[Fis] Could you formulate your idea in short abstract (about 200 words)?
Karl Javorszky
karl.javorszky at gmail.com
Thu Oct 22 16:07:04 CEST 2020
Cuts and Information
Dear Krassimir,
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”.
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 *C*, the
aggregate distance of elements is *km, *the number of members in the corpus
of the cycle is *n*. Cycle *C *has the properties *C(km,n). *The
information content of cycle C is counted by building a combination of *two
*kinds of deviations from expectations: Kind *A *is an expectation for the
value *n*, based on the fact of the value *km*; Kind *B *is an expectation
for the value *km*, based on the fact of the value *n*. *InfA = exp_val(n,
f(km)), InfB = exp_val(km, f(n)), *where *exp_val(i,(f(j)) *is an
algorithm, which yields the most probable extent of *i, *based on actual
value *j*. (Whether or not the two values *InfA and InfB *are actually
additive, and if so, how, remains to be established, based on observations.)
We are habituated and well at home in the techniques of establishing the
value *km, *because the measure roots in *N, *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 *diversity measure* which is
descriptive of the members of the cycle. What we refer to here as *diversity
*means the *qualitative differences *among the members of the cycle
(generally: collection), which is calculated using a background that is
different to *N. *(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 *N*, in
contrast relative to their mutual distances, which are counted in units of
*N*).
We now address the task of developing a numbering and counting system that
perceives, identifies, distinguishes, categorises, focuses on, counts
*diversity*. For this errand, the cuts come in handy. We can describe the
collection by saying that of *n *balls,* n1 *are light red cum dark green,*
n2 *are XL size big*, n3 *are thinly striped, etc. Whether *n1 + n2 + n3 =
n, *will tell, how many of the elements share symbols of differing
categories. This is a description which leaves room for variants. (*Where *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 *∑(1, n) kmi = km.* The rest is information.)
For practical purposes, it appears to be helpful to use the *cuts *as
descriptive words of a sentence about the collection. The cuts, in the
understanding of *2k *parentheses, where *k=1,2,3,.., *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 *{Dramas,
Greek dramas, published before 1976} *can be colour-coded to signify the
end of *{n1* *dramas, n2 Greek dramas, n3 published before 1976}. *Cuts are
composite symbols.
The proposition is reiterated to devote time, brain, creativity and
scientific curiosity to the task of *learning how to count by using cuts as
basic units. *The proposition is a small, technical part of no big value as
such, within the innovative general idea of using *two *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 *it cannot be otherwise than *a specific
linear arrangement being quasi-bijectively mapped to a spatial arrangement:
then we will have understood, how theoretical genetics functions.
Let me offer you a *risquée *allegory. Imagine that someone is advocating
to count the cuts in Roman numerals, and the *km *distances among the
members in Arabic numerals. It is self-evident, that although Roman
numerals MDCIXL and XVII point to the same elements of *N *as *1639 *and *17
*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.
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 *n1 + n2 + n3 = n *leaves room for *n *to be
anything between *nmin *and* nmax. *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 *diversity *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 *‘spatial distance can be hidden up to a point by
intensifying being different or by being less’, etc.).*
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 *N. *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.
Thank you again for your attention to detail.
Best wishes:
Karl
Am Mi., 21. Okt. 2020 um 21:25 Uhr schrieb Krassimir Markov <
markov en foibg.com>:
> Dear Karl,
> Thank you.
> Now I can understand the idea of “cuts”.
> How it is applicable to theory about information?
> Friendly greetings
> Krassimir
>
>
>
> *From:* Karl Javorszky <karl.javorszky en gmail.com>
> *Sent:* Wednesday, October 21, 2020 5:50 PM
> *To:* Krassimir Markov <markov en foibg.com> ; fis <fis en listas.unizar.es>
> *Subject:* Re: Could you formulate your idea in short abstract (about 200
> words)?
>
> Dear Krassimir,
>
> Hopefully this is helpful. Thank you for highlighting the weak points of
> the article.
>
> Karl
>
>
> 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.
>
> Am Mi., 21. Okt. 2020 um 13:27 Uhr schrieb Krassimir Markov <
> markov en foibg.com>:
>
>> Dear Karl,
>> Could you formulate your idea in short abstract (about 200 words)?
>> For me it is not clear what really you want to say.
>> Friendly greetings
>> Krassimir
>>
>> *From:* Karl Javorszky <karl.javorszky en gmail.com>
>> *Sent:* Wednesday, October 21, 2020 12:27 PM
>> *To:* fis <fis en listas.unizar.es>
>> *Subject:* [Fis] Entropy and Information
>>
>>
>> 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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