Dear Jerry, My apologies for taking so long to reply! I have been overwhelmed with queries on email, civic and social obligations and responsibilities for liturgical rubrics in my parish. I havent spent very much time online as a result.
I sympathize entirely with your apprehensions, but I think they are inapplicable here. I share your concerns that homogeneous variables like mass, energy, charge, etc. are inappropriate to heterogeneous situations. Gregory Bateson made the distinction between the former, which he called pleroma and the latter, which he characterized as creatura. He pointed out how the former are insufficient to describe the latter. Later, Walter Elsasser pointed out how the logic of the laws of physics, equivalent as they are to operations on homogeneous sets, does not apply to heterogeneous systems, especially biological ones. <http://www.vordenker.de/elsasser/we_logic-biol.pdf> You are certainly correct in pointing out that one neednt be concerned only with living systems, in that the transition from physics to chemistry already crosses this divide. The problem is that I do not see the divide as being as dichotomous as you portray it. You are probably aware of the realm of chemical thermodynamics, where the effort has been made to incorporate attributes of heterogeneity into variables that characterize the entire system. For example, the Gibbs (and Helmholz) free energies are defined for chemical reaction systems. Changes in the various tokens will contribute to changes in the whole system quantity. It is an attempt to marry the two domains by folding the heterogeneous tokens into a pseudo-homogeneous system function. Of course this is precisely what the Shannon formula does. The key to my assertion is that the Shannon variable can be decomposed WITH RESPECT TO A SECOND, REFERENCE DISTRIBUTION into two terms one which quantifies the order (amount of constraint) that the two orders exert one each other and a second that quantifies the freedom that the two enjoy from each other. The second term, called the conditional entropy in information theory is actually a better homolog to physical entropy than the Shannon formula. In applying this calculus to arbitrary networks, Rutledge et al. (J. theor. Biol. 57:355) showed true genius by identifying the first distribution with the distribution of inputs into the nodes and the second as the distribution of outputs from the same nodes. Hence the mutual information (total effective mutual constraints) becomes a measure of the internal order in the system and the second is a surrogate for its entropy. The key to my assertion is that these two terms are precisely complementary, so that if one is somehow indeterminate, the other must be likewise. Now, I confess that I have taken a major liberty in identifying statistical entropy with physical entropy. But the third law has its homolog in information theory in the result that statistical entropy is always relative. Whence, the inherent structural information of the network must likewise always remain relative. I further confess that I have always inveighed against identifying physical entropy with statistical entropy. They are, however, accurate homologs of one another, and that is all that I am claiming. I remark in passing that the mapping of physical elements into the integers is decidedly homomorphic and not isomorphic. The number 12 refers to the number of protons in the nucleus of a carbon atom, nothing more. There are a variety of isotopes, ionic and radical forms that also map into the same integer. Each has its own properties that would factor into any physical measurement on a mixture of these varieties. So, in conclusion, I would readily agree that a thermodynamics that is strictly confined to pleroma cannot fully illumine attributes of a heterogeneous system. But contemporary thermodynamics is not so constrained. Neither is information theory, nor is chemistry without its own hidden heterogeneities. As regards information theory, statistical entropy is always relative, which forces its complementary information to be likewise. Cheers, Bob > List, Bob: > >> On Mar 27, 2017, at 10:37 AM, Robert E. Ulanowicz <u...@umces.edu> >> wrote: >> >> First off, that information is always relative is the obverse of the >> third >> law of thermodynamics. It cannot be otherwise. >> <http://people.clas.ufl.edu/ulan/files/FISPAP.pdf >> <http://people.clas.ufl.edu/ulan/files/FISPAP.pdf>> > > First off? > > I fear that I am rather skeptical about this assertion for a simple > structural reason that illuminates the scientific inadequacy of > thermodynamics as source of scientific apperceptions. > > The notion of a general mathematical form of information residing within > the Third Law of Thermodynamics is difficult for me to image because of > the chemical table of element assigns a unique physical structural form > and mathematical count to each individual chemical element. > > The apprehension of matter in the theory of thermodynamics is constrained > to use of the symbol for mass (as a continuous variable.) > But, the electrical structural information content is different for each > element of the table of elements. > > This fact is a major impediment to the application of thermodynamic > principles to the chemical and biological sciences. The closure of the > thermodynamic symbol system (P, V, T, F, G, S, m) excludes the direct use > of chemical symbols within the entropic framework. > > Can anyone conjure up a compelling counter-argument to this line of > argumentation? > For example, does the chemical structure of DNA contain information > (independent of temperature)? > > Cheers > > Jerry > > âThe union of units unifies the unity.â > âThe disunion of the unity separates the units" > _______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
