There’s already an equivalent formulation where S.I. works by feeding an infinite string of random bits into the Turing machine on the input tape.
In a non-deterministic universe this works by setting up a code which converts subsequent bits into guesses with correct probability distribution.
I think the issue with S.I. is… well. Why on Earth would we even think it is a particularly good prior, to begin with? It is not even one prior, it’s a bunch of priors that have little in common other than that the difference between a couple priors is bounded by a constant, which sounds good except that the constant can be big in comparison to anything you would care about. Granted, if we postulate that environment is a Turing machine, S.I. is a good prior, especially if based on the same machine, but that’s a very tautological measure of “good”.
If we look at the actual environment, it got those highly symmetrical laws of physics, which are even time-reversible (after mirroring and charge flip). The laws of physics are expressed compactly in terms of high level abstractions such as vectors, tensors, etc—the more symmetrical, the more compact. This works absolutely great—the baseline complexity of our laws of physics is low, the excess complexity for various insane theories (e.g. a doomsday at a specific date) is very high (giving them low priors).
Contrast that with S.I. The baseline complexity, as far as we can tell*, is very high—to say the least, it’s difficult to make a simulation that’s running on one dimensional tape but got 4-dimensional Lorentz symmetry, exact or approximate. And for each theory there’s various slightly more complex (say, 10 extra bits) variations that will make the simulator do something insane and unpredictable from earlier data. Because digital simulators are incredibly fragile—with all those tags to make the Turing machine head do passes over the data.
Granted, one could postulate a yet-unknown way to code symmetrical laws of physics, but that just proves another point with regards to impracticality—you can postulate anything, e.g. a yet-unknown way to compactly code a god.
Physical significance is not a part of predicting. The implementation details can differ vastly between different machines anyway. Call it what it is: a physics simulator written entirely in brainfuck, most of the code having to do with difficulty of coding things in brainfuck and having nothing to do with physics. Calling it a hypothesis makes you confuse it with what we get when we are striving to understand what actually really exists. Which we achieve by things such as not confusing the way we compute something, with the general laws something follows.
Also, an example of non-deterministic sequence. Let’s suppose the sequence consists of lengths of 0s separated by 1s, with the length of consecutive 0s following a (truly random) binomial distribution with p=0.5 and n=20.
There will be a short prefix that works as following pseudocode:
loader sequence that loads following stuff as code from the input and then runs it:
loop forever:
loop for 20 steps:
read a from input
if a==0 print '0'
end loop
print '1'
end loop
and for a given output tape, this prefix will be the beginning of a fairly large fraction of the input tapes that produce given output tape, giving it a large prior, in the sense that the probability that the input tape that produces desired output begins with it, is big, compared to other contenders.
edit: i give up, markdown is completely retarded and eats all the indentation. edit2: also, restricting to programs that halt make the programs predict arbitrary doomsdays for no reason whatsoever, so I’m only considering formalisms where it is not restricted to programs that do halt.
The baseline complexity, as far as we can tell*, is very high—to say the least, it’s difficult to make a simulation that’s running on one dimensional tape but got 4-dimensional Lorentz symmetry, exact or approximate.
I don’t see why this should be the case. A simple descriptions usually implies a simple program (e.g. “for i from 3↑↑↑3 to infinity, if i encodes a multiverse with 4-dimensional Lorentz symmetry, output i”). What does a one dimensional tape have to do with anything?
How are you going to check if i encodes such? Search through the programs looking for a program that tells if another program implements an universe the laws of physics of which got Lorentz symmetry? ;) (edit: the problem is not so much with programming but with describing symmetries. Exact real numbers can’t even be described properly, let alone anything more fancy. Ergo, you can’t even have exact translational symmetry)
One dimensional tape makes any multidimensional simulations difficult/impossible with exact symmetries. (Not that 3-dimensional grid would be any better, though).
Exact real numbers can’t even be described properly, let alone anything more fancy. Ergo, you can’t even have translational symmetry
It seems like your suggesting that no short program would be able decide if a multiverse-history exhibited translational symmetry. I don’t know enough physics to flat-out say “that’s wrong”, but I don’t see why short programs should be unable to read universe-histories and reject any universe-history that violates conservation of momentum.
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) .
There’s already an equivalent formulation where S.I. works by feeding an infinite string of random bits into the Turing machine on the input tape.
In a non-deterministic universe this works by setting up a code which converts subsequent bits into guesses with correct probability distribution.
I think the issue with S.I. is… well. Why on Earth would we even think it is a particularly good prior, to begin with? It is not even one prior, it’s a bunch of priors that have little in common other than that the difference between a couple priors is bounded by a constant, which sounds good except that the constant can be big in comparison to anything you would care about. Granted, if we postulate that environment is a Turing machine, S.I. is a good prior, especially if based on the same machine, but that’s a very tautological measure of “good”.
If we look at the actual environment, it got those highly symmetrical laws of physics, which are even time-reversible (after mirroring and charge flip). The laws of physics are expressed compactly in terms of high level abstractions such as vectors, tensors, etc—the more symmetrical, the more compact. This works absolutely great—the baseline complexity of our laws of physics is low, the excess complexity for various insane theories (e.g. a doomsday at a specific date) is very high (giving them low priors).
Contrast that with S.I. The baseline complexity, as far as we can tell*, is very high—to say the least, it’s difficult to make a simulation that’s running on one dimensional tape but got 4-dimensional Lorentz symmetry, exact or approximate. And for each theory there’s various slightly more complex (say, 10 extra bits) variations that will make the simulator do something insane and unpredictable from earlier data. Because digital simulators are incredibly fragile—with all those tags to make the Turing machine head do passes over the data.
Granted, one could postulate a yet-unknown way to code symmetrical laws of physics, but that just proves another point with regards to impracticality—you can postulate anything, e.g. a yet-unknown way to compactly code a god.
What’s the physical significance of those infinite bits?
Physical significance is not a part of predicting. The implementation details can differ vastly between different machines anyway. Call it what it is: a physics simulator written entirely in brainfuck, most of the code having to do with difficulty of coding things in brainfuck and having nothing to do with physics. Calling it a hypothesis makes you confuse it with what we get when we are striving to understand what actually really exists. Which we achieve by things such as not confusing the way we compute something, with the general laws something follows.
Also, an example of non-deterministic sequence. Let’s suppose the sequence consists of lengths of 0s separated by 1s, with the length of consecutive 0s following a (truly random) binomial distribution with p=0.5 and n=20.
There will be a short prefix that works as following pseudocode:
and for a given output tape, this prefix will be the beginning of a fairly large fraction of the input tapes that produce given output tape, giving it a large prior, in the sense that the probability that the input tape that produces desired output begins with it, is big, compared to other contenders.
edit: i give up, markdown is completely retarded and eats all the indentation. edit2: also, restricting to programs that halt make the programs predict arbitrary doomsdays for no reason whatsoever, so I’m only considering formalisms where it is not restricted to programs that do halt.
http://code.google.com/p/lesswrong/issues/detail?id=348
what was weird is that the first line did get indented with 1 more space than the rest.
That’s an awesome expression.
I don’t see why this should be the case. A simple descriptions usually implies a simple program (e.g. “for i from 3↑↑↑3 to infinity, if i encodes a multiverse with 4-dimensional Lorentz symmetry, output i”). What does a one dimensional tape have to do with anything?
How are you going to check if i encodes such? Search through the programs looking for a program that tells if another program implements an universe the laws of physics of which got Lorentz symmetry? ;) (edit: the problem is not so much with programming but with describing symmetries. Exact real numbers can’t even be described properly, let alone anything more fancy. Ergo, you can’t even have exact translational symmetry)
One dimensional tape makes any multidimensional simulations difficult/impossible with exact symmetries. (Not that 3-dimensional grid would be any better, though).
It seems like your suggesting that no short program would be able decide if a multiverse-history exhibited translational symmetry. I don’t know enough physics to flat-out say “that’s wrong”, but I don’t see why short programs should be unable to read universe-histories and reject any universe-history that violates conservation of momentum.
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) .