---------- Forwarded message ----------
From: karl javorszky <<mailto:[EMAIL PROTECTED]>
[EMAIL PROTECTED]>
Date: 25.09.2007 15:54
Subject: Re: [Fis] info & meaning
To: bob logan <<mailto:[EMAIL PROTECTED]>
[EMAIL PROTECTED]>, Pedro Marijuan
<<mailto:[EMAIL PROTECTED]>[EMAIL PROTECTED] >,
<mailto:fis@listas.unizar.es>fis@listas.unizar.es
Dear Bob and FIS,
let us further clarify the object of these discussions:
+ we discuss the concept of information;
+ we discuss how the idea of information shows itself in sociology,
biology, medicine, etc.;
+ we discuss how information is understood in a relational context within
its context;
+ we discuss how information is different in one set of relations to an
information contained in a different set of relations.
We do NOT discuss here:
+ the concept of information is beyond human understanding;
+ we have no idea what information is;
+ there is no numeric-logical definition of information;
+ we don't want to confront information as a numeric task.
The whole point of FIS was so far to reach an agreement on:
* there is a well-circumscribed concept of information,
* information is that what we neglect as we conduct an addition,
* using that what we neglect as we conduct an addition as a logical
ordering principle we can very well calculate and relate information,
* using that what we neglect while we conduct an addition as a logical
ordering principle a multitude of logical truths, numeric constants and
mathematical functions appear,
* the collection of logical constants which appear as we use as an ordering
principle that what we ususally neglect while conducting an addition
resebles very much that what is called the periodic system of elements,
* quite many of the functions and constants which become apparent as one
orders and reorders the numbering system according to that what we neglect
as we conduct an addition resemble very much such fucntions and constants
and procedures as known from books on Physics, Chemistry and Genetics.
It is funny that the task itself got out of focus in this discussion. We
should not lament about the lack of a consistent function to measure
information with but start using seriously that what has been evolved and
poresented within FIS.
To repeat:
Information is that what we neglect as we conduct an addition.
In the more detailed definition:
1. Information is the relation of symbols to their meaning on both sides of
an equivalence sign.
Expl.1:
3+4=5+2
contains the following amount of information.
step 1: establish number of symbols
there are 4 symbols in this equivalence.
step 2: establish meaning of symbols
there is (3+4)=7 on the left side and (5+2)=7 on the right side, therefore
the meaning of this equivalence is 2*7 that is 14.
step 3: divide meaning by number
the meaning of 14 is divided by the number of symbols, that is 4. The
result is 14/4, 7/2, that is 3.5.
The information content in "3+4=5+2" is 3.5.
2. The tautology's information is the tautology itself
3=3 has the info content of 6/2=3
3. The unit-type counting understates the information content of an equivalence
1+1+1+1+1=5 has the info content of 10/6. Generally, n=1+1+1+1+...+1 has
the information content of 2n/(n+1).
4. Information is both a scalar and an indexed value
The information S1=3 (symbol 1 has the value 3) is a fixed scalar in the
unit-type counting. It is an indexed value in the relational counting,
because the information lies in (and depends from) many other properties:
+ in which unit-type result equivalence is S1 included (what is the 2n
being stated on both sides);
+ in which side is S1 included (3+3+3+3=1+1+1+1+1+1+1+1+1+3);
+ how many symbols;
+ how different the symbols;
+ which smallest symbol;
+ level of truth
and so forth.
5. Information density is material density
That what we consider "material" is certainly the truest form of logical
existence. Relative to this extent of truth, there exist lesser true forms
of logical existence. "Material" is both true and certain to a specific
degree, "space" is true and certain to a specific pair of degrees, "forces"
are differently true and differently certain to those describing a "field".
There exists a subset among the subsets of the set of true sentences which
is certain and true to the maximal extent.
Let us build on these common understandings. The definitions presented here
agree to the dot to the predictions of Shannon. This is a probability
function free of dimensions and it can be used to predict (actually, the
size of the average symbol, that is, the average size of matter as a
mathematical entity) those structural constants which we use in our
perception and cognition as background, which evolve as the results of the
interaction between the traditional interpretation of the term
"mathematical" in this sentence, namely unit-based and the extended
interpretation of a term "mathematical" which is being proposed here, which
would also include the concepts of diversity. By using a numbering system
based on diversity alongside the traditional system one discovers quite
many natural constants and relations. By using both systems in tandem, one
can discuss interference phaenomena.
The average size of a symbol is a corollary of a natural matrix of logical
relations. Nature appears o use it all over the place.
This table of truths reveals itself once one learns how to count in tandem.
It is not complicated, it is only strange. Not revulsive but somehow
unnatural. It needs some self-discipline to learn to count differences. To
use a diversity-based basic algorithm alongside the normal does indeed need
some inner work. Yet, this is the task Wittgenstein speaks about, that the
looking eye cannot - well - see itself. Our thinking is based on the
algorithm of differences and nuances, that is the background. So the task
is equivalent to wanting to change the perspectives.
There is more well-prepared work in FIS than meets the eye. Let us not
restart from inventing the idea of information. This is well done. Now the
task is to figure out how to manage the consequences.
All the best:
Karl
=============================================
Pedro C. Marijuán
Cátedra SAMCA
Institute of Engineering Research of Aragon (I3A)
Maria de Luna, 3. CPS, Univ. of Zaragoza
50018 Zaragoza, Spain
TEL. (34) 976 762761 and 762707, FAX (34) 976 762043
email: [EMAIL PROTECTED]
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