Definitions

standard of measurement

Ancient Mesopotamian units of measurement

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.

Archaic system

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

  • 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
  • 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 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 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 'gun2' 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.

Classical system

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. His reform is considered the first standardized system of measure in Mesopotamia. The royal gur-cube (LU2.GAL.GUR, , šarru kurru) was a theoretical cube of water approximately 6m × 6m × 0.5m 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.

Length

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-du3-a šīzu
cubit 1 0.497m kuš3 ammatu
step 2 1.000m ĝiri3 šēpu
reed 6 3.000m gi qanû
rod 12 6.000m nindan nindanu
cord 120 60.000m eše2 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 eše2 aslu
cable 1 360m
league 30 10,800m da-na bêru

Area

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

Basic Area
Unit Ratio Dimensions Ideal Value Sumerian Akkdian Cuneiform
shekel 1/60 1kuš3 × 1kuš3 1 gin2 šiqlu
garden 1 12kuš3 × 12kuš3 36 sar mūšaru
quarter-field 5 60kuš3 × 60kuš3 900 uzalak ? ?
half-field 10 120kuš3 × 60kuš3 1,800 upu ubû
field 100 60ĝiri3 × 60ĝiri3 3,600 iku ikû
estate 1,800 3eše2 × 6eše2 64,800 bur būru

Capacity

Capacity was measured by either the ŠE system Š for dry capacity or the ŠE system Š* for wet capacity
Basic Volume
Unit Ratio Capacity Ideal Value Sumerian Akkdian Cuneiform
shekel 1/60 ?L ? gin2 šiqlu
bowl 1 1L 0.001 sila3
vessel 10 10L 0.01 ban2 sutū
bushel 60 60L 0.06 ba-ri2-ga parsiktu
gur-cube 300 300L 0.3 gur kurru

Mass

Mass was measured by the EN system E
Basic Mass
Unit Ratio Ideal Value Sumerian Akkdian Cuneiform
grain 1/180 0.15g še uţţatu
shekel 1 9g gin2 šiqlu
pound 60 497.7g ma-na manû
load 3600 30,000g gun2 biltu

Time

In the Archaic System time notation 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. 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 sideral day.

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

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. The Classical Mesopotamian System also has a relationship, by virtue of commerce, to Bronze Age Harappan and Egyptian metrologies.

See also

Historical weights and measures
Weights and measures
Statues of Gudea
Babylonian mathematics

Notes

References

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Further Reading

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External links

  • An online calculator
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