[Fis] Number theory and chemical syntax

Dear John, Karl, Stan, Malcom:

This response addresses several questions raised in recent contributions.

I start with John?s contribution concerning language usage.

Firstly, John, I believe that your concerns about language usage are well grounded. As long as we restrict ourselves to everyday events, we find ways to communicate with one another. When we move the conversation into any technical discipline ? yes, even discussions of music or poetry, the specialized usage of language limits understanding to a small fraction of the community. Is this not due to the richness of human mind and the richness of theworld. It is not necessary to ascribe mal intent to anyone. Rather, the barriers to communication seem related the limitations of individuals and individual goals and aspirations.

John, with regard to your assertion about the phrase, ?I love you?, please re-read what I wrote and you will find that we are agreement. I attempted to make clear that the metaphor was in terms of correspondence of meanings, and not in the Heidiggerian sense of ?A is A.? Obviously, when one moves from one natural language to another, one often leave the exact historical roots of each word with the first language and picks up a new historical trace of roots and meaning in the second language. Nevertheless, skillful translation is still possible.

With regard to chemical syntax, it is of critical importance that the atomic numbers are in exact correspondence with the integers of the natural language. This exact correspondence relation is critical component of chemical logic and chemical calculations. Indeed, discussion of quantum physics begins with the presupposition that this correspondence relation exists ? without it, quantum physics would not be possible. It is from this logical root that exact correspondences within molecular genetics becomes possible. It is of important to keep the origin and roles of numerical concepts crisply separated.

Your quote of Saussure is of interest. I would argue that a system of signs is intrinsic to nature (chemical and biosemiotics) but that we have unbounded freedom in alternative representations of the sign systems. For example, the number seven has a correspondence relation with seven units in all languages that count to seven.

You mention Koichiro?s brilliant arguments about quantum theory and time. It seems the issue is how to apply Koichiro?s line of reasoning to living systems. I can image living systems being poised to act, but I struggle to imagine how ?time itself? is poised to ?act.? The more I understand of mathematics, the more I find that physical theory and physical philosophy is enslaved by mathematics. No such enslavement has yet occurred in chemistry or biology despite the repeated claims of the thought leaders of physics. I am not questioning the utility of mathematics, but rather the philosophies that are often substituted for empirical knowledge.

Stan asks for simple examples of chemical syntax. For modern chemistry, the first principles are well established for more than seventy five years. The atomic numbers form an ordering relation for all chemical elements that correspond exactly with the natural language integers. The identity of any pure material is given by a multiset of atoms (molecular formula) and an exact correspondence with the molecular structure (identity). Any chemical change conserves matter and necessities a role of time. All chemical changes are expressed as changes in structure. The electroneutrality principle applies to isolated substances ? the same size of the positive and negative charges. Any introductory chemistry text will provide examples of the syntax. The syntax of chemistry works to distribute elements over structures in a regular manner. That the syntax operates in living systems has been repeated documented.

(Karl and Malcolm: Please note that application of set theory to chemical syntax has not been demonstrated. Presupposing that either set theory or model theory is fundamental to informational concepts of chemistry or molecular biology may or may not be fruitful.)
  

Karl ? Your response is appreciated. My knowledge of number theory is slowly increasing such that the algebraic roots of work are beginning to show. It seems that you wish to invoke numerous arithmetic operations in order to get to a structure that is meaningful in the sense that you can classify it into one of three classes. (But, chemical classifications of structures are exact!)
While chemical structures are represented as a multi set which could be viewed like you partition, I do not see a further connection. The multiplicative functions of Sigma and Tau (of Gauss?) also do not seem to vbe very useful.
Unfortunately, the arithmetic operations do not include the chemical syntax. For example, the arithmetic operation of division is not applicable to indivisible natural objects such as atoms and most molecules. How do you propose to deal with this important fact? Another example is the fact that Na+ and K+ and Cl- ions all operate directly in neurons ? without the intervention of intermediary arithmetic operations. How does one apply mechanistic mathematics to these mechanisms?

Malcolm ? you examples from the visual system are an excellent illustration of the extraordinary sensitivity and perplexity of human sensory systems. For practical purposes, I question if one wants to start developing a theory of information from such data. I am aware of Karl Pribram?s massive collections of results. By mingling discrete and continuous mathematics, one is in constant danger of confusing the abstractions of mathematics with empirically supported derivations. Thin ice and dangerous sledding from a theoretical perspective.

With regard to the concept of mass, it is defined as a generic quality of matter, in particular, of universal attractive forces. If one wishes to use this abstract quantity in either chemistry or biology, one is faced with constructing a concept of species from a generic quality. Have you a proposition on how to go about this construction?

Cheers to All

Jerry LR Chandler

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Received on Wed Nov 10 04:55:25 2004