Archaic Metrological Systems from Ur: Notes
1 I want to thank G. Cifoletti and J. Ritter who were the first academic referees of the work on which this article is based. Grateful acknowledgement is also made to J.-M. Durand, B. Foster, J. Friberg and especially B. Lafont and R. K. Englund for their many helpful comments.
2 The tablets will be designated in this paper by their publication number.
3 S. L. Woolley, Ur Excavations II: The Royal Cemetery (London: The British Museum and the University Museum, University of Pennsylvania, 1936); S. L. Woolley, Ur Excavations IV: The Early Periods (London: The British Museum and the University Museum, University of Pennsylvania, 1956).
4 Antiquaries Journal 10 (1930) 327-337; for the papers about Woolley’s work, see E. L. Mallowan, Iraq 22 (1960) 1-19.
5 S. L. Woolley, Ur of the Chaldees: A Record of Seven Years of Excavation (London 1929, revised edition 1954).
6 E. Burrows, Ur Excavations Texts II: Archaic Texts (London: The British Museum and the University Museum, University of Pennsylvania, 1935).
7 In chronological order: I. Golgher, “La structure économique et sociale de Sumer présargonique II,” Thèse pour obtenir le diplôme de l’Ecole des Hautes Etudes (Section IV) à la Sorbonne (Paris 1959); H. J. Nissen, Zur Datierung des Königsfriedhofes von Ur (Bonn 1966); H. T. Wright, The Administration of Rural Production in an Early Mesopotamian Town (=Museum of Anthropology, University of Michigan no. 38; Ann Arbor 1969); P. Charvat, “Early Ur,” ArOr 47 (1979) 15-20; P. Charvat, “Early Ur-War Chiefs and Kings of Early Dynastic III,” AoF 9 (1982) 43-59; J. Bauer, “Ortsnamen in den frühen Texten aus Ur ,” WO 18 (1987) 5-6; P. Steinkeller, “Grundeigentum in Babylonien von Uruk IV zur frühdynastischen Period II,” in Das Grundeigentum in Mesopotamien, Jahrbuch für Wirtschaftsgeschichte (Berlin 1988) 11-27.
8 S. L. Woolley, Ur Excavations II: The Royal Cemetery.
9 Tablets nos. 24, 68b, 73, 87, 90, 122, 133, 183, 188 and 218. I would like to thank the Trustees of the British Museum and the University Museum of the University of Pennsylvania for having provided me with these photos, and in particular J. Ritter who acted as intermediary.
10 For example, in tablet no. 87, the signs inscribed by Burrows in obv. iii 1 are not two notches with two “circles” but four notches. The signs which he has copied in i 1 of the tablet no. 122 are not visible on the photo (the tablet is very damaged).
11 A. Falkenstein, “Keilschriftforschung: Ur Excavations Texts II von E. Burrows,” OLZ 2 (1937) 95.
12 F. Pomponio and A. Alberti, Pre-Sargonic and Sargonic Texts from Ur edited in UET 2. Supplement (=Studia Pohl Series Maior 13; Rome: Biblical Intitute Press, 1986) p. 9. Pomponio studied the evolution of ten signs (BA, DA, DI, E2, IGI, KA, MU, NINDA, PA, ŠE and ŠU-NIGIN2) in texts from eight different sites: Ur, Fara, Abu Salabikh, Ebla, Lagash, Adab, Nippur and Zabala.
13 P. Steinkeller, “Studies in Third Millennium Paleography 1: Signs TIL and BAD,” ZA 71 (1981) 19-28.
14 Ibid., table A on p. 13.
15 For example, in the texts from ED IIIb Lagash.
16 See R. D. Biggs, OIP 99, p. 44, fn. 8, for further discussion of this phrase.
17 UET 2, p. 4.
18 The formats of the Jemdet Nasr and Late Uruk texts have been dealt with by R. K. Englund and J.-P. Grégoire in The Proto-Cuneiform Texts from Jemdet Nasr (=MSVO 1; Berlin 1991) pp. 10-12, and Englund in J. Bauer, R. K. Englund, M. Krebernik, Mesopotamien: Späturuk-Zeit und Frühdynastische Zeit (=OBO 160/1; Freiburg, Switzerland, 1998) pp. 56-64, respectively.
20 M. W. Green and H. J. Nissen, Zeichenliste der Archaischen Texte aus Uruk (=ATU 2; Berlin, 1987).
21 R. K. Englund, ATU 5, p. 31. Englund argues that the second tablet is to be dated to the Early Dynastic periods I or II, because the “rectangular shaped signs” are very common in the archaic texts from Ur.
22 M. A. Powell, “Sumerian Area Measures and the Alleged Decimal Substratum,” ZA 62 (1972) 171.
23 R. D. Biggs, “On Regional Cuneiform Handwriting in Third Millennium Mesopotamia,” OrNS 42 (1973) 39-46 as well as M. Lambert, RA 53 (1959) 218.
24 Many scholars have taken part in the “Berlin Workshop” at one time or another: P. Damerow, R. K. Englund, J. Friberg, J. Høyrup, M. Powell , H. Nissen and J. Ritter. See Høyrup’s introduction to the volume J. Høyrup and Peter Damerow, eds., Changing Views on Ancient Near Eastern Mathematics (=BBVO 19; Berlin, 2001) vii-xvi.
25 J. Friberg, The Third Millennium Roots of Babylonian Mathematics I ; A Method for the Decipherment, throught Mathematical and Metrological Analysis of Proto-Sumerian and Proto-Elamite Semi-Pictographic Inscriptions (Department of Mathematics, The University of Göteborg, 1979).
26 The minimal number is possibly 5, if the systems “area” 1 and 2 are identical, but this hypothesis is very uncertain.
27 Despite the cumbersome notations chosen by the Berlin project ATU to identify numerical signs, it is important to avoid unnecessary confusion by accepting “Nn” as convention in future discussions of archaic texts.
28 ATU 2, 136-141.
29 ATU 2, 132-135.
30 I have established six groups, but I am not sure that systems “area” 1 and 2 can be clearly dissociated.
31 UET 2, plts. 35-37.
32 Rural Production p. 100.