文王序卦
The King Wen Sequence
The traditional ordering of the 64 hexagrams, attributed to King Wen of Zhou (周文王), circa 1050 BC. This arrangement encodes a cosmological and philosophical progression through paired opposites — a structure that has shaped Chinese thought for three millennia.
Classical Context
The Xugua zhuan 序卦傳 (Sequence of Hexagrams commentary) is one of the Ten Wings (十翼), the canonical commentaries traditionally attributed to Confucius. It provides the philosophical rationale for the ordering of the hexagrams.
Each hexagram follows from the previous through a logic of cosmological and human development. Heaven and Earth give rise to all things; difficulty follows creation; from youthful folly comes the need for patience — and so the sequence unfolds, tracing the arc of existence from genesis to the perpetual state of incompletion.
Structural Overview
64
Hexagrams
All possible six-line figures
32
Paired Opposites
Every hexagram has a partner
28
Inverse Pairs 反覆
Flipped upside down (fanfu)
4
Complement Pairs 旁歸
All lines inverted (pangui)
Of the 32 pairs, 28 are formed by inversion — flipping a hexagram upside down yields its partner. Four hexagrams are vertically symmetric (they look the same upside down), so their pairs are formed by complementation — flipping every line from solid to broken and vice versa. These special pairs are hexagrams 1/2, 27/28, 29/30, and 61/62.
The Sequence Visualized
All 32 pairs in King Wen order. Each pair shows both hexagrams with their structural relationship.
Sources & Further Reading
- 序卦傳 (Xugua zhuan, “Sequence of Hexagrams Commentary”). One of the Ten Wings (十翼), traditionally attributed to Confucius (551–479 BC). The canonical explanation for the King Wen ordering of the 64 hexagrams.
- Wilhelm, Richard, trans. The I Ching, or Book of Changes. Rendered into English by Cary F. Baynes. 3rd ed., Princeton University Press, 1967. The standard scholarly English translation, including the Ten Wings commentary.
- 王弼 (Wang Bi, 226–249 AD). 周易注 (Zhouyi zhu). The foundational commentary on the I Ching that established the “Images and Numbers” school of interpretation.
- 孔穎達 (Kong Yingda, 574–648 AD). 周易正義 (Zhouyi zhengyi). Tang dynasty subcommentary on Wang Bi, part of the 十三經注疏 (Thirteen Classics with Commentaries and Subcommentaries).
- Shaughnessy, Edward L. Unearthing the Changes: Recently Discovered Manuscripts of the Yi Jing. Columbia University Press, 2014. Archaeological evidence from Mawangdui and Shanghai Museum manuscripts illuminating the sequence's history.
- 韓仲民 (Han Zhongmin). “帛書周易卦序研究” (“Research on the Silk Manuscript Zhouyi Hexagram Sequence”). Comparative analysis of the Mawangdui sequence against King Wen ordering.
- Chan, Augustin. King Wen Sequence as Learning Optimization: Testing Ancient Algorithms Against Modern ML. Zenodo, 2025. [PDF]
Pair Analysis
Detailed examination of each pair's structural relationship, Hamming distance, and shared lines.
ExploreInformation Theory
Shannon entropy, Hamming distance distribution, and the sequence's information-theoretic properties.
ExploreAll 64 Hexagrams
Browse individual hexagrams with classical Chinese text, commentary, and translation.
Browse