List, Loet, Joe: This email responds to several questions raised in response to my long post of Oct. 16, 2011.

Loet asks: 1. What is the equivalent in chemo-informatics of a bit of information? Can this be operationalized as a formula like Shannon's H? 2. Can one compute with this formula in fields other than chemistry? For example, in economics; without using metaphors? ("As if") JLRC: 1. There is no equivalence between a bit of information and the science of chemistry. Chemical information must be encoded into a number just as any other semantic message. If their were such an equivalence, there would be no need for the clear, separate and distinct natural symbol system developed from signs from natural things and Dalton's rule that material things can be categorized as ratio of small whole numbers of weights and volumes. Chemistry can be thought of as a semiotic science. C.S.Peirce stated it well when he insisted (rejecting Kant) that the following role of symbols is necessary for formal logic: "Thing - Representation - Form." or, more precisely: "Thing - Representation - Iconic form" In other words, the formal logic of chemistry depends on the sort of representation selected. This formal logic is an encoding of impressions on the mind into a coherent symbol system that constructs iconic representations of particular things. . In Shannon information, the concept of encoding any message is used to assert that every thing can be encoded (represented in Peircian rhetoric) into a number AS a string of bits, a string of 0,1's, a string of true-false propositions. (Note the ambiguity of meaning of encoding as a representation!) The purpose of Shannon's logic was to communicate any message within a generalized inductive argument about communication. The purpose of Dalton's was to communicate a particular graph form that was particular to a specific form. The following are a list of propositions that underlie the communication of chemical information. 1. The chemical concept of an atomic number is a rhetoric phrase. 2. The adjective "atomic" modifies the noun "number". 3. Consequently, the concept of a chemical number is not the same as the concept of a artificial number. 4. The adjective "atomic" has a particular meaning that modifies the the LOGIC of operations on the noun. 5. The concepts of an atomic number and of an artificial number both are exact representations of concepts. 6. The representations of number in both cases are positions in a list. 7. The adjective "atomic" as used to represent chemical things, corresponds exactly with the count of the positive charge on the nucleus and the count of the negative charges of the electrons. 8. These two counts are identical. ((Schelling's "polar opposites" neutralizing one another.) 9. These two counts correspond with a specific thing with specific physical properties. 10. These two counts correspond to the rhetorical name of each chemical element. 11. These two counts form TWO SORTS of nodes in a mathematical graph. 12.One sort of node represents each electron as a unit. 13. The other sort of node represents the integer count of the nucleus. 14. These two sorts of nodes can be represented as a graph. 15. This graph is terms a labeled bipartite graph because it has two sorts of nodes that can not be substituted for one another. 16. All logical operations in the chemical sciences are based on the atomic numbers. 17. The simple logical operations are logical conjunctions of two or more atoms to form a particular molecule. 18. The conjunctive operation of creating a molecule from two atoms is a copulative verb, not a predicative verb. 19. The logic of this conjunctive operation creates a new identity, a new graphic object (a new icon in the sense of Peirce) 20. The conjunctive operation of two atomic numbers is an additive relation with respect to the properties of both number and weight (or mass), giving rise to the logical terms, molecular formula and the molecular weight. 21, The conjunctive operations on atomic numbers are formal operations that are extensive to all the sciences that study things with specific identities and properties. 22. The atomic numbers are the source of all molecular biological descriptions of life - genetic, development, anatomy, much of physiology, toxicology, pharmacology, clinical medicine. 23,.The atomic numbers are not applicable to artificial numbers such as irrational numbers, imaginary numbers, transcendental numbers, surrealistic numbers, the various efforts that attempts to represent infinity or the continuum. 24. A series of relationships can be used to transliterate the atomic numbers into artificial numbers - these are the Rosetta relationships. Such transliterations change the formal logical relations between the symbols from the copulative logic of the chemical sciences to the predicative logic of physical sciences. 25. The communication of chemical structures as Shannon information is routine because of the flexibility of the human mind to translate among a large range of symbol systems - see for example, the SMILES notation, or the Wiswasser line notation which were developed by chemists to store, transmit and calculate on the iconic forms of chemical structures composed from atomic numbers. With these 25 propositions, I can now give you a simple answer to your question. Chemical proof of structure draws conclusions about a singular entity. Chemical informatics seeks to draw conclusions about a plurality of different chemical entities. In other words, chemical information (proof of structure) is for a single identity of matter that is distinguished from all other forms of matter. Chemical informatics seeks to analysis the relationships among a plurality of chemical identities. Chemical informatics does analysis on multi-sets of molecules to compare properties of either the chemical graphs or the physical, chemical, biological, toxicological, pharmacologic, or ecological effects on another system. Often, statistical analysis is used to compare the similarity of effects in the search to find that structure that works best for the particular human purpose of does the analysis. Loet asserts: However, the strength of Shannon's information theory is its grounding in probability theory. This is more abstract and not field specific. At that level, the specifics of the morphology and spatial arrangements have first to be rewritten numerically (e.g., in terms of coordinates) before they can be made a subject of analysis and calculation. I agree only partially. (I developed and taught for over a decade a graduate level class on "Human Health Risk Analysis". In these lectures I derived from basic mathematical principles over a dozen statistical models for calculating risks and benefits of exposures to chemicals and radiation.) The true utility of Shannon's theory of communication is that it is an engineering theory of message transmission that actually works. The fact that the " specifics of the morphology and spatial arrangements have first to be rewritten numerically (e.g., in terms of coordinates)" is precisely the reason Dalton's principles of "ratio of small whole numbers" MUST BE PRIOR to physical representation of the form. The chemical representation must be prior to the physical representation such the relations between atoms can be represented in terms of the International system of units. The extensibility of chemical logic to things with billions of atoms (DNA) indicate and the genetic code of life are extremely strong arguments that chemical logic is vastly more abstract that probability theory which is effectively useless for any precise calculations on large systems ( In dynamical systems series, attractors are described in terms of probabilities and attractor identification are limited to a dozen or two variables, no more. Probability theory lacks the extensibility of chemical logic.) Loet - we both know that we have radically different philosophies of science. The social sciences are vastly more difficult that the biological sciences as they must build on the already vast complexity of life itself. While I admire your efforts, I remain skeptical that your path will be durable or fruitful. In my opinion, the social sciences will not progress very far until they find a system of symbolic communication that clearly and distinctly expresses the correspondence between human behavior and the representations in the symbol system. No small task is that! (This is a Peircian / biosemiotic perspective). I now turn to Joseph's post of Oct. 18, 2011. I will consider Joseph's points in terms of the 25 propositions point by point. But, as Joseph introduces some issues that are referenced to personal discussions in Liege several years ago and that are not familiar to FIS readers, allow me to first address these issues. My paper, An Introduction to the Perplex Numbers was based on a invited talk in Ankora, Turkey in 2006(?). [ B.C. - wonderful memories! :-) ] The formal logic has progressed substantially in the intervening five years. Some of the progress is reflected in the 25 propositions stated above. A comprehensive exposition of the perplex number system is in preparation. It will show the exact relations between the artificial number system and the natural number system of chemistry - that is, the relationships between the chemical sciences and the physical sciences in terms of the rosetta relations. The distinction between the discrete and the continuum is profound. Some aspects of the relations between category theory, chemistry, biology, and philosophy are addressed in a paper reviewing Andree Ehresmann / Jean-Paul Vanbremeersch book, Memory Evolutive Systems published in Axiomathes in 2009. (Andree, Jean-Paul and I have enjoyed an extremely fruitful collaborated for many years but now separated by the differences between the natural philosophy of chemistry and the philosophy of (artificial) mathematics.) Now to Joseph's points: JB: 1. Jerry's theory of Perplex Numbers, underlying his comments, is not a physical theory. JLRC: I agree. see propositions 1-25 above. However, it is based on the work of Moseley's physical interpretation of atomic structure (1914). JB 2. Are the dynamics of atomic and chemical structures, and their potential for reaction not also information? JLRC: Chemical information is represented (as a prior to form) in a different symbol system than Shannon information. The chemical encoding of information is in terms of Dalton's ratio of small whole numbers. NOT ALL SYMBOL SYSTEMS REPRESENT INFORMATION IN TERMS OF MATHEMATICS FUNCTIONS. Neither music nor dance nor nor law nor medicine nor many other symbol systems use Shannon symbolism to encode information. Chemical information is historically (evolutionally, emergence-wise) prior to artificial mathematics of irrational, imaginary, transcendental and surrealistic numbers.) JB 3. 3. There is no problem in talking about "parity of iconic representations" as irregular, but if you say electrical, you bring in physics, the iconic representations are no longer applicable, JLRC: False premise. The notion of polar opposites is integral to both chemistry and physics. Volta's concept of electrical potential underlies all chemical phenomena. Volta's premise is essential to the construction of the atomic number system, to the study of oxidation-reduction, etc. The iconic representations of chemical structures are static representations. They are necessary to serve as the initial conditions for dynamical representations JB 4. 4. No "practice of mathematics" or proof theory could have applied to the results of my own research nor could apply to recent major advances in, say, organometallic catalytic chemistry (see any recent issue of SCIENCE). Combinatorial chemistry and its efficacy for screening, in which I see Jerry was personally successful, is only one, limited domain of chemistry. JLRC: See propositions 1-25. The relations between the perplex numbers and the proof of chemical structures is the basis for the rosetta relations. The chemical proof of structures is a formal logical process based on the graph operations on the atomic numbers. See response to Loet with respect to chemical information and chemical informatics. The perplex numbers, as transliterations of atomic numbers, have not yet been applied to chemical combinatorial problems, at least in so far as I am aware. JB 5. Jerry understates Rosen's contribution, even if he is correct about the chemoinformatics aspects. Rosen's work is valuable because his vision went beyond thermodynamic considerations to concepts like anticipation which underlie some current systems approaches. JLRC: The profoundly deep and unequivical tensions between Robert Rosen "Life Itself" (and prior works) and Andree work on "Memory Evolutive System" (and prior works) motivated my search for a logical pathway that embraced the rhetoric, grammar and logic of molecular biology. The iconic logic of the perplex number system is a formal system of numbers that expresses genetic relationships that are abstracted from empirical observations. Both Andree and Robert and I enjoyed a collegial relationship with one another, but, eventually, I found it necessary to express chemical logic in a unique form of graph theory, closely akin to category theory in many ways. Here I should note that the complete logic of the perplex number system, as an electrical system, requires additional graphs beyond the labelled bipartite graph. The four additional sorts of graphs express the additional forms of electrical interactions. The graphs are supra and sub graphs of the Labeled bipartite graphs. JB 6. To conclude, the "physical basis of chemical logic" may be well understood, but this "chemical logic" is an abstract, partial model of what is going on. It cannot be an adequate basis for the informational processes that occur in real chemical systems. JLRC: see propositions. [This conclusion suggests that you are thinking solely in terms of predicate logic and not giving weight to the foundational principle of Stoic logic - that an antecedent must precede a consequence.] The critical contribution of chemical logic to the history of science is that it gives an exact mathematical description of material causality. It is not merely a further refinement of efficient causality and the Vienna school of philosophy of a physical metaphysical (logical positivism) and Comtism. Strict numerical chemical logic is atemporal. It manifests itself in the molecular formula and the molecular weight. These are not dynamic concepts. Chemical logic can be extended to temporal relations by adding the dimension of time, that is, by applying the law of mass action to a particular situation. (see Koichiro's remarkable efforts in this direction.) Adding the dimension of time is symbolic necessity into order to construct a path from chemical logic to thermodynamics. This path of temporal logic requires the further notion of chemical equilibrium. The perplex number system is a a complete model of copulative relations between parts and wholes. Chemical logic includes a rudimentary form of space in the sense of adjacency relations in parts of the graph and distance relations in the sense of steps (propositions) in the paths of the graphs. The Rosetta relations trans-symbolize the discrete logic of the perplex number system to the more-widely understood artificial number system. This trans-symbolization of representation of form necessitates deeply profound loss of practical information necessary for calculation of categorical relationships. The consequence of this trans-symbolization is the lose of the crucial mathematical property of extension and tha ability to do calculations on large systems. Metaphysics can be substituted for calculations whenever the systematic calculations are occluded the extended sorites of propositions. Chemical logic, by nature of its "proof of structure", resist the metaphysical urges by insisting upon empirical foundations for the logical steps in the proof of structure. In the post of Oct. 18, 2011, you write, JB: Logic: absolute separation of premisses and conclusion Set Theory: absolute separation of set and elements of the set Mereology: absolute separation of part and whole Category Theory: exhaustivity and absolute separation of elements of different categories. (The logics of topoi are Boolean logics). I disagree, Joseph, with you foundational premise about the nature of logic and also with your assertion of mereology. In my view, traditionally, logic is about establishing a clear and distinct relationship between premisses and CONCLUSIONS. The essential nature of the Aristotelian syllogism is that the premisses and the conclusions are tightly BOUND to one another. This is intrinsic to the concept of illation. I may be wrong about this, but it appears to me that you are conflating the use of symbols with the ostensive, nature of Peirce's "thing-representation-form". Chemical logic demands the absolute inclusion of the premisses in the conclusion. This directly contradicts you statement. The ostension of the mathematical bijection of a chemcial reaction is what is meant by a balanced chemical equation. Every chemical equation is a logical bijection between the left side and the right side. All the symbols appearing on the right side must appear on the right side. The logic of mereology requires an absolute conjunction of parts to create the whole. This directly contradicts your assertion. Your comment on mereology does not capture the essential logical nature of the iconic representation of chemical mereology. The perplex number systems insists that every part of the atomic numbers is represented in the whole of the molecule. It further insists that every part of the atomic number is represented in the molecular biology of the cell. It further insists that every part of the atomic numbers in the cell is represented in the organism as a whole. In short, the perplex numbers lie at the base of the hierarchical logical structures of organisms and eco-systems. This concept of number and identity coheres with the Copenhagen school of biosemiotics. Note that Andree Ehresmann's "Memory Evolutive Systems" captures the essential features of mereology within the framework of dynamical systems. This is a substantial achievement in applied mathematics. I will close this long communication with a brisk comment on the conceptual relationship between chemical category theory and mathematical category theory. The identity of a chemical category is represented as a commutative relations among three separate and distinct symbol systems as represented by (1) the rhetorical nominal term, (2) the rational iconic graphic term and (3) the metric 'system international' of physical units. The identity of an artificial category is represented as a commutative relations among artificial numbers as represented by rhetorical terms such as irrational, imaginary, transcendental, and surrealistic numbers, conjoined by functional relations, all within a single symbol system. The critical distinction between these two forms of commutative relations is that the chemical commutative relations are extensible to exact calculations on an unbounded number of terms, thus enabling the exact descriptions of the structures of Life Itself. If artificial category theory is to make its mark on molecular biology and medicine, it must find a path to the natural identity of things such that correspondence relations can be measured. It must move from the abstract to the concrete. This wide-ranging communication covers a host of topics relevant to the distinctions between physical/engineering information and chemical/biological information. I would summarize the essentials. These two forms of communication are connected mathematically by two different symbol systems. At the root of the distinction is the nature of the scientific logic used to construct messages. Physical information uses a generalized inductive logic to reduce all messages to a transmissible form. Chemical information uses a particular inductive logic that constructs new messages such that the messages are the messengers. Cheers Jerry

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