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[[Numbers & Metrology in the 2nd millennium]]
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numbers_metrology_2nd_millennium [2014/12/19 10:00] – gombertnumbers_metrology_2nd_millennium [2016/01/26 21:12] (current) – [Numbers & Metrology in the 2nd millennium] gombert
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 ====== Numbers & Metrology in the 2nd millennium ===== ====== Numbers & Metrology in the 2nd millennium =====
-(Return to [[numbers_metrology]]) +(Return to [[numbers_metrology]])\\
-[[Old Assyrian private trade]]+
  
- +  * [[Old Assyrian private trade]] 
-------- +  * [[Old Babylonian scribal schools]] 
-==== Old Babylonian scribal schools ==== +  * [[Nuzi]] 
- +  * [[Old Babylonian Dyala]]
-**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 (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. [[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> | {{:obab_gan2.jpg?nolink|}} | ca. 3600 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).\\ +
- +
-===  Numerical systems === +
-== 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 | +
- +
-== 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 <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 (sila3, gin2, 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.\\ +
- +
-== System G, used for counting the highest unit of surface == +
- +
-| {{:obab_shar_u.png?nolink|}} |   **× 2\\ ←**   | {{: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 | ::: | 1 080  | ::: | 180 | ::: | 18 | ::: | 6 | ::: | 1 | ::: | ½ | +
- +
- +
-=== 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)+
numbers_metrology_2nd_millennium.1418983223.txt.gz · Last modified: 2014/12/19 10:00 (external edit)
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