Hence, we have a way of getting hold of the concept of Euclidean
angle, starting from a purely combinatorial scheme
...
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.
Consider Penrose’s “Angular momentum: An approach to combinatorial space-time” (math.ucr.edu/home/baez/penrose/Penrose-AngularMomentum.pdf)
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.