AW: [Fis] Music in group-theoretic biology

From: Karl Javorszky <[email protected]>
Date: Fri 06 Jun 2003 - 13:38:22 CEST

Hi John,
Thanks for introducing Scott Muller's work. I am really interested in
peiople who have own, creative ideas and are industrious enough to pursue
them, regardless of general public opinion. Multidimensional partitions are
a slimy, unpleasant, yecchy affair, because they have so many forms and
varieties. (Some discussions in the last weeks about quantum physics and
multi-valued logic etc. might greatly benefit if the subject had been, would
be, earnestly addressed by logicians and mathematicians.)
So, I am pleased to help Scott in his travails. Please advise him that I
have counted these beauties all in 1985 (and published it in
"Biocybernetics: A Mathematical Model of the Memory", deposited with the
Austrian National Library and the University libraries in Wien, Graz and
Innsbruck TU's), so he needs not redo the work already done. "Zaragoza
Lectures on Granularity Algebra" repeats the same, a bit more elaborately.
Easier access can be found via the J of Theoretical Biology, where I discuss
the combinatorics of theoretical genetics, by comparing information carrying
capacities of temporally transversal and temporally longitudinal assemblies
(of things that are here all at the same time, like the cell itself vs.
things that are read one after the other, like the DNA). A good introduction
and some proposals as to how to go about structures on sets can be found in
the online article Messages Transmission By Counting States of Sets,
published on http://fis.iguw.tuwien.ac.at/resources/preprints.html.

One more point: it is in fact not relevant, what the objects are made of."
the possible partitions are object dependent (they depend on properties of
the object or kind of object in real situations)." is not true. "At least
that is so inasmuch as I understand what you said in relation to Scott's
language " is definitely not what I tried to say. Really, a mathematical
object has absolutely no properties to start with.
Instead: 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.

Cheers to Scott. Does he write letters?
Karl
-----Ursprungliche Nachricht-----
Von: John Collier [mailto:collierj@nu.ac.za]
Gesendet: Donnerstag, 5. Juni 2003 17:38
An: Karl Javorszky (by way of "Pedro C. MarijuXn"
<marijuan@posta.unizar.es>)
Cc: fis-listas.unizar.es
Betreff: Re: [Fis] Music in group-theoretic biology

At 10:50 AM 2003/06/03, Karl Javorszky wrote:
>Best regards to Scott Muller and please give him the hint that he should
>count how many multidimensional partitions are possible on n objects (that
>is: how many distinct group relations can be generated on a set of n
>objects). Once he has this, he will no doubt compare this upper limit (of
>information carrying capacity) to the number of distinct sequences one can
>generate on a set of n objects. Then, the surprise will be perfect. He
shall
>tell you that he will have found the mechanism by which theoretical
>genetics works. Then, we shall all rejoice!

I am not sure we can go as far as the last, but his method does
involve "count how many multidimensional partitions are possible on n
objects (that
is: how many distinct group relations can be generated on a set of n
objects). Once he has this, he will no doubt compare this upper limit (of
information carrying capacity) to the number of distinct sequences one can
generate on a set of n objects." Another part of his argument is that
the possible partitions are object dependent (they depend on properties
of the object or kind of object in real situations). At least that is so
inasmuch
as I understand what you said in relation to Scott's language.

John

----------
I've found the link between apes and civilised men - it's us.
                         -- Konrad Lorenz
John Collier collierj@nu.ac.za
Philosophy, University of Natal, Durban 4041 South Africa
T: +27 (31) 260 3248 / 260 2292 F: +27 (31) 260 3031
http://www.kli.ac.at/research.html?personal/collier
http://www.nu.ac.za/department/members/members.asp?dept=philundund&id=3248

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Received on Fri Jun 6 13:41:34 2003

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