AW: [Fis] molecular discussion

Dear Xerm�n,

please allow me to forward a model that may (or may not) help you to
conceptualise ideas like "attraction" and "bond" (ideas very closely related
to our psychological, anthropomorphic views on interaction among humans).

The molecules and the space between them may be seen as differing densities
of elements of a set. The molecule occupies a place where very many elements
are present, while the space consists of elementar places where on each
place 1 or a few elements are there.

The distance between two knots (heaps, agglomerations) will be dependent on
the similarity and dissimilarity of the units that make up the two knots.
Let me give an example (this example should be familiar to Pedro, as we have
worked on this example before):
We assemble the students of the CPS in the main hall. We tell them to build
groups, according to their grades in Mathematics. There shall be 5 groups
(if in Spain there are 5 grades). Then we ask them to group again according
to their mark in Sports. There would be in all probability 25 groups, and
some students would have trouble defining into which group they belong more.
But this matrix can still be built in the main hall, if the students make a
square with grades 1-5 in one subject in N-S, and the same in E-W direction.
Then we ask them to regroup according to the month they were born in. This
will definitely bring chaos. It will depend on the relative strength of the
cells in this {12,5,5} matrix which of the ordering criteria shall determine
how many students shall have no well-defined place within a group and how
many of the students shall move constantly between the groups they belong
to.

Now the conclusion:
a) the number of dense groups (knots) and their expected size is simply
f(n);
b) the number of ordering criteria is also f(n);
c) if n is suffficiently big, there will be crystallisation centers (knots);
d) the pattern of attraction and bonding between the knots is predictable.

It would be worth playing this experiment in reality with living,
flesh-and-blood students. One would predict the spatial structure simply
from knowing the total number of students.

Please let me have your thoughts on this thought experiment.
Best wishes
Karl

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Received on Wed Jul 2 13:26:31 2003