Exact translational symmetry (edit: as in, can move literally any distance and the laws work the same) requires true real numbers.
As for the simple programs, well, first off those have to specify how the spacetime is encoded on the tape, to be able to tell any properties of the spacetime. Secondarily, they have to literally analyze the code to see if the code is close enough to invariant over some transformations on that spacetime, for which it has to define those transformations. Before you know it, you have the full code necessary for directly simulating the laws of physics and then some icing on top.
Granted, if we were writing a science fiction story, that would’ve been great—much anything can be claimed without much risk of an obvious wrongness...
edit: or is your point that we can find solutions to any system of equations by mere iteration of possibilities? That’s not the issue, the issue is that we have to somehow encode the world as a TM tape. What we get is huge excessive complexity that has nothing to do with properties of the universe and everything to do with our choice of an incredibly impractical representation.
Before you know it, you have the full code necessary for directly simulating the laws of physics and then some icing on top.
I agree! Is that a problem? I expect that program to be less than a few hundred bits long, so Solomonoff induction will zero in on the correct laws of physics with less than a few hundred bits* of evidence. That seems perfectly acceptable.
*a few hundred bits of evidence will take more than a few hundred bits of sensing data, unless the sensing data is incompressible.
agree! Is that a problem? I expect that program to be less than a few hundred bits long
You see, this is why I kind of don’t even want to bother ever discussing it any more. Ohh, I expect this, I expect that… on what basis, none whatsoever. It’s hundreds bits merely to locate the camera, for god’s sake. Let’s say I expect a god in 50 bits, for the sake of argument.
edit: and by the way, for the laws of physics as we know them—non discrete—an exact representation is not even possible.
*a few hundred bits of evidence will take more than a few hundred bits of sensing data, unless the sensing data is incompressible.
Up to BusyBeaver(a few hundreds) bits of sensing data (edit: which is due to it being easy to set up codes that are identical until very many bits are outputted) .
Exact translational symmetry (edit: as in, can move literally any distance and the laws work the same) requires true real numbers.
As for the simple programs, well, first off those have to specify how the spacetime is encoded on the tape, to be able to tell any properties of the spacetime. Secondarily, they have to literally analyze the code to see if the code is close enough to invariant over some transformations on that spacetime, for which it has to define those transformations. Before you know it, you have the full code necessary for directly simulating the laws of physics and then some icing on top.
Granted, if we were writing a science fiction story, that would’ve been great—much anything can be claimed without much risk of an obvious wrongness...
edit: or is your point that we can find solutions to any system of equations by mere iteration of possibilities? That’s not the issue, the issue is that we have to somehow encode the world as a TM tape. What we get is huge excessive complexity that has nothing to do with properties of the universe and everything to do with our choice of an incredibly impractical representation.
I agree! Is that a problem? I expect that program to be less than a few hundred bits long, so Solomonoff induction will zero in on the correct laws of physics with less than a few hundred bits* of evidence. That seems perfectly acceptable.
*a few hundred bits of evidence will take more than a few hundred bits of sensing data, unless the sensing data is incompressible.
Nope, the first one
You see, this is why I kind of don’t even want to bother ever discussing it any more. Ohh, I expect this, I expect that… on what basis, none whatsoever. It’s hundreds bits merely to locate the camera, for god’s sake. Let’s say I expect a god in 50 bits, for the sake of argument.
edit: and by the way, for the laws of physics as we know them—non discrete—an exact representation is not even possible.
Up to BusyBeaver(a few hundreds) bits of sensing data (edit: which is due to it being easy to set up codes that are identical until very many bits are outputted) .