In order to make claims like that, you have to put a measure on your multiverse. I do not like doing that for three reasons:
1) It feels arbitrary. I do not think the essence of reality relies on something chunky like a Turing machine.
2) It limits the multiverse to be some set of worlds that I can put a measure on. The collection of all mathematical structures is not a set, and I think the multiverse should be at least that big.
3) It requires some sort inherent measure that is outside of the any of the individual universes in the multiverse. It is simpler to imagine that there is just every possible universe, with no inherent way to compare them.
However, regardless of those very personal beliefs, I think that the argument of simpler universes show up in more other universes does not actually answer any questions. You are trying to explain why you have a measure which makes simpler universes more likely by starting with a collection of universes in which the simpler ones are more likely, and observing that the simple ones are run more. This just walks you in circles.
I guess what I’m saying is that since simpler ones are run more, they are more important. That would be true if every simulation was individually important, but I think one thing about this is that the mathematical entity itself is important, regardless of the number of times it’s instituted. But it still intuitively feels as though there would be more “weight” to the ones run more often. Things that happen in such universes would have more “influence” over reality as a whole.
I am saying that in order to make the claim “simple universes are run more,” you first need the claim that “most universes are more likely to run simple simulations than complex simulations.” In order to make that second claim, you need to start with a measure of what “most universes” means, which you do using simplicity. (Most universes run simple simulations more because running simple simulations is simpler.)
I think there is a circular logic there that you cannot get past.
In order to make claims like that, you have to put a measure on your multiverse. I do not like doing that for three reasons:
1) It feels arbitrary. I do not think the essence of reality relies on something chunky like a Turing machine.
2) It limits the multiverse to be some set of worlds that I can put a measure on. The collection of all mathematical structures is not a set, and I think the multiverse should be at least that big.
3) It requires some sort inherent measure that is outside of the any of the individual universes in the multiverse. It is simpler to imagine that there is just every possible universe, with no inherent way to compare them.
However, regardless of those very personal beliefs, I think that the argument of simpler universes show up in more other universes does not actually answer any questions. You are trying to explain why you have a measure which makes simpler universes more likely by starting with a collection of universes in which the simpler ones are more likely, and observing that the simple ones are run more. This just walks you in circles.
I guess what I’m saying is that since simpler ones are run more, they are more important. That would be true if every simulation was individually important, but I think one thing about this is that the mathematical entity itself is important, regardless of the number of times it’s instituted. But it still intuitively feels as though there would be more “weight” to the ones run more often. Things that happen in such universes would have more “influence” over reality as a whole.
I am saying that in order to make the claim “simple universes are run more,” you first need the claim that “most universes are more likely to run simple simulations than complex simulations.” In order to make that second claim, you need to start with a measure of what “most universes” means, which you do using simplicity. (Most universes run simple simulations more because running simple simulations is simpler.)
I think there is a circular logic there that you cannot get past.