From: Chris Ho-Stuart <>
Newsgroups: aus.religion.christian,aus.religion,nz.soc.religion
Date: Friday, 12 March 1999 11:33
Subject: Re: Some hard questions for Able


In aus.religion.christian Edward Ruvinski <> wrote:
> Yes, you're right.  I do assume that the universe has boundaries.
> But I have an argument somewhat different from yours.
?
> Whether a person accepts that "God created the Heavans and the
> Earth" or that during the occurance of the Big Bang (let's not
> get too caught up in the technical jargon of the latter's school
> - I don't think that this should become a predicate-slugging
> match), time and space began to exist at those events.  Was there
> something at spot of Creation / Big Bang / Whatever-you-call-it,
> before the event?  That's beyond the scope of what we're talking
> about and is actually irrelevant to the discussion.

I do not believe so. The question itself reveals some
fundamental misunderstandings of the so-called Big Bang
model of cosmology.

> Now, since the universe had a definite beginning, and the
> universe isn't expanding at an infinite rate of movement (that
> is, the expansion of the universe isn't happening at infinity
> Km per hour), then the universe cannot be infinite in size.

This is incorrect. You are arguing from logic, which means
that you are deriving consequences of your starting assumptions,
some of which are implicit, and incorrect.

One of the assumptions is that expansion starts from a zero
"size". This assumption is quite possibly false. I suspect it is
true. But we will not be able to distinguish these two possibilities
by logic. We need to actually get more information which is not
merely derived from present knowledge.

> That which is not infinite in size has a boundary.

This is based on the assumption of cartesian geometry, and
is false.

> Since the universe cannot be infinite in size, the universe
> has a boundary.
>
> >   Define universe boundary  please.
>
> The point beyond which space-time does not exist.

Since points are in space-time, this sentence is meaningless.

The geometry of space is complex. We can visualise some of the
notions; but bear in mind that this is only an informal guide;
and includes a number of simplifications which are technically
incorrect. Also bear in mind that I am a rank amateur, and you
will easily find much better information if you take up any
study of this area in a library or on the net.

The universe has three spatial dimensions. We think of things
located in space, and we describe locations with three co-ordinates
in a kind of abstract cartesian grid, extending to infinity.

Imagine now a two-dimensional universe, where locations are
described with two co-ordinates. This hypothetical universe
is in a space like an infinite sheet of paper. So now think
of a two-dimensional universe, but curved in on itself like
a sphere. The universe is only the surface of the sphere;
locations are described with two dimensions; but the universe
has a strictly bounded spatial extent. Lines do not extend
to infinity, they ultimately curve back on themselves. This
cannot be avoided; you cannot pick a direction for the lines
which prevents them curving back on themselves.

Note that the space is bounded, but there is no boundary.

Our universe might be a bit like this -- except that it is
in three dimensions, not two. Also, we tend to visualize a
two dimensional spherical surface as being embedded in a
larger three dimensions crtesian space. This is misleading.
Space is not embedded in a higher dimensional space: it is
itself intrisically curved. The curvature of space does not
enclose anything... it is just a description of the fact that
large spatial extents do not correspond to a nice regular
cartesian grid.

A two dimensional universe can have other kinds of curvature.
Imagine an infinite curved two dimensional sheet shaped like
a hyperboloid, or a saddle point in the mountains. It has an
unbounded extent, and as you move large distances lines do
not inevitably curve in on themselves. In a sense they curve
out in ways which have more freedom rather than less. This also
is not a simple cartesian space.

These two cases are highly simplified two dimensional analogs
of the two major alternatives for our universe; called "open"
and "closed".

I've omitted time.... our universe has one time-like dimension;
we locate objects with three spatial co-ordinates and one time
co-ordinate (indicating "when" an object was at the spatial
position). Over time, the curvature of space changes. It is
as if the sphere or saddle point was expanding. This is an
expansion of space itself... not just a movement of objects
away from one another in space.

So about the big bang... in the past, the universe was hotter and
denser. Space itself had "tighter" curvature. Taken to a limit in the
past, it turns out that the universe tends to unbounded density and
temperature at somewere from 12 to 15 billion years in the past.
It also turns out that space itself tends to unbounded curvature,
and that time itself does not extend past this singularity.

If the universe is infinite in extent (open) then it was *always*
infinite in extent, even right up to the singularity.  If the
universe is finite in extent (closed) then it was always finite
in extent.

The "big bang" singularity is not a finite point "in" space and time
out of which the universe expanded. It is a state "of" space and time,
or better it is a limit or bound on spacetime.

Cheers -- Chris