Solomonoff induction creates models of the universe from the point of view of a single observer. As such, it wouldn’t probably have any particular problem with Einstenian relativity.
On the other hand, if you want a computational model of the universe that is independent from the choice of any particular observer, relativity will get you into trouble.
Relativity doesn’t depend to observer, it depends to reference frame… (or rather, doesn’t depend). I can launch Michalson-Morley experiment into space and have it send data to me, and it’ll need to obey Lorentz invariance and everything else. edit: or just for GPS to work. You have a valid point though, S.I. has a natural preferred frame coinciding with the observer.
Lorentz invariance is a very neat, very elegant property, which as far as we know, only incredibly complicated computations have, and only approximately. This makes me think that algorithmic prior is not a very good idea. Universe needs not be made of elementary components, in the way in which computations are.
Universe needs not be made of elementary components, in the way in which computations are.
Moreover, all computational models assume some sort of global state and absolute time. These assumptions don’t seem to hold in physics, or at least they may hold for a single observer, but may require complex models that don’t respect a natural simplicity prior.
If it were possible to realize a Solomonoff inductor in our universe I would it expect it to be able to learn, but it might not be necessarily optimal.
Relativity doesn’t depend to observer, it depends to reference frame… (or rather, doesn’t depend). I can launch Michalson-Morley experiment into space and have it send data to me, and it’ll need to obey Lorentz invariance and everything else. edit: or just for GPS to work. You have a valid point though, S.I. has a natural preferred frame coinciding with the observer.
Lorentz invariance is a very neat, very elegant property, which as far as we know, only incredibly complicated computations have, and only approximately. This makes me think that algorithmic prior is not a very good idea. Universe needs not be made of elementary components, in the way in which computations are.
Moreover, all computational models assume some sort of global state and absolute time. These assumptions don’t seem to hold in physics, or at least they may hold for a single observer, but may require complex models that don’t respect a natural simplicity prior.
If it were possible to realize a Solomonoff inductor in our universe I would it expect it to be able to learn, but it might not be necessarily optimal.