> No machine can distinguish randomness from the behavior of a more complex
machine than herself

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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;
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. 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".
John K Clark
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