Re: poly: eschatology

Nick Bostrom, <bostrom@ndirect.co.uk>, writes:
> 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?

In "classical" general relativity the three alternatives are as I listed
them. They are referred to as Friedmann cosmologies, and assume that
the universe is homogeneous and that there is no cosmological constant.
If you introduce a CC then you can make a spatially closed universe
which expands forever (just throw in an expansion term) or a spatially
open universe which eventually recontracts (need a compression term).

In Gravitation, by Misner, Thorne and Wheeler, box 27.2 describes the
three alternatives. Section A describes the closed-universe case,
spherical geometry. It has a finite volume which is described by the
integral at the end of that section. Section B describes the flat case,
and ends with "and its volume is infinite". Section C describes the
negative spatial curvature case, and also ends with a comment that the
volume is infinite.

The introduction of inflationary theories adds some new twists. As I
understand it, an inflationary model is technically not homogeneous.
The universe forms as an initially small, rapidly expanding bubble off of
a larger manifold. Near the center of the bubble the observed properties
may be different from at the edges. (I don't understand inflation very
well so take this with a grain of salt.)

At http://epunix.biols.susx.ac.uk/Home/John_Gribbin/Cosmology.html is an
article which describes some exotic variations of inflation which can
make the universe appear locally (i.e. within the visible universe) to
be low density. I am not sure what the geometry and topology is supposed
to be in this case. I think we have hyperbolic geometry locally, but in
some distant parts of the universe the curvature would become positive.
It seems to be a very complicated model. Gribbin's article also mentions
the idea of seeing different mass densities at different parts of the
inflationary bubble.

> 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.

This is an interesting philosophical speculation. You have a similar
result in the many-worlds interpretation of QM. I agree that the idea
of an infinite number of copies of yourself does raise some new issues.
Larry Niven had a story where people made contact with parallel universes,
and it produced widespread feelings of nihilism and frustration, leading
to a rash of suicides.

The way I look at this case is to define my consciousness, my sense of
self, to encompass all those instances throughout the universe which are
in the same state (to the limits of perception). As time goes on, there
is divergence, as fluctuations or differences in the various instances
begin to make their presence felt. This is analogous to the splitting
of universes in the MW interpretation.

In this case you could still hope to make a difference in the universe,
as your decisions affect more than the local instance of you, but all
the infinite numbers which share your mental state. Even where there
is divergence, you could use "super-rational" reasoning (the idea that
if you decide to do something, it makes it more likely that people
sufficiently similar to you will decide the same thing). Super-rationality
is pretty questionable but it seems more convincing when you're dealing
with near-duplicates of yourself.

Hal
Received on Tue Jan 13 03:06:38 1998