The King Wen sequence, explained

The one rule

Number a hexagram’s lines 1 to 6 from the bottom, as each hexagram page does. Turning the figure upside down puts line 6 at the bottom and line 1 at the top. Take hexagram 3, Zhūn: from the bottom it reads solid, broken, broken, broken, solid, broken. Read from the top down instead and you get broken, solid, broken, broken, broken, solid, which is hexagram 4, Méng. Every odd-numbered hexagram works this way, except where turning it over changes nothing.

Eight of the 64 figures look the same upside down: 1, 2, 27, 28, 29, 30, 61 and 62. For those the sequence uses the other obvious partner, the figure with every line flipped. Hexagram 1 is six solid lines and hexagram 2 is six broken ones; 27, Yí (Nourishment) is solid at top and bottom with four broken lines between, and 28, Dà Guò (Great Exceeding) is the exact reverse. The eight symmetric figures fall as four whole pairs, so the rule never has to split one.

In four other pairs, 11/12, 17/18, 53/54 and 63/64, the two operations happen to agree: turning the figure over gives the same result as flipping every line. 63, Jì Jì alternates solid and broken from the bottom up; upside down, it alternates broken and solid, which is also every line swapped, and that is 64, Wèi Jì. Those four are labelled ‘turned upside down’ above, because that is the rule that applies to every figure that is not symmetric; the card notes the coincidence.

What the figures show, counted

28 pairs are one figure turned upside down; 4 (1/2, 27/28, 29/30, 61/62) are one figure with every line flipped. In 4 of the upside-down pairs (11/12, 17/18, 53/54, 63/64) the two operations happen to give the same figure.

The first row is forced by the rule. Turning a figure over swaps line 1 with 6, 2 with 5 and 3 with 4, so lines always differ two at a time, and the two halves of a pair differ in 2, 4 or 6 lines, never an odd number. The second row is not forced by anything: the rule says which hexagram follows an odd-numbered one, but nothing in the lines says which pair should come next. That ordering of the 32 pairs is the part people have tried to explain for more than two thousand years, and no explanation is generally accepted.

Every label and number on this page is computed from the six lines of each hexagram, read from the trigrams its own page shows, by a script in this site’s repository; none is typed by hand.

Who arranged the order?

Nobody knows. The name is a tradition, not a record. Wikipedia’s summary of the scholarship puts it plainly: the sequence’s “true age and authorship are unknown”, while “traditionally, it is said that King Wen of Zhou arranged the hexagrams in this sequence while imprisoned by Di Xin in the 12th century BC” [1]. The same tradition credits him with much of the text itself; the I Ching’s core text was “traditionally ascribed to the Zhou cultural heroes King Wen of Zhou and the Duke of Zhou” [2].

James Legge, whose 1882 translation this site quotes, kept the story but marked it as his own picture rather than history: “I like to think of the lord of Kâu, when incarcerated in Yû-lî, with the 64 figures arranged before him” [3].

What the manuscripts show:

• The oldest known copy agrees with it. The oldest known manuscript of the text, found in 1987 and held by the Shanghai Library, “was almost certainly arranged in the King Wen sequence” [2].
• Another early copy does not. The silk manuscript from tomb 3 at Mawangdui, sealed in 168 BC [4], “arranges the hexagrams into eight groups sharing the same upper trigram” [2]. So the King Wen order was not the only one in use in the Han period.
• The numbers are later than the order. “it is not evident that the order of the hexagrams was of interest to the original authors of the Zhou yi”, and “the assignment of numbers, binary or decimal, to specific hexagrams, is a modern invention” [2].

The ancient explanation: the ‘Sequence of the Hexagrams’

One of the Ten Wings, the commentaries bound to the text, exists only to justify this order. The Xugua (序卦傳), which Legge prints as his sixth appendix, walks through all 64 and gives each step a reason. It opens:

有天地，然後萬物生焉。盈天地之間者，唯萬物，故受之以屯。

‘There are heaven and earth [hexagrams 1 and 2], and after that the myriad things are born. What fills the space between heaven and earth is nothing but the myriad things; so it is followed by Zhūn [3].’

and it ends at 64 with 物不可窮也，故受之以未濟；終焉: ‘things cannot come to an end, so it is followed by Wèi Jì (Before Completion), and there it ends.’ Its links are links of meaning, built on the hexagrams’ names, not of line patterns; it never mentions the upside-down rule at all.

Where the traditions differ is over who wrote it and how much it explains. The Ten Wings “were traditionally attributed to Confucius, possibly based on a misreading of the Records of the Grand Historian” [2]. Legge, who translated it, wrote that “there is nothing in the treatise to suggest anything about its authorship”, and judged that its essays “resemble ‘a heap of orient pearls at random strung’” [6].

A second, entirely different order is often printed alongside this one: the ‘binary’ or Fu Xi sequence, which “originated in the Song dynasty” and is believed to be the work of the scholar Shao Yong (1011–1077). Both names follow a habit the same article describes: “it was customary to attribute authorship to these legendary figures”, and “the King Wen sequence is, however, of much greater antiquity than the Fu Xi sequence” [1]. The figures in that Fu Xi order, read as the binary numbers 0 to 63, are drawn on the binary sequence, with the diagram Joachim Bouvet sent to Gottfried Leibniz. The King Wen numbers are the ones every hexagram on this site uses, and the order Legge’s translation follows.

Cast a hexagram and look up its partner in the pairs above.