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> > Try adapting Shannon's information theory. If we assume a probability
> > distribution on the set of messages, then the information of a given
> > message m is given by -log(p(m)) [1]. That is, the less likely a
> > message, the more informative.
>
> Since only frequencies of symbols are counted, entropy depends only on
> them.
> A set of random numbers can have the form
> 0,0,0,0...1,1,1,1...2,2,2,2...
> It has the same entropy as any number (permutation) formed from this
> set.
> The strings of random numbers are randomly ordered digits.
> Any sensefull text is a carefull ordered string of symbols.
> Newertheless, the long distances between consecutive symbols (or words,
> if we take them as the smallest information unit) have properties of
> randomly ordered strings.
> The number e is generated by an algorithm. Newertheless, the distances
> between its numerals are quite random.
> kunzmilan
>
I think that the problems of the concept of randomness are only compounded
when we introduce the RND function. It's easy to think of things as being
random when you do alot of programming and you can just paste an RND command
anywhere you want. Still, the question of order and disorder is still
unresolved.
I was reading something about Wolfram.
http://www.businessweek.com/technology/content/may2002/tc20020516_7010.htm
I think that Wolfram is great, but a little constructive criticism. In this
article he seems to be obsessing over rule 30. I think that rule 30 is just
a rule which happens to make pretty pictures. What Wolfram seems to have
missed is a formalization of order/disorder. His treatment of CA comes very
close to addressing order/disorder more precisely, but CA in it's present
state simply does not accomplish this. I'll try to do something on my blog
which I think that he may have missed.
Wolfram's work does indeed seem to suggest some profound things about
disorder, and Wolfram seems to be moving away from randomness and more
toward order/disorder. This is brilliant and bold in my opinion, but still
there is no formalization of order/disorder on paper. His work suggests that
there is a great body of unknown fact out there which is still wild and
unformalized, that disorder could arise spontaneously out of orderly
things - CA is evidence that the concept of randomness is simply
insufficient. This evidence - this is Wolfram's greatest contribution to
science in my opinion, and I think that indeed one day CA will rank right up
there with calculus.
order-disorder-randomness.blogspot.com/">http://order-disorder-randomness.blogspot.com/
I'll be adding to this - please feel free to comment - gotta run
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