[extropy-chat] what is probability?

[scerir]

gts:
> I think a genuinely random sequence 
> is one in which the next digit is both
> 1) unpredictable and 2) undetermined.

I would say uncomputable.
Let us suppose a 'random' sequence
would be computable.
In this case, the computation(s) involved
would produce definite number(s) associated
with definite outcome(s), that is to say
definite element(s) of physical reality.
We know that the assumption of value definiteness
often results in a sharp contradiction
(at least when the quantic nature of physical
reality becomes important).
One is forced to conclude (in that case) 
that the assumption of computability has 
to be given up.

[Calude, Svozil]
http://www.arxiv.org/abs/quant-ph/0611029 
[Quantis machine]
http://www.idquantique.com/ 
http://www.idquantique.com/products/quantis.htm
[Calude]
www.idquantique.com/products/files/quantis-mcu04.pdf