Reverse algorithms in several Mesopotamian texts 415
relatively unifi ed with that of the reciprocal algorithm. Th e function of the
reverse algorithm seems the same in all cases. It does not enact a verifi ca-
tion of the result, or even a verifi cation of the algorithm itself in the case
of the square roots, since the direct and reverse sequences do not rely on
the same algorithm. Th eir presence seems to indicate something else with
respect to the nature of the operations themselves. It stresses the fact that
the reverse operation of a square is the square root, and the reverse opera-
tion of the reciprocal is the reciprocal itself.
Conclusion
I can now reconsider several questions left aside from the preceding dis-
cussion. Th e function of the tablet is at the heart of these questions, and I
will treat these questions before returning to the ways of reasoning we can
detect in the text.
It has been seen that the content of Tablet A is connected with the context
of teaching but that it cannot be interpreted as a simple collection of data
intended to provide exercises for the education of young scribes. I have
suggested that its relationship with the school exercises could be the reverse
of what is generally supposed. It might not be a ‘teacher’s textbook’ from
which the school exercises were taken but rather a text constructed and
developed from existing school material. Indeed the relationships between
school exercises and scholarly texts were probably not so unidirectional and
the two relations could well be combined. However, the point which inter-
ests us here is that Tablet A appears in the form of an original inquiry and
its purpose seems to have been communication between erudite scribes.
Seen from this perspective, the same piece of text takes on another dimen-
sion. Th e way in which the text is organized and arranged, and the reper-
tory of numeric data on which it is built, are essential components of the
text. In a certain way, these components constitute the means of expression
by which Tablet A refers to the reciprocal algorithm.
But what is the relationship between Tablet A and the algorithm for recip-
rocals? Is it a practical text in the sense that the text executes concretely the
operations necessary for the determination of a reciprocal? It is not certain
that the writing of a text was essential to the execution of the algorithm,
since the known texts obviously record only part of the series of actions that
allow the result to be obtained. On the one hand, the multiplications are
probably executed elsewhere. On the other hand, by the standards of school
practices, the written traces are incomplete. Th ey oft en state only the fi rst