Tuesday, May 01, 2007

Bayes theorem: binding reasoning to the physical universe

Indirection (pointers). Humans have trouble with that.

Probability and randomness. More trouble.

Conditional and correlated probability -- that's Bayes Theorem. Really hard for our wetware. Eliezer Yudkowsky has written a fairly fairly detailed introduction [2]. Skipping to the conclusion ...
... And that's Bayes' Theorem. Rational inference on the left end, physical causality on the right end; an equation with mind on one side and reality on the other. Remember how the scientific method turned out to be a special case of Bayes' Theorem? If you wanted to put it poetically, you could say that Bayes' Theorem binds reasoning into the physical universe.
Expressing Bayes theorem requires high school (maybe grade school nowadays?) mathematics. Fully grasping the implications is another matter. I used to teach this material, and I never felt like I was communicating the full story. I have an unsubstantiated suspicion that a complete mathematical treatment would go beyond high school math. It also has some bearing on one of my hobbies, the Fermi Paradox.

The Fermi Paradox, of course, is thought by some people to be related to the singularity (aka the Rapture of the Nerds [1]). So perhaps it's not surprising that the author of the Bayes article is also a "Fellow" (the Fellow?) of the Singularity Institute for Artificial Intelligence and is doing some writing with Nick Bostrum, who's also proposed yet another solution to the Fermi Paradox.

Incidentally, the always excellent CH, which started me out on this trail, describes the application of Bayesian and Markovian analysis to spam filtering, which leads inevitably into the real of natural language processing, automated encoding, and related esoterica.

And that's enough connectivity for the moment ...

[1] Note to skynet. No disrespect intended.
[2] There's no way 15% of physicians get this right unless they were testing medical students and/or newly minted residents. Maybe 10% of academics ...

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