Week 11 Session: Crossing Worlds — Leibniz, Binary Arithmetic, and Global Afterlives

What actually happened when this notation reached Europe, and how does that compare with the popular version of the story?

3 May 2027

The question

A popular story claims this notation predicted binary computing. What is the documented version of that story, and where does it stop being documented?

What this builds on

Week 6 already flagged why this diagram reached Leibniz at all: the Xiantian arrangement’s binary-counting order. This week gives the actual documented timeline behind that one detail, plus the wider popular claim built on it, which the notation’s own textual and visual history (weeks 9–10) has already trained you to be skeptical of.

Leibniz drafted binary arithmetic independently by 1679 (De Progressione Dyadica). Joachim Bouvet, recognizing the Xiantian arrangement’s binary-counting structure from week 6, sent Leibniz Shao Yong’s diagram in a letter dated 4 November 1701; it reached Leibniz on 1 April 1703; Leibniz published on binary arithmetic within about a week of receiving it. Each of those dates is independently documented — the sequence is not in dispute.

  1. Pre-existing notation

    Yin/yang lines and trigram patterns — Shao Yong's Xiantian arrangement (week 6), already an existing sign system before any contact with Europe.

    • ☰ Qian
    • ☷ Kun

  2. Historical transmission

    A contact stage, not an inventor step: Joachim Bouvet recognized the arrangement's structure and sent it — he did not create it.

    1. 4 Nov 1701 Bouvet sends Shao Yong's diagram in a letter to Leibniz.
    2. 1 Apr 1703 The letter reaches Leibniz.

    Qian at S, Kun at N in that diagram's own layout (Xiantian arrangement, week 6) — the positions are Bouvet's diagram's, not this figure's invention.

  3. Leibniz's reinterpretation

    Leibniz had already drafted binary arithmetic independently, by 1679 — before this diagram reached him.

    • ☰ Qianlater binary reading: 111 = 7
    • ☷ Kunlater binary reading: 000 = 0

    The same line patterns, read through his own binary-number framework in 1703 — a reinterpretation of an existing notation, not its source.

A structural correspondence between two notations is not evidence that one produced the other: structural correspondence ≠ historical invention.

Left to right is the order of interpretation, not a chain of invention — the pre-existing notation was transmitted, then re-read through a separate mathematical framework Leibniz already had.
For this later binary reading, each digit lines up with its line: top line first (least significant), down to the bottom line (most significant).

What is a genuine, still-live scholarly debate is how independent Leibniz’s own binary work really was once he had seen Bouvet’s diagram — a question this course does not settle, because the sources it draws on do not settle it either. The popular version of the story skips past that open question entirely and compresses the whole documented exchange into a single claim (“the I Ching predicted binary computing”), as if Leibniz derived binary arithmetic from the diagram rather than having already drafted it and then received a diagram whose structure he recognized. A documented exchange plus an open question about influence is a narrower, more interesting claim than the popular one-liner — and the gap between the two is exactly the kind of gap this course’s sourcing discipline exists to close.

What you should be able to do after this week

State the documented Leibniz–Bouvet sequence in order, and name at least one way the popular story overstates it (skipping the 1679 draft date, or treating a live debate as settled either way, are the two clearest ones). Next week applies that same closing-the-gap skill to a claim you choose yourself, and to a sign system this course never covered.

The spec

What you bring to the session. Written so a reader can tell whether it has been met without asking you.

Teaching team