I Ching

The I Ching was already counting in binary

In 1701 a Jesuit in Beijing posted a diagram of the I Ching’s hexagrams to Germany. When Gottfried Leibniz read it, he found his own new arithmetic of nothing but 0s and 1s.

The Plutto Magazine · 13 October 2026 · 2 min read

A woodcut diagram of the sixty-four I Ching hexagrams arranged in a square and a circle, with numbers added by hand.
The diagram Joachim Bouvet sent to Leibniz in 1701: the sixty-four hexagrams in the order attributed to Fuxi, set in a circle and a square. Leibniz wrote the matching numbers above them by hand.Gottfried Wilhelm Leibniz Bibliothek, Hannover. Public domain, via Wikimedia Commons.

By 1679 Leibniz had worked out a way of writing every number with two digits, 0 and 1. He thought it beautiful and kept it in a drawer: it made sums longer, and no one had a use for it yet.

A letter from Beijing

Joachim Bouvet was a French Jesuit mathematician at the court of the Kangxi Emperor, and a correspondent of Leibniz. On 4 November 1701 he wrote from Beijing and enclosed a woodcut of the I Ching’s sixty-four hexagrams in the arrangement attributed to the legendary sage Fuxi, as set out by the eleventh-century scholar Shao Yong.

Each hexagram is six stacked lines, each line either broken or whole. Read a broken line as 0 and a whole line as 1, and Shao Yong’s order runs through the sixty-four hexagrams exactly as the numbers 0 to 63 run in binary.

Read a broken line as 0 and a whole line as 1, and the hexagrams count from 0 to 63.

The letter reached Leibniz in 1703. He wrote the numbers over the hexagrams himself, and that year he finally published his binary arithmetic, in the journal of the French Academy of Sciences, with a section on the hexagrams of Fuxi.

What it was, and what it wasn’t

The I Ching was not doing arithmetic; it is a book of divination and philosophy, and Shao Yong’s order is a picture of the cosmos unfolding from yin and yang. What Leibniz recognised was a structure: the same two-way choice, repeated, building everything. Today that structure runs every phone and computer on Earth.

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Sources

  1. G. W. Leibniz, “Explication de l’arithmétique binaire,” Mémoires de l’Académie Royale des Sciences (1703).
  2. James A. Ryan, “Leibniz’ Binary System and Shao Yong’s Yijing,” Philosophy East and West 46 (1996).
  3. Frank J. Swetz, “Leibniz, the Yijing, and the Religious Conversion of the Chinese,” Mathematics Magazine 76 (2003).

Plutto presents these traditions for reflection; it does not claim that astrology predicts events.

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