“The whole is not equal to the sum of its parts”.

What Is Chiralkine?

Chiralkine is a new method for performing computation in ordered 1s and 0s that works on the principle of bilateral symmetry – the symmetry of the human body – instead of balance and equations. We perceive the body as being bisected into two mirror opposite (mutually exclusive) sides by an imaginary plane of symmetry. Perpendicular to the plane the two sides are inverted, but parallel to the plane their order is conserved. Chiralkine exploits this symmetry. It works in two mutually exclusive (as in 1 and 0 or a and A), yet commonly ordered (as in 010 and 101 or aBc and AbC) sides, such that as a whole it is not equal to the sum of its parts. These mirror-opposite sides are called chiralkines. They are the fundamental elements of a distinction being drawn and the building blocks from which chiralkine systems are constructed.

The human body has a right side and a left side, which are mutually exclusive. They are separated by a plane of symmetry. When the right side is in mind, the left is not and when the left is in mind, the right is not. However, they are connected in one body.

Chiralkine treats all objects (including 1 and 0 as well as numbers – countable quantities) as mirror opposite sides of bilateral relationships. Whatever an object is, the same mechanism is being used to draw the distinction that is constructing it.

A person is shown with space blanked out and space with the person blanked out. Similarly 1 is shown with 0 blanked out and 0 with 1 blanked out. Each pair member is NOT the other. The elements of abstract thought – the abstract concepts of 1 and 0 in mathematics and logic – are coordinated like the left and right sides of a moving human body.

The purpose of chiralkine is to protect systems from the growth of asymmetries that can be caused by computation treating 1 and 0 asymmetrically when it is being performed on the principle of balance and equations. The build up of these asymmetries can cause inequality and system failure, for example trade imbalances, financial crashes and flawed democratic decision making.

Chiralkine achieves its purpose through a new way of ordering 1s and 0s in cycles so that together they behave as the mirror opposite left and right sides of a bilaterally symmetric body – mutually exclusive and yet dynamically interconnected.

An object is observed (emerges) when a mirror-symmetric (chiral) distinction is being drawn. (Think of a rainbow as an object being observed when a distinction is being drawn between different colours in sunlight). This unconscious act of drawing a distinction synchronises in time (past, present and future) the separation of what an object was (A), is (B) and will be (C) from what it was not (a), is not (b) and will not be (c).

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 (A), first finger (B) and second finger (C) 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 (a, b, c), 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:

In chiralkine these pairings emerge from symmetry breaking when a distinction is being drawn.

These comparisons form the truth tables that underpin all logic gates. Each truth table contains four columns (one for each of 00, 11, 01 and 10 as input pairs) and three rows (one for each input and one for an output): 4 x 3.

But chiralkine takes these further by treating each pair as a symmetrical relationship, not an absolute value. The truth tables lie on a mirror plane, such that each 1 on one side is perpendicular to a 0 on the other, but the order of the 1s and 0s in the rows and columns parallel to the plane is conserved. This means that whatever happens on one side also happens mirror opposite on the other.

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).

It is known that the six truth tables form into three mirror opposite pairs, such that the the four input pairings give mirror opposite outputs. What chiralkine does is to lock not only the outputs, but also the inputs into mirror pairs, because that is fundamentally how the distinction that separates 1 and 0 is being drawn.

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.

Hidden in plain sight in the cube is a regular skew hexagon defined by the corners a, B, c, A, b, C. This possesses three planes of symmetry. This provides chiralkine’s mechanism for drawing a mirror symmetric distinction between 1 and 0, and for ordering 1s and 0s in a new way that models the bilateral symmetry of the human body (separate, yet dynamically connected).

Breaking the symmetry across the mirror plane duplicates the points in the skew hexagon where the plane crosses, creating two mirror opposite 4 x 3 forms (enantiomers).

A skew hexagon is mirror symmetric across each plane of symmetry, but the identifiers (letters/colours) across these planes are not. The order around the ring is a, B, c, A, b, C, so when the mirror plane crosses through a and A, the letter B is opposed to c and the letter b is opposed to C. This inversion of order, which takes place for each mirror plane, is responsible for the dynamic mechanism that maintains the integrity of the system. It is hidden in plain sight, because the duplication that takes place while a distinction is being drawn is treated as if it is generating a fourth oppositional pair (d,D). For example, when a distinction is being drawn across (a, A), the resultant chains (a, B, c, A) and (a, C, b, A) present as mirror opposites (a, B, c, D) and (A, b, C, d).

In the skew hexagon, each of A, a, B, b, C and c is indistinguishable as one of the six corners and each of the connecting sides is indistinguishable as one of the six connecting sides. They form a ring. When the symmetry is broken as a distinction is being drawn, the duplicated end letters become distinguishable from those they are connected to, but there are still two pairs of three connecting sides. In the same way, the symmetry of the mirror-opposite XOR and XNOR truth tables interpenetrating in rings is broken. Hidden in plain sight is the mechanism that connects the input 1 and output rows at the ends into a six-membered rings.

This symmetry breaking is fundamental not only to how a chiralkine system works, but also to the construction of meaning. Without the symmetry breaking, the corners and sides of the skew hexagon would simply be related as each is not the other. The symmetry breaking gives rise to the truth tables for the six logic gates (AND, OR, NAND, NOR, XOR and XNOR) and for the fundamental distinction between self and not self – self reference – (0 turns 0 into 0 as in XOR and 1 turns 1 into 1 as in XNOR).

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.

The column tracking D and d is a duplication created when a distinction is being drawn. It is the blanked out area shown in the drawings at the start of this document. It anticipates the next colour in the six-membered cycle. The “excluded middle” that appears to separate a person’s right from left, the person from space and 1 from 0 is being generated by duplication. The two relational sides of each distinction remain connected by the dynamic mechanism through which the distinction is being drawn. This website explains how it works and why it matters.

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. Instead of 1 and 0 being exchanged in a two step counting process, opponent colours are exchanged in a three step counting process. Each countable unit in a quantity is a relational pair of chiralkines that loses and regains an individual identity over this three step process. Absolute objects do not move from an uncounted to a counted set during a counting process (the arithmetic steps of subtraction and addition) – the system defined by a quantity transforms relationally (for intuition, think that when a mortgage creates credit and debt so that one person can “buy” a house off another, the counting process is not completed (remains asymmetric) until the house “buyer” has paid off the debt AND the house “seller” has paid off the credit). Because a quantity is a relational object, it transforms as such during counting, for example when five sheep are being counted – 1, 2, 3, 4, 5 – the relational object that is the quantity five is conserved whether none, all five or three of the five sheep have so far been counted. Think of the quantity of the completed count being light, the frequency of which is proportional to its energy. Although the energy of light of frequency 2 and the energy of light of frequency 3 is the energy of frequency five (2 + 3 = 5), light of frequency 2 and light of frequency 3 do not sum to light of frequency 5 (2 + 3 ≠ 5). For example, if relationally counted 3 (a ring of 3) is green, and relationally counted 5 is red, then when 3 is reached during a count up to five, the colour is purple (a mixture of colours). Light intensity (quantity) builds up by stacking perpendicular to the mirror plane, but colour changes relationally through changing order parallel to the plane. Stacked 1s and 0s are permuted during the counting process, conserving order on both sides of the plane of symmetry, until counting is complete. There are always two complementary colours, one of which is perceived. Such is not the case when the house “buyer” has paid off the debt, but the house “seller” has not paid off the credit – there is an asymmetry in the accounting system, even though it is operating on the principle of balance.

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.

A New Way To Perform Computation