On 25 Mar 2013, at 15:47, John Clark wrote:
> No machine can distinguish randomness from the behavior of a more
complex machine than herself
It's true that in general a machine cannot prove that something is
purely random, but a human can't do that either nor can anything
else. If the smallest computer program that can generate a string of
numbers is larger than the string itself then you could confidently
say 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 be
certain that there is not a program shorter than the one you are
looking at that will generate the string. Thus although almost all
strings of numbers are random and thus incompressible, you can't
prove that any particular string is random.
OK.
Almost all the real numbers are random and not computable but
neither humans nor computers can point to a single real number and
truthfully say with certainty "that number is not computable, that
number 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
John K Clark
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