The Letter to Leibniz, and a Coincidence Both Men Over-Read

The one lasting result of the Figurist programme came out of correspondence. Bouvet sent Leibniz a diagram of the sixty four hexagrams in the arrangement attributed to Fuxi. Leibniz had been working on binary arithmetic for years and recognised his own notation at once: read a broken line as nought and a solid line as one, and the Fuxi order counts from zero to sixty three in binary. Each man took the coincidence as confirmation of what he already held. For Bouvet it proved that the classics preserved a lost science. For Leibniz it suggested that the ancient Chinese had known a truth their descendants had forgotten, and it fitted his own theological reading of binary, in which everything is generated from one and nothing.

Almost every later Western treatment of the Book of Changes as a binary, mathematical or informational system descends from that exchange, and it is worth being clear about what the exchange did and did not establish. The correspondence between the Fuxi order and binary counting is exact and is not in dispute. What neither man could show is that anyone in China had ever read the arrangement that way, and the ordering itself is a product of the Song dynasty rather than of high antiquity.