ever seen such advertisements?

“start making money entering data online!
work from home at your own time. anyone from any where in the world can do this job. available worldwide.
easily make $250+ per day!
fill out simple web forms at home
sign up here >>>>”

sometimes, i really wonder what people got to do if they sign up. my guess is that they are signing up to work as little spam bees: sit at home, surf the web, spam peoples forums, guestbooks, blog comments, … with spam!
let’s face it. during its lifespan, spielwiese got 310 spam comments so far, and blackness got 34 spam comments. and none of them ever got published; i never let them pass through. one would think that they’d maybe give up after some time, but it seems they don’t want to. maybe because they get paid for entering the spam over and over again?
as spielwiese is based on wordpress, which is a rather common blog software, it’s not surprising that there exists programs which feed wordpress based blogs with spam. so maybe the spam for spielwiese is automatically generated. but the software for blackness is completely self-brewn, so either someone is entering the spam manually, or someone adjusted their program to post spam there, too. or someone wrote a program which puts spam in basically everything which looks like a comment form. i’d guess it’s the latter, or some poor fellow gets paid to do it.
anyway.
spam is freaking annoying, both email spam, guestbook spam, forum spam, blog spam, and hopefully once our governments unite and will really try to do something against it. but then, i’d guess that won’t happen during my life…

today i stumbled about a song called gloomy sunday, originally composed by the hungarian pianist rezső seress. there are probably as many urban myths about this song, which is also known as the hungarian suicide song, as there are cover versions… i like the original lyrics the most; you can read them here (both the original hungarian version and a literal translation). reads like a typical doom song, just written around 50 years too early…
for me, it seems like a really strange idea to kill yourself because of listening to a song, and in particular, it seems really strange to blame a song for making people commit suicide. for me, it sounds like an excuse for not having to search for other reaons… maybe it was the last straw to tip people off, or suicideers decided to listen to it on or shortly before their suicide because it expresses their feelings.
but anyway. i’m somehow wondering whether a doom metal band has covered this one, too; the only metal band i found who did this is a german black metal act called negator; a video of a life performance can be seen at their homepage (don’t watch it if you don’t like black metal); they are performing sam m. lewis‘ english version of the song. i didn’t like it too much, first of all because i don’t think black metal fits here and, secondly, i’d prefer something more close to the original lyrics.

it is autumn and the leaves are falling
all love has died on earth
the wind is weeping with sorrowful tears
my heart will never hope for a new spring again
my tears and my sorrows are all in vain
people are heartless, greedy and wicked…

literal translation of the first stanza taken from phespirit.info.

after watching a horror movie which i didn’t like too much (it felt too constructed, the horror was too obvious), i watched another movie, den tredje vågen (imdb), a swedish one, called the third wave in english, and this one was really, really good. despite being an action movie. reason is, it has a story. a good one. the only bad point was that i could only watch the german dubbed version, as the original was in swedish and i don’t happen to understand that language…
the setting is europe, being threatened by organized crime. the hero, an ex cop, is dragged together with his family into a chase through europe (london to the netherlands to munich) after a backer’s wife who wants to give information to europol. the story is solid, seems to be well investigated and plausible, is mostly not predictable, tension increasing until the end, which is a partially happy end with a deep dark shade left, leaving my mind rattling, chunking on different thoughts. making me fear the environment is too real, too realistic. this is way more creepy than creep.
it’s really a shame this movie wasn’t shown in german cinemas, as it’s way better than most of the movies which were.

every time i plan to start a new project, let it be a web project, a programming job, a latex document (or a combination of those), i’m thinking hard on whether to use something already existing as a base or whether to do everything myself, from the scratch. for latex documents, i usually reuse macros i’ve written myself. for programs, i use libraries like opengl and zlib (two random names coming to my mind, there are of course a lot more), i reuse my own code, and write the rest from scratch. for this blog, i used wordpress, for usage statistics i use phpopentracker. and, of course, i use php and mysql as backends. even though i could implement the whole stuff myself. if i just would have enough time… but i don’t, and so i have to cope with all the restrictions, specialities, whatever these programs and libraries are throwing at me.
the reason why i’m thinking about this at the moment is a new project of mine i’m thinking about, which i’m planning to code more or less from the scratch (using, of course, some backend stuff like php, mysql, phpopentracker, you name it). i just started drawing some sketches, like its logical structure with hints on the physical implementation. sometimes i wonder whether i should spend more time on such things. despite there probably already exists a system which does exactly what i want, making one yourself is way more fun. although its also way more work.
let’s see if i manage to pull this one through… wish me luck.

it’s amazing how fast it is getting dark outside; it’s pretty obvious that summer is gone. even though, today the weather was pretty nice, at least during the afternoon: the sun was shining, and in the sun it was pretty warm. well. after spening two more hours in the darkness (why are there seminar rooms with no window to the outside?), i decided to grab the chance to enjoy the scenery at the zürisee, and then, on the way there, i decided to take a boat trip. and so i did. it was really beautiful, watching the waves, the sun, though it tried blinding me, letting the thoughts wander around, listening to good music (communic, unholy, swallow the sun). it was fantastic. even though the sun began hiding, swallowed by the mountains, the air getting chilly, even cold. the waves are fascinating, changing from a plastic like look to very complex patterns in a minute, somehow reminding me of fractals.
then, coming home, while darkness is crawling upon the sky, changing into blackness, as it is now, only artifical light left. me sitting here, typing, drinking hot chocolate, thinking. the sun is gone for today.

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?

opeth‘s fifth masterpiece blackwater park contains a gorgeous song called bleak. dark poetry painting pictures of betrayal, of frustration, of anger. luring me into deep thoughts, making me float in sadness. at the same time, making me adoring the music, the interplay between mellow and heavy parts, interwoven into a complex composition. carrying me into it’s world. making me addicted to it.
having listened to it so often, it still touches me, hits me, drags me away, as it did the first time i listened to it. you may want to take a look at a beautiful picture created by rose of sharyn, which captures well some of the emotions i feel when listening to this song.

leaving traces is easy. just think on how many fingerprints you leave outside your home every day.
and this does not only apply to your real life, but also to your online life. every little thing you do in the internet leaves traces at many different places. for example, think of typing in a url like spielwiese.fontein.de in your browser and pressing enter. first, your browser will put that address in its history (for the pedants out there: i’m fully aware that there are situations in which this does not happen. as i don’t want to blow up this article with technicalities, i’ll simply ignore that.), so days later you can still see that you visited that page. you’ll also find copies of the page in your browser cache. back to the incident itself. in order to access the site, your browser has to establish a connection with my web server and send a request for that site. this request is relayed though different places, every one able to see that you (identifyable by your ip number, which can be traced back to you by your internet provider) requested this specific site (except in case you’re accessing pages using https, in that case, the intermediate relays just know your ip address and the ip address of the destination server).
finally, in any case, my web server will receive your request to deliver the page / from my domain to you. and, as most web servers do, it will note that down into it’s logfile, so i can see that you accessed my site. in fact, i see a lot more. usually, in the request, your browser sends a lot of additional information: for example, a string identifying the user agent. for example, this could be

Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.8.1.6) Gecko/20070802 SeaMonkey/1.1.4

it usually also includes information on your operating system (in this case, linux) and the exact version of your browser. usually, the browser will also send on which site you were before (the so called referer). this information will be sent for any web page you click on, and for every image or other object contained in that page. hence, i am, without any tricks, able to track you on your way through my web page, and i can see where you’re coming from.
being a bit more clever, i can find out a lot more. for example, i could modify the urls of outgoing links on my page to go though some kind of `gate’, like the forward.php which you might have noticed. then, if you click any link on my site which leaves it, your browser will first contact my webserver to retrieve the forward.php output (which will tell your browser `go to that other site’) and, surprise!, it will leave an entry in the web server’s log that you clicked that link. so i also know where you’re going from my site. next, there’s a lot more information on you which one can find out using javascript, like your screen’s resolution. i’m including a little script on my site which tells the browser to include a little picture, simply consisting of one complete transparent pixel, on every page of my site. to the images url, it adds the screen resolution. so by looking into my server’s log, i can see your screen resolution—at least if you haven’t turned javascript off, but most people have it turned on anyway.
so, now i have a big log file containing a lot of information: which user came from where, looked at which sites, left where, used which browser, which operating system and which screen resolution, at which time. if i feed this log file into an analysis tool, it will gather the information and present them to me in a useable way—whatever that might mean.
are you surprised? some of you won’t be, i know. anyone interested in this subject can find out about this on lots of places on the web (for example, look here). and, in fact, one can do much better than me. first, by using cookies, i could identify you uniquely and connect your different sessions to see how your surfing behaviour varies over a larger time scale. then, i could combine the data from several servers. if i would have data from enough servers, i could throw together a very detailed survey on what you are doing on the web. in that case, i’m your big brother, watching (almost) every step you do online. luckily, for you, i’m not doing that. but other people do. for example, the big web advertisement companies, which have their advertisements on a huge amount of web servers, can see you everytime you view such a web page (if you’re not using an ad blocker). or assume that your web page is using the service of another server which tracks statistics for you. many people are using such services (may it be in the form of a simple counter), so the provider of the service knows when you are looking at which site. and now assume that some of these data collectors cooperate. sharing their huge amount of data. a creepy thought, isn’t it?

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.