48 karine chemla
exists. 54 As alluded to above, Th e Nine Chapters , like Babylonian tablets,
describes some of the algorithms in such a way that they are transparent in
regard to the reasons accounting for the correctness of the computations
they prescribe. At this stage in the reasoning, ‘transparency’ is an observer’s
category. However, it is crucial that, with respect to this Chinese document,
the commentators did read the text of the algorithm as transparent and
made precisely these reasons explicit in their exegesis. ‘Transparency’ can
thus also be shown to correspond to an actor’s category.
It is in this context that the commentators bring to light exactly the
same type of ‘meaning’ that Høyrup suggests reading in the transparent
algorithms found in Babylonian tablets. In the Chinese case, we can thus
demonstrate that this is the way in which the earliest observable readers
actually did ‘interpret’ the texts. Such evidence supports the hypothesis
that the practitioners of mathematics in ancient China designed a kind
of text to formulate algorithms, similar to that shaped in Mesopotamia to
express algorithms transparent about the reasons of their correctness. Th e
proof expressed in this way was read as such by ancient readers. 55 F r o m t h e
point of view of the reception, aft er all, the historical continuity between
Babylonian and Arabic sources also indicates that Babylonian proofs were
read in this way by subsequent practitioners. On the other hand, from the
point of view of the text itself, it is remarkable that in diff erent contexts, the
mode of expression chosen for indicating the reasons of the correctness was
the same. In my view, this remark indirectly reinforces Høyrup’s argument,
in that it shows the usefulness of this property of the statements for practi-
tioners. Th e important point here is that for the Chinese commentators, in
my interpretation, such a reading was a way of making the ‘meaning’ of the
classic explicit. It is in order to designate that ‘meaning’ that they used the
concept of yi , which I introduced above. 56
Th is brings us back to the question, for which we now have plenty of
evidence, of how the commentators made use of the context of a problem,
or the geometrical analysis of a body, to formulate the ‘meaning’ they read
54 Using ancient commentaries to interpret an ancient text does not mean that we attribute
anything found in the commentaries to the text commented upon without caution. Chemla
1997 –8 constitutes an example of how the two kinds of sources are treated separately and only
thereaft er articulated with each other.
55 Th e commentators read the expression of the reasons for the correctness in various elements of
the classic. Th e structure of the text is one of them; compare Chemla 1991. Th e terms used in
Th e Nine Chapters to prescribe an operation is another one – see, for instance, Chemla 1997 –8.
Chemla 2010 attempts to give a systematic treatment of this question and to highlight elements
of a history of these kinds of text.
56 On the fact that commentators assumed that the classic indicated the ‘meaning’ or ‘reasoning’,
see Chemla 2003 , Chemla 2008a , Chemla 2008b.