Each hexagram consists of six places, each occupied by a broken or unbroken line. In the received tradition those lines came to be read through yin and yang. Two graphic alternatives across six positions generate sixty-four possible figures.

That combinatorial fact is exact; the figures' meanings are not produced by arithmetic alone. Names, judgments, images, casting practices and centuries of commentary turn a small visual alphabet into a cultural text about particular situations and change.

The Zhouyi is a divination text organised around situations and change. Its judgments and images address moments such as waiting, returning, approaching and breaking apart; later commentarial traditions developed richer cosmological readings around them.

It is tempting to say that the book anticipated a universe made only of transformations. That is a modern synthesis, not one doctrine stated uniformly by every layer of the text. The safer wonder is already large: a small set of figures became a language through which generations interpreted change.

In the received King Wen sequence, neighbouring hexagrams are often related by inversion or by changing every line, though the pairs do not all behave in one identical way. In divinatory practice, changing one or more lines can relate one figure to another.

Calling the sequence a map of every possible transformation turns a finite arrangement into a total metaphysics. Its actual achievement is more exact: sixty-four figures built from six two-state positions, ordered and interpreted through a textual tradition that never stopped generating further readings.

In the Song dynasty, Shao Yong arranged the hexagrams in a pattern that can be mapped onto counting in base two. He was not presenting binary arithmetic: the resemblance emerges when broken and unbroken lines are assigned modern numerical values.

That distinction matters. The arrangement made Leibniz's later comparison possible without turning an ancient divination system into a premature computer.

Jesuit missionary Joachim Bouvet sent Leibniz a diagram of the sixty-four hexagrams in an arrangement associated with Shao Yong. Leibniz assigned numerical values to solid and broken lines and recognised an ordering compatible with his binary arithmetic.

The encounter is profound because it is an act of translation. A received Chinese diagram and a European number system became newly legible beside one another through Leibniz's mapping. It does not show that the Zhouyi was binary arithmetic or that two cultures independently discovered one universal code.

Leibniz mapped unbroken lines to 1 and broken lines to 0, reading the 64 hexagrams through his own binary number system. The ancient symbolic structure and early-modern mathematics suddenly touched.

The correspondence is real, but historical direction matters: Leibniz supplied the numerical interpretation. The Zhouyi's lines were created for divination and commentary, not as a claim about digital machines.

Any six positions with two alternatives yield sixty-four combinations. That combinatorial parallel is exact. What those combinations mean is not.

In the Zhouyi, lines belong to divination, commentary and patterned change. In binary arithmetic, positions encode powers of two; digital computing adds further physical and logical conventions. Their meeting shows how one form can carry unlike worlds of meaning. It invites comparison without claiming that reality itself is binary or that distant traditions were speaking one hidden language.

Binary arithmetic became part of the architecture of modern computing. The I Ching offers a much older two-state symbolic system: a guide for navigating uncertainty and transformation.

Their meeting is valuable precisely because the systems are not identical. One encodes numbers for calculation; the other composes figures for divination and interpretation. Leibniz's comparison shows how a shared combinatorial form can carry very different cultural meanings.