<div dir="ltr"><div>Dear Krassimir,</div><div><br></div><div>Hopefully this is helpful. Thank you for highlighting the weak points of the article.</div><div><br></div><div>Karl</div><div><br></div><div>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif">Abstract: We propose an algorithm which is based on
properties of cuts. A cut is a separation symbol that dissects a continuity into
two separate continuities. Based on the properties of the continuities which
the cut separates, cuts can have different types and variations. We propose to
use dedicated symbols for cuts: four parentheses. During periodic changes that
affect the assembly, specific types of cuts will periodically appear in the
linear picture of the assembly. The cuts are concurrently in well-defined
distances to each other, and also implicate that specific group structures are in
existence among the members of the assembly. The state of the assembly can be
described by an enumeration of the cuts. Switching from counting the
continuities to counting the discontinuities allows for more precision, because
there are several more types of discontinuity than of continuity. The structure
of an assembly is expressed by the collection of cuts that are in existence in
the assembly. There is an interplay between number and type of cuts and the
number of possible linear, planar, spatial arrangements of the groups that have
been delineated by the including property of parentheses. The model is best applicable
in the context of cycles.<span></span></p>
</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">Am Mi., 21. Okt. 2020 um 13:27 Uhr schrieb Krassimir Markov <<a href="mailto:markov@foibg.com">markov@foibg.com</a>>:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div dir="ltr">
<div dir="ltr">
<div style="font-size:14pt;font-family:"Calibri";color:rgb(0,0,0)">
<div><font size="4">Dear Karl,<br>Could you formulate your idea in short abstract
(about 200 words)?<br>For me it is not clear what really you want to
say.<br>Friendly greetings</font></div>
<div><font size="4">Krassimir<br></font></div>
<div style="font-size:small;text-decoration:none;font-family:"Calibri";font-weight:normal;color:rgb(0,0,0);font-style:normal;display:inline">
<div style="font:10pt tahoma">
<div> </div>
<div style="background:rgb(245,245,245) none repeat scroll 0% 0%">
<div><b>From:</b> <a title="karl.javorszky@gmail.com" href="mailto:karl.javorszky@gmail.com" target="_blank">Karl Javorszky</a> </div>
<div><b>Sent:</b> Wednesday, October 21, 2020 12:27 PM</div>
<div><b>To:</b> <a title="fis@listas.unizar.es" href="mailto:fis@listas.unizar.es" target="_blank">fis</a> </div>
<div><b>Subject:</b> [Fis] Entropy and Information</div></div></div>
<div> </div></div>
<div style="font-size:small;text-decoration:none;font-family:"Calibri";font-weight:normal;color:rgb(0,0,0);font-style:normal;display:inline">
<div dir="ltr">
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt">Entropy
and Parentheses in Sociocultural Context<span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;text-align:right;margin:0cm 0cm 8pt" align="right">2020-10-21<span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt">Several
among the Learned Friends keep repeating that entropy shows that <b>information
is observed to level out in assemblies</b>. 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. <span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt">This
has again <b>connections to <i>a+b=c</i> </b>and how we interpret it. We agree
with Francesco, that <i>c </i>remains the same before, during and after the
entropy procedure. Then, the procedure called entropy has to do with our
statements regarding <i>(a,b)</i>. <span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt 36pt"><span style="font-size:10pt">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.<span>
</span><span></span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt"><b>Grouping
objects</b> together on the basis of their <b>similarity </b>is a great
invention. Giving names like <i>1,2,3,…</i> 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.
<b>The idea has been victorious</b>.<span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt"><b>History
and epistemology</b> 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 <i>Donatio Constantini </i>is an
actual example for the principle.) History is being written by the victorious,
historians tell us. <span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt"><b>The
victorious history</b>, told by <i>c</i>, says that <i>all things are basically
alike, and this is what is important</i>. The simplification principle of
similarity is supported by our neurology, perception, logic, social conventions.
<span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt 36pt"><span style="font-size:10pt">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 <i>c </i>with regard to the
adventures of what used to be <i>a</i> and <i>b</i>, 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.<span></span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt"><b>How
can you catch the soul of the dead?</b> 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 <i>a </i>and
<i>b,</i> 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 <i>a
</i>and <i>b </i>is called a <i>cut</i>, 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 <i>cut</i> that denotation which refers to <b>pairs of
opposing parentheses</b>. The understanding in the case of <i>2+3=5 </i>was so
far that <i>one </i>separation symbol has disappeared in the course of the
operation. The new denotation of the word <i>cut </i>is demonstrated by deictic
method: <i>(x,x()x,x,x) = (x,x,x,x,x)</i>. In the new understanding, there is an
apparent equivalence between the <i>two </i>symbols ‘(‘,’)’ and <i>one </i>‘,’.
In common language: if we speak of <i>cuts, </i>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>i </i>elements, e.g. <i>c<sub>0</sub> = ‘//’, c<sub>1</sub> = ‘##’,
c<sub>2</sub> = ‘()’, c<sub>3</sub> = ‘[]’, c<sub>4</sub> = ‘{}’, etc.
</i><span>or</span><i> c<sub>0</sub> = ‘(<sub>0</sub>)<sub>0</sub>’,
c<sub>1</sub> = ‘(<sub>1</sub>)<sub>1</sub>’, etc.</i> There are many ways to
introduce and agree on specific symbols for cuts. The above example e.g. can be
written as <i>(2[)3] = /*5*/ </i><span>or as</span><i>
(<sub>2</sub>2(<sub>3</sub>)<sub>2</sub>3)<sub>3</sub> =
(<sub>5</sub>5)<sub>5</sub>, </i>or more succinctly:<i> ([)] = /**/ </i><span>or
as</span><i> (<sub>2</sub>(<sub>3</sub>)<sub>2</sub>)<sub>3</sub> =
(<sub>5</sub>)<sub>5</sub></i><span> 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
</span><i>‘,’</i><span> between elements, as in <i>((x,x),(x,x,x))</i>, there is
nothing, no slack, no space, no irrelevant noise on that place, of which the
width is assumed to be </span><i>0</i><span>. The upgraded approach, with hairs
splitted even more finely, allows for <i>anything </i>between relevant,
corresponding, periodically returning cuts. If we have a complex like
‘<i>(</i></span><i><sub>5</sub><span>)</span><sub>4</sub><span>(</span><sub>2</sub><span>)</span><sub>3</sub><span>’</span></i><span>,
there can be any number of intermittent elements until
‘<i>(</i></span><i><sub>5</sub><span>)</span><sub>4</sub><span>(</span><sub>2</sub><span>)</span><sub>3</sub><span>’
</span></i><span>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 <i>in
appearance</i>, but are retraceable to being two combinations of positions on
pairwise planes interpreted in three phases </span><i>in accounting
reality</i><span>. </span>One needs not go into much detail to make the idea
credible, that separation exists, wherever continuities do not continue.
<b>Entropy</b> 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.<span><span></span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt"><b>Is
it legitimate</b> to support the case for those miscreant separatists <i>a
</i>and <i>b? (Defender:) </i>It is evident that they have been done wrong.
(<i>Prosecutor:) </i>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><span style="font-size:10pt">(, I believe mistakenly)</span></i>. 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. <i>(Defender:)</i> 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. <i>(Prosecutor:) </i>Your ideas can get you in trouble. <i>In hoc
signo: ‘=’ vinces. </i>We actually do things. We function. Look on my works and
despair. <i>(Defender:)</i> You speak of my clients in terms of natural
catastrophes, disasters and other inexplicable, mostly disturbing, at least
puzzling habits of Nature. <i>(Prosecutor:)</i> 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? <i>(Defender:) </i>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.<span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt"><b>The
topics in this workshop</b> tend to touch on subjects that possess also a
connotation that is socially relevant. We are approaching the <b><i>intersection
of</i> <i>two taboos, with a logical contradiction thrown in</i></b><i>.
</i>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.
<i>(Francesco!)</i>. <span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt 36pt"><span style="font-size:10pt">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
<i>umpteenth</i> time, that <i><something is such and such></i>, this is
not only boring, but is also redundant. Nevertheless, being boring and redundant
does not take away the <i>existence </i>of the sentence. As a contribution in a
dialogue, it can be important, that the antagonist speaks, and says knowingly
nothing. <span></span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt">Here
is Heisenberg’s cat reappearing with a Cheshire smile: do the relations that
have remained a <i>maybe</i>, 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 <b>black
holes</b> would appear to fit well into an idea of <b>duality</b> of the world
concept, where the fact is, that some things at some times at some places are
not the case. <span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt 36pt"><span style="font-size:10pt">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. <span></span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt">The
greatest breach of taboo is that we <i><u>add </u></i>to the first sentence of
the Tractatus: “The world is everything that is the case<i><u>,
</u></i><i><u>plus that has been the case and that will be the case, in the
process of periodic changes</u></i><span>.</span><i>” </i>The <b>syntax</b> of
the statements about what will have ceased to be the case after the unification
of <i>a </i>and <i>b</i> will have been achieved, necessarily must have a
<b>generative grammatic</b> 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 <i>‘(), (}, [(}’, etc. </i>between units of an interval, if
the interval is finite. <span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt"><b>In
formal concepts</b>, we are raising the triple taboo subjects of <i>not the
case, infinity, multidimensional partitions. 1) </i>We discuss states of the
world that are not the case: which have passed or will follow in the course of a
cycle; <i>2)</i> 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 <i>3)</i> 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
<i>f(n)</i> in the interval picture of the collection containing <i>n
</i>elements.<span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt"><b><span>The
Pizza Symposion </span></b><span>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. <span></span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt"><span><span></span></span> </p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt"><span>Karl<span></span></span></p>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt"><i><span><span></span></span></i> </p></div>
<p>
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