Re: poly: eschatology

From: Nick Bostrom <>
Date: Mon Jan 12 1998 - 16:15:21 PST

> From: (Damien R. Sullivan)
> On Jan 11, 9:57am, Hal Finney wrote:
> > Unless there are some ad hoc topology wraparounds, the zero and negative
> > curvature universes are infinite in spatial extent, with an infinite
> > number of stars, unlike the closed universe.
> Say what? I have heard no cosmologist besides Eric Lerner suggest the
> universe is infinite in extent and mass. Finite and expanding is the
> canon, no?

Now, that was what I have heard some people say, and it confused me
because I've also heard people saying its infinite. Hal is saying
its infinite (if open), and Ithink he is right, but I
want to be certain. At this stage I want to find an autoritative
texts and settle the question once and for all. Could anybody please
give me a page reference?

 Anders Sandberg <> wrote:
> Imagine a plane which expands, so that the point (x,y) (like a star
> at rest relative to its surroundings) at time 1 becomes (tx,ty) at
> time t. As you approach t->0, the stars move closer and closer
> together; for any remote star there will be a time when it is within
> radius 1 of the origo.

Though there will be no time (different from t=0) at which all stars
will be within a radius 1 of the origo. If the universe is open then
there are infinitely many stars and the only thing that happens as
one goes backward in time is that they get closer together, the
density increase. The spatial extent remains infinite until t=0, at
which point we reach a singularity, unless, which seems rather
plausible, GTR breaks down as density goes toward infinity, and some
quantum gravity effects intervenes. This is what I now think is the
right way to picture the scenario, but I want to be absolutely sure.
It makes a big difference to my world view whether the universe is
only big or whether it is literaly spatially infinite at the present
time. If it's infinite, then I can be sure that there are infinitely
many exact copies of myself in existence right now, and none of my
actions will make any difference to the total quantity of anything in
the universe that is not local: for example, I can't in the slightest
increase of decrease the total amount of pleasure in the universe.
This seems interesting enough that it is surprising that not
attracted more attention.

Nick Bostrom
London School of Economics
Department of Philosophy, Logic and Scientific Method
Received on Tue Jan 13 00:16:13 1998

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