logical archetypes and chemical elements

Dear FIS colleagues,

Thanks to Edwina and Jerry for their positive comments on my message weeks
ago about the counting problem in FIS. I'd like to answer Jerry's question
which runs:

"Karl: Is chemical and biochemical counting sufficiently complex to
>address your concerns about the nature of counting in FIS? Is
>correspondence with chemical counting a necessity for biological
>counting?"

In my opinion, the entries in the periodic table of elements by Mendeleiev
can well be regarded as entries into a multi-dimensional truth table. Now,
which kind is the truth question to which these answers yield always .t.
(true)?

We presently have reason to assume that there exist about 104
distinguishable kinds of logical .t. values, which are to be splitted up
into some several hundred varieties, as each entry may have from 1 up to
some dozen of equivalent forms (what the physicists call "isotopes"). The
roughly 100 main archetypes of logical truths are subject to a manifold of
logical relations. (there are some that cannot be present both at the same
time--but it is another separate discussion).

The entries into the above truth table have an intrinsic ordering principle
which does not adhere strictly to their "weight". This would be like saying
that some subsets are similar to each other irrespective of their
cardinality. Also, their building grammar appears to start at integer
values of n=2i**2, with i = 1,2,3,... One may want to look into the
generating function:

Function m(n); local integer tmp, first, len, zero, m; tmp = int(sqrt(n/2));
first = 2*tmp**2; len = 4*tmp + 2; zero = if(n-first < len/2, first + tmp,
first + len/2 + tmp); m = n - zero; return(m).
which gives one a "long" periodicity starting off at values of n=2i**2, with
half-periodicities included.

Once one generates this recoding, there is lots to talk about, although it
will be understood better what I means if I try to answer to the second
question: "what is the meaning of logical archetypes? Are chemical elements
logical archetypes? If so, how?"

The general idea is that one builds (finds in the world) subsets made out
of overlapping parts of other sets and looks into their distinguishing
properties. This is a technique borrowed from opinion research and
marketing. One builds the {consumer, buyer, listener, sick, interested,
criminal, ...} subsets of the population regardless of the size of the city
one investigates. Let us do a trivial exercise with hair-care marketing
targets:

Our product is good for {Red, brown, black, yellow, gray} hair color;
{15-19,20-24,25-29,....,55-59} age brackets; {celibate, single,
steady-going, true, philandering, promiscuous} sexual orientation; {brown,
blue, black, green, mixed} eye colour; {black, yellow, red, pale, mixed}
skin fabric.

These categories cover the whole population and they are arranged in the
order of falling frequencies. (That is, e.g. the eye colour is in the
population like n1 + n2 + n3 + n4 + n5 = n with n = 100% and n1 >= n2 and
n4 >= n5 and all in between also.) Then we may reasonably say that the
probability that one meets a person with a combination of any combinations
of realisations from the categories is a virtual certainty. (There are no
people in the city with age <15 or 60+, and each one has one of the skin,
eye, hair colours categories and sexual orientation. Each individual is
fitting into one of the theoretically possible 5 * 9 * 6* 5 * 5 cells of a
nice matrix. (5 hair, 9 age, 6 sex, 5 eye, 5 skin). The grand total in the
right bottom corner will be n.

What properties will the most probably met person (the person we shall meet
most probably) have? If the attributes in the categories have been arranged
in falling order of probability, this person shall be a red-haired, 17.5
years old, celibate, brown-eyed, black-skinned hair-care-product target.
The implicit logical statement about this person shall be: "the set is a
normal set", or " I am a non-interesting logical occurrence, I represent
but the dull average".

On the other hand, if we meet a series of black-haired, 35 years old,
more-or-less faithful, black-eyed person of native American descent then we
shall hear their implicit murmuring "the set is containing bigger chunks
than usual, you just don't meet them: you meet me, because the set is
over-granulated. We come here in smaller groups. There is less of us but we
come more around."

In drawing-of-samples it helps to add to the Gauss distribution the Euler
distribution which is hugely asymmetric. In my opinion, the Euler
distribution is far more important than the Gauss one. With it, one finds a
extremely useful connection between "size-of-set", "number-of-chunks" and
"size-of-chunk". (And of course also the other two ways around, too.) The
Euler distribution is very simple and elegant, although shamefully
neglected. Just chart the number of partitions into k summands for each n
(1 graph per each number, k horizontally, f vertically) and then integrate
with n -> inf.

Then, to speculate on whether there is a material 'constant' of which these
logical chemical archetypes are built up (the second question we are trying
to answer), one needs to generate the .2. set of partitions. Those for
which sum(m(ni))=m(n). On these, one may start adding pairwise: those that
fall down where .3. holds true, these converge. One does not know whether
the left or the right half-periodicity is the right one and they differ
ever so slightly. My hypothesis is that his type of simple partitional
exercise, reminding a random walk, may serve quite well for making sense of
the interactions between the atomic components (how neutrons, protons and
electrons may add up to compose the multi-dimensional atomic truth table).

I have had to condense quite a lot the 'partitional' maths involved. I hope
that at least I have brought some further hints... and look forward to
discussing these matters in more detail.

Best

Karl
Received on Wed Oct 9 14:32:47 2002