Chiralkine is a control system that operates in cycles on the principle of mirror symmetry instead of balance (equations and double entry bookkeeping), which hidden in plain sight treats the two sides of relationships asymmetrically, leading to growing instability and eventually to system failure. It was invented and has been developed as a tool to reveal and counter this asymmetry.
Chiralkine performs computation by drawing (01 and 10 from 00 and 11) and clearing (00 and 11 from 01 and 10) distinctions in coupled, mirror-symmetric rotations of three rings of formula
in which each of a, b and c is a different kind of 0 and each of A, B and C is a different kind of 1, two of said rings being positioned in mirror symmetric orientations and the other ring being rotatable stepwise between the mirror symmetric orientations
wherein each of the letters in the rings in the mirror symmetric orientations is paired with the aligned letter of the rotatable ring
such that stepwise rotation of the rotatable ring switches from pairings in which on one side the letters are the same and their sizes are the same (00 and 11) and on the other side the letters are the same and their sizes are different (01 and 10) to pairings in which the letters and their sizes are mixed up and back again to the reverse in three steps whereby distinctions are drawn (01 and 10 from 00 and 11) and cleared (00 and 11 from 01 and 10) in three coupled mirror-symmetric steps:
and the original mirror symmetric orientation is restored in three further steps.
Chiralkine operates on the principle of mirror symmetry – the symmetry of the human body, not balance. The two rings in mirror symmetric orientations are related as the left and right sides of the body. The rotating ring is related to the mirror orientations as the “excluded middle” of the body is to the left and right sides or in Cartesian axes as the origin (zero) is related to the positive and negative number lines. Instead of treating where the distinction between left and right is cleared as nothing (zero), chiralkine treats this as a dual in a cycle, duplicating the contribution of the rotating ring to create two pairs (four rings – one pair for distinct and one pair for same) out of three. In so doing it allows left and right to be perceived as being separate mutually exclusive objects, yet keeps them connected together. Put another way, it can act as a “fuzzy boundary” between them (analogous to a concept known as gradience in linguistics, where the boundary between words of opposite, mutually exclusive meanings can be fuzzy).
Chiralkine is deeply rooted in the symmetry properties of a skew hexagon – a ring traced out by following six consecutive edges around a cube. A skew hexagon has six sides and six corners. It also possesses three planes of bilateral symmetry. When you perceive the skew hexagon as being divided by this plane of symmetry into left and right sides, two of the corners are duplicated, creating two mirror opposite objects (enantiomers) each consisting of three sides and four corners – a corner has been duplicated. This is what the rotating ring contributes in chiralkine – it breaks the symmetry of the skew hexagon, and yet keeps a memory of how the two enantiomers are connected together in the ring.
The result is a system that works just like the lyrics in the song “Windmills of Your Mind”.
“Like a circle in a spiral, Like a wheel within a wheel, Never ending or beginning, On an ever-spinning reel”.