Consider Penrose's "Angular momentum: An approach to combinatorial space-time" (math.ucr.edu/home/baez/penrose/Penrose-AngularMomentum.pdf)
Hence, we have a way of getting hold of the concept of Euclidean angle, starting from a purely combinatorial scheme
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The central idea is that the system defines the geometry. If you like, you can use the conventional description to fit the thing into the ‘ordinary space-time’ to begin with, but then the geometry you get out is not necessarily the one you put into it
It seems that euclidean space, at least, can be derived as a limiting case from simple combinatorial principles. It is not at all clear that general relativity does not have kolmogorov complexity comparable to the cellular automata of your "aether universes".
Kolmogorov complexity of GR itself (text of GR or something) is irrelevant. Kolmogorov complexity of universe that has the symmetries of GR and rest of physics, is. Combinatorial principles are nice but it boils down to representing state of the universe with cells on tape of linear turing machine.
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?