[Fis] Fis Digest, Vol 105, Issue 12 Human Wisdom vs Meta-Intelligence. Universal contextual contradictory wisdom

[Karl Javorszky]

Trivial Algorithms

2023 10 29



   1. Historical context

Pedro brought FIS into life around 1995. In the first years, we talked
often about the precedent set by encounters in Iberia around the 11th
century. There were nuclei of intellectual cooperation between Oriental and
Western knowledge in Grenada, Sevilla and elsewhere. To the guiding
principles of FIS, established and enforced by Pedro, belongs a cultured
interaction style, and, within that framework, an openness towards ideas
coming from widely differing backgrounds.

We could not avoid the subject of the *liberal arts *discussion. We as a
group stand today before the same problems as our forefathers stood: which
is the right method to deal with Nature? Since the Greeks, intellectual
approaches to discovering the world were split into the four scientific
(music, arithmetic, geometry, astronomy) and the three humanity (grammar,
logic, rhetoric) “arts”. The four formers are roughly equivalent to our
modern notion of STEM (science, technology, engineering, and mathematics).
The trivial arts of rhetoric, logic and grammar are distinct to the former
four, because trivial things can be discussed and debated without coming to
one definite result. The quadrivium is exact, the trivium is practically a
marketplace, where everything is in dependence of everything else, and
results are situation-elastic, not unique.

   1. The term ‘trivial’

Opposed to the exact sciences, trivial matters of grammar, logic, rhetoric
do not deliver single results that are recognizably correct or otherwise
false. In the world of trivialities, everything can be also an illusion
(justifiable error), and there are degrees of and within everything, but no
established scales for the degrees.

Thanks to Shannon, our generation has gained a new perspective on the
conflict between unique results to questions and several answers to
questions. Let us call the former ‘dual’ and keep the name ‘trivial’ for
the latter. The dual method of solving problems uses the maximal contrast
between *<so> **↔ <otherwise>, *expressed as *{0,1}. *Once agreed,
which of *0,1
*is semantically *black, white, *and in which *sequence *to read the
symbols, one can unambiguously identify any member of *N, *and the rest is
easy.

The trivial way of solving problems appears not only at first glance to be
more complicated, less unambiguous, but is indeed more complicated and less
unambiguous. It deals with *three *symbols, as the name says, namely with
the words of the sentence *a+b=c. *The interpretation of the symbol ‘=’ is
wider than a numeric equivalence.

We see this way of using ‘=’ e.g. in the application of translation
machines in: *table **[EN] = table [FR] = Tisch [GE]. *

The rhetoric corps of the trivial force of persuasion asks: *“What is the
difference between a+b and c?”. *The logic army gives a perspective to the
field by stating: *“Two stages, two sets of actors, before and after, or
rather contemporaneous, that would be three stages and double sets of
actors.” *The final thrust comes from the army of arguments of the grammar
corps: *“**Our quadrivial learned friends simply wish away the symbol
differentiating a,b; and the many small symbols differentiating 1s that are
part of a, from those differentiating 1s that are a part of b, and these
from those that differentiate 1s that are a part of c. This is the recipe
for grammatical inconsistencies, all generated by the ach so famously exact
quadrivials!”*

The grammar freaks of the trivial persuasion come up with an example:

Imagine that our language is more exact than we observe among the spoken –
natural – languages. In a culture with complicated inheritance rules, one
would have an extra word each for a single child of parents, for one of
twins, triplets, quadruplets and so forth. In addition, the name of the
child would, by convention, include the number of the child among its
siblings. (see “Quintus”, “Otto”, “Decimus”). At the simple act of
introduction, one would know, how many brothers and sisters a person has,
and where in the sequence – as the how-many-eth – the person came into
life, as a single child or as a part of a multiparturition.

It is self-evident that one who has an inheritance coming that goes *4 *ways
has potentially more resources than someone who is an inheritor to a part
in a wealth that will go *10* ways. If these two families merge,
individuals will gain something or suffer a loss. These are each trivial
amounts, but the many small amounts can add up and create havoc by way of
levels, ranges, thresholds, and tipping points. We recognize their
existence, because they are the cause for (translate into) distances in the
course of resorts.

   1. Rehabilitation, Restitution, Victory, Revenge, Vengeance, Vendetta

Extremely trivial person speaking here. Full of engagement for a trivial
way of life. Always used rhetoric, grammar, logic, never arithmetic,
geometry, astronomy, and only *en passant* music, in my professional life.

The trivial way of counting has arrived in the saddle of a white unicorn in
Zaragoza in the hallowed metal boxes of *listas.unizar.es
<http://listas.unizar.es>. *It has taken a long time since Salamanca in the
11th century, but now we are here. The trivials can make their voice heard
next to the self-aggrandizement of the quadrivials.

As a harmonizing counterpart to the classic, STEM, quadrivial (dual) way of
counting, we proudly introduce the *trivial way of counting, the trivial
algorithms. *

These are based on a combination of place and quantity attributes of
symbols. We interpret *a+b=c *as saying: “Symbols read in a context of ≠
before a background of = we call *a. *The same symbols read in a context of
= before a background of ≠ we call *b. *The two interpretations of the
symbols set *a,b *have an intersection *c, *in which the sentences *a *and
sentences *b *are consistent.”

For the practical application of the trivial algorithms in everyday
calculation, one needs the tables that register the *what, when, where
*coincidences
that are the basis of trivial thinking. These tables are the grammar of
sentences of the form *a+b=c.*

For her trivial calculations, Nature appears to use Cohort 16, the etalon
collection of *(a,b). *The C16 is subjected to periodic changes
(resortings). The cycles that appear in the course of resortings are linear
sequences. The numeric aggregates of cycles are termed *liens* (bonds,
cohesion extents), the system of liens is termed *liaison. *The members of
the cycles are considered *allies. *The elements’ appurtenance to cycles is
termed *association. *

Some of the spectacles Nature entertains us with can be explained as
conflicts between geometric (dual) and trivial calculations regarding what
should be on which place and to what extent and how predictably. Using the
trivial algorithms (aka liaison algorithms) allows further research in the
subjects of memory, genetic. (Inevitably, the logic that becomes visible
while co-executing dual and trivial calculations necessitates some
fundamental rearrangements of concepts in other fields, too.)
Self-referencing feedback loops are an inbuilt feature of the tautomatic
technique of reading natural numbers. Self-referencing feedback loops are
the building blocks of intelligent systems. (Liaison algorithms : dual
algorithms = transistors : semiconductors.) The basic unit must be in more
than 2 possible different positions. The basic unit must by its nature give
rise to several alternatives. Combining it with dual symbols gives an
entity that can and must continuously decide *{to be or not to be}, {which
place, what extent}. *The matrix of switches that makes an AI system cannot
consist only of on-off switches. It needs switches of the form *{lower
limit /predecessor/, actual value, upper limit /successor/}, *in
combination with *{true, false} *switches. The order develops as a
consequence of neighborhoods in Nature, even if we generate neighborhoods
by order in our modeling of the process.

We shall only be able to address the architecture of a thinking system
after we shall have arrived at an agreement about its basic components. The
three-way switch is necessary to produce alternatives among which a
decision can be made. The liaison values, which come from pairing, sorting,
resorting, cycling, synchronizing, and evaluating natural numbers are
natural switches by their yes/no answers to ranges regarding their
predecessors and successors in dependence of order. A piece of cake to
program, as all ingredients are natural numbers.

Let us wash the word ‘trivial’ from its undeserved connotations and give it
its old glory back! (In some periods, the humanities were taught before the
STEM subjects, quasi as philosophical fundamentals of all exactitude.) It
was only impossible to detect the trivial algorithms for a lack of
computers, but there is, and has always been, quite a lot of rationality
and science in logic, grammar and rhetoric. It is debatable, whether more
different calculations can be made using the dual or the trivial way of
dealing with symbols. The trivial algorithms appear to be as universal and
mighty as the dual algorithms. Progress lies in the concurrent application
of the rules of counting. FIS may be happy to be the birthplace of a great
integration between quadrivial and trivial arts and sciences, just like its
founders have dreamed it to become!

   1. Again, context and meaning

Krassimir has already raised the subject of whether symbols have a context
and meaning. Let me repeat the answer again:

Answer: The geometry of the tautomat shows us two 3D Euclid spaces (being
transcended by 2 planes /that may well depict the electro-magnetic
fields/). These have Central Element Right*a* coordinate (70,70,70), resp.
Central Element Left*b* at coordinate (67,67,67). Our usual, traditional
system based on *N* has no central, but rather a Null element at coordinate
(0,0,0). The context of the information that *p **≠ q *in aspects *{b-a,
2a-b, 3b-2a, … etc.} *with values *{l1=x1, l2=x2, l3=x3, … etc.} *is the
comparison of the relevant values with the background of other cycles in
which *p, q *are (a) member(s). The meaning is the relation of the *p **≠ q
*to one or both of the Central Elements. There is also a neutral,
objective, absolute meaning to *p **≠ q*, namely its relation to the Null
element. (like vectors and weighted and directed vectors.)

   1. Deictic definition


   1. Existence of cycles

An explanation has often the form of a deictic definition. The explanations
offered by the trivial, liaison algorithms are one logical sentence that
uses the index finger to point at entities while telling “*this is called
…”*.

You need to educate yourself about some small details in the procedure of
resorting. The best exercise is to take say *12 *books and order them in a
sequence based on *author – title. *Please line up the books on your table.
Put a stick-it note on each of the books, saying “AT: *i*” where *i *is the
sequential number of that book in the order author first, title second.

Now reorder the books into an order determined by the sequence *title –
author. *Take the first book from the current *author – title *sequence and
find its place in the *title – author *sequence. Write that number on the
yellow sticker as “TA: *j”* where *j *is the sequential number of that book
in the order title first, author second.

It is extremely unlikely that your 12 books will resort from *author –
title *into *title – author *in one uninterrupted sequence of place
changes. Very probably it will arrive that you place a book into a place
that is empty, having been emptied by a book that previously had been
already moved to its new place. Occupying an empty place in the course of a
resort is termed “closing the cycle”, creating an empty place in the course
of a resort is termed “opening the cycle”.

Count and tabulate the cycles.

   1. Properties of cycles

Generalize the problem by calling the two properties *title, author *in the
sequel *a,b. *Generate a few random values of *(a,b) *and convince yourself
of the existence of cycles.

Now use cohorts of objects generated in a systematic fashion, by generating
cohort C16, which is generated by the rule *a** ≤ b;** a,b **≤** 16. *Find
the *12 *cycles of the reorder [ab] ↔ [ba]. Take cycles *3,6 *which are *18,
30 *long. Create aggregates for each by *Σ**a, **Σ**b, **Σ**dist(pos(memberk)
– pos(memberk+1)). *Use the two expressions *(**Σ**b – **Σ**a)/**Σ**dist) *to
point at their differences with your index finger while saying “This
(exemplary appearance of the general) inbuilt difference within the symbol
set I shall call *information, *and the extent of their differences I shall
call *Unit of information.”*

   1. Who is crazy?

In a private mail, one of the learned friends has indicated that for a
short time they believed me to be crazy. After the cognitive dissonances
have dissipated, they now believe me not to be crazy.

The deconstruction of systems of thought causes that matter which causes
the feeling of evidence (which results in the subject saying to be
convinced that something is such as they believe it to be) to be released.
The conviction hormone is comparable to the happiness hormone. Disturbing
that system that produces inner convictions alters the hormonal state of
the individual (see eg experimental neuroses).

Let me express my deep sympathies and commiseration towards those who are
confronted by feelings of conviction but having not enough different
concepts to merge into something convincing, and unavoidably included in
this, becoming confronted with different concepts that are in lack of a
coherent convincing. This is the normal course of life if one learns that
something is otherwise than expected. Children, having less expectations,
learn without unlearning. As a grown-up, as one learns something new, it is
often unavoidable to say *adieux *to some previously held beliefs. Do not
despair, Nature will make sure that the balance is regained. Maybe you even
learn something new.



All the best

Karl

Am Mo., 30. Okt. 2023 um 12:33 Uhr schrieb Karl Javorszky <
karl.javorszky en gmail.com>:

> Trivial Algorithms
>
> 2023 10 29
>
>
>
>    1. Historical context
>
> Pedro brought FIS into life around 1995. In the first years, we talked
> often about the precedent set by encounters in Iberia around the 11th
> century. There were nuclei of intellectual cooperation between Oriental and
> Western knowledge in Grenada, Sevilla and elsewhere. To the guiding
> principles of FIS, established and enforced by Pedro, belongs a cultured
> interaction style, and, within that framework, an openness towards ideas
> coming from widely differing backgrounds.
>
> We could not avoid the subject of the *liberal arts *discussion. We as a
> group stand today before the same problems as our forefathers stood: which
> is the right method to deal with Nature? Since the Greeks, intellectual
> approaches to discovering the world were split into the four scientific
> (music, arithmetic, geometry, astronomy) and the three humanity (grammar,
> logic, rhetoric) “arts”. The four formers are roughly equivalent to our
> modern notion of STEM (science, technology, engineering, and mathematics).
> The trivial arts of rhetoric, logic and grammar are distinct to the former
> four, because trivial things can be discussed and debated without coming to
> one definite result. The quadrivium is exact, the trivium is practically a
> marketplace, where everything is in dependence of everything else, and
> results are situation-elastic, not unique.
>
>    1. The term ‘trivial’
>
> Opposed to the exact sciences, trivial matters of grammar, logic, rhetoric
> do not deliver single results that are recognizably correct or otherwise
> false. In the world of trivialities, everything can be also an illusion
> (justifiable error), and there are degrees of and within everything, but no
> established scales for the degrees.
>
> Thanks to Shannon, our generation has gained a new perspective on the
> conflict between unique results to questions and several answers to
> questions. Let us call the former ‘dual’ and keep the name ‘trivial’ for
> the latter. The dual method of solving problems uses the maximal contrast
> between *<so> **↔ <otherwise>, *expressed as *{0,1}. *Once agreed, which
> of *0,1 *is semantically *black, white, *and in which *sequence *to read
> the symbols, one can unambiguously identify any member of *N, *and the
> rest is easy.
>
> The trivial way of solving problems appears not only at first glance to be
> more complicated, less unambiguous, but is indeed more complicated and less
> unambiguous. It deals with *three *symbols, as the name says, namely with
> the words of the sentence *a+b=c. *The interpretation of the symbol ‘=’
> is wider than a numeric equivalence.
>
> We see this way of using ‘=’ e.g. in the application of translation
> machines in: *table **[EN] = table [FR] = Tisch [GE]. *
>
> The rhetoric corps of the trivial force of persuasion asks: *“What is the
> difference between a+b and c?”. *The logic army gives a perspective to
> the field by stating: *“Two stages, two sets of actors, before and after,
> or rather contemporaneous, that would be three stages and double sets of
> actors.” *The final thrust comes from the army of arguments of the
> grammar corps: *“**Our quadrivial learned friends simply wish away the
> symbol differentiating a,b; and the many small symbols differentiating 1s
> that are part of a, from those differentiating 1s that are a part of b, and
> these from those that differentiate 1s that are a part of c. This is the
> recipe for grammatical inconsistencies, all generated by the ach so
> famously exact quadrivials!”*
>
> The grammar freaks of the trivial persuasion come up with an example:
>
> Imagine that our language is more exact than we observe among the spoken –
> natural – languages. In a culture with complicated inheritance rules, one
> would have an extra word each for a single child of parents, for one of
> twins, triplets, quadruplets and so forth. In addition, the name of the
> child would, by convention, include the number of the child among its
> siblings. (see “Quintus”, “Otto”, “Decimus”). At the simple act of
> introduction, one would know, how many brothers and sisters a person has,
> and where in the sequence – as the how-many-eth – the person came into
> life, as a single child or as a part of a multiparturition.
>
> It is self-evident that one who has an inheritance coming that goes *4 *ways
> has potentially more resources than someone who is an inheritor to a part
> in a wealth that will go *10* ways. If these two families merge,
> individuals will gain something or suffer a loss. These are each trivial
> amounts, but the many small amounts can add up and create havoc by way of
> levels, ranges, thresholds, and tipping points. We recognize their
> existence, because they are the cause for (translate into) distances in the
> course of resorts.
>
>    1. Rehabilitation, Restitution, Victory, Revenge, Vengeance, Vendetta
>
> Extremely trivial person speaking here. Full of engagement for a trivial
> way of life. Always used rhetoric, grammar, logic, never arithmetic,
> geometry, astronomy, and only *en passant* music, in my professional
> life.
>
> The trivial way of counting has arrived in the saddle of a white unicorn
> in Zaragoza in the hallowed metal boxes of *listas.unizar.es
> <http://listas.unizar.es>. *It has taken a long time since Salamanca in
> the 11th century, but now we are here. The trivials can make their voice
> heard next to the self-aggrandizement of the quadrivials.
>
> As a harmonizing counterpart to the classic, STEM, quadrivial (dual) way
> of counting, we proudly introduce the *trivial way of counting, the
> trivial algorithms. *
>
> These are based on a combination of place and quantity attributes of
> symbols. We interpret *a+b=c *as saying: “Symbols read in a context of ≠
> before a background of = we call *a. *The same symbols read in a context
> of = before a background of ≠ we call *b. *The two interpretations of the
> symbols set *a,b *have an intersection *c, *in which the sentences *a *and
> sentences *b *are consistent.”
>
> For the practical application of the trivial algorithms in everyday
> calculation, one needs the tables that register the *what, when, where *coincidences
> that are the basis of trivial thinking. These tables are the grammar of
> sentences of the form *a+b=c.*
>
> For her trivial calculations, Nature appears to use Cohort 16, the etalon
> collection of *(a,b). *The C16 is subjected to periodic changes
> (resortings). The cycles that appear in the course of resortings are linear
> sequences. The numeric aggregates of cycles are termed *liens* (bonds,
> cohesion extents), the system of liens is termed *liaison. *The members
> of the cycles are considered *allies. *The elements’ appurtenance to
> cycles is termed *association. *
>
> Some of the spectacles Nature entertains us with can be explained as
> conflicts between geometric (dual) and trivial calculations regarding what
> should be on which place and to what extent and how predictably. Using the
> trivial algorithms (aka liaison algorithms) allows further research in the
> subjects of memory, genetic. (Inevitably, the logic that becomes visible
> while co-executing dual and trivial calculations necessitates some
> fundamental rearrangements of concepts in other fields, too.)
> Self-referencing feedback loops are an inbuilt feature of the tautomatic
> technique of reading natural numbers. Self-referencing feedback loops are
> the building blocks of intelligent systems. (Liaison algorithms : dual
> algorithms = transistors : semiconductors.) The basic unit must be in more
> than 2 possible different positions. The basic unit must by its nature give
> rise to several alternatives. Combining it with dual symbols gives an
> entity that can and must continuously decide *{to be or not to be},
> {which place, what extent}. *The matrix of switches that makes an AI
> system cannot consist only of on-off switches. It needs switches of the
> form *{lower limit /predecessor/, actual value, upper limit /successor/},
> *in combination with *{true, false} *switches. The order develops as a
> consequence of neighborhoods in Nature, even if we generate neighborhoods
> by order in our modeling of the process.
>
> We shall only be able to address the architecture of a thinking system
> after we shall have arrived at an agreement about its basic components. The
> three-way switch is necessary to produce alternatives among which a
> decision can be made. The liaison values, which come from pairing, sorting,
> resorting, cycling, synchronizing, and evaluating natural numbers are
> natural switches by their yes/no answers to ranges regarding their
> predecessors and successors in dependence of order. A piece of cake to
> program, as all ingredients are natural numbers.
>
> Let us wash the word ‘trivial’ from its undeserved connotations and give
> it its old glory back! (In some periods, the humanities were taught before
> the STEM subjects, quasi as philosophical fundamentals of all exactitude.)
> It was only impossible to detect the trivial algorithms for a lack of
> computers, but there is, and has always been, quite a lot of rationality
> and science in logic, grammar and rhetoric. It is debatable, whether more
> different calculations can be made using the dual or the trivial way of
> dealing with symbols. The trivial algorithms appear to be as universal and
> mighty as the dual algorithms. Progress lies in the concurrent application
> of the rules of counting. FIS may be happy to be the birthplace of a great
> integration between quadrivial and trivial arts and sciences, just like its
> founders have dreamed it to become!
>
>    1. Again, context and meaning
>
> Krassimir has already raised the subject of whether symbols have a context
> and meaning. Let me repeat the answer again:
>
> Answer: The geometry of the tautomat shows us two 3D Euclid spaces (being
> transcended by 2 planes /that may well depict the electro-magnetic
> fields/). These have Central Element Right*a* coordinate (70,70,70),
> resp. Central Element Left*b* at coordinate (67,67,67). Our usual,
> traditional system based on *N* has no central, but rather a Null element
> at coordinate (0,0,0). The context of the information that *p **≠ q *in
> aspects *{b-a, 2a-b, 3b-2a, … etc.} *with values *{l1=x1, l2=x2, l3=x3, …
> etc.} *is the comparison of the relevant values with the background of
> other cycles in which *p, q *are (a) member(s). The meaning is the
> relation of the *p **≠ q *to one or both of the Central Elements. There
> is also a neutral, objective, absolute meaning to *p **≠ q*, namely its
> relation to the Null element. (like vectors and weighted and directed
> vectors.)
>
>    1. Deictic definition
>
>
>    1. Existence of cycles
>
> An explanation has often the form of a deictic definition. The
> explanations offered by the trivial, liaison algorithms are one logical
> sentence that uses the index finger to point at entities while telling “*this
> is called …”*.
>
> You need to educate yourself about some small details in the procedure of
> resorting. The best exercise is to take say *12 *books and order them in
> a sequence based on *author – title. *Please line up the books on your
> table. Put a stick-it note on each of the books, saying “AT: *i*” where *i
> *is the sequential number of that book in the order author first, title
> second.
>
> Now reorder the books into an order determined by the sequence *title –
> author. *Take the first book from the current *author – title *sequence
> and find its place in the *title – author *sequence. Write that number on
> the yellow sticker as “TA: *j”* where *j *is the sequential number of
> that book in the order title first, author second.
>
> It is extremely unlikely that your 12 books will resort from *author –
> title *into *title – author *in one uninterrupted sequence of place
> changes. Very probably it will arrive that you place a book into a place
> that is empty, having been emptied by a book that previously had been
> already moved to its new place. Occupying an empty place in the course of a
> resort is termed “closing the cycle”, creating an empty place in the course
> of a resort is termed “opening the cycle”.
>
> Count and tabulate the cycles.
>
>    1. Properties of cycles
>
> Generalize the problem by calling the two properties *title, author *in
> the sequel *a,b. *Generate a few random values of *(a,b) *and convince
> yourself of the existence of cycles.
>
> Now use cohorts of objects generated in a systematic fashion, by
> generating cohort C16, which is generated by the rule *a** ≤ b;** a,b **≤**
> 16. *Find the *12 *cycles of the reorder [ab] ↔ [ba]. Take cycles *3,6 *which
> are *18, 30 *long. Create aggregates for each by *Σ**a, **Σ**b, **Σ**dist(pos(memberk)
> – pos(memberk+1)). *Use the two expressions *(**Σ**b – **Σ**a)/**Σ**dist)
> *to point at their differences with your index finger while saying “This
> (exemplary appearance of the general) inbuilt difference within the symbol
> set I shall call *information, *and the extent of their differences I
> shall call *Unit of information.”*
>
>    1. Who is crazy?
>
> In a private mail, one of the learned friends has indicated that for a
> short time they believed me to be crazy. After the cognitive dissonances
> have dissipated, they now believe me not to be crazy.
>
> The deconstruction of systems of thought causes that matter which causes
> the feeling of evidence (which results in the subject saying to be
> convinced that something is such as they believe it to be) to be released.
> The conviction hormone is comparable to the happiness hormone. Disturbing
> that system that produces inner convictions alters the hormonal state of
> the individual (see eg experimental neuroses).
>
> Let me express my deep sympathies and commiseration towards those who are
> confronted by feelings of conviction but having not enough different
> concepts to merge into something convincing, and unavoidably included in
> this, becoming confronted with different concepts that are in lack of a
> coherent convincing. This is the normal course of life if one learns that
> something is otherwise than expected. Children, having less expectations,
> learn without unlearning. As a grown-up, as one learns something new, it is
> often unavoidable to say *adieux *to some previously held beliefs. Do not
> despair, Nature will make sure that the balance is regained. Maybe you even
> learn something new.
>
>
>
> All the best
>
> Karl
>
>>
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