Leibniz: the documents
Bouvet, Shao Yong and the binary arithmetic of 1703
Reference page, for reading
The Chinese did not practise binary arithmetic. Shao Yong was after a cosmology; the hexagrams were symbols, not numbers to be added. It was Leibniz who, with his binary already invented, recognised the coincidence of structure. The identity is real as form; the reading that “China invented binary” is an anachronism.
The connection between the 64 hexagrams and the binary system is not a legend: it is documented, with dates and publications. But it is worth telling precisely. These are the milestones, each with its source.
Shao Yong (邵雍, 1011–1077) formalises the “Earlier Heaven” arrangement (先天): the 64 hexagrams in the order we read today as binary. His motivation was cosmological and numerological, not arithmetical.
source: Ryan, J. A. (1996), Philosophy East and West 46(1), 59–90.
Long before he knew of the I Ching, Leibniz (1646–1716) had already developed binary arithmetic; his manuscript De Progressione Dyadica is from 1679.
source: Leibniz, De Progressione Dyadica (1679), manuscript; see the Leibniz Archive, Hanover.
The Jesuit Joachim Bouvet (1656–1730), a missionary in China, writes to Leibniz on 4 November 1701 and encloses the circular and square diagrams of the Fu Xi hexagrams, pointing out their likeness to binary numbering. Leibniz does not receive the letter until 1 April 1703.
source: Bouvet–Leibniz correspondence; chronology in Ryan (1996) and the Leibniz Archive.
Leibniz publishes his exposition of the binary system and, in it, acknowledges the structural identity with the Fu Xi hexagrams that Bouvet had sent him. It is the first documented bridge between the I Ching and European binary.
source: Leibniz, G. W. (1703), “Explication de l’Arithmétique Binaire”, Mémoires de l’Académie Royale des Sciences, Paris.
The diagram Bouvet sent is exactly the one reconstructed by the experiment on the square and circle of Shao Yong: reading it in order is counting from 0 to 63. That two traditions so different (a cosmology of the 11th century and an arithmetic of the 17th century) should describe the same structure is the heart of this laboratory. The rest is reading carefully who did what, and when.
The Chinese did not practise binary arithmetic: Shao Yong was after cosmology, and it was Leibniz, with his binary already invented, who recognized the structural identity.
Documented chronology: Bouvet communicated the analogy in a letter of 4 November 1701, received by Leibniz on 1 April 1703; the Explication de l'arithmetique binaire appeared in 1703.
The types of claim and the full bibliography (APA) are in Foundations.