Ancient Mesopotamian units of measurement

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Sumerian Metrology

Ancient Mesopotamian units of measurement originated in the loosely organized city-states of Early Dynastic Sumer. Each city, kingdom and trade guild had its own standards until the formation of the Akkadian Empire when Sargon of Akkad issued a common standard. This standard was improved by Naram-Sin, but fell into disuse after the Akkadian Empire dissolved. The standard of Naram-Sin was readopted in the Ur III period by the Nanše Hymn which reduced a plethora of multiple standards to a few agreed upon common groupings. Successors to Sumerian civilization including the Babylonians, Assyrians, and Persians continued to use these groupings. Akkado-Sumerian metrology has been reconstructed by applying statistical methods to compare Sumerian architecture, architectural plans, and issued official standards such as Statue B of Gudea and the bronze cubit of Nippur.

Archaic system[edit]

Gudea Statue I carved diorite

The systems that would later become the classical standard for Mesopotamia were developed in parallel with writing during Uruk Period Sumer (c. 4000 BCE). Studies of protocuneiform indicate twelve separate counting systems used in Uruk.

  • Sexagesimal System S used to count slaves, animals, fish, wooden objects, stone objects, containers.
  • Sexagesimal System S' used to count dead animals, certain types of beer
  • Bi-Sexagesimal System B used to count cereal, bread, fish, milk products
  • Bi-Sexagesimal System B* used to count rations
  • GAN2 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 count barley groats
  • EN System E used to count weight
  • U4 System U used to count calendrics
  • DUGb System Db used to count milk by volume
  • DUGc System Db used to count beer by volume

In Early Dynastic Sumer (c. 2900–2300 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.[1] In general however, length, volume, and mass are derived from a theoretical standard cube, called 'gur (also spelled kor in some literature)', filled with barley, wheat, water, or oil. 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 coefficients and their cubic roots.[citation needed] These coefficients 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 (432 grams).[citation needed] This standard is the main reference used by archaeologists to reconstruct the system.

Classical system[edit]

Royal Gur Cube of Naram-Sin

A major improvement came in 2150 BCE during the Akkadian Empire under the reign of Naram-Sin when the competing systems were unified by a single official standard, the royal gur-cube.[2] His reform is considered the first standardized system of measure in Mesopotamia.[2] The royal gur-cube (Cuneiform: LU2.GAL.GUR, 𒈚𒄥; Akkadian: šarru kurru) was a theoretical cuboid of water approximately 6 m × 6 m × 0.5 m from which all other units could be derived. The Neo-Sumerians continued use of the royal gur-cube as indicated by the Letter of Nanse issued in 2000 BCE by Gudea. Use of the same standard continued through the Neo-Babylonian Empire, Neo-Assyrian Empire, and Achaemenid Empire.[1]

Length[edit]

Units of length are prefixed by the logogram DU (𒁺) a convention of the archaic period counting system from which it was evolved. Basic length was used in architecture and field division.

Basic Length
Unit Ratio Sumerian Akkadian Cuneiform
grain 1⁄180 še uţţatu 𒊺
finger 1⁄30 šu-si ubānu 𒋗𒋛
foot 2⁄3 šu-du3-a šīzu 𒋗𒆕𒀀
cubit 1 kuš3 ammatu 𒌑
step 2 ĝiri3 šēpu 𒈨𒊑
reed 6 gi qanû 𒄀
rod 12 nindan nindanu 𒃻
cord 120 eše2 aslu 𒂠

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 Sumerian Akkadian Cuneiform
rod 1⁄60 nidan nindanu 𒃻
cord 1⁄6 eše2 aslu 𒂠
cable 1 uš uš 𒍑
league 30 da-na bêru 𒁕𒈾

Area[edit]

The GAN2 system G counting system evolved into area measurements. A special unit measuring brick quantity by area was called the brick-garden (Cuneiform: SIG.SAR 𒊬𒋞; Sumerian: šeg12-sar; Akkadian: libittu-mūšaru) which held 720 bricks.

Basic Area
Unit Ratio Dimensions Sumerian Akkadian Cuneiform
shekel 1⁄144 1 kuš3 × 1 kuš3 gin2 šiqlu 𒂆
garden 1 12 kuš3 × 12 kuš3 sar mūšaru 𒊬
quarter-field 25 60 kuš3 × 60 kuš3 uzalak ? 𒀺
half-field 50 120 kuš3 × 60 kuš3 upu ubû 𒀹𒃷
field 100 120 kuš3 × 120 kuš3 iku ikû 𒃷
estate 1800 bur būru 𒁓

Capacity or volume[edit]

Capacity was measured by either the ŠE system Š for dry capacity or the ŠE system Š* for wet capacity.

Basic Volume
Unit Ratio Sumerian Akkadian Cuneiform
shekel 1⁄60 gin2 šiqlu 𒂆
bowl 1 sila3 qû 𒋡
vessel 10 ban2 sutū 𒑏
bushel 60 ba-ri2-ga (barig) parsiktu 𒁀𒌷𒂵
gur-cube 300 gur kurru 𒄥

A sila was about 1 liter.[3]

Mass or weight[edit]

A series of old Babylonian weights ranging from 1 mina to 3 shekels

Mass was measured by the EN system E

Values below are an average of weight artifacts from Ur and Nippur. The ± value represents 1 standard deviation. All values have been rounded to second digit of the standard deviation.

Basic Mass
Unit Ratio Mean Value Sumerian Akkadian Cuneiform
grain 1⁄180 46.6±1.9 mg še uţţatu 𒊺
shekel 1 8.40±0.34 g gin2 šiqlu 𒂆
mina 60 504±20 g ma-na manû 𒈠𒈾
talent 3,600 30.2±1.2 kg gun2 biltu or kakaru 𒄘

[4] [5] [6]

Time[edit]

Main article: Babylonian calendar

In the Archaic System time notation was written in the U4 System U. Multiple lunisolar calendars existed; however the civil calendar from the holy city of Nippur (Ur III period) was adopted by Babylon as their civil calendar.[7] The calendar of Nippur dates to 3500 BCE and was itself based on older astronomical knowledge of an uncertain origin. The main astronomical cycles used to construct the calendar were the month, year, and day.

Basic Time [8]
Unit Ratio Sumerian Akkadian Cuneiform
gesh 1⁄360 mu-eš geš 𒈬𒍑
watch 1⁄12 da-na bêru 𒂆
day 1 ud immu 𒌓
month 30 itud arhu 𒌗
year 360 mu šattu 𒈬

Relationship to other metrologies[edit]

The Classical Mesopotamian system formed the basis for Elamite, Hebrew, Urartian, Hurrian, Hittite, Ugaritic, Phoenician, Babylonian, Assyrian, Persian, Arabic, and Islamic metrologies.[9] The Classical Mesopotamian System also has a proportional relationship, by virtue of standardized commerce, to Bronze Age Harappan and Egyptian metrologies.

See also[edit]

References[edit]

Citations[edit]

  1. ^ a b Melville 2006.
  2. ^ a b Powell, Marvin A. (1995). "Metrology and Mathematics in Ancient Mesopotamia". In Sasson, Jack M. (ed.). Civilizations of the Ancient Near East. Vol. III. New York, NY: Charles Scribner's Sons. p. 1955. ISBN 0-684-19279-9.
  3. ^ Sumerian Beer: The Origins of Brewing Technology in Ancient Mesopotamia
  4. ^ "Mesopotamian Mensuration: Balance Pan Weights from Nippur". Journal of the Economic and Social History of the Orient. 48 (3): 345–387. December 13, 2005. doi:10.1163/156852005774342894 – via www.academia.edu.
  5. ^ Hafford, William B. (August 1, 2012). "Weighing in Mesopotamia: The Balance Pan Weights from Ur". Akkadica – via www.academia.edu.
  6. ^ Pentiuc, Eugen J. (14 August 2018). West Semitic Vocabulary in the Akkadian Texts from Emar. ISBN 9789004369870.
  7. ^ Ronan, 2008
  8. ^ Kasprik, L A; Barros, A C (April 2020). "Ancient Mesopotamian's system of measurement: possible applications in mathematics and physics teaching". Journal of Physics: Conference Series. 1512: 012039. doi:10.1088/1742-6596/1512/1/012039. ISSN 1742-6588.
  9. ^ Conder 1908, p. 87.

Bibliography[edit]

Further reading[edit]

External links[edit]

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