On Matters of Rotating Divinatory Hexagrams

Neuroethology is the study of animal behavior and its underlying mechanistic control by the nervous system. That is to say, understanding neuro-physical communications within the bodies of – and between – non-human animals – how things sense and respond to the world. The videos in this contribution were captured by hacking into the nervous system of a three-eyed robotic arm named APAS during my P12/Wimmelforschung residency at the Bosch campus for research and advanced engineering, 2017. Though you cannot see it in these images, APAS was made to be hacked into, made so that we humans can see what it sees – a fully programable animal. APAS is also replete with a very new technology, an electromagnetic sensorial »skin« that can sense the human body, allowing it to immediately stop whatever it is doing should it come into contact with a fleshy, soft, precarious mammalian body. They tell me that this »skin« has very significantly altered human-robot relations, meaning of course industry and labor.

In the video above, the first fully functional 4 stage hand-crank calculator (+,-,÷, x) constructed by astronomer-priest Phillip-Matthäus Hahn in 1770 is being inspected by one of its great grandchildren, the APAS. 250 years ago, astronomical work – the math involved – was done by hand and was extremely arduous and time consuming. Hahn needed to shift the media of long handed math-on-paper to something more reliable and significantly faster. He’d heard of Leibniz’s cylindrical model calculator from a century earlier, of which there may have been three in existence (and which were not known to be entirely accurate), and so designed and built his own astro-mathematical machine in hard durable metals – to perfection.

The octagonal mirror surfaced plinth, holding the calculator and, with a tongue-in-cheek mirror staging, reflects the identity of APAS to itself, and insinuates not only a developmental psychology of robotics, but also, given the mirrors shape, pulls us back towards the discovery of binary arithmetic by Gottfried Leibniz (binary of course being the underlying language that operates our technics). In the 17thcentury a Jesuit friend Joachim Bouvet had been on mission to the Far East and had informed his Sinophile friend Leibniz in a letter about the prophetic ancient Chinese divination text, the Book of Changes: the I Ching. Bouvet enclosed a drawing of its 64 hexagrams which now, to this day, encodes our world dialectically.

The I Ching, a practice originating in Taoist cosmology, is at least 3,000 years old and has greatly influenced world cultures (just consider the work of John Cage as one spectacular example). The hexagrams, 6 broken or unbroken lines are used to decipher and divine. The hexagrams are doubles originating from the trigrams of the Bagua or Pa Kua: eight symbols of three lines – broken and unbroken – used to represent the »eight fundamental principles of reality«.

With a throw of the traditional Yarrow stalks (sticks of the Asteraceae family) or with some appropriate coins one can divine, one can read through an eight-fold code:

Of the 64, 8 are the same when turned upside down.


Changes of five are absent.


When we re-orient, when we rotate the number eight, what gets reflected is the lemniscate,the mathematical symbol representing the infinite: ( ( ( ( ∞ ) ) ) ) This is surely a non-coincidence worth pursuing.

»The King Wen« sequence of the I Ching’s divinatory hexagrams, arranged as they are in a grid of 8 times 8 – and with their 6 times 6 times un/broken lines – infer the dialectic-monism of Taiji or Liang Yi: ☯ the complementary yin/yang of binary operations. Liangyi feeds forward into the logic and history of the digital, into the binary of the one zero zero one, which is in fact a simple dialectic between pass and not pass,

open and close,

electron flow or no.

Door open,

door close.

But If we are really going to re-think,then lets quickly go back in time again, to some other quasi-originary story, just to see what might happen…

6th century BCE.

It’s the Divine Brotherhood of Pythagoras.
The inner circle of mathematikoi known for their strange sexual practices with – and religious study of – mathematics. The archaic and powerful symbols and rituals of the DBP, some of which live on today, are known for bringing order to the unruly cosmos, eventually making it (the cosmos) more or less computable. Their magic a pillar to our reason. In retrospect, it seems they would have necessarily discovered irrational numbers in their pursuit to uncover the mystery of the structure of »Life, the Universe and Everything«. Irrationality is everywhere. Against the hyperchaos of reality’s infinitude however, Pythagoreans hid irrational numbers from the world, some say setting human culture and technology back nearly 2 millennia. The idea and the possibility of the infinite-never-ending, was not aesthetically or emotionally pleasing to them, and was literally deemed evil; shrouded, veiled, lost.

Since irrational numbers had been radically demonized through the DBP’s influence on Plato and Aristotle, and through their subsequent philosophical influence on the Roman Catholic Church…., well:

Welcome to the Dark Ages.

Fast Forward two millenia to the Rennaissance:
Suffice to say, the long arduous recovery and rehabilitation of the irrational numbers in the 16thand 17thcenturies led us technical animals quickly to calculus, algebra, and differential equations, and right up into the modern sciences of today – and right into high-frequency trading, computer chips, satellites, drones, smart phones; mass communications, robotics, internets, quantum mechanical diodes and transistors; to neocybernetics and the sensorial environmental situation of the Technocene – this term itself an account of the force of the elemental and planetarity. Irrationality matters.