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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

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
• 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 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. In general however, length, volume, and mass are derived from a theoretical standard cube, called 'gur', filled with 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 coefficients and their cubic roots.Template:Cn 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 (432g).Template:Cn 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. His reform is considered the first standardized system of measure in Mesopotamia. The royal gur-cube (Cuneiform: LU₂.GAL.GUR, Template:CuneiformTemplate:Cuneiform; Akkadian: šarru kurru) was a theoretical cuboid 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 (Template:Cuneiform) 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	Ideal Value	Sumerian	Akkadian	Cuneiform
grain	1/180	0.0025m	še	uţţatu	Template:Cuneiform
finger	1/30	0.015m	šu-si	ubānu	Template:CuneiformTemplate:Cuneiform
foot	2/3	0.333m	šu-du3-a	šīzu	Template:CuneiformTemplate:CuneiformTemplate:Cuneiform
cubit	1	0.497m	kuš3	ammatu	Template:Cuneiform
step	2	1.000m	ĝiri3	šēpu	Template:CuneiformTemplate:Cuneiform
reed	6	3.000m	gi	qanû	Template:Cuneiform
rod	12	6.000m	nindan	nindanu	Template:Cuneiform
cord	120	60.000m	eše2	aslu	Template:Cuneiform

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	Template:Cuneiform
cord	1/6	60.000m	eše2	aslu	Template:Cuneiform
cable	1	360m	uš	uš	Template:Cuneiform
league	30	10,800m	da-na	bêru	Template:CuneiformTemplate:Cuneiform

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 Template:CuneiformTemplate:Cuneiform; Sumerian: šeg₁₂-sar; Akkadian: libittu-mūšaru) which held 720 bricks.

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

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	Template:Cuneiform
bowl	1	1L	0.001m³	sila3	qû	Template:Cuneiform
vessel	10	10L	0.01m³	ban2	sutū	Template:Cuneiform
bushel	60	60L	0.06m³	ba-ri2-ga	parsiktu	Template:CuneiformTemplate:CuneiformTemplate:Cuneiform
gur-cube	300	300L	0.3m³	gur	kurru	Template:Cuneiform

Mass

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

Mass was measured by the EN system E

Basic Mass
Unit	Ratio	Ideal Value	Sumerian	Akkdian	Cuneiform
grain	1/180	0.05g	še	uţţatu	Template:Cuneiform
shekel	1	9g	gin2	šiqlu	Template:Cuneiform
pound	60	497.7g	ma-na	manû	Template:CuneiformTemplate:Cuneiform
load	3600	30,000g	gun2	biltu	Template:Cuneiform

Time

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. 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. 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	Template:CuneiformTemplate:Cuneiform
watch	1/12	7,200s	da-na	bêru	Template:Cuneiform
day	1	86,400s	ud	immu	Template:Cuneiform
month	30	2,592,000s	itud	arhu	Template:Cuneiform
year	360	31,104,000s	mu	šattu	Template:Cuneiform

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 proportional relationship, by virtue of standardized commerce, to Bronze Age Harappan and Egyptian metrologies.

Although not directly derived from it, there is a 1:2 proportional relationship between SI and Sumerian metrology. SI 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.

See also

• Babylonian mathematics
• Historical weights and measures
• Weights and measures

References

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
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• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• Template:Cite web
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

Further reading

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

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