by PWrong » Sat Jan 01, 2011 3:48 am
The idea of probability as a dimension doesn't actually mean much outside of science fiction as far as I'm aware. The way it's usually presented doesn't make any sense given what dimension actually means.
If there are multiple universes, then the dimension of the multiverse might be quite simple.
If there are countably infinite universes in the multiverse, there are zero extra dimensions (So the dimension is just the maximum dimension of all the universes)
If there are uncountably many, and they're not connected at all, then there is at least one dimension, but the dimension doesn't matter as you can just reorder the set to get back to one.
If there are uncountably many universes and they're all related by some bizarre probability universe-splitting thing, then dimension is too simple a term. There are probably infinitely many dimensions and you'd be better off using markov chains or something than treating it as a vector space.