Tuesday 27th May 2003
Brain Food
Wow, I think I can almost understand the Banach-Tarski Paradox, or, seeing as I’m being a part-time mathematician, I can more accurately understand the Banach-Tarski Paradox as it is set out in the linked article. Subtly different perhaps, but there’s an entire branch of science devoted to that kind of thing. The paradox isn’t, in that it’s quite easy to split up one sphere and rearrange the pieces into two spheres identical to the first - easy, that is, if you are talking about infinitely dense spheres. If you did that with two spheres of lead, you would end up with two spheres the same size, but each with half the density that you started with (and I’ll not go into the chemistry or energetics of said spheres), but if the density was infinite to start with, it’ll still be infinite when you divide it by two. The mathematical spheres are infinitely divisable, but it still results in the same kind of thing. Read the explanation of splitting N into odds and evens if you’re still struggling (and, at the same time, wonder what kind of a ‘Layman’ reads these kuro5hin articles!)