Re: reasoning under computational limitations

Wei Dai (
Sun, 4 Apr 1999 18:22:25 -0700

On Sun, Apr 04, 1999 at 08:13:17PM +0000, Nick Bostrom wrote:
> How do you define this "fraction" when both the number of observers
> and the size of the universe may be infinite? If you think of
> density, note that (1) The distribution need not be uniform, so there
> can be different densities for different regions, and (2) It seems
> strange if it would matter where in the universe the observers happen
> to be, how they are grouped.

This density computation has to converge, and I see two ways this can happen when the size of the universe is infinite. The universe repeats itself in every dimension that is infinite, or the the density computation is weighed by a factor that decreases with the distance to a prefered space-time position and decreases fast enough for the density to converge.

This rules out the possibility of an infinite universe that does not repeat and does not have a prefered position, but such a universe leads to various paradoxes so I don't think it can be logically consistent anyway.