**Peter Wegner** (*pw@cs.brown.edu*)

*Sat, 10 Apr 1999 23:36:36 -0400 (EDT)*

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Stepehen and Ben

I hesitate to come in in the middle of the discussion about finiteness versus infiniteness of the universe.

But I have a preference for an infinite model, at least from the subjective viewpoint of observers, for the following kinds of reasons.

1. From the viewpoint of general principles of relativity, observable properties should not depend on whether you are near the edge of the universe or near the center.

If the observer cannot detect the edge of the universe this suggests an infinite model, at least from the subjective viewpoint of any observer.

2. I prefer to think of the universe as an open rather than a closed system

in that any part can be subject ot forces from unknown parts.

An open universe is subject to nondeterministic external forces, while a closed universe can be modeled at some level in a deterministic (algorithmic) way.

The existence of a closed deterministic universe seems to violate a general relativity principle.

Openness is better matched by an infinite than a finite universe.

This notion of openness is like that in topology.

Topology allows us to clearly see that open sets can be finite, for example the open unit sphere, while still having the property that the complete set cannot be effectively defined.

3. Mandelbrot sets are an attractive model for an infinite universe.

This would allow a principle of relativity for scale, in that structures at any

particular scale would replicate themselves at both lower and higher scales.

Some of Eddington's work suggests that the scale factor for replication might be about 10**80.

If the universe has relativity of scale like a Mandelbrot set it is an infinite universe.

Ben, has there been work on modeling the universe in terms of Mandelbrot sets?

Are there models that focus especially on open versus closed systems?

peter

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