The Third Power

The I Ching is not a fortune-telling device. It is the oldest surviving intellectual framework for understanding change.

Its origins stretch back more than three thousand years to the Western Zhou dynasty, though the system of solid and broken lines may be older still. The title itself is often translated as "The Book of Changes," but the Chinese character Yi carries a richer meaning: change that is simultaneously constant and patterned, transformation that follows discernible laws.

As the philosopher Robin Wang writes, the I Ching represents an "organismic process without beginning or end, characterized by continuity, wholeness, and dynamism." It does not divide the world into fixed categories. It maps the patterns through which one state transforms into another — the way winter becomes spring, the way crisis gives way to opportunity, the way a relationship moves through phases of intimacy and distance.

The system's genius lies in its simplicity. Everything begins with a single distinction: a solid line and a broken line.

The solid line represents yang — the active, the initiating, the expansive. The broken line represents yin — the receptive, the completing, the contracting. But this is not a story about opposites. It is a story about complementary forces that define each other, require each other, and transform into each other in an endless dance.

The yin-yang symbol — the taijitu — captures this dynamic perfectly. It is not a pie chart divided neatly in half. It is two fish-shaped forms, each containing the eye of the other, swirling in perpetual rotation. At the fullest expression of yin, the seed of yang appears. At the height of yang, yin is already emerging. The symbol is not static. It is a snapshot of a process in motion.

The trigrams describe eight fundamental states of being. But reality is not static — it is relational. Things don't just exist; they encounter each other, interact, and transform through contact. The I Ching captures this by combining two trigrams into a hexagram — a six-line figure that represents one trigram's quality meeting another's.

The lower trigram represents the inner world: your disposition, your question, your internal state. The upper trigram represents the outer world: the situation, the environment, the forces acting upon you. A hexagram is a conversation between self and circumstance.

Eight trigrams combining with eight trigrams produces sixty-four hexagrams: 8 × 8 = 64. Mathematically, this is identical to saying that six binary choices yield sixty-four outcomes: 2⁶ = 64. Both descriptions are correct, and both reveal something important about the system's structure.

Each hexagram carries a name, an image, and a judgment — an interpretation of what happens when these two forces meet in this particular configuration. Hexagram 1, Qian, is pure creative force: Heaven above and Heaven below, yang at every position. Hexagram 2, Kun, is pure receptive power: Earth above and Earth below, yin throughout. Between these two poles lie sixty-two hexagrams that describe every shade of interaction between active and receptive, initiative and response, doing and being.

Significantly, the I Ching ends not with completion but with incompletion. Hexagram 63, Ji Ji ("Already Fulfilled"), gives way to Hexagram 64, Wei Ji ("Not Yet Fulfilled"). The message is deliberate: the process of transformation never concludes. Even at the end, a new beginning stirs.

In the spring of 1703, a letter arrived in Hanover, Germany, that would change the history of ideas. It had traveled for eighteen months from Beijing, carried by merchant ships and overland couriers, written by a Jesuit missionary named Joachim Bouvet. Inside was a diagram of the sixty-four hexagrams arranged in a sequence attributed to the legendary Emperor Fu Xi.

The letter's recipient, Gottfried Wilhelm Leibniz, had been waiting for something like this — though he did not know exactly what form it would take. Twenty-four years earlier, in 1679, Leibniz had completed a manuscript called De Progressione Dyadica, laying out the principles of binary arithmetic: a system for representing any number using only 0 and 1.

When Leibniz saw Bouvet's diagram, he recognized his own invention staring back at him across three thousand years and six thousand miles. The hexagram sequence, reading broken lines as 0 and solid lines as 1, perfectly reproduced the binary counting sequence from 0 through 63.

Scholars Lloyd Strickland and Harry Lewis have carefully documented this exchange. The key point, as they emphasize, is that Leibniz did not derive binary from the I Ching. He had independently developed his system more than two decades before he ever saw a hexagram arrangement. What the I Ching gave him was something different: confidence. He had hesitated to publish his binary work, uncertain of its practical value. The hexagram correspondence convinced him that binary was not merely an intellectual curiosity but a structure woven into the fabric of reality itself.

Leibniz published his "Explication de l'Arithmétique binaire" in 1703, the same year he received Bouvet's letter. In it, he framed binary as a reflection of divine creation: all numbers emerging from 1 and 0, mirroring God's creation of everything from unity and nothing.

This is the first documented instance of convergent discovery between the I Ching and Western mathematics. It would not be the last.

The I Ching's influence in the twentieth century extended well beyond mathematics. Carl Jung found in it a framework for his theory of synchronicity. Fritjof Capra's The Tao of Physics drew explicit parallels between Eastern philosophy and modern physics. Niels Bohr, when knighted by the Danish crown in 1947, chose the yin-yang symbol for his coat of arms, pairing it with the Latin motto Contraria sunt complementa — "Opposites are complementary" — connecting the ancient Chinese concept directly to his principle of complementarity in quantum mechanics.

These are not casual borrowings. They represent a pattern — a recurring recognition by independent minds that the I Ching's binary framework captures something genuine about the structure of reality. What no one had done, until now, was identify the specific mathematical relationship that makes these convergences possible.

That is the work of Part Two.

Here is something that should stop you in your tracks.

The number 8, written as a numeral, is two circles stacked vertically. Now rotate it ninety degrees. What do you see?

The infinity symbol. ∞.

The Third Power — the cube, the eight trigrams, the byte — and infinity are the same figure, viewed from different angles. The finite number of complete states (eight) and the infinite expanse of possibility (∞) are not opposites. They are perspectives on the same structure.

This is not a proof of anything. It is an invitation to wonder. But it is a remarkably precise invitation. The lemniscate — the mathematical name for the infinity symbol — was introduced by John Wallis in 1655, likely derived from the Roman numeral for 1,000 (CƖƆ), which itself evolved from the Etruscan character for an uncountably large number. Neither Wallis nor the Etruscans nor the Chinese sages who developed the eight trigrams were thinking about each other. Yet the same visual form connects them all: a continuous curve that crosses itself, containing two lobes in eternal exchange.

Like yin and yang.

Now consider this: the number sixty-four does not appear only in the I Ching. It appears independently in two other systems — one biological, one technological — through the same mathematical path.

Imagine a coin spinning on a tabletop.

While it spins, the coin is neither heads nor tails. It contains both possibilities simultaneously, held in suspension by its own motion. You can see both faces flickering as it rotates — not one or the other, but a blur that encompasses both.

Now slap your hand down on the coin.

In that instant, possibility collapses into fact. The coin is heads. Or tails. One or the other, definitively, irrevocably. The spinning is over. The ambiguity is resolved. Reality has been determined.

This is the simplest illustration of what quantum physicists call superposition and measurement. A quantum bit — a qubit — exists in a state analogous to the spinning coin. It is not a zero or a one, but a combination of both, with mathematical weights that determine the probability of each outcome. Only when measured does the qubit "collapse" into a definite value.

IBM's quantum computing team explains it this way: a classical bit is a light switch, definitively on or off. A qubit is more like a dimmer — capable of existing at any position along a continuum between fully on and fully off. But the metaphor breaks down at measurement, because a measured qubit doesn't stay at the dimmer position. It snaps to on or off, and the act of measuring is what forces the snap.

The I Ching has been performing a version of this operation for three thousand years. Before you toss the coins or sort the stalks, your hexagram is undetermined — all sixty-four possibilities coexist. The moment you generate a line, possibilities collapse. By the sixth line, the field of sixty-four has narrowed to one.

The spinning coin. The superposed qubit. The undetermined hexagram. Three images of the same structure: a binary system held in suspension, waiting for the act that resolves it.

Waiting for the Third Power.

In August 2023, a team of physicists at the University of Ottawa and Sapienza University of Rome accomplished something that would have astounded Leibniz and the ancient sages alike. Using a technique called biphoton digital holography, they created the first direct visualization of a quantum wavefunction shared between two entangled photons.

The image they produced — published in Nature Photonics — looks almost exactly like a yin-yang symbol.

This is not a metaphor imposed after the fact. The researchers themselves noted the resemblance. The physics produces a pattern where two entangled particles — correlated regardless of distance, their states inseparable — manifest in a visual form that ancient Chinese philosophy had been drawing for millennia.

Quantum entanglement is one of the most counterintuitive phenomena in physics. When two particles become entangled, measuring one instantly determines the state of the other, no matter how far apart they are. Einstein called it "spooky action at a distance." But entanglement is not communication — no information travels between the particles. Rather, the two particles are aspects of a single quantum system. They are, in a precise technical sense, one thing appearing as two.

In the I Ching, entanglement is structural. Every hexagram contains its complement: reverse every line, and you get another hexagram that is intimately connected to the first. The yin-yang symbol encodes this — each half contains the seed of the other, and neither can exist in isolation. The system is not built from independent parts. It is a unified whole that appears as multiplicity.

Entanglement is not a Fourth Power. It is the hidden principle that makes the Third Power a coherent whole. It is why the cube is a unified structure rather than eight disconnected points. It is why the hexagrams form a web of relationships rather than a list of isolated entries. It is the unity beneath the multiplicity, the dots within the yin-yang, the reason the binary system holds together.

Step back now and see the whole.

From the Taiji — the undifferentiated whole, the supreme ultimate — yin and yang emerge. Each divides again: four bigrams. Again: eight trigrams. The binary tree branches and branches, each level doubling the complexity of the one before. This is the same pattern by which cells divide, species branch, decisions fork, and rivers delta. The binary tree is the universe's fundamental algorithm for generating diversity from oneness.

It is fractal — the same pattern repeating at every scale. A trigram is three binary choices. A hexagram is two trigrams in conversation. A life is an uncountable number of hexagrams unfolding in sequence, each one a snapshot of the forces at work in a given moment, each one transforming into the next through changing lines.

We live in the spinning coin. At every moment, our lives contain multiple possible futures — yin and yang, this way and that way, yes and no. We are, in a sense, in superposition: multiple versions of the next instant coexist until we act. And when we act, we collapse the possibilities into one actuality. We choose. We measure the qubits of our own existence. We exercise the Third Power.

This is not quantum mysticism. I am not claiming your brain is a quantum computer or that consciousness literally collapses wavefunctions. The parallels are structural, not literal. But they are real. The mathematics of binary choice — the same mathematics that generates trigrams, codons, and computer words — also describes the structure of human decision-making. We face binary branches. We navigate them through action. And our actions determine which of the possible futures becomes the actual one.