Abstract
Mesopotamian administrative documents provide an extraordinary insight into the mathematics used in the recording of economic data from various sectors of early state economies. This paper will discuss the computation and quantification procedures as related to the administration of irrigation systems in Southern Mesopotamia in the third millennium BCE. The largest and the most detailed corpus of such administrative texts derives from the highly bureaucratic Ur III state (2112–2004 BCE) that controlled an area roughly corresponding to modern Southern Iraq at the end of the third millennium BCE. Texts discussed in this paper provide insight into one of the earliest examples of geographic surveys by which the natural environment was translated into quantifiable units, necessary to compute workloads, labor demands and the division of the work amongst different social groups and state institutions. It has been proposed that Ur III bookkeeping served to keep track of the fulfillment of a province’s tax obligations and/or was the result of a planned economy. However, this paper suggests that it equally functioned as a means to streamline the workflow associated with the upkeep and operation of irrigation systems.
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC Grant Agreement No. 269804, Mathematical Sciences in the Ancient World.
I wish to thank Robert C. Hunt, Elizabeth C. Stone and Piotr Steinkeller for their valuable comments and suggested corrections. Any mistakes or omissions are of course the sole responsibility of the author. I also want to thank Maurits Ertsen for reviewing the hydraulic feasibility of my proposed reconstructions of ancient irrigation devices and systems. I want to give special thanks to Kelliann Volsario for proofreading this paper. I am particularly indebted to Christine Proust for checking and correcting (!) the calculations and mathematical discussions of this paper. My frequent miscalculations in the sexagesimal system made me realize that I would have been quite a lousy Sumerian bureaucrat. This research has been made possible thanks to the financial support granted by the Wenner-Gren Foundation.
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Notes
- 1.
Note that the Sumerian terms pa4 a-da-ga and pa4/5 refer to lower order canals and not to primary canals. There are very few linear dimensions recorded for these lower order canals as well as canals with the Sumerian determinative i7/id2 which designates either a river or a larger man-made canal. A systematic study of these terms is provided in my doctoral thesis.
- 2.
There has been some debate about the reading of Ur-Namma’s name. The more traditional reading is Ur-Nammu while more recent studies show that the name should be read Ur-Namma (see full discussion Flückiger-Hawker 1999: 8–9). Note, that years are counted after the years of reigns of the respective kings. Thus, AS 8 refers to the eighth year of Ama-Suens reign.
- 3.
For a detailed study of the succession in the royal family at Ur and the ruling family of the province Umma, see Dahl (2007).
- 4.
The exact number of provinces in the Ur III state is still not known (Sharlach 2008: 80).
- 5.
For the reading of the name of this settlement, see Steinkeller (2011: 377).
- 6.
Ur-E’e also held the position of chief livestock administrator (šuš3) of the province Umma, a position he inherited from his farther Ur-Nigar, the ancestor of the ruling family at Umma. Ur-E’e never referred to his father Ur-Nigar as the previous chief livestock manager. A practice that can also be observed for Lu-Haya, Ur-E’e’s son and who succeeding him as chief livestock administrator. The same applies to Šara-izu, the son of ARAD2(mu) the chief of the granary (Dahl 2007: 86).
- 7.
MCS6, 83, BM 105334 (AS 2); MVN21 341 (n.d.) and AnOr 1, 303 (n.d.).
- 8.
This subdivision only existed in the fourth decade of Šulgi’s reign. Prior, the agricultural land was subdivided into the so-called Menkar (later Gu’edena and Mušbiana) and Lamah-field (later Da-Umma) (Vanderroost 2012a Vol. I: 119).
- 9.
According to text AAS 83 (Š 35 iv to Š 36 i) 104 plows were in operation in the year Š 35 and according to MCS 6, 83, BM 105334 (AS 2) 101 in the year AS 2 (Vanderroost 2012a Vol. I: 85, 94, 103–108, 178).
- 10.
This term is related to a set of tablets which are documenting the inspection of plow-oxens, listed under the responsibility of a certain ‘inspector of the plow-oxen’ (nu-banda3 gu4) and their subordinated ‘cultivators’ (engar) (Heimpel 1995). The plows operating in Da-Umma ki district amounted to approximately 54, 22 for the Apisal district and around 28 for the Gu’edena and Mušbiana district (Vanderroost 2012a Vol. I: 85, 94, 103–108, 178).
- 11.
As could be shown in text Talon-Vanderroost 1 and 2, children are listed as being provided with rations ranging between 10–30 sila (1 sila3 = 1 l) of grain per month. They were included in the plow team as junior males working between 1/3–2/3 of an adult workload, depending on their age. Once a new team mate was needed they were promoted to full wages and adult work-loads (Vanderroost 2012a: 137–138, 143–145).
- 12.
Note that during Šulgis reign the more common used term for scribe of the (plow-)oxen was šabra gu4 which is equivalent with dub-sar gu4 10 but became obsolete during Amar-Suens reign (Vanderroost 2012a Vol. I: 111–115).
- 13.
Thus, the subsistence plot of a low-class workers amounted to 4 iku while the amount granted for example to governor Ur-Lisi from Umma amounted to 60 bur (389 ha) of land (Dahl 2007: 61; Steinkeller 1987a: 27, 2013: 351). Land allotments for agricultural staff varied between 3 iku for ox-driver (ša3-gu4) and 6 iku for cultivators (engar). The size of plots allotted to inspectors of the plow oxen (nu-banda3-gu4) amounted to 1 bur and those allotted to a scribe of 10 plow teams (dub-sar gu4) to 3 bur (Vanderroost 2012a Vol. I: 126).
- 14.
Thus, for example amongst the individuals conscripted to perform corvée labor at the construction site of the palace of Tummal we find even members of the governor’s family of Umma; Ur-e’e, the brother of the governors Ur-Lisi, A’a-kala, and Dadaga (Steinkeller 2013: 350–351). Even though it can be assumed that individuals of such social standing would hire a laborer who would perform the corvée duty on their behalf, they were nevertheless required to contribute the required amount of workdays to the central government (Steinkeller 2013: 367).
- 15.
- 16.
According to Maekawa (1987b: 39) the term ugula did not designate a specific position in the administrative hierarchy. However, according to Koslova (2008: 154) the term describes a position at the very bottom of the administrative hierarchy. According to Vanderroost (2012a: 34, fn. 111) the term ugula in the agricultural sector simply denotes the person in charge of a group of workmen engaged in carrying out a work project. Thus, if an inspector of the (plow-)oxens (nu2-bada gu4) supervised his subordinated cultivators and ox-drivers at a work project, he is listed by the title ugula and not by his administrative position of a nubanda gu.
- 17.
Presenting the full argument for the translation of kab2-ku5 with ‘flow divider’ goes beyond the scope of this paper. The argument including the supporting evidence is discussed in my doctoral thesis (Rost 2015)
- 18.
The agricultural personnel considered are two scribes of 30 plow teams (dub-sar gu4-30), ten inspectors of the (plow-)oxen (nu-banda3-gu4) and 54 cultivators (engar) and their respective ox-drivers (sa3-gu4) and additional family members (male, minors or elders). The other professions listed as agricultural staff were individuals responsible for guarding the grain silos (lu2-i3-dub), some inspectors of unclear function (šar2-ra-ab-du), vegetable gardeners (lu2-nisig), watchers of water (a-igi-du8), carpenters (nagar), leatherworkers (ašgab), felt makers (tug2-du8), scribes (dub-sar) and the guardians of orchards (agar4-nigin2) (Vanderroost 2012a Vol. I: 128–129). Erdingir is listed as ‘old’ (šu(-gi4)), which indicates that he must have already been retired from his position which was probably taken over by his son Šarakam (Steinkeller 1988: 79, fn 48; Vanderroost 2012b Vol. II: 54, fn 172, 100, 179).
- 19.
- 20.
There is no conclusive evidence that the feature described in this text with the dimensions of 12 m width, 2 m depth and 6780 m length is a canal. However, the presence of a flow-divider points to a watercourse. The width and the length of this canal (the text might only describe a section of it) as well as the depth point to a large canal or natural watercourse, such as a tributary of the Tigris River that had over time been considerably modified.
- 21.
Fernea reports an average annual silt accumulation of 30 cm within a 1–2 m wide canal. The workload for that particular canal section is summarized in a subtotal (r.i 2) that is later combined with the subtotal of the workload of the second part of the texts. Noticeable is a subsection of the canal stretch of 1.3 km (o.ii 17–19) for which no depth and thus no work volume is recorded. This evidence might be pointing to the conclusion that we might be dealing with a 7 km extension of a pre-existing major canal.
- 22.
I am indebted to Dr. Maurits W. Ertsen for reviewing and discussing the hydraulic feasability of the proposed reconstruction of this flow divider (May 2013).
- 23.
The Sumerian terminology of various dam structures is not yet completely understood and is addressed in full in Rost (2015).
- 24.
Civil (1994: 125–126) suggests that eg2-sa-dur2-ra described a dam at the end of a field. “To understand the meaning of eg2-sa-dur2, one must remember the shape and location of Mesopotamian fields. The plots were narrow, sometimes extremely narrow, long strips of land with the upper end (sag an-na or sag 1-kam) facing a water course. The orientation of the field was chosen in such a way that the water runoff would be parallel to the long sides (ús2) of the plots. This arrangement gave the cultivator of each plot direct access to and control of the water. The lower end (sag a-ki-ta or sag 2-kam) was part of the field more subject to flooding on the one hand, and where water had to be stopped when the land was irrigated, on the other. The low-lying area next to this end of the field was termed sa-dúr. Its dikes (ég sa-dúr-ra) were naturally of great importance and can be defined as the levees or embankments other than the once built alongside the water courses, concretely the ones at the end of the fields opposite to the canal, and, presumably, on the sides too. These levees, probably relatively low, allow basin or border irrigation of the field… Physically, sa-dúr-ra levees, inasmuch as their dimensions are given are remarkable wide: 6 m in TENS 459.”
- 25.
- 26.
See for example, RA 73 031 31: o.i 8–14 ‘23 nindan gid2 1/2 nindan dagal 1 kuš3 bur3 sahar-bi 11 1/2 sar u2 kin a-bi 3 5/6 sar eg2 Muru13 uš2-a sahar si-ga’ ‘138 m length, 3 m width and 0.5 m height—its volume is 207 m3 and its plant-matter earth mixture is 69 m3—pilling up earth (in order to) close the dam of the Murub-field.’
- 27.
CBCY 3, NBC 02932: o. 1–4 ‘kab2-ku5 gu-la da E2-duru5-a-ša3-gana2-mah’; UTI 5, 3121: o. 1–3 ‘kab2-ku5 gu-la gana2-mah’; BPOA 6 0900: o. 1–4 ‘kab2-ku5 gu-la gana2-mah’.
- 28.
UTI 6 3713: o. 1–3 ‘kab2-ku5 gu-la a-ša3 I7-lugal’; UTI 6 3810: r.i 16–17 ‘kab2-ku5-gu-la I7-lugal’.
- 29.
The only evidence of measuring tools for linear dimensions is a depiction of a graded ruler on the statues B (fragmentary) and F of the ruler Gudea of the city state Lagaš (2200 BCE) that implies a cubit in the 50 cm range. Further, a notched bronze bar was found in the ancient city of Nippur, probably predating the standard cubit found from Gudeas’ time, measuring 5.18 cm (Powell 1987–1990: 462).
- 30.
‘a-am-še-e ša 2 EŠ2 aš-la-tim idnašunūšim’ ‘give them enough date palm fiber for two ropes (and send me seventy date fronds). YOS 2 95: 16 Old Babylonian letter (Chicago Assyrian Dictionary ašlu c).
- 31.
Akala and Kuli are quiet common Sumerian names and thus, it is difficult to know which individual is mentioned in the text. There is an Akala and a Kuli known as inspectors of (plow-)oxen for the Gu’edena and Mušbiana, however, there is too little evidence to isolate them any further (Vanderroost 2012b Vol. II: 62, 286, 2012a Vol. II: 249–252).
- 32.
As mentioned above, the term ugula is used instead of nubanda gu, when inspectors of the (plow-)oxen are functioning as supervisors of their subordinated work crew and ‘took charge’ of the operation (Vanderroost 2012b Vol. II: 124).
- 33.
To my knowledge, the dimensions of flow-dividers are never given in surface units, but always in units of volume. Thus, I would argue that this line refers to the number of flow dividers located within an area of 6 bur that correspond to the standardized size of one unit of agricultural land. This might be an indication that we are dealing with Ur-Šulpa’e, the cultivator, under the supervision of the inspector of the (plow-)oxen Gutar, who was in charge of this particular agricultural unit. However, it is also possible that we are dealing with the inspector of the (plow-)oxen Ur-Šulpa’e who operated in the Da-Umma ki district (Vanderroost 2012b Vol. II: 183–184, 270, Table 14). The tablet was written at a time when Lugalemah(e), the scribe of 30 (plow-)oxen of the Da-Umma ki had already been succeeded (around ŠS 3–5) by three scribes of 10 (plow-)oxen, Lugalnesag(e), Abbagina and Kaš. Thus, this would have been the superiors to Ur-Šulpa’e in case we are dealing with the inspector of the (plow-)oxen of the Da-Umma ki district.
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Rost, S. (2020). Insights into the Administration of Ancient Irrigation Systems in Third Millennium BCE Mesopotamia. In: Michel, C., Chemla, K. (eds) Mathematics, Administrative and Economic Activities in Ancient Worlds. Why the Sciences of the Ancient World Matter, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-030-48389-0_5
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