From: Anders Sandberg (asa@nada.kth.se)
Date: Thu Jun 27 2002 - 17:27:36 MDT
On Thu, Jun 27, 2002 at 05:43:17PM -0400, Mike Lorrey wrote:
> Since numbers like pi and e do not end, it is impossible to tell if they
> are random or not. I doubt that there is any way to tell if something is
> 'truly random', there are only degrees of randomness.
One of the stronger ways of defining randomness of a string of bits is
that having access to all previous bits give you no information about
the next. This can be expressed in algorithmic information theory by
saying that the shortest program that can generate the first N bits of
the string is N bits long. If they can be generated by a shorter
program, they are less random. In this sense pi and e are rather
nonrandom numbers, while the vast majority of numbers have truly random
bit sequences. The problem is that proving that a number is
algorithmically random is not possible in general...
As always, G. J Chaitins page is worth perusing:
http://www.cs.auckland.ac.nz/CDMTCS/chaitin/
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