Two objects are said to be coupled when they interact with one another. For example, two astronomical bodies, such as the earth and moon, can be coupled by gravity. Chiralkine counting can couple two or more objects together mathematically.

Chiralkine counting treats an object as a relationship that draws a distinction between what it is and what it is not. When an object is counted that distinction is erased and another is drawn. What an object is and what it is not are counted at the same time.

Chiralkine counting works in dual numbers that cycle through three mirror pairs.

For example, a sheep is defined by a relationship between what it is (a) and what it is not (a). Counting the sheep through a cycle maintains a mirror relationship between the two letter symbols of opposite kinds (a, a; b, b; c, c, etc).

To understand how chiralkine counting can couple two or more objects together mathematically, consider a sheep and a wolf. In chiralkine counting, the sheep is treated as a relationship between what it is (a) and what it is not (a) and the wolf is also treated as a relationship between what it is (a) and what it is not (a). Instead of counting each separately, what the sheep is (a) and what the wolf is not (a) can be counted at the same time, to afford sheep (b, b) and wolf (b, b) chimeras. Each of the sheep and wolf chimeras can then independently form chimeras with other objects, for example a mouse (a, a) and a cat (a, a). By this time, there is now a chain of four objects coupled together. The sheep is now in state (c, c) and so is the wolf.

Now we have a chain with a mouse at one end and a cat at the other. Suppose now that the cat catches the mouse to form a ring. We count what the mouse is not (b) and what the cat is (b). Forming the ring changes the relationships between all four objects, like forming an electrical circuit. Each of the four objects in the ring is now in state (c, c). We can now break the couplings by counting again, placing each object in state (a, a).

So, chiralkine counting can couple objects mathematically in a chain and in a ring.

One very powerful application is in providing a solution alternative to money for solving the double coincidence of wants problem inherent in barter.

Consider two owners of animals: one who owns a sheep, but wants a wolf and the other who owns a wolf but wants a sheep. The two can barter, so that the sheep owner now owns the wolf and the wolf owner now owns the sheep. To the sheep owner, the sheep is in state (a, a): mine, not yours and the wolf is in state (a, a), not mine, yours. To the wolf owner, the wolf is in state (a, a): mine, not yours and the sheep is in state (a, a), not mine, yours. Performing the barter inverts all these relationships. It is performed in a sequence of counting steps. First we couple the sheep and the wolf into a chain. Next we couple them into a ring. Finally we break the couplings such that the sheep now belongs to the original wolf owner and the wolf now belongs to the original sheep owner.

The process can be applied to any quantity of objects: first form a chain, then join the ends to form a ring and finally decouple the objects so that each owner ends up owning what they wanted.

Each economic agent is like a battery, and when a ring is formed, an “electric current” can flow. The “battery” is a source of potential energy – a mismatch between each economic agent’s offers and wants – that is presently exploited to do work by the financial service industry, through charging fees and interest, and governments, through charging tax – to permit clearing of offers and wants. There is more than just an analogy here: there is a blueprint for a new way to model and possibly even construct an economy.