Conventionally we interpret the drawing of a distinction in terms of a boundary being drawn between what an object is and is not, for example night and day separated by the dawn, a fish in the sea, and 1 separated from 0 in conventional mathematics and classical logic.
Chiralkine draws distinctions differently, without drawing a boundary.
When an object is being observed, a mirror-symmetric distinction is being drawn. The action drawing this distinction confers perspective that is both spatial and temporal. The object is not absolute, as it is perceived to be, but relational and fractal. The separating function of a drawn boundary in conventional thought is inherent in the manner in which the distinction is being drawn. 1 and 0 are defined relationally such that each separates its own kind from the other. This contrasts sharply with how the physical hardware for AI works, in classical Boolean logic gates, where electrical signals draw a boundary between each 1 and each 0.
The key step is to label all the oppositely paired vertices of a cube as 1 and 0 such that each face constitutes a ring 0101, where each 1 is separated by 0s and each 0 by 1s, then label these vertices a,A; b,B; c,C and d,D such that a lower case letter is 0 and an upper case letter is 1. Next order the letters alphabetically a/A, b/B, c/C and d/D, such that each of the six faces is coded in a different permutation of two 1s and two 0s. Perspective emerges, whether it be spatial or temporal (past, present, future). It is inherent in the symmetry of a cube and an octahedron.
When distinction is drawn in this mirror-symmetric way, the conventional concept of dimensions gives way to a fractal concept. For example, the imaginary infinitesimally small point 0 separating positive and negative numbers where axes cross in Cartesian co-ordinates behaves the same as a universe. A distinction drawn in this way is scale invariant.
For mathematicians with an interest in geometry, the hexagon is a regular skew hexagon (a Petrie polygon).
It follows that when a distinction is being drawn, symmetry is being broken into two mirror-symmetric (chiral) relational elements. Each element is NOT its mirror counterpart, but together, being ordered by recursive application of XOR and XNOR, give rise to perception of spatial and temporal depth.
In a cycle there are three pairs of letters and three pairs of connectors. When a distinction is being drawn, symmetry is being broken, such that there are now four pairs of letters (one pair being duplicated) and three pairs of connectors. This gives rise to the fourth letter pair d/D. The whole is less than the sum of its parts, because of this duplication.
The mirror symmetry in a regular skew hexagon and the way breaking symmetry generates two enantiomers that emerge from drawing a distinction between left and right recalls the symmetry of the human body.
The enantiomers recall the left and right arms and legs, which consist of three ordered bones, the coordination of movement of which is controlled by the brain.
The chiralkine symbol with its four distinct circles arranged in a ring as the corners of a square was designed to capture the essence of this dynamic concept of interconnection and symmetry breaking. Four ordered objects generated by drawing a mirror-symmetric distinction nest in a system controlled by the six (three pairs of) ways in which they can be permuted.
The way in which a distinction is drawn between 1 and 0 controls how arithmetic and counting are performed. In conventional mathematics, XOR is used to draw an asymmetric distinction between 1 and 0. Closure in counting is achieved in two arithmetic steps – subtraction from an uncounted set and addition to a counted set. In chiralkine, XOR and XNOR are used to draw a mirror symmetric distinction between 1 and 0. Closure in counting requires three arithmetic steps.
The properties of numbers: 1 and 0, real and imaginary, are all nested in this mirror-symmetric system.