Ideas

The Leibniz Hexagrams

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The 1701 correspondence in which a Jesuit's diagram of the 64 hexagrams arrived in Leibniz's study and matched his new binary arithmetic, line for line.
Documented

The Bouvet correspondence

Jesuit missionary Joachim Bouvet, working in Beijing, sent Leibniz the Fuxi sequence of hexagrams in 1701. Leibniz mapped broken lines to 0 and unbroken to 1 and found the hexagrams count 0 to 63 in order. He published his binary arithmetic in 1703 with the hexagrams as supporting exhibit, reading the match as proof of a universal, God-revealed mathematics.

Assessment: Documented: the letters survive; the 1703 paper is printed; the mapping is arithmetically exact.
Stories

The ancient computer

The internet's version: the Yijing as a prehistoric binary computer, sages running code in milfoil stalks. The story omits that the ordering Leibniz received was Shao Yong's 11th-century rearrangement, not a Western Zhou original.

Assessment: Stories: the numerology outruns the philology; the sequence is medieval, the counting is modern, the awe is misplaced twice.
Interesting claims

Convergence or contagion

The serious version of the debate: doubling schemes converge on binary structure inevitably, so the match may prove nothing, or the match proves that any exhaustive doubling notation is binary, which is the deeper point. The Yijing did not predict the computer; it demonstrated that the computer's grammar was always available.

Assessment: Interesting: both sides cite the same letters; the divergence is entirely interpretive.
Sources and further reading
  1. Leibniz-Bouvet correspondence, 1701, Fuxi hexagram sequence
  2. Leibniz, 'Explication de l'arithmétique binaire,' Mémoires de l'Académie Royale des Sciences (1703)
  3. Franklin Perkins, Leibniz and China (2004), on the Shao Yong ordering caveat
Worth asking

Did the Yijing anticipate binary, or did binary finally give the Yijing a reader who could count?

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GR8YFILES · competing origin stories, labeled by the strength of their evidence · readers 14+