Re: Re: Re: Re: Evidence: Open vs. Closed Universe

Anders Sandberg (
27 Nov 1997 11:34:36 +0100 writes:

> In other words, if you get to the end of the universe then what's beyond
> that?
> Then what's beyond that? Etc.

I actually read this argument in Lucretius De Rerum Natura yesterday
(wonderful book, by the way; I really recommend it), he argues that
the universe must be infinite, since if you stood at the edge and
threw a spear, it would either hang in the air (impossible, or
requiring some force from the outside) or fly into space (and hence
there is something out there).

The fallacy in this argument is the assumption of some kind of edge,
of course. But you can have a finite surface with no edges, like a
sphere, and with nothing "outside it". A manifold (a surface, volume
or spacetime) doesn't need to be embedded in anything at all to have
an intrinsic geometry that is consistent and has all the necessary
properties to run a physics; this is basic differential geometry, see
any introductory book in the subject for a proof of Gauss Theorema

Of course, this *sounds* extremely counter-intuitive and silly to
anybody who is used to handling objects embedded in three-space, but
it is actually self-consistent and parsimonious. See any introductory
book about cosmology for more discussions of how you can have a
finite, closed space with no edges and nothing outside.

Anders Sandberg                                      Towards Ascension!                  
GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y