Chiralkine counting treats a distinct object as a relationship between what a distinct object is and what it is not. It treats the two sides of a relationship defining a distinct object symmetrically. It works on a new principle, different from equations and balance.

When a distinct object is counted, the relationship defining it is replaced with another relationship, which records the counting step. The process repeats in a six-step cycle.

This simple cycle is controlled by the mirror opposite truth tables for the logic gates XOR (exclusive OR) and XNOR effecting permutation of four ordered objects, each defined by a relationship between what it is and what it is not. In each of these truth tables one symbol represents distinct, not same and the other represents not distinct, same.

The permutation corresponds with rotation of 3D space. This can be modelled by the way in which the four opposed corners of a cube, each representing a relationship between what an object is and is not, are permuted as the cube is rotated from one face to another.