Quoting Loet Leydesdorff <l...@leydesdorff.net>: > Dear Bob, > > I now read the book: the description of autocatalysis is very convincing. It > really clarifies how a "triple helix" (of university-industry-government > relations) can operate in generating synergy (reducing uncertainty).
Dear Loet, I'm unsure to which book you are referring? "A Third Window" or "Ecology, the Ascendent Perspective"? > You then go on with "Average Mutual Information" (AMI). You don't mention > that AMI (that most of us call "mutual information") is necessary positive > since a Shannon-type information, but that "mutual information in more than > two dimensions" can be negative and thus used as an indicator of synergy or > autocatalysis. It's true, I don't refer to the possibility of negative 3-D mutual information in any of my books. What Claudia Pahl-Wostl and I agreed to call information in the 3-D case was the entire ensemble (1+2+3+4) in the attached diagram. While 1 can go negative, the full ensemble does not. Recall that information is always relative, so whether a particular component is viewed as information or as conditional entropy is a matter of perspective. For example, any of the "ears" 2, 3, or 4 can be viewed as a conditional entropy in the context of all three variables, or they can be viewed as information in the context of their respective binary associations. Finally, Gennaro Auletta in his book, "Cognitive Biology: Dealing with Information from Bacteria to Minds", maintains that complexity is a property of more than 2 dimensions and that the magnitude of the "ears" is a gauge of such complexity. His definition makes some sense in that an "ear" represents how two variables influence one another in complete abstraction of variation in the third -- certainly one manifestation of complex behavior. > I usually make reference for this to Ulanowicz (1986, pp. 143 ff.). Is that > methodologically the same argument? I assume so. Or have you taken these > measurement issues also further? That reference is fine. I really haven't taken this issue much further. I do remark on p336 of <http://people.biology.ufl.edu/ulan/pubs/METHODS.PDF> that the 3-D or higher mutual informations can be negative. Somewhere I also remarked that a negative mutual information might act like the Pauli-Exclusion principle in physics. That is, it would signify an untenable or unstable configuration. Unfortunately, I can't find where I wrote that speculation. Sorry. > Best, > Loet The best as always, Bob _______________________________________________ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis
