[Fis] Information = Expectation - Fulfilment

[Karl Javorszky]

Dear Colleagues,



No summer heat and no contagious diseases can hinder this noble society in
its quest for a *generally acceptable definition and understanding of the
term ‘information’*. The definition being there all right, the remaining
task is to make it generally acceptable and understood.



As to the *generally acceptable*: this has something to do with
expectations connecting



Socially elevated position

saying something true

saying something true

not contributing to semantic

not contributing to semantic

stating the obvious

stating the obvious

being a social irritant



As the child cries ‘The Emperor has no clothes’, she speaks from a position
of social inferiority. The statement about the clothing of the Emperor has
nothing to do with the agenda of ongoing important and valuable discussions
being conducted at the highest level of well-connected counsellors, who are
of course deeply in the know. One can say, very politely, that the general
knowledge of the child relating to the overall subject of matters of state
is not quite convincingly up to date. The child lacks any credibility to be
a co-discutant in that group of insiders. The child does not contribute to
the semantics of the matter discussed. The obvious fact which the child
states may well be true and obvious, but it is an entirely different matter
to that being discussed, namely how the theories relating to information
can be weaved such, that the cloth covers all aspects of the imperial body,
and follows, accentuates and visually enhances all the noble features of
the emperor.



*There is no such thing *as a general description of all particularities.
The cloth hiding information or anything else cannot simultaneously show
the general outline of the package and its minute details. Ask Christo (may
he rest in peace) about packaging and unveiling, general principles and
details of application. You cannot have both at the same time. That part of
the picture which is the background has to be excluded, otherwise that what
is the fact, that what is the case, would not be accessible to perception.
Perception is based on the principle of contrast; we perceive something as
being opposed to something different. The being different is always local,
so the foreground-background picture will show wildly differing
observations and explications to the observations. It may be true, that
information as a thermodynamic process will degenerate into entropy, as
asserted by many in this group. Pedro keeps repeating that information does
not result in entropy, is far from ideas of entropy, as the constituents of
the cell system do interact with each other and if a part commits
auto-elimination, it is a kind of seppuku, where the constituent involved
has no other choice but to cease to exist, to self-liquidate. Seppuku as a
part and parcel of autopoiesis is conceptually opposed to entropy: the
non-existence comes about differently.



If we succeed in establishing a general acceptance and understanding of the
term information, it will lead to a *segmented understanding of the term*.
Compare it with ‘energy’. No one will misunderstand in the actual
conversation their colleague, who says, while pointing to something “Has
not enough energy”. In each of the situations it will be clear, what is
meant, although the sentence can have come about in a conversation among
windmill operators, sportsmen, medical professionals, theatre critics or
music performers. Energy is used as a general concept of possible
fulfilments, with many levels of observing a lack thereof.



The problem of the *analogy of information with energy* is that energy does
dissipate and we do not see it (or do not recognise it) doing the
dis-dissipation, the agglomeration, the densifying in the same sensual
experience as we are subjected to in the case of entropy. With information,
we see and experience that it can get slowly, step by step more congruent.
This process does exist, as anyone who plays sudoku or accompanies Hercules
Poirot and Sherlock Holmes will testify. The solidification of generalities
into concrete particularities is the other side of the ledger, the
processes of de-composition, into entropy, having already been understood.



The cry of the little girl about the *cloth having become invisible*,
therefore for all practical purposes useless, notwithstanding any of its
theoretical elegance, is the trumpet call for Act V., the Finale. It is
time now to leave this dead-end of optimisation procedures and address the
issue from a new angle. Some face-saving harrumping about global changes
and absolutely no mention of the little girl are of dramaturgical
necessity. Some may have heard the girl shout: “The Emperor is covered in
fur! He has a membrane! He is delineated!” as she was led away, and may
have wondered, what the brat could possibly have meant.



*The Rorschach plates* contain no information. What the customer says is
translated into information by comparing it to its background and
enumerating what is not the case, deviating to the expected usual. The
profession makes use of tabulated experiences about what is usual. There is
consensus in the profession about an axiomatic property of epistemology,
namely that expectations are a fact of life. Expectations exist like hope
or a signalling message that a threshold has been met. After we have
breathed in, the expectation is that we shall breath out. It is one’s own
decision, how one uses the term ‘expectation’, which connotations on which
context level. In the context of the basic rules of information theory,
expectations are the collection of possible pairs of element and place in
the next step of any cycle in which the collection of actually observed
pairs of element and place had been observed. The rule is an expectation,
as are patterns.



*The evergreen discussion of a=a *is now added the reading that the two
narrations do indeed describe the same state of the world (what is the
case), in two different languages. In the cultural tradition of trying to
avoid any misunderstandings, we have so far always used that interpretation
of *a+b=c *which is normed on *c, *where any differences between what
formerly were *(a,b)* have got successfully wished away. The simplified
version has served us well, but only so far. After we have learnt, how to
count by using *one *item of reference, we are confronted now with the
necessity to find an inbuilt eccentricity of the logical system, where *two
*descriptions of the same state of the world exist, which are both
factually and logically true, yet they differ in syntax between each other.
When one contrasts a narrative of a marital crisis, as told by the wife,
with the description of the same story, as told by the husband, one will
get used to the idea, that a description of the world based on sentences of
the form *b=c-a, a=c-b *creates the collection of basic possibilities of
interpretation and misinterpretation: the duet is the introduction to the
logic of information.



*The narratives *are about the basic contrast between *similar and
different. *Thanks Marcus, we have a name for the experimental objects we
use to weave a new cloth for the Emperor, namely *logical primitives. *We
can build expectations based on place-element coincidences. The
expectations relate to two basic properties of cycles, namely the
similarity-based metric, which is measured in *N* (the sequential numbers
in linear orders, therefrom derived: how many steps of equal length are
needed before the state we have started with is again reached?), and the
diversity-based metric, which is calculated according to some rules of
arithmetic, which rules *need urgent professional attention*. (How many
different elements do I encounter until the starting stage is reached
again?) The measure *bd *is the aggregate number of steps on a carthesian
plane related to the cardinality of the corpus of the cycle. How much
moving around for how many heads is a characteristic of every cycle.



The concept of a cycle has been added an *additional connotation*, namely
the bd-ness of the cycle, which is expressed as a quotient of the sum of
Euclidean distances done by the primitives partaking in the cycle, divided
by the number of primitives in the cycle. Describing the cycle by two
methods:

a. describing the movements of the primitives of the cycle, in succession
and aggregate, and

b. describing the primitives’ differences, in succession and aggregate,

allows recognising that the two narratives are both true and grammatically
correct. They allow predictions from the one to the other (and of course:
back). This is how information is rooted: it is immanent in the counting
system. There is an expectation measure, as a built-in feature of the
system, which is an innate property of (a corpus of) logical primitives (as
they present themselves as being ready to be contained in the corpus of a
cycle) which can be subject to different ordering principles, specifically
periodic changes. If the collection can be ordered in Order A, there is an
inbuilt expectation that it can be ordered in order B. The process of
reordering introduces us to cycles. The corpus of cycles consists of
logical primitives that exchange places one with the next. The procedures
resulting from applying different ordering principles (periodic changes)
are *inbuilt properties of natural numbers*.

Example: Information processing as a search in a database. Identical groups
of cases in the database are indexed differently. (Person X can be found by
the sequential Social Security Number, and by building the union of *{female,
age 35-45, 3 kids, PhD, has car insurance, buys organic}*.) Here, we use:
During reorder from - to *{Q-R, T-W, S-P, …} *logical primitive* p6 *teams
up with* {(p32, p11, p5,…), (p4, p25 p14,…), (p16, p13, p9,…),…
respectively}*. Then we say: 1) if *Q-R *is the case, then *p32 *cannot be
concurrently the case with *p11, p5*; and further we say: 2) if *p32 *was
the case, *p11* is the case, then we expect* p5* to be the case next.
Method 1 is a search on categories, method 2 is a sequential search.



On which level the *general definition Information = Expectation –
Fulfilment* is put to use is for the validity of the definition irrelevant.
(One would have to look up, how 1 cm is currently defined, which lack of
knowledge does not hinder one in performing measurements.) Information is
different from energy. While we appear to understand the dissipation of the
latter, the former does some self-congregation, the rules of which are not
yet understood. Expectation has two forms: based on meters run, guess the
number of players, or, based on the number of players, guess the number of
meters run. Each cycle is a team with its own property of being bd-y. In
this sense, every cycle is an information deposit. It contains a kind of
potential informational energy or informational potential energy. A cycle
is a word in a language which describes periodic changes. The words have
got a new semantic marker: marker bd describes the planar agitation
measure, normed on primitives. We hope that by utilising this new meaning
of the word, placing words in contexts of usual-unusual, we shall be able
to predict and publish the most predictable prediction soon. (The sentence
stating the most usual case is pointedly devoid of any information:
relative to this statement of the message “minimally deviating” the other
sentences contain information.) Its extent of being unusual will be the
etalon for all eccentricities. (In fact, some are placing bets that there
is not *one *sentence describing the ideal strategy of becoming maximally
usual, because if it were so, we had no diversity. If there was a secret
winning strategy to ruling the world, cats would already have found it out,
and we in that case had only cats. Anyway, the bouquet of the least
meaningful sentences will then be termed “Some of the least meaningful
sentences: these state that everything is as close to the most usual as is
customary”. What an exciting lecture!)



Nice summer to you all!

Karl
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