Chiralkine is a way for performing computation that works on the principle of mirror symmetry instead of balance.
Computation performed on the principle of balance (equations) treats the two sides of a relationship asymmetrically. This is especially undesirable when it is being used to process quantitative information about relationships between people, because users can perceive that they are being treated asymmetrically, alienating them from systems that everyone needs to rely upon, for example the financial system (money and debt) and democratic decision making. Chiralkine was invented and is being developed to address this problem inherent in equation-based mathematics. It is applicable across all disciplines, including science and technology.
There are many ways to teach what chiralkine is and how it works, but one way is to start with the concept of an object, because mathematics constructed on the principle of balance treats as countable an object identified as being distinct (1), as opposed to the same (0). We count 1s, but not 0s.
In chiralkine, an object is a mirror symmetric relationship maintained between two sides, 1 and 0. Think of the relationship as a coin being held up in front of a mirror so that the two sides are separated. One side is observed directly and the other in the mirror. The two sides cannot occupy the same space – be observed as one. They are distinct.
However, the two mutually exclusive sides are also the same, because they are one and the same relationship. There is more going on.
The reason is inherent in the mirror symmetry that defines the relationship. Respecting mirror symmetry prevents us from identifying each of the two sides of the relationship absolutely – the way we identify the two sides of a coin when we label them head and tail. The analogy with a coin can only be taken so far. Each side of a mirror symmetric distinction must identify with itself as itself (0 must identify with 0 as 0 and 1 must identify with 1 as 1), and each opponent must identify with its opponent as its opponent (0 must identify with 1 as 1 and 1 must identify with 0 as 0). The identities are defined by triplets.
Respecting mirror symmetry mandates that the 1s and 0s, while appearing locally to be distinct, must couple in mirror opposite triplet pairs such that they transform together as one and the same global relationship.
While an object is being observed (having its two sides maintained as mirror symmetric opponents), a mirror symmetric distinction is in the process of being drawn (incompletely separating 00 and 11 into 01 and 10) and another is in the process of being cleared (incompletely separating 01 and 10 into 00 and 11). While one oppositional pair defining an object is observable, two others are not. The “object” is acting as a pivot for the other two to change about. What is being observed is not one half, but one sixth of what is going on!
There are only six (3!) ways of ordering four objects in rings. Hence there are six ways of generating outputs (1 or 0) from four pairs of inputs (00, 11, 01 and 10) such that mirror symmetry is conserved. The simple arithmetic steps of addition and subtraction used in equation-based mathematics, which steps can easily be handled using ordered pairs of numbers as in double entry bookkeeping, are not compatible with mirror symmetry. When you treat 1 and 0 as mirror symmetric sides of a distinction, you cannot treat counting simply as subtraction from one quantity and addition to another, because the two mutually exclusive sides of a distinction, 1 and 0, are interconnected. What is being treated as an absolute distinct and hence countable object 1 (like the absolute head or tail of a coin) is one side of a mirror symmetric relationship between 1 and 0, which relationship is such that the 1 is actually one sixth of the system. Counting is a three-step process, which steps are neither subtraction nor addition – they have no arithmetic counterparts. Quantity is conserved throughout these three steps, just as it is using equation-based mathematics, but so is the mirror symmetry of the underlying relationships – neither side is privileged over the other.