Compactified spaces
As you probabely know the idea of there being more than 4 dimensions is a very persistent one in speculative physics. Most prominently there is string theory which needs 11 dimensions, but there are many other fancyful ideas. (Which are a bit more economical in the number of dimensions they need). Me myself I work on such a model for my PhD.
Normally, the dimensions d > 4 are discussed away from every day experience by claiming that they are compact and small and hence we cannot walk into them. They only unfold for a very high energetic probe.
At least in popular books these ideas are illustrated with a picture like this:
That is people tell you that you should imagine a small circle or (something more complicated as in the picture) attached at each point in your 4d space. That is you think of some lattice like in the picture, attach your circles and then take a continuum limit, ie let the circles move closer and closer together. Not so difficult is it? But this is blatantly wrong. Because according to this picture you have a compactified space at each point on the plane, but once you move into this plane, you get detached from the surface holding it. Whereas in reality at each point in the compact manifold there also extends the extended plane again. And from there it continues until you get mad.
That is to say the above picture is very different from the one of a infinite cylinder of radius R:
In the cylinder, which is extended in 1 dimension and compact along another, when you move along the circle at every point you have a inifinite line. Staying whith this two dimensions the above picture would correspond to a straight inifinite line, where there are circles attached at each point. So at every point in the line you are free to move into the circle or to continue along the line, but once you have left the line and entered a circle, there is really only one direction open to you until you have walked all along the circle.
Or take a torus (donut) which is 2 dimensional and compact in both directions. Each point is the intersection of two circles. The thing above isn't such.
Honestly, I can imagine 3 dimensions because that's the space I live in, and then I am fine with the fourth, because I know what time is, but all the other things I have no intuitive grasp.
J'ai pris l'image de ce site.Merci
Memo for myself...
Vielleicht hilft's ja irgendwann...
Es wird immer widerlicher....
Eigentlich bin ich ja Bahn Grosskunde, da ich aus oekologischen Gruenden Bahnfahren dem Fliegen vorziehe. Aber zur Zeit bin ich mir nicht so sicher, ob man nicht einfach die Bahn boykottieren sollte bis die ihren
Saustall aufgeraeumt haben und den lieben Herrn Mehdorn in die Wueste geschickt. Am Schluss ist dass alles nur eine Bereicherungsanstalt fuer Gutbetuchte auf dem Ruecken der Bahnfahrer, einfachen Bahnangestellten und Steuerzahler. Wahrscheinlich hat die Bahn einfach noch Glueck, dass grad alle damit beschaeftigt sind mit dem Finger auf die Banken zu zeigen. Wenn man schnell und koordiniert alle Reisenden einen Monat lang auf Alternativen umsteigen, dann ist Herr Mehdorn weg in Null Komma nix. Und warum auch nicht mit einer solchen Drohung diesen idiotischen Boersengang auch gleich noch vom Tisch wischen? Die deutschen Bahnfahrer wollen ihn ja nicht, dass hinreichend bekannt. Und fuer ne Bahn mit der keiner mehr faehrt zahlt auch keiner was an der Boerse.
Changing Matlab's Java version
I have students version of
Matlab (release 2007a) running on my laptop.
It is actually the only piece of non-free software that I run. And indeed, I find their licence/company policy embarrassing. And it's plain expensive, only those students licences are cheap (ca. 70 Euros...) But still so it's a bad deal, because they are normally out-of-date releases and quite buggy. In my case I had no way
to get certain frequently used characters like "^" (exponentiation) and "~" (negation) printed unless I switched to an American keyboard layout. But me, I don't now by heart where all the special characters are. So using the American layout worked but caused a lot of typos and wild character binding guessing.
Not very comfortable. And then whenever I tried to edit certain features in the preferences the whole thing crashed. Until I noticed from the lots of JAVA exceptions that Matlab uses its own JRE. So I changed it to my newer Java version.
Now it works beautifully, I can browse the prefs without crashes, and I even get the "^"s and "~"s where they should be. But hey, if you ship a JRE with your program, why don't you check it's together working beforehand? It's a bit embarrassing, no?
So here is what I did:
How to change Matlabs Java version
By default Matlab ships with its one JRE, which is in (for linux 32bit)
$MATLABHOME/sys/java/jre/glnx86/jre_xx
where $MATLABHOME is your installation directory and xx stands for the Java version. In my case (release 2007a) it's Java 5.
I created a link in this directory
$ cd $MATLABHOME/sys/java/jre/glnx86
$ ln -x /usr/lib/jvm/java-6-sun/jre jre1.6
Then I edited the file jre.cfg in the same directory to contain this link instead of the
old version. But this is not enough. You have to set the environment variable MATLAB_JAVA.
So I added the line
export MATLAB_JAVA=/usr/lib/jvm/java-6-sun/jre
in my .bashrc then open a new shell and start Matlab from it.
Note that for me java-6-openjdk did not it crashed right after startup.
You might ask why I you have this "evil" software in the first place? Right.
I know there is
Octave to replace it, and I use that as well. The reason why I still have Matlab is that we teach courses in the
Master's programme in Matlab. Oh, well this is even worse. We hook the student on to it... I totally agree, we should migrate all the material to Octave or even C (which the students are more at ease with anyway, they normally don't manage to get into the matrix/vector programming model of Octave/Matlab), but that is out of my hands.
I even had to buy the student licence for my laptop because there was no other way that I could show the programs in class.
(No, there is no University owned laptop that I could use. And no, the computers in the lab cannot be used with a projector, and no I could not login to a remote computer and run it there, because there was no network plug with a DHCP service in the computer lab at that time. I have tried it all. Uff, you are free to imagine by yourself, what I my opinion is about all this...)
Nerdy winds they have in Turkey...
On the back of my notepad there is the schedule of a workshop. (I must have picked it up in the printer room or so, not that I
know what workshop it was) One of the talks is entitled
How the wind created strangely shaped rocks in Turkey by computer simulation
I'd really like to get to know this wind. Seems to be a smart guy, maybe it could do my simulations once it is done with the rocks.
