What Is Chiralkine?
Chiralkine is a new method for performing computation that works on the principle of mirror symmetry (chirality) instead of balance alone. Its purpose is to protect relationships from the growth of asymmetries caused by treating 1 and 0 asymmetrically in computation about them.
Relationships between objects have two sides. For example there is a relationship between me the writer and you the reader. Each of us identifies with one side of the writer/reader relationship. What chiralkine does is to recognise not only that a relationship between two objects has two sides, one for each object, but also that each object itself is defined by a relationship having two sides. It treats all of these relationships mirror symmetrically – in accordance with the principle of chirality.
Chiral objects, such as the left and right hands, are superposable on themselves, but not on their mirror images. They are mutually exclusive. They are defined relationally by what they are and are not. Each identifies with itself as itself and not with its mirror image – like me and you from our respective viewpoints.
Chiralkine treats an object not as a fixed identity, but as a mirror symmetrical relationship – a distinction between what it is (a) and what it is not (A) – a pair (a, A). The pair members are related as the two local sides of one global object, one side of which is seen reflected in a mirror. Each of 1 and 0 is thus treated as one of the two local sides of one global object.
A mirror exchanges front and back, but not order. For example if the right hand is positioned with the thumb, first finger and second finger pointing in clockwise order away from you towards a mirror and the wrist towards you away from the mirror, the three digits in the mirror reflection also point in clockwise order, but towards you, while the wrist points away. Chiralkine treats the relationship between 0 and 1 as that between a hand and its mirror reflection, so 0110 reflected in a mirror is 1001 and the two together form a mirror pair.
As in language where meaning emerges from the order of letters in words and sentences, meaning emerges from the outputs produced when 1s and 0s are compared in different orders. The interactions between them are redrawings of distinctions – from one pair, (a, A), defined by one mirror pair of ordering of 1s and 0s (e.g. 0110, 1001) to another, (B, b), defined by another mirror pair of ordering of 1s and 0s (e.g. 0011, 1100).
The ordered 1s and 0s in each mirror pair have mirror opposite meanings. Neither is privileged over the other. By conserving mirror symmetry in the treatment of 1s and 0s during computation about relationships, balance is inherently conserved, but without privileging one side of any relationship over the other.
The Problem With Balance
Traditional computation is based on equations, which follow the principle of balance. In this view:
- An object (a) is treated as absolute, not relational.
- The difference between two identical objects (a and a) is considered to be nothing (0).
- Truth tables treat 1 and 0 as fixed meanings: true/false, countable/not countable.
This principle does not conserve symmetry. Instead, it erases the distinctions that define meaning.
By contrast, chiralkine maintains the distinction between both sides. Whatever happens to one side of a relationship must also happen to its mirror opposite. The difference between two objects is two objects, not zero, because each is defined in relation to its opposite.
A Finite Set of Meaningful Distinctions
In mathematics and logic, all meanings assigned to 1 and 0 arise from comparisons between the two symbols. There are four such comparisons:
- 00
- 11
- 01
- 10
These comparisons form the truth tables that underpin all logic gates.
But chiralkine takes these further by treating each pair as a symmetrical relationship, not an absolute value.
An object is a chiral, kinetic relationship. The relationship is being constructed dynamically by drawing a distinction between two mirror opposite sides (1 and 0). Each side self-identifies with itself as itself and with its mirror opposite as not itself, like me and you in our relationship. So 1 identifies with 1 as 1 and with 0 as 0 (truth table for XNOR) and 0 identifies with 0 as 0 and with 1 as 1 (truth table for XOR).
The Symmetry of Four Ordered Objects
Chiralkine builds on a well-known property of four-object systems:
- Four objects (a, b, c, d) can be ordered in 3D space in two mirror-opposite (chiral) ways — like your left and right hands.
- These arrangements form a group of Order 4.
- This group has six generators (unique relational orderings).
What chiralkine newly contributes is this: it treats each object as a pair of opposites – e.g. (a, A), (b, B), (c, C), (d, D). This constrains the system to rotate through three relational states, as each distinction is cleared and another drawn.
From Distinctions to Cycles
When we replace each lower-case letter with 0, and each upper-case letter with 1 – but code each ring as if the letters remain in alphabetical order – we reveal the hidden cycle.
This cycle is universal. It applies across logic, computation, matter, and meaning – but has remained hidden because our systems rely on balance, which treats only one side (a) of a distinction (a, A) as meaningful.
Whereas counting is a two step process when performed on the principle of balance: (uncounted set: 1 – 1 = 0, counted set: 0 + 1 = 1), it is a three step process when performed relationally: (1a → 1B → 1c → 1A when 1A → 1b → 1C → 1a), which ensures that the symmetry of any relationship defined by 1a, 1A (for intuition, think for example of a creditor, debtor relationship) is conserved.
What Happens When Symmetry Is Lost?
A chiralkined system is inherently relationally balanced. But when processed using the principle of equation-based balance, relational symmetry is lost. This leads to the emergence of otherwise inexplicable imbalances – in logic, in economics, and in physical systems.
Why Rechiralkining Matters
To restore these lost relationships, a system must be rechiralkined – not merely rebalanced. Rebalancing erases distinctions. Rechiralkining redraws them.
The Chiralkine Project
The chiralkine project was conceived – and has always been intended – as a social enterprise: a tool to make people’s lives better by restoring relational meaning to the systems we rely on.
Contact: Martin A. Hay
📧 martin@chiralkine.com 👉 Explore the rest of the site to see how chiralkine logic applies to physics, economics, computing, and more.