I had seen Tegmark’s four multiverses before, but relating it to this is something I hadn’t considered. The first level of multiverses, with different initial conditions but the same laws, is a lot like how I understand Pearl’s ensemble of possible worlds.
As for the universe being a mathematical structure, that seems to be pretty much what physicists assume by default. The formulations of string theory that I’ve seen (casually—I’ve never worked in that area) replace the space-time manifold with a non-geometric matrix, making it math all the way down.
Even if it is math all the way down, I would consider physical reality to be a different thing from mathematical reality because the physical fact is which mathematical structure is actual. The same way that Chalmers calls consciousness a “further fact” above and beyond material brains, the fact of which mathematical structure is the one that is our world, as opposed to just being logically possible, is a further fact above and beyond the mathematical possibilities.
I had seen Tegmark’s four multiverses before, but relating it to this is something I hadn’t considered. The first level of multiverses, with different initial conditions but the same laws, is a lot like how I understand Pearl’s ensemble of possible worlds.
As for the universe being a mathematical structure, that seems to be pretty much what physicists assume by default. The formulations of string theory that I’ve seen (casually—I’ve never worked in that area) replace the space-time manifold with a non-geometric matrix, making it math all the way down.
Even if it is math all the way down, I would consider physical reality to be a different thing from mathematical reality because the physical fact is which mathematical structure is actual. The same way that Chalmers calls consciousness a “further fact” above and beyond material brains, the fact of which mathematical structure is the one that is our world, as opposed to just being logically possible, is a further fact above and beyond the mathematical possibilities.