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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.^[1] The counting tokens were used to keep accounts of personal wealth and had both metrological and mathematical functions. Each city, kingdom and trade guild had its own standards until the Formation of the Akkadian Empire when Sargon the Great issued a common standard. This standard was improved by Naram-Sin, but fell into disuse after the Akkdian Empire dissolved. The standard of Naram-Sin was readopted in the Neo-Sumerian Period by the Letter of Nanse 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. In recent times Archeologists have found a relationship between the Sumerian and SI metrologies.

Archaic system

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.

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
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.^[2] In general however, length, volume, and mass are derived from a theoretical standard cube, called 'gur', filled with either barley, wheat, water, or oil.^[3] 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.^[4] 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).^[5] 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.^[6] His reform is considered the first standardized system of measure in Mesopotamia.^[7] The royal gur-cube (LU₂.GAL.GUR, 𒈚𒄥, 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^[8].

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 survey.

Basic Length
Unit	Ratio	Ideal Value	Sumerian	Akkdian	Cuneiform
grain	1/180	0.00025m	še	uţţatu	𒊺
finger	1/30	0.015m	šu-si	ubānu	𒋗𒋛
foot	2/3	0.333m	šu-du₃-a	šīzu	𒋗𒆕𒀀
cubit	1	0.497m	kuš₃	ammatu	𒌑
step	2	1.000m	ĝiri₃	šēpu	𒈨𒊑
reed	6	3.000m	gi	qanû	𒄀
rod	12	6.000m	nindan	nindanu	𒃻
cord	120	60.000m	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	Ideal Value	Sumerian	Akkdian	Cuneiform
rod	1/60	6.000m	nidan	nindanu	𒃻
cord	1/6	60.000m	eše₂	aslu	𒂠
cable	1	360m	uš	uš	𒍑
league	30	10,800m	da-na	bêru	𒁕𒈾

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 𒊬𒋞, šeg₁₂-sar, libittu-mūšaru) which held 720 bricks

Basic Area
Unit	Ratio	Dimensions	Ideal Value	Sumerian	Akkdian	Cuneiform
shekel	1/60	1kuš₃ × 1kuš₃	1m²	gin₂	šiqlu	𒂆
garden	1	12kuš₃ × 12kuš₃	36m²	sar	mūšaru	𒊬
quarter-field	5	60kuš₃ × 60kuš₃	900m²	uzalak	?	?
half-field	10	120kuš₃ × 60kuš₃	1,800m²	upu	ubû	𒀹𒃷
field	100	60ĝiri₃ × 60ĝiri₃	3,600m²	iku	ikû	𒃷
estate	1,800	3eše₂ × 6eše₂	64,800m²	bur	būru	𒁓

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	?m³	gin₂	šiqlu	𒂆
bowl	1	1L	0.001m³	sila₃	qû	𒋡
vessel	10	10L	0.01m³	ban₂	sutū	𒑏
bushel	60	60L	0.06m³	ba-ri₂-ga	parsiktu	𒁀𒌷𒂵
gur-cube	300	300L	0.3m³	gur	kurru	𒄥

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	𒊺
shekel	1	9g	gin₂	šiqlu	𒂆
pound	60	497.7g	ma-na	manû	𒈠𒈾
load	3600	30,000g	gun₂	biltu	𒄘

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.^[9] 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	𒈬𒍑
watch	1/12	7,200s	da-na	bêru	𒂆
day	1	86,400s	ud	immu	𒌓
month	30	2,592,000s	itud	arhu	𒌗
year	360	31,104,000s	mu	šattu	𒈬

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.^[10] The Classical Mesopotamian System also has a proportional relationship, by virtue of standardized commerce, to Bronze Age Harappan and Egyptian metrologies. Although not directly derived from the Sumerian metrology, there is a 1:2 proportional relationship between the SI and Sumerian metrologies. The SI system inherited the convention of the second as 1/86,400th of a solar day from Sumer thus, two Sumerian seconds are approximately one SI second.^[11] Moreover, because both systems use a seconds pendulum to create a unit of length the one meter is approximately two kuš₃, a liter 2 sila₃, and a kilogram is 2 ma-na.

Notes

^ Stecchini 1971, section 1.1
^ Melville 2006.
^ Stenecci 1971, section 1.1
^ Stecchini 1971, section 5.4
^ Stecchini 1971, section 5.4
^ Powell 1995, p.1955.
^ Powell 1995, p.1955.
^ Melville 2006.
^ Ronan, 2008
^ Conder 1908, p. 87.
^ Butler 2005

References

Butler, Alan (2005). Civilization One: The World is Not as You Thought It Was. London: Watkins. p. 272. ISBN 1-84293-166-0. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

Conder, Claude Reignier (1908). The Rise of Man. University of Michigan: J. Murray. p. 368.

Melville, Duncan J (2006-06-06). "Old Babylonian Weights and Measures". Retrieved 2008-06-28.

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. 3024, ISBN 0684192799

Ronan, Colin Alistair (2008). Measurement of time and types of calendars » Standard units and cycles. Encyclopædia Britannica Online. Retrieved 2008-06-28.

Stecchini, Livio C. (1971). "A History of Measure". Retrieved 2008-06-28.

Whitrow, G.J. (1988). Time in History: Views of Time from Prehistory to the Present Day. New York: Oxford University Press. p. 217. ISBN 0192852116.

External links

An online calculator [1]
Robson, Eleanor (2007). "Digital Corpus of Cuneiform Mathematical Texts". Retrieved 2008-08-13.

Aleff, H. Peter (2008). "Auspicious latitudes". Retrieved 2008-08-13.

Category:Sumerian art and architecture Category:Babylonia Category:Sumer Category:WikiProject Ancient Near East articles Measurement Mesopotamian Mesopotamian Mesopotamian

[1] Stecchini 1971, section 1.1

[2] Melville 2006.

[3] Stenecci 1971, section 1.1

[4] Stecchini 1971, section 5.4

[5] Stecchini 1971, section 5.4

[6] Powell 1995, p.1955.

[7] Powell 1995, p.1955.

[8] Melville 2006.

[9] Ronan, 2008

[10] Conder 1908, p. 87.

[11] Butler 2005

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