From: Jeff Davis (jrd1415@yahoo.com)
Date: Thu Aug 15 2002 - 18:57:14 MDT
Friends,
--- Andrew Clough <aclough@mit.edu> wrote:
> At 10:17 PM 8/15/2002 +1000, you wrote:
> >At 07:57 AM 8/15/02 EDT, Mitch wrote:
> >
> > >The balloon analogy, that astronomers frequently
> use, really stinks.
> >
> >True. The simplification they should stick to,
> although maybe it's regarded
> >as too `girly' (ugh, *cooking*, we don't need to
> know about no steenking
> >*cooking*) is the cake or fruitloaf that expands in
> all directions as it's
> >heated and cooked, moving all the raisins apart
> from each other in an
> >unprejudiced way; the raisins, like galaxies,
> retain their integrity.
> >
> >Damien Broderick
>
>
> There does seem to be a difference between the two
> analogies, though. If
> an ant walks along the outside of a balloon for far
> enough, it will
> eventally come back to where it started. On the
> other hand, an ant
> tunnelling through a fruitcake will eventually get
> to the outside of the
> fruitcake. As far as I've heard (and I'd welcome
> someone who knows more
> about cosmology weighing in here) the balloon
> analogy is better in this
> sense. The fruitcake does have the advantage of
> being three dimensional
> though, so I guess its really a trade off of
> "Unreachable outside" vs. "3-D."
>
Thanks, Andrew, I was poised to comment similarly. I
find, with a really nifty thread like this, that if
you sit back and wait, someone else will get at what
needs to be gotten at.
Nevertheless, if I may, I'll expand (;-) on this a
bit.
The drawback is that a balloon in the real world is a
spherical object and that sphericity, and the
expansion of the sphere with inflation, may
inadvertantly be compared to the 'apparent'
sphericity and 'inflation' of the universe. In the
mind's eye, one somewhat naturally places the balloon
and the universe side by side, which is totally
counter to the intention of the model, which as Gene
points out, is a strict 2d-maps-to-3d usage. To apply
the model correctly, you must consider the surface in
the pure and abstract mathematical sense. 'Balloon'
with its real-world character corrupts the model and
tends to lead one away from the pure 2d-maps-to-3d
intent. Led away to where?, to the problem which
Spudster(Mitch?) points out: what to make of the
'inside', 'outside', (and to a lesser extent, the
thickness) of the balloon.
A seeming value of the ballon model is, as Andrew
observes, that the surface of the balloon is closed,
ie it has no spacial (as contrasted with
'temporal')edges.
But a further problem with the ballon model arises
from this, and is seen with Andrew's
ant-walking-along-the-surface comment. On a balloon,
an ant can follow a straight path which closes back on
itself. I don't think that corresponds faithfully to
what would happen in the 'real' universe. If you head
straight 'out' into the universe, comparable to
heading straight along the surface of the balloon, you
will not--or perhaps I should say IMO, or
'intuitively'--'circle back' to where you started.
So the real universe is 'edgeless'. And, at the same
time, the real universe is quite distinctly bounded.
"How can that be?", you ask. "How can it be bounded,
which seems to correspond in some sense to 'have an
edge', and yet not have an edge? Because that 'edge'
out there is not a spacial edge, but rather a temporal
edge. It is the 'edge' of time, and as such it is an
edge 'of' space rather than an edge 'in' space. An
edge 'in' space is the usual meaning of edge, with
space on both sides of the boundary. An edge 'of'
space is an edge of spacetime, 'beyond' which
existence (or a 'non-state' of 'non-existence') may be
possible. As to the character of existence 'outside
of' or 'beyond' spacetime--well,...musing in the
darkness, I speculate thus: it is (1)'eternal', and
(2)there is no there there.
The rising-raisin-dough-ball model has its own
problems. The 2d-onto-3d conceptual problem is gone,
and the raisons moving away from each other in the
rising dough-ball, nicely model the galaxies moving
away from each other in the expanding universe. After
that, you start to get into trouble.
The cake is three-dimensional and spherical. The
universe, though easily misperceived as such--"Gaze
out upon the celestial sphere, my child."--is not.
Yet the raisin dough-ball model promotes this
misperception.
The universe is four-dimensional, and lacking a
radially-symmetric spatial boundary, cannot be
spherical in the conventional, spatial sense.
Finally, the universe is bounded; and--despite
perception or intuition--not by space, but by time.
If time is one dimensional, ie thought of as a single
dimension in the mathematical sense, then the 'outer
edge' of the universe (really the 'outer surface' or
meta-surface) maps onto that point on the 'line of
time' corresponding to t=0.
At this point I pause. I've wandered about and
stumbled on the idea that the outer boundary of the
universe is a time thingee not a space thingee. It
exists as a when: t=0; the beginning. That's as far
as I've gotten. Just begun to think about the precise
character of the edge of the universe, the boundary
out there between spacetime and non-spacetime.
What happens to the boundary as the universe
'expands'? If it's not a space thingee, does the
boundary not have a surface area with a size? What
happens to a 'temporal' boundary as the universe it
encloses/(delineates?) expands? Could the boundary be
a non-smoothly varying quality, but rather have a
quantum, unitary quality?
Help me, I've fallen and I can't get up.
Best, Jeff Davis
"That's the whole problem with science. You've got a
bunch of empiricists trying to describe things of
unimaginable wonder."
--Calvin (& Hobbes)
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