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

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. These coefficients are given as:

  • Komma = 8081 correction when planning rations with a 360-day year
  • Leimma = 2425 conversion from decimal to a sexagesimal number system
  • Diesis = 1516
  • Euboic = 56

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). This standard is the main reference used by archaeologists to reconstruct the system.

Classical system

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 Babylonian, Assyrian, and Persian Empires.[1]

Length

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
UnitRatioSumerianAkkadianCuneiform
grain1180šeuţţatu𒊺
finger130šu-siubānu𒋗𒋛
foot23šu-du3-ašīzu𒋗𒆕𒀀
cubit1kuš3ammatu𒌑
step2ĝiri3šēpu𒈨𒊑
reed6giqanû𒄀
rod12nindannindanu𒃻
cord120eše2aslu𒂠

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

Distance
UnitRatioSumerianAkkadianCuneiform
rod160nidannindanu𒃻
cord16eše2aslu𒂠
cable1𒍑
league30da-nabêru𒁕𒈾

Area

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
UnitRatioDimensionsSumerianAkkadianCuneiform
shekel11441 kuš3 × 1 kuš3gin2šiqlu𒂆
garden112 kuš3 × 12 kuš3sarmūšaru𒊬
quarter-field2560 kuš3 × 60 kuš3uzalak?𒀺
half-field50120 kuš3 × 60 kuš3upuubû𒀹𒃷
field100120 kuš3 × 120 kuš3ikuikû𒃷
estate1800burbūru𒁓

Capacity or volume

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

Basic Volume
UnitRatioSumerianAkkadianCuneiform
shekel160gin2šiqlu𒂆
bowl1sila3𒋡
vessel10ban2sutū𒑏
bushel60ba-ri2-ga (barig)parsiktu𒁀𒌷𒂵
gur-cube300gurkurru𒄥

A sila was about 1 liter.[3]

Mass or weight

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
UnitRatioMean ValueSumerianAkkadianCuneiform
grain118046.6±1.9 mgšeuţţatu𒊺
shekel18.40±0.34 ggin2šiqlu𒂆
mina60504±20 gma-namanû𒈠𒈾
talent3,60030.2±1.2 kggun2biltu or kakaru𒄘

[4] [5] [6]

Time

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 synodic month, equinox year, and sidereal day.

Basic Time [8]
UnitRatioSumerianAkkadianCuneiform
gesh1360mu-ešgeš𒈬𒍑
watch112da-nabêru𒂆
day1udimmu𒌓
month30itudarhu𒌗
year360mušattu𒈬

Relationship to other metrologies

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

References

Citations

  1. 1 2 Melville 2006.
  2. 1 2 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

Further reading

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