> 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
