We have all been taught, wrongly, to count distinct objects once each. This incorrect way of counting is producing mounting social, economic, political and environmental problems. It has come about, because our languages and mathematics are constructed out of oppositions (black and white) in a way that privileges one side over the other.

We should be counting distinct objects twice each, once in respect of each side of black and white. We could then use these dual numbers to perform computation in a way that prevents one side of a relationship being privileged over the other. This would be a huge step towards solving many of the social, economic, political and environmental problems that we are facing. The way we think about relationships now is asymmetric, and that is the root cause.

A distinct object is defined by a relationship created by drawing a distinction between what it is and what it is not: an opposition (black and white). We have been taught to count only one side of this relationship (black). We call the other side of this relationship (white) nothing, and represent it with the symbol 0. This incorrect teaching causes us to privilege one side of our relationships over the other. We should be counting both, to ensure that the two sides of our relationships are treated symmetrically.

There are two mutually exclusive, mirror opposite ways to draw a distinction between what an object is and what it is not. These are defined by the rules of the truth tables for the logic gates exclusive or (XOR) and not exclusive or (XNOR). White is self-referential (itself compared with itself outputs itself) in one and black in the other.

We incorrectly count each distinct object once only, in respect of what it is, because we assume erroneously that we can use either one of these two mutually exclusive ways of drawing distinctions without also using the other. This allows us to perform computation on the principle of equations and balance. For example, 1 is the same as 1, they balance, so 1-1 = 0.

Chiralkine counting treats a distinct object as a relationship between what it 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. According to this principle, the meanings of what it is and what it is not are exchanged as between the logic of XOR and XNOR, so the “not” side of a relationship that means uncountable nothing (same) in one logic means countable (distinct) in the other. Me, not you and you, not me mean opposite things to each of us in our relationship as writer and reader.

When a distinct object is counted, the distinction defining the relationship between what it is and what it is not is cleared and another distinction is drawn creating 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. Each of the four mirror opposite columns in the respective truth tables defines a relationship between what one of four objects is and what it is not. There are six possible ways of ordering four objects, which is why chiralkine counting works in a six-step cycle.

The permutation of four ordered objects, each defined by a relationship between what it is and what it is not, 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. The four black corners and four white corners define chiral tetrahedrons of opposite sense (handedness). The name chiralkine was selected to allude to this handed (chiral) movement (kinetics).

What appears to be the last of four ordered objects coding a cube face and generated by the controlling logic is actually related to the first object as not to is. There is duplication, which comes fundamentally from the way in which logic is controlled by chirality.

What appears to be a mirror pair of quaternions a,b,c,d generated simply by using XOR and XNOR symmetrically to draw a distinction between what is and what is not a countable object is actually a mirror pair of strings of six ordered objects, two of which are hidden. These mirror pairs of strings simply slide along through the cycle each time a counting step is performed.

The creation of countable money (+1) and debt (-1) out of uncountable balance (0) and independent return of countable (+1) and (-1) to uncountable balance (0) by spending the money and clearing the debt respectively is not possible in chiralkine counting. It takes three steps to switch between the countable (is) and uncountable (is not) sides of a relationship defining a countable object, which steps are controlled from both sides of the relationship, such that one side cannot complete the three steps without the other doing so as well.