From: Wei Dai (weidai@eskimo.com)
Date: Wed Apr 07 1999 - 19:51:34 MDT
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?
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