as you may have noticed, i use wikipedia a lot – both for linking to descriptions of terms i use in this blog, and for looking up stuff myself which i encounter somewhere, may it be offline or online. usually, chances are good that wikipedia offers at least some kind of description which answers my questions, or at least helps me getting an idea. but from time to time, it happens that you try to look something up on wikipedia, only to find out that such an article existed but was deleted – for example, because it was “not relevant”. i can understand that people do not want to see wikipedia flooded by biographies of john doe and jane roe – only a handful people are interested in these, probably most notably john doe and jane roe themselves.
but there are cases where i simply can’t understand the decision. for example, there is the chilenian doom metal band mar de grises, which i discovered by chance in zurich’s now deceased knochenhaus. according to the wikipedia deletion log, it is “not noteable” and failes some guidelines. so, who decides what is noteable and what is not? and, after all, the simplified ruleset explicitly mentiones

ignore all rules – rules on wikipedia are not fixed in stone. the spirit of the rule trumps the letter of the rule. the common purpose of building an encyclopedia trumps both.

i can pretty well understand that not every small band hobby band project should be mentioned – in particular the ones which sound bad and dissolve quickly with none or almost no productions. but that’s not the case for mar de grises. besides that, the deletion log also mentiones other problems with the article (namely, being badly written and failling to provide references for some claims), but why not throw these parts out or reduce the article to a stub?
two other examples, this time from the german wikipedia, are sinnlos im weltraum and lord of the weed, two fandubs. according to the english wikipedia, sinnlos im weltraum (a redub of a star trek series), dating back to 1994, is one of the first such projects, essentially starting the whole genre of fandubs. i don’t know how many people know it, probably a huge number. lord of the weed (a redub of the beginning of 2001′s lord of the rings) is also rather well-known; i don’t remember how often i saw it – at least ten times. well, it is obviously true that these movies haven’t been shown in movie theaters or on television – as they contain copyrighted material (i.e. the original movie), used without permission. for the same reason, they haven’t been shown on film festivals, you can’t buy them on dvd. they are also not listed on the imdb. but – so what? does that make them not noteable? irrelevant?
on the other hand, a lot of totally trashy movies – which, compared to sinnlos im weltraum and lord of the weed, are really crappy and lame – are featured on media, two good examples are a music video by grup tekkan and the infamous star wars kid, making a fool out of himself. these are pushed by media as “youtube movies you have to see” or are even shown on tv. and they can be found on wikipedia. even though they are real crap. in the case of star wars kid, the really embarrassing movie was uploaded by “friends” of its actor and will probably haunt him for a very long time. to make this even better, a lot of online versions of famous newspapers or magazines feature this video as well, showing it to an even wider audience. and i thought the use of a pillories are outlawed in modern countries.
anyway. i’m still using wikipedia, even though of these reasons. and i even created an account at the english wikipedia and started writing an article about infrastructures (number theory). as so far, nobody else dared to write something on this subject, and a google search only gives documents featuring other kinds of infrastructures, or scientific articles about this subject, i thought it would be time to add something to the web. i’ve started a series of posts on my math blog on infrastructures, but as google usually ranks wikipedia articles higher, i decided to also add something to wikipedia. so far, it is more a stub and far from being a complete article, but at least provides some information and several references to literature.

i finally started another project: a math blog. the aim of this one is to write about mathematical things which interest me, for example things related to my research. the formulae will be rendered with latex; mathml is simply unuseable so far.
an example post shows a feature with i added to my wp-latex enhancer plugin: (primitive) environments for definitions, theorems, proofs, etc., including a very basic labeling system allowing hyperlinks which jump to the right environment; for example, here’s a link to a lemma in the post. the post features my favorite proof of the fundamental theorem of algebra, using complex analysis.

mathematics is nothing but the search for structures. beautiful structures. i myself tend to think i understood something if i manage to have a picture of it in my head, some geometric interpretation. sometimes it’s more easy to understand something if one can somehow draw it, by hand, or using a computer, which can sometimes give insights which would not be possible without it; the best example maybe is the beautiful mandelbrot set. most visualizations are by no means as impressive as the mandelbrot set, unless the viewer is acquainted with the underlying mathematics. like the following one, produced by the programs i wrote yesterdays and today, whose beauty probably won’t unfold if you don’t know what it depicts:

do you know the feeling when, while doing something completely unrelated, like taking a shower, you get an idea? an idea which is somehow cool, which will change life completely, in some sense? with such ideas, usually lots of endorphines and adrenaline is set free, making you unable to sleep, to rest, to think clearly. then, after spending the day working the idea out, you finally notice a tiny flaw, something that didn’t worked as smoothly as you thought it would or should. such tiny, but yet so fatal, killing the whole idea, throwing you back to the ground of the pit, where you continue to lurk around, in search for new ideas. but then, it’s not as bad as it sounds. usually you learn something. you get a better understanding of something, the object in question has turned into something which you can see better with your mind, from a bit farer away, not as near as before, so near that you can see every bump but have no clue what these bumps belong to. like a new stack of jigsaw pieces, given to you to plug it into your big world puzzle, to complete it a bit more, to widen your glance on the truth. the universe got a bit smoother.

no, this post is not about the area of abstract algebra in mathematics, but about the experimental metal project abstrakt algebra founded after candlemass‘ dismanteling by leif edling. they released one album and started with a second, but ran out of money, and leif ended up escaping bankrupcy by re-using some of the second albums material to create another candlemass album, dactylis glomerata (named after a flower he’s allergic to). the 2006 reissue of dactylis glomerata contains as a bonus disk the unfinished version of the second abstrakt algebra album, entitled abstrakt algebra ii (now guess how the first one was called). well. the arrival of that one kicked me out of bed this morning, when the mailman rang the doorbell. but it was worth getting up for it, and even if it is not a very good album, it is not good, it is interesting, and it is one of the albums every mathematician who has a similar strange taste of music than me should have in his cd shelf. of course, together with their first album, which i just ordered. ;-)

consider the field of all numbers. meaning, of course, the complex numbers. we say that a number is representable if we can describe it by a text (for example, by a binary coded string of 0′s and 1′s of finite length). the set of all representable numbers is countable, as there’s a surjection of the set of binary strings (which is countable) onto it. moreover, it is a field, as if a and b are representable numbers, we have that a + b, a − b, a ⋅ b and a / b are represented by strings as “sum of (description of a) and (description of b)”. obviously, every algebraic number is representable, so our field of representable numbers contains the algebrically closed field of the algebraic numbers. but then, our field also contains euler’s number e and archimedes’ constant π, so it’s strictly larger. this opens the question: how does it’s algebraic closure looks like? not too surprisingly, it turns out to be already algebraically closed: every element in its closure can be represented by “root of polynomial with coefficients (description of coefficients)”, as all coefficients are representable. hence, our field, being countable, is strictly larger than the smallest algebraically closed subfield of the complex numbers, but still countable. and it contains lots of transcendental numbers. isn’t that cool?

i’ve always thought that mathml is a great idea, allowing you to write formulae in html which look good afterwards. or so i thought. then, today, i saw this. at least in my browser (firefox 2.0.0.6), i have the feeling that word by default produces nicer formulae than this. then, i started searching the web for other examples, maybe it is possible to produce better output. but then, even when looking at (seemingly) standard examples as this and this (the latter supposed to display that 44.997 is an element of the reals), i’m shocked how bad this looks, if it works after all (the first did, more or less, and the latter didn’t). i mean, i know that it might be illusive to expect that the formulae look as good as in latex, but i would have at least expected them to be rendered correctly…
well, i’d guess the only way is to stick to rendering formulae with latex and including them as images, as it is standard practice on basically all sites displaying good looking formulae on the web, as wikipedia, matroids matheplanet, matheraum, etc.
or simply don’t use any formulae in html files, as i’m doing so far. too bad.

i’m currently staying in dublin, attending the 11th workshop on elliptic curve cryptography. our view on the countryside has been very brief, basically being limited to the view out of our cabs window on the way from the airport to our hotel. we haven’t seen much more from the city, mainly exploring the way from our hotel to the ucd campus, which means walking next to a big busy street for 20 minutes, walking a bit over trinity college yesterday on the way to the conference dinner, and then seeing the inside of some restaurants and pubs. a very nice pub was a real, completely non-touristic irish pub which we’ve been in two days ago (the only tourists in there being us). it were actually two pubs, connected by a small door and owned by the same person, the difference being a bit the ambient—the one more aristocratic, the other for the plebs—and, suprisingly, the prices, being slightly higher in the aristocratic part. well, and the people were slightly different too, like more suits could be seen in the aristocratic part. opposing to that, we were in a very touristic pub yesterday, with “folk” music and dancing. probably only remotely related to real irish traditions. but very popular among tourists.
another strange thing we encountered is the fact that almost noone here speaks irish. ask a random irish person on the streets, chances are really small he does. well, they apparently learn it in school, but they probably like it as much as the germans like to learn frensh in school: most aren’t able to do a conversation exceeding something like “hi, my name is felix, who are you?”…
this afternoon, we’ll probably see a bit more ireland; planning’s still to be done, we are aiming at something but it’s not sure yet that we can get there in time. if we do, i’ll write about it tomorrow, after my return home. stay tuned.

sometimes i wonder why mathematics is working so smooth as it is. for me, this is one of the most intriguing things around, next to the questions on why do we live and on whats the question to the answer 42… based on a small set of axioms, nobody knowing whether they are free of contradiction, an enormous building of constructions and proofs has been built. so huge, that no one can learn about all of it in one lifetime. and inside this building, between lots of dirty corners with ugly computations and hard work, there sit so many beautiful small and big results, sometimes showing surprising connections to completely different parts of mathematics. this connectivity is what surprises me most. every time again. that’s what i like about mathematics, and that’s what’s keeping me doing math. and makes me even more curious about the question on why it is working so smooth.