourier transform of the probability distribution of the position variable. Furthermore, there is a general theorem about Fourier transforms (unrelated to the above theorem about operators) which says something like "the standard deviation of g(x), times the standard deviation of G(s) (the Fourier transform of g(x)), is always bigger than 1/2." (See [6]; this is often called the "uncertainty principle for Fourier transforms".) This then yields an alternative proof of the physical uncertainty principle. The advantage of this proof is that it doesn't need fancy Hilbert space operator magic, and that it gives some intuition behind the uncertainty relation: just like a signal cannot be simultaneously concentrated in time and frequency, a measurement cannot be simultaneously concentrated in position and momentum. The disadvantage of this second proof is that it only works for these particular observables (position and momentum), or slightly more generally for any pair of observables whose operators are related by the Fourier transform. AxelBoldt 13:28, 26 Feb 2004 (UTC)

Uh... You lost me at Hilbert space. Maybe I will go and learn about it someday, but for now I guess I am hardly qualified to write this section of the article... Omegatron 16:03, Feb 26, 2004 (UTC)

As an occasional contributor to the Nivokov self-consistency principle article, I'm hoping that you have some familiarity with Newcomb's paradox. I am asking for informed comment on that article. Thanks for any assistance you can provide. Rossami

Hello, actually I didn't know Newcomb's paradox, but it looks very interesting. I'll read over it and put comments in Talk. Cheers, AxelBoldt 13:14, 20 Mar 2004 (UTC)

Follow-up request for you on Newcomb's paradox. I replied on the talk page and would like your thoughts on what I misunderstood. Thanks. Rossami

Ahhh. I was misremembering the definition of the Nash equilibrium. When the rest of the Newcomb's paradox article stabilizes, I am going to add a few words to try to make that distiction come through more clearly just from the context. Thanks. Rossami

If you have some time, I need some help with Ramanujan modular functions. JWSchmidt 20:03, 24 Mar 2004 (UTC)

Sorry, I don't know the Ramanujan modular function and I certainly don't know its connection to string theory. AxelBoldt 13:40, 25 Mar 2004 (UTC)

Germans[edit]

I've for long (a year, actually) been itched by the way Wikipedia-links are done with often sloppy distinctions between nationality, citizenship and ethnicity (with regard to persons) and also between nations and countries. This is particularly obvious in the case of people or entities that are denoted as German. A link to the Federal Republic of Germany is often outright unhistorical and wrong, but this has until now been the most usual.

Therefore I'm considering an article on Germans, which I've started at User:Ruhrjung/Germans. I would wish to avoid lots of edit wars. In particular, I would not wish to see the current disputes over German-Polish matters automatically extend also to this article, why I kindly ask you for comments now, in advance, in order to try to find wordings acceptable to as many as possible of concerned wikipedians.

I look forward to your comments at User talk:Ruhrjung/Germans.
--Ruhrjung 23:33, 14 Apr 2004 (UTC)

Old Request[edit]

Axel, I noticed on Wikipedia:Requested_pictures#List_of_Pictures_Requested that several months ago you requested a drawing of the inner workings of the heart. When I checked the article, it has a very good drawing. Is that request still valid or can it be removed from the request list? Thank you. SWAdair | Talk 09:50, 24 Apr 2004 (UTC)

The excellent drawing of heart is a result of my request, so the picture request can be deleted, which I just did. Cheers, AxelBoldt 10:11, 10 Jun 2004 (UTC)

Axel, I just wanted to note that I made a response to an older comment of yours in Talk:Twin_prime_conjecture - Taxman 12:33, Jun 9, 2004 (UTC)

New layout kudos[edit]

from the pump

The new page layout is just wonderful: clean, logical, functional and uncluttered. To whoever is responsible for the new design: Thanks for the great work! AxelBoldt 10:26, 9 Jun 2004 (UTC)

Good to hear there's at least one user who likes the new layout ;-) MediaWiki_talk:Monobook.css seems to indicate most would prefer returning to the standard skin... -- Gabriel Wicke 15:24, 9 Jun 2004 (UTC)

Nah, you only hear from the unsatisfied. I went back to standard for a while, but found it crufty and old-fashioned, so I'm back with monobook. I guess 50% of the complaints (and the most bitter) stem from the cache-snafu prone transitional period (and the categories layout bug period). The only long-lasting issue is (I think) the verdana diacrita placement bug, which (if it isn't sorted already - I wouldn't know!) is something we do need to address. -- Finlay McWalter | Talk 15:49, 9 Jun 2004 (UTC)

I agree - I like the new layout after the initial shock - The javascript errors seem to be finally dieing out too! good on you! Erich 19:21, 9 Jun 2004 (UTC)

Yes, I find Monobook to be a lot better too. Great work! --Chopchopwhitey 06:58, 10 Jun 2004 (UTC)

I love the new layout. As I experience it (Mac OS X 10.3.4, Safari) it looks prettier and the text is more legible and the pages are just as information-dense or maybe denser than before. There are very minor glitches—for example, the article creation text tells you to click "edit this page" but the tab, of course, just reads "edit." Dpbsmith 00:06, 10 Jun 2004 (UTC)

I like the new layout too - especially how each user can customize it for themselves. Perhaps we should create a page for Monobook fans? - jredmond 00:17, 10 Jun 2004 (UTC)

In general, I like the new layout, but I still can't agree with overriding the user's default font choices, and forcing a sans-serif font in particular. See also Wikipedia_talk:Serif or sans-serif and MediaWiki_talk:Monobook.css#Font typeface —Steven G. Johnson 06:04, Jun 10, 2004 (UTC)

The new layout is great and professional looking. That way Wikipedia will become mainstream - massa 16:38, 12 Jun 2004 (UTC)

When I first saw MonoBook, I actually went to IRC to ask who made this amazing-looking artistic theme. People who like the standard skin don't value aesthetics! --Menchi 16:40, 13 Jun 2004 (UTC)

Well, in fact they value aesthetics as much as you do, but they feel that bare functionality is more important that glossy looks. — Monedula 10:48, 16 Jun 2004 (UTC)

Sickle cell anemia image[edit]

Hi there! I'm doing a bit of work on sickle cell anemia and was hoping that you could provide the copyright status of the image you've placed there. (Since it's from NIH, I'm guessing it's PD, but it's good to double-check :-) Thanks! --Diberri | Talk 18:17, Jun 21, 2004 (UTC)

Yes, automatically public domain as part of a US government publication. AxelBoldt 18:41, 21 Jun 2004 (UTC)

Polymethyl methacrylate[edit]

Great work on the PMMA article (IMHO). Thanks!

Well thanks, it has been fun. AxelBoldt 11:49, 26 Jul 2004 (UTC)

Inline TeX[edit]

Re: fiber bundle. Please contribute to the LaTeX discussion with your opinions on inline TeX. mat_x 21:29, 8 Aug 2004 (UTC)

Re: Tor functor. I see you have undone some of my TeXifying again. I would like to know why you feel this is a good idea. Best, mat_x 10:43, 17 Aug 2004 (UTC)

Well, it's a matter of taste really; I don't like to inline TeX because the TeX's font size doesn't match the font size of the surrounding HTML, and because it seems a waste to transmit a whole png file where a simple HTML character would do. But if you feel strongly about this, feel free to revert. Cheers, AxelBoldt 11:23, 17 Aug 2004 (UTC)

I think I agree with Ardonik's view of things, which is covered in some detail on the TeX talk page. He claims there that there isn't really a significant difference in the transfer of a .png and HTML; I was initially under the impression that HTML had to be faster. I also agree that the problem seems to lie in the rendering of .pngs inline. However, I'm definitely not savvy on the intricacies of this matter, and as a relative newcomer to Wikipedia I won't be entering into these debates too deeply. I was just checking that you knew what you were doing ;-) mat_x 13:33, 17 Aug 2004 (UTC)

taxobox documetation[edit]

Just wanted to give you a head's up: The documentation is in the works. You can see the working copy at Wikipedia:WikiProject_Tree_of_Life/Taxobox_Usage. Feel free to edit at your leisure or discuss on its talk page. - UtherSRG 17:51, 10 Aug 2004 (UTC)

Image without image entry[edit]

Hello Axel,

you edited the image description page Image:Kathoey.jpg. This image has no upload information, did you upload it? See also this list for all such images I found. --SirJective 12:45, 12 Aug 2004 (UTC)

Yes I uploaded it. I remember that there was some sort of timeout when I uploaded (the image is very large), so I first assumed it hadn't uploaded properly, but in fact it was all there, only my user information was missing. There's a bug somewhere. AxelBoldt 12:58, 12 Aug 2004 (UTC)

Index set[edit]

Hi Axel, I was reading Cartesian product, and I wondered if the cardinality of the Index set needs to be (at most) the same as of the natural numbers, or can it be higher. In none of those articles is explicity stated. Thanks --AstroNomer 00:52, Sep 8, 2004 (UTC)

The cardinality of the index set can be as high as you like, and higher :-) For instance, the set of all functions from R to R is often written as R^R, i.e. a cartesian product of many copies of R, where as index set we take R itself. AxelBoldt 02:09, 8 Sep 2004 (UTC)

LTP[edit]

Thanks for your edits to LTP. It's about time someone pored over my original contributions :-) --Diberri | Talk 22:10, Sep 9, 2004 (UTC)

Well, thank you, it's a good article, I learned a lot. AxelBoldt 20:04, 10 Sep 2004 (UTC)

could you take a look at Natural units? it appears that you have made some contribution there. i do have a couple of objections that noted at the talk page. i don't think that the Planck Current is either historically correct nor keeping with the original concept of Planck Units. personally i wish that Planck had normalized 4*pi*G instead of just G, but that is a different (and later) argument.

r b-j (talk page)

Islam & menstruation[edit]

Adha does literaly means 'a hurt'! Why did you change the text? Do you understand Arabic? A. 04:42, 12 Sep 2004 (UTC)

I replied on talk:menstrual cycle. AxelBoldt 19:45, 12 Sep 2004 (UTC)

more on Natural Units[edit]

could you take a look at my talk page? i posted a more current version of that sci.physics.research article that i called "The Most Natural Physical Units". i really believe that the Planck current is wrong on the Natural units page. but, in addition, more thought should be put into the concept of Natural Units and not simply equate them to Planck Units.

r b-j 18:28, 13 Sep 2004 (UTC)

I think it would be ok to list your concerns about natural current on the Natural units page, especially if Planck never used that notion (but others clearly do, so we shouldn't just delete it). Your other thoughts on natural units make sense to me, but I think they fall into the category of "original research", i.e. ideas that haven't been published and are not (yet) widely accepted, and we try to keep original research out of Wikipedia. AxelBoldt 22:14, 13 Sep 2004 (UTC)

Menstruation picture[edit]

Hi. I will do so soon, but currently i am on a trip and away from my regular computer with the neccessary software. I hope to get around to do it next week. I will also include some comments I got when I tried to nominate the image as a featured image, but recalled the nomination. May nominate it again at a later point after fixing it. Cheers -- Chris 73 Talk 21:21, Sep 14, 2004 (UTC)

Thanks, and have fun on your trip. AxelBoldt 22:36, 15 Sep 2004 (UTC)

Trip was highly sucessful. I updated the image based on different online sources (google image search). The lines match now, and there is a "average only" sentence at the bottom. (Press CTRL-Reload if you still see the old image) -- Chris 73 Talk 13:35, Sep 20, 2004 (UTC)

Very nice, thanks again. AxelBoldt 22:01, 20 Sep 2004 (UTC)

Intermediate Value Theorem[edit]

Thanks for picking that up. I had only skimmed the article text before drawing it up, and i was working off my uni notes which had k. It should be u now Enochlau 01:16, 17 Oct 2004 (UTC)

Thanks! AxelBoldt 07:29, 17 Oct 2004 (UTC)

Cyclooxygenase[edit]

Well done for tidying up cyclooxygenase. Is there a chance you can perform the same magic on COX-2 selective inhibitor? This was filled with waffle by some people, and is now a dense mess. JFW | T@lk 21:57, 19 Oct 2004 (UTC)

Wow, that article is a mouthful. I'm not sure if I want to open that can of worms, but maybe I'll find the time one of these days. AxelBoldt 01:35, 20 Oct 2004 (UTC)

Unary[edit]

In Wikipedia:WikiMoney, you mention that ψ1 can be earned by finding an factual error in one of the many articles listed on your main page. I think I may have found one or two in Unary:

"Counting on one's fingers is effectively a unary system."
- While this may be the case for the kind of counting taught (most) little children. I count on my fingers in the binary method which allows me to count to 31 on one hand. I was going to point to you a wikipedia article on it, but couldn't find one. Maybe we need one.
  - Ok, how about "the standard way of counting on one's fingers..." ? AxelBoldt 19:20, 14 Nov 2004 (UTC)
"Addition and subtraction are particularly simple in the unary system, as they involve little more than string concatenation."
- How can subtraction be performed by string concatenation? It kinda could be done by doing a reverse write on a turing machine, but this is before the article mentions turing machines.
  - You subtract by finding a string that can be concatenated to the second to yield the first. That's the "little more" part. AxelBoldt 19:20, 14 Nov 2004 (UTC)

Mebibyte[edit]

same as above

"The mebibyte is closely related to the megabyte, which is equal to 10⁶ bytes = 1 000 000 bytes"
- This one is kinda trivial, but even according to megabyte the megabyte can mean 10²⁰. This is the reason for Mebibytes and similar ilk in the first place. Mega- can mean either, Mebi- is unambiguous.
  - Yup, I lost the battle of having Wikipedia conform to standards and have "megabyte" always stand for 10⁶. The winning crowd forgot to change this line... AxelBoldt 19:20, 14 Nov 2004 (UTC)
"Mistaking the two has not encumbered the IT world so far..."
- Actually, it has [7].
  - That sentence seems to have been inserted by the winning crowd; I agree with you though. AxelBoldt

Thanks! I'll send over ψ4. AxelBoldt 19:20, 14 Nov 2004 (UTC)

LTP rewrite[edit]

Hi there! I just finished a substantial revamp of LTP to update it with current research and make it more relevant and useful to interested readers. Considering your helpful comments/contributions to the page in the past, I'd really appreciate your feedback (and any contributions, of course!). I'm taking a few days' break from editing the page myself, and hope to come back to it with a fresh pair of eyes. Thanks! --David Iberri | Talk 07:48, Nov 16, 2004 (UTC)

Great! I'll have some time next weekend to read it. Cheers, AxelBoldt 18:25, 17 Nov 2004 (UTC)

Thanks so much for your comments at Talk:Long-term potentiation. I'll have some time this weekend to answer your questions and incorporate your suggestions. Thanks again! --David Iberri | Talk 17:59, Nov 29, 2004 (UTC)

Wikipedia usage question[edit]

Hi AxelBoldt. I am doing a small research project on Wikipedia and have a couple questions about your contribution to Long-term potentiation and dopamine listed on my discussion page. If you have time, I'd really appreciated if you could send me answers. Great articles and thanks!

--Caromk 22:23, 18 Nov 2004 (UTC)

Baireness of Sorgenfrey line[edit]

The Baire question turned up on the http://at.yorku.ca/cgi-bin/bbqa which I answered there. See talk on Sorgenfrey line.

Regards

Henno Brandsma (henno_brandsma@hotmail.com)

Natural transformations[edit]

Regarding your changes at Poincaré duality: Why not allow natural transformations between covariant and contravariant functors? One just need to reverse the appropriate arrow — indeed, the natural transformation article states precisely this. One can then say that a vector space equipped with a inner product is naturally isomorphic to its dual whereas an ordinary vector space is not. -- Fropuff 04:49, 2004 Dec 1 (UTC)

That's an interesting point. I never really thought about it, I guess the definitions I saw were always stated for two covariant or for two contravariant functors. One problem may be that the inverse of a natural isomorphism in your sense need not be a natural isomorphism anymore, so the relation of "being naturally isomorphic" ceases to be symmetrical, which is kind of unintuitive. Also, I don't think that your example works, an Euclidean space won't be naturally isomorphic to its dual in your sense: take the zero morphism V->W; then the induced diagram involving V, W, V* and W* won't commute.

Have you seen the notion of natural transformation between covariant and contravariant functors defined somewhere? If not, then I propose we remove it from the natural transformation article again. Cheers, AxelBoldt 18:02, 1 Dec 2004 (UTC)

As far as the example goes: in the category of vector spaces with inner products the morphisms should be linear maps which preserve the inner product; in which case 0 is no good. Actually it's not hard to see that the diagram involving V, W, V* and W* commutes iff the linear map preserves the inner product. So the example still works.

The only category theory book I have is Mac Lane. As far as I can tell he only defines NT between covariant functors. The place where I have seen the more general definition is in a book by John Lee called An introduction to smooth manifolds. He uses a variation of the above example to claim that the tangent bundle and cotangent bundle of a Riemannian manifold are naturally isomorphic.

I'm not sure about your point regarding symmetry. The construction seems symmetrical to me. I'll have to think about it more. Can you think of any counterexamples? -- Fropuff 21:26, 2004 Dec 1 (UTC)

You are of course right with the morphisms in the category of inner product spaces, sorry about that. Let's stick to finite-dimensional real inner product spaces for now. I see that, given an inner product space (V,<,>), there's a canonical inner product on V* and a canonical isomorphism between V and V* which respects the inner products, but I don't see how it turns into a natural isomorphism in your sense. In fact, I don't even see how the assignment V |-> V* can be made into a (contravariant) functor. If f : V → W is a map that is compatible with the respective inner products, then I would like to define f^* : W^* → V^* by f^*(φ) = φf for every φ in W^*, but that won't be compatible with the inner products on W^* and V^* (unless V and W happen to have the same dimension). So I guess it really only works if we consider the category of inner product spaces of a fixed dimension.

Regarding the asymmetry: if there exists a natural transformation η from the covariant F to the contravariant G, and every map η_X is an isomorphism, then it's clear that F(φ) is a mono and G(φ) is an epi for all morphisms φ. On the other hand, if there exists a natural isomorphism from G to F then G(φ) is mono and F(φ) is epi for all φ. Since these conditions are asymmetrical, I assumed that one can construct an example where only one of the two conditions is true, i.e. where F is naturally isomorphic to G but G is not naturally isomorphic to F.

Here's such an example: take C to be the category with two objects a and b, two identity morphisms and one morphism φ from a to b. Let D be the category of sets. Let F(a) = G(a) be the set {0} and F(b)=G(b) be the set {0,1}. Let F(φ)(0)=0. Let G(φ)(x) = 0 for x=0,1. Then F : C → D is a covariant functor and G : C → D is a contravariant functor. Taking η_a and η_b to be the identity maps on {0} and {0,1} respectively, we have η_a = G(φ)η_bF(φ), so F is naturally isomorphic to G in your sense. But G is not naturally isomorphic to F since G(φ) is not mono.

The two examples seem to suggest that your notion of natural transformation makes good sense only if all morphisms in D are invertible. In that case, D is a groupoid, and it is isomorphic to its own opposite category. Your notion of natural transformation can then be reduced to the ordinary notion, by using this isomorphism. AxelBoldt 01:57, 3 Dec 2004 (UTC)

Ah, I see your point now. Thank you. You are quite right. Your point about the dimension of the vector spaces is also correct; I hadn't thought about that. In any case, one can always define natural transformations between co- and contravariant functors (whether or not it's a useful definition is another question). I agree, however, that natural isomorphisms only make sense in groupoids (where the auxillary definition isn't really necessary). Somehow, I still like the vector space example, even in the restricted setting you mention. It's nice to analyze the naturality without having to jump through the hoop of turning the dual space functor into a covariant one.

Regarding Poincaré duality: it would make more sense to me to claim that H^k and H_n−k are not naturally isomorphic because the associated diagram doesn't commute for all f : M → N rather than to say that one is contravariant and one covariant (I believe the diagram does commute if f is a homeomorphism). Wouldn't this imply that Poincaré duality is natural in the category of orientable Riemannian manifolds of fixed dimension (again, a groupoid)?

Incidentely, one can make a statement about the naturality of the cap product along the lines we've been discussing, albeit in a somewhat weird way -- see Hatcher's Algebraic topology book, top of p. 241. -- Fropuff 15:53, 2004 Dec 3 (UTC)

Ok, I agree that we should mention the way in which Poincaré duality is natural, so I added it to the article now. I guess we still have to do something with natural transformation to point out the problem with natural isos. AxelBoldt 18:44, 4 Dec 2004 (UTC)

Changes to Mathematics[edit]

I'm trying to make a change to the main Mathematics page, which you seem to be active in. I'd like some input. I started the discussion at Category_talk:Mathematics#Change_first_sentence -- Sean Kelly 17:54, 8 Dec 2004 (UTC)

RFC pages on VfD[edit]

Should RFC pages be placed on VfD to be deleted? I'm considering removing Wikipedia:Requests for comment/Slrubenstein, Wikipedia:Requests for comment/Jwrosenzweig and Wikipedia:Requests for comment/John Kenney from WP:VFD. Each of them was listed by CheeseDreams. Your comments on whether I should do this would be appreciated. - Ta bu shi da yu 03:20, 10 Dec 2004 (UTC)

How are monads monoids in a functor category?[edit]

If I understood the history of "Monad (Category Theory)" correctly, you are the person who wrote that a monad can be seen as a monoid object in a functor category. How is this supposed to work? Are you claiming that T o T is the product of an endofuctor T : C → C in the functor category C^C? That seems wrong. Please clarify, since I am tempted to change it.

As far as I can see, the functor category C^C has products if C has products, in which case they are computed point-wise. So, it cannot be right that a monad is a monoid in C^C.

If you would like a relationship between monads and monoids, you can say this: a monoid M can be seen as a monad defined by T(X) = M x X, mu_X : M x M x X --> M x X maps (m, n, x) to (m n, x) and eta_X maps x to (e, x) where e is the unit of M.

You are perfectly right, it's not a monoid object. Thanks! I deleted the offending statement. AxelBoldt 05:02, 13 Dec 2004 (UTC)

Ejaculation[edit]

The only problem I found with your edits was deleting the link to anorgasmia, a disorder of ejaculation. Doug22123 10:10, 18 Dec 2004 (UTC)

Image copyright[edit]

Hi! Thanks for uploading Image:Acrylamide.png. I noticed that it currently doesn't have an image copyright tag. Could you add one to let us know its copyright status? (You can use {{gfdl}} if you release it under the GFDL, or {{fairuse}} if you claim fair use, etc.) I know you say that all your written word is public domain, but what about images? Thanks so much. --[[User:Ricky81682|Ricky81682 (talk)]] 20:49, Dec 19, 2004 (UTC)

Done. Thanks for letting me know. AxelBoldt 04:22, 21 Dec 2004 (UTC)

Hi, I am also one of those people who are working on image copyright issues. I noticed that Image:Stein_by_picasso.jpg is described as public domain and untagged. I think {PD-art-US} is a good tag for it because Picasso has passed away less than 50 years ago, and his works are therefore fully protected in many non-US jurisdictions. But I would contact you first and ask your opinion. Thank you for your attention, Tomos 14:31, 21 Dec 2004 (UTC)

I'm sure you know more about this than I do; I wasn't aware that other countries base the protection on the date of the author's death. So please adjust the copyright notice as you see fit. Thanks, AxelBoldt 21:31, 21 Dec 2004 (UTC)

Thank you :) I tagged it with {PD-art-US}. Tomos 21:35, 21 Dec 2004 (UTC)