[Fis] Five Clouds over Fundamental Information Science

[Karl Javorszky]

Dear
Krassimir,
(DefInf 241206)



Thank you for focusing on and confronting the Learned Friends with the
question:

“What is *your *{approach / idea / concept / definition} of information?”

Mine is:

   1. Colloquially

*Information is the extent of being otherwise.*

This presupposes the existence of an *expected *value, relative to which
the *observed *value is in deviation: “otherwise”. This simple and
straightforward approach is widely used today in technical surroundings.
Shannon’s approach of a vector of *n* length, which is originally set to
the expected value *void* shows its application.

   2. In context

*Information is the difference between ideal and optimal.*

(Maybe one wants to refresh one’s Wittgenstein, TLP 2.0123, the thing is
the totality of its partaking in relations.) One uses the definition of a
Gestalt as being “more than the sum of its parts”. The Gestalt is the
ideal-typical form of parts relating together to generate one Whole. (E.g.
a pictogram of a human.) In the ideal, all proportions of constituents are
included in such a way as to be the best approximation of describing the
common among all realizations of the general idea of the thing. The ideal
includes such properties of the thing also that are mutually exclusive.
(The pictogram of a human refers to both females and males, the pictogram
of a taxi refers to both Mercedes and Skoda.) Some of the properties of the
ideal version of a Whole are mutually exclusive. The ideal Whole exists as
a logical construct, but not as a physical reality.

The optimal arrangement of parts is such that it contains no contradictory
elements and yet comes the closest possible to the general proportions
embodied in the ideal.

There are several optimal versions of a thing realizable, but it’s one and
only ideal form is not realizable.

   3. Numerically

*Information is the difference between sentences that say ‘=’ and that say
‘**≠’*

The expressions *n!, n? *are explained e.g. in Liaisons Among Symbols. The
relevant Figure is easily found by Googling ‘A242615’.

Taking the explanations there, and doing *∫ 1….137.03, *

            * Ideal               =         **∫ max (n!, n?)*

*            Optimal           =         **∫ min(n!, n?)*

*            Information     =         ∫ ∆ (n!, n?)*

In this approach, information is a natural unit, like π.
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