Re: reasoning under computational limitations

Nick Bostrom (
Thu, 8 Apr 1999 01:31:16 +0000

Wei Dai wrote:

> 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.

Ah, I thought you had some independent paradox in mind. This is just a version of our plain old observer self-selection paradox when infinities are involved. And I am suspicious of the claim that the solution is to declare such universes logically impossible.

> 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.

If you knew where you were, maybe you could define the preferred position to be the place where you are. But in the case we are considering, you don't know where you are, and any choice of a preferred point seems equally arbitrary.

> 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.

I think there is an infinity of such points, and because of quantum randomness, those points would (with prob 1) house an infinity of consciousness-instances.

Nick Bostrom Department of Philosophy, Logic and Scientific Method London School of Economics