OO ah - the math. OOOO OOOOO O to those who say "there is no uniform OOOO probability over an infinite set", i say "sure OOOOOOO there is" - as long as we don't let ourselves be OOOO O O tempted into trying to order that set. OOOO O OOO OO consider a series of sets, A_i, all of whom are OO finite subsets of the natural numbers, where: OOO OO O OOOO OO A_0 is the empty set, and OOOOOO OOOOO O A_n is a strict subset of A_(n+1), OOOOO OO OOOOOO you could say that as n approaches infinity, A_n OO OO approaches the natural numbers. OOO O OOOOOO there are many possible choices for the series O OOOOO A_i - but regardless of which you choose, the OO following is true: OOOOOO O O OOOOOO as n approaches infinity, the expected value O O of a uniformly chosen member of A_n approaches OOOOOO infinity. OOOO OO OOOOOO a similar argument can be made for universes. OOO O O as we approach the set of all universes, the OOOO expected value for the K-complexity of a OOO uniformly chosen universe approaches infinity. OOOO OOOOOO O a VERY good question to ask is: what other O O O probabilities can be defined over the set of OOO OOO universes. |