[ExI] Some new angle about AI

[scerir]

> no Turing machine can enumerate an infinity of correct bits of the sequence 
produced by a quantum device.

It's worse than that, there are numbers (almost all numbers in fact) that a 
Turing machine can't even come arbitrarily close to evaluating. A Quantum 
Computer probably couldn't do that either but it hasn't been proven.
John K Clark

It is difficult stuff for me. Difficult. But there is some literature. In 
example:

Quantum randomness and value indefiniteness
http://arxiv.org/abs/quant-ph/0611029v2
-Cristian S. Calude, Karl Svozil
Abstract: As computability implies value definiteness, certain sequences of 
quantum outcomes cannot be computable.

How Random Is Quantum Randomness? An Experimental Approach
http://arxiv.org/abs/0912.4379v1
-Cristian S. Calude, Michael J. Dinneen, Monica Dumitrescu, Karl Svozil
Our aim is to experimentally study the possibility of distinguishing between 
quantum sources of randomness--recently proved to be theoretically 
incomputable--and some well-known computable sources of pseudo-randomness. 
Incomputability is a necessary, but not sufficient "symptom" of "true 
randomness". We base our experimental approach on algorithmic information 
theory which provides characterizations of algorithmic random sequences in 
terms of the degrees of incompressibility of their finite prefixes. Algorithmic 
random sequences are incomputable, but the converse implication is false. We 
have performed tests of randomness on pseudo-random strings (finite sequences) 
of length 2^{32} generated with software (Mathematica, Maple), which are cyclic 
(so, strongly computable), the bits of pi, which is computable, but not cyclic, 
and strings produced by quantum measurements (with the commercial device 
Quantis and by the Vienna IQOQI group). Our empirical tests indicate 
quantitative differences, some statistically significant, between computable 
and incomputable sources of "randomness". 

Happy new year! 

s.

John von Neumann: “Anyone who considers arithmetical methods of producing 
random digits is, of course, in a state of sin.” From J. von Neumann, “Various 
Techniques Used in Connection With Random Digits,” National Bureau of Standards 
Applied Math Series 12, 36–38 (1951), reprinted in John von Neumann, Collected 
Works, (Vol. V), A. H. Traub, editor, MacMillan, New York, 1963, p. 768–770.