Looking at it from Asia: the Processes that Shaped the Sources of History of Science by Florence Bretelle-Establet

Author:Florence Bretelle-Establet
Language: eng
Format: epub, pdf
Publisher: Springer Netherlands, Dordrecht

Reading The Nine Chapters as a Canon

On the basis of what we see above, the question of understanding what it means, in the commentators’ view, that The Nine Chapters be considered a canon can be reformulated more specifically. We may ask what motivated the search for the yi of The Nine Chapters. What was the ambition of this quest carried out by the exegetes, which assumed that The Nine Chapters was a (very) special type of text?

The answer I give to the questions relies on two observations.

First, all the commentators on The Nine Chapters whose exegesis survive to this day have formulated a list of fundamental operations from which, in their view, all mathematical knowledge derives.58

Second, the way in which proofs are carried out in the commentaries brings to light fundamental operations that underlie the procedure, the correctness of which is to be established.

The two facts are correlated since the operations brought to light through inquiring into the yi of a procedure are the very ones that are found in the lists stated by the commentators. This fact implies that the proofs on distinct procedures were not carried out independently of each other. Rather, they seem to have been reworked in correlation to each other, in order that the common fundamental operations they point to are brought out.

These observations lead me to the hypothesis that the commentators believed that the canon indicates in this way the most fundamental operations required for devising any procedure. In other ways, the fact for The Nine Chapters to be a canon meant for the commentators the belief that, through delving into its depths, they would unearth the most fundamental operations. Moreover, as a canon, The Nine Chapters would contain in this way all fundamental operations and thereby cover all mathematical procedures. Let us note that, even though all the commentators express their faith that the canon encompasses all mathematical knowledge, they differ on the list of fundamental operations they suggest.

Two pieces of evidence seem to me to support this conclusion. On the one hand, we encountered earlier another term referring to a type of “meaning” for procedures: the term yi’ 義. If we analyze the way in which our commentators use this term, it appears to refer precisely to the meaning of a procedure expressed by means of the fundamental procedures underlying it and brought to light through the proof. Let me stress that such a meaning could only be found through ‘tuning’ the proofs of different procedures, as the strings of a musical instrument are tuned relative to one another, in such a way that together they reveal the yi’. Moreover, if we turn again to Liu Hui’s preface, it clearly indicates the aim of his commentary as attempting to synthesize the “source of mathematical procedures.” This source can be interpreted as referring to the list mentioned.59 Identifying what constitutes this source may be what Liu Hui eventually understood and what convinced him to compose his commentary, as we saw above.

In conclusion, in

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