Friday, March 10, 2006

Good Math, Bad Math: Tasty Brain Food.

If you are looking for some good brain food, you could do worse than Good Math, Bad Math. It has an easy style that leads you painlessly through interesting subjects without bogging down in the actual math.

And it is funny:

"Godel presented an extremely complicated proof that showed, essentially, that no formal system could be both complete and consistent.

Most people saw Godel's proof, did the equivalent of saying 'Oh, shit!', and then pretending that they hadn't seen it. It does mean that there are fundamental limits to what you can do using mathematical formalization, but for the most part, they don't affect you in normal day to day math. (Sort of the way that car designers didn't change the way they build cars because of relativity. Yes, it showed that the fundamental physical model that they were using was wrong - but at the speeds that cars move, that wrongness is so small that it just doesn't matter.)"