I want to thank my colleague, Andrea Bréard, for the time she spent reading and commenting. My experience of the editing process was not apleasant one. There were some communication difficultiesmeaning that, for instance, Icannot explain why my glossary, which contained 400 terms, was reduced to fewer than 250 terms. Ihope that oneday Iwill be given the opportunity to correct this book, to meet my own highest requirements.
The purpose of my book is to explore alink between philosophy and mathematics in China and to raise questions of methodology. It is as aphilosophy educator, classroom practitioner, and non-mathematician that Iwrite. When Bréard writes that “I could not make up my mind,” this is not the case: Ivoluntarily chose not to enclose Li Ye’swork within traditional disciplinary divisions. As long as the reader considers the object of study to be “simply” Yigu yanduan 益古演段 (Development of Pieces [of Areas] [according to] [the collection] Augmenting the Ancient [knowledge]), this text will indeed come across as of less interest. The text written by Li Ye in 1259 will never be anything but alist of problems concerning the solution of quadratic algebraic equations. Many historians have regarded it as adidactic text to introduce readers to the knowledge necessary to understand Li Ye’s other work, Ceyuan haijing 测圆海镜 (Sea Mirror of Circle Measurements), which is commonly viewed as the centerpiece of his oeuvre. What Iwant to demonstrate is that this text is not only atreatise on mathematics, but also the support of philosophical-type practices, even meditative ones, independent of Ceyuan haijing. The many diagrams inserted into the text are not illustrations of equations, but support for apractice of representation and visualization. Ihave chosen to point out the connection that exists here between the history of mathematics, the philosophy of language, and the anthropology of meditative practices (Heifring Citation2016; Robinet Citation1995). In my view, that is the most fruitful approach to Li Ye’s experiment. Acknowledging its complexity, Iwillfully avoided once again reducing the text to what it is not: simple narration.
