Research Project


The Role of Mathematical Practice and Theory in Divination in Late Imperial China

Andrea Bréard
Humanities and Social Sciences Department, École Polytechnique, Paris
Institute of Mathematics, Université Sciences et Technologies Lille 1

During her stay at the IKGF, Andrea Bréard analyzed the interrelation between games of chance, divination and mathematical knowledge as described in the "popular" sources in late Imperial China. Using dominos (literally, "ivory tiles") as the material objects that link these three categories of combinatorial practice, she focused on investigating how "rationality" evolved historically as a knowledge producing value.

Combinatorial practices in China date back to high Antiquity, when divinatory techniques relied on configurations of broken and unbroken lines. The Book of Changes (Yijing 易經), compiled under the Zhou dynasty, has transmitted these practices until today, and is a widely discussed and read source. The combinatorial practices in early China are not limited to divination, however, or the equally well-known magic squares: a large number of sources also describe games like Go, chess and games involving cards, dominoes and dice that show a combinatorial interest from a more mathematical point of view. The hexagrams from the Book of Changes certainly served as THE mathematical model for an emerging combinatorial theory in China in the early 17th century. Divination procedures also figure among the collections of mathematical procedures in the algorithmic mode and prescriptive style. Late Imperial Chinese sources confirm what one might deduce from early mathematical commentarial writings such as Liu Hui′s 263 AD commentary on the canonical Nine Chapters of Mathematical Procedures: there, conceptual similarities bring the Yijing into close connection with philosophical considerations of the dynamics of mathematical calculations but, in the 17th and 18th century texts on mathematical combinatorics, hexagrams explicitly are the model for thinking mathematically about algorithms to determine, generally, the number of possible permutations and combinations. On the other hand, from the historian of probability′s point of view, A. Bréard has been interested in the inverse question: whether mathematical theories were applied when devising winning schemes to predict the outcome of chance mechanisms. Her focus was on divination techniques based on a random throw of a set of dominos. By reconstructing mathematically and analyzing historically the role of mathematical theory in the case of balancing outcomes in divination procedures in late imperial China, she demonstrated that there was a shift in the ′rationality′ underlying the attribution of points to certain combinations of tiles. There was, what she designated as a numerological turn, a time when the symbolic value of numbers was more important than the relative frequencies of obtaining a certain combination, in other words, a scientifically rational mathematical and fair distribution of points was superseded by a numerological rationality as a basis for deciding the value of certain combinations of tiles.

back to "Notions of Fate and Prognostication and their Taxonomies" Overview