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. [Stecchini 1971, section 1.1] 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
* 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. [Melville 2006.] In general however, length, volume, and mass are derived from a theoretical standard cube, called 'gur', filled with either barley, wheat, water, or oil. [Stenecci 1971, section 1.1] 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. [Stecchini 1971, section 5.4] 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). [Stecchini 1971, section 5.4] 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. [Powell 1995, p.1955.] His reform is considered the first standardized system of measure in Mesopotamia. [Powell 1995, p.1955.] The royal gur-cube (LU₂.GAL.GUR, cuneiform|𒈚cuneiform|𒄥, "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 [Melville 2006.] .

Length

Units of Length are prefixed by the logogram DU (cuneiform|𒁺) a convention of the archaic period counting system from which it was evolved. Basic length was used in architecture and survey.

Capacity

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

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. [Conder 1908, p. 87.] 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

*cite book
last = Conder
first = Claude Reignier
authorlink =
coauthors =
title = The Rise of Man
publisher = J. Murray
date = 1908
location = University of Michigan
pages = 368
url = http://books.google.com/books?id=-qu42RL1YAwC&pg=PA87&lpg=PA87&dq=hittite+metrology&source=web&ots=zkzCVaZFdw&sig=ZJKEATwROQMNyjOd0au6hUzdKmU&hl=en&sa=X&oi=book_result&resnum=9&ct=result
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
format =
doi =
accessdate = 2008-06-28

* Citation
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 = 0684192799

* 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
date = 2008
url = http://www.britannica.com/EBchecked/topic/89368/calendar
format =
doi =
accessdate = 2008-06-28

* cite web
last = Stecchini
first = Livio C.
authorlink = Livio Stecchini
coauthors =
title = A History of Measure
work =
publisher =
date = 1971
url = http://www.metrum.org/measures/index.htm
format =
doi =
accessdate = 2008-06-28

*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
date = 1988
location = New York
pages = 217
url = http://books.google.com/books?id=o8Nb5KLBxVQC
doi =
id =
isbn = 0192852116

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
date = 2007
location =
pages = 712
url = http://books.google.com/books?id=3ullzl036UEC&printsec=frontcover&dq=The+Mathematics+of+Egypt,+Mesopotamia,+China,+India,+and+Islam:+A+Sourcebook&sig=ACfU3U1Q92WlZZHB84AfkuXvDW9g_p_K5g
doi =
id =
isbn = 0691114854

*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
date = 1993
location =
pages = 169
url = http://books.google.com/books?id=YBAzXV4YtQ8C&pg=PA47&lpg=PA47&dq=sumerian+metrology&source=web&ots=pKE58XV4W2&sig=uppdYyBgUjeEYLk9Iga4Ko0qdGQ&hl=en&sa=X&oi=book_result&resnum=10&ct=result#PPA56,M1
doi =
id =
isbn = 0226586596

*cite book
last = Robson
first = Eleanor
authorlink =
coauthors =
title = Mesopotamian Mathematics, 2100–1600 BC: Technical Constants in Bureaucracy
publisher = Oxford University Press
date = 1999
location =
pages =
url = http://books.google.com/books?id=5gdVQRDYjYsC&pg=PA3&lpg=PA3&dq=sumerian+metrology&source=web&ots=3fgPNr6-dF&sig=UAkMehfYluJy8iuOZqFucZiez-g&hl=en&sa=X&oi=book_result&resnum=10&ct=result
doi =
id =
isbn = 0198152469

*cite book
last = Sarton
first = George
authorlink =
coauthors =
title = Ancient science through the golden age of Greece
publisher = Courier Dover Publications
date = 1993
location =
pages = 646
url = http://books.google.com/books?id=VcoGIKlHuZcC&pg=PA71&lpg=PA71&dq=sumerian+metrology&source=web&ots=t98Qs2Tzon&sig=D42yGqjph2HJZ9gXYP9rVHccHRc&hl=en&sa=X&oi=book_result&resnum=6&ct=result#PPA73,M1
doi =
id =
isbn = 0486274950

External links

*An online calculator [http://it.stlawu.edu/~dmelvill/mesomath/calculator/lengthh.html]
* cite web
last = Robson
first = Eleanor
authorlink =
coauthors =
title = Digital Corpus of Cuneiform Mathematical Texts
work =
publisher =
date = 2007
url = http://cdl.museum.upenn.edu/dccmt/metrology.html
format =
doi =
accessdate = 2008-08-13

* cite web
last = Aleff
first = H. Peter
authorlink =
coauthors =
title = Auspicious latitudes
work =
publisher =
date = 2008
url = http://www.recoveredscience.com/consta333latitudes.htm
format =
doi =
accessdate = 2008-08-13