Ben Goertzel (ben@goertzel.org)
Tue, 6 Apr 1999 16:57:35 -0400
>Observed randomness is due to limitations of the observer rather than to
inherent randomness of the universe.
Randomness is necessarily subjective, in a finite universe. Random to a
given observer X means "has no patterns detectible by X." That is the only
definition of randomness that
there is.
For infinite entities, one can define objective randomness over the space of
finite observers -- i.e. there are infinite entities that are random for
all finite observers.
But for finite entities, random to X may not be random to Y. (This has to
do with the
fact that bisimulation of Turing machines only works when you assume
arbitrarily
long tapes)
There is no way for me to empirically distinguish something that is "really"
random from something that "looks random to any observer of complexity less
than or equal to my own."
As has been shown by G. Chaitin, this is a reformulation of Godel's
Incompleteness
Theorem.
Ben
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