Proto-cuneiform numerals

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Time period
c. 3500–2000 BCE
ISO 15924
ISO 15924Pcun (015), ​Proto-Cuneiform

The proto-cuneiform numerals are one of the most complex systems of enumeration in any early writing system. Their decipherment took place over several phases in the 20th century, including major advances in Adam Falkenstein’s 1936 signlist, followed by specific studies by Jöran Friberg [de] and A. A. Vajman, and ultimately the identification and decipherment of fifteen distinct subsystems of enumeration in the collaborative efforts of Peter Damerow [de] and Robert Keith Englund in the 1980s as part of the Archaische Texte aus Uruk [de] project.[1]


Alongside the decipherment of specific numerical systems, Denise Schmandt-Besserat has long argued that the proto-cuneiform signs used in ancient Sumer, including both numerical and non-numerical signs, were generally based on three-dimensional tokens that were in use in the ancient Near East for millennia.[2] This idea, which seems to be based on a suggestion from Amiet, has been subjected to a great deal of discussion and criticism.[3] 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.[4]


Many numerical signs, and some systems of enumeration, are shared between the proto-cuneiform systems and that in the proto-Elamite script, More surprising is that the same numerals can appear in different numerical systems with different values within proto-cuneiform.[5] This led to the misinterpretation of its subsystems, such as the one for measuring grain, for decades in the mid-20th century. S. Langdon, probably influenced by V. Scheil, argued that grain notations were based on a decimal system,[6] but this was disproven by Jöran Friberg in the late 1970s.[7] Building on Friberg's work on the system for grain measurement as well as A. A. Vajman's work on the sexagesimal and bisexagesimal systems,[8] Peter Damerow and Robert 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.[9]

See also[edit]


  1. ^ Nissen, Hans J. (1986). "The archaic texts from Uruk". World Archaeology. 17 (3): 317–334. doi:10.1080/00438243.1986.9979973. ISSN 0043-8243.
  2. ^ Schmandt-Besserat, Denise (1992). Before Writing. Volume 1: From Counting to Cuneiform. University of Texas Press.
  3. ^ Zimansky, P. (1993). "Review of D. Schmandt-Besserat, 'Before Writing, vol. 1'". Journal of Field Archaeology. 20: 513–517. doi:10.2307/530080. JSTOR 530080.
  4. ^ Lieberman, Stephen J. (1980). "Of Clay Pebbles, Hollow Clay Balls, and Writing: A Sumerian View". American Journal of Archaeology. 84 (3): 339–358. doi:10.2307/504711. JSTOR 504711. S2CID 191407076.
  5. ^ Englund, Robert K. (1998). Texts from the Late Uruk Period. pp. 111–117.
  6. ^ Englund, Robert K. (1998). Texts from the Late Uruk Period. p. 113.
  7. ^ Friberg, Jöran (1978–1979). The Early Roots of Babylonian Mathematics, vols. 1–2. Göteborg. pp. I 7–10, II 19–27.{{cite book}}: CS1 maint: location missing publisher (link)
  8. ^ Vajman, A. A. (1989). "Protosumerische Mass- und Zählsysteme". BaM. 20: 114–120.
  9. ^ Damerow, Peter; Englund, Robert K. (1987). "Die Zahlzeichensysteme der Archaischen Texte aus Uruk".