How a reading is built

Nothing on this page is interpretation. It is the arithmetic. Once you have read it once, you can look at any reading in this app and say exactly where every part of it came from.

1. Three coins make one line

Each coin is worth 2 or 3. Three coins are thrown together and their values added, so a line is always 6, 7, 8, or 9. You throw six times, and the first throw is the bottom line.

Because there are more ways to add up to 7 or 8 than to 6 or 9, stable lines are three times as likely as changing ones. A 6 or a 9 has a 1 in 8 chance; a 7 or an 8 has 3 in 8.

The yarrow stalks are not the same

The older method divides forty-nine stalks three times per line and counts the heaps off in fours. It is not the coin method with different props: it produces a different distribution, and this app carries out the procedure rather than relabelling a coin toss.

With coins a changing yin and a changing yang are equally likely. With yarrow a changing yang is three times as likely as a changing yin. Which method you use changes what you are likely to see, which is why a saved reading records the one you chose.

2. Three lines make a trigram

Only the polarity matters here, not whether the line is changing. Lines 1 to 3 form the lower trigram and lines 4 to 6 the upper one. There are eight possible combinations.

• 乾 qián

  Heaven · Initiating

  Father · bits 111 bottom to top

• 兌 duì

  Lake · Open

  Youngest daughter · bits 110 bottom to top

• 離 lí

  Fire · Clinging

  Middle daughter · bits 101 bottom to top

• 震 zhèn

  Thunder · Arousing

  Eldest son · bits 100 bottom to top

• 巽 xùn

  Wind · Penetrating

  Eldest daughter · bits 011 bottom to top

• 坎 kǎn

  Water · Deep

  Middle son · bits 010 bottom to top

• 艮 gèn

  Mountain · Still

  Youngest son · bits 001 bottom to top

• 坤 kūn

  Earth · Yielding

  Mother · bits 000 bottom to top

3. Two trigrams make a hexagram

Each of the 64 upper and lower pairs has a number in the King Wen sequence, the traditional ordering. That number is looked up in a fixed table. It is not computed from the bits, and there is no formula for it: the sequence is a received ordering that has to be checked against sources, which is why this app keeps a verification note for it.

4. Changing lines make a second hexagram

Flip every changing line and leave the rest alone: a 6 becomes yang, a 9 becomes yin. Look the result up in the same table and you have the transformed hexagram. It is a derived fact about the same six throws, not a prediction about later.

What to do when several lines change is a real disagreement between traditions, not a settled rule. Rather than pick one and present it as law, this app treats a convention as something named and selectable.

• Show every changing line

  Every changing line is shown in bottom-to-top order. No line is ranked above another.

  Deliberately unsourced: it encodes no interpretive claim.

• Zhu Xi (Yixue Qimeng)

  Rules from Zhu Xi's Introduction to the Study of the Changes (c. 1186). The reading method changes with the number of changing lines: one reads that line, two read both with the upper prioritised, three read the Judgements of both hexagrams, four read the non-changing lines of the transformed hexagram, five read the single non-changing line, six read the transformed Judgement.

  Zhu Xi, Yixue Qimeng (易学啟蒙), c. 1186. English: Joseph A. Adler, Introduction to the Study of the Classic of Change, Global Scholarly Publications, 2002.

• Huang (governing line)

  Alfred Huang's method: each hexagram has a governing line (the host) that carries its central theme. When multiple lines change, the changing line that occupies the host position is shown first. If none of the changing lines is the host, all are shown in bottom-to-top order.

  The host of a hexagram is Alfred Huang's teaching, set out in The Numerology of the I Ching (Inner Traditions, 2000). The 64-entry table used here is transcribed from the Wikibooks I Ching compilation, en.wikibooks.org/wiki/I_Ching/Host_Of_The_Hexagrams (CC BY-SA), not from Huang's books directly.

5. Where the words come from

Every block of text in a reading is labelled with its layer, so you never have to guess what you are reading.

Source text

The received Chinese text, in a stated edition.

Translation

A named translator’s words, with the edition and licence.

Commentary

Attributed historical or modern commentary.

Our explanation

Written by this project. Carries no scholarly authority, and is never presented as a translation.

AI reflection

Model-generated, always optional, always last, and only ever written against passages that are already on the page.

Where a reading says source text has not been imported, that is literal. Showing remembered or generated text in its place would defeat the point of the labels.