Re: reasoning under computational limitations

Wei Dai (
Wed, 7 Apr 1999 18:51:34 -0700

On Thu, Apr 08, 1999 at 01:31:16AM +0000, Nick Bostrom wrote:
> 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.

I would say the hypothesis that I am equally likely to be any of an infinite number of observers is logically inconsistent. This is simply because there is no uniform distribution on an infinite set of discrete events. The universe may contain an infinite number of observers, but if that is true I can't be equally likely to be any of them. This is really a very simple and obvious idea.

> 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 don't understand this. The preferred point is supposed to figure into your a priori distribution for where you are. If you already know for certain where you are, the preferred point is no longer relevant. The preferred point is like a physical constant, it is somewhat arbitrary but like other physical constants it has to be part of a complete theory of an infinite universe.

> > 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.

I don't understand this either. How can there be a infinity of points at one Planck time after the Big Bang at the center of mass of the universe?