Table of Contents
Return to Numbers & Metrology in the 2nd millennium
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
gin_{2} | ca. 17 cm^{3} | |
↓ × 60 | ||
sila_{3} | ca. 1 l | |
↓ × 10 | ||
ban_{2}^{1)} | ca. 10 l | |
↓ × 6 | ||
barig ^{2)} | ca. 60 l | |
↓ × 5 | ||
gur | ca. 300 l |
Units of weight
še | ca. 0.04 g | |
↓ × 180 | ||
gin_{2} | ca. 8 g | |
↓ × 60 | ||
ma-na | ca. 500 g | |
↓ × 60 | ||
gun_{2} | ca. 30 kg |
Units of surface and volume
sar | ca. 36 m^{2} | |
↓ × 100 | ||
GAN_{2}^{3)} | ca. 3600 m^{2} |
System G, used before the sign GAN2
× 10 ← | × 6 ← | × 10 ← | × 3 ← | × 6 ← | × 2 ← | |||||||
šar’u | šar_{2} | bur’u | bur_{3} | eše_{3} | iku | ubu | ||||||
10 800 iku | 1 080 iku | 180 iku | 18 iku | 6 iku | 1 iku | ½ iku |
Examples:
1(iku) GAN_{2} represents ca. 3600 m^{2}
2(eše_{3}) GAN_{2} represents ca. 2×6×3600 m^{2}, that is, 43 200 m^{2}
Units of length
šu-si | ca. 16 mm | |
↓ × 30 | ||
kuš_{3} | 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 gin_{2} 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 gin_{2} 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 kuš_{3} (example: 1 sar-volume = 1 sar-surface × 1 kuš_{3}).
Bridge between volume and capacity units: 1 sar-volume is equivalent to 60 gur (ca. 18 m^{3} or 18 000 liters).
Numbers and fractions
System S, used for counting discrete items
× 10 ← | × 6 ← | × 10 ← | × 6 ← | × 10 ← | ||||||
šar’u | šar_{2} | geš’u | geš_{2} | u | diš | |||||
36 000 | 3 600 | 600 | 60 | 10 | 1 |
Some metrological lists or tables provide very large (and unrealistic) numbers:
- 1 šar_{2} gal (60 times 1 šar_{2}) appears in CBS 10990, CBS 8214, CBS 10181, HS 249, Ist Ni 4840, YBC 2392, CBS 472, Ash 1931.137
- 1 šar_{2} gal šu-nu tag (60 times 1 šar_{2} 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 (gun_{2}) 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 (sila_{3}, gin_{2}, 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-gal_{2}) |
1/3 | |
1/2 | |
2/3 | |
5/6 |
Page prepared by CP
(digital version prepared by BG)