Karl:

I will respond to both your new title to the thread and to your philosophy of mathematics.

When you ask the question, "what is life, logically?" what is the nature of the question that you wish to address? Given your history of posts, I am almost certain that I do not understand what you are asking.

The principle issue that separates our views is not the nature of life or information, it is the nature of scientific logic and a philosophy of mathematics.

The concept of "logic" dates back to pre-Aristotelian days and it is no clearer today, in my opinion, than when Aristotle defined his views of causality and categories. (The small book, "Logic, A short introduction" by Graham Preist, OU Press, is to be recommended.) Model theory and various sorts of set theory are often promoted by promoters. Yet, no one has succeeded in applying set theory to chemical theory and phenomena. The oft stated claim that "quantum theory" covers all of chemistry lacks supporting evidence. It really refers to calculating properties of molecules AFTER one is given the exact enumerations of structural organization in space.

If anyone would like to demonstrate that quantum theory covers chemistry, the place to start is to show how quantum theory applies to a simple enzymatic reaction. For example, give an exact calculation of the transfer of electrons from ethyl alcohol to NAD via the enzyme alcohol dehydrogenase, starting from physical principles. Chemists have developed exact methods to give an accounting of the particles and their positions for this reaction. The simple fact of the matter is that physical quantum theory is derived from the chemical table of elements and chemical relations and not vice versa. The list of chemical elements is an abstraction about invisible particles with electrical properties and relations among them. Chemical quantum mechanics simply places the objects in motion. (Physical quantum mechanics is awash in the mathematical approximations that attempt to use 1 or 2 or 3 or 4 different mathematical definitions of force into a logically consistent framework. Which notion of force should I believe in? Have you a favorite definition of force? If one makes a sufficient number of approximations, one can eventually fit empirical data - this is remote from the exactness of chemical calculations!)

More generally, I believe that the nature of logic itself is intertwined with the the semiotics of the symbol systems. Logical methods are not general. We have many classes or types of logic. These logics are intimately intertwined with the grammar of the particular symbol system that is being used. The grammar of addition is hardly the grammar of our emotions, is it? The grammar of music is hardly the grammar verbal expression. The grammar of chemistry is highly context dependent. a modal grammar that is closer to Aristotle than to quantum mechanics and its inability to correspond directly with human sensory perceptions. Can anyone point out how the axioms of set theory or group theory express the grammar of genetic systems?

I point I am seeking to make is that the oft expressed notion that certain logical statements are "true for all time and place" is a statement that can not be placed directly in correspondence with empirical observations in the many, many many areas of biology and medicine.

So, when you ask, "what is the life, logically?", I think you will get many answers and that these answers are more apt to reflect on the individual philosophy of mathematics and science and little to do with the question.

For me, a rough answer that is little more than a tautology is " Life is a chemical system that co-operates with an ecosis to reproduce systems similar to itself. "

Enough venting of my views! A few comments are interlaced into to your response below.

On Nov 14, 2006, at 6:00 AM, [EMAIL PROTECTED] wrote:

From: "[EMAIL PROTECTED]" <[EMAIL PROTECTED]> (by way of Pedro Marijuan <[EMAIL PROTECTED]>)
Date: November 13, 2006 7:21:08 AM EST
To: fis@listas.unizar.es
Subject: [FIS] what is life, logically?


Dear  Fis,

Both Stan and Jerry raise points about whether the fact of having figured out how genetic information, in its abstracted and formalised version, can be transferred between the living organism and its dna, does or will generally
improve a chemist's lot.
Both interjections address important questions.
Stan says:
> SS: What I meant is no compelling model of an 'RNA First world'
> as a model of the origin of life.  That is, life begins with
> spontaneously synthesized catalytic RNA molecules.  My point is a
> materialist one, not a logical one.

I concur with Stan and add that the problem is the nature of catalysis, not a particular structure.
Jerry says:
> Chemical information is grounded in the list of chemical elements and the >
relations among them.
> The terms "DNA" and "RNA" etc, are chemical names of specific relationally >
rich bio-molecules.
> The information content of chemical molecules must be expressed in
> terms of atomic numbers and relations among the electrical particles (graphs). > Biological information emerges as flows of changes of chemical relations - >
metabolic dynamics.
> In general, chemical structures / information does support transitive
> relations among the atomic numbers organized into graphs.
> Thus, if one wishes to develop a compelling argument about chemical
> numbers and structures and genetic information, one should start with
> relational algebras that keep track of changes of relations.

The common question both Jerry and Stan raise, as I understand it, is:
Does the fact that a slight inner inconsistency has been found in our counting system mean anything for actual science? Will the existence, extent and other properties of the inner duality of the counting system allow modelling, even
simulating biology?

Karl: No. The issue is not the validity of your mathematics. As far as I know, your mathematics is perfectly fine number theory. The question is, how does your number theory result relate to empirical genetic observations? What is the path between your interiority, your thinking, and the exteriority of the natural world, reality if you will, and genetic systems in general?

My answer is:
Yes, it does. By finding a. the principle, b. the numeric properties of a basic building block, the road is open to define a mathematical object which serves well as an "atom". The Lego building block, which the last posting explained how to find, is a "density with properties" that certainly exists. This is what
one calls an atom in chemistry.
Nonsense.  it is closer to Russell's notion of an atom of logic.
A chemical atom is defined in terms of the number of particles, properties of same, and relations.

Our semantic differences are just that, trade language differences.
The situation is comparable to that of writing a compiler that translates input (as a symbol arrangement on a commutative assembly) into output (as a symbol arrangement on a sequenced multitude) and back. The data processing trade uses its own slang. The meaning of the news this person advocates in FIS is exactly
that what you ask for, as future users of the compiler.

Chemical computations of valence are based on context dependent relations. In general, arithmetic operations (with associative and distributive laws) of compilers are not used to compute valence.
Your user requirements are a specific aspect of what the compiler can and will do. In the data processing view chemistry is a part of user requirements. It is too early to discuss the user interfaces yet. The inner workings of the compiler allow (and require) for the certain existence of logical objects that
have properties that can and cannot come to lie next to each other in
dependence of the properties.

What is the linkage to genetics?  To heredity?
What is the correspondence between "the inner workings of compliers" and inheritance of biological properties?

The last time the task was attacked it had the name of "Unified Field Theory". The present approach presupposes the Field to be quite densely full with mathematical objects which have predictable properties. The a- priori structured Field gets its a-priori structure from the slack (torsion, over- underdensity)
that exists between counting lines.

Your user requirements show the keen interest and high expectations you set into the improved counting system. They are a bit early to discuss. Shannon might have nodded friendly as they asked him: shall we be able to download without wires music from computers and listen to them in a tiny device the size of a credit card? Yes, whatever can be enumerated, can be found on N. This was
Shannon's answer and dead right he was.
You ask me: shall we be able to build molecules that <...please insert your futuristic idea here...>? The friendly answer is again: Yes, whatever can be enumerated, can be found on N and, depending the case, on M, or on M, and,
depending the case, on N.

This is fine mathematical philosophy for variables and calculations on variables. Now, can you show how these calculations can be used to relate genetic sequences to biological properties? What is the semantic path between your nouns and verbs and the nouns and verbs of chemistry and biology and medicine?


The user may not be satisfied with the technician's answer. Yet, presently this
is the best answer you can get from the workshop.
Basic research has come up with a gadget. The gadget looks promising and basic research swears by its ancestors' bones that it is that gadget all were looking for. This is the wheel, calendar, electricity, radio and the dishwasher that each revolutionised whole societies in a historic dimension. Just, it happens to have got evolved as a data processing question, and later migrated into the philosophy of numbers, in fact, a kind of number theory, and that trade has as an added disadvantage that its sales force does not have anything to carry around in order to demonstrate the practicality of the wheel, the steam engine, etc. on, but the numbers. We deal with the order among our concepts as we
discuss how and what we measure.
The improved measurement instrument does have by itself, available at power-up time, certainly existing subsets with definite properties, and these properties do simulate the basic ideas about neutron and proton+electron, and there are only a few of them, and they have an intricate logical relation among each other. Rest assured, the gadget does deliver usable concepts of atom so you can
start building molecules in the not so distant future.
The fate of a great invention depends on many factors. The results of basic research will become application in dependence of the behaviour of the people surrounding basic research, the scientists and the science managers. How fast,
and for which applied science tailored to measure it will appear in an
application first, is a managerial question, not one of cuts and stitches. Even, if the present audience does nothing to further the translation of stereo
counting into his or any trade,
*counting the cuts together with the stitches is a principle that will make its way to the general public, by its own merits, inevitably, sooner or later.
*
This is an idea for which the time is always right to propose, but in times afore, computers were not as readily available, so the idea was impossible to investigate (because it involves quite a lot of counting). There is a little bit of common sense to this idea, and it smells to the layman, too, like it
could be useful in chemistry and theoretical physics.
It depends on many factors, how an idea translates into profit (whatever form profit will appear in). Among the factors that influence the fate of this idea
you and your action or inaction are quite important and relevant.
Thank you for the inquiry whether one may model chemistry better than
heretofore by an improved counting system, which also considers the cuts along with the stitches. The answer is positive: yes, this is the direction the research is taking. More helping brains can well improve the speed and the
precision of the effort. Thanks again for thinking along.

Karl, your argument wanders over vast domains. What I am seeking is a particular path, a particular collation of syllogisms (sorites) that relate the concepts of number theory to the concepts of chemistry, biology and medicine. If such a path is stated, then we can compare the statements to particular observations in the experimental sciences.

Cheers

jerry


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