Brian Tung wrote:
Paul Schlyter wrote:
...and where is that "somewhere else" supposed to be?

I mean, isn't the universe supposed to be "everything that is, everything that
was, and everything that will be", instead of merely everything we could
in principle observe? If the universe really is *everything*, there cannot
be any "somewhere else".

From the context, I hope it is clear that we have been talking about the
universe as "a connected piece of space-time." Therefore, it need not
be "everything there is." If that piece of space-time is embedded in
some higher space (such as four-dimensional Euclidean space), which is
not actually necessary, then there can be a center to that universe that
does not lie within it.


OK. My understanding of (one variety of) four-dimensional Euclidean
space is, that if we head off any direction, after an arbitrarily long
time we will arrive at our starting position. Reduce all dimensions by
one, and you have the 'ant on a balloon'.

However, I always understood this to be an analogy just used to aid in
visualisation, so that the centre of the balloon was simply an artifact
of the geometry of the analogy, and not a 'place' in any meaningful
sense of the term. Therefore, when we describe our universe as
'four-dimensional', all we are really saying is, that if we travel in a
straight line for long enough, we eventually end up at the starting
position. We are not making any claims on whatever higher geometry there
may be.

My question is: If the universe is described as four-dimensional, does
that mean that it necessarily has a geometrical centre. That is to
ask, is there a place that is an equal distance from every place that we
can observe, (and travel to).

Of course I'm thinking of a 3-sphere, not a 3-torus. I'm a little too
tired to think about those at the moment....

Stupot - higher dimensional layperson.