Reverse algorithms in several Mesopotamian texts 387
in Nippur, Ur and elsewhere. 9 Th e school texts yield precious information
about the context of the use of the reciprocal algorithm and will be used on
a case-by-case basis to supplement the small, essential body of texts pre-
sented in Table 12.1.^10
Th e historical problem posed by relationships that may have existed
between the authors of diff erent texts is diffi cult to resolve because the
provenance is usually unknown and the dating is uncertain. Some available
information seem to indicate that the numeric texts and their pedagogical
parallels may pertain to the southern tradition (Ur, Uruk, Nippur), and the
verbal texts, notably Tablet B which may come from Sippar, belong to the
northern tradition of Old Babylonian Mesopotamia. 11 Th e possible historic
opposition between the north and the south, however, did not exclude
certain forms of communication, since the two traditions were not iso-
lated and the scribes from diff erent regions had contact with one another
through numerous exchanges, notably circulating schoolmasters. 12 E v e n
though uncertainty about the sources does not permit the establishment of
a clear geographic distribution, it is entirely possible that the two types of
texts existed in the same contexts. Regardless of the relationship between
the authors of these diff erent styles of texts, it is possible to hypothesize two
points of view about the same algorithm. Th e important point, whether
or not these two points of view emanate from the same scribal context,
is that they clearly have diff erent objectives. Th e verbal texts are series of
instructions, which appear to have been intended to help someone execute
the algorithm. Some portion of the numeric tables are school exercises
intended for the training of student scribes. Th e function of Tablet A seems
to have been of a diff erent nature.
Tablet A does not conform to the typology of a school tablet, even though
it was used in an educational context, as was probably the case with all the
mathematical texts of the Old Babylonian period. Th rough a comparison of
Tablet A with parallel or similar texts, I would like to provide more detailed
9 What are called ‘school tablets’ in Assyriology are the products of students in scribal schools.
Th ese tablets generally have a standardized appearance and contents, and because of this fact
are easily recognizable, at least in the case of those that date from the Old Babylonian period.
10 Th is documentation may be specifi ed further: the list of parallels with A is presented in Table
12.6 ; the other tablets containing reciprocals are assembled in Table 12.7 ; those which contain
calculations of square and cubic roots are in Table 12.8.
11 Th e provenances of diff erent tablets and their parallels are detailed in the notes relative to
Tables 12.1 , 12.6 , 12.7 and 12.8. In the case of Mari, it is interesting to note that the tablets from
this northerly site seem more akin to the tablets of the south than those of the north. Th us, if
diff erent scribal traditions were confi rmed, they would clearly reveal complex trans-regional
phenomena of communication, and not only local peculiarities.
12 Charpin 1992 ; Charpin and Joannès 1992.