From: Kenneth Hurst (k_hurst18@hotmail.com)
Date: Sat Jun 29 2002 - 18:57:05 MDT
On Thursday, June 27, 2002 4:27 PM, Anders Sandberg wrote,
> 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...
I fail to see why this would classify a number as "less random." If I
generated a six bit number string randomly, 111111 could be generated. This
has exactly the same probability as generating 847952. Since there is a
pattern to 111111, it is classified as "less random," even though (as it
seems to me) it is just as random because it was randomly generated. I
suppose the essential question is: Is randomness the fact that a string was
randomly generated, or is it the characteristic of having no pattern?
--Kenneth Hurst
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