On 25 Mar 2013, at 15:47, John Clark wrote:

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> No machine can distinguish randomness from the behavior of a morecomplex machine than herselfIt's true that in general a machine cannot prove that something ispurely random, but a human can't do that either nor can anythingelse. If the smallest computer program that can generate a string ofnumbers is larger than the string itself then you could confidentlysay it is random;

`Which, in passing entails, for pure combinatoric reason, that most`

`survivers to the WM-duplication writes a WM random sequence, in that`

`very sense, in their personal diaries.`

(Just to illustrate the FPI (First Person Indeterminacy)).

but Greg Chaitin proved a few years ago that in general you can't becertain that there is not a program shorter than the one you arelooking at that will generate the string. Thus although almost allstrings of numbers are random and thus incompressible, you can'tprove that any particular string is random.

OK.

Almost all the real numbers are random and not computable butneither humans nor computers can point to a single real number andtruthfully say with certainty "that number is not computable, thatnumber is random".

`Well, for some we can, and in some case we can even approximate them,`

`but without computable modulus, and with some practical uncertainty,`

`for long period, for some decimals.`

`But randomness is a shallow notion compared to Emil Post's creativity,`

`provably equivalent with Turing Universality, or Sigma_1-completeness.`

`That notion does not filtered out the redundancy, which is at play for`

`the global FPI.`

`The border of a creative set is more like the border of the Mandelbrot`

`set. It is not pure randomness, but it is fractal, chaotical,`

`infinitely self-multiplying, infinitely self-merging, but always with`

`some order and natural elegance.`

`Randomness as some role, like the recursive has its role too, but the`

`interesting happening are in between.`

Bruno

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