[Fis] A rational definition of information

[Karl Javorszky]

*A rational definition of information*
            (20200307)



*Semantic description of the meaning of the term information*

Information is understood to relate to the framework, background of the
assertion. That, what is the case, is imbedded in such surroundings, to
which that what is the case, contrasts. Information relates to that, what
we do not focus on, such parts of the stage, which are not highlighted. In
this sense, information is the description of the remaining alternatives,
of that what is not the case. This property of the mental construct
information makes it so complicated and tricky to get a clear definition of
the concept: as we want to investigate that, what remains in the half-shade
or shade, we cannot avoid directing the torch of our intellect towards the
subject to be investigated, therefore removing it from the half-shade or
shade.



*Information, definition of*

*a.: semantic*

The sentence

*It was Peter who did it*

is a statement and contains no information



The sentence

*It was Peter, from among {Peter, Paul, Susan, Mary}, who did it *

contains the information *{Paul, Susan, Mary} did not do it *



*b: formal*

The sentence

Let *x = ak*

is a statement and contains no information



The sentence

Let *x = ak* and *k **Î {1,2,...,k,...,n}*

contains the information *k **Ï {1,2,...,k-1,k+1,...,n}*



*Information, semantic examples*

We watch a group consisting of *Alma, Bella, Cesar, Daniel.*

*x = ak*

*k **Ï {1,2,...,k-1,k+1,...,n}*

Cesar does the cooking today

The other three can go out;

It is undecided, who among A,B,D will do the dishes

Bella got arrested

That will be the talk among A,C,D

Daniel deceived us all

We shall build an alliance; we are a natural alliance

Alma can’t leave poets and composers alone

If you need someone with moral rectitude, ask for any of us.



We observe the assignment of a symbol of assertion to 1 of the elements in
a group of 4, which leaves the remaining 3 elements being assigned a symbol
of negation. One will find using the notation of *(1,3) *practical for the
above examples.



*(Assertion, negation) : (inclusion, exclusion) : (is the case, remaining
alternatives)*

The notation *(n1,n2) (where n1 + n2 = n) *is a description of the
informational value of an assertion. It has *two values. *The concept is
well known in test theory, where we speak of item discrimination
characteristics.



*Extracting information by using double negation*

The systematics presented here allows integrating the so-called Shannon
school of information, by showing that the Shannon concept is but a simple,
degenerated, trivial special case of the general principle expressed here.
If we possess a symbol set of *{0,1}, *then *0 *is “*not among those which
are different to 0 /are not 0/”* and *1* is* “not among those which are not
1 /are different to 1/)” *

The logical operators are *{same, different}* and *{included, excluded}. *For
organisms that possess a memory, the *{included, excluded} *property is but
a variant of the *{same, different} *property of constituents of perception.



*Relevance for calculation of properties of informational processes in
Nature*

The approach of using the “remaining alternatives” method for modelling
processes of Nature stands and falls with the availability of a catalogue
of alternatives, of which always some remain. This is no problem, as we
consider that processes of Nature are *periodic, *at least those which we
experience on this here planet we inhabit.

Periodic processes consist of a limited number of distinct states, which
follow each other in a strict sequence. In the following example, we shall
speak of the periodic changes caused by the rotation of the Earth, using
the notation D/N for day/night changes, and of the periodic changes caused
by the movements of the Moon, using the notation H/L for high and low tide.



*To be well ordered*

Let us imagine a collection of some proto-somethings that are dissolved in
a small niche in the sea. The things will become adapted to their
surroundings by being ordered according to the ordering principle D/N.
Concurrently, the things will become adapted to their surroundings by being
ordered according to the ordering principle H/L, also. For the argument’s
sake, we shall assume that being optimally ordered for the changes coming
from day/night will be different to that order, which is optimal for the
changes coming from the tides.



*Concurrent ordering requirements*

Some of the learned friends here will remember that the term *cycles *had
already been mentioned a few times in this excellent chat room. Cycles
appear as movement patterns and as constitutors of groups of elements
(members of the corpus of the cycle) which move together during a
resequencing. The corpus of the cycle contains elements which share the
common symbol of the cycle, and also symbols that are sequential, depicting
the strict sequence in which the members of the corpus follow each other
during a resequencing.

The proto-somethings that are subject to both D/N and H/L periodic changes
will inevitably fall into cycles during the reorders that are the
consequences of the periodic processes: day/night and high/low tide. The
paths created by the cycles remain unchanged for millions and billions of
repetitions of identical rearrangements. One can well speak of a stable
collection of possible states the collection of the proto-somethings are
in. Here we have the collection of remaining alternatives, that is: an
environment with information content.



*Variations on a theme by Nature*

The re-arrangements of the elements of the collection of proto-somethings
are in principle all alike. Yet, their appearance may have a wide range of
varieties. This comes from two main causes:

a. differing numbers of elements in the corpora: this causes appearances of
faster /slower changes within sub-systems of one and the same system;

b. differing offsets causing differing collections of elements to be
contemporaneous: this causes appearances of types and individuals among the
realisations.



*Closing remarks*

One would wish for the mechanics behind the Laws of Nature to be more in
accordance with our imaginations about, how a self-evident,
self-explanatory set of interdependences of rules will look like.
Unfortunately, sequencing has to do with sequences, and these deal with
order and changes of places. The pictures arising from re-ordering mental
concepts can cause some inner disturbances, the more so for learned friends
who are used to the idea that they have their mental concepts in the best
order possible, and any re-arrangements can only be irritating. Let me end
on an encouraging note: once one has accepted the thought, that properties
and order determine places, the underlying mechanism of wheels, cogs,
belts, valves and pistons creates a highly fascinating and educative inner
entertainment. Good luck!


Karl
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