Esoteric Diagrams of Yi Numerology 易数钩隐图

Authored by Liu Mu of the Northern Song Dynasty,

Liu Mu was a scholar of diagram-based Zhouyi studies in the Song Dynasty. It is said that his academic thought originated from Chen Tuan, a Taoist priest of the early Song Dynasty.

Esoteric Diagrams of Yi Numerology

Bibliography of the History of the Song Dynasty and Bibliography of the Zhongxing Imperial Library recorded this work as one volume, while Tongzhi (Comprehensive Records), Secret Catalogue and Chao Gongwu’s Bibliography of Read Books all recorded it as three volumes.

The present version in The Daozang has three volumes and is classified under the Lingtu (Spiritual Diagrams) category of the Dongzhen Section.

There is also a three-volume version included in the Siku Quanshu (Complete Library of the Four Treasuries). The core tenet of this book is to interpret the hexagram images of the Zhouyi through the combinations and changes of numbers. The author held that the sages created hexagrams to observe images, arguing that "forms are generated from images, and images are established by numbers". Thus, he drew diagrams and put forward arguments to clarify that hexagram images originate from mathematical principles. The book contains a total of fifty-five diagrams, each followed by a brief discussion, as do groups of diagrams in some cases. Among them, diagrams 1 to 16 expound on the Taiji (Supreme Ultimate), the Two Principles, the Four Symbols, the Eight Trigrams, heaven and earth; diagrams 17 to 48 elaborate on yin and yang, Qian and Kun, the five elements, and the Three Realms (heaven, earth and humanity); diagrams 49 to 54 discuss the Hetu (Yellow River Diagram) and Luoshu (Luo River Writing); diagram 55 expounds on the ten suns and the mutual generation of the five elements. Attached at the end of the book is On the Dragon Diagram and the Turtle Script, which focuses on discussing the origin and purpose of diagram-based Zhouyi studies. The author pioneered diagrams composed of black and white dots representing numbers, identifying the diagram of the generating numbers of the five elements as the Hetu and the diagram of the Nine Palaces numbers as the Luoshu. His theories were opposed to those of Ruan Yi’s Commentary on the Zhouyi by Guan Lang and Cai Yuanding’s Annotated Introduction to Zhouyi Studies. Many Confucian scholars in the Song and Yuan dynasties wrote treatises to refute his viewpoints, and these academic debates also became an important part of the development of Taoism-influenced Zhouyi studies.