That’s because the absolute-speed irreversible aether universes like 3d versions of Conway’s game of life are so much more computationally compact than highly symmetric universe with many space-time symmetries (to the point of time and space intermixing in the equations) and the fully reversible fundamental laws of physics.
Can you explain why this is the case? Also, when you say “aether” universes are more computationally compact than “relativity” universes, is this before or after taking into account our observations (i.e., are you restricting your attention to universes that fit our observations, or not)?
Saying this to you as applied mathematician with experience actually implementing laws of physics in software.
Is it possible that what you said is true only if we want the laws of physics to run fast on current computers? I’m afraid that most software people, including myself, probably have bad intuitions about Solomonoff Induction because we only have experience with a very small subset of possible computations, namely those that can be run economically on modern computers. Perhaps the laws of physics can be implemented much more compactly if we ignored efficiency?
As intuition pump consider the reversible vs irreversible cellular automata. If you pick at random, vast majority will not be reversible. Ditto for the symmetries. (Keep in mind that in Solomonoff probability we feed infinite random tape to the machine. It is no Occam’s razor. Elegant simplest deterministic things can be vastly outnumbered by inelegant, even if they are most probable. edit: that is to say you can be more likely to pick something asymmetric even if any particular asymmetric is less likely than symmetric)
Also, when you say “aether” universes are more computationally compact than “relativity” universes, is this before or after taking into account our observations (i.e., are you restricting your attention to universes that fit our observations, or not)?
There can always be a vast conspiracy explaining the observations… ideally if you could simulate whole universe (or multiverse) from big bang to today and pick out the data matching observations or the conspired lying, then maybe it’d work, but the whole exercise of doing physics is that you are embedded within universe you are studying. edit: and that trick won’t work if the code eats a lot of random tape.
Is it possible that what you said is true only if we want the laws of physics to run fast on current computers?
I don’t think relaxing the fast requirement really helps that much. Consider programming Conway’s game of life in Turing machine. Or vice versa. Or the interpreter for general TM on the minimal TM. It gets way worse if you want full rotational symmetry on discrete system.
Of course, maybe one of the small busy beavers is a superintelligence that likes to play with various rules like that. Then I’d be wrong. Can not rule even this possibility out. Kolmogorov/Solomonoff name drop is awesome spice for cooking proven-untestable propositions.
One could argue that second order logic could work better, but this is getting way deep into land of untestable propositions that are even proven untestable, and the appropriate response would be high expectations asian father picture with “why not third order logic?”.
edit: also you hit nail on the head on an issue here: i can not be sure that there is no very short way to encode something. You can ask me if I am sure that busy beaver 6 is not anything, and I am not sure! I am not sure it is not the god almighty. The proposition that there is a simple way is a statement of faith that can not be disproved any more than existence of god. Also, I feel that there has to be scaling for the computational efficiency in the prior. The more efficient structures can run more minds inside. Or conversely, the less efficient structures take more coding to locate minds inside of them.
Can you explain why this is the case? Also, when you say “aether” universes are more computationally compact than “relativity” universes, is this before or after taking into account our observations (i.e., are you restricting your attention to universes that fit our observations, or not)?
Is it possible that what you said is true only if we want the laws of physics to run fast on current computers? I’m afraid that most software people, including myself, probably have bad intuitions about Solomonoff Induction because we only have experience with a very small subset of possible computations, namely those that can be run economically on modern computers. Perhaps the laws of physics can be implemented much more compactly if we ignored efficiency?
As intuition pump consider the reversible vs irreversible cellular automata. If you pick at random, vast majority will not be reversible. Ditto for the symmetries. (Keep in mind that in Solomonoff probability we feed infinite random tape to the machine. It is no Occam’s razor. Elegant simplest deterministic things can be vastly outnumbered by inelegant, even if they are most probable. edit: that is to say you can be more likely to pick something asymmetric even if any particular asymmetric is less likely than symmetric)
There can always be a vast conspiracy explaining the observations… ideally if you could simulate whole universe (or multiverse) from big bang to today and pick out the data matching observations or the conspired lying, then maybe it’d work, but the whole exercise of doing physics is that you are embedded within universe you are studying. edit: and that trick won’t work if the code eats a lot of random tape.
I don’t think relaxing the fast requirement really helps that much. Consider programming Conway’s game of life in Turing machine. Or vice versa. Or the interpreter for general TM on the minimal TM. It gets way worse if you want full rotational symmetry on discrete system.
Of course, maybe one of the small busy beavers is a superintelligence that likes to play with various rules like that. Then I’d be wrong. Can not rule even this possibility out. Kolmogorov/Solomonoff name drop is awesome spice for cooking proven-untestable propositions.
One could argue that second order logic could work better, but this is getting way deep into land of untestable propositions that are even proven untestable, and the appropriate response would be high expectations asian father picture with “why not third order logic?”.
edit: also you hit nail on the head on an issue here: i can not be sure that there is no very short way to encode something. You can ask me if I am sure that busy beaver 6 is not anything, and I am not sure! I am not sure it is not the god almighty. The proposition that there is a simple way is a statement of faith that can not be disproved any more than existence of god. Also, I feel that there has to be scaling for the computational efficiency in the prior. The more efficient structures can run more minds inside. Or conversely, the less efficient structures take more coding to locate minds inside of them.