Tegmark cosmology implies not only that there is a universe which runs this one as a simulation, but that there are infinitely many such simulations.
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. After all, a universe which contains a perfect simulation of this one would need to be larger (in duration and/or size) than this one. But there is a largest possible finite simple group, so why not a largest possible universe? I am not confident enough of my understanding of the constraints applicable to universes to be confident that we are not already in the biggest one possible.
There is a spooky similarity between the Tegmark-inspired argument that we may live in a simulation and the Godel/St. Anselm-inspired argument that we were created by a Deity. Both draw their plausibility by jumping from the assertion that something (rather poorly characterized) is conceivable to the claim that that thing is possible. That strikes me as too big of a jump.
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.
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. After all, a universe which contains a perfect simulation of this one would need to be larger (in duration and/or size) than this one. But there is a largest possible finite simple group, so why not a largest possible universe? I am not confident enough of my understanding of the constraints applicable to universes to be confident that we are not already in the biggest one possible.
There is a spooky similarity between the Tegmark-inspired argument that we may live in a simulation and the Godel/St. Anselm-inspired argument that we were created by a Deity. Both draw their plausibility by jumping from the assertion that something (rather poorly characterized) is conceivable to the claim that that thing is possible. That strikes me as too big of a jump.
There isn’t a largest finite simple group. There’s a largest exceptional finite simple group.
Z/pZ is finite and simple for all primes p, and if you think there is a largest prime I have some bad news...
Doooohhh!
Thx.
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.