2007

Wed, Jul 25

<02:23 EEST> Read the Finnish translation of The Jungles of Randomness by Ivars Peterson. The book is occasionally a little incoherent, as probably befits the topic, which is about how poorly randomness and probability are understood by current science. In the end game, it reflects my long standing point that probability is not a truly scientific concept, but merely a vague measure of someone's knowledge of an issue.

In a way this viewpoint is part of the "stuff happens" philosophy. Say you get hit by a car. Before the incident, you were in the "not hit" state by 100% certainty, and afterwards you were in the "hit" state, again with full certainty. Perhaps there was a theoretical transition probability between the states, but the fact is now that you are hit. Any event either happens or doesn't.

This is, of course, without going to quantum mechanics where something can happen halfway if not observed. While I'm not fully comfortable with the whole of current QM, it does present a rather credible theoretical framework for probability. Especially the many-worlds interpretation, which IMHO gives the only tangible definition of probability: the ratio of the number of succesful worlds to the total number of worlds.

The book's only mention of QM relates to the idea of Gregory J. Chaitin, also developed by Joseph Ford, that the incompleteness of mathematics (as proved by Gödel) is at the heart of the problem of randomness. It's what causes mathematicians to resort to experiments in their otherwise exact science, and possibly explains the probabilistic nature of QM as well.

Thu, Jul 12

<00:53 EEST> ~ C₆H₁₂O₆ ~. 40100 <3. \o/

Mon, Jul 9

<02:14 EEST> Once again, Project Euler has made me study some new math, this time more than ever. I've struggled with the aptly numbered problem 66 since Saturday, and after learning about Pell's equation and Continued fractions the problem was eventually solved. It was again one of these questions where you can try and brute-force the answer in hours, but a clever algorithm finishes in a fraction (pun intended) of a second.

An interesting by-problem came up with some numerical precision issues. Problems with floating point numbers in Python inspired me to rewrite the algorithm in Fortran 90, which the standard GNU compilers now grok. It didn't offer any improvement besides of course being much faster, and I needed an external library for big numbers. GMPY turned out nice, as the crucial square root needed no fewer than 225 bits of precision :-j

Fri, Jul 6

<00:47 EEST> I've now finished 23 different problems from Project Euler, and I don't see an end to this addiction :) It's one of the best things I've experienced during this stay in Varkaus, with the incredible sense of learning and accomplishment that reminds me of Sigma activieties back in Lyseo.

It's a little strange that I haven't enjoyed this level of recreational mathematics/coding in years. Of course, a professional in a related field will probably find something completely different during their spare time, and my recent dealings with theatrical tech and music also come close. Here I don't have anything to stretch my intellectual muscle, and it's fun to notice I still have the Sigma touch ;)

For most of the exercises I've used Python and learned a little more about things like map/reduce that facilitate functional and parallel programming. I also like to focus on the algorithmic side rather than wrestling with obscure language issues. Then again, the project should be a nice way to learn a new language as well.