[Fis] Could you formulate your idea in short abstract (about 200 words)?

[Krassimir Markov]

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 
Sent: Wednesday, October 21, 2020 12:27 PM
To: fis 
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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