Dear all,
Information as "reduction of uncertainty", applies according to some
absolute point of view. How can it be transposed in a more pragmatic
view if we consider, at a first stage, information according to a
subjective domain or within a specific point of view, or if we consider
that any theory can always potentially constantly evolve, can reach
higher and higher levels of accuracy or fields of application, can be
extended or replaced or abandoned, etc...I am trying to handle some of
these aspects in this first quick following formulation:
As practical examples to keep in mind, let us consider the process of
solving any type of problem (from elaborating a scientific theory or an
experimental hypothesis to simple practical problems, or e.g. when
trying to solve a detective novel).
Let S1 be the set of "informations" at hand and let us suppose that S1
leads to a coherent universe/hypothesis H1 by means of relationships
between the elements of S1 (comprising subjective/relative aspects). Let
us call R1 this set of relationships. H1 can then be considered as the
couple (S1,R1) (i.e. a graph).
The relationships (elements of R1) between the elements of S1 may
comprise any type of subjective aspects at varying levels, inductive and
deductive inferences, statistical considerations, etc...and may come
from any discipline (mathematics,
physics,sociology,history,philosophy,etc....)
An information is not an isolated entity, it is an element within a set.
We can consider it merely as the couple (information, universe to which
it belongs). And it modifies this set and the related
universe/hypothesis as it is added to the initial set e.g.:
If a new information favorable to H1 (say INFi) is added to S1 it
reduces the "uncertainty" of H1.
If the new information (say INFn) is in contradiction whith the yet
elaborated hypothesis H1, this hypothesis has to be reconsidered totally
or partially; INFn has increased the "subjective uncertainty" of H1 and
has decreased the uncertainty of some other hypothesis H2.
The process is recursive leading to larger and larger sets that we can
call "recursive informational sets".
In S1, before adding INFn, H2 has some type of existence, even some
"potential" existence of whatever probability, or even, it cannot be
deduced from S1 before INFn (total novelty, new concepts,...)
An information of type INFn may occur only after multiple occurrences of
informations of type INFi, which may practically results in a low
"subjective" uncertainty of universe/hypothesis of type H1 (persistence
of wrong interpretations). (note that, in practical cases, we should
also consider different possible levels of contradiction between H1 and
H2 -totally or more or less partially)
Let S1i = S1 + INFi ; S1n = S1 + INFn; S1in = S1i + INFn; S1ni = S1n +
INFi.
(the sign "+" is used here to add an element to a set).
The information depends on the universe to which it is related: in the
above example, a favorable information INFi for H1 is not the same
wether it is included in the set before or after the information INFn
(unfavorable to H1) (S1 and S1n are related to different relative
universes; INFi decreases uncertainty of H1 in S1 and not in S1n).
But ounce INFi and INFn are both included in the set, wether in S1in or
in S1ni (according to the order) these resulting two sets seem to define
the same related universe (cumulative aspect of information).
Is the set momentaneously ordered? How to consider this dynamic aspect?
Role of the relative/absolute points of view? It seems that any
observation brings always "something" (an information according to some
point of view) , but keeps always intrinsically "something else". We can
only get endlessly successive approaches when the set grows and the
related universes change. At a given level, we build at best a coherent
system according to some point of view and its interpretations.
Recursively.
Very sincerely,
Roger ATTIAS
Roger.Attias@univ-paris5.fr
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Received on Mon Sep 19 18:13:48 2005
