Tall, Dark, and Mysterious

7/17/2004

Up-to-the-minute math

File under: Queen of Sciences. Posted by Moebius Stripper at 2:33 pm.

Via RandomWalks, a blog with a lot of mathematical content, written for an audience of non-experts. I haven’t had a chance to look through much fo it, but RW linked this article about random walks. It’s a really cool result: a two-dimensional random walk - a sequence of steps of fixed length in random directions in a two-dimensional space - has a 100% chance will return to its starting point (though it’s easy enough to think of some paths that will never return). This is often expressed in terms of a drunk aimlessly wandering around - he’ll make it back all right. In three dimensions - the drunk bird flying around - there’s only a 0.3405373296… chance of ever getting back. More room to get lost in three-space. Also explains why, before I knew my way around the neighbourhood forest, I’d always find my way back. (Quite helpful in the small town I’m in right now, which few people visit if they’re not from here, which leads to laziness when it comes to putting up street signs.)

I’m especially digging the game theory section, which every political pundit - particularly those interested in the military - should study. Ethics and economics are important decision-making metrics, but they don’t tell anywhere near the entire story. Second-guessing people’s intentions and developing strategy in order to account for them is where it’s at.