A chiralkine cycle can be defined by a ring aBcAbC where each lower case letter is a kind of 0 and each upper case letter is a kind of 1 such that the ring consists of an oscillation between 0s and 1s. The ring pairs with its own mirror image (AbCaBc), which corresponds with rotation of the ring through 180 degrees. Hence the ring is 01010 and pairs with its own mirror image 101010.
Viewed from this perspective, 0s are separated one from another by 1s and 1s are separated one from another by 0s. They are mutually exclusive – they cannot sit side by side as in 00 or 11 wherein they appear to be separated by other than a 1 or a 0.
However, two rings can also rotate relative to one another, there being six possible relative positions of the two rings.
Each ring pair itself pairs with its own mirror image, which corresponds with rotation of the ring pair through 180 degrees. There are four couplings in which the kinds of letters are mixed up in their pairings (e.g. a pairs with b or with c) and two in which the kinds of the letters are not mixed up in their pairings.
In a cycle through all the possible pairings, there is an oscillation between the case where 1s and 0s are mutually exclusive and do not sit next to one another (as in 01 and 10) and the case where 1s and 0s do sit together (as in 00 and 11).
We have noted above that two chiralkine rings can simply overlie one another as in 2aBcAbC, wherein each ring pairs with its own mirror image as in 2AbCaBc. Now note that when two rings and their partners are rotated half way through a cycle (generating the pairings 00 and 11), we still have 2aBcAbC and 2AbCaBc, but the partners have been swapped. This lies at the very heart of how a chiralkine system works. Through relative rotation of the rings, you can switch between 01 and 10 pairings and 00 and 11 pairings, with the three different kinds of letter (aA, bB, cC) constraining this to take place in three steps.
To understand the deep significance of this, you need to recall how zero (nothing) is defined in conventional mathematics and how equations work. Zero is defined as the difference between two objects that are the same, as in 00 and 11 – balance. When the two are distinct, as in 01 and 10, they are treated as being countable. Hence if 01 is +1 and 10 is -1, 01 plus 10 is 11, which is zero (balance). The order in which the two signed integers interact does not matter – the system is commutative. Chiralkine is non-commutative. One order generates 11, but reversing the order generates the mirror image 00.
So chiralkine provides a mechanism for interconverting between the pairing 01 and 10, where there is a distinction, and the pairing 00 and 11, where there is no distinction.
Suppose we are in an economic relationship where you want peas but have carrots and I want carrots but want peas. Two objects are involved – peas and carrots, and two distinctions (between what each of us wants and what each of us offers). We are both in the mirror pairings 01 and 10. If we exchange the objects, we now each have what we want. We are both in the mirror pairings 00 and 11. In a chiralkine system we together started and ended with 2aBcAbC and 2AbCaBc, but the partners were swapped. Throughout the process, the quantity of distinctions was conserved, but locally it appeared that a distinction (that between offer and want) was erased.
Chiralkine provides a mechanism for clearing offers and wants in an economy. It will release a lot of energy as these are cleared, like a battery being short-circuited, and requires new local distinctions between offers and wants to emerge in order for economic activity to be sustained. The energy being released can be exploited, like a light bulb being inserted between the two terminals of the battery, through an equivalent of taxation. The potential inherent in the local distinction between offers and wants can be made to do useful work – benefit not just those whose wants are being satisfied through exchange of what they have to offer for what they want.
We count distinct objects – 1, 2, 3, 4, etc. We imagine that when an object has been counted it has switched from one of two mutually exclusive states (uncounted) to the other (counted) – like we imagine a sheep moved from one field to another.
What we are imagining is not all that is going on! The problem lies not in the act of counting 1, 2, 3, 4, etc., but in the mathematical system we have constructed so as to fit with what we are imagining is going on (equations).
A distinct object, such as a sheep, is one side of a mirror symmetric distinction that emerges when a distinction is being drawn. Both sides of that distinction switch when the object is counted. The “object” is in both sides of the distinction – uncounted and counted. When it is counted, it switches from 01 to 00 in the uncounted state and from 00 to 01 in the counted state. But there is even more than that going on than that, because the system is mirror symmetric. Three coupled steps are required to clear the distinction that defined an object in the uncounted state and now define an object in the counted state – from aA/Aa to aa/AA in the uncounted state and from aa/AA to aA/Aa in the counted state.
It is counter intuitive to think in this way – to imagine that an object is in two places at once. It is how we explain how things behave at a quantum level, in the world of qubits, but not at a macroscopic level. Well, if you apply mirror symmetry to the everyday macroscopic world we live in, it does work and it does explain why the quantitative systems we have constructed using conventional mathematics (equations and double entry bookkeeping) to process information about our economic relationships keep failing. We are each of us a bilaterally symmetric life form – one unitary life consisting paradoxically of two mutually exclusive yet interconnected left and right sides – and we should be using mirror symmetric mathematics that connect our interests together through coupled rotations.