### Old Babylonian scribal schools

Sources: the diagrams below represent data provided by metrological lists and tables from Nippur scribal schools. These sources are available on CDLI (here).

Scope: Similar metrology is attested in other Old Babylonian scribal schools. The metrology taught in scribal schools was adopted in a large part of Mesopotamia. However, some minor variants may be observed in some administrative or economic archives from Southern Mesopotamia.

Bibliography:

• Proust, Christine. 2007. Tablettes mathématiques de Nippur. Istanbul: Institut Français d'Etudes Anatoliennes, De Boccard.
• Proust, Christine. 2009. "Numerical and metrological graphemes: from cuneiform to transliteration." Cuneiform Digital Library Journal, 2009:1.
• Robson, Eleanor. 2002. "More than metrology: mathematics education in an Old Babylonian scribal school." Pp. 325-365 in Under One Sky. Astronomy and Mathematics in the Ancient Near East, vol. 297, Alter Orient und Altes Testament (AOAT), edited by J. M. Steele and A. Imhausen. Münster: Ugarit-Verlag.

#### Metrological systems, in the order in which they appear in metrological lists and tables

##### Units of capacity
 gin2 ca. 17 cm3 ↓ × 60 sila3 ca. 1 l ↓ × 10 ban21) ca. 10 l ↓ × 6 barig 2) ca. 60 l ↓ × 5 gur ca. 300 l
##### Units of weight
 še ca. 0.04 g ↓ × 180 gin2 ca. 8 g ↓ × 60 ma-na ca. 500 g ↓ × 60 gun2 ca. 30 kg
##### Units of surface and volume
 sar ca. 36 m2 ↓ × 100 GAN23) ca. 3600 m2

System G, used before the sign GAN2

 × 10 ← × 6 ← × 10 ← × 3 ← × 6 ← × 2 ← šar’u šar2 bur’u bur3 eše3 iku ubu 10 800 iku 1 080 iku 180 iku 18 iku 6 iku 1 iku ½ iku

Examples:
1(iku) GAN2 represents ca. 3600 m2
2(eše3) GAN2 represents ca. 2×6×3600 m2, that is, 43 200 m2

##### Units of length
 šu-si ca. 16 mm ↓ × 30 kuš3 ca. 50 cm ↓ × 12 ninda ca. 6 m ↓ × 60 UŠ ca. 360 m ↓ × 30 danna ca. 10,5 km

Note: in mathematical texts, the unit gin2 is also used for sub-dividing the surface unit sar into 60 parts, and the unit še is also used in capacity and surface systems for sub-dividing the unit gin2 into 180 parts. In other words, if we consider all of the OB mathematical texts, the sequence ←×60− gin2←×180−še can be grafted in capacity and surface systems.

##### Bridges

Bridge between length and surface units: 1 ninda × 1 ninda = 1 sar
Bridge between surface and volume units: 1 volume-unit = 1 surface-unit × 1 kuš3 (example: 1 sar-volume = 1 sar-surface × 1 kuš3).
Bridge between volume and capacity units: 1 sar-volume is equivalent to 60 gur (ca. 18 m3 or 18 000 liters).

#### Numbers and fractions

##### System S, used for counting discrete items
 × 10 ← × 6 ← × 10 ← × 6 ← × 10 ← šar’u šar2 geš’u geš2 u diš 36 000 3 600 600 60 10 1

Some metrological lists or tables provide very large (and unrealistic) numbers:

• 1 šar2 gal (60 times 1 šar2) appears in CBS 10990, CBS 8214, CBS 10181, HS 249, Ist Ni 4840, YBC 2392, CBS 472, Ash 1931.137
• 1 šar2 gal šu-nu tag (60 times 1 šar2 gal) appears in CBS 10990, CBS 8214, CBS 10181, Ist Ni 4840 (for another reading and interpretation, see Chambon & Robson 2011, "Untouchable or unrepeatable? The upper end of the Old Babylonian metrological systems for capacity and area 127", Iraq 73)

A school tablet from Nippur CBS 11319 +) contains on the obverse the unique known text which displays the entire System S in a systematic way (see copy and transliteration in Proust 2008, in Proceedings of the 51st Rencontre Assyriologique Internationale, Biggs et al. ed., SAOC 62, p. 151-152).

##### Variants of System S

The highest units of capacity (gur) and weight (gun2) are counted with a variant of System S, where the number 1 is represented by the sign aš (and not the sign diš as in the System S used for discrete item).

The other measuring units (sila3, gin2, še, sar, danna, UŠ, ninda, kuš and šu-si) are counted with (1) and (10) repeated as many times as necessary.

#### Fractions

 1/6 (igi-6-gal2) 1/3 1/2 2/3 5/6

Page prepared by CP
(digital version prepared by BG)

1)
1 (ban2): , 2 (ban2): , 3 (ban2): , 4 (ban2): , 5 (ban2):
2)
1 (barig): , 2 (barig): , 3(barig): , 4 (barig):
3)
see system G below