Ishango Bone

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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.

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Location

Jean de Heinzelin tumbled upon the Ishango Bone  in 1956 on the banks of Lake Rutanzige (located on the border between present-day Uganda and the Democratic Republic of Congo). This area, also referred to as 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.

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Characteristics

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.

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Functions 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:

• 11=10+1
• 21= 20+1
• 19 = 20-1
• 19 = 20-1
• 9 =10-1

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

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.

Claudia Zaslavsky

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.

Chukwunyere Kamalu

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 Libyan 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.

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Legacy

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 present-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.