Week 8 Session: Lines That Move — Hexagrams and Changing Lines

How does the notation encode transformation itself, not just a static state?

12 April 2027

The question

Everything so far has built static objects — lines, bigrams, trigrams. What in this notation actually represents one state becoming another?

What this builds on

This week stacks two trigrams (weeks 4–7) into a hexagram, then introduces the mechanism the whole course has been building toward: a changing line, whose value flips it to its opposite and produces a transformed hexagram. This is the direct, structural answer to the course’s central question, and the point where the course pivots from constructing signs to studying how their meanings developed historically.

Six lines, and the line that isn’t fixed

Stack any two trigrams — one below, one above — and the result is a hexagram: six lines, read bottom to top, with sixty-four possible combinations at this depth (the same doubling arithmetic from weeks 3–4, one more level). Which trigram sits below and which sits above is not interchangeable — Qian-below-Kun and Kun-below-Qian are two different hexagrams, not the same pair read differently.

The changing-line mechanism is what makes this notation different from a static combinatorial diagram. A line can be marked as “old” — old yin (traditionally valued 6) or old yang (valued 9) — rather than merely yin or yang, and an old line is one that flips: old yin becomes yang, old yang becomes yin, and the result is a second, transformed hexagram, derived directly from the first by that single rule. Nothing about which hexagram comes next is stored anywhere except in the marked line itself — the transformation is structural, not a separate description bolted onto the diagram. This is the direct technical answer to the question week 1 opened with: a state that carries, inside itself, which state it becomes next.

Try it

Build a hexagram below, mark one or more lines as changing, predict what the transformed hexagram will look like, then reveal it and check your prediction line by line.

Build a hexagram

Toggle the lower trigram's lines, then the upper trigram's — in any order. They stack into the hexagram below. Then mark the lines you want to change.

Lower trigram

  1. Line 1
  2. Line 2
  3. Line 3

Upper trigram

  1. Line 4
  2. Line 5
  3. Line 6

Combined hexagram

  1. Line 1Yang
  2. Line 2Yang
  3. Line 3Yang
  4. Line 4Yang
  5. Line 5Yang
  6. Line 6Yang

Predict the transformation

Before revealing, set every line to what you think it becomes once the marked lines flip. All six must be set before you can reveal.

  1. Line 1
  2. Line 2
  3. Line 3
  4. Line 4
  5. Line 5
  6. Line 6

Set all six predicted lines before revealing (0 of 6 set).

What you should be able to do after this week

Given a hexagram and a marked changing line (or lines), derive the transformed hexagram by hand. Assignment 1 (due this week) tests this ability directly, along with a short check on the Xiantian/Houtian arrangements from weeks 6–7 — see the assessment page for the brief. From here, the course turns from building this notation to studying how the meanings layered onto it took shape historically, starting with the text itself next week.

The spec

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

Teaching team