Seven questions, one machine

Seven Chinese calculators that look like variants of each other. They share one substrate — the sexagenary cycle, the solar terms, the He Tu and Luo Shu, the five phases — and agree on almost nothing about what a reading is for. Every figure here is derived from documented mechanics, not quoted from a practitioner.

The family tree

Only two of the seven read a person at all. Filter by what each one is actually looking at.

How much each one is willing to say

The number of distinct readings a system is capable of producing — not what it claims, but what its own machinery can distinguish. Drawn on a log scale, because the range is three orders of magnitude wide.

What they are all made of

The same small kit of counting devices, most of it in place by the Han.

Then the tradition audited its own dice

Liu Yao is the only one of the seven in which anything happens at the moment of asking. There are two accepted ways to cast, and the claim in circulation is that coins make change more likely than yarrow stalks. Add the columns up.

Then we built all seven

A rule that survives implementation is a rule someone else can check. A rule that only survives prose is not. We wrote a working calculator for each of the seven and let the arithmetic argue back.

Charts we can reproduce exactly.
    Gaps the build closed.
      Things the arithmetic taught us.

        What we could not find out

        Standing gaps, carried rather than papered over.