[Fis] Consilience and Distribution of Energy in Chemical Systems

Dear Stan, Michel, and Colleagues.

This message addresses several issues related to Energy Distribution and a few words about "inductive jumps" in the context of chemical and biological systems. Portions of this email were distributed to a subset of the FIS list in an offline discussion with Prof. Lambert whose work contributed to earlier posts.

First, why is the distinction between the concept of a distribution and Stan's suggested use of the term dispersion so important?

The normative concept of probability theory is that of a unity over all possibilities presupposed in the narrative.

The mathematical term "distribution" can refer to either the concept of a continuous probability function (such that the "area under the curve" sums to a value of one) or it can refer to a discrete probability "function" in which the sum of a collection of ratios of numbers sum to one.
 In the later case, when the ratio of numbers sum to one, then, for chemical systems, one has a collection of particular paths that can be viewed like "tributaries" of a river, each tributary contributing to the distribution in a definite fashion.

 Obviously, in the continuous case, no such collection of tributaries is intrinsic to the definition. The term dispersion, technically speaking, does not specify the distribution but rather a property of a distribution. A distribution can have an unlimited number of properties. Thus, for chemical syntax, the term distribution can be placed in correspondence with structural processes and pathways of communication among structural processes while the term dispersion can not be placed in such correspondence.

  The roots of the semantic distinctions between the term "distribution" and the term "dispersion" are thus remote from one another and no logical substitution of one term for the other is permitted in a formal context.

Secondly, the concept of a syntax for chemistry must be taken into account. The chemical sciences are not merely vehicles for natural language semantics. A unique syntax has emerged from the empirical experimentation of the past three sentences (since Bolye). A formal syntax grounds the relationships between chemical mathematics and other branches of mathematics. This syntax forms the basis of such well established concepts as chemical structural representation as well as simple processes of change (transformations) such as oxidation and reduction. It is this chemical syntax that gives us confidence that the every day semantics of names of objects has consistent and reproducible semantics. For example, the specification of the molecular basis of genetics, the necessity of specific structures for vitamins and drugs and thousands of other usages of chemical terminology in natural language and commerce emerge from this unique syntax.

Stan, you seldom recognize the role of chemical syntax in your views of hierarchy theory. It is my view that by omitting the syntax of chemistry from your line of reasoning, you omit the syntax that underlies both biological and mental systems. The fact that chemical syntax is profoundly different from the usual Boolean syntax of classical mathematics leaves your arguments with only philosophical support.

How does this line of argument relate to consilience?
This line of reasoning requires several steps:
"Induction", technically, is a formal procedure for a mathematical proof. The generic line of argumentation of an inductive proof is simple enough.

1. If it works for one case, the first case, fine.
2. If it works for two cases, fine.
3. If it works for the nth case and the n +1 cases, then it is a "proof."

Thus, induction by its very nature, involves jumps from one number to the next.

A problem with the technical definition of induction is that it denies closure.
Neither the logic of chemistry nor the logic of genetics follow this pattern of reasoning.

It also presupposes that all jumps are logically equivalent in some sense of another (by invoking the variable symbol "n").
In a distributive view of internal energy within a molecule, the "jumps" of position are not logically equivalent. Each probability value is created (constructed) by the local circumstances.

>From a systematic point of view, the underlying conceptual problem is the question:

What is a species?
How can one specify a species as a system?
How can one obtain a consistent specification of a species in order to specify organizational structures?

In my papers on the construction of the concept of Degrees of Organization, I specifically sought to make an abstract logical framework for addressing the questions on the nature of species and to provide examples of the meanings. In other words, I was developing a distributive argument relating species, not a dispersive argument about categories.

Stan's classification, it seems to me, goes in the other direction. Stan's arrangement of general categories obscures the notion of species and the syntax of relations among species. It also moves the issue of species from technical languages into a vague collection of nouns from natural language, none of which can be exactly specified in the sense of numbers.

I close with an open question:

What exactly (precisely) are we seeking to communicate when we say that two species of information are related to one another?

Cheers to All

Jerry

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Received on Wed Oct 27 23:01:41 2004