[ExI] What should survive and why?

[Stathis Papaioannou]

On 07/05/07, Samantha Atkins <sjatkins at mac.com> wrote:

> If the universe is infinite and uniform, then I think that everything that
> can happen, does happen. By infinite I mean that there exists a countable
> infinity of any given finite volume of space. By uniform I mean that the
> physical laws remain uniform everywhere and that physical parameters such as
> density and temperature limit towards some universal mean in any
> sufficiently large volume, an assumption that most astronomers make about
> subsets of our own Hubble volume. Now, with the conditions described there
> is a non-zero probability, call it p, that any given physically possible
> event E will be found to occur in a given volume of space, and this
> probability is uniform over the infinite volumes of space available. So the
> probability that E does not occur within n volumes of space is (1-p)^n. You
> can see that as n-> infinity, (1-p)^n approaches zero, which means that for
> sufficiently large finite n, Pr(E) can be made arbitrarily close to 1. E
> could be something like "an arbitrarily close functional analogue of my
> brain at the present moment".
>
>
> Not so fast.  If the number, n(E), of possible things that can occur is
> much larger (much less a different order of infinity) than the number of
> places/states/chances it could occur in then your argument fails.
>

That would be so, but the Bekenstein bound in quantum mechanics sets an
upper limit to the amount of information or number of distinct physical
states contained in a finite volume of space. So even if you specified E
down to the quantum level (which is overkill: you don't care if your copy is
identical to you aside from one atom in her hair), the number of possible
things that can happen in a finite volume of space is finite. If the number
of volumes is infinite, then E has to occur.

-- 
Stathis Papaioannou
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