[extropy-chat] 44th mersenne prime verified

scerir scerir at libero.it
Fri Sep 15 08:40:22 UTC 2006


> The weird thing is that these numbers are in a sense completely
> deterministic, defined by simple rules,, while at the same time appearing
> totally random.  Other patterns involving the primes and many other
> kinds of numbers have this property, this paradoxical combination of
> determinism and randomness.

Yes. I do not know if it is really paradoxical. 
Pure randomness (uncomputability?) alone and pure 
determinism alone would be more paradoxical maybe?
[ This theorem seems to suggest a sort of
thermodinamics of numbers, a concept that
also G.Chaitin likes ...
http://en.wikipedia.org/wiki/Erd%C5%91s-Kac_theorem ] 

> Wei Dai proposed a few years ago that measure could be defined 
> based on Greg Chaitin's notion of algorithmic complexity.
> Basically systems that can be defined by simple rules have 
> higher measure than those that require complex rules.

Dunno if 'simple rules' is so easy to define.
In example is the 'superposition' (in linear QM) 
a 'simple' rule? (Maybe it is, in the sense of
J.Schmidhuber's answer to the question 'So which 
is the best universe-computing algorithm for any 
decent "Great Programmer" with resource constraints?').   


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