Vladimir_Nesov comments on Open Thread: October 2009 - Less Wrong

5 Post author: gwern 01 October 2009 12:49PM

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Comment author: Vladimir_Nesov 01 October 2009 05:30:09PM *  1 point [-]

Generalize that to a good chunk of classical math.

Comment author: SilasBarta 01 October 2009 05:34:01PM 0 points [-]

The analog would be to theorem proving. No one claims that knowing the axioms of math gets you to every theorem "very fast" -- because the problem of finding a proof/disproof for an arbitrary proposition is also uncomputable.

Comment author: Vladimir_Nesov 01 October 2009 05:40:57PM *  0 points [-]

A "solution" might be that only proofs matter, while theorems (as formulas) are in general meaningless in themselves, only useful as commentary on proofs.

Comment author: SilasBarta 01 October 2009 05:51:16PM 0 points [-]

Nevertheless, the original point stands: no one says "I've discovered math! Now I can can learn the answer to any math problem very fast." In contrast, you are saying that because we have Solomonoff induction, we can infer distributions "very fast".

Comment author: Vladimir_Nesov 01 October 2009 06:00:02PM *  0 points [-]

In contrast, you are saying that because we have Solomonoff induction, we can infer distributions "very fast".

To be more precise, we can specify the denotation of distributions very close to the real deal from very few data. This technical sense doesn't allow the analogy with theorem-proving, which is about algorithms, not denotation.

Comment author: SilasBarta 01 October 2009 06:08:43PM 0 points [-]

But the analogy is in terms of the "fast but uncomputable" oxymoron.