Chiralkine Systems


A chiralkine system is a new, experimental technology that codes and processes information about economic relationships between people and resources (exchange, taxation and voting) relativistically. It links the interests of people together in a reciprocal manner, without privileging one side of a relationship over the other. It achieves this by using mirror opposite symbolic logic to handle the two sides of a relationship.

The system we all use today for exchange, taxation and voting uses the same symbolic logic (- means same and + means different) to handle both sides of a relationship. It works on the principle of a balance (-1 + 1 = 0 = +1 -1). 

A chiralkine system codes and processes information about relationships using mirror opposite logic for the two sides (- means same and + means different for one side and + means same and – means different for the other side). It works on the principle of order (yellow, blue, green).The two sides are related as the mirror opposite logic gates XOR and XNOR.

Chiralkine systems have been developed with the objective of finding a solution to the problem of rising inequality and trade imbalances. It is believed that these will turn out to be side-effects of coding both sides of a relationship using the same logic. When the same logic is used to code both sides, one side can end up being privileged over the other, so that interactions intended to be reciprocal are actually not. Voting can produce outcomes that are not representative of voter’s views.

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In our economy we identify ourselves and our resources in words and then use a simple mathematical equation, +1 -1 = 0, to code and process information about the changing relationships between them.

When we express ideas in words, we combine them in an order characteristic of our language:

I (subject), own (verb) bread (object): my viewpoint

You (subject), own (verb) bread (object): your viewpoint


There are six different ways in which subject, verb and object can be combined, and our different languages collectively use all six. However, the mathematical equation that we use to process economic relationships works on the principle of a balance, not order.

-1 +1  = 0

 +1 -1= 0

arithmetic in chiralkine numbers

Underlying the equation of a balance (-1 + 1 = 0 = +1 -1) is a simple logic that can be expressed in two symbols, + and -. The two symbols always have the same meaning: + means different and – means same. It follows that + compared with – is + and – compared with + is also +. However – compared with – is – and  so is + compared with +. This is why we cancel down (+ +)  to (- -). We count the + symbols, but not the – symbols, so +1 (- +) add +1 (- +) is +2 (- 2+); -1 (+ -) add -1 (+ -) is -2 (2+ -) and +1 (+ -) add -1 (- +) is (+ +), which we cancel down to 0 (- -). 0 (- -) add +1 (- +) is +1 (- +) and 0 (- -) add -1 (+ -) is -1 (+ -). Numbers of the same kind stack up on one another, so that they can be counted, but numbers of different kinds change one another: + turns + into – and turns – into +;  – turns – into – and + into +. +1 (- +) turns 0 (- -) into +1 (- +). -1 (+ -) turns 0 (- -) into (+ -). +1 (- +) turns -1 (+ -) into (+ +) which cancels down to 0 (- -). Notice how this works just like language: subject, verb and object: one thing turns a second thing into a third thing.

Processing information based on the principle of a balance filters out information content encoded in a particular order. It is the negation of +1 and -1 to a single zero that does this. As a consequence, the two sides of a relationship are treated asymmetrically. Over time, the effects of repeatedly doing this accumulate, widening inequality.

Chiralkine systems code and process information about the changing relationships between words that identify people and resources based on the principle of order, not a balance. They track each relationship from both sides through ordered steps using a code consisting of 2+ and 2- in order.

The diagram below illustrates this. It shows steps in the transfer of ownership of bread from one person to another in a cycle of exchange controlled by a chiralkine system. The system couples these steps in the transfer of the bread to steps in the transfers of other things and so links the interests of all its users together. The system ensures reciprocal exchange.

transfer in words, colour and quaternion units

Underlying this is a symbolic logic that treats the two sides of a relationship (e.g. bread seller and bread buyer) in mirror opposite ways.

Side 1                                                                            Side 2

+ turns + into –                                                           – turns – into +

+ turns – into +                                                           – turns + into –

– turns – into –                                                             + turns + into +

– turns + into +                                                           + turns – into -.

These eight statements form six columns of four symbols, each consisting of two + and two -. The order in which the statements are made does not matter, provided that they are kept in mirror opposite pairs. There are 4 x 3 x 2 x 1 = 24 permutations for the statements. In all statements on the left, there is always one column containing three +, while on the other side there is always one column containing three –. The 24 permutations of numbers sort into six sets of four: six being the number of permutations of subject, object and verb!

When the permutations are analysed together, it is apparent that the eight statements can be condensed down to six:

Side 1                                                                              Side 2

(+ -) turns (- -) into (+ -)                                           (- +) turns (+ +) into (- +)

(- +) turns (- -) into (- +)                                           (+ -) turns (+ +) into (+ -)

(- +) turns (+ -) into (+ +)                                        (+ -) turns (- +) into (- -)

Chiralkine systems are based on the principle of chirality, which is a fundamental symmetry in nature that arises when two seemingly identical objects can have two different forms due to the two different orders in which their components can be arranged. The chemistry of life is encoded in molecules of one chirality, not the other. Why this should be is a problem engaging the interest of scientists. It is the symmetry that distinguishes the left from the right hands. The thumb, first finger and second finger can be ordered either clockwise or anticlockwise relative to the wrist. In abstract, the two chiral forms are related as two chiral tetrahedrons as shown below.


This website contains detailed descriptions of what a chiralkine system is, how it works, why it is worth developing, and how it is connected with the symmetry properties of space and the chemistry of life.