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
The non computable maximal compression of Post number gives Chaitin
Omega number, which delete all redundancies in the UD, and thus the
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).
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