[Fis] RE: Philosophy of Mathematics and Information Re: Visual Semantics

Hi Karl,

You suggested:

<Let us discuss the concepts of <"element", "number", "size", "quality"
<and such in more depth and detail.

It is interesting to notice the emergence of nonlinear semantics
mirroring the interest in non-Euclidian mathematics
(yourself Michael Leyton, Mark Burgin)
adumbrated in this forum. Like acts of counting, the elements of
language have sound, visual array and 'minimal logical extent'.

The recently available Visual Thesaurus from the
Princeton Cognition Labs might help us explore
concepts on a semantic level beyond 'Sachverhalte',
Carnapian intension or etymological hermeneutics.

http://www.visualthesaurus.com/desktop/index.jsp

When playing with the VT meaning
seems to generate spontaneously
from the immanent configurations rather
than prescriptively.

To visualise words as floating groups
(try 'symmetry' and see what appears
in the 'background of associative diversity'
or our friend 'information' and its
little cousin 'info') may even bring
us closer to the relationship between
language and molecular or (for all we know)
musical grouping and aesthetic dynamics.

Any tools that might free us from
linear thought processes should
be welcome.

The Health Language Technologies Group
in Colorado produced a similar visual map of
MEDLINE terms which throws into relief
working concepts masked by traditional
hierarchical thesauri.

It would be interesting to develop
a working visual theaurus for the
word 'information'including
all those tangential concepts
that have been floating around
our FIS discussions.

Cheers,

John H

PS Did Suzi enjoy her visit to Adelaide?

-----Original Message-----
From: Karl Javorszky [mailto:javorszky@eunet.at]
Sent: Thursday, 3 July 2003 20:34
To: fis-listas.unizar.es
Subject: AW: Philosophy of Mathematics and Information Re: AW: [Fis]
Group Theory, Quantum Mechanics, and Music

Dear FISers:

Let us discuss the concepts of "element", "number", "size", "quality" and
such in more depth and detail.
The word "element" can be understood both in a set-theoretical and in a
chemico-logical sense. The concept goes back to the Greek a-tomos (not
divisible). It is basically a tactile experience. If you can touch it and it
is of minimal extent, we call it "object", "element", "idealised thing" and
such. If you cannot touch it and it is of a minimal extent, we call it
"force", "space", "relation", "logical principle" and the like.
As we play with cards, we distinguish the cards as physical things we can
bite on and sensually experience and the ways of playing (with) them which
we cannot sense by older regions of the brain. Experiences we make before
having learnt to speak we treat differently to experiences we store in such
parts of the brain the lexicon is in connection with.
So, we have avoided mixing (linking) the two levels up: the set of objects
and the set of their relations. Yet, it is a great difference if we speak of
a set, whether we mean the number of "Sachverhalte" (Wittgenstein: ~ logical
facts) or the number of tactile things.
My approach integrates the Kant concept of the thing as such and the
Wittgenstein concept of the (number of) ways of being included in
Sachverhalte (logical relations). My starting point is to investigate:
"How many logical relations are there per object AND which fraction of thing
is needed to represent a logical relation with?". These symmetric questions
touch the information carrying ability of carriers, therefore have some
relevance. The answers are: a) it depends (of the number of objects) and b)
it depends (of their diversity).
Kant has solved the question in a marginally optimizing way: he treats the
objects as all absolutely alike, so there can be no logical relations
between them above their number. (Apples or eggs nonmarked, all absolutely
alike, you can only divide into subsets and say 3+3+5 is different to 1+2+8,
without taking into account, what kind are there in each subset and which of
the elements is individual.) Humanistic psychology and some approaches
towards theoretical genetics (including the presently preferred technical
way of treating info, based on the Shannon algorithm) optimise also in a
marginalising way, by saying that the diversity has no quantitative aspects:
each individual is individual and you cannot use weighing and averaging. If
you treat each byte individually, you have to know its place.
Therefore, the integrative approach counts as well the diversity and the
similarity of objects. Going deep down into the philosophy of mathematics
(and counting) we see that what we compare whichever extent with is a basic
etalon of background being made up of elementar units, all alike. We believe
that 5 or 10 are made up of 5 times the 1 and 10 times the 1, respectively,
and that each of the 1-s is absolutely like the next. We see the diversity
(which is in this case the extent: 5 or 10) before a background of
similarity (namely of the series of 1-s, all alike).
Now to the similarity: I have invented a measure for the diversity of
extents and I may warmly propose its use. It is a nice, cute, slick little
invention. It disregards the absolute extent and denotes the diversity of
the parts the thing is made up of. One can count the number of non-alike
logical relations in the set of logical relations the thing is generating.
This is an approach towards "information content". By re-enumerating the set
N, one finds a background of diversity, afore which one may recognise the
similarities.

The idea is to use those logical sentences that are formally, grammatically
true both with respect to their referring to similarities and to
diversities. Roughly 10% of all additions on N are true on M also. Those
additions that describe something more .t. than other additions, do have
some more body, substance, corpus, content, value, density, kick, elementary
precedence, don't they.
Then, we make combinations of these sentences. We are still just generating
logical sentences and watch whether we find some agglomerations of logical
relations (non-tactile stuff) into fractions of objects (tactile, sensuous
stuff). We do. These agglomerations of objects will become different to each
other, with some fascinating details and regularities to observe.

I have tried to draw a picture of a middle thing between a hard, solid thing
(you can put into the mouth and be sure that it is there) and a possibility.
Some 2-3 generations ago one has shown that indeed there is a numeric
relationship between non-tactile logical concepts and tactile materials.
Based on this insight, some have stuffed things so much densely together
that the non-tactile logical relations had no more place and the thing blew
up. We know that there is a real, physical interdependence between density
and places for this density. Presently, we are in the midst of the task of
understanding how this happens. I advance that we look into the expected
number of logical relations per object of a set.
Hope you like the concepts.
Karl

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