In Statu Nascendi, Part.2
Socrates & the intangible force of Antanairesis.
“Antanairesis is an intangible force that knows no calculation but a creative process. Matrix of numbers.”
In this chapter of In Statu Nascendi, self-reflection becomes profound.
Inspired by several passages of the philosophical dialogue ‘Meno’, I created this semi-installation using different mediums, remaining faithful to the vision of a fractal concept seen at its primal origins while reading it: imagining it as a crack, a fracture from which light comes out; a division between the upper and lower part of this composition.
By reading this text, I hope you will perceive the emotional thrust behind this process.
The video on my official YouTube channel, will also accompanies and exude different elements I’ve studied to develop it.
Tips of icebergs.
This may be a suitable image to help one understand what one observes when coming across one of the mathematical passages of Plato’s dialogues.
Enormous conformations of ice in the ocean of the Psyche; only a little part emerges on the surface while majority remains in the abyss of one’s subjectivity; grand constructions of rigorous mathematical thought, products of the irrational.
Committing to understanding these mathematical steps behind these dialogues as much as possible, appears to be an extreme adventure, capable of shaking any reader of Plato from his daily habits and securities.
It is a confusion and numbness that puts oneself in a better condition to continue the research, similarly to what happened to the young Meno, after Socrates’ touch, similar to that of the submarine-torpedo; it gives the consciousness of not knowing something one assumed to know.
Visually, it takes on the elegant form of an archaic fractal figure: a Pythagorean square, repeating itself, contracting infinitely around the same point, the ever-elusive terminal limit point of its contraction; ancients called it also ‘Kairos’
https://medium.com/the-collector/time-perceptions-in-ancient-greek-culture-eb3985dab15
An infinite choreography and succession of dancing figures follows the graphic lines of this fractal figure, which reproduces in perpetual movement the same figure in a permanent contraction. Generally, the famous short dialogue between Socrates and Meno’s young slave is considered the dramatic representation of a simple geometry lesson.
It is a theatrical, dramatic performative; characters give life to a real musical drama, in which action and Art are united, therefore, endlessly.
Everything revolves around the irrational which, by definition, has no definition in itself and appears on the scene in a mathematical guise. The incommensurability of the diagonal and the side of the square; those of the number which should express the relation between diagonal and the side of the square which does not exist, is in fact not a number, but a fracture, a crack towards the absurd.
Numerical value ‘square root of 2’ with which we have been used to expressing the relation between diagonal and the side of the square since middle school, does not seem so absurd to us; this is because we are unable to identify our perceptions with Pythagorean mathematics and how the world was regulated by it. For the ancient Pythagoreans, only positive integers were numbers, and all reality can be traced back to them and their relations.
Discovery of the mathematical irrational constitutes, in the ancient Greek world, a tragic event that soon assume repercussions beyond boundaries of mathematics transforming itself into a question about the thinkability of things in reality.
Other doubts in regards of the nature of artificial intelligence?
How can one assume that the value corresponding to the incommensurability of the diagonal on the side of the square exists, is thinkable and expressible, if this value cannot be traced back to a positive integer?
Socrates’ reasoning, in fact, for a while, follows the infinitesimal procedure of measuring a segment of a straight line through another segment of a straight line.
A process that Aristotle calls ‘Antanairesis’, after which the philosopher and Meno proceed to search for the measurement of the side of the square double, concluding it in failure, because the side, again is without measure.
A light comes out from the abyss between my ears.
If we look forward, towards dialogues that Plato wrote few years later, we can identify the side of the double square with the ineffable diagonal mentioned in ‘The Republic’. That is a quantity, because all geometric objects have one; every thought, during the creative process in the studio is a little part of a geometric object, but is devoid of length or measurement.
In an absolutely unpredictable way, the presence of irrational lines in the universe of geometry, the penetration of ineffable words into the world of Pythagorean logos, have led ineluctably to the dramatic dilemma of the Eleatic ontology that have posed the disturbing question: ‘to be or not to be’.
Credits: text, artworks and translations by Alberto Ballocca. In Statu Nascendi, 2024.
