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Ancient Mesopotamian units of measurement originated in the loosely organized city-states of Early Dynastic Sumer. The units themselves grew out of the tradition of counting tokens used by the Neolithic (c 6000 BCE) cultural complex of the Near East. Consequently each city, kingdom and trade guild had its own standards until the Letter of Nanse reduced a plethora of multiple standards to a few agreed upon common groupings. Successors to Sumerian Civilization including the Babylonians, Assyrians, and Persians continuted to use these groupings. Akkado-Sumerian metrology has been reconstructed by applying statistical methods to compare Sumerian architecture, architectural plans, and issued official standards.

- Sexigesimal System S used to count slaves, animals, fish, wooden objects, stone objects, containers.
- Sexigesimal System S' used to count dead animals, certain types of beer
- Bi-Sexigesimal System B used to count cereal, bread, fish, milk products
- Bi-Sexigesimal System B
^{*}used to count rations - GAN
_{2}System G used to count field measurement - ŠE system Š used to count barley by volume
- ŠE system Š' used to count malt by volume
- ŠE system Š" used to count wheat by volume
- ŠE System Š
^{*}used to barley groats - EN System E used to count weight
- U
_{4}System U used to count calendrics - DUG
_{b}System Db used to count milk by volume - DUG
_{c}System Db used to count beer by volume

In Early Dynastic Sumer (c 3500-2300 BCE) metrology and mathematics were indistinguishable and treated as a single scribal discipline. The idea of an abstract number did not yet exist, thus all quantities were written as metrological symbols and never as numerals followed by a unit symbol. For example there was a symbol for one-sheep and another for one-day but no symbol for one. About 600 of these metrological symbols exist, for this reason archaic Sumerian metrology is complex and not fully understood. In general however, length, volume, and mass are derived from a theoretical standard cube, called 'gur', filled with either barley, wheat, water, or oil. The mass of a gur-cube, called 'gun_{2}' is defined as the weight a laden ass can carry. However, because of the different specific gravities of these substances combined with dual numerical bases (sexagesimal or decimal), multiple sizes of the gur-cube were used without consensus. The different gur-cubes are related by proportion, based on the water gur-cube, according to four basic coefficents and their cubic roots. These coefficents are given as:

- Komma = $80/81$ correction when planning rations with a 360 day year
- Leimma = $24/25$ conversion from decimal to a sexagesimal number system
- Diesis = $15/16$
- Euboic = $5/6$

One official government standard of measurement of the archaic system was the Cubit of Nippur (2650 BCE). It is a Euboic Mana + 1 Diesis (432g). This standard is the main reference used by archeologists to reconstruct the system.

Units of Length are prefixed by the logogram DU a convention of the archaic period counting system from which it was evolved. Basic length was used in architecture and survey.

Basic Length | ||||||
---|---|---|---|---|---|---|

Unit | Ratio | Ideal Value | Sumerian | Akkdian | Cuneiform | |

grain | 1/180 | 0.00025m | še | uţţatu | ||

finger | 1/30 | 0.015m | šu-si | ubānu | ||

foot | 2/3 | 0.333m | šu-du_{3}-a
| šīzu | ||

cubit | 1 | 0.497m | kuš_{3}
| ammatu | ||

step | 2 | 1.000m | ĝiri_{3}
| šēpu | ||

reed | 6 | 3.000m | gi | qanû | ||

rod | 12 | 6.000m | nindan | nindanu | ||

cord | 120 | 60.000m | eše_{2}
| aslu |

Distance units were geodectic as distinguished from non-geodectic basic length units. Sumerian geodesy divided latitude into seven zones between equator and pole.

Distance | ||||||
---|---|---|---|---|---|---|

Unit | Ratio | Ideal Value | Sumerian | Akkdian | Cuneiform | |

rod | 1/60 | 6.000m | nidan | nindanu | ||

cord | 1/6 | 60.000m | eše_{2}
| aslu | ||

cable | 1 | 360m | uš | uš | ||

league | 30 | 10,800m | da-na | bêru |

Basic Area | ||||||
---|---|---|---|---|---|---|

Unit | Ratio | Dimensions | Ideal Value | Sumerian | Akkdian | Cuneiform |

shekel | 1/60 | 1kuš_{3} × 1kuš_{3}
| 1m² | gin_{2}
| šiqlu | |

garden | 1 | 12kuš_{3} × 12kuš_{3}
| 36m² | sar | mūšaru | |

quarter-field | 5 | 60kuš_{3} × 60kuš_{3}
| 900m² | uzalak | ? | ? |

half-field | 10 | 120kuš_{3} × 60kuš_{3}
| 1,800m² | upu | ubû | |

field | 100 | 60ĝiri_{3} × 60ĝiri_{3}
| 3,600m² | iku | ikû | |

estate | 1,800 | 3eše_{2} × 6eše_{2}
| 64,800m² | bur | būru |

Basic Volume | ||||||
---|---|---|---|---|---|---|

Unit | Ratio | Capacity | Ideal Value | Sumerian | Akkdian | Cuneiform |

shekel | 1/60 | ?L | ?m³ | gin_{2}
| šiqlu | |

bowl | 1 | 1L | 0.001m³ | sila_{3}
| qû | |

vessel | 10 | 10L | 0.01m³ | ban_{2}
| sutū | |

bushel | 60 | 60L | 0.06m³ | ba-ri_{2}-ga
| parsiktu | |

gur-cube | 300 | 300L | 0.3m³ | gur | kurru |

Basic Mass | ||||||
---|---|---|---|---|---|---|

Unit | Ratio | Ideal Value | Sumerian | Akkdian | Cuneiform | |

grain | 1/180 | 0.15g | še | uţţatu | ||

shekel | 1 | 9g | gin_{2}
| šiqlu | ||

pound | 60 | 497.7g | ma-na | manû | ||

load | 3600 | 30,000g | gun_{2}
| biltu |

Basic Time | ||||||
---|---|---|---|---|---|---|

Unit | Ratio | Ideal Value | Sumerian | Akkdian | Cuneiform | |

gesh | 1/360 | 240s | mu-eš | geš | ||

watch | 1/12 | 7,200s | da-na | bêru | ||

day | 1 | 86,400s | ud | immu | ||

month | 30 | 2,592,000s | itud | arhu | ||

year | 360 | 31,104,000s | mu | šattu |

Weights and measures

Statues of Gudea

Babylonian mathematics

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Last updated on Friday October 10, 2008 at 12:34:34 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Friday October 10, 2008 at 12:34:34 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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