[Fis] Murakami and Swift.The Principle of l'Hôpital

[Joseph Brenner]

Dear All,

A good but difficult discussion; it can be simplified by relaxing the absolute separation between continuity and discontinuity. As the paraconsistent logician Itala D’Ottaviano shows, the principle of L’Hôpital, the 17th Century mathematician who codified infinitesimal calculus, can be formulated rigorously. This principle states that it cannot be said of any two quantities separated by an infinitesimal whether they are the same or different. The continuity in an interval on the (real or hyper-real) number line is to be replaced by a para-continuity. This concept also defines a para-discontinuity, and that para-continuity and para-discontinuity are in fact the same! The principle holds for relational entities in the real world.  

Karl, Mark and Louis are all right, all having illuminated the problem from different angles. The applicable logic is one that can accept real contradictions, such as those involved here.

Cheers,

Joseph 

 

 

  _____  

From: Fis [mailto:fis-bounces at listas.unizar.es] On Behalf Of Mark Burgin
Sent: mardi, 30 mars 2021 20:40
To: karl javorszky
Cc: fis
Subject: Re: [Fis] Murakami and Swift

 

What biologists and psychologists call continuity is called fuzzy continuity in mathematics.

 

  _____  

From: "Karl Javorszky" <karl.javorszky at gmail.com>
To: "Mark Burgin" <markburg at cs.ucla.edu>
Cc: "fis" <fis at listas.unizar.es>
Sent: Tuesday, March 30, 2021 3:08:42 AM
Subject: Re: [Fis] Murakami and Swift

 

Discontinuity, Integration and Alienation

2021 03 30

 

In psychology, the standard assumption about the individual is that it lives and experiences in a continuous fashion. Sleep inhibits the acknowledgement of continuity, but does not negate it. If there are continuity problems, like amnesia or depersonalisation, these are irregularities which deserve an extra name. Life is a continuous adaptation to changes; the discontinuity is not a feature but a bug.

In the excellent lecture Krassimir has drawn our attention to, expectations are in the process of being axiomatized. The idea of expectations is in the process of being introduced into rational thinking, because it had not yet been a part of it. A biologic construction – the hypophysis – is used as an empirical basis from which to attempt to explain the phenomenon of regulation, namely that there is a target value and an actual value. Great courage is needed by a mathematician to refer to the processes of the glands, because if there is one thing neurologists, physiologists and histologists can agree on, then that is that the hypophysis is a really complicated something that causes effects in ways that are presently far from being understood. One could as well have said “God” for the complex system of interrelations that are causing effects over a wide field. The lecturer extends himself and leaves the terrain of mathematics. He needs to introduce a causing principle which acts in mysterious fashions, like the hypophysis does. Yet, the lecturer does address the subject of expectations, because one has to deal with the term if one wants to understand a world in which there are things that can be otherwise.  Expectations are a bug in the mathematical theory, not a feature. In biology, expectations are the fundament of all thinking: be it that the protozoa expect the Sun to rise again and rise to the surface of the sea, be it that the K-Na pump is switched into reverse on reaching one of the limit levels, be it that we breath out a short while after we have breathed in. Expectations are very much a feature in biology, definitely not a bug.

To have expectations, one must have alternatives, from among which one learns to rank some as highly probable and some as among the least expected. The idea necessarily presupposes the existence of a duality of how it is and how it could/should/will be. (A compliment here goes to Joe Brenner, who has given intellectual birth to a concept of a two-ways-existing mental construct, evolved solely by induction. One who has built by Lego blocks a two-ways-existing mental construct, raises the hat before the ingenuity of the artist who has created the construction only by means of brain, paper and pencil.)

Let me digress into the world of games. Chess and Go are suitable examples. The description of the positions of the figures in a middle stage of the game is a narration of facts. This narrative can be seen as consisting of two parts: A) Description of the positions of Black, B) Description of the positions of White.

The set of possible moves is different to the set of reasonable, clever, expected moves. This is the moment, where the term ‘expectation’ becomes one of its meanings. There is a result of a utility function attached to each of the possible moves and players, and nowadays computers, too, evaluate the gain in their strategic situation when choosing one of the possible moves. This evaluation procedure is no more in the physical, but rather in the metaphysical realm. While the player collects and sorts his available moves, nothing happens on the physical board. The narrative about this phase would be considered traditionally contentious; that computers have been taught to play Chess and Go up to the theoretically possible best level is of no philosophical relevance. There remain for the foreseeable future sufficiently many and diverse such games, where we have no evaluating algorithm, like in the case of the hypophysis, because we do not yet understand the game’s goals and rules. There remain two sets of expectations regarding the next move of W or B, and we cannot be sure whether we anticipate the next move of the opponent correctly. Whatever happens, there will be expectations that have gone unfulfilled.

We need to have an entry point into discussing expectations and the density of unfulfilled expectations. Thanks to the Sumerians, we do have such a plaything and thanks to the last four generations, we have powerful machines with which to create a habitat for the playthings to go forth and do their thing. We can hammer iron into a circle, we can chop an axle out of a tree trunk and we can weave liana to hold a leather bearing: here we have the wheel. The idea will turn out to be useful beyond imagination, presently it is unheard-of, unorthodox, frivolous, barbarian, unprofessional.

Expectations are a part of the package if one takes a fresh look at a+b=c. We are so much habituated to concentrating on the result, the summary, the essence of the operation, c, that we have forgotten how to read the previous stage, the commencement, that what has been, a+b. This state of the world is by no means gone, a, b are by no means actually unified, they remain different, although they share many common straits. 

Importance, pre-eminence, superiority are principles one meets in a concept of adaptation and evolution. Whether a or b are pre-eminent does make a great difference. The world is quite different if seen by the eyes of a, as opposed to the arrangements considered normal by b. If there is order, there are alternatives to that order. Between the competing orders, actual and target values exist. The term expectation is rooted in facts, like the possible moves of a game are rooted in the facts of the actual dispersion of the figures. One needs only to order some elements and reorder them differently to see the term expectation, without taking recourse to some incomprehensible otherworldly inventions like the hypophysis. 

The funny thing about continuity and expectations is, that they both are aspects of the same fact. The linear position (“rank”) of an element is a corollary of an order A. The rank of that same element in order B is also a fact. Of the two ranks a place on a plane can be pointed out. The tautology goes: the position on a plane is the same as ranks in two orders. The seemingly non-tautological secret of life is hidden in the fact, that the axis A necessarily registers among the properties of each of its elements the planar place of that element, if a plane exists with axes A and B. The surprise is that the Sumerian invention hyped up with Wittgenstein machines shows that once axis A creates plane AB, a space is created by itself with axes ABC. The wanderings of the logical primitives show, that the continuous truth a=a is maintained by a jump-hop, disperse-gather, turn-once mechanism based on twice three phases. In order for the DNA to be logically the same as the organism, the rank of a token along an axis has to register the planar place of something referred to twice, and the planar places must be positioned in a space of which the spatial directions are given by axes AB, BC, BA. This is indeed the case.

Nature has very clear expectations about what is a position in space, based on two planar places, based on three linear ranks. She is actually economising on the third descriptive axis, using the expectations carry_aA + carry_aB + carry_aC = 18, carry_bA + carry_bB + carry_bC = 33. The spatial reference to the objects can keep existing and be valid during the non-existence of space in the third direction, because if two summands of a partition of a given number into three are given, the third summand is tautologic.

How much the left and the right hemispheres of the brain are different and in what dimensions, can best be left presently in the hands of the people in white coats. The same is valid about the differences between Dr Jekill and Mr Hyde. Let us set our sights on achievable goals. Let us find out what the term order means, and what rules a sustainable order could follow, in theory.

Best

Karl

 

 

Am Di., 30. März 2021 um 07:54 Uhr schrieb Mark Burgin <markburg at cs.ucla.edu>:

>From the point of view of mathematics, there is no real continuity in nature!

 


  _____  


From: "Karl Javorszky" <karl.javorszky at gmail.com>
To: "fis" <fis at listas.unizar.es>
Sent: Friday, March 26, 2021 3:23:32 AM
Subject: [Fis] Murakami and Swift

 

Murakami and Swift                                                                                       2021 03 26

 

These last, long weeks being very much conductive to staying at home, one would address the task of reading a long novel or two. Haruki Murakami’s “1Q84” and “Killing Commendatore” touch on subjects that are, in this person’s opinion, worthy of discussing in this present scientific-intellectual debating society. 

Let us put Murakami in a connection with Jonathan Swift. The Irishman has presaged with his “Gulliver’s Travels” massive changes in the perception of royalty, authorities, rules and conventions. Although King Charles II was tried and executed in 1649, the Restoration twelve years later has eradicated the positive connotations to getting rid of a ruler. Up to Gulliver, it seems that the common understanding has continuously accepted the religious-mythical connotations of political force. The belief in authorities and their possession of transcendent powers has been the unspoken background of the idea of a functioning society. Swift has challenged the prevailing meme, by substituting it by a narrative, where Kings are minuscule, pompous dotards. The slogans of state get deflated if the common cause is reduced to the conflict of opening up the breakfast egg on which end. You can’t adore a God-Emperor if he is that naïve, completely lacking common sense and decency. Laughing about a mighty ruler is a necessary step towards guillotining the formerly mighty same. As a medicine, Swift’s Gulliver has the characteristics of a depot forte. Its effects establish themselves almost imperceptibly, over a long time period. It took over three generations from Gulliver to the French Revolution.

Murakami appears to me to exert a similar influence on contemporary thinking as Swift had. It may take another generation or two to be able to speak in rational terms about his ideas. Like the ideas brought home by Gulliver from his Travels, the ideas expressed in 1Q84 elicit in their reader a smile and a wonderment, ending in a relieved realisation: this is only a phantasy, a tale, a story; this is nothing real. Swift has stated, although not expressis verbis, 

*       Kings come in all kinds of varieties;

*       There is no unified, general rule of how Kings are to be;

*       Kings maintain their rule by earthly methods of power and by elaborate memes;

*       Almost anybody has more common sense and decency than the Kings.

Murakami does the same work of destroying, levelling and salting intellectual empires by stating, in the guise of an elaborate cloak-and-dagger sci-fi mystery phantasy:

*       Realities come in all kinds of varieties;

*       There is a specific variety of non-standard reality, which people (not: Murakami) call metaphysics;

*       This parallel reality is actually merged with the common reality, deviating visibly from that only in specific circumstances;

*       There are rules and axioms and protagonists in metaphysics very similar to those in common reality (“physics”);

*       If we had different sensory organs, we could perceive parts of the other (“metaphysical”) reality, possibly losing some perceptions of the normal reality (if we could sense the Earth’s magnetism, we might not be able to distinguish some colors: we would live in a different reality);

*        The density of relations in the other variant influences actual facts in this variant (the density of charge in the parallel world of relations causes an actual lightning in the world of realised facts; the density of desire causes space to conflate/merge and people to synchronise/co-resonate);

*       Both variants are subject to identical axioms of inner consistency of the sequel being a deduction/corollary of the present: both worlds have an inner logic, which deviates only partly from the logic of the parallel world;

*       Time is a recurring element; one who remembers is partly identical to one who is perceiving/had perceived;

*       The continuity is not really continuous, not even for one and the same individual;

*       Aside from one global clock, about which we do not speak, there are local clocks which run at differing speeds;

*       It is possible for the two worlds to merge and to disunite without any problems, the worlds can /and do/ exist alongside each other;

*       The moral of the story on the example of the protagonist heroes is, that a full, ideal life includes the knowledge and ability to surf both waves and to connect with one’s alternate selves, be these laterally or temporally distinct.

 

Well, of course, a phantasy is a phantasy. Thank God, thank our Kings, thank our Schools we can well recognise a phantasy from hard-core reality. Heaven forbid establishing Murakami’s unified dual space-time concept as a credible and sensible idea of which the time has come. 

Murakami’s idea of the parallel world appears to me like a smear, lubrication, veil, packaging cellophane foil or skin. It is well attached to the surface of the factual world, and agglomerates only at times into such droplets or crumplets which modificate the actual things, all the while dramatically influencing the properties of the things they lubricate and separate at the same time. One would hope that time and patient research will bring to the surface such rational words, connected by rationally imaginable relations, which support the vision of two narratives running concurrently: one details what are the facts and one details what are the expectations, based on the facts so far. The two rhetorical strands could support Murakami’s vision. In case one had such a story to tell, about facts and expectations based on facts, one could call that what Murakami calls the Q-time/space also the information content of the story. This point makes the literary work a suitable subject for a submission to FIS.

 

Happy and healthy Eastern to you all!

Karl

 

 


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