View source for Proto-cuneiform numerals

{{Context|date=September 2020}}
{{Infobox writing system
|name        = Proto-cuneiform
|type        = 
|time        = 3500&nbsp;BCE&ndash;2000&nbsp;BCE
|languages   = 
|creators    = 
|iso15924    = Pcun
|unicode     = 
|note        = none<!-- no IPA warning -->
|direction   = Left-to-right
}}
{{Numeral systems|expand=Sign-value notation}}

The '''[[Social:Proto-Cuneiform|Proto-Cuneiform]] numerals''' are one of the most complex [[Numeral system|systems of enumeration]] in any early [[Social:Writing system|writing system]]. Their decipherment took place over several phases in the 20th century, including major advances in Adam Falkenstein’s 1936 signlist, specific studies by Jöran Friberg <small>[<nowiki/>de]</small> and A. A. Vajman, and ultimately the identification and decipherment of fifteen distinct systems of enumeration in the collaborative efforts of Peter Damerow and Robert K. Englund in the 1980s as part of the Archaische Texte aus Uruk project.<ref>{{Cite journal|last=Nissen|first=Hans J.|date=1986|title=The archaic texts from Uruk|url=http://dx.doi.org/10.1080/00438243.1986.9979973|journal=World Archaeology|volume=17|issue=3|pages=317–334|doi=10.1080/00438243.1986.9979973|issn=0043-8243}}</ref>

== Basis ==
Alongside the decipherment of specific numerical systems, Denise Schmandt-Besserat has long argued that [[Social:Proto-Cuneiform|Proto-Cuneiform]] signs generally, including both numerical and non-numerical signs, were based on three-dimensional tokens that were in use in the ancient Near East for millennia.<ref>{{cite book |last1=Schmandt-Besserat |first1=Denise |title=Before Writing. Volume 1: From Counting to Cuneiform |date=1992 |publisher=University of Texas Press}}</ref> This idea, which seems to be based on a suggestion from Amiet, has been subjected to a great deal of discussion and criticism.<ref>{{cite journal |last1=Zimansky |first1=P. |title=Review of D. Schmandt-Besserat, 'Before Writing, vol. 1' |journal=Journal of Field Archaeology |date=1993 |volume=20 |pages=513–517|doi=10.2307/530080 |jstor=530080 }}</ref> There is a widespread consensus that the plain tokens, particularly those found within clay bullae, correspond to the proto-cuneiform numerical signs, but the link that Schmandt-Besserat posited between complex or decorated tokens and the non-numerical proto-cuneiform signs is disputed.<ref>{{cite journal |last1=Lieberman |first1=Stephen J. |title=Of Clay Pebbles, Hollow Clay Balls, and Writing: A Sumerian View |journal=American Journal of Archaeology |date=1980 |volume=84 |issue=3 |pages=339–358 |doi=10.2307/504711 |jstor=504711 |s2cid=191407076 }}</ref>

== Decipherment ==
Many numerical signs and some systems of enumeration are shared between the [[Social:Proto-Cuneiform|Proto-Cuneiform]] numerical system and the [[Social:Proto-Elamite script|Proto-Elamite]] numerical signs, but the most surprising feature of the proto-cuneiform numerals is that the same numerals can appear in different numerical systems with different values.<ref>{{cite book |last1=Englund |first1=Robert K. |title=Texts from the Late Uruk Period |date=1998 |pages=111–117}}</ref> Because of this, certain numerical systems, such as the system for measuring grain, were misconstrued for decades in the mid-20th century. S. Langdon, probably influenced by V. Scheil, argued that grain notations were based on a decimal system,<ref>{{cite book |last1=Englund |first1=Robert K. |title=Texts from the Late Uruk Period |date=1998 |pages=113}}</ref> but this was disproven by Jöran Friberg in the late 1970s.<ref>{{cite book |last1=Friberg |first1=Jöran |title=The Early Roots of Babylonian Mathematics, vols. 1–2 |date=1978–1979 |location=Göteborg |pages=I 7–10, II 19–27}}</ref> Building on Friberg's work on the system for grain measurement as well as A. A. Vajman's work on the [[Sexagesimal|sexagesimal]] and bisexagesimal systems,<ref>{{cite journal |last1=Vajman |first1=A. A. |title=Protosumerische Mass- und Zählsysteme |journal=BaM |date=1989 |volume=20 |pages=114–120}}</ref> Peter Damerow and Robert K. Englund carried out a systematic classification and study of the proto-cuneiform numerals in all known texts in the 1980s, ultimately identifying fifteen distinct numerical systems.<ref>{{cite news |last1=Damerow |first1=Peter |last2=Englund |first2=Robert K. |title=Die Zahlzeichensysteme der Archaischen Texte aus Uruk |date=1987 }}</ref>

== See also ==
* [[Babylonian cuneiform numerals]]

== References ==
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[[Category:Numeral systems]]

{{Sourceattribution|Proto-cuneiform numerals|1}}