§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 KU_{b2 } ŠIM_{a } (possibly “beer bread,” see below). The first entry seems related to a month, or to a special event (EZEN AN MUŠ_{3 } = ezen ^{ d}inanna ?).[7]
grain capacity system

case

transliteration


Š

obv. i 1a

1N_{14 } 2N_{1 } HIgunû_{a } AN U_{4 } SIG MUŠ_{3a } ˹NAGAR_{a}˺ EZEN_{b }


Š'

obv. i 1b

2N_{18 }


Š

obv. i 2a

1N_{14 } 4N_{1 } 1N_{28 } KINGAL


Š'

obv. i 2b

4N_{3} 1N_{40}



obv. i 3

KU_{b2 } ŠIM_{a }


Š*

rev. i 1

3N_{20 } 1N_{28* } HIgunû_{a }


Š'

rev. i 2

2N_{18 } 4N_{3 } 1N_{40 }



rev. i 3

KU_{b2 } ŠIM_{a }

§2.2. The entries of malt are measured and totaled in the final Š' notation. The grain product qualified as HIgunû_{a } 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 HIgunû_{a } is not necessarily associated with malt, and is occasionally delivered separately as “food” (GU_{7}).[10]
§3. Š* and & Š’ totaled as Š*
§3.1. Tablet MSVO 3, 52 (from Uruk?), a similar account of two grain products (HIgunû_{a } and malt) whose destination is also qualified as KU_{b2} ŠIM_{a} (“beer bread” ?), presents some peculiarities.
grain capacity system

case

transliteration


Š&Š'

obv. i 1a

2N_{47} 1N_{20} 1N_{5} 1N_{40} HIgunû_{a} BA


Š*

obv. i 1b1

8N_{20} 4N_{5} 2N_{42a} HIgunû_{a}


Š'

obv. i 1b2

1N_{45'} 2N_{18} 2N_{3} 4N_{40}



obv. i 2

KU_{b2} ŠIM_{a}

§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 (HIgunû_{a } BA), and measured in the derived numerical Š* system,[11] with the exception of the least significant grain measure, represented by the numerical sign 1N_{40} 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 (GU_{7}).
grain capacity system

case

transliteration


Š'

obv. i 1

3N_{40} 1N_{24}' MUD 3N_{57} TE


Š'

obv. i 2

1N_{3} E_{2a} U_{4} KASKAL


Š'

obv. i 3

1N_{3} 1N_{40} 1N_{24'} GA_{2a2}+GU_{4}+ŠE_{3} U BU_{a}


Š'

obv. i 4

2N_{40} 1N_{24}' EN_{a} SANGA_{a} TUR 1N_{58} ŠIM_{a}


Š'

obv. ii 1

1N_{3} 2N_{40} 1N_{24'} GA_{2a2}+GU_{4}+ŠE_{3} SAGŠU


Š'

obv. ii 2a

1N_{18} 4N_{3}



obv. ii 2b1

KAŠc



obv. ii 2b2

KAŠc SUKKAL


Š'

obv. ii 3

4N_{40} 1N_{24'} E_{2a} PIRIG_{b1}+3N_{57}


Š'

obv. ii 4

2N_{40} 1N_{24'} AN MUŠ_{} DU PAP_{a} E_{2a} NUN_{a}


Š'

obv. iii 1

˹4N_{40}?˺ [1N_{24'}] NIN GAL_{a} E_{2a}


Š

obv. iii 2

3N_{39a} GI_{4a}+A



obv. iii 3

˹GU_{7}˺


Š

rev. i 1

2N_{14} ŠE_{a} BULUG_{3} E_{2a}+KUR_{a}?


Š'

rev. i 2

3N_{18} GU_{7}



rev. i 3

SAGŠU GA_{2a2}+GU_{4}+ŠE_{3}



rev. ii 1

GU_{7}

§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 1N_{24'}, also expected by analogy with the preceding cases,
with the consequential reading 4N_{40} 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 BULUG_{3} (= munu_{x}, “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 doubleentry 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 
6N_{14} 3N_{19} ŠE_{a} LU_{2}
MUD_{3d} 

Š 
obv. i 1b1 
6N_{14} ŠE_{a} 

Š" 
obv. i 1b2 
3N_{19} U_{4} 

Š" 
obv. i 2a 
1N_{46} ŠE_{a} UNUG_{a} E_{2a}


Š 
obv. i 2b1 
5N_{14} ŠE_{a} 

Š" 
obv. i 2b2 
5N_{19} 

Š 
obv. i 3 
5N_{14} ŠUBUR SUG_{5} PA_{a} 

Š 
obv. ii 1 
4N_{14} TItenû ZAG_{a} 


obv. ii 2 
LU_{2} MUD_{3d} 

Š Š" 
rev. i 1a 
1N_{45} 1N_{46} 8N_{14} ŠE_{a}


Š 
rev. i 1b1 
2N_{45} ŠE_{a} 

Š" 
rev. i 1b2 
8N_{19} 


rev. i 2 
LU_{2} MUD_{3d} 
§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” = N_{1}).
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 subtotals,
and finally the single entries.
grain capacity system 
case 
transliteration 

Š 
obv. i 1a 
1N_{45} 9N_{14} 2N_{39a} HIgunû_{a} 

Š* 
obv. i 1b1 
9N_{20} 1N_{5} 3N_{42a} HIgunû_{a} 

Š' 
obv. i 1b2 
9N_{18} 4N_{3} 4N_{40} 

Š* 
obv. i 1c1a 
7N_{20} 4N_{42a} HIgunû_{a}
NAGA_{a} 

Š' 
obv. i 1c1b 
7N_{18} 4N_{3} 4N_{40} 

Š* 
obv. i 1c2a 
2N_{20} <4N_{42a}> HIgunû_{a}
DUB_{a} 

Š' 
obv. i 1c2b 
2N_{18} 4N_{40} 


obv. i 2 
KU_{b2} ŠIM_{a} 
§ 6.2. The cumulative amount of grain products is recorded
in the first case (obv. i 1a), qualified as HIgunû_{a}.
The two grain products are then subtotaled in terms of HIgunû_{a
} (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 NAGA_{a} and DUB_{a}.
As in the accounts MSVO 3, 52
and 55
(treated in §§23 above), the products’ destination
is designated as KU_{b2} ŠIM_{a} (“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 4N_{42a} 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 subtotals 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 subtotals 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 1obv. ii 8 

111 

obv. iii 1obv. iv 7 


65 ^{2}/_{5} ^{2}/_{25} 
rev. i 1a 
2N_{45} 3N_{14} 3N_{1} ŠE 
141 

rev. i 1b1 
1N_{45} 7N_{14} 3N_{1} X X 
105 

rev. i 1b2 
6N_{14} [...] 
36 

rev. i 1c1 
1N_{45} 8^{!}N_{14} 3N_{14} GU_{7} 
111^{!} 

rev. i 1c2 
6N_{14} BA KI 
30 

rev. i 2a 
1N_{46} 1N_{19} 2N_{4} 

68 
rev. i 2b1 
9N_{19} [2N_{4}] 

56 
rev. i 2b2 
2N_{19} NUMUN GAN_{2} NAGAR 

12 
rev. i 2c1 
1N_{46} 5N_{4} 2N_{41} 1N_{29a}
1N_{29a} GU_{7} 

65 ^{2}/_{5} ^{2}/_{25} 
rev. i 2c2 
2N_{4} 2N_{41} 1N_{24"} KI BA 

2 ^{2}/_{5} ^{1}/_{10} 
§ 7.2. It is evident that the structure of the totals
and subtotals of the two products is identical. The subtotal in case
rev. i 2c1, qualified as “food” (GU_{7}), corresponds
to the sum of the quantities of emmer listed on the obverse (cases obv.
iii 1obv. iv 7); it follows that the subtotal in case rev. i 1c1,
also qualified as GU_{7}, should correspond to the sum of the
quantities of barley listed on the obverse (cases obv. i 1obv. ii 8),
although the tablet clearly records 105 N_{1} (1N_{45}
7N_{14} 3N_{1}), 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 
5N_{1} DUG_{c} DUB_{a} 
obv. i 1b1 
1N_{1} ZABALAM_{a} AN BA ZATU751a 
obv. i 1b2 
1N_{1} SAL BA X ANŠE_{b}^{?} 
obv. i 1b3 
3N_{1} BA KI_{a} 
obv. i 2a1 
1N_{1} 
obv. i 2a2 
1N_{1} KU_{3a} 
obv. i 2b 
ZATU649 
obv. i 3 
1N_{1} KU_{3a} ZABALAM_{a} AB_{2}

obv. i 4 
1N_{1} SI_{4a} NE_{a} ŠE_{a}
GI 
obv. i 5 
GA_{a} [...] 

obv. ii 1 
2N_{1} ZATU648 
obv. ii 2 
PIRIG_{b1}+3N_{57} AB_{b} SU_{a}

obv. ii 3 
3N_{1} SI U_{4} AB_{2} 
obv. ii 4 
2N_{1} TUR_{3a} A 
obv. ii 5 
GA_{a} BU_{a} HI 
rev. i 1 
[2N_{1} ZATU648] 
rev. i 2 
3N_{1} SI U_{4} AB_{2} 
rev. i 3 
2N_{1} TUR_{3a} A 
rev. i 4a1 
1N_{1} 
rev. i 4a2 
1N_{1} KU_{3a} 
rev. i 4b 
ZATU649 
rev. i 5 
1N_{1} KU_{3a} ZABALAM_{a} AB_{2}

rev. i 6 
1N_{1} NE_{a} SI_{4a} GI ŠE_{a}

rev. ii 1 
1N_{14} 3N_{1} ZATU648 DUG_{c} GI+GI BA

§ 7.4. The total reported in case rev. ii 1 (13 DUG_{c}/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 DUG_{c}), qualified as BA KI_{a}, 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 KI_{a} 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 KI_{a}
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” (GU_{7}), 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 N_{4} (ZIZ_{2} ?) and GIŠ+TE,[21]
and totals and subtotals on the reverse. The provisions are qualified
as “food” distribution (GU_{7}).
obv. i 1 
3N_{19} 1N_{4} 1N_{41} SAL
ZATU810 KAŠ_{} 
obv. i 2 
3N_{19} 2N_{4} APIN_{a} MAR_{a}

obv. i 3 
1N_{19} NIN TUR_{3a} 
obv. i 4 
2N_{19} 5N_{4} UR_{5a} NIN TUR_{3a}

obv. i 5 
1N_{19} 3N_{41} ˹SAL˺ 
obv. i 6 
2N_{4} ˹BALAG˺ 
obv. ii 1 
5N_{4} SANGA_{a} EN_{a} NAGAR_{a}
URI_{3a} 
obv. ii 2 
2N_{4} MUŠ_{} 
obv. ii 3 
1N_{19} DUB_{a} E_{2a} 
obv. ii 4 
2N_{19} EN_{a} ˹AB_{a}˺ TAR_{a}

obv. ii 5 
2N_{4} 3N_{41} ˹SAL ZATU751a˺ 
obv. ii 6 
3N_{4} ˹3N_{57}˺ [GIŠtenû?]
˹E_{2a} SI TUN_{3a}˺ 
obv. ii 7 
˹2N_{4}˺ NINDA_{2}+AN 
obv. ii 8 
˹4N_{4} EN_{a} NI_{a} PIRIG_{b1}˺ 
obv. ii 9 
1N_{4} 
obv. iii 1 
3N_{19} DUB_{a} E_{2a} 
obv. iii 2 
2N_{19} 2N_{41} SAG TUR_{3a} 6N_{57}

obv. iii 3 
2N_{4} 3N_{41} UMUN_{2} MA 3N_{57}
AMA_{a} 
obv. iii 4 
GIŠ+TE GU_{7} 
rev. i 1a 
2N_{46} 3N_{19} SI_{4f} AZ GAL_{a}
SANGA_{a} SANGA_{a} 
rev. i 1b1 
1N_{46} 7N_{19} 1N_{4} 
rev. i 1b2 
6N_{19} GIŠ+TE 
rev. ii 1 
2N_{46} 3N_{19} 1N_{4} 2N_{41}
GU_{7} 
§ 8.2. In rev. i 1a, the total of emmer (138 barig), with
subtotals in rev. i 1b1 (102 barig) and rev. i 1b2 (36 barig), are
recorded. The sign N_{4} in rev. i 1b1 corresponds to N_{4}
in obv. ii 9 and should be rendered as ZIZ_{2}, by parallelism
with GIŠ+TE in obv. iii 4 and subtotal rev. i 1b2. In any case,
the position of the sign N_{4} in rev. ii 1 would exclude it's
interpretation there as a nonnumerical 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 1N_{4}
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
subtotals in cases rev. i 1b12, 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 (1N_{4})
and ^{2}/_{5} (2N_{41}) “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 subtotal (case rev. i 1b2),
and recorded together with the other reference value 1N_{4}
in the final total (case rev. ii 1). As a consequence of such “standardization,”
the subtotal with the reference value 1N_{4} had to be calculated
by difference, resulting in 13836=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 doubleentry calculation for the subtotals, 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 subtotaled 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.
