Chiralkine is a way of counting that works on a new principle, not balance and equations. It treats the two sides of a relationship defining a countable object as mirror opposites, symmetrically. Each side is defined by self reference (itself compared with itself is itself, not its mirror opposite); the way that people identify one another as me and you.
It treats the two sides of the relationship symmetrically by using dual, mirror opposite logic to draw and clear distinctions in the relationships defining objects. Each time an object is counted, the distinction between “is” and “not” defining the object is cleared and another distinction between “not” and “is” is drawn recording the counting of the object. This dual logic defines an oscillation. It controls the counting process such that the two sides are confined to rotation in opposition through a six-membered cycle. In this cycle, “is” is turned by “not” into “is” and “not” is turned by “is” into “not”.
The dual logic changes the relative order of the “is” and “not”, which further draws a distinction between each of the three “is” and “not” in the cycle.
This reordering under the control of the dual logic is such that the six states behave like opponent colours. The cycle can therefore be represented by a colour wheel in which any two opposed members are related as additive to subtractive colours. Each colour in a pair is itself, not its counterpart. Each counting step in accordance with the oscillating logic permutes the “is”s and “not”s, such that a new colour pair is formed.

For example, when four objects defined by the relationship between yellow and blue are counted, the distinction between yellow and blue is erased and the count is recorded by drawing a distinction between red and cyan. Counting again erases the distinction between red and cyan and creates a distinction between magenta and green. The cycle inverts after three steps and repeats after six steps.
Counting three times through a chiralkine counting cycle provides closure, because compared with the original arrangement it superposes all three of the “me” and “you” pairs that define each “me” and “you” symmetrically, restoring symmetry that has been broken during the transition states. This inversion in three steps is inherent in the way that meaning for symbols is constructed logically by treating them as outputs of comparisons between two input symbols.
An object that appears as mine, not yours to me and not mine, yours to you can be exchanged in three counting steps for an object that appears as mine, not yours to you and not mine, yours to me. The counting steps can couple the two transfers of the exchange together.
Chiralkine counting thus provides a new kind of book keeping (accounting).
Chiralkine counting can be used to perform mathematical calculations without privileging one side of a relationship over the other. The relational states take the place of positive and negative real and imaginary numbers used in equation-based computation. Performing calculations using the dual numbers produced by counting in this way ensures that whatever is done for one side of any relationship is also done for the other. A new economic system could be constructed based on using these calculations which would treat human to human relationships and mankind’s relationship with the environment symmetrically.
The chiralkine project was conceived and has always been intended to be a social enterprise, to make people’s lives better. The inventor, Martin A. Hay, can be contacted by email: martin@chiralkine.com.