Numbers & Metrology in the 2nd millennium

(Return to Numbers & Metrology) Old Assyrian private trade

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 (see metrology in Old Babylonian Larsa, etc.), and important differences were cultivated in Northern regions (see metrology for example in Mari, Diyala Valley, Assur).

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.
  

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.

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).

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.

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

Page prepared by CP
(digital version prepared by BG)