# Re: reasoning under computational limitations

Wei Dai (weidai@eskimo.com)
Mon, 5 Apr 1999 16:46:14 -0700

On Mon, Apr 05, 1999 at 07:36:35PM +0000, Nick Bostrom wrote:
> What are these grounds? (You referred to "various paradoxes"--which
> ones do you have in mind?)

I can think of several paradoxes and they all relate to the fact that averages taken over the universe are not guaranteed to converge if the universe is infinite. Expectations are a kind of average, and they do not necessarily converge either. Here is an example. Suppose you are offered a bet where you can win or lose \$1. You are in an infinite universe with an infinite number of people in your situation and you can't tell which of them you are. Some of them are potential winners and some of them are potential losers. The (potential) winners and losers are distributed as follows: 1 winner, followed by 2 losers, followed by 4 winners, followed by 8 losers, and so on. The paradox is that if you try to compute an expected payoff for the bet under the assumption that you are equally likely to be any of these people your computation won't converge.

> The Big Bang is a singularity but not really a position.
> Immediately after the Big Bang, if the universe is open or flat, the
> universe was spatially infinite. So if you assign number 1 to the Big
> Bang, what spacetime point is number 2?