AW: [Fis] Group Theory, Quantum Mechanics, and Music

Hi folks,

Jerry has given me a well-circumscribed task. Thank you for the opportunity
to discuss modeling of theoretical chemistry as a stochastical process.

The task is (here comes what Jerry wrote):
>Karl, my favorite molecule is known as NAD (Nicotinamide Adenine
Dinucleotide).
>It structural formula is H(27)C(21)N(7)O(14)P(2). Six of the 21
>carbon atoms are optically active. The NAD molecule includes five
>covalent rings, three aromatic and two aliphatic. (See an elementary
>biochemistry textbook for the exact structure.)

>Karl, can you demonstrate how your approach would generate the
>particular biological isomer of NAD that is common to all living
>organisms?

The answer is:
We return to my last communication in this matter:
What comes out of the deeper investigation of mathematical objects
that are parts of a set (that gets partitioned according to stochastic
principles) is, that there appear KINDS or TYPES or ARCHETYPES of (clusters
of) objects. These can be compared to the physical and chemical objects that
the natural scientists refer to when they speak of "entries in the periodic
table of elements".
You take a sufficiently big set (somewhere between 32 and 97, for some
obscure number theoretical reasons), make subsets on it and will see that
there appear kinds, types or archetypes of objects that are definitely
present. You cannot avoid meeting these.

If you understand sociology and market research, you will understand the
following:
in any city, in any culture, in any field research, if you ask more than a
few dozen people, you will have types of answer collections. There will be
some "really average", "rather average" and "slightly off-stream" and
"eccentric" types, characters, kinds or archetypes.
If you understand this, you have understood the periodic table of elements
as truth values of a multidimensional partition table of a sufficiently big
set.

Jerry, you have to visualise the periodic table of elements as a truth
table. (So far, a truth table has been taught at Computers I for freshmen
with following essence:
"
(1) there are 2 constants: .t. and .f..
(2) combinations of logical sentences build up a truth table
(3) Sentence A .t. .AND. sentence B .t.: A .and. B = .t. ; A .or. B = .t.
(4) Sentence A .f. .AND. sentence B .t.: A .and. B = .f. ; A .or. B = .t.
(5) Sentence A .f. .AND. sentence B .f.: A .and. B = .f. ; A .or. B = .f."

Please look up the current way of putting this. A truth table describes the
logical truth of some combinations of logical sentences.

Now the invention:
The undersigned (that is me, Karl Imre Javorszky) has extended the concept
of a truth table to include more dimensional combinations of logical
sentences. There are not only 2 possibilities for a logical value to be
somehow, but more. The idea is to use the .t. and .f. values to denote the
"is included in a subset of size ...." logical fact. This leaves you in a
fashion with the same old .t. and .f. values, but there are more of these
and they are at the second look not all exactly the same worth.

The undersigned has introduced the concept of multidimensional truth tables
by using statistical, stochastical methods that are taught at Marketing,
Economics, Statistics, Sales, Sociology, Social research and the other
faculties, but also for freshmen. I hope that a professor for theoretical
chemistry can apply methods of Marketing I.

In Marketing I one learns to segment the market. The market is viewed as
segmented for people who sell. They know that they don't target the whole
market but a segment of it. They say "segment" and what they mean is
"subset". It is called correctly a subset but one does not always use the
correct name for it.

So they segment the market - in their words. If they would want to talk
about what they do with mathematicians, they would say that they partition a
set. They do the same but don't say it in the same fashion. They partition a
set.
If they want to sell to middle-aged, divorced women or to self-employed
professionals in small towns, they generate multidimensional partitions.
They just don't say so, because it is a complicated business and
mathematicians like to wait up until it is clear they really have to work a
bit.

We agree that marketing does use multidimensional partitions. (Ask a dealer
in e-mail addresses whether he can subsegment the set into mutually
exclusive subsets and generate overlaps according to your wishes.)

Now the BIG INVENTION: (so far there was no real invention, just looking up
what other people do.)
If the set is big enough, there shall be always such a segment (subset) that
is the most probable.

Meditate on this and you shall have great rewards.

Your concrete question translates into marketing-speak as follows:
H(27)C(21)N(7)O(14)P(2). Six of the 21
>carbon atoms are optically active.

Give me the well-and-classical archetypical inhabitant of the market: he/she
comes in two varieties (he/she), equipped with 14 credit cards, has 7 living
relatives, meets weekly 21 other persons and spends money on 27 differing
occassions in the period. Six of the spending social interactions happen
with cash.

This being the most common member of the market, this lemming shall be the
most easily observable unit. Why, computer artists will draw you the traffic
simulation based on the most probable behaviour of the most probable
inhabitant. Why they can't (or won't, because the definitely could) do this
for a more abstract inhabitant, I don't know. (Saying: now show me the most
probable social group size for the most probable inhabitant during the most
probable period of time, while you let the city grow in size.) But this is a
psychological question of why people don't find the answer if they are paid
for looking everywhere for that elusive answer. Would you research yourself
out of your job?

Ask your friendly neighbourhood mathematician what must happen until someone
shall define the term multidimensional partition. Everyone uses them but the
mathematicians. "Not defined" - it is like in socialism used to be: "not in
the party rules", therefore it does not exist.

Hope to have helped you a bit.
Cheers
Karl

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Received on Mon Jun 23 21:47:55 2003