Sean Carroll in Preposterous Universe:
We’ve talked a lot recently about the Many Worlds of quantum mechanics. That’s one kind of multiverse that physicists often contemplate. There is also the cosmological multiverse, which we talked about with Brian Greene. Today’s guest, Max Tegmark, has thought a great deal about both of those ideas, as well as a more ambitious and speculative one: the Mathematical Multiverse, in which we imagine that every mathematical structure is real, and the universe we perceive is just one such mathematical structure. And there’s yet another possibility, that what we experience as “reality” is just a simulation inside computers operated by some advanced civilization. Max has thought about all of these possibilities at a deep level, as his research has ranged from physical cosmology to foundations of quantum mechanics and now to applied artificial intelligence. Strap in and be ready for a wild ride.
More here.