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==== 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 [[http://cdli.ucla.edu/search/search_results.php?SearchMode=Text&requestFrom=Search&PrimaryPublication=&order=PrimaryPublication&Author=&PublicationDate=&SecondaryPublication=&Collection=&AccessionNumber=&MuseumNumber=&Provenience=Nippur&ExcavationNumber=&Period=&DatesReferenced=&ObjectType=&ObjectRemarks=&Material=&TextSearch=&Language=&Genre=&SubGenre=Metrological&CompositeNumber=&SealID=&ObjectID=&ATFSource=&CatalogueSource=&TranslationSource=|(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. [[http://cdli.ucla.edu/pubs/cdlj/2009/cdlj2009_001.html|"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<sub>2</sub> | {{ :obab_gin2.jpg?nolink |}} | ca. 17 cm<sup>3</sup> |
|   **↓ × 60 **   |||
| sila<sub>3</sub> | {{ :obab_sila3.jpg?nolink |}} | ca. 1 l |
|   **↓ × 10 **   |||
| ban<sub>2</sub>(( 1 (ban<sub>2</sub>): {{:1_ban2_.png?nolink|}}, 2 (ban<sub>2</sub>): {{:2_ban2_.png?nolink|}}, 3 (ban<sub>2</sub>): {{:3_ban2_.png?nolink|}}, 4 (ban<sub>2</sub>): {{:4_ban2_.png?nolink|}}, 5 (ban<sub>2</sub>): {{:5_ban2_.png?nolink|}})) | {{ :obab_ban2.jpg?nolink |}} | ca. 10 l |
|   **↓ × 6 **   |||
| barig ((1 (barig): {{:obab_barig.jpg?nolink|}}, 2 (barig): {{:2_barig_.png?nolink|}}, 3(barig): {{:3_barig_.png?nolink|}}, 4 (barig): {{:4_barig_.jpg?nolink|}}))| {{ :obab_barig.jpg?nolink |}} | ca. 60 l |
|   **↓ × 5 **   |||
| gur | {{ :obab_gur.jpg?nolink |}} | ca. 300 l|

== Units of weight ==

| še | {{ :obab_se.jpg?nolink |}} | ca. 0.04 g |
|   **↓ × 180 **   |||
| gin<sub>2</sub> | {{ :obab_gin2.jpg?nolink |}} | ca. 8 g |
|   **↓ × 60 **   |||
| ma-na | {{:obab_ma.jpg?nolink|}}{{:obab_na.jpg?nolink|}} | ca. 500 g |
|   **↓ × 60 **   |||
| gun<sub>2</sub>| {{:obab_gun2.jpg?nolink|}} | ca. 30 kg |

== Units of surface and volume ==

| sar  | {{:obab_sar.jpg?nolink|}} | ca. 36 m<sup>2</sup>  | 
|   **↓ × 100 **   |||
| GAN<sub>2</sub>((see system G below)) | {{:obab_gan2.jpg?nolink|}} | ca. 3600 m<sup>2</sup> |

System G, used before the sign GAN2

| {{:obab_shar_u.png?nolink}}  |  **× 10\\ ←**  | {{:obab_shar2.png?nolink}}  |  **× 6\\ ←**  | {{:obab_bur_u.png?nolink}}  |  **× 10\\ ←**  | {{:obab_u.png?nolink}}  |  **× 3\\ ←**  | {{:obab_eshe3.png?nolink}}  |  **× 6\\ ←**  | {{:obab_ash.png?nolink}}  |  **× 2\\ ←**  | {{:obab_ubu.png?nolink}}  |
| šar’u                        | :::            | šar<sub>2</sub>             | :::           | bur’u                       | :::            | bur<sub>3</sub>         | :::           | eše<sub>3</sub>             | :::           | iku                       | :::           | ubu                       |
| 10 800 iku                   | :::            | 1 080 iku                   | :::           | 180 iku                     | :::            | 18 iku                  | :::           | 6 iku                       | :::           | 1 iku                     | :::           | ½ iku                     |
\\
Examples:\\
{{:obab_ash.png?nolink|}}{{:obab_gan2.jpg?nolink|}}1(iku) GAN<sub>2</sub> represents ca. 3600 m<sup>2</sup>\\
{{:2sysg.png?nolink&25|}}{{:obab_gan2.jpg?nolink|}}2(eše<sub>3</sub>) GAN<sub>2</sub> represents ca. 2×6×3600 m<sup>2</sup>, that is, 43 200 m<sup>2</sup>



== Units of length ==

| šu-si | {{:obab_shu.jpg?nolink|}}{{:obab_si.jpg?nolink|}} | ca. 16 mm |
|   **↓ × 30 **   |||
| kuš<sub>3</sub> | {{:obab_kush3.jpg?nolink|}} | ca. 50 cm |
|   **↓ × 12 **   |||
| ninda | {{:obab_ninda.jpg?nolink|}} | ca. 6 m |
|   **↓ × 60 **   |||
| UŠ | {{:obab_ush.jpg?nolink|}} | ca. 360 m |
|   **↓ × 30 **   |||
| danna | {{:obab_danna.jpg?nolink|}} | ca. 10,5 km |

Note: in mathematical texts, the unit gin<sub>2</sub> 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<sub>2</sub> 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<sub>3</sub>  (example: 1 sar-volume = 1 sar-surface × 1 kuš<sub>3</sub>).\\
Bridge between volume and capacity units: 1 sar-volume is equivalent to 60 gur (ca. 18 m<sup>3</sup> or 18 000 liters).\\

===  Numbers and fractions ===
== System S, used for counting discrete items ==



| {{:obab_shar_u.png?nolink|}} |   **× 10\\ ←**   | {{:obab_shar2.png?nolink|}} |   **× 6\\ ←**   | {{:obab_gesh_u.png?nolink|}} |   **× 10\\ ←**   |  {{:obab_barig.jpg?nolink|}} |   **× 6\\ ←**   |{{:obab_u.png?nolink|}} |      **× 10\\ ←**   | {{:obab_barig.jpg?nolink|}} |   
| šar’u | ::: | šar<sub>2</sub> | ::: | geš’u | ::: | geš<sub>2</sub> | ::: |  u  | ::: | diš |
| 36 000 | ::: | 3 600 | ::: | 600 | ::: | 60 | ::: | 10  | ::: |  1 |


\\ 

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

  * 1 šar<sub>2</sub> gal (60 times 1 šar<sub>2</sub>) appears in CBS 10990, CBS 8214, CBS 10181, HS 249, Ist Ni 4840, YBC 2392, CBS 472, Ash 1931.137 
  * 1 šar<sub>2</sub> gal šu-nu tag (60 times 1 šar<sub>2</sub> 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 [[http://www.cdli.ucla.edu/P225766|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<sub>2</sub>) are counted with a variant of System S, where the number 1 is represented by the sign aš <sub>{{:obab_ash.png?10*5|}}</sub> (and not the sign diš <sub>{{:obab_barig.jpg?4*5|}}</sub> as in the System S used for discrete item).\\

The other measuring units (sila<sub>3</sub>, gin<sub>2</sub>, še, sar, danna, UŠ, ninda, kuš and šu-si) are counted with  <sub>{{:obab_barig.jpg?4*5|}}</sub> (1) and  <sub>{{:obab_u.png?4*5|}}</sub> (10) repeated as many times as necessary.\\



=== Fractions ===

| 1/6 | {{:obab_igi.png?nolink|}}{{:obab_6.png?nolink|}}{{:obab_gal2.png?nolink|}} (igi-6-gal<sub>2</sub>) |
| 1/3 | {{:obab_1.3.png?nolink|}} |
| 1/2 | {{:obab_1.2.png?nolink|}} |
| 2/3 | {{:obab_2.3.png?nolink|}} |
| 5/6 | {{:obab_5.6.png?nolink|}} |


Page prepared by CP\\
(digital version prepared by BG)