On 30 Dec 2013, at 06:28, Jason Resch wrote:
In the space of all possible movies, the ones that are watchable or meaningful to human viewers would all be highly compressible. The ones that are random snow, despite containing more information, would not make interesting movies. So maybe there is something to your idea that interesting is related to short descriptions. We did evolve to find entirely predictable and entirely unpredictable things boring, there may be some ideal blend of predictability and unpredicability that we find most engaging.
Yes, it is the redundancy of the information related to the notion of universal machine. It is contained in Post numbers, which is a sort of UD by itself (when seen in some way): 0, 00000011011110010110001111100101001001110 ... with nth digit = 0 or 1 according to the fact that the nth programs (with 0 input) stop or not. (It is an halting oracle, and of course is not computable, but it is compressible).
The non computable maximal compression of Post number gives Chaitin Omega number, which delete all redundancies in the UD, and thus the whole physics!
Anything interesting and beautiful is highly redundant, like the Mandelbrot set for example.
In recursion theory, it is the difference between two complementarities: the simple/immune complementarity discovered by Post (and rediscovered by Chaitin in term of algorithmic compression) on one par, and the creative/productive complementarity, also discovered by Post, where "creative" has been shown later to be equivalent with Turing universality (or sigma_1 completeness) by John Myhill, (using Kleene second recursion theorem).
Bruno
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