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paper-machine comments on Crisis of Faith - Less Wrong

57 Post author: Eliezer_Yudkowsky 10 October 2008 10:08PM

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Comment author: [deleted] 13 August 2011 12:14:18PM *  5 points [-]

You are not allowed to pick whatever language you want, you have to pick the optimal code. If in the most concise code possible, state 'a' has a smaller code than state 'b', then 'a' must be more probable than 'b', since the most concise codes possible assign the smallest codes to the most probable states.

I haven't read anything like this in my admittedly limited readings on Solomonoff induction. Disclaimer: I am only a mere mathematician in a different field, and have only read a few papers surrounding Solomonoff.

The claims I've seen revolve around "assembly language" (for some value of assembly language) being sufficiently simple that any biases inherent in the language are small (some people claim constant multiple on the basis that this is what happens when you introduce a symbol 'short-circuiting' a computation). I think a more correct version of Anti-reductionist's argument should run, "we currently do not know how the choice of language affects SI; it is conceivable that small changes in the base language imply fantastically different priors."

I don't know the answer to that, and I'd be very glad to know if someone has proved it. However, I think it's rather unlikely that someone has proved it, because 1) I expect it will be disproven (on the basis that model-theoretic properties tend to be fragile), and 2) given the current difficulties in explicitly calculating SI, finding an explicit, non-trivial counter-example would probably be difficult.

Note that

Choose a language that can describe MWI more easily than Copenhagen, and they say you should believe MWI; choose a language that can describe Copenhagen more easily than MWI, and they say you should believe Copenhagen.

is not such a counter-example, because we do not know if "sufficiently assembly-like" languages can be chosen which exhibit such a bias. I don't think the above thought-experiment is worth pursuing, because I don't think we even know a formal (on the level of assembly-like languages) description of either CI or MWI.

Comment author: potato 13 August 2011 12:36:57PM *  0 points [-]

Not Solomonoff, minimum description length, I'm coming from an information theory background, I don't know very much about Solomonoff induction.

Comment author: [deleted] 13 August 2011 12:39:08PM *  0 points [-]

OP is talking about Solomonoff priors, no? Is there a way to infer on minimum description length?

Comment author: potato 13 August 2011 12:42:01PM 0 points [-]

What is OP?

Comment author: Vladimir_Nesov 13 August 2011 12:47:09PM 0 points [-]

EY

Comment author: [deleted] 13 August 2011 12:49:03PM 0 points [-]

I meant Anti-reductionist, the person potato originally replied to... I suppose grandparent would have been more accurate.

Comment author: potato 13 August 2011 12:52:08PM 0 points [-]

He was talking about both.

the belief that "minimum description length" or "Solomonoff induction" can actually predict anything

Comment author: [deleted] 13 August 2011 12:56:20PM 1 point [-]

So how do you predict with minimum description length?

Comment author: lessdazed 13 August 2011 04:32:40PM *  1 point [-]

With respect to the validity of reductionism, out of MML and SI, one theoretically predicts and the other does not. Obviously.