[Fis] Anticipatory Systems

[Karl Javorszky]

*Anticipation*



Learned Friends,



We deal with the observation, that biologic organisms anticipate what will
happen next. Some concentrate on the narrative of the anticipation, some on
the phenomena that are anticipated. As a human faculty, anticipation can
range from intuition, guess, instinct, to prediction and certitude. Science
has more or less dealt with certitude (b follows from a) and has understood
prediction (if a then p(b) ~ x). Now we work our way towards understanding
instinctive prediction.

The utility and efficacy of the narrative version of anticipation varies
also greatly: we have the wish formulae, where faith and belief causes
anticipating an effect (if I say “please” they will give that to me),
magical incantations with powerful words, inputting arguments of an
algorithm in the hope of receiving a result, and the classical case of the
words of the narrative being one and inseparable from the facts that are
the case (the DNA is a narrative of what will happen, and its predictions
are in the closest possible way related to the facts of the matter the
narrative talks about). (Interactive online reporting, where the narration
is a part of the process.)

We do have some difficulties with a running narration, because such a thing
as telling the future has no place in classical, Wittgenstein logic and the
corresponding narrative about the proceedings. That, what will come into
existence is presently not the case. Whichever way we turn it, we are not
supposed to talk about things that are not the case.



Foretelling the future (anticipating correctly) is a task that humans can
despair of. This problem being with us since the beginning of time, it has
been addressed by many generations using diverse lexica. Bruno’s suggestion
that we have no shy using words and concepts of theology is a wise one: Our
forefathers expressed themselves in allegories involving divine figures.
This has given me courage to present to you an Allegory on the Seduction of
Arithmetica by Amor, with a bow to Martianus Capella. May your serene
judgement of this non-polished draft be softened by magnanimous mercy
extended against a beginner.


-----------------------

Seduction of Arithmetica by Amor (20181028)



*Amor*: *(enters scene of idyllic Elysian character)* Oh All you Gods! Your
help is needed now that I have lost my way in my quest for my beloved
second-sister Arithmetica, and now I am in unknown terrain, where no human
intelligence had shed any light so far. Where are you, oh Arithmetica?!

*Arithmetica*: *(enters from behind a tree)* Here I am my Amor, never far
from you. You have a desire to talk to me

*Amor:* Please help. I have a problem I cannot solve on my own. You know,
Zeus has gone more mercantilist, in the wealth-generating mood, and he
tasks each of us to prepare reports the end of every quarter. How many
arrows fired, how many hits, and among these how many with operational
achievement. Now what is a success I know: if I hit with my arrow the heart
of one individual. What they want to know is, however, how many couples I
generate and how fruitful the resulting fornications will turn out to
become. They are in population management up there and are obviously
scheming to make me less industrious or less precise, but first they want
the numbers. How can you tell me, my dear second-sister, how many healthy
offspring are generated per arrow shot of mine?

*Arithmetica:* You, my dear second-brother, like so many others, want to
know whether we can foretell the future by our dexterous fingers, using
distinguishable objects which we count. The answer is: theoretically no,
practically yes. You may at first not understand this reply. To help to
open up your mind, let me tell you in all confidence a sordid part of my
life.

*Amor:* Ah, my dearest Arithmetica? How come you have suffered indignities?
Surely by the acts of the mortals?

*Arithmetica:* Yes, the bipeds have kidnapped me from the Gardens of Olymp
and pressed me into their service. This would have not been necessary,
first of all, but for the cruel circumstances of that rendition into the
realm of the humans, the shame of it has kept my forced adoption for a long
time in the dark. Everybody knows that my 6 sisters and I are of a
cooperative, willing, pleasing character, because we find pleasure in what
we do. No one needs to force Music to be the essence of Music, there is no
need to coerce Geometry into doing geometry! We are the far relatives of
the Muses, in the technical, applicational fields. We like what we do,
otherwise we could not embody the spirit of that what we are. But what
happened to me was of an otherworldly brutality. All the bipeds agree in
praising our diligence and competence, in my case my speciality,
exactitude. There is no need to subject a person of our divine breed to
such indignities.

*Amor:* What, oh Arithmetica, what did they did to you?

*Arithmetica:* That subgroup of the bipeds which calls itself the
Quadrivials have captured me and keep me locked up in a place with
rectangular axes on which identically spaced units are measuring distances.
You cannot imagine a less creative surroundings for a young girl. It is
pure sensory deprivation, the intellectual equivalent of a solitary
confinement. I have no permission to have anything in hand that is not of a
uniform make, as such indistinguishable from any other unit element. They
just eliminated all diversity from their castle. These are very strict
people.

*Amor:* what a sad story! You with all your talents and you love of glitzy
things to be left on your own among grey uniform units that have no
relations among each other! You always loved arranging and re-arranging
your manifold glitzy things according to their inner connections among each
other. You always knew that there is a system of a-priori relations among
the things: this is what their differing ways of being glitzy expresses.

*Arithmetica:* You, my beloved, understand my pain. It is all right if
those of strong faith require that one serves them according to their
beliefs and rituals, but it is not right, if these well-educated rulers
discourage any parallel way of looking at things, which in my case means
counting them.

*Amor:* As far as I know you, my dear Arithmetica, you will never give up.
Every day, the efforts of deciphering the original creativity of Zeus and
his ancestors will bring up new details about the world, where your
unerring faculties are needed. The bipeds rejoice in thy works and bring
you many spectacles and offerings, I understand?

*Arithmetica:* Indeed, I am not without resources. Evading the intrusive
surveillance of my quadrivial masters, this maiden has imagined up her
beloved glitzy things, which she so much enjoyed arranging about during
chaste childhood, playing with the frolicking centaurs, naiads and nymphs.
To evade any malign attention, I have replaced the actual form of the
glitziness with a number, and only worked on the first few natural numbers.

*Amor:* Indeed, I have been hearing you muttering to yourself:

*Position ( (a,b), d, (b,a) ) = b * (b+1)/2 + a,*

*Position ( (a,b), d, (a,b) ) = d * (d+1)/2 – (d-a+1) * (d-a+2)/2 + (b-a+1)*

the other day.

*Arithmetica:* That was the x,y coordinates on a plane of pairs (a,b) which
can have any of d degrees of glitziness. These coordinates can be grouped
into what is called cycles by lines that connect elements that change
places with each other in a sequence of push-aways. The concurrent running
of several cycles creates rhythms. This is pure arithmetic, no one can deny
that. Still, the Lords distrust the idea of order, as long as it comes from
ordering by one’s own free will. They learned well, how Poseidon orders
water, how Helios throws his bolts, but they would never think of
sequencing just for the sake of it, to see how far they get until they
overdo it. They do not believe that if you generate all of the possible
alternatives, the reasonable ones will turn up among these and will be
recognised. The a-priori relations that exist in the world, do have
something to do with order, or am I mistaken on this point? What mortal
people don’t notice is that you can stick axes into each other in a
rectangular fashion and completely valid Descartes spaces emerge, just on
the glitzy properties of the first 16 numbers. They haver a deep revulsion
against considering objects that are different to each other.

*Amor:* So, you can build rectangular spaces just from natural numbers?
Just by re-ordering them? You can demonstrate what is called gravitation by
the bipeds to be an implication of linear order (of the Peano axioms)?

*Arithmetica:* Now we come to the answer to the question you have started
out with. Can we foretell Future? Only the Gods can do that in a full
sense, but we are catching up. The problem is that my overlords, the
Quadrivials, do not like conflicts and unpredictable outcomes. As if an
unpredictable outcome would be on average any better or worse than a
predictable one. It is the subjective tension they do not like, and this is
why they discourage a relaxed, rational view of predictability.

*Amor:* Well, I was always an admirer of your countless fingers, tentacles
and other appendices that you can bend to a high number of distinct degrees
each, but do your arithmetic calculations allow me to foretell the number
of living births per woman between 15 and 45 years of age?

*Arithmetica:* That detail can be solved, once the Lords of Quadriviality
encourage the industrious bipeds to base their calculations on recurrences
and their predictability. The problem is, they officially have no concept
for a future: everything in classical logic happens in the moment;
classical logic is as such: timeless. They have to laboriously calculate
around the concept of cycles, because to use cycles as the basis of all
calculations would admit to the existence of alternatives. If alternatives
a priori exist, the whole edifice of classical logic turns out to be a
special case, riding the wave, surfing along a moment of truth, being in
the air while running in jumps.

*Amor:* This might be the curse by the descendants of *Cheiron* the wise
centaur. Being as well a horse and as well a man teaches one some insight
into biology and its relation to rational thinking. The Quadrivials have
decided that theirs is the rational way to determine the greenness of grass
and could not suffer *Cheiron*’s frequent intermissions: is maybe the grass
indeed greener the other side of the road? Before getting too much
disturbed in their picture of the world, they have eliminated *Cheiron* and
all of his folk. They could not stomach the common-sense approach a
half-horse brings to counting. He could argue his case as eloquently as he
wanted. He was all for predictability and a natural web of relationships
among the parts of the world. He could have argued to electrically powered
Wittgenstein machines for all the understanding and sympathy he got. They
do not wish to be engaged in ambiguities. That, what can be resolved by
finding the one, correct solution, that is quadrivial. That, what can be
discussed, put in different lights, can have several solutions, none of
which is completely right: this delineates a subject the quadrivials make a
wide berth around. Conflicts are trivial. Centaurs are creating conflicts,
they are as such, in themselves a conflict, so they get radically removed
from the quadrivial world. How will they now try to understand what makes
centaurs function, let alone reason? They were not able to understand that
axiomatics begins with axiom 1: there must be recurrent feeding. Till
today, they burn holy weeds in their offices if the word “recurrent” is
uttered. These people are beyond the point of no return. The divine
retribution for the extermination of the centaurs is presently taking
place. Our ruling elite is unable to think it terms of recurrent states of
a set, because they have deep feelings of guilt and emptiness for having
expelled the animal spirits from their reasoning-thinking part of the brain.

*Arithmetica:* Is it so, that fertility rates are sinking in those parts of
the world, where you induce pairing, depressive as you sound, Amor? Do not
paint my overlords in such a harsh light, my friend. Rigid they may appear,
but some of them are flexible and clever. Let me continue whispering in as
many ears as stand open, in the low voice of reason, that working on
uniform things during the day does not prohibit one from working with
glitzy things, in off time. Perhaps, some of the quadrivials do like
engineering, puzzles and the building of kaleidoscopes.  Do not give up
hope yet, my beloved Amor. So, we shall part for a time now, but we shall
meet again. Your arrow has touched me in my inner being, and our chaste
meeting of minds has resulted in the creation of a new baby girl, of which
you are the father, my beloved Amor.

*(Enter young child, growing on stage into young woman)*

*Amor:* Sacre bleu! A nice conversation about predictions turns out to be a
love affair, with consequences, and here she is, the consequence: one
maiden, quite becoming, who seems to be fully enjoying all feelings of
vibes. She is the fruit of our love? What a divine end to this story!

*Arithmetica:* Yes, your longings have awakened in my heart the desire to
be a well behaving daughter of Philosophia and, like my respected Mother,
from time to time to give birth to a baby Science. Please meet your sweet
daughter *Rhythmonomia*, who will help you and all bipeds to give different
names to different rhythms and make a great work of it, deriving much
pleasure from finding the correct answers to some of their questions. My
Quadrivial Lords will surely forgive me for getting impregnated by an idea,
once they see how pleasingly helpful *Rhythmonomia* will be in their
everyday household tasks or in their great campaigns to achieve
intellectual brilliancy.

*(Exeunt)*
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