On 29 Dec 2013, at 11:37, LizR wrote:
On 29 December 2013 13:11, Edgar L. Owen <edgaro...@att.net> wrote:
Jason and John,
If something is random it can't be computed by any deterministic
process. That's the meaning.
I thought the digits of pi were random, but computable by a
deterministic process?
Well, this is just a question of vocabulary, and we have to agree on
some definition.
Empirically, we know that pi pass the statistical test of normality,
and so it is random in that sense (but this is empirical, and the
question of pi being normal is an open problem in math).
Of course the digit are computable, and so pi is not random, in the
incompressibility sense.
"random" is just a fuzzy terms which can have different meaning in
different context. Passing normality test is a weak notion of
randomness, compatible with computable. Being incompressible is a
stronger form of randomness. The second notion implies the first, but
the first does not imply the second, like pi illustrates indeed.
Bruno
http://iridia.ulb.ac.be/~marchal/
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