AW: [Fis] Group-theoretic biology

Jerry and colleagues,

A constructive contribution to the group theory discussion:

There is a very rational and actually quite simple (numerical, rational,
logical) explanation how group theory and biology map into each other
--they do.

I have created a children's toy to demonstrate the concept on (with). It
consist of 64 small cubes that have differing symbols on each side. Some
green squares, red circles, yellow dots, blue stars, etc. Then there are
differing combinations of color, shape and number. Any cube (like a building
block for a child) offers you 6 differing ways of looking at it, and on each
face you can choose among at least three dimensions (color, shape, number)
of the symbol. So you can select to make (like with domino) connections
based on color, shape, number to the neighbors. A well-integrated cube has
neighbors connecting on more than one dimensions. One builds surfaces in a
two or three dimensional way.

Then one lays down the same cubes in a long row. Inevitably, some of the
neghborhood relations will not fit. (Either you choose the common color to
connect two cubes or the shape or the number of symbols: it is very seldom
that you find a match where more than one dimensions will connect.) One may
then discuss the depth of cuts.

For those children who are interested in the functioning of theoretical
genetics, I have explained with this toy as an illustrative tool that the
combinatorics between the cuts and the spatial arrangement works at best if
one describes the relations by using 3 logical markers that can be each one
of 4 varieties. The children had no problem visualizing this.

I am available to repeat the exercise.

Karl

-----Urspr�ngliche Nachricht-----
Von: fis-bounces@listas.unizar.es [mailto:fis-bounces@listas.unizar.es]Im
Auftrag von jlrchand@erols.com
Gesendet: Dienstag, 3. Juni 2003 01:50
An: fis@listas.unizar.es
Betreff: Re: [Fis] Group-theoretic biology

An Open Comment:

I had sought to identify a link between group theory and biological
processes for many years.

Later, I had sought to identify a link between chemical processes and
group theory.

Even later, I sought to identify a linkage between chemical structure
and group theory (not merely the spatial relations among the nuclei
of a molecule, e.g., x-ray crystallographic results).

At present, I do not seek to identify linkages between chemical
structures, chemical processes or biological processes and the
abstract mathematical structure of group theory.

You ask "why"?

Because the simplest possible mathematical representation of a
chemical molecule is a labeled bipartite graph.

And, because the structure of a mathematical object need not
represent the relations among or correspond to the structure of
natural object.

I conclude that the languages and structures of natural systems are
vastly richer than I was able to state or imagine.

Cheers

Jerry LR Chandler

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Received on Wed Jun 4 11:18:06 2003