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[[File:Sumerian Calendar ISO B0.svg||thumb|right|300px|Sumerian Metrology]]
Golda is what's written on my birth certification although it is not the title on my birth certificate. For a whilst I've been in Alaska but I will have to move in a yr or two. She is truly fond of caving but she doesn't have the time lately. Invoicing is my profession.<br><br>my site real psychics ([http://www.edmposts.com/build-a-beautiful-organic-garden-using-these-ideas/ edmposts.com])
 
'''Ancient Mesopotamian units of measurement''' originated in the loosely organized city-states of [[Early Dynastic Period of Sumer#Early Dynastic period|Early Dynastic]] [[Sumer]].  Each [[city]], [[Monarchy|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 of Akkad|Naram-Sin]], but fell into disuse after the Akkadian Empire dissolved.  The standard of Naram-Sin was readopted in the [[Third Dynasty of Ur|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 plan]]s, and issued official standards such as [[Statues of Gudea|Statue B of Gudea]] and the bronze cubit of Nippur.
 
==Archaic system==
[[File:Gudea of Lagash Girsu.png|thumbnail|right|[[Statues of Gudea|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|Uruk Period Sumer]] (c 4000 BCE).  Studies of [[Cuneiform|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<sup>*</sup>''' used to count rations
* '''GAN<sub>2</sub> 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<sup>*</sup>''' used to count barley groats
* '''EN System E''' used to count weight
* '''U<sub>4</sub> System U''' used to count calendrics
* '''DUG<sub>b</sub> System Db''' used to count milk by volume
* '''DUG<sub>c</sub> 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 [[numeral system|numeral]]s 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.<ref name="Melville 2006">Melville 2006.</ref>  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 'gun<sub>2</sub>' is defined as the weight a laden [[donkey|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.{{cn|date=September 2013}}  These coefficients are given as:
 
*'''Komma''' =  <math>80/81</math> correction when planning rations with a 360-day year
*'''Leimma''' =  <math>24/25</math> conversion from decimal to a sexagesimal number system
*'''Diesis''' =  <math>15/16</math>
*'''Euboic''' =  <math>5/6</math>
 
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'''g''').{{cn|date=September 2013}}  This standard is the main reference used by archaeologists to reconstruct the system.
 
==Classical system==
[[File:Royal gur.svg|thumb|right|300px|Royal Gur Cube of Naram-Sin]]
A major improvement came in 2150 BCE during the [[Akkadian Empire]] under the reign of [[Naram-Sin of Akkad|Naram-Sin]] when the competing systems were unified by a single official standard, the royal gur-cube.<ref name="Powell 1995, p.1955">Powell 1995, p.1955.</ref>  His reform is considered the first standardized system of measure in Mesopotamia.<ref name="Powell 1995, p.1955" />  The royal gur-cube ([[Cuneiform]]: LU<sub>2</sub>.GAL.GUR, {{cuneiform|&#x1221A;}}{{cuneiform|&#x12125;}}; [[Akkadian language|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 [[Third Dynasty of Ur|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 [[Babylonia]]n, [[Assyrian Empire|Assyrian]], and [[Persian Empire]]s.<ref name="Melville 2006" />
 
===Length===
Units of Length are prefixed by the logogram DU ({{cuneiform|&#x1207A;}}) a convention of the archaic period counting system from which it was evolved.  Basic length was used in architecture and field division. 
{| class="wikitable"
!colspan="7"| Basic Length
|-
!Unit ||Ratio ||Ideal Value ||Sumerian ||Akkadian ||Cuneiform
|-
| grain ||1/180 ||0.0025'''m'''  ||še ||''uţţatu'' ||{{cuneiform|&#x122BA;}}
|-
| finger ||1/30 ||0.015'''m'''  ||šu-si ||''ubānu''||{{cuneiform|&#x122D7;}}{{cuneiform|&#x122DB;}}
|-
| foot ||2/3 ||0.333'''m'''  ||šu-du<sub>3</sub>-a ||''šīzu'' ||{{cuneiform|&#x122D7;}}{{cuneiform|&#x12195;}}{{cuneiform|&#x12000;}}
|-
| [[cubit]] ||1 ||0.497'''m'''  ||kuš<sub>3</sub> ||''ammatu'' ||{{cuneiform|&#x12311;}}
|-
| step ||2 ||1.000'''m'''  ||ĝiri<sub>3</sub> ||''šēpu'' ||{{cuneiform|&#x12228;}}{{cuneiform|&#x12291;}}
|-
| reed ||6 ||3.000'''m'''  ||gi ||''qanû'' ||{{cuneiform|&#x12100;}}
|-
| rod ||12 ||6.000'''m'''  ||nindan ||''nindanu'' ||{{cuneiform|&#x120FB;}}
|-
| cord ||120 ||60.000'''m'''  ||eše<sub>2</sub> ||''aslu'' ||{{cuneiform|&#x120A0;}}
|}
 
Distance units were geodectic as distinguished from non-geodectic basic length units.  Sumerian [[geodesy]] divided [[latitude]] into seven zones between equator and pole.
 
{| class="wikitable"
!colspan="7"| Distance
|-
!Unit ||Ratio ||Ideal Value ||Sumerian ||Akkdian ||Cuneiform
|-
| rod ||1/60 ||6.000'''m'''  ||nidan ||''nindanu'' ||{{cuneiform|&#x120FB;}}
|-
| cord ||1/6 ||60.000'''m'''  ||eše<sub>2</sub> ||''aslu'' ||{{cuneiform|&#x120A0;}}
|-
| cable ||1 ||360'''m'''  ||uš ||''uš'' ||{{cuneiform|&#x12351;}}
|-
| league ||30 ||10,800'''m'''  ||da-na ||''bêru'' ||{{cuneiform|&#x12055;}}{{cuneiform|&#x1223E;}}
|}
 
===Area===
The '''GAN<sub>2</sub> system G''' counting system evolved into area measurements.  A special unit measuring brick quantity by area was called the brick-garden (Cuneiform: SIG.SAR {{cuneiform|&#x122AC;}}{{cuneiform|&#x122DE;}}; Sumerian: šeg<sub>12</sub>-sar; Akkadian: ''libittu''-''mūšaru'') which held 720 bricks.
 
{| class="wikitable"
!colspan="7"| Basic Area
|-
!Unit ||Ratio ||Dimensions ||Ideal Value ||Sumerian ||Akkdian ||Cuneiform
|-
| shekel ||1/60 ||1kuš<sub>3</sub> × 1kuš<sub>3</sub> ||1'''m²'''  ||gin<sub>2</sub> ||''šiqlu'' ||{{cuneiform|&#x12086;}}
|-
| garden ||1 ||12kuš<sub>3</sub> × 12kuš<sub>3</sub> ||36'''m²'''  ||sar ||''mūšaru'' ||{{cuneiform|&#x122AC;}}
|-
| quarter-field ||5 ||60kuš<sub>3</sub> × 60kuš<sub>3</sub> ||900'''m²'''  ||uzalak ||? ||{{cuneiform|&#x1203a;}}
|-
| half-field ||10 ||120kuš<sub>3</sub> × 60kuš<sub>3</sub> ||1,800'''m²'''  ||upu ||''ubû'' ||{{cuneiform|&#x12039;}}{{cuneiform|&#x120F7;}}
|-
| field ||100 ||60ĝiri<sub>3</sub> × 60ĝiri<sub>3</sub> ||3,600'''m²'''  ||iku ||''ikû'' ||{{cuneiform|&#x120F7;}}
|-
| estate ||1,800 ||3eše<sub>2</sub> × 6eše<sub>2</sub> ||64,800'''m²'''  ||bur ||''būru'' ||{{cuneiform|&#x12053;}}
|}
 
===Capacity===
Capacity was measured by either the '''ŠE system Š''' for dry capacity or the '''ŠE system Š<sup>*</sup>''' for wet capacity
{| class="wikitable"
!colspan="7"| Basic Volume
|-
!Unit ||Ratio ||Capacity ||Ideal Value ||Sumerian ||Akkdian ||Cuneiform
|-
| shekel ||1/60 || ?'''L'''||?'''m³'''  ||gin<sub>2</sub> ||''šiqlu'' ||{{cuneiform|&#x12086;}}
|-
| bowl ||1 || 1'''L'''||0.001'''m³'''  ||sila<sub>3</sub> ||''qû'' ||{{cuneiform|&#x122e1;}}
|-
| vessel ||10 || 10'''L'''||0.01'''m³'''  ||ban<sub>2</sub> ||''sutū'' ||{{cuneiform|&#x1244f;}}
|-
| bushel ||60 || 60'''L'''||0.06'''m³'''  ||ba-ri<sub>2</sub>-ga ||''parsiktu'' ||{{cuneiform|&#x12040;}}{{cuneiform|&#x12337;}}{{cuneiform|&#x120B5;}}
|-
| gur-cube ||300 || 300'''L'''||0.3'''m³'''  ||gur ||''kurru'' ||{{cuneiform|&#x12125;}}
|}
 
===Mass===
[[File:Mesopotamian weights made from haematite.JPG|thumb|right|A series of old Babylonian weights ranging from 1 mina to 3 shekels]]
Mass was measured by the '''EN system E'''
{| class="wikitable"
!colspan="7"| Basic Mass
|-
!Unit ||Ratio ||Ideal Value ||Sumerian ||Akkdian ||Cuneiform
|-
| grain ||1/180 ||0.05'''g'''  ||še || ''uţţatu'' ||{{cuneiform|&#x122BA;}}
|-
| shekel ||1 ||9'''g'''  ||gin<sub>2</sub> ||''šiqlu'' ||{{cuneiform|&#x12086;}}
|-
| pound ||60 ||497.7'''g'''  ||ma-na ||''manû''||{{cuneiform|&#x12220;}}{{cuneiform|&#x1223E;}}
|-
| load ||3600 ||30,000'''g'''  ||gun<sub>2</sub> ||''biltu'' ||{{cuneiform|&#x12118;}}
|}
 
===Time===
 
{{main|Babylonian calendar}}
In the Archaic System time notation was written in the '''U<sub>4</sub> System U'''.  Multiple [[lunisolar calendar]]s existed; however the civil calendar from the holy city of [[Nippur]] ([[Ur III period]]) was adopted by Babylon as their civil calendar.<ref>Ronan, 2008</ref>  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]].
 
{| class="wikitable"
!colspan="7"| Basic Time
|-
!Unit ||Ratio ||Ideal Value ||Sumerian ||Akkdian ||Cuneiform
|-
| gesh ||1/360 ||240'''s'''  ||mu-eš || ''geš'' ||{{cuneiform|&#x1222c;}}{{cuneiform|&#x12351;}}
|-
| watch ||1/12 ||7,200'''s'''  ||da-na ||''bêru'' ||{{cuneiform|&#x12086;}}
|-
| day ||1 ||86,400'''s'''  ||ud ||''immu''||{{cuneiform|&#x12313;}}
|-
| month ||30 ||2,592,000'''s'''  ||itud ||''arhu'' ||{{cuneiform|&#x12317;}}
|-
| year ||360 ||31,104,000'''s'''  ||mu ||''šattu'' ||{{cuneiform|&#x1222c;}}
|}
 
==Relationship to other metrologies==
The Classical Mesopotamian system formed the basis for [[Elam]]ite, Hebrew, [[Urartu|Urartian]], Hurrian, Hittite, [[Ugarit]]ic, [[Phoenicia]]n, Babylonian, Assyrian, Persian, Arabic, and Islamic metrologies.<ref>Conder 1908, p. 87.</ref>  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.<ref>Butler 2005</ref>
 
==See also==
* [[Babylonian mathematics]]
*[[Historical weights and measures]]
*[[Weights and measures]]
 
==Notes==
{{Script/Cuneiform}}
<references/>
 
==References==
*{{cite book
  | last = Conder
  | first = Claude Reignier
  | authorlink =
  | coauthors =
  | title = The Rise of Man
  | publisher = J. Murray
  | year = 1908
  | location = University of Michigan
  | pages = 368
  | url = http://books.google.com/?id=-qu42RL1YAwC&pg=PA87&lpg=PA87&dq=hittite+metrology
  | doi =
  | id =
  | isbn = }}
* {{cite web
  | last = Melville
  | first = Duncan J
  | authorlink =
  | coauthors =
  | title = Old Babylonian Weights and Measures
  | work =
  | publisher =
  | date = 2006-06-06
  | url = http://it.stlawu.edu/~dmelvill/mesomath/obmetrology.html
  | doi =
  | accessdate = 2008-06-28| archiveurl= http://web.archive.org/web/20080513131154/http://it.stlawu.edu/~dmelvill/mesomath/obmetrology.html| archivedate= 13 May 2008 <!--DASHBot-->| deadurl= no}}
* {{Cite book
  | last = Powell
  | first = Marvin A
  | contribution = Metrology and Mathematics in Ancient Mesopotamia
  | year = 1995
  | title = Civilizations of the Ancient Near East
  | editor-last = Sasson
  | editor-first = Jack M.
  | volume = III
  | pages = 3024
  | place = New York, NY
  | publisher = Charles Scribner’s Sons
  | isbn = 0-684-19279-9
  | postscript = <!--None-->}}
* {{cite web
  | last = Ronan
  | first = Colin Alistair
  | authorlink =
  | coauthors =
  | title = Measurement of time and types of calendars » Standard units and cycles
  | work =
  | publisher = Encyclopædia Britannica Online
  | year = 2008
  | url = http://www.britannica.com/EBchecked/topic/89368/calendar
  | format =
  | doi =
  | accessdate = 2008-06-28| archiveurl= http://web.archive.org/web/20080625052752/http://www.britannica.com/EBchecked/topic/89368/calendar| archivedate= 25 June 2008 <!--DASHBot-->| deadurl= no}}
*{{cite book
  | last = Whitrow
  | first = G.J.
  | authorlink =
  | coauthors =
  | title = Time in History: Views of Time from Prehistory to the Present Day
  | publisher = Oxford University Press
  | year = 1988
  | location = New York
  | pages = 217
  | url = http://books.google.com/?id=o8Nb5KLBxVQC
  | doi =
  | id =
  | isbn = 0-19-285211-6}}
 
==Further reading==
*{{cite book
  | last = Katz
  | first = Victor,J
  | authorlink =
  | coauthors =
  | title = The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook
  | publisher = Princeton University Press
  | year = 2007
  | location =
  | pages = 712
  | url = http://books.google.com/?id=3ullzl036UEC&printsec=frontcover&dq=The+Mathematics+of+Egypt,+Mesopotamia,+China,+India,+and+Islam:+A+Sourcebook
  | doi =
  | id =
  | isbn = 0-691-11485-4}}
*{{cite book
  | last = Nissen
  | first = Hans Jörg
  | authorlink =
  | coauthors = Peter Damerow, Robert K. Englund, Paul Larsen
  | title = Archaic Bookkeeping: Early Writing and Techniques of Economic Administration
  | publisher = University of Chicago Press
  | year = 1993
  | location =
  | pages = 169
  | url = http://books.google.com/?id=YBAzXV4YtQ8C&pg=PA47&lpg=PA47&dq=sumerian+metrology
  | doi =
  | id =
  | isbn = 0-226-58659-6}}
*{{cite book
  | last = Robson
  | first = Eleanor
  | authorlink = Eleanor Robson
  | coauthors =
  | title = Mesopotamian Mathematics, 2100&ndash;1600 BC: Technical Constants in Bureaucracy
  | publisher = Oxford University Press
  | year = 1999
  | location =
  | pages =
  | url = http://books.google.com/?id=5gdVQRDYjYsC&pg=PA3&lpg=PA3&dq=sumerian+metrology
  | doi =
  | id =
  | isbn = 0-19-815246-9}}
*{{cite book
  | last = Sarton
  | first = George
  | authorlink =
  | coauthors =
  | title = Ancient science through the golden age of Greece
  | publisher = Courier Dover Publications
  | year = 1993
  | location =
  | pages = 646
  | url = http://books.google.com/?id=VcoGIKlHuZcC&pg=PA71&lpg=PA71&dq=sumerian+metrology
  | doi =
  | id =
  | isbn = 0-486-27495-0}}
 
==External links==
*An online calculator [http://it.stlawu.edu/~dmelvill/mesomath/calculator/lengthh.html]
* {{cite web
  | last = Robson
  | first = Eleanor
  | authorlink = Eleanor Robson
  | coauthors =
  | title = Digital Corpus of Cuneiform Mathematical Texts
  | work =
  | publisher =
  | year = 2007
  | url = http://cdl.museum.upenn.edu/dccmt/metrology.html
  | doi =
  | accessdate = 2008-08-13}}
* {{cite web
  | last = Aleff
  | first = H. Peter
  | authorlink =
  | coauthors =
  | title = Auspicious latitudes
  | work =
  | publisher =
  | year = 2008
  | url = http://www.recoveredscience.com/consta333latitudes.htm
  | doi =
  | accessdate = 2008-08-13}}
* {{cite journal
  | last = Kreidik
  | first = L. G.
  | authorlink =
  | coauthors = T. S. Kortneva and G. P. Shpenkov
  | title = 4. Fundamental periods of the World and ancient metrology
  | work = Journal of theoretical Dialectics-Physics-Mathematics
  | publisher = Dialectical Academy, Russia-Belarus
  | year = 2005
  | url = http://dialectical-physics.org/b01/04/en/b0104en.htm
  | doi =
  | accessdate = 2009-08-20}}
 
{{systems of measurement}}
 
{{DEFAULTSORT:Ancient Mesopotamian Units Of Measurement}}
[[Category:Sumerian art and architecture]]
[[Category:Babylonia]]
[[Category:Sumer]]
[[Category:WikiProject Ancient Near East articles]]
[[Category:Babylonian mathematics|Measurement]]
[[Category:Science and technology in Iraq|Mesopotamian]]
[[Category:Obsolete units of measurement|Mesopotamian]]
[[Category:Human-based units of measurement|Mesopotamian]]
[[Category:Systems of units|Mesopotamian]]

Latest revision as of 01:13, 18 November 2014

Golda is what's written on my birth certification although it is not the title on my birth certificate. For a whilst I've been in Alaska but I will have to move in a yr or two. She is truly fond of caving but she doesn't have the time lately. Invoicing is my profession.

my site real psychics (edmposts.com)

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