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Are the people here speaking about the Bayesian approach to rationality

familiar with Solomonoff's principle of induction?

It seems to me that Solomonoff uncovers a bigger part of the picture

than just the Bayesian deduction principle.

Ray Solomonoff, one of the co-founders of the field of Algorithmic

Information Theory, simultaneously with Kolmogorov and Chaitin,

introduced a nice way to explain how rational induction is possible.

Roughly said, rational induction consists in dynamically trying to

find a minimal algorithmic model for the observations of the world;

when you add new observations, you try to find the minimal model update.

The actual probability measure is not computable, but can be computably

approximated from below. It verifies Bayes' theorem with respect to adding

new information. It depends on an algorithmic context, although up to a

constant factor, that tends toward one when comparing the outcome of two

different rational predictors faced with the same long sequences of random

observations. It thus defeats Karl Popper's limitation against

context-independent induction, by being context-dependent; yet with an

asymptotically irrelevant initial context. It is an induction principle

that neatly formalizes Moore's Law (commonly retro-stated as "pick the

simplest available explanation"). Now of course, see how a Solomonoff

predictor can only be _approximated_ by computational agents. This entails

that we (rational sentient beings, including AIs and ETs) are all irrational,

when faced with complex enough problems. However, there are convergent

algorithms to extract all information there is from "simple enough" systems

that can be described in rules polylogarithmically simpler than the observed

system. Etc.

Considering that, I'd rather say of rational agents that they are

Solomonovian than Bayesian.

PS: Solomonoff Induction is well-explained in chapter 5 of Li and Vitányi's

"Introduction to Kolmogorov Complexity and its Applications, 2nd Edition".

[ François-René ÐVB Rideau | Reflection&Cybernethics | http://fare.tunes.org ]

[ TUNES project for a Free Reflective Computing System | http://tunes.org ]

If the human mind were simple enough to understand,

we'd be too simple to understand it.

-- Pat Bahn

**Next message:**Technotranscendence: "Re: Dinosaur extinction anyone?"**Previous message:**Dave Sill: "Re: cryonics risk/payoff matrix"**In reply to:**Lee Corbin: "Re: Fun with Bayes' Theorem"**Next in thread:**Michael M. Butler: "Re: Solomonoff vs Bayes"**Reply:**Michael M. Butler: "Re: Solomonoff vs Bayes"**Reply:**James Rogers: "Re: Solomonoff vs Bayes"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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