Bob, If the notions of Entropy and Shannon Information are alternative approaches to characterize the same phenomenon in Nature, then the ways they have been modeled would not necessarily reveal an underlying and fundamental commonality. I think that many of us suspect that this is the case and we are striving to understand and articulate (model) the fundamental commonality. We may be wrong, of course, but your argument doesn't dissuade me. In fact, I must admit sheepishly that I'm not sure how one would go about analyzing the relationship between these ideas in a way that could dissuade me. If such an analysis is not possible, then I suspect that the question of a fundamental commonality will have to die slowly as progress fails to occur.
Regards, Guy on 10/12/07 12:01 PM, bob logan at [EMAIL PROTECTED] wrote: > Loet et al - I guess I am not convinced that information and entropy > are connected. Entropy in physics has the dimension of energy divided > by temperature. Shannon entropy has no physical dimension - it is > missing the Boltzman constant. Therefore how can entropy and shannon > entropy be compared yet alone connected? > > I am talking about information not entropy - an organized collection > of organic chemicals must have more meaningful info than an > unorganized collection of the same chemicals. > > > On 11-Oct-07, at 5:34 PM, Loet Leydesdorff wrote: > >>> Loet - if your claim is true then how do you explain that a random >>> soup of >>> organic chemicals have more Shannon info than an equal number of >>> organic >>> chemicals organized as a living cell where knowledge of some >>> chemicals >>> automatically implies the presence of others and hence have less >>> surprise >>> than those of the soup of random organic chemicals? - Bob >> >> Dear Bob and colleagues, >> >> In the case of the random soup of organic chemicals, the maximum >> entropy of the systems is set by the number of chemicals involved (N). >> The maximum entropy is therefore log(N). (Because of the randomness of >> the soup , the Shannon entropy will not be much lower.) >> >> If a grouping variable with M categories is added the maximum entropy >> is log(N * M). Ceteris paribus, the redundancy in the system increases >> and the Shannon entropy can be expected to decrease. >> >> In class, I sometimes use the example of comparing Calcutta with New >> York in terms of sustainability. Both have a similar number of >> inhabitants, but the organization of New York is more complex to the >> extent that the value of the grouping variables (the systems of >> communication) becomes more important than the grouped variable (N). >> When M is extended to M+1, N possibilities are added. >> >> I hope that this is convincing or provoking your next reaction. >> >> Best wishes, >> >> >> Loet > > _______________________________________________ > fis mailing list > [email protected] > http://webmail.unizar.es/mailman/listinfo/fis _______________________________________________ fis mailing list [email protected] http://webmail.unizar.es/mailman/listinfo/fis
