Comment on Causal Universes

Sun, 18 Aug 2013 18:13:41 GMT

a googolplex times more graphs with one cycle than there are acyclic paths

(I assume you meant "acyclic graphs")

And I don't have a prior that says that an acausal universe should have a probability penalty of one over googolplex.

If this sort of reasoning worked, you could find strong arguments for all sorts of (contradictory) hypotheses. For instance:

Surely, the universe has an underlying n-dimensional (topological) manifold. Since all of the infinitely many n-dimensional manifolds are not homotopy equivalent to the n-sphere, except for the sphere itself, the universe must not be an n-sphere. Therefore, there are holes in the universe.

or

Surely, the universe has an underlying set. Let A be the cardinality of that set. Then, since all cardinalities (except for countably many) are larger that Aleph_0, the universe is not countable. Therefore, the universe is not Turing computable.

or

There probably isn't a God because topology

or

By the Poincare recurrence theorem, all of this has happened before and all of this will happen again.

I mean, your observation is interesting, but I don't think it constitutes a "large argument". You can't just slap reasonable-ish priors onto spaces of mathematical objects, and in general using math for long chains of inference often only works if it's exactly the right sort of math.

Discuss