Motus Mentis

3 Comments

1. the one eyed man says

   I have yet another off-topic contribution to your blog. Have you ever wondered why Google is a misspelling of the word googol?

   This is because of a neighbor of mine, who owned the domain googol.com before Google became a company. First Google offered to buy it, and then they sent lawyers after him, but my neighbor refused to sell, and Google had to settle for a misspelling.

   The Wikipedia entry for googol states that “The googol is of no particular significance in mathematics, but is useful when comparing with other incredibly large quantities such as the number of subatomic particles in the visible universe or the number of possible chess games.” Which brings up an interesting question: is there a finite limit on the number of possible chess games? And if so, how would you find out what that limit is?

   Posted March 19, 2007 at 11:35 pm | Permalink
2. Malcolm says

   Peter, that’s a very interesting question indeed. Due to the rules that govern draws, the number of possible games would indeed have to be finite, I think. Furthermore, as far as counting them is concerned, it would be trivial to write a computer program that would explore every possible sequence of moves to its conclusion, although it would take a very long time to run.

   But the interesting bit — which is, I’m sure, why you raised the question — is whether there is a simplifying insight that might allow one to model the set of possible games in such a way as to be able to calculate directly how many there are, and about that I have no idea. I rather doubt it could be done; I don’t think chess is “compressible” enough.

   Posted March 19, 2007 at 11:48 pm | Permalink
3. the one eyed man says

   One would suppose that there is a finite number of moves in the game of go, and the calculation of that number would be relatively easy to do.

   The Economist magazine recently had an article which stated that while powerful computers can beat human beings in chess, the opposite is true of go, where strong players routinely beat computers. The article further speculates that this is not because programs built around go are not good enough, but rather because of the intrinsic nature of the game.

   It would be an interesting exercise to find out which game has a greater number of possible moves, although I’m not sure the information would be actionable.

   Posted March 20, 2007 at 12:04 am | Permalink