Number Names

Cai Chen (1167-1230) composed a divination manual grounded in the Yijing, organizing it into 81 matrices that share the features of magic squares. This achievement had gone largely unnoticed until now, yet it marks an important episode in the history of mathematics. The study brings the work to light and substantially broadens our knowledge of the Chinese number theory developed by the "Image and Number" school of Confucian thought.

Scholars in that tradition arranged the binary figures of the Yijing, known as trigrams and hexagrams, into graphic grids to examine how the chance outcomes of divination relate to the classic's interpretations. Cai extended this approach into his 81-matrix series, which he understood as charting the cycles of time that recur in the natural world. He also carried the structure of the series into the wording of his divination texts, calling them "number names," which is where the book takes its title.

The book is written for readers of philosophy, the history of science and mathematics, and Chinese intellectual history. Because the divination text has both literary and philosophical qualities, its readership extends beyond specialists to general readers curious about recreational mathematics, divination, Taiji and Fengshui.