Dear FISers:
This message responds to Karl's message (copied below). I bring up
some philosophical issues in hopes of stimulating some of the
biologists and philosophers to consider the semantic problems
associated with this particular area -- trans disciplinary
communication within the informational sciences.
Karl, thank you for your efforts in response to my example with NAD
(Nicotinamide Adenine Dinucleotide, H(27)C(21)N(7)O(14)P(2).)
Please note that the standard representation of a chemical
(molecular) formula includes both chemical symbols and number or
mathematical symbols. Both classes of symbols are necessary to
convey the empirical facts about the ratio of chemical elements
present.
From a semiotic point of view, the meaning of each chemical symbol is
well defined and unambiguous. Each chemical element represents a
concept of a specific class of matter. Each chemical element as a
class of matter is not a single factor or a single concept, rather it
represents a set of properties which includes a dozen or more
interrelationships associated with the concept. For example, the
symbol Au represents not only the verbal concept (word) of gold, but
also such properties as density, electrical conductivity, thermal
conductivity, electrochemical equivalence, electron work function,
specific heat and so forth. In addition to these empirical
properties, gold also represents a concept within the ordering
relation of chemical elements. In this addition role, it is
represented by the atomic number 79.
In contrast to the diversity of the empirical properties of gold,
consider the mathematic concept of a set and the relation with
number.
Both set and number are abstract concepts. As such, different
opinions exist on the meaning of these concepts.
Examination of standard textbooks on logic and set theory reveal the
following definitions: ( The concept of set is an artificial
construct, it was invented by G. Cantor about 1870.)
1. "According to his definition a set S is any collection of definite
distinguishable objects of our intuition or of our intellect to be
conceived as a whole. The objects are called the elements or members
of S." (Stoll, Set Theory and Logic, 1979)
2. "Axiomatic Set Theory. The basic character of this theory are as follows:
1. propositional functions are taken extensionally, ie, they
are are identified when they have always the same truth values.for
the same arguments.
2. propositional functions of more than one argument can be
reduced to to functions of one argument, i.e., classes;
3. there is a class whose elements are called sets such that
a class cane be an element of another if and only if the former is a
set."
Curry, Foundations of mathematical Logic, 1976.
3. "A set can be defined as by a characteristic property that is
possessed by every element of the set but not possessed by any object
that is not an element of the set." Stolyar, Introduction to
Elementary Mathematical Logic, 1971.
We can ask the following questions about the chemical elements and
numerical elements:
1. What are the references for the two concepts, chemical element and
set theory element?
2. What are the empirical relations that tie the two concepts together?
3. When can the concept of a chemical element symbol be substituted
for a mathematical element symbol?
4. How is it possible to substitute a chemical element symbol into a
mathematical function?
5. When will a string of chemical symbols be considered to be
"ordered" in the sense of ordering of the natural numbers?
6. Under what circumstances can a multi-conceptual concept such as
that of a chemical element be entered into a syllogism of the type
used for numbers or classes of sets?
These questions are raised because of their fundamental relationship
to chemical and biological communication and the the necessity for
creating correspondence relationships between semantic concepts,
chemical symbols, and mathematical symbols.
To illustrate what I mean, I quote from an earlier paper:
"The semiotic dilemma is exemplified by noting that the terms
organic, organism and organization are all derived from the same
root." (Chandler, Information Processing in Cells and Tissues.1998)."
It is well known that the relationship between physical methods and
mathematical representation and operations have co-evolved.
Remarkable cross-fertilization between the two disciplines. While a
potential cross fertilization between chemical methods and
mathematics may be possible, the logical foundations for such a cross
fertilization have not yet evolved.
Now, to Karl's specific interpretation of my example:
>Your concrete question translates into marketing-speak as follows:
>H(27)C(21)N(7)O(14)P(2). Six of the 21
> >carbon atoms are optically active.
>
>Give me the well-and-classical archetypical inhabitant of the market: he/she
>comes in two varieties (he/she), equipped with 14 credit cards, has 7 living
>relatives, meets weekly 21 other persons and spends money on 27 differing
>occassions in the period. Six of the spending social interactions happen
>with cash.
>
>This being the most common member of the market, this lemming shall be the
most easily observable unit.
I point out the following problems in trans-disciplinary communication:
1. NAD is a specific chemical structure. It is a specific geometric
relation (in crystal form) among 71 "atoms" bound together as a
whole. It is a single member (a single isomer) of a very large class
of structures with the same chemical composition.
2. NAD, as a chemical structure, is a stationary object. (Time is not
represented in the formula.)
3. 67 of the 71 atoms occupy unique chemical positions and thus form
separate subclasses.
4. The critical role of multiple optical isomers is specific to
chemical language and seldom plays a role in normal language.
5. Karl correctly notes the distinction between the symbol of the
class and the number of class members, but misses completely the
uniqueness of the individual components within the class.
6. The introduction of statistical distributions is apparently an
essential part of Karl's method; it is purely gratuitous from the
perspective of chemical structure.
Among the defining attributes of life are the specificity of
relations and the sensitivity of these relations in time and place.
Karl's method appears to miss these attributes in this example.
From a philosophical perspective, Karl (and Michael?) appear to
assume a neo-Kantian view of mathematics. Or, perhaps, even
neo-Platonic. Karl's views could also be classified as almost
Pythagorean. As group theory is often viewed as an application of
set theory, the remarks about the definitions of sets are relevant to
Michael's mathematical explication of music.
Underlying my concerns is direct question: How does one create a
narrative that is consistent with the empirical facts, the scientific
correspondence relations and the structures of mathematics?
In my opinion, the chemical sciences (chemistry, biology and
medicine) are closer to Aristotelian categories and Liebnizean logic.
Cheers
Jerry LR Chandler
>Hi folks,
>
>Jerry has given me a well-circumscribed task. Thank you for the opportunity
>to discuss modeling of theoretical chemistry as a stochastical process.
>
>The task is (here comes what Jerry wrote):
> >Karl, my favorite molecule is known as NAD (Nicotinamide Adenine
>Dinucleotide).
> >It structural formula is H(27)C(21)N(7)O(14)P(2). Six of the 21
> >carbon atoms are optically active. The NAD molecule includes five
> >covalent rings, three aromatic and two aliphatic. (See an elementary
> >biochemistry textbook for the exact structure.)
>
> >Karl, can you demonstrate how your approach would generate the
> >particular biological isomer of NAD that is common to all living
> >organisms?
>
>The answer is:
>We return to my last communication in this matter:
>What comes out of the deeper investigation of mathematical objects
>that are parts of a set (that gets partitioned according to stochastic
>principles) is, that there appear KINDS or TYPES or ARCHETYPES of (clusters
>of) objects. These can be compared to the physical and chemical objects that
>the natural scientists refer to when they speak of "entries in the periodic
>table of elements".
>You take a sufficiently big set (somewhere between 32 and 97, for some
>obscure number theoretical reasons), make subsets on it and will see that
>there appear kinds, types or archetypes of objects that are definitely
>present. You cannot avoid meeting these.
>
>If you understand sociology and market research, you will understand the
>following:
>in any city, in any culture, in any field research, if you ask more than a
>few dozen people, you will have types of answer collections. There will be
>some "really average", "rather average" and "slightly off-stream" and
>"eccentric" types, characters, kinds or archetypes.
>If you understand this, you have understood the periodic table of elements
>as truth values of a multidimensional partition table of a sufficiently big
>set.
>
>Jerry, you have to visualise the periodic table of elements as a truth
>table. (So far, a truth table has been taught at Computers I for freshmen
>with following essence:
>"
>(1) there are 2 constants: .t. and .f..
>(2) combinations of logical sentences build up a truth table
>(3) Sentence A .t. .AND. sentence B .t.: A .and. B = .t. ; A .or. B = .t.
>(4) Sentence A .f. .AND. sentence B .t.: A .and. B = .f. ; A .or. B = .t.
>(5) Sentence A .f. .AND. sentence B .f.: A .and. B = .f. ; A .or. B = .f."
>
>Please look up the current way of putting this. A truth table describes the
>logical truth of some combinations of logical sentences.
>
>Now the invention:
>The undersigned (that is me, Karl Imre Javorszky) has extended the concept
>of a truth table to include more dimensional combinations of logical
>sentences. There are not only 2 possibilities for a logical value to be
>somehow, but more. The idea is to use the .t. and .f. values to denote the
>"is included in a subset of size ...." logical fact. This leaves you in a
>fashion with the same old .t. and .f. values, but there are more of these
>and they are at the second look not all exactly the same worth.
>
>The undersigned has introduced the concept of multidimensional truth tables
>by using statistical, stochastical methods that are taught at Marketing,
>Economics, Statistics, Sales, Sociology, Social research and the other
>faculties, but also for freshmen. I hope that a professor for theoretical
>chemistry can apply methods of Marketing I.
>
>In Marketing I one learns to segment the market. The market is viewed as
>segmented for people who sell. They know that they don't target the whole
>market but a segment of it. They say "segment" and what they mean is
>"subset". It is called correctly a subset but one does not always use the
>correct name for it.
>
>So they segment the market - in their words. If they would want to talk
>about what they do with mathematicians, they would say that they partition a
>set. They do the same but don't say it in the same fashion. They partition a
>set.
>If they want to sell to middle-aged, divorced women or to self-employed
>professionals in small towns, they generate multidimensional partitions.
>They just don't say so, because it is a complicated business and
>mathematicians like to wait up until it is clear they really have to work a
>bit.
>
>We agree that marketing does use multidimensional partitions. (Ask a dealer
>in e-mail addresses whether he can subsegment the set into mutually
>exclusive subsets and generate overlaps according to your wishes.)
>
>Now the BIG INVENTION: (so far there was no real invention, just looking up
>what other people do.)
>If the set is big enough, there shall be always such a segment (subset) that
>is the most probable.
>
>Meditate on this and you shall have great rewards.
>
>Your concrete question translates into marketing-speak as follows:
>H(27)C(21)N(7)O(14)P(2). Six of the 21
> >carbon atoms are optically active.
>
>Give me the well-and-classical archetypical inhabitant of the market: he/she
>comes in two varieties (he/she), equipped with 14 credit cards, has 7 living
>relatives, meets weekly 21 other persons and spends money on 27 differing
>occassions in the period. Six of the spending social interactions happen
>with cash.
>
>This being the most common member of the market, this lemming shall be the
>most easily observable unit. Why, computer artists will draw you the traffic
>simulation based on the most probable behaviour of the most probable
>inhabitant. Why they can't (or won't, because the definitely could) do this
>for a more abstract inhabitant, I don't know. (Saying: now show me the most
>probable social group size for the most probable inhabitant during the most
>probable period of time, while you let the city grow in size.) But this is a
>psychological question of why people don't find the answer if they are paid
>for looking everywhere for that elusive answer. Would you research yourself
>out of your job?
>
>Ask your friendly neighbourhood mathematician what must happen until someone
>shall define the term multidimensional partition. Everyone uses them but the
>mathematicians. "Not defined" - it is like in socialism used to be: "not in
>the party rules", therefore it does not exist.
>
>Hope to have helped you a bit.
>Cheers
>Karl
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Received on Thu Jul 3 04:25:09 2003
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