Ishango bone
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This image shows both the front and back of the Ishango bone. |
The
Ishango bone is a
bone tool, dated to the
Upper Paleolithic era, about 18000 to 20000 BC. It is a dark brown length of bone, with a sharp piece of quartz affixed to one end, perhaps for engraving or writing. It was first thought to be a
tally stick, as it has a series of
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.
The Ishango bone was found in 1950 by Belgian
Jean de Heinzelin de Braucourt while exploring what was then the
Belgian Congo.
[de Heinzelin, Jean: "Ishango", Scientific American, 206:6 (June 1962) 105--116.] It was discovered in the
African area of
Ishango, which was centered near the headwaters of the
Nile River at
Lake Edward (now on the border between modern-day
Uganda and
Congo). The lakeside Ishango population of 20000 years ago may have been one of the first counting societies, but it lasted only a few hundred years before being buried by a volcanic eruption.
[Williams, Scott W.: "Mathematicians of the African Diaspora" The Mathematics Department of The State University of New York at Buffalo.]The artifact was first estimated to originate between 9000 BC and 6500 BC.
[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.] However, the dating of the site where it was discovered was re-evaluated, and is now believed to be more than 20,000 years old.
[Marshack, Alexander (1991): The Roots of Civilization, Colonial Hill, Mount Kisco, NY.][Brooks, A.S. and Smith, C.C. (1987): "Ishango revisited: new age determinations and cultural interpretations", The African Archaeological Review, 5 : 65-78.]The Ishango bone is on permanent exhibition at the
Royal Belgian Institute of Natural Sciences,
Brussels,
Belgium.
[Exhibition at the Royal Belgian Institute of Natural Sciences, Brussels, Belgium.]Mathematical calculations?
The three columns of asymmetrically grouped notches imply that the implement was more functional than decorative. The Ishango grouping may have been used to construct a number system, which is speculated to have spread north to
Egypt and contributed to the development of mathematics.
Columns of tally marks:
| (left) | 19 | 17 | 13 | 11 | | | | | | (center) | 7 | 5 | 5 | 10 | 8 | 4 | 6 | 3 |
| (right) | 9 | 19 | 21 | 11 | | | | |
The central column begins with 3 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 then, are not purely random and instead suggests 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 number of notches on either side of the central column may indicate more counting prowess. 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, 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. Both of these numbers are multiples of 12, again suggesting an understanding of multiplication and division.
Lunar calendar?
Alexander Marshack examined the Ishango bone microscopically, and concluded that it may represent a six-month
lunar calendar.
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.
[Zaslavsky, Claudia: Africa Counts: Number and Pattern in African Culture, L. Hill, 1979.],
[Zaslavsky, Claudia: "Women as the First Mathematicians", International Study Group on Ethnomathematics Newsletter, Volume 7 Number 1, January 1992.]Several tally sticks predate the Ishango bone, and cuts on sticks or bones have been found worldwide. The
Lebombo bone, a 37000-year-old baboon
fibula was found in
Swaziland. A 32000-year-old wolf
tibia with 57 notches, grouped in fives, was found in
Czechoslovakia in 1937.
# Shurkin, J.:
Engines of the mind: a history of the computer, W. W. Norton & Co., 1984., p21# Bogoshi, J., Naidoo, K. and Webb, J.: "The oldest mathematical artifact",
Math. Gazette, 71:458 (1987) 294.
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Virtual display of the Ishango bone, in
QuickTime VR
