Given such-and-such initial conditions, and given such-and-such cellular automaton rules, what would be the mathematical result?
Not even God can modify the answer to this question, unless you believe that God can implement logical impossibilities. Even as a very young child, I don’t remember believing that. (And why would you need to believe it, if God can modify anything that actually exists?)
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.
A couple of related ideas and work you might find interesting / relevant:
Tegmark’s mathematical universe hypothesis, with four levels of hierarchy.
Beyond the Reach of God. Key quote:
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.