[Fis] Number theory and chemical syntax

Dear Karl and Rafeal and All:

This email addresses your posts concerning counting, number and philosophy from the perspective of chemical syntax.

karl writes:

"The numbering system
is flexible enough to privide a transportable background on which we can
calculate and predict the effects of a position change of a genome in the
same classical fashion as we are able to calculate and predict the
occurrence of the next eclipse of the Moon in Central Europe. One has only
to understand the tricks the numbering system plays when describing
diversity, similarity, probability and size. The size attribute of an
interdependent, autoregulated system is of a secondary importance. It
appears that the more diverse the parts of an assembly are, the more "inner
tension" (maybe, energy) is there. The size itself is not the important
attribute when discussing the inner diversity of subsets of a set. (In
actual fact, there is - to top it off - a super little trick concerning
size: if one categorises sets according to their inner diversity, there are
two virtually equivalent sizes.)".

karl clearly expresses the power of calculations with numbers.

But, the source of the power of calculations is not merely the numbers themselves. The arithmetics operations are essential as well. By arithmetic operations I mean addition, subtraction, multiplication, division, and exponentiation and roots - the ordinary operations taught in primary schools.

>From the perspective of definition, an atom is "indivisible". Thus, the atomic number of an atom is not divisible by an arithmetic operation. Note that ordinary physical syntax, mass is often expressed a real number and divisibility is not an issue.

So, I conclude that the concept of number as described by karl is not applicable to chemical syntax. Nevertheless, I doubt if anyone (perhaps Stan is an exception!) will argue against the concept of the atomic number and the natural language correspondence between particular atomic numbers and particular chemical elements.

Karl further writes:

"We have to capture the obvious feeling:
"this is the same just bigger / smaller" in order to begin understanding
phaenomena which appear to belong to different sciences. We have to come to
terms about what we do as we recognise two things that are the same (but
bigger or smaller) before we can attack the task of describing what we do as
we compare two things that are different in order to find similarities among
them. "

What exactly does karl wish to imply with the phrase:
"we recognise two things that are the same (but bigger or smaller)"

I do not understand what is the meaning of "the same" in this context. Nevertheless, I can construct large sets of numbers, each with the have same numbers of divisors (for example , the primes). The difficulty of untangling the similarity from the homology from the analogy from the metaphor can be be overwhelming at times.

Rafeal writes:
"the only problem I see with your materialistic stance is... that numbers are not material! so your whole underlying (ontological) argument (being=being material) is constructed upon a contradiction."

>From the perspective of chemical syntax, it appears if Rafeal is staking a particular argument of epistemological uniqueness on the concept of number. (Or, have I not understood the argument?) The atomic numbers are referenced in both natural language as a object and as a counting number in the sense of mathematics. Thus, the atomic numbers form a logical 'commutative diagram' with references in three distinctive languages - natural language, arithmetic language and chemical language. The logical coherence of chemical syntax is not violated by the three sources of reference - the three references merely correspond with one another. A metaphor for this situation would be that the same sentence ("I love you.") could be expressed in three languages and the meanings would correspond with one another.

If this issue were addressed from the perspective of phenomenology, is the same phenomena under description / narrative construction?

Cheers

Jerry

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Received on Thu Nov 4 04:43:13 2004