The

Proto-Cuneiform The Proto-Cuneiform script was used in Mesopotamia from roughly 3300 BC to 2900 BC. It arose from the token based system used in the region for the preceding millennia and was replaced by the development of early Cuneiform script in the Early Dy ...

numerals are one of the most complex systems of enumeration in any early

writing system A writing system is a method of visually representing verbal communication, based on a script and a set of rules regulating its use. While both writing and speech are useful in conveying messages, writing differs in also being a reliable for ...

. Their decipherment took place over several phases in the 20th century, including major advances in

Adam Falkenstein Adam Falkenstein (17 September 1906 – 15 October 1966) was a German Assyriologist. He was born in Planegg, near Munich in Bavaria and died in Heidelberg. Life Falkenstein studied Assyriology in Munich and Leipzig. He was involved primarily ...

’s 1936 signlist, specific studies by Jöran Friberg de">:de:Jöran Friberg">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 Peter may refer to: People * List of people named Peter, a list of people and fictional characters with the given name * Peter (given name) ** Saint Peter (died 60s), apostle of Jesus, leader of the early Christian Church * Peter (surname), a sur ...

and

Robert K. Englund The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of '' Hruod'' ( non, Hróðr) "fame, glory, honou ...

in the 1980s as part of the Archaische Texte aus Uruk project.

Basis

Alongside the decipherment of specific numerical systems,

Denise Schmandt-Besserat Denise Schmandt-Besserat (born August 10, 1933 in Ay, Marne, France) is a French-American archaeologist and retired professor of art and archaeology of the ancient Near East. She spent much of her professional career as a professor at the Univer ...

has long argued that

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. This idea, which seems to be based on a suggestion from Amiet, has been subjected to a great deal of discussion and criticism. 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.

Decipherment

Many numerical signs and some systems of enumeration are shared between the

numerical system and the

Proto-Elamite The Proto-Elamite period, also known as Susa III, is a chronological era in the ancient history of the area of Elam, dating from . In archaeological terms this corresponds to the late Banesh period. Proto-Elamite sites are recognized as the o ...

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. 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, but this was disproven by Jöran Friberg in the late 1970s. Building on Friberg's work on the system for grain measurement as well as A. A. Vajman's work on the

sexagesimal Sexagesimal, also known as base 60 or sexagenary, is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form� ...

and bisexagesimal systems,

and

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.

References

{{reflist Babylonian mathematics Numeral systems

Basis

Decipherment

See also

References