- History of writing ancient numbers
The first method of counting was counting on fingers. By placing the thumb on various finger joints a person can count up to 90,000. [ The Earliest Calculating - The Hand, Ifrah (2000), pages 47-61. ] This evolved into sign language for hand-to-eye communication of numbers. But this was not writing.
Tallies by carving notches in wood, bone, and stone were used for at least forty thousand years. [ Tally Sticks, Ifrah (2000), pages 64-67. ] Stone age cultures, including ancient American Indian groups, used tallies for gambling with horses, slaves, personal services and trade-goods.
Roman Numeralsevolved from this primitive system of cutting notches. [ The Origin of Roman Numerals, Ifrah (2000), pages 191-194. ] The V for five was cut as two notches to represent a person's hand of five fingers (four fingers separated from the thumb by a V shaped gap). The X for ten was cut as two crossed notches to represent two hands.
Invention of tokens for record keeping
The earliest known writing for record keeping evolved from a system of counting using small clay tokens that began in
Sumerabout 8000 BC. [ Strings of Tokens and Envelopes, Besserat (1996) pages 39-54. ] When they wanted to represent "two sheep", they selected two round clay tokens each having a + sign baked into it. Each token represented one sheep. Representing a hundred sheep with a hundred tokens would be impractical, so they invented different clay tokens to represent different numbers of each specific commodity, and strung the tokens like beads on a string. There was a token for one sheep, a different token for ten sheep, a different token for ten goats, etc. Thirty-two sheep would be represented by three ten-sheep tokens followed on the string by two sheep tokens. To insure that nobody could alter the number and type of tokens, they invented a clay envelope shaped like a hollow ball into which the tokens on a string were placed, sealed, and baked. If anybody disputed the number, they could break open the clay envelope and do a recount. To avoid unnecessary damage to the record, they pressed archaic number signs and witness seals on the outside of the envelope before it was baked, each sign similar in shape to the tokens they represented. Since there was seldom any need to break open the envelope, the signs on the outside became the first written language for writing numbers in clay.
Beginning about 3500 BC the tokens and envelopes were replaced by numerals impressed with a round stylus at different angles in flat clay tablets which were then baked. [ Impressed Tablets, Besserat (1996) pages 55-62. ] A sharp stylus was used to carve pictographs representing various tokens. Each sign represented both the commodity being counted and the quantity or volume of that commodity.
About 3100 BC written numbers were dissociated from the things being counted and abstract numerals were invented. [ Tokens, Their Role in Prehistory, Besserat (1996) pages 123-124. ] The things being counted were indicated by pictographs carved with a sharp stylus next to round-stylus numerals.
The Sumerians had a complex assortment of incompatible number systems and each city had their own local way of writing numerals. In the city of Uruk about 3100 BC, there were more than a dozen different numeric systems. [ Archaic Numerical Sign Systems, Nissen (1993) pages 25-29. ] One number system was used for counting discrete objects such as animals, tools, and containers. A different system was for counting cheese and grain products. Another system was used to count volumes of grain and included fractions. Another system counted beer ingredients. Another system counted weights. Another system counted land areas. Another system counted time units and calendar units. And these systems changed over the years. Numbers for counting volumes of grain changed whenever the size of the baskets changed. People who added and subtracted volumes of grain every day used their arithmetic skills to count other things that were unrelated to volume measurements.
Sumeriansinvented the wheel and also invented arithmetic. Multiplication and division were done with multiplication tables baked in clay tablets.
Conversion of archaic numbers to cuneiform
Between 2700 BC and 2000 BC, the round stylus was gradually replaced by a reed stylus that had been used to press wedge shaped cuneiform signs in clay. To represent numbers that previously had been pressed with a round stylus, these cuneiform number signs were pressed in a circular pattern and they retained the additive
sign-value notationthat originated with tokens on a string. Cuneiform numerals and archaic numerals were ambiguous because they represented various numeric systems that differed depending on what was being counted. About 2100 BC in Sumer, these proto-sexagesimal sign-value systems gradually converged on a common sexagesimal number system that was a place-valuesystem consisting of only two impressed marks, the vertical wedge and the chevron, which could also represent fractions. [ Sexagesimal Place Value System, Nissen (1993) pages 142-143. ] This sexagesimalnumber system was fully developed at the beginning of the Old Babylonia period (about 1950 BC) and became standard in Babylonia.
Sexagesimal numerals were a
Mixed radixsystem that retained the alternating base 10 and base 6 in a sequence of cuneiform vertical wedges and chevrons. Sexagesimal numerals became widely used in commerce, but were also used in astronomical and other calculations. This system was exported from Babylonia and used throughout Mesopotamia, and by every Mediterraneannation that used standard Babylonian units of measure and counting, including the Greeks, Romans and Egyptians. In Arabic numerals, we still use sexagesimal to count time (minutes per hour), and angles (degrees).
History of Sumer
History of writing
* [http://www.historyworld.net/wrldhis/PlainTextHistories.asp?historyid=ab34 History of Counting Systems and Numerals] . Retrieved
11 December 2005.
* Denise Schmandt-Besserat [https://webspace.utexas.edu/dsbay/index.html HomePage] , "How Writing Came About", University of Texas Press, 1996, ISBN 0-292-77704-3.
* Georges Ifrah. "The Universal History of Numbers: From Prehistory to the Invention of the Computer", Wiley, 2000. ISBN 0-471-37568-3.
* Hans J. Nissen, P. Damerow, R. Englund, "Archaic Bookkeeping", University of Chicago Press, 1993, ISBN 0-226-58659-6.
Wikimedia Foundation. 2010.
Look at other dictionaries:
History of writing — Writing systems History Grapheme List of writing systems Types Featural alphabet Alphabet Abjad Abugida Syllabary Logography Shorthand … Wikipedia
History of Sumer — The history of Sumer, taken to include the prehistoric Ubaid and Uruk periods, spans the 5th to 3rd millennia BC, ending with the downfall of the Third Dynasty of Ur around 2004 BC, followed by a transition period of Amorite states before the… … Wikipedia
Writing — is the representation of language in a textual medium through the use of a set of signs or symbols (known as a writing system). It is distinguished from illustration, such as cave drawing and painting, and the recording of language via a non… … Wikipedia
History of Mongolia — This article is part of a series Ancient History … Wikipedia
Ancient astronauts — Ancient paintings from Val Camonica, Italy are believed to depict forgotten deities; ancient astronaut proponents claim these pictures resemble modern day astronauts despite being painted ca. 10,000 BC. Claims Intelligent extraterrestrial life… … Wikipedia
History of mathematics — A proof from Euclid s Elements, widely considered the most influential textbook of all time. … Wikipedia
History of the world — The history of the world [Williams, H. S. (1904). The historians history of the world; a comprehensive narrative of the rise and development of nations as recorded by over two thousand of the great writers of all ages. New York: The Outlook… … Wikipedia
History — This article is about the academic discipline. For a general history of human beings, see History of the world. For other uses, see History (disambiguation). Historia (Allegory of History) By Nikolaos Gysis (1892) … Wikipedia
Writing system — Predominant scripts at the national level, with selected regional and minority scripts. Alphabet Latin Cyrillic Latin Greek … Wikipedia
Ancient Egyptian religion — Part of a series on Ancient Egyptian religion … Wikipedia