gedymin comments on An additional problem with Solomonoff induction - Less Wrong

2 Post author: gedymin 22 January 2014 11:34PM

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Comment author: private_messaging 23 January 2014 07:51:38AM *  5 points [-]

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.
Comment author: gedymin 26 January 2014 07:15:24PM 0 points [-]

What's the physical significance of those infinite bits?

Comment author: private_messaging 26 January 2014 08:53:25PM *  1 point [-]

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.

Comment author: gwern 26 January 2014 11:26:40PM 1 point [-]

edit: i give up, markdown is completely retarded and eats all the indentation.

http://code.google.com/p/lesswrong/issues/detail?id=348

Comment author: private_messaging 27 January 2014 05:48:46AM 0 points [-]

what was weird is that the first line did get indented with 1 more space than the rest.

Comment author: Lumifer 26 January 2014 11:15:33PM 0 points [-]

a physics simulator written entirely in brainfuck

That's an awesome expression.

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