Interpretive systems

Trigrams and hexagrams

Everything else in this section is a way of using one small formal system: two kinds of line, stacked three deep to make eight trigrams, stacked six deep to make sixty-four hexagrams. Learn how the figures are built and related and the rest of the tradition becomes legible.

8
trigrams
64
hexagrams
16
possible nuclear figures

The structures

Start with the line, build up to the hexagram, then learn the relations that let one figure be read against another. This is the vocabulary every method in the section assumes.

➖

The line

China Zhou onward

Solid for yang and broken for yin. Two states, and every structure in the system is a stack of them. The tradition's cosmology begins here, with the claim that one distinction repeated is enough to describe change.

☰

The trigram

China Zhou onward

Three lines give eight arrangements, each with an image, an element, a family role, a direction and a season. Learning the eight is the single highest-value investment in the whole subject.

䷀

The hexagram

China Zhou onward

Two trigrams stacked, six lines in all, giving sixty-four figures exactly. The lower trigram is the inner and earlier half of a situation, the upper the outer and later.

⬆️

Counting from the bottom

China Zhou onward

Line one is at the foot and line six at the top, because the figure is read as something growing or unfolding in time. The classic even names them 'beginning' and 'above' rather than first and sixth.

✅

Correctness

from the Ten Wings c. 3rd century BCE

Odd places want solid lines and even places want broken ones. A line in its proper place is correct, which is generally favourable and routinely outweighed by other factors.

🎯

Centrality

from the Ten Wings c. 3rd century BCE

The second and fifth lines sit at the middle of their trigrams. Centrality is praised more consistently than anything else in the commentaries and usually beats correctness when the two conflict.

🔗

Correspondence

from the Ten Wings c. 3rd century BCE

Lines one and four, two and five, three and six answer each other, and the pairing works when the two are of opposite kinds. The second-and-fifth relation carries most of the classic's political thinking.

🪜

Riding and supporting

from the Ten Wings c. 3rd century BCE

A yin line directly above a yang one is said to ride it, which is uncomfortable; below it, to be supported, which is not. Small relations between neighbours that often decide a line's verdict.

✳️

Moving lines

China Zhou onward

Only lines the cast marks as sixes or nines have their texts read, and flipping them produces the second hexagram. The stable lines shape the figure and stay silent.

🫀

The nuclear hexagram

China Han onward

Lines two to four and three to five give a figure hidden inside the original, read as what is really going on underneath. Only sixteen of the sixty-four ever appear as one.

🔄

The opposite hexagram

China Han onward

Every line changed to its other state, giving the complementary condition. Useful for seeing what the situation is defined against, and used systematically by Lai Zhide in the Ming.

🙃

The reversed hexagram

China Han onward

The figure turned upside down, usually the same situation seen from the other party's side. Eight hexagrams look identical either way up, and the King Wen sequence pairs figures with their reversals.

Orders, relations and reference points

The arrangements the figures have been put in, the derived figures read alongside them, and the terms commentaries use without explaining.

The King Wen sequence

the received order China

The order the classic uses, arranged in pairs where each figure is followed by its reversal, or by its opposite in the eight cases where reversal changes nothing. Not numerical, and traditionally credited to the Zhou founder.

The Fu Xi arrangement

11th century Song China

Shao Yong's Before Heaven ordering, generated by repeated binary division. Reading broken as zero and solid as one gives the integers nought to sixty-three in sequence, which is what Leibniz recognised.

The Later Heaven arrangement

traditional China

The trigram circle used for divination, geomancy and medicine, ordered by season and direction. Distinct from the Before Heaven circle, which pairs each trigram with its exact opposite.

The eight palaces

1st century BCE Han China

Jing Fang's grouping of all sixty-four into eight families headed by the doubled trigrams. The working arrangement for Six Lines divination, and a second way to browse the figures.

The family of trigrams

from Shuogua China

Qian and Kun as father and mother; the six others as sons and daughters, named by which line is the odd one out. A mnemonic that also carries interpretive weight.

The Unicode block

1999 onward worldwide

All sixty-four hexagram characters occupy a contiguous Unicode range in King Wen order, and the eight trigrams have their own characters. Typography that quietly encodes the tradition's ordering.

Shuogua's correspondences

c. 3rd century BCE China

The Wing that lists what each trigram signifies. Every method that reads images rather than text depends on it, and it is the first thing a practitioner memorises.

Lai Zhide

1525–1604 Sichuan

Spent decades organising the hexagrams by their opposite and reversed pairings and produced the diagram of the paired figures still reproduced in Chinese editions.

The eight symmetrical figures

structural fact —

Hexagrams 1, 2, 27, 28, 29, 30, 61 and 62 read identically upside down. The King Wen sequence pairs each of them with its opposite instead, which is why the pairing rule has an exception.

Nine and six

Zhou onward China

Line texts are labelled by the casting numbers, so a moving yang line in the fifth place is 'nine in the fifth place'. This is why those two numbers saturate the classic.

Reading by structure alone

3rd century Wei China

Wang Bi discarded the Han correlations and read hexagrams purely from these internal relations. The meaning-principle school is what this apparatus looks like when it is the whole toolkit.

Sixty-four is two to the sixth

structural fact —

Six binary positions give exactly sixty-four states, which is why the set is complete and closed. The classic uses all of them and there is nothing left over.

A very small system

The Book of Changes rests on almost nothing. There is one distinction, solid or broken. Stack three of them and you have eight trigrams. Stack six and you have sixty-four hexagrams. That is the entire formal apparatus, and everything else in this section is a way of putting it to work.

Six binary positions give two to the sixth, which is sixty-four exactly. The set is complete and closed, with nothing left over, and the classic uses all of it. That completeness is part of why the system has been so durable: it is not a selection from a larger set of possibilities but the whole of a small one.

The trigrams first

Learning the eight trigrams is by a wide margin the highest-value thing a student of the Changes can do. Once they are familiar, the sixty-four stop being a list to memorise and become combinations that can be read: water over thunder, fire under a lake, mountain above earth.

Each trigram carries an image, a Five Phase agent, a family role, a direction and a season. Qian is heaven, strong, the father, Metal, northwest. Kun is earth, yielding, the mother, Earth, southwest. The six others are made by putting one odd line into one of those two, and are named as sons and daughters by where that line sits.

Position matters as much as identity. The lower trigram is the inner, private, earlier half of a situation; the upper is the outer, public, later half. Fire under a lake destroys and gives hexagram 49, Revolution. Fire over a lake merely diverges and gives hexagram 38, Opposition. Same two trigrams, opposite meanings.

Reading inside a hexagram

The commentaries supply four relations, and they are the whole of classical line analysis.

Correctness: odd places want solid lines, even places want broken ones. Centrality: the second and fifth lines sit at the middle of their trigrams, and the commentaries praise this more consistently than anything else, generally preferring a central line to a merely correct one. Correspondence: lines one and four, two and five, three and six answer one another, and the relation works when the two are of opposite kinds. Riding and supporting: a yin line sitting directly on a yang line is uncomfortable, sitting beneath it is not.

A hexagram whose second and fifth lines are central, correct and in correspondence is about as well-ordered as the system allows, and the Judgment texts frequently explain their own good fortune by pointing at exactly that.

Which lines speak

A cast produces one of four values per line, and only two of them move. Sixes and nines are lines at the end of their range, turning into their opposites; their texts are read, and flipping them gives a second hexagram showing where the situation is going. Sevens and eights are stable, contribute to the structure, and stay silent.

This is why the same hexagram can answer two people quite differently. The figure is the situation; the moving lines are the parts of it actually in play.

Figures derived from figures

Three transformations are worth knowing, and every hexagram page in this section links to all three.

The nuclear hexagram takes lines two to four as a lower trigram and three to five as an upper, giving a figure concealed inside the original and read as its inner constitution. Only sixteen of the sixty-four ever appear as one, and applying the operation repeatedly always ends at hexagram 1, 2, 63 or 64.

The opposite changes every line, giving the complementary condition. The reversed turns the figure upside down, which usually shows the same situation from the other party's position. Eight hexagrams are unchanged by reversal, and the King Wen sequence, which otherwise pairs each figure with its reversal, pairs those eight with their opposites instead.

The orders

The received text uses the King Wen sequence, which is not numerical. Its logic is the pairing just described, and the Xugua wing supplies a chain of reasons why each hexagram follows the last.

Shao Yong's Before Heaven arrangement is the mathematical one, generated by repeated binary division, and it produces the integers nought to sixty-three when broken lines are read as zero. That is the ordering Bouvet sent to Leibniz. The eight palaces give a third arrangement, grouping the sixty-four into families of eight for divinatory use, and the trigram circles come in Before Heaven and Later Heaven forms with quite different purposes.

None of these is the correct order. They are different indexes to the same closed set, and which one is in front of you tells you what the person who drew it was trying to do.

Frequently asked questions

All I Ching methods

Latest Posts

Discover the ancient wisdom of tarot cards and unlock the mysteries of your spiritual journey. Our blog is your gateway to understanding the rich symbolism, meanings, and practical applications of tarot reading.