On Thu, Jun 5, 2008 at 3:56 PM, Robert Ulanowicz <[EMAIL PROTECTED]> wrote:
Dear Loet, You are absolutely correct! My formulation of ascendency is a strict analog of the formula you gave. Trouble is, H, in this instance, is the "entropy" or more precisely, the diversity of the distribution. It is not information per-se (as I discuss in Chapter 5 of Growth and Development [Springer 1986].) That is captured better by the mutual information of the distribution with itself an instant later. Secondly, it does not conform to Shannon's communication format, and so most feel that it does not truly deal with information. But you're right, there really is no mystery, once one gets one's definitions straight. The best, Bob Dear Bob, I don't know if I follow you using the mutual information of the distribution with itself an instant later. The would be something like the auto-covariation, wouldn't it? The crucial question seems to me whether a system is able to generate negative (Shannon-type) entropy endogenously. Following your advice, I use the mutual information in three dimensions as a measure for that. But the measure is static. For the dynamic development, I would follow Theil (1972) "Statistical decomposition analysis" for the specification of the Shannon entropy: I = Sigma(i) q(i) log q(i)/p(i) in which Sigma q(i) is the posterior distribution and Sigma p(i) the prior one. (This measure is also known as the Kuhlbach-Leibler divergence measure.) This measure allows one to compare transitions in systems in terms of probabilistic entropy. An advantage is its asymmetry, while the mutual information is symmetrical. Thus, we are able to distinguish, for example, between diffusion (in the forward direction) and codification of the information from the perspective of hindsight. In other words, I am not clear what you wish to show with the mutual information between S(t=1) and S(t=2) and how this can be provided with an interpretation. Can you, please, clarify? I bounce this back to the list because, in my opinion, it is interesting. (It is my second mail this week, but the week is almost done.) With best wishes, Loet Quoting Loet Leydesdorff <[EMAIL PROTECTED]>: Dear Bob and colleagues, Great that you brought the book to our attention. I ordered it, this morning. Although I agree with most what you say, I cannot follow why the relation between information and thermodynamics would needed to be bridged: S = k(B) H S is thermodynamic entropy, H probabilistic entropy. H is dimensionless and can be applied to any probability distribution. S is expressed in Joule/Kelvin (because of k(B) ) and is only meaningfull in the physical domain. What has to be bridged? It seems clear to me. Best wishes, Loet _____ Loet Leydesdorff Amsterdam School of Communications Research (ASCoR), Kloveniersburgwal 48, 1012 CX Amsterdam. Tel.: +31-20- 525 6598; fax: +31-20- 525 3681 <mailto:[EMAIL PROTECTED]> [EMAIL PROTECTED] ; <http://www.leydesdorff.net/> http://www.leydesdorff.net/ <http://topics.scirus.com/Measuring_Research_Output_with_Science_Technology_ Indicators.html> http://topics.scirus.com/Measuring_Research_Output_with_Science_Technology_I ndicators.html _____ From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Pedro Clemente Marijuan Fernandez Sent: Wednesday, June 04, 2008 11:30 AM To: [email protected] Subject: [Fis] (msg. from Bob Ulanowicz) Asunto: Re: [Fis] order/disorder De: Robert Ulanowicz <mailto:[EMAIL PROTECTED]> <[EMAIL PROTECTED]> Fecha: Tue, 3 Jun 2008 14:42:30 -0400 (EDT) Para: [email protected] Just another word about the nature of information: As humans we are naturally self-centered and self-interested. Well and good. But we often miss connections by not casting our nets of interest a little wider. In particular and as regards information, there is a tendency to become bogged down in the theory of communication and digital forms of information, because that's what's closest to our immediate interests. But analog information was around long before evolution brought digital forms on the scene. What's more, the calculus of information theory, patterned after the leads of Boltzmann and Shannon, apply nicely to analog information as well. In the larger sense information can be regarded as constraint -- that which causes a non-random response to a random input. The beauty of this identification is that it allows information to be tied to the concept of work. This is done quite nicely by Stu Kauffman in Chapter 7 of his latest book, "Re-inventing the Sacred". Stu follows the lead of Peter Atkins in defining work as "the constrained release of energy into a few degrees of freedom". Stu then marries that definition with the notion of information cum constraint and the result is a work function resembling my own "ascendency", which Stu refers to without naming it. Notice there's nothing in the narrative about senders or receivers or alphabets. Those are particular instantations of a much more general phenomenon. And Boltzmann's calculus generalizes without difficulty, as well. I realize many are impatient with the Boltzmann/Shannon type of information, feeling that it cannot apprehend the concept of "meaning". Simply put, I do not agree. The *mutual* information between two distributions captures proto-meaning quite well. One can use it, for example, to quantify such things as the correspondence between the protein structures of antigen and antibody to each other. The mutual information between their surfaces peaks when they match in lock-and-key fashion -- precisely when each has greatest importance (meaning) to each other. The gulf between information and thermodynamics has now been bridged. The late Gregory Bateson once lamented, "Ecology has currently two faces to it: the face which is called bioenergetics-the economics of energy and materials and, second, an economics of information, of entropy, negentropy [exergy], etc. These two do not fit together very well precisely because the units are differently bounded in the two sorts of ecology." But identifying information with the constraint that identifies work melds the two faces into one (with consistent dimensions, I might add.) The best to all, Bob ------------------------------------------------------------------------- Robert E. Ulanowicz | Tel: (410) 326-7266 Chesapeake Biological Laboratory | FAX: (410) 326-7378 P.O. Box 38 | Email <mailto:[EMAIL PROTECTED]> <[EMAIL PROTECTED]> 1 Williams Street | Web <http://www.cbl.umces.edu/%7Eulan> <http://www.cbl.umces.edu/~ulan <http://www.cbl.umces.edu/%7Eulan> > Solomons, MD 20688-0038 | -------------------------------------------------------------------------- -- Loet Leydesdorff Amsterdam School of Communications Research (ASCoR) Kloveniersburgwal 48, 1012 CX Amsterdam Tel.: +31-20- 525 6598; fax: +31-20- 525 3681 [EMAIL PROTECTED] ; http://www.leydesdorff.net/ --------------------------------------- Now available: The Knowledge-Based Economy: Modeled, Measured, Simulated, 385 pp.; US$ 18.95;
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