[Fis] Entropy and Information

[Karl Javorszky]

Entropy and Parentheses in Sociocultural Context

2020-10-21

Several among the Learned Friends keep repeating that entropy shows
that *information
is observed to level out in assemblies*. Francesco has insistently brought
up the aspect, that a kind of Grand Balance should be established as a
basic idea of what we discuss. If we have a working Grand Total included in
our concept of the world, then that what dissipates is still there, albeit
distributed much more commonly. Previously, one had had 99 cold objects and
1 hot. After entropy, one has 100 slightly warm objects.

This has again *connections to a+b=c *and how we interpret it. We agree
with Francesco, that *c *remains the same before, during and after the
entropy procedure. Then, the procedure called entropy has to do with our
statements regarding *(a,b)*.

In the present discussion on the subject of information, each one of us has
a common education and understanding about how abstract concepts relate to
each other when the abstractification of the objects into concepts has
happened by the property of the similarity of the objects that had been
abstracted into concepts from. If we speak about houses, we silently agree
that we do not speak of chateaux nor of makeshift temporary accommodations.
Similarly, if one speaks of a nice day in Spring, or of fish. There is an
expectation of what is usual, shared by the narrator and the audience if
one uses a term that refers to a multitude. The objects that are covered by
the concept are imagined to be more or less alike in everyday parlance, and
are defined to fulfil equality requirements to qualify as objects that are
covered by the concept in the context of a technical discussion.

*Grouping objects* together on the basis of their *similarity *is a great
invention. Giving names like *1,2,3,…* to objects generally, if these are
differently many, is owed to the Sumerians. Much progress has since been
made in the rhetoric used in the discussion of alike properties of things.
The idea that one can mentally merge differing things with respect to their
similarity has carried the day since decades, centuries and millennia. This
is a success story. *The idea has been victorious*.

*History and epistemology* are intimately entwined, as Orwell has pointed
out. He who has possession of the archives can plausibly produce supporting
evidence for his arguments for a war with Oceania, because the archives
show, that there was always a reason to be at war with Oceania. (The *Donatio
Constantini *is an actual example for the principle.) History is being
written by the victorious, historians tell us.

*The victorious history*, told by *c*, says that *all things are basically
alike, and this is what is important*. The simplification principle of
similarity is supported by our neurology, perception, logic, social
conventions.

It is socially immensely more gratifying to be a uniting voice and to
recognise the common interest, as opposed to someone who advocates dissent,
sows differences, tries to disunite and to create conflicts and
polarisations. Tendencies of separatism, let alone the open advocation of
the ideas of separatism, can land one in hot water if one is not careful.
Social convention has come solidly down on the side of *c *with regard to
the adventures of what used to be *a* and *b*, formerly. Thanks to their
unification or reunification, they now share something, like things
undergoing entropy. Their differences have magically disappeared. No one
dares to talk about their not so far history, the archives have been razed
blank and no stupas, memorials, mausolea or lecture halls named in their
honour help us in recalling them in our fond memories. The separation
symbols are gone, as if they had never existed.

*How can you catch the soul of the dead?* All the efforts of those
separation symbols have come to naught, their effects disappeared like the
cultures of Troy or of Cartago. We cannot recreate the actual interplay
between *a *and *b,* those times are far gone, (we live now in a world
united, no relevance of separations worth speaking of). Yet, we can
establish a working hypothesis, a screenplay of their since destructed
relations, by finding in the sand the fundaments of their compartments. In
the brutal, social-Darwinist terminology of epistemology and of number
theory, that what aforetimes had separated *a *and *b *is called a *cut*,
separating two segments of a line. The name implies an outside force, and
shows that we are deeply in the tradition of brave, regular, Godfearing
folk. Wittgenstein has established a precedent: it is permissible to talk
in such terms which neglect, by circumnavigating, the idea of any outside
interference into the life of abstract objects. Using this precedent as a
legal basis, the proposition is offered to add to the meaning of the
commonly used word *cut* that denotation which refers to *pairs of opposing
parentheses*. The understanding in the case of *2+3=5 *was so far that *one
*separation symbol has disappeared in the course of the operation. The new
denotation of the word *cut *is demonstrated by deictic method: *(x,x()x,x,x)
= (x,x,x,x,x)*. In the new understanding, there is an apparent equivalence
between the *two *symbols ‘(‘,’)’ and *one *‘,’. In common language: if we
speak of *cuts, *we mean the interaction of at least two pairs of
parentheses. Name-givers can refine the notation, e.g. by saying that one
distinguishes cuts on their property of the parentheses enclosing *i *elements,
e.g. *c0 = ‘//’, c1 = ‘##’, c2 = ‘()’, c3 = ‘[]’, c4 = ‘{}’, etc. *or* c0 =
‘(0)0’, c1 = ‘(1)1’, etc.* There are many ways to introduce and agree on
specific symbols for cuts. The above example e.g. can be written as *(2[)3]
= /*5*/ *or as* (22(3)23)3 = (55)5, *or more succinctly:* ([)] = /**/ *or as*
(2(3)2)3 = (5)5* The main point is that we agree that there is both a
necessity and a practical solution to the necessity for some kinds of
dedicated symbols, which we need in order to be able to speak consistently
about cuts that separate different things. In the traditional view, where
there is a *‘,’* between elements, as in *((x,x),(x,x,x))*, there is
nothing, no slack, no space, no irrelevant noise on that place, of which
the width is assumed to be *0*. The upgraded approach, with hairs splitted
even more finely, allows for *anything *between relevant, corresponding,
periodically returning cuts. If we have a complex like ‘*(**5)4(2)3’*,
there can be any number of intermittent elements until ‘*(**5)4(2)3’ *reappears
again. This is an important aspect, as we are looking for a language, which
is interpretable both in a linear, sequenced fashion, and in twice two
versions of planar positions, sequenced in triplets, too. We are looking
for an origami (kirigami) procedure, where linear distances between logical
tokens determine constellations, which are 3,4,5,-etc.-dimensional *in
appearance*, but are retraceable to being two combinations of positions on
pairwise planes interpreted in three phases *in accounting reality*. One
needs not go into much detail to make the idea credible, that separation
exists, wherever continuities do not continue. *Entropy* is an observed
fact, and can be abstracted into a procedure resulting from the
annihilation or transformation of two parentheses. That, what had been
separated by the pair of parentheses from the other elements, is now common
within a more general pair of parentheses.

*Is it legitimate* to support the case for those miscreant separatists *a *and
*b? (Defender:) *It is evident that they have been done wrong. (*Prosecutor:)
*They deserved what they got. The guillotine solves a great part of
problems of disallocations, in pursuit of egalité and entropy. Information
is what we all share, if it is distributed evenly *(, I believe mistakenly)*.
No secret diplomacy any more, we have had enough of the mighty few, making
deals networking in closed, well-connected circles, in smoke-filled back
rooms or in the nurseries of crown princes or of mother bees. *(Defender:)*
Mine is a quiet voice. You will see how far you will get without allowing
for agglomerations into disjunct groups. These get inevitably recreated.
The rise and the end of tyrants is a pattern of Nature. Their periodic
existence is written into the rules of the game. *(Prosecutor:) *Your ideas
can get you in trouble. *In hoc signo: ‘=’ vinces. *We actually do things.
We function. Look on my works and despair. *(Defender:)* You speak of my
clients in terms of natural catastrophes, disasters and other inexplicable,
mostly disturbing, at least puzzling habits of Nature. *(Prosecutor:)* They
are a disturbance factor in my world. How would you deal with something,
which constantly disagrees with you, interferes with your plans and is an
insubordinate rascal, hiding her secrets and mysteries? *(Defender:) *Maybe,
time has come to change your way of looking at them. If they stubbornly
resist and will not go away, and in this case, they apparently do so, then
it is often helpful to investigate one’s own simplifications and ingrained
ways of looking at the antagonist. Maybe you can understand them then
better. They act in their own enlightened self-interest, too.
Self-preservation and such.

*The topics in this workshop* tend to touch on subjects that possess also a
connotation that is socially relevant. We are approaching the *intersection
of two taboos, with a logical contradiction thrown in**. *Firstly, in
learned circles, it is not usual to talk about things that are not the
case. Secondly, it is rather impolite to keep on talking about a subject,
of which all relevant aspects have already been spoken of. We are
addressing a noble cross-breed of these two social taboos, as we attempt to
speak about information as a property of Nature. That, what is not the
case, is redundant. It does not cease to exist, even if we have wished it
away. Those alternatives, which got not realised are somewhere, have to be
somewhere. *(Francesco!)*.

The totality of logical sentences that can be said about a collection will
contain also those, which are – presently – not the case, at least if the
collection undergoes periodic changes. If someone states the *umpteenth*
time, that *<something is such and such>*, this is not only boring, but is
also redundant. Nevertheless, being boring and redundant does not take away
the *existence *of the sentence. As a contribution in a dialogue, it can be
important, that the antagonist speaks, and says knowingly nothing.

Here is Heisenberg’s cat reappearing with a Cheshire smile: do the
relations that have remained a *maybe*, the expectations that have not been
realised, the statements that contain nothing, but fill space with nothing,
do such logical entities have a material consequence (reflection,
influence)? The *black holes* would appear to fit well into an idea of
*duality* of the world concept, where the fact is, that some things at some
times at some places are not the case.

The idea would be charming to set up an army of computers and add up all
that what is not the case at any time and compare this with the lump sum of
that what is the case at that time. This method is good for research, but
is not how Nature works. Nature works from bottom up, not from top down.
That, what is not the case must have begun being together with that what is
the case from the very first few moments on.

The greatest breach of taboo is that we *add *to the first sentence of the
Tractatus: “The world is everything that is the case*, **plus that has been
the case and that will be the case, in the process of periodic changes*.*” *The
*syntax* of the statements about what will have ceased to be the case after
the unification of *a *and *b* will have been achieved, necessarily must
have a *generative grammatic* in the sense of Piaget and Chomsky, as there
are rules to it, at least in a world undergoing periodic changes. We are
presently not used to counting opening and closing parentheses during
simple additions or rearrangements, but we are able to learn the technique.
There are only so many ways of placing, say *‘(), (}, [(}’, etc. *between
units of an interval, if the interval is finite.

*In formal concepts*, we are raising the triple taboo subjects of *not the
case, infinity, multidimensional partitions. 1) *We discuss states of the
world that are not the case: which have passed or will follow in the course
of a cycle; *2)* we point out, that the length and duration of a cycle is
infinite, because there is no last element in a cycle: at the same time the
cycle is finite, because the number of members in the corpus of a cycle is
finite; and *3)* we state, that about a collection with a finite number of
members, only a finite number of distinct sentences can be said. The last
statement refers to the fact, that overlaid hybrids of
partitions-cum-permutations cannot contain more than a fixed upper limit of
cuts *f(n)* in the interval picture of the collection containing *n *
elements.

*The Pizza Symposion *is at its present stage a rather clandestine affair,
almost a conspiracy among innovative freethinkers, who gradually morph,
with great circumspection, ever so slowly and cautiously, into reluctant
revolutionaries. We display curiosity about subjects that are obscured by
veils of several taboos. Hopefully the ongoing transgression shall not end
up in eviction, eating such which is forbidden.



Karl
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