Author: Alvaro Polo
Date: 23:16:41 07/22/00
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On July 22, 2000 at 17:32:38, Ralf Elvsén wrote: >On July 22, 2000 at 16:47:58, Alvaro Polo wrote: > >>>Could you please define "complicated". >>> >>>Ralf >> >>I will do it. The complexity of a system is proportional to the length of the >>description of its regularities. I don't believe that such description is >>shorter for any program that for Kasparov's evaluation. >> >>Alvaro > >Hmm, this sounds interesting. Is this from some theory on computation >or some such? I don't know much about this. Can this measure be >applied to physical systems? Can you be just a *little* >more explicit on what a regularity is? > >Oh, I forgot the usual question: any websites? :) > >Ralf I haven't invented this definition. I took it from Murray Gell-Mann (the Nobel Prize physicist) book "The Quark and the Jaguar", where he states the Theory of Complexity developed by him and the Santa Fe institute. I read the book in spanish but I am quite sure that you have it available in english since Gell-Mann is american. The complexity measure can be applied to any system that provides information to us, physical or otherwise. The subject is long and interesting (in fact I recommend you that if you are interested you get the book), but I will give a small example, small, on the one hand, because english is not my langage and a longer explanation could obscure things, and, on the other hand, because there are a lot of things to say and this is not the best place to write a 50k message. Suppose a very "simple" system, a bit string. For example: 01010101010101010101... (and so on) This string is not very complex. You can describe its regularities: "a string where 0 and 1 alternates", a short description. Now, an even simpler string. 000000000000000000... This is really simple, "a string composed by 0s". Now, something more interesting, a random string. 01010010110010011001101010010010... (lets suppose it is aleatory) Here we could think that it is very complex, but the informational content is what interest us. An aleatory string has no information and hence it is equivalent to any other aleatory string. So the description of its regularities would be "an aleatory string". A random string has the same level of complexity than a string mades by zeros, since they share the same amount of information. Sorry to have explained things so badly. If you find the subject interesting you could search by Gell-Mann and complexity theory and Santa Fe Institute and also get the book. Alvaro Polo
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