precursors in Mesopotamia, it now seems most probable that Mesopotamia had no
idea of a sabbath.^34 They did not have weekends, but certain phases of the lunar cycle
were holidays. At Girsu, for instance, the “new light” of the moon (usually the
twentieth day of the month) was always a day off (Sallaberger 1993 : 96 and footnote
418 ). Workers generally had five or six days off per month (Gomi 1984 : 6 ).
CONCLUSIONS
It is hard not to wonder at the contrast between the evolution of counting and
mathematics in Mesopotamia, which seems to have a clear progression and concrete
stages of development, with the anarchy and perhaps conceptual stagnation of the third
millennium calendrical systems. Our own methods of calendrics are somewhat archaic
and convoluted, so we would be uncharitable to throw stones. Most importantly,
however, as I have tried to stress, calendars in the third millennium were subordinate
to other, chiefly cultic needs, and could be adjusted as needed. Both calendars and
counting provide windows into the fascinating world of third millennium Babylonia,
a world in which everything had its proper place.NOTES
1 Originally put forward by Hildegard Lewy in 1949 , the idea of a decimal substratum to Sumerian
counting was soundly rejected by Powell ( 1972 : 166 ).
2 Edzard 2003 : 62.
3 Englund 1988 : 133. These sixty signs are to be found in the Uruk Signlist and are referred to by
scholars as ZATU N- 1 through N- 60 , or N 1 etc.
4 Also there were systems for liquid measurement, which we will not consider here.
5 Note the local variations: Lagash had had a gurof 144 sila 3.
6 Boyer 1991 : 30. That is to say, Babylonians could solve three-term quadratic equations which, in
our systems of writing, would look like x^2 + px = q, or x^2 + q = px.
7 Powell 1976 : 430 (the table of squares is sometimes identified as a metrological table); Robson
1999 : 168 ; Robson 2008 : 31 – 32.
8 The Sargonic problem texts are also discussed in Friberg 2005 : 1.
9 Positional notation, also called place notation, or in Robson’s terminology, the sexagesimal place
value system (SVPS), had as its function the aim to “ease movement between one metrological
system and another. Lengths, for instance, that were expressed in sexagesimal fractions of the rod
instead of a combination of rods, cubits and fingers, could be much more easily multiplied...
and then converted to more appropriate units if necessary. The SVPS, in other words, was only
a calculational device: it was never used to record measurements or counts. That is why it
remained a purely positional system” Robson 2008 : 16. Note that Friberg doubts that place value
notation was operational in the Sargonic corpus: he notes that his is a minority opinion, Friberg
2005 : 1 , 21.
10 Powell 1976 : 421. The tablet in question is YOS 4. 293.
11 Dialouge 3 : 15 ff; Civil 1966 : 123.
12 This school dialog appears in A. Sjoberg, “Der Examenstext A,” ZA 64 ( 1975 ): 144 ; discussed in
Robson 1999 : 181.
13 This translation of Shulgi B is from ETCSL, available online at http://etcsl.orinst.ox.ac.uk.
14 The Gregorian calendar was adopted in 1582 , though some places – such as Sweden – did not
adopt it until the early eighteenth century.
15 Usually a year name would commemorate only one category at a time. There are occasional
exceptions, such as Naram-Sin year k, which refers both to the laying of the foundations of a–– Tonia Sharlach ––