From: Wei Dai (weidai@eskimo.com)
Date: Mon Apr 05 1999 - 17:46:14 MDT
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 only way I can see to get around the paradox is to assume that you are
a priori more likely to be near the center/beginning of the universe (or
some other point), and that's what I meant by the preferred position. The
exact choice of the preferred position, how "near" is defined, and how
much more likely you are to be near it should all be part of the
hypothesis that you are considering.
> 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?
I wasn't being very precise when I said the conventional model has a
preferred position which is the Big Bang. What I meant is that the Big
Bang is a natural choice for the preferred position. There are many ways
to define "near" and thus to pick point number 2. The simplest would be to
to pick the point that comes immediately after the Big Bang in the rest
frame of the universe.
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