Can you explain why this is the case?
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.
Solomonoff Induction seems clearly "on the right track", but there are a number of problems with it that I've been puzzling over for several years and have not made much progress on. I think I've talked about all of them in various comments in the past, but never collected them in one place.
Apparent Unformalizability of “Actual” Induction
Argument via Tarski’s Indefinability of Truth
Suppose we define a generalized version of Solomonoff Induction based on some second-order logic. The truth predicate for this logic can’t be defined within the logic and therefore a device that can decide the truth value of arbitrary statements in this logical has no finite description within this logic. If an alien claimed to have such a device, this generalized Solomonoff induction would assign the hypothesis that they're telling the truth zero probability, whereas we would assign it some small but positive probability.
Argument via Berry’s Paradox
Consider an arbitrary probability distribution P, and the smallest integer (or the lexicographically least object) x such that P(x) < 1/3^^^3 (in Knuth's up-arrow notation). Since x has a short description, a universal distribution shouldn't assign it such a low probability, but P does, so P can't be a universal distribution.
Is Solomonoff Induction “good enough”?
Given the above, is Solomonoff Induction nevertheless “good enough” for practical purposes? In other words, would an AI programmed to approximate Solomonoff Induction do as well as any other possible agent we might build, even though it wouldn’t have what we’d consider correct beliefs?
Is complexity objective?
Solomonoff Induction is supposed to be a formalization of Occam’s Razor, and it’s confusing that the formalization has a free parameter in the form of a universal Turing machine that is used to define the notion of complexity. What’s the significance of the fact that we can’t seem to define a parameterless concept of complexity? That complexity is subjective?
Is Solomonoff an ideal or an approximation?
Is it the case that the universal prior (or some suitable generalization of it that somehow overcomes the above "unformalizability problems") is the “true” prior and that Solomonoff Induction represents idealized reasoning, or does Solomonoff just “work well enough” (in some sense) at approximating any rational agent?
How can we apply Solomonoff when our inputs are not symbol strings?
Solomonoff Induction is defined over symbol strings (for example bit strings) but our perceptions are made of “qualia” instead of symbols. How is Solomonoff Induction supposed to work for us?
What does Solomonoff Induction actually say?
What does Solomonoff Induction actually say about, for example, whether we live in a creatorless universe that runs on physics? Or the Simulation Argument?