AW: [Fis] Number theory and chemical syntax

Hi Jerry,
I shall answer to those points which you address to me:
"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?"

To the points you raise:
While chemical structures are represented as a multi set which could be
viewed like you partition, I do not see a further connection.
Yes, this is why I asked you to look up the chi-square function. Then,
maybe, you will indeed see further connections.

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?
Multiplication and division have as their implicit axiom that the underlying
entities are ALIKE (similar, have the same properties). You learn that you
cannot add apples and pears at elementary school. In the model I try to
massage into public knowledge there are several levels of units. Like
"children", "child", "organ", "cell", "mitochondria", "complexes",
"molecules", "atoms". Each of these is a unit on its own level.
We have a basic unit, named "1". But we need at least 32 of these to make up
a unit, called "<has-no-name-yet>" or "aggregation unit level 2". Of these,
we shall again need some few dozens to make up a unit called
"<has-no-name-yet>" or "aggregation unit level 3". Giordano Bruno wrote in
the XVI-th century "About the Principle, the Cause and Unit". The question
of what we consider to be a unit is a deep one.
In my investigations, I have found reason to assume that it is useless to
talk about properties of an assembly consisting of less than 6 or 7
elementar units. To be able to give a good definition of "property", one
would need at least several dozen objects.
To my knowledge, there is currently consensus about the a-tomos
(in-divisible) being very well subject to splitting and fusing technologies.
(cf. fusion and fission bombs and reactors). So, maybe, your question is to
be rephrased in light of technological advances of the last 70 years.

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?"
Mechanistic mathematics proposes to 1) evolve basic types of
"objects-with-properties" (to do so, one MUST a) understand the chi-square
function and its applications; b) have understood the probability
distribution of partitions, by having generated a few dozen of these and
looked at the diagrams. Without having learnt Egyptian and Greek, the
Rosetta stone is of no use.), 2) categorise the evolved basic types of
"objects-with-properties" into a schema, which will look surprisingly like
the periodic system of elements; 3) understand the "bonus" piece of matter
not within the right (dexter, not proper. As opposed to left) assembly of
"object-with-property" (please see "Possible Uses" for details); 4)
understand the interdependence between freely circulating fragments and
spatially fixed main body (where is the right place for that which has this
property); 5) understand the interdependence between neighbourhood relations
of not-naturally neighboured entities (the "tension" one sees on M between
a) two halves of a grand period, b) between two periods.
After one has understood these preliminary banal basics, one will understand
by which intermediary arithmetic operations Na+ and K+ and Cl- ions all
operate directly in neurons.
On the other hand: do you actually argue that mathematics has no place in
chemistry? In this case, you would fall back to alchimistic grandstanding,
before Laplace and the Encyclopaedists and generally, Enlightement. The idea
of that period was that Nature is understandable and au fond, rational.
Please, do declare whether you believe that Chemistry is a part of the
Natural Sciences or whether it has something transcendental and religious in
it, not subject to mechanistic arithmetics. It is a different question, HOW
we can massage our concepts of measurements and what we believe to observe
into each other. I have no wish to discuss WHETHER Natural Sciences and
mathematics can be made congruent.

Hope these answers have motivated you to ask someone to go thru the
chi-square distribution with you. That basic method details the relation
between expected and observed. One needs this.

Thanks for your interest. Looking forward your next questions.
Karl
E-mail address new: kj04@chello.at

-----Urspr�ngliche Nachricht-----
Von: fis-bounces@listas.unizar.es [mailto:fis-bounces@listas.unizar.es]Im
Auftrag von Jerry_Lr_ Chandler
Gesendet: Mittwoch, 10. November 2004 04:54
An: fis@listas.unizar.es
Betreff: [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 12:59:37 2004