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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