Name: Ishango Bone
Date: 20,000 years old
Origin: present-day Uganda and Democratic Republic ago
Utility: Mathematical tool
The Ishango Bone is a quartz and mammal bone found in the 1950s by Belgian geologist Jean de Heinzelin at Ishango, on the shore of Lake Rutanzige in Central Africa. The bone is estimated to be over 20,000 years old. Ishango was home to a large population of upper Paleolithic people. European archeological expeditions found thousands of different objects and bones, including the Ishango Bone. The bone was said to be a mathematical tool by Heinzelin exhibiting the use of prime numbers, multiplications and additions. Many others have hypothesised the significance of the bone. Either way, the bone represents one of the many methods used by the people of Ishango to keep track of data important to their community.
The Ishango Bone was found in 1956 in the Ishango area, on the banks of Lake Rutanzige (located on the border between modern-day Uganda and Congo). The Ishango area is an important archeological site. It was first described in Europe by Belgian zoologist Hubert Damas (1910-1964) after surveying the area in 1935. In the publication, Damas mentions the remains of ancient human activity in the area, including the existence of human bones and bone harpoons. As these findings were not relevant to him at the time of his research, Damas described the necessity to survey the area in the future.
Belgian geologist Jean de Heinzelin de Braucourt (1920-1998) undertook the mission in 1957. His mission was composed of two objectives. First, he hoped to learn more about the geological formation of the lake and its surroundings. Secondly, he wanted to find evidence of the ancient human activity his predecessor had published. Heinzelin undertook this mission by digging a slice of the sediment (earth) layers of the lake shore. From observing the different layers of sediment, Heinzelin found evidence of volcanic activity and was able to deduce the topology of the lake shore. The sediments indicated that the water level was much higher in the past. The sediments also showed traces of human activity from prehistoric times.
Thousands of remains were found at Ishango during Heinzelin’s mission, including a hundred human bones which seemed to belong to nine different bodies. The many objects in quartz and bones found at Ishango were surprisingly well preserved in the sediments, owing to the ashes present in the different layers of sediment. They were preserved for millenia thanks to the volcanic ash which helped rapidly fossilize them before they were able to degrade.
Approximately a hundred human bones were found at Ishango. The bones identified belong primarily to Homo sapiens sapiens, the species to which all modern human beings belong. Analysis of the remains can help understand the Ishango people’s environment and characteristics. The people of Ishango were primarily sedentary with a balanced diet. The many remains of animal and fish bones indicated that inhabitants of the area made use of the abundant resources on the Lake bank throughout the year. These bones included those of warthogs, different species of antelope, ibis and pelican birds and buffalos. While it isn't possible to deduce what types of fruits, vegetables and herbs the Ishango people ate – those matters disintegrate quicker over time – the presence of instruments to grind grains are evidence of a varied diet. Heinzelin’s mission, however, was most remembered for the uncovering of what came to be known as the “Ishango Bone”.
Heinzelin’s mission stumbled across the Ishango bone, while surveying the Ishango area on the shore of Lake Rutanzige. The bone is ten centimetres long and made of fine quartz and mammal bone (most likely a baboon). The bone was first estimated by Heinzelin’s mission to originate between 9,000 BC ad 6,500 BC. Since then, a re-evaluation in the 1980s and 1990s using carbon dating places the bone at over 20,000 years old. Its shaft (handle) is carved with 168 lines distributed on three sides of the handle. The asymmetrical and grouped notches on the bone imply that the bone was functional more than decorative. Several hypotheses emerged as to the significance of the lines of the bone.
Jean de Heinzelin’s hypothesis
In 1957, Heinzelin published his hypothesis on the significance of the lines of the bone. He hypothesised that the different notches (lines) on the bone were mathematical. According to him, the bone was divided into three columns with mathematical significance. The central column represents a number with its doubles: three and six, four and eight, five and ten, with two numbers (five and seven) which do not fit this pattern. The right column represents four numbers in their relation to ten:
19 = 20-1
19 = 20-1
The left column finally represents the prime numbers between ten and twenty: eleven, thirteen, seventeen, nineteen. Prime numbers are numbers which can only be divided by themselves and one. Moreover, all three columns are multiples of twelve, which implies that the tool helped understand multiplications and divisions.
Alexander Marshack (1918-2004), a Paleolithic archaeologist, analysed the bone by microscope and provided a hypothesis of his own in "The Roots of Civilization" (1972). By plotting the engraved marks of the Ishango bone against a lunar model, he found that the grouped notches resembled close lunar approximations. According to him, the Bone therefore represents evidence of one of man's earliest intellectual activities based on a lunar calendar comprising six months.
The ethnomathematician, Claudia Zaslavsky (1917-2006), developed Marshack’s research further. In “Africa Counts: Number and Pattern in African Culture” (1979), she argues that given the Ishango bone represents a lunar calendar, its creator was most likely a woman keeping track of the lunar phases in relation to the menstrual cycle. Its female creator was therefore most likely an agriculturalist within her community.
Unlike other theories, Dr. Chukwunyere Kamalu provides a hypothesis which makes use of each side and notch of the Ishango bone. He suggests that the bone represents one of the first uses of sieving of the small prime numbers. A sieve for prime numbers is a way of finding all prime numbers until a given number limit. The first sieve for prime numbers is said to be created by Eratosthenes of Cyrene (276-194 BC), the ancient Greek director at the Alexandria library in Ancient Egypt. If Dr. Kamalu’s hypothesis is correct, this means that the Ishango Bone would precede Eratosthenes’ invention by 19,700 years. It would also put into question the Greek origins of mathematics.
While none of these hypotheses are confirmed, the Ishango Bone demonstrates that Central African Palaeolithic humans already demonstrated well-developed mathematics. The Lebombo Bone, which was discovered in modern-day eSwatini in the 1970s and is estimated to date back to 35,000 BC resembles the Ishango Bone and the many calendar sticks used by bushmen in modern-day Namibia. This suggests that the Ishango Bone may be one of the many methods used by the people of Ishango to keep track of data important to their community.
The bone is permanently displayed at l’Institut Royal Belge des Sciences Naturelles in Bruxelles, in Belgium.
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Association pour la Diffusion de l’Information archéologique (ADIA). ‘Have You Heard of Ishango?’ Bruxelles: Royal Belgium Institute of National Sciences (RBINS), n.d. https://www.naturalsciences.be/sites/default/files/Discover%20Ishango.pdf.
Kamalu, Chukwunyere. ‘THE ISHANGO BONE: The World’s First Known Mathematical Sieve and Table of the Small Prime Numbers’. AfricArXiv, 22 February 2021. https://doi.org/10.31730/osf.io/6z2yr. Marshack, Alexander. The Roots of Civilization: The Cognitive Beginnings of Man’s First Art, Symbol and Notation. Moyer Bell, 1991. Zaslavsky, Claudia. Africa Counts: Number and Pattern in African Cultures. Lawrence Hill Books, 1999.
Zaslavsky, Claudia. ‘Women as the First Mathematicians’. International Study Group on Ethnomathematics. ISGEm Newsletter, 1992. https://web.nmsu.edu/~pscott/isgem71.htm.