<div dir="ltr">
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif"><span lang="DE-AT">Cuts and
Information<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif"><span lang="DE-AT"><span> </span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif"><span lang="DE-AT">Dear
Krassimir,<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif">it is very kind and considerate of you to insist on a
clarity of terms and that the terms used be connected to terms already in use.
In our case, the term “cut” may be understood better and more precisely, than
the term “information”, (former generally agreed on to mean a separation symbol
dissecting an interval into two segments, the latter has not yet gained general
recognition as the difference between target value and actual value). On your
wish, I shall undertake to explain the term “cut” in such a fashion, that it blends
in within the picture of “information”.<span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif">Information is understood to refer to the remaining alternatives.
The term ‘information’ refers to a state of the world which is – presently –
not the case. The simplest demonstration of the concept is a temporal one:
information is that part of the day (week, month, year, etc.) which has already
passed or will yet come. Information does however also exist in the moment. To
operationalise the term, we had to find some properties of that what is the
case, which can be otherwise than expected. Information is the difference
between expectations and realisations (hence the difference between target
value and actual value). We have found properties of cycles to be suited to
demonstrate the existence of information in the world of cycles: any cycle is a
concept that has properties which are similarity-based and also such properties
which are diversity-based. The former measure counts the linear, planar, spatial
distances that separate the members of a cycle; the latter measure refers to
the diversity among the members that follow each other. (In simple terms: in
cycle <i>C</i>, the aggregate distance of
elements is <i>km, </i>the number of members
in the corpus of the cycle is <i>n</i>. Cycle
<i>C </i><span style="display:none">has the properties <i>C(km,n).
</i>The information content of cycle C is counted by building a combination of <i>two </i>kinds of deviations from
expectations: Kind <i>A </i>is an
expectation for the value <i>n</i>, based on the fact of the value <i>km</i>; Kind
<i>B </i>is an expectation for the value <i>km</i>,
based on the fact of the value <i>n</i><span>.
<i>Inf<sub>A</sub> = exp_val(n, f(km)), Inf<sub>B</sub> = exp_val(km, f(n)), </i>where
<i>exp_val(i,(f(j)) </i>is an algorithm, which yields the most probable extent
of <i>i, </i>based on actual value <i>j</i>. (Whether or not the two values <i>Inf<sub>A
</sub>and Inf<sub>B</sub> </i>are actually additive, and if so, how, remains to
be established, based on observations.)<span></span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif">We are habituated and well at home in the techniques of
establishing the value <i>km, </i>because
the measure roots in <b>N, </b>as we count
Cartesian distances between the coordinates of members of the cycle. The
novelty in the approach to the exact and numerically approachable definition of
information lies in the calculation of a <i>diversity
measure</i> which is descriptive of the members of the cycle. What we refer to here
as <i>diversity </i>means the <i>qualitative differences </i>among the members
of the cycle (generally: collection), which is calculated using a background
that is different to <b>N. </b>(Balls being
coloured in differing shades of red and green, being differently big and
differently striped, show properties, where their differences are counted on scales
that are others than <b>N</b>, in contrast relative
to their mutual distances, which are counted in units of <b>N</b>). <span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif">We now address the task of developing a numbering and
counting system that perceives, identifies, distinguishes, categorises, focuses
on, counts <i>diversity</i>. For this
errand, the cuts come in handy. We can describe the collection by saying that
of <i>n </i>balls,<i> n<sub>1</sub> </i><span>are light
red cum dark green,</span><i> n<sub>2 </sub></i><span>are XL size big</span><i>, n<sub>3</sub> </i><span>are thinly
striped, etc. Whether <i>n<sub>1</sub> + n<sub>2</sub> + n<sub>3</sub> = n, </i>will
tell, how many of the elements share symbols of differing categories. This is a
description which leaves room for variants. (<i>Where </i>the elements are, appears
at first of no relevance. In a subsequent step, we shall filter out such, which
agree to a concurrent description of the assembly by stating that </span><i><span>∑(1,<sup> </sup>n)</span> km<sub>i</sub>
= km.</i><span> The rest is information.)<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif"><span>For practical
purposes, it appears to be helpful to use the <i>cuts </i>as descriptive words
of a sentence about the collection. The cuts, in the understanding of <i>2k </i>parentheses,
where <i>k=1,2,3,.., </i>group elements together and, at the same time, separate
elements from each other. Their notation is exact, and also versatile, because
they can build up families. (On the shelf of a library, the separation placeholder
at the end of <i>{Dramas, Greek dramas, published before 1976} </i>can be
colour-coded to signify the end of <i>{n<sub>1</sub></i> <i>dramas, n<sub>2</sub>
Greek dramas, n<sub>3</sub> published before 1976}. </i>Cuts are composite
symbols.<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif">The proposition is reiterated to devote time, brain, creativity
and scientific curiosity to the task of <i>learning
how to count by using cuts as basic units. </i>The proposition is a small, technical
part of no big value as such, within the innovative general idea of using <i>two </i>measuring and counting systems that
are syntactically different, while – in cases of agreement – both say semantically
the same. The cuts as words of a statement do not convey any different meaning
to the meaning of a statement the words of which describe continuities. They
are simply – at first - more cumbersome to deal with. The advantage lies in
their richness in details. The details restrict the ways the assembly can be
represented in a linear enumeration (as a linear, planar, spatial
configuration.) If the restrictions reach a stage, where <i>it cannot be otherwise than </i>a specific linear arrangement being
quasi-bijectively mapped to a spatial arrangement: then we will have understood,
how theoretical genetics functions.<span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif">Let me offer you a <i>risquée
</i>allegory. Imagine that someone is advocating to count the cuts in Roman
numerals, and the <i>km </i>distances among
the members in Arabic numerals. It is self-evident, that although Roman
numerals MDCIXL and XVII point to the same elements of <b>N </b><span>as <i>1639 </i>and <i>17 </i>do,
they are much more complicated to conduct a multiplication with. The algorithm
of multiplication of two Roman numerals is, however, much richer on implicated
axioms and is quite educative. One has to assume that diverse upper limits exist,
and ascribe significance to the fact, whether a symbol is to the left or to the
right of its next threshold. This is almost the philosophy of particle physics.
<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif"><span>Please do not
misunderstand me: No one is advocating that we should use Roman numerals in our
calculations. The allegory is correct in the suggestion to imagine different
kinds of mightiness of symbols, consider upper limits and take care to
distinguish different sub-kinds of symbols, standing left or right of a
higher-level symbol (which small difference would be, in the case of
parentheses, e.g. whether they open or close). Where we partly follow the allegory,
is that one can establish a matrix of relations /like IIII=IV, VV=X, etc./,
where units can be translated into each other. The sentence </span><i>n<sub>1</sub>
+ n<sub>2</sub> + n<sub>3</sub> = n </i><span>leaves
room for <i>n </i>to be anything between <i>n<sub>min</sub> </i></span>and<i> n<sub>max</sub>.
</i><span>The cuts remain invariant with
respect to the size of the collection. Some of the patterns that are created by
the cuts can be spatially realisable, some not. This is the point we discuss.
The proposition to use pairs of parentheses as symbols for cuts is but a small
technical detail. It may, however, simplify our efforts in an extent which is comparable
to the simplifications achieved by doing multiplication in the Arabic notation,
not in the Roman one. Today, we are figuring out those complications which we
have simplified away from, with the end goal in sight, to be able to discuss
the <i>diversity </i>property of assemblies. Who knows, maybe processes of
physiology are easier to calculate by using as complicated rules as come by
using Roman numerals. The algorithms one has to learn help clarifying the
underlying relations among concepts. (E.g. ‘)]’ = ‘}’ or <i>‘spatial distance
can be hidden up to a point by intensifying being different or by being less’,
etc.).<span></span></i></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif"><span>Information is the
difference between expectation and realisation. We build a system of references
where being similar is contrasted to being different. Similar we measure using <b>N. </b>For measuring being different (=diversity),
we have to develop a suitable metric. Pairs of parentheses appear to be useful as
symbols to register group structures in the assembly. Using cuts as description
of the state of a collection can be helpful in getting an exact and solid,
congruent picture of which spatial constellations are possible and which not,
and within the possible, which are quasi-bijective: that would be the DNA. This
is how cuts fit in into the general idea of a hunt for information as a stable,
numeric concept, with us since the beginning of time in objective reality, and
with us since FIS intellectually.<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif"><span>Thank you again for
your attention to detail.<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif"><span>Best wishes:<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 8pt;font-size:12pt;font-family:"Times New Roman",serif"><span>Karl</span><span><span></span></span></p>
</div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">Am Mi., 21. Okt. 2020 um 21:25 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,</font></div>
<div><font size="4">Thank you.</font></div>
<div><font size="4">Now I can understand the idea of “cuts”.<br>How it is
applicable to theory about information?<br>Friendly greetings</font></div>
<div><font size="4">Krassimir</font></div>
<div><font size="4"></font> </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 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 5:50 PM</div>
<div><b>To:</b> <a title="markov@foibg.com" href="mailto:markov@foibg.com" target="_blank">Krassimir Markov</a> ; <a title="fis@listas.unizar.es" href="mailto:fis@listas.unizar.es" target="_blank">fis</a> </div>
<div><b>Subject:</b> Re: Could you formulate your idea in short abstract (about
200 words)?</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">
<div>Dear Krassimir,</div>
<div> </div>
<div>Hopefully this is helpful. Thank you for highlighting the weak points of
the article.</div>
<div> </div>
<div>Karl</div>
<div> </div>
<div>
<p class="MsoNormal" style="font-size:12pt;font-family:"Times New Roman",serif;margin:0cm 0cm 8pt">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>
<div> </div>
<div class="gmail_quote">
<div class="gmail_attr" dir="ltr">Am Mi., 21. Okt. 2020 um 13:27 Uhr schrieb
Krassimir Markov <<a href="mailto:markov@foibg.com" target="_blank">markov@foibg.com</a>>:<br></div>
<blockquote class="gmail_quote" style="padding-left:1ex;margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204)">
<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>
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