Reading instructions of the past, classifying them, and reclassifying them: commentaries on the canon The Nine Chapters on Mathematical Procedures from the third to the thirteenth centuries

Abstract

AbstractThis essay approaches the knowledge required to write up and use instructions with a specific method. It relies on specific procedures taken from the Chinese canon The Nine Chapters on Mathematical Procedures (九章算術), which, in the author's view, was completed in the first century CE. These procedures enabled readers to do things. To analyse the type of knowledge required to produce these texts of procedures and to use them, the essay puts into play two layers of commentary. The ancient layer was written between the third and the seventh centuries, whereas the later layer was composed between the eleventh and the thirteenth centuries. The author shows that these two layers of commentary read the same text of procedure differently, using different approaches and understanding it differently. The author also shows how the two layers of commentary use mathematical problems to approach a procedure, even though problems are used differently in the two contexts. This illustrates how, in different contexts, actors interpreted the same instructional text differently, both with respect to what the text meant and with respect to how one could make sense of it.