Divination with Hexagrams as Combinatorial Practice ¹

The production of broken and unbroken lines in yarrow stalk divination did not only serve the purpose of prognostication. This contribution shows that it was also considered as a model for mathematical reflections to solve combinatorial questions. By analyzing and translating entirely a text by the mid-Qing scholar Wang Lai (1768–1813), it turns out that mantic figures—without being limited to the six lines as in a hexagram—were used as the paradigmatic model in his manuscript Mathematical Principles of Sequential Combinations . Other authors, like Jiao Xun (1763–1820), too, brought mathematical concepts systematically close to conceptualizations of line transformations in hexagrams and even produced algebraically an ordering of the 64 hexagrams (and more general mantic figures with 1 to 5 broken and unbroken lines). The integration in mathematical writings of problems related to the Zhouyi thus reveals an epistemological proximity between divination and mathematics that became an entire program of research for Qing scholars.