Leibniz, Binary & the I Ching

In 1703, Gottfried Wilhelm Leibniz — the German polymath who co-invented calculus, pioneered symbolic logic, and dreamed of a universal language of reason — published a paper that would echo across centuries: "Explication de l’Arithmétique Binaire" (Explanation of Binary Arithmetic). In it, he laid out a complete system of arithmetic using only two symbols: 0 and 1. Every number, he showed, could be expressed as a combination of these two digits. It was an elegant, even mystical insight — and Leibniz knew it.

But what astonished Leibniz was not merely the mathematical elegance of his system. It was the discovery that an ancient Chinese text — the I Ching (易经), the Book of Changes, composed over three millennia earlier — already contained the very same binary encoding. The 64 hexagrams of the Fuxi sequence (先天八卦), when read as broken and solid lines, mapped perfectly onto the numbers 0 through 63 in binary notation. The ancients, it seemed, had known.

The I Ching is built upon a deceptively simple foundation: two types of lines. A solid line (———) represents Yang, the active, creative principle. A broken line (— —) represents Yin, the receptive, yielding principle. From these two fundamental symbols — and nothing else — the entire system of 64 hexagrams is generated, each consisting of six stacked lines.

Leibniz recognized immediately that this was binary arithmetic in symbolic form. Assign Yang (solid line) the value 1, and Yin (broken line) the value 0. Each hexagram then becomes a six-digit binary number. The principle is identical to the one underlying every modern computer: all information, no matter how complex, can be encoded using only two states.

In the Fuxi sequence (先天八卦次序) — the arrangement attributed to the legendary sage-emperor Fu Xi — the hexagrams follow a precise binary counting order. The first hexagram, Kūn (坤), consists of six broken lines: 000000 in binary, or 0 in decimal. The last hexagram, Qián (乾), consists of six solid lines: 111111 in binary, or 63 in decimal. Between them, every number from 0 to 63 appears exactly once.

The connection between binary arithmetic and the I Ching was catalyzed by correspondence between Leibniz and Father Joachim Bouvet, a French Jesuit missionary stationed at the court of the Kangxi Emperor in Beijing. Bouvet, who had been studying the I Ching, sent Leibniz a diagram of the Fuxi hexagram sequence in 1701. When Leibniz received it, he was electrified: here was his binary system, already perfectly encoded in an arrangement attributed to a Chinese sage who lived thousands of years before him.

For Leibniz, this was no mere coincidence. He saw it as evidence of a universal mathematical truth — a perennial wisdom shared across civilizations. He believed the ancient Chinese sages had grasped a fundamental insight about the nature of reality: that all of creation could be understood through the interplay of two opposing principles, fullness and emptiness, being and non-being, 1 and 0.

Three centuries after Leibniz’s paper, binary arithmetic became the foundation of the digital revolution. Every computer, every smartphone, every piece of digital information on Earth operates on the same principle the I Ching encoded: two states, on and off, 1 and 0, Yang and Yin. The transistors in a modern processor are, at their most fundamental level, doing exactly what the hexagram lines do — switching between two states to encode information.

This is not to claim that the ancient Chinese invented computers. It is to recognize something more profound: that the binary principle — the insight that all complexity can arise from the interplay of two fundamental states — is not a modern Western invention but a universal mathematical truth that was intuited independently by Chinese sages millennia before it was formalized by European mathematicians.

The connection to BaZi (八字) is direct and structural. Your birth chart — the Four Pillars of Destiny — is fundamentally a binary encoding. Every Heavenly Stem (天干) is either Yin or Yang. Every Earthly Branch (地支) is either Yin or Yang. The interplay of these binary polarities across your four pillars creates the unique pattern that defines your elemental constitution. Your Day Master, your Ten Gods, your favorable and unfavorable elements — all emerge from the binary dance of Yin and Yang.

In this sense, your BaZi chart is a binary code — a six-thousand-year-old technology for encoding the pattern of cosmic forces at the moment of your birth, using the same fundamental principle that powers the device you are reading this on. The ancients did not need transistors. They had Yin and Yang.

Leibniz’s discovery bridges two worlds. It demonstrates that mathematical truth is not the exclusive property of any one civilization but belongs to humanity as a whole. The Chinese sages who arranged the hexagrams were not performing binary arithmetic as a formal exercise — they were mapping the fundamental structure of change itself. That this mapping turned out to encode a complete number system was, for Leibniz, confirmation that mathematics and metaphysics are not separate domains but two faces of the same reality.

What the ancients knew intuitively, modern science has confirmed: the universe operates through the interplay of opposing and complementary forces. From the quantum bits of computation to the Yin-Yang polarities of a BaZi chart, the principle remains the same. MyDayMaster stands in this tradition — using the ancient binary wisdom of the I Ching and BaZi to illuminate who you are, encoded at the moment of your birth in the most universal language there is: the language of two.