# Ishango bone

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

The Ishango bone is a bone tool, 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 was first thought 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, but some scientists have suggested that the groupings of notches indicate a mathematical understanding that goes beyond counting. 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]

The Ishango bone was found in 1960 by Belgian Jean de Heinzelin de Braucourt while exploring what was then the Belgian Congo.[4] It was discovered in the area of Ishango near the Semliki River.[5] 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 Congo). The bone was found among the remains of a small community that fished and gathered in this area of Africa. The small settlement had been buried in a volcanic eruption.[6][7]

The artifact was first estimated to have originated between 9,000 BC and 6,500 BC.[8] 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.[9][10]

The Ishango bone is on permanent exhibition at the Royal Belgian Institute of Natural Sciences, Brussels, Belgium.[1][11][12]

## Possible meaning

### Mathematical calculations

Left column
Center column
Right column

Some[who?] believe the three columns of asymmetrically grouped notches imply that the implement was used to construct a numeral system.

The central column begins with three notches, and then doubles to 6 notches. The process is repeated for the number 4, which doubles to 8 notches, and then reversed for the number 10, which is halved to 5 notches. These numbers may not be purely random and instead suggest some understanding of the principle of multiplication and division by two. The bone may therefore have been used as a counting tool for simple mathematical procedures.

Furthermore, the numbers on both the left and right column are all odd numbers (9, 11, 13, 17, 19 and 21). The numbers in the left column are all of the prime numbers between 10 and 20 (which form a prime quadruplet), while those in the right column consist of 10 + 1, 10 − 1, 20 + 1 and 20 − 1. The numbers on each side column add up to 60, with the numbers in the central column adding up to 48. [13]

In the book How Mathematics Happened: The First 50,000 Years, Peter Rudman argues that the development of the concept of prime numbers could only have come about after the concept of division, which he dates to after 10,000 BC, with prime numbers probably not being understood until about 500 BC. He also writes that "no attempt has been made to explain why a tally of something should exhibit multiples of two, prime numbers between 10 and 20, and some numbers that are almost multiples of 10."[14]

### Lunar calendar

Alexander Marshack examined the Ishango bone microscopically, and concluded that it may represent a six-month lunar calendar;[9] but Judy Robinson argues that Marshack overinterprets the data and that the evidence does not support lunar calendars.[15] Claudia Zaslavsky has suggested that this may indicate that the creator of the tool was a woman, tracking the lunar phase in relation to the menstrual cycle.[16][17]

## Second Bone

During excavations at the site in 1959 another bone was found. It is lighter in color, had been 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. The notches, are categorized as "major" and "minor" according to their length. Jean de Heinzelin interpreted the major notches as being units or multiples, the minor notches as fractions or subsidiary. He believed the bone to be an "interchange rule between bases 10 and 12."[18]

## References

1. ^ a b Introduction, Royal Belgian Institute of Natural Sciences, Brussels, Belgium.
2. ^ A very brief history of pure mathematics: The Ishango Bone 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. ^ de Heinzelin, Jean: "Ishango", Scientific American, 206:6 (June 1962) 105--116.
5. ^ "Lake Edward". Royal Belgian Institute of Natural Sciences. Retrieved 12 October 2014.
6. ^ Williams, Scott W.: "Mathematicians of the African Diaspora" The Mathematics Department of The State University of New York at Buffalo.
7. ^ D. Huylebrouck, The Bone that Began the Space Odyssey, The Mathematical Intelligencer vol 18 no. 4
8. ^ 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.
9. ^ a b Marshack, Alexander (1991): The Roots of Civilization, Colonial Hill, Mount Kisco, NY.
10. ^ Brooks, A.S. and Smith, C.C. (1987): "Ishango revisited: new age determinations and cultural interpretations", The African Archaeological Review, 5 : 65-78.
11. ^ Flash presentation, Royal Belgian Institute of Natural Sciences, Brussels, Belgium.
12. ^ 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
13. ^ Williams, Scott W.: "Mathematicians of the African Diaspora" The Mathematics Department of The State University of New York at Buffalo.[1]
14. ^ Rudman, Peter Strom (2007). How Mathematics Happened: The First 50,000 Years. Prometheus Books. p. 64. ISBN 978-1-59102-477-4.
15. ^ 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.
16. ^ Zaslavsky, Claudia: Africa Counts: Number and Pattern in African Culture, L. Hill, 1979.
17. ^ Zaslavsky, Claudia: "Women as the First Mathematicians", International Study Group on Ethnomathematics Newsletter, Volume 7 Number 1, 1992|January 1992.
18. ^ "The Second Bone". Royal Belgian Institute of Natural Sciences. 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.