Ishango bone

The Ishango bone is a bone tool and possible mathematical object, dated to the Upper Paleolithic era. It is a dark brown length of bone, the fibula of a baboon,[2] with a sharp piece of quartz affixed to one end, perhaps for engraving. It is thought by some to be a tally stick, as it has a series of what has been interpreted as tally marks carved in three columns running the length of the tool, though it has also been suggested that the scratches might have been to create a better grip on the handle or for some other non-mathematical reason.[3] Others argue that the marks on the object are non-random and that it was likely a kind of counting tool and used to perform simple mathematical procedures.[4][5]

The Ishango bone on exhibition at the Royal Belgian Institute of Natural Sciences[1]

The Ishango bone was found in 1950 by Belgian Jean de Heinzelin de Braucourt while exploring what was then the Belgian Congo.[6] It was discovered in the area of Ishango near the Semliki River.[7] Lake Edward empties into the Semliki which forms part of the headwaters of the Nile River (now on the border between modern-day Uganda and D.R. Congo). The bone was found among the remains of a small community that fished and gathered in this area of Africa. The settlement had been buried in a volcanic eruption.[8][9]

The artifact was first estimated to have originated between 9,000 BC and 6,500 BC.[10] However, the dating of the site where it was discovered was re-evaluated, and it is now believed to be more than 20,000 years old (between 18,000 BC and 20,000 BC).[11][12]

The Ishango bone is on permanent exhibition at the Royal Belgian Institute of Natural Sciences, Brussels, Belgium.[1][13][14]

Mathematical interpretations
First (sometimes called "center") column (invisible in picture), from bottom to top
Second (or "right") column (to the left in picture), from bottom to top
Third (or "left") column (to the right in picture), from bottom to top

The etchings on the bone are in three columns with marks asymmetrically grouped into sets, leading to "various tantalizing hypotheses" such as that the implement indicates an understanding of decimals or prime numbers. Though these propositions have been questioned, it is considered likely by some scholars that the tool was used for simple mathematical procedures or to construct a numeral system.[5]

The third column has been interpreted as a "table of prime numbers",[15] but it is more likely to be a coincidence.[5] Historian of mathematics Peter S. Rudman argues that prime numbers were probably not understood until about 500 BC, and were dependent on the concept of division, which he dates to no earlier than 10,000 BC.[16]

Alexander Marshack speculated that the Ishango bone represents a six-month lunar calendar.[11] This has led Claudia Zaslavsky to suggest that the creator of the tool may have been a woman, tracking the lunar phase in relation to the menstrual cycle.[17][18] This is countered with the argument that Marshack overinterprets the data and that the evidence does not support lunar calendars.[19]

More recently Vladimir Pletser has proposed that the Ishango bone is a counting tool using the base 12 and sub-bases 3 and 4, and involving simple multiplication, somewhat comparable to a primitive slide rule."[4]

Caleb Everett has also stated of the object, that "the quantities evident in the groupings of marks are not random", and are likely evidence of prehistoric numerals. He suggests that the first column may reflect some "doubling pattern" and that the tool may have been used for counting and multiplication and also possibly as a "numeric reference table".[5]

Second bone

During earlier excavations at the Ishango site in 1959, another bone was also found. It is lighter in color and was scraped, thinned, polished, and broken on one end, revealing it to be hollow. The artifact possibly held a piece of quartz like the more well-known bone or it could have been a tool handle. The 14-cm long bone has 90 notches on six sides, which are categorized as "major" or "minor" according to their length. Jean de Heinzelin interpreted the major notches as being units or multiples and the minor notches as fractions or subsidiary. He believed the bone to be an "interchange rule between bases 10 and 12."[20]

See also

References
  1. Introduction Archived 2016-03-04 at the Wayback Machine, Royal Belgian Institute of Natural Sciences, Brussels, Belgium.
  2. A very brief history of pure mathematics: The Ishango Bone Archived 2008-07-21 at the Wayback Machine University of Western Australia School of Mathematics - accessed January 2007.
  3. Rudman, Peter Strom (2007). How Mathematics Happened: The First 50,000 Years. Prometheus Books. p. 63. ISBN 978-1-59102-477-4.
  4. Pletser, Vladimir (2012). "Does the Ishango Bone Indicate Knowledge of the Base 12? An Interpretation of a Prehistoric Discovery, the First Mathematical Tool of Humankind". arXiv:1204.1019 [math.HO].
  5. Everett, Caleb (2017). Numbers and the Making of Us: Counting and the Course of Human Cultures. Harvard University Press. pp. 35–36. ISBN 9780674504431.
  6. de Heinzelin, Jean: "Ishango", Scientific American, 206:6 (June 1962) 105--116.
  7. "Lake Edward". Royal Belgian Institute of Natural Sciences. Archived from the original on 23 June 2016. Retrieved 12 October 2014.
  8. Williams, Scott W.: "Mathematicians of the African Diaspora" The Mathematics Department of The State University of New York at Buffalo.
  9. D. Huylebrouck, The Bone that Began the Space Odyssey, The Mathematical Intelligencer vol 18 no. 4
  10. Gerdes, Paulus (1991): On The History of Mathematics in Africa South of the Sahara; African Mathematical Union, Commission on the History of Mathematics in Africa.
  11. Marshack, Alexander (1991): The Roots of Civilization, Colonial Hill, Mount Kisco, NY.
  12. Brooks, A.S. and Smith, C.C. (1987): "Ishango revisited: new age determinations and cultural interpretations", The African Archaeological Review, 5 : 65-78.
  13. Flash presentation Archived 2016-05-27 at the Wayback Machine, Royal Belgian Institute of Natural Sciences, Brussels, Belgium.
  14. The Ishango Bone, Democratic Republic of the Congo, on permanent display at the Royal Belgian Institute of Natural Sciences, Brussels, Belgium. UNESCO's Portal to the Heritage of Astronomy
  15. Williams, Scott W.: "Mathematicians of the African Diaspora" The Mathematics Department of The State University of New York at Buffalo.
  16. Rudman, Peter Strom (2007). How Mathematics Happened: The First 50,000 Years. Prometheus Books. p. 64. ISBN 978-1-59102-477-4.
  17. Zaslavsky, Claudia: Africa Counts: Number and Pattern in African Culture, L. Hill, 1979.
  18. Zaslavsky, Claudia: "Women as the First Mathematicians", International Study Group on Ethnomathematics Newsletter, Volume 7 Number 1, 1992|January 1992.
  19. Robinson, Judy. 1992. Not counting on Marshack: a reassessment of the work of Alexander Marshack on notation in the Upper Palaeolithic. Journal of Mediterranean Studies 2(1): 1-16.
  20. "The Second Bone". Royal Belgian Institute of Natural Sciences. Archived from the original on 23 June 2016. Retrieved 12 October 2014.

Further reading
  1. Shurkin, J.: Engines of the mind: a history of the computer, W. W. Norton & Co., 1984., p21
  2. Bogoshi, J., Naidoo, K. and Webb, J.: "The oldest mathematical artifact", Math. Gazette, 71:458 (1987) 294.
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