I’m not sure that this is true. My understanding is that IF a universe which runs this one as a simulation is possible, THEN Tegmark cosmology implies that such a universe exists. But I’m not sure that such a universe is possible.
You’re right, that is an additional requirement. Nevertheless, it seems very highly likely to me that such a universe is possible; for it to be otherwise would imply something very strange about the laws of physics. The most-existant universe simulating ours might exist to a degree 1/BB(100) times as much as our universe exists, though; in that case, they would “exist”, but not for any practical purposes. This seems more likely than our universe having some property we don’t know about that makes it impossible to simulate.
Yes, but unfortunately, there are many measures to choose from, and you can’t possibly tell which is correct until you’ve visited Permutation City and at least a dozen of its suburbs.
I agree with the question. It may make sense to attach “probabilities of existing” to universes arising in a chaotic inflation model, but not, I think, in an “ultimate ensemble” multiverse, which seems to be the one being examined here.
But, to be honest, I had never even considered the possibility that a particularly large bubble universe might contain a simulation of a much smaller bubble. Inflation, as I understand it, does make it possible for a simulation of one small piece of physical reality to encompass an entire isolated ‘universe’.
Not yet, as far as I know. Big World cosmology seems to be going in the right direction, but it’s not yet understood well enough that we should be coming to any epistemological or ethical conclusions based on it.
You’re right, that is an additional requirement. Nevertheless, it seems very highly likely to me that such a universe is possible; for it to be otherwise would imply something very strange about the laws of physics. The most-existant universe simulating ours might exist to a degree 1/BB(100) times as much as our universe exists, though; in that case, they would “exist”, but not for any practical purposes. This seems more likely than our universe having some property we don’t know about that makes it impossible to simulate.
If one accepts general Tegmark, is there any natural measure for describing how common different universes should be in any meaningful sense?
Yes, but unfortunately, there are many measures to choose from, and you can’t possibly tell which is correct until you’ve visited Permutation City and at least a dozen of its suburbs.
I agree with the question. It may make sense to attach “probabilities of existing” to universes arising in a chaotic inflation model, but not, I think, in an “ultimate ensemble” multiverse, which seems to be the one being examined here.
But, to be honest, I had never even considered the possibility that a particularly large bubble universe might contain a simulation of a much smaller bubble. Inflation, as I understand it, does make it possible for a simulation of one small piece of physical reality to encompass an entire isolated ‘universe’.
Not yet, as far as I know. Big World cosmology seems to be going in the right direction, but it’s not yet understood well enough that we should be coming to any epistemological or ethical conclusions based on it.