Re: FIS 2002

Dear FIS colleagues,

Thanks to Andrei and Pedro for their encouraging comments about my
theoretical proposals. In the present discussion context, may I introduce
some more concrete conceptualizations on what we are talking about
(information)?

Let us start of with the concept of information being "<such> is next to
<such>" where <such> can come in different kinds and extents. The important
point is the kinds of <such> that may exist and that may or may not come to
succeed each other in a linear arrangement:

1) we consider the natural numbers as one specific aggregation state of an
extent. The natural number i says that an object of the overall extent i is
in one (i) piece.

2) the same extent can have different aggregational states. These are
logical sentences consisting of k arguments. The sentences have the form n1
+ n2 + n3 + ... + nk = n where n, and n1, n2, n3, ..., nk are natural
numbers and the addition is true. (The logical sentences describing the
aggregational state of an object with the overall extent n are known in
mathematics as "partitions of the natural number n")

3) there are several concurrently true logical sentences describing an
aggregational state of an object. Several concurrently true logical
sentences may refer to an identical extent. (This introduces the concept of
multidimensional partitions, hitherto left undefined in mathematics.)

4) as long as the extent is finite, there is a finite number of
nonredundant true logical sentences that describe (each) an aggregational
state of an object. The collection of concurrently true logical sentences
referring to an object shall be called the structure of the object. (This
introduces the concept of maximally structured sets.)

5) in a linear sequencing of the elements of the set, the elements of the
set may or may not come to lie next to each other in dependence of the
structure of the set.

6) the structure of the set and the linear neighbourhood relations refer to
each other.

This approach (see my contribution to this confeence) opens up several good
approximations of the information theory, also of theoretical genetics and
splicing grammars. There, too, we see that what matters, is that <such>
comes next to <such>.

Karl
Received on Wed May 15 10:42:36 2002