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> Randomness is not a property of a single file. You can't look at a byte sequence and say that "it's random". Interestingly, this is less true than you might
by bo1024 12y ago
> Randomness is not a property of a single file. You can't look at a byte sequence and say that "it's random".
Interestingly, this is less true than you might think. The mathematics of Kolmogorov complexity[1] formalizes the idea that a given finite fixed string is "random". In this framework, you can have a byte sequence that definitely is random. (However, your second sentence I quoted is still technically true here as well because it is algorithmically undecidable how random the string is.)
(In fact one of the definitions of a random string is one that is incompressible, i.e. there is no algorithm with shorter description than the string that produces the string.)
[1] http://en.wikipedia.org/wiki/Kolmogorov_complexity http://en.wikipedia.org/wiki/Kolmogorov_complexity
- leni536 12y ago>The mathematics of Kolmogorov complexity[1] formalizes the idea that a given finite fixed string is "random". I read into the wiki article and this approach is certainly interesting. However this complexity depends on the description language so there is no unique way to determine if a string is random.
- bo1024 12y agoRight. However, the idea is for any two ways (say Java and Haskell), there will be a constant so that they will agree on all strings up to a constant. So it's quite robust and seems to capture something fundamental or deep about randomness and information...