Cuneiform Digital Library Journal
2005:1
ISSN 1540-8779
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Unusual Accounting Practices in
Archaic Mesopotamian Tablets

Salvatore F. Monaco < vesnadavidovic@tin.it >
UPE, Monterotondo, Italy

Keywords
proto-cuneiform, accounting, rations, weighted means


§1.1. The archaic texts examined in this paper all come from the earlier Erlenmeyer Collection. As is widely known, this tablet collection was auctioned off in December of 1988 by the London auction house Christie’s, and the majority of them were purchased by the State of Berlin and transferred to the Vorderasiatisches Museum as a permanent loan.[1] Many of the tablets are fully preserved and in very good condition, allowing unequivocal analysis of their administrative contents. Unfortunately, deriving from irregular excavations, the provenience of the tablets is unknown and can be only tentatively proposed on the basis of similarity with other tablets.

 

§1.2. The administrative accounting of grain products in the archaic texts follows in general (for the period Uruk III/Jemdet Nasr) the practice of listing on the obverse of the tablet a number of transactions, recording the quantity of each product with its corresponding derived numerical ŠE system.[2] These products are normally totaled using numerical notations that qualify them, or combined for a grand total on the reverse of the tablet and recorded generically in the numerical Š system.[3] In some instances, the total may precede the list of the detailed grain products.[4] In the following paper, a few exceptions to such administrative practices will be analysed, with the intention of investigating the rationale followed by the scribes in those peculiar accounting notations. For the sake of clarity, the numerical notation used for each entry or summation will in most cases be presented together with the transliteration of the texts.

 

§2. Š totaled as Š*[5]

§2.1. MSVO 3, 55 (from Uruk?), is an account of two different entries of a grain product and malt[6] (both beer ingredients). The two entries are totaled on the reverse of the tablet and their destination is qualified as KUb2 ŠIMa (possibly “beer bread,” see below). The first entry seems related to a month, or to a special event (EZEN AN MUŠ3 = ezen dinanna ?).[7]

 

grain capacity system case transliteration
 
Š
obv. i 1a 1N14 2N1 HIgunûa AN U4 SIG MUŠ3a ˹NAGARa˺ EZENb
 
Š'
obv. i 1b 2N18
 
Š
obv. i 2a 1N14 4N1 1N28 KINGAL
 
Š'
obv. i 2b 4N3 1N40
 
obv. i 3 KUb2 ŠIMa
 
Š*
rev. i 1 3N20 1N28* HIgunûa
 
Š'
rev. i 2 2N18 4N3 1N40
    rev. i 3 KUb2 ŠIMa

 

§2.2. The entries of malt are measured and totaled in the final Š' notation. The grain product qualified as HIgunûa is totaled in case rev. i 1 in a derived numerical Š* notation,[8] which usually denotes grain groats. The present context may therefore indicate the equivalence of the two products, probably in different phases of the beer brewing process.[9] It should be noted, however, that the grain product HIgunûa is not necessarily associated with malt, and is occasionally delivered separately as “food” (GU7).[10]

 

§3.Š* and & Š’ totaled as Š*

§3.1. Tablet MSVO 3, 52 (from Uruk?), a similar account of two grain products (HIgunûa and malt) whose destination is also qualified as KUb2 ŠIMa (“beer bread” ?), presents some peculiarities.

 

grain capacity system case transliteration
 
Š&Š'
obv. i 1a 2N47 1N20 1N5 1N40 HIgunûa BA
 
Š*
obv. i 1b1 8N20 4N5 2N42a HIgunûa
 
Š'
obv. i 1b2 1N45' 2N18 2N3 4N40
    obv. i 2 KUb2 ŠIMa

 

§3.2. The quantities of the two beer ingredients recorded in their respective derived numerical ŠE systems are totaled in the first entry, qualified as grain rations (HIgunûa BA), and measured in the derived numerical Š* system,[11] with the exception of the least significant grain measure, represented by the numerical sign 1N40 of the Š' systsem. Accounts that combine grain products recorded in different capacity systems are not infrequent,[12] particularly in Jemdet Nasr tablets.

 

§3.3. The peculiarity of this text consists of its having totaled both the recorded grain products using the Š* notation, leaving one single sign in the other (Š') notation.[13] It seems evident that the reason for the adoption of such notation was due to the scribe’s intention to put in evidence the mixed nature of the grain products totaled, as subsequently detailed in the rest of the tablet.

 

§4.Š and Š' totaled as Š'

§4.1.MSVO 3, 12 (from Uruk?), is an account of malt that includes a small quantity of barley measured in the derived numerical Š system, totaled with a Š' notation and delivered as “food” provisions (GU7).

 

grain capacity system case transliteration
  Š' obv. i 1 3N40 1N24' MUD 3N57 TE
  Š' obv. i 2 1N3 E2a U4 KASKAL
  Š' obv. i 3 1N3 1N40 1N24' GA2a2+GU4+ŠE3 U BUa
  Š' obv. i 4 2N40 1N24' ENa SANGAa TUR 1N58 ŠIMa
  Š' obv. ii 1 1N3 2N40 1N24' GA2a2+GU4+ŠE3 SAGŠU
  Š' obv. ii 2a 1N18 4N3
    obv. ii 2b1 KAŠc
    obv. ii 2b2 KAŠc SUKKAL
  Š' obv. ii 3 4N40 1N24' E2a PIRIGb1+3N57
  Š' obv. ii 4 2N40 1N24' AN MUŠ DU PAPa E2a NUNa
  Š' obv. iii 1 ˹4N40?˺ [1N24'] NIN GALa E2a
  Š obv. iii 2 3N39a GI4a+A
    obv. iii 3 ˹GU7˺
  Š rev. i 1 2N14 ŠEa BULUG3 E2a+KURa?
  Š' rev. i 2 3N18 GU7
    rev. i 3 SAGŠU GA2a2+GU4+ŠE3
    rev. ii 1 GU7

 

§4.2. My interpretation of case obv. iii 1 is based on traces of the slash, typical of the signs belonging to the derived system Š', present on the edge of the break in the upper right corner of the tablet. This break may have only included the numerical sign 1N24', also expected by analogy with the preceding cases, with the consequential reading 4N40 of the preceding signs.[14] The listed quantities of malt, including the small quantity of unprocessed barley (ŠE) in case obv. iii 2, total 17.9 barig, rounded off to 18 barig in case rev. i 2 of the reverse. The additional quantity of barley registered on the reverse (case rev. i 1) is qualified as BULUG3 (= munux, “malt”) and therefore represents an additional confirmation of the correct interpretation of the derived numerical Š' system as referring to malt.

 

§5.Š and Š" totaled as Š": A double-entry account

§5.1.MSVO 3, 42 (from Uruk?), is a tablet in the British Museum (BM 140853) that contains an account of barley and emmer. Single entries of the two products are recorded on the obverse, together with their destinations. The reverse contains two different summations, both in terms of barley and emmer.

 

grain capacity system case transliteration
  Š Š" obv. i 1a 6N14 3N19 ŠEa LU2 MUD3d
  Š obv. i 1b1 6N14 ŠEa
  Š" obv. i 1b2 3N19 U4
  Š" obv. i 2a 1N46 ŠEa UNUGa E2a
  Š obv. i 2b1 5N14 ŠEa
  Š" obv. i 2b2 5N19
  Š obv. i 3 5N14 ŠUBUR SUG5 PAa
  Š obv. ii 1 4N14 TItenû ZAGa
obv. ii 2 LU2 MUD3d
  Š Š" rev. i 1a 1N45 1N46 8N14 ŠEa
  Š rev. i 1b1 2N45 ŠEa
  Š" rev. i 1b2 8N19
rev. i 2 LU2 MUD3d

 

§5.2. The first entry records a quantity of barley plus a quantity of emmer measured in their respective numerical systems Š and Š", followed by a separate list of the two products. The second entry records a quantity of barley in the Š" system, again followed by the separate list of the two products (and again measured in their respective systems Š and Š"). Two additional entries of barley complete the account on the obverse of the tablet. The entries are totaled on the reverse according to two criteria. First, the totals of the cumulative entries of the obverse (cases obv. i 1a, obv. i 3 and obv. ii 1 for the barley and case obv. i 2a for the emmer) are recorded in the same case (rev. i 1a) using their respective numerical systems; hence, the details of the quantities of barley and emmer listed on the obverse are totaled together in their respective Š and Š" systems. The following table offers a synoptic view of the double accounting in this text (counting “barig” = N1).

 

grain capacity system
Š
Š"
Š
Š"
Š
36
36
 
(obv. i 1a)
(obv. i 1b1)
 
Š"
18
18
(obv. i 1a)
(obv. i 1b2)
Š"
60
30
(obv. i 2a)
(obv. i 2b2)
Š
30
(obv. i 2b1)
 
Š
30
30
 
(obv. i 3)
(obv. i 3)
 
Š
24
24
 
(obv. ii 1)
(obv. ii 1)
 
 
Š
108
120
 
(rev. i 1a)
(rev. i 1b1)
 
Š"
60
48
 
(rev. i 1a)
(rev. i 1b2)

 

§5.3. The calculations are clearly based on a methodology compatible with the criteria of recording cumulative quantities of two different grain products under the same derived numerical systems (Š or Š"). The rationale of the adoption of such methods cannot, however, be directly deduced from the context of the tablet.[15]

 

§6. Š* and Š' totaled as Š
§ 6.1. MSVO 3, 51 (from Uruk?), is a tablet in the Louvre Museum (AO 29562) with an account of beer products (grain groats? and malt) totaled as a general grain measure in the capacity system Š. In contrast to most similar accounts, this tablet records first the total quantity, then the sub-totals, and finally the single entries.

 

grain capacity system case transliteration
  Š obv. i 1a 1N45 9N14 2N39a HIgunûa
  Š* obv. i 1b1 9N20 1N5 3N42a HIgunûa
  Š' obv. i 1b2 9N18 4N3 4N40
  Š* obv. i 1c1a 7N20 4N42a HIgunûa NAGAa
  Š' obv. i 1c1b 7N18 4N3 4N40
  Š* obv. i 1c2a 2N20 <4N42a> HIgunûa DUBa
  Š' obv. i 1c2b 2N18 4N40
obv. i 2 KUb2 ŠIMa

 

§ 6.2. The cumulative amount of grain products is recorded in the first case (obv. i 1a), qualified as HIgunûa. The two grain products are then sub-totaled in terms of HIgunûa (in a Š* notation) and malt (in a Š' notation). Finally, the quantities of the two products are listed in two separate entries, qualified respectively as NAGAa and DUBa. As in the accounts MSVO 3, 52 and 55 (treated in §§2-3 above), the products’ destination is designated as KUb2 ŠIMa (“beer bread”?). The table below shows the relationships among the single cases of the tablet.

 

grain capacity system
Š
Š*
Š'
114 2/5
55 3/5
58 4/5
(obv. i 1a)
(obv. i 1b1)
(obv. i 1b2)
42 4/5
46 <4/5>
(obv. i 1c1a)
(obv. i 1c1b)
12 4/5
12 4/5
(obv. i 1c2a)
(obv. i 1c2b)

 

§ 6.3. The quantity 4N42a in case obv. i 1c1b, indicated as <4/5> in the table, is best disregarded as a scribal mistake due to the “dragging effect” of the presence in the other cases of the same fractional quantity.


§ 7. The administrative term BA KI
§ 7.1. MSVO 3, 67 (from Uruk?), exhibits the common practice of listing on the obverse of an account certain quantities of grain products (barley and emmer) destined for various deliveries, with sub-totals and totals on the reverse. The two types of commodities are measured in their respective numerical systems Š and Š". On the reverse are first registered the totals, divided into two quantities according to criteria not recognizable for the barley (the tablet was unfortunately effaced in the corresponding case), and finally sub-totals that correspond to the sums of the listed quantities on the obverse with an additional quantity for each type of product. The following table shows the numerical relationship between the sums on the obverse and the totals on the reverse (all quantities measured in “barig”).

Case transliteration
capacity systems
Š
Š"
obv. i 1-obv. ii 8
111
obv. iii 1-obv. iv 7
65 2/5 2/25
rev. i 1a 2N45 3N14 3N1 ŠE
141
rev. i 1b1 1N45 7N14 3N1 X X
105
rev. i 1b2 6N14 [...]
36
rev. i 1c1 1N45 8!N14 3N14 GU7
111!
rev. i 1c2 6N14 BA KI
30
rev. i 2a 1N46 1N19 2N4
68
rev. i 2b1 9N19 [2N4]
56
rev. i 2b2 2N19 NUMUN GAN2 NAGAR
12
rev. i 2c1 1N46 5N4 2N41 1N29a 1N29a GU7
65 2/5 2/25
rev. i 2c2 2N4 2N41 1N24" KI BA
2 2/5 1/10


§ 7.2. It is evident that the structure of the totals and sub-totals of the two products is identical. The sub-total in case rev. i 2c1, qualified as “food” (GU7), corresponds to the sum of the quantities of emmer listed on the obverse (cases obv. iii 1-obv. iv 7); it follows that the sub-total in case rev. i 1c1, also qualified as GU7, should correspond to the sum of the quantities of barley listed on the obverse (cases obv. i 1-obv. ii 8), although the tablet clearly records 105 N1 (1N45 7N14 3N1), which I interpret to be a scribal mistake due to the “dragging effect” of the adjacent case rev. i 1b1 (a similar mistake has been noted to MSVO 3, 51, §6 above). In a similar way, the sum of the two quantities of emmer in cases rev. i 2b1 and rev. i 2b2 corresponds to the total reported in case rev. i 2a, and the sum of the two quantities of barley in cases rev. i 1b1 and rev. i 1b2 corresponds to the total reported in case rev. i 1a.


§ 7.3. The two additional quantities in cases rev. i 1c2 and rev. i 2c2 are qualified as BA KI or KI BA.[16] This term is attested in a number of Uruk III administrative[17] and lexical[18] tablets. The tablet W 20274,89 (see n. 17) from Uruk, offered below in transliteration, helps to clarify the meaning of this administrative term.

obv. i 1a 5N1 DUGc DUBa
obv. i 1b1 1N1 ZABALAMa AN BA ZATU751a
obv. i 1b2 1N1 SAL BA X ANŠEb?
obv. i 1b3 3N1 BA KIa
obv. i 2a1 1N1
obv. i 2a2 1N1 KU3a
obv. i 2b ZATU649
obv. i 3 1N1 KU3a ZABALAMa AB2
obv. i 4 1N1 SI4a NEa ŠEa GI
obv. i 5 GAa [...]
obv. ii 1 2N1 ZATU648
obv. ii 2 PIRIGb1+3N57 ABb SUa
obv. ii 3 3N1 SI U4 AB2
obv. ii 4 2N1 TUR3a A
obv. ii 5 GAa BUa HI
rev. i 1 [2N1 ZATU648]
rev. i 2 3N1 SI U4 AB2
rev. i 3 2N1 TUR3a A
rev. i 4a1 1N1
rev. i 4a2 1N1 KU3a
rev. i 4b ZATU649
rev. i 5 1N1 KU3a ZABALAMa AB2
rev. i 6 1N1 NEa SI4a GI ŠEa
rev. ii 1 1N14 3N1 ZATU648 DUGc GI+GI BA


§ 7.4. The total reported in case rev. ii 1 (13 DUGc/ZATU648) includes all the quantities listed in cases obv. i 1a1–obv. ii 5 on the obverse, and recorded in cases rev. i 1–rev. i 6 on the reverse of the tablet, with the addition of the two quantities listed in cases obv. i 1b1 and obv. i 1b2. The quantity recorded in obv. i 1b3 (3 DUGc), qualified as BA KIa, is consequently not included in the total. The transactions recorded in the total are qualified as GI+GI BA (which can be translated “deliveries of rations,” but also “deliveries” and “rations,” the last term to be referred to the two first transactions, qualified as BA). Therefore, the administrative term BA KIa should denote rations not delivered, and might be rendered with the expression “locally (supplied) rations.”[19]


§ 7.5. The proposed interpretation of the term BA KIa would explain the reason for the separate entries in the tablet MSVO 3, 67, for the “locally (-supplied) rations” recorded in case rev. i 1c2 for the barley, and in rev. i 2c2 for the emmer, as opposed to the rations delivered as “food” (GU7), listed on the obverse and totaled respectively in rev. i 1c1 and rev. i 2c1.


§ 8. A “unicum” or a rare practice?
§ 8.1. MSVO 3, 75 (from Uruk?), is a tablet in the Vorderasiatisches Museum, Berlin,[20] that records a number of provisions of a grain product (emmer), all measured in the derived capacity system Š". The arrangement of the tablet would suggest that the text includes on the obverse a list of provisions structured in two separate sections, qualified respectively by N4 (ZIZ2 ?) and GIŠ+TE,[21] and totals and sub-totals on the reverse. The provisions are qualified as “food” distribution (GU7).

obv. i 1 3N19 1N4 1N41 SAL ZATU810 KAŠ
obv. i 2 3N19 2N4 APINa MARa
obv. i 3 1N19 NIN TUR3a
obv. i 4 2N19 5N4 UR5a NIN TUR3a
obv. i 5 1N19 3N41 ˹SAL˺
obv. i 6 2N4 ˹BALAG˺
obv. ii 1 5N4 SANGAa ENa NAGARa URI3a
obv. ii 2 2N4 MUŠ
obv. ii 3 1N19 DUBa E2a
obv. ii 4 2N19 ENa ˹ABa˺ TARa
obv. ii 5 2N4 3N41 ˹SAL ZATU751a˺
obv. ii 6 3N4 ˹3N57˺ [GIŠtenû?] ˹E2a SI TUN3a˺
obv. ii 7 ˹2N4˺ NINDA2+AN
obv. ii 8 ˹4N4 ENa NIa PIRIGb1˺
obv. ii 9 1N4
obv. iii 1 3N19 DUBa E2a
obv. iii 2 2N19 2N41 SAG TUR3a 6N57
obv. iii 3 2N4 3N41 UMUN2 MA 3N57 AMAa
obv. iii 4 GIŠ+TE GU7
rev. i 1a 2N46 3N19 SI4f AZ GALa SANGAa SANGAa
rev. i 1b1 1N46 7N19 1N4
rev. i 1b2 6N19 GIŠ+TE
rev. ii 1 2N46 3N19 1N4 2N41 GU7

 

§ 8.2. In rev. i 1a, the total of emmer (138 barig), with sub-totals in rev. i 1b1 (102 barig) and rev. i 1b2 (36 barig), are recorded. The sign N4 in rev. i 1b1 corresponds to N4 in obv. ii 9 and should be rendered as ZIZ2, by parallelism with GIŠ+TE in obv. iii 4 and sub-total rev. i 1b2. In any case, the position of the sign N4 in rev. ii 1 would exclude it's interpretation there as a non-numerical qualifier, and since it was not included in the total, it shall be regarded as a reference value. The fractional quantities in obv. i 1 and 5; obv. ii 5; obv. iii 2, 3; and rev. ii 1 shall be regarded as reference ration values as well.[22] The text can be better understood in the following arrangement.

 

Case
Value in “barig”
Reference Value
obv. i 1
19
1/5
obv. i 2
20
obv. i 3
6
obv. i 4
17
obv. i 5
6
3/5
obv. i 6
2
obv. ii 1
5
obv. ii 2
2
obv. ii 3
6
obv. ii 4
12
obv. ii 5
2
3/5
obv. ii 6
3
obv. ii 7
2
obv. ii 8
4
obv. ii 9
1
obv. iii 1
18
obv. iii 2
12
2/5
obv. iii 3
2
3/5
rev. i 1a
138
rev. i 1b1
102
1
rev. i 1b2
36
rev. ii 1
138
1, 2/5


§ 8.3. By default, all the listed entries on the obverse without a reference fractional value will be considered to have 1N4 as the reference ration value and thus be converted in the total at a rate of 1:1. If the quantities of emmer in all such entries without accompanying fractional values are combined, we obtain a total of 97 barig. Similarly, if the quantities of emmer qualified by reference fractional values are combined, not including those reference values, a total of 41 barig is obtained. These values do not correspond to the sub-totals in cases rev. i 1b1-2, as demonstrated in the table below.

Case
Recorded Value
Expected Value
Reference Value
rev. i 1a
138
138
rev. i 1b1
102
97
1
rev. i 1b2
36
41
fractional


§ 8.4. The key for understanding the rationale of the reported values is to be found in case rev. ii 1, where 1 (1N4) and 2/5 (2N41) “barig” are given as reference values.[23] It is probable that the scribe has performed the following calculation:


19 × 1/5 + 6 × 3/5 + 2 × 3/5 + 12 × 2/5 + 2 × 3/5 = 73/5
      = (36 × 2 + 1)/5 = 36 × (2/5 + 1/180) ≈ 36 × 2/5


The approximation (2/5 + 1/180) ≈ 2/5 is due to the fact that the quantity 1/180 is so negligible that a numerical sign for it was not considered worthy of use.[24]


§ 8.5. The expression above represents the calculation of the “weighted mean” of the (fractional) reference ration values of the single entries, and the resulting value 2/5, according to this interpretation considered a standard value, was used as a reference for the calculation of the sub-total (case rev. i 1b2), and recorded together with the other reference value 1N4 in the final total (case rev. ii 1). As a consequence of such “standardization,” the sub-total with the reference value 1N4 had to be calculated by difference, resulting in 138-36=102 (case rev. i 1b1).


§ 8.6. There is no other known evidence of a similar use of the “weighted mean” calculation in the available administrative texts from the Uruk III period. This tablet would, therefore, represent a “unicum,” and should be considered as an irregular scribal exercise.


§ 8.7. The presence in MSVO 3, 42 (see §5), of a double-entry calculation for the sub-totals, whose rationale is not decipherable from the limited context of the account, suggests that a similar practice could have been the basis of this calculation.[25] Should that prove to be true, it would indicate the existence of quite complex administrative practices, although apparently infrequently used, in ancient Mesopotamia.[26]


§ 9. Conclusions
§ 9.1. Textual analysis has shown that administrative accounting of mixed grain products occasionally employed, in the totals, derived numerical ŠE systems that were different from the notations normally associated with the products listed in the tablet. In a number of instances, the most common adoption of the Š notation to indicate grain in general is replaced by the use of several specific derived grain capacity systems. One main reason for such practices could be the necessity to identify in the total, by adopting the appropriate numerical notation, the basic grain product used for the production of the different derived products listed and sub-totaled in the tablets.


§ 9.2. Another peculiarity in archaic scribal administrative practices can be found in the texts which adopt mixed notations in totals combining different grain products. The use of one numerical notation in totaling two different grain products, qualifying a single number sign with recourse to some member of the other numerical notation, can be easily explained as a means to simplify the recording of the accounts, at the same time indicating the presence of the two different products.


§ 9.3. More important for understanding the administrative practices in the archaic period is the apparent presence, at least in one text, of an account based on the “weighted mean” calculations. Use of the “weighted mean,” or any other numerical mean, may imply the development of the concept of “statistics” and their employment in the administrative statement of accounting. It is worth noting that the use of statistics in town/state administration makes sense, expecially if its purpose is to calculate budget accounts for future expenditures based on the “mean” expenditures of past periods. It seems we may be able to trace such practices, which were certainly common in later periods,[27] back as early as in the Uruk III/Jemdet Nasr period.

 


Version: 1 May 2005