gts, About the Principle of Indifference and probability theory...
The question is what should an AGI system does when the data available to it appears to support multiple contradictory conclusions. It has to decide, somehow. The PI is one way to decide... Another approach however is the Occam prior (to prefer simpler explanations, according to some fixed measure of simplicity, provided e.g. by assumption of some reference universal turing machine). I think that in general the Occam prior is preferable to the PI as an assumption. I note that the Occam prior connects more closely to neuroscience than the PI, in that there are plausible arguments the brain uses an "energy minimization" heuristic in some cases. Read Montague makes an argument in this direction in: http://www.amazon.com/Why-Choose-This-Book-Decisions/dp/0525949828 However, when multiple choices seem to have roughly equivalent complexity, then the Occam prior basically degenerates to the PI. There are mathematical relationships between algorithmic information and Shannon entropy, which indicate that the Occam prior and the maxent prior are equivalent in some cases; e.g. http://prola.aps.org/abstract/PRA/v40/i8/p4731_1 which shows "Algorithmic randomness is typically very difficult to calculate exactly but relatively easy to estimate. In large systems, probabilistic ensemble definitions of entropy (e.g., coarse-grained entropy of Gibbs and Boltzmann's entropy H=lnW, as well as Shannon's information-theoretic entropy) provide accurate estimates of the algorithmic entropy of an individual system or its average value for an ensemble." Zurek argues, further, that " Physical entropy, I suggest, is a sum of (i) the missing information measured by Shannon's formula and (ii) of the algorithmic information content—algorithmic randomness—present in the available data about the system. " A clear, freely available exposition of Zurek's views is found here: http://arxiv.org/pdf/quant-ph/9807007 This suggests that the physically correct prior might be a combination of maxent and Occam priors. The PI then emerges as a kind of degenerate version of this more sophisticated approach. And, just as with the PI, these more sophisticated approaches must be applied correctly and intelligently to be useful. -- Ben On 2/10/07, gts <[EMAIL PROTECTED]> wrote:
On Sat, 10 Feb 2007 15:27:23 -0500, Jef Allbright <[EMAIL PROTECTED]> wrote: > On the contrary, a subjectivist understands that even to pose a > question, one must have some prior. That observation does not speak to the question at hand concerning the principle of indifference. The principle of indifference is seen as a 'logical principle' only under objective bayesianism. Under subjective bayesianism it is at most a heuristic device. Subjectivists know better than to believe they are bound by some 'universal principle of logic' (to use your term) to invoke the principle of indifference under conditions of total ignorance about the true state of nature, which is of course the only condition under which it can be invoked. You were wrong to suggest earlier that the principle of indifference can be derived from De Finetti coherence. The axioms of probability can be derived from coherence but the principle of indifference is certainly not one of them. > You're also confusing "zero" with "nothing." Nope. -gts ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=303
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