The Ishango bone: a prehistoric lunar calendar? A note of caution
The Ishango bone, found in 1950 in the Congo: its notches, the prime numbers, Marshack's lunar hypothesis, the Lebombo bone and the limits of interpretation.
Among the prehistoric objects most often cited in histories of mathematics is a small dark bone, about ten centimetres long, with a fragment of quartz set into one end. This is the Ishango bone, found in 1950 by the Belgian geologist Jean de Heinzelin de Braucourt on the shores of Lake Edward, in what was then the Belgian Congo and is now the Democratic Republic of the Congo. Its notches have fuelled fascinating hypotheses, including that of a lunar calendar.
The object and its notches
The bone, mostly thought to be a baboon fibula, bears three columns of grouped notches. In one column the groups count 11, 13, 17 and 19 notches, the prime numbers between 10 and 20; in another 11, 21, 19 and 9; in the third 3, 6, 4, 8, 10, 5, 5 and 7. The first two columns total 60 notches each, the third 48. The object is now kept in Brussels, at the Royal Belgian Institute of Natural Sciences.
Its dating has long been debated. Early estimates placed the site around the ninth millennium BC, but later studies of the archaeological layers have proposed an age of about twenty thousand years. This figure, too, should be taken as indicative, because it depends on correlating the bone with the dated levels of the site, not on a measurement made on the bone itself.
The interpretations
De Heinzelin, in a popular article of 1962, suggested that the notches revealed a knowledge of prime numbers and of a system based on ten. In the 1970s the American researcher Alexander Marshack, examining the bone under the microscope, proposed instead an astronomical reading: the notches would record the phases of the Moon over about six months. His hypothesis was part of a wider research programme on the notations of the Upper Palaeolithic.
Others have seen in the bone a simple tool with incisions that improve its grip, a generic counting object or a support for calculation games. Bolder readings have also been proposed, such as a calendar linked to the menstrual cycle, but these rest on no independent evidence and remain in the realm of conjecture.
Why caution is needed
The main problem is that a single object, without written context, can support many interpretations. Series of numbers lend themselves to the discovery of regularities: with a little ingenuity one can recognise primes, doublings or lunar cycles in almost any sequence of notches. Without other similar finds from the same culture, and without a way of verifying the intention of whoever carved them, no reading can be called proven.
The same applies to the Lebombo bone, found in a cave in the Lebombo Mountains, on the border between South Africa and Eswatini, with twenty-nine notches and an estimated age of more than forty thousand years. The number twenty-nine recalls the length of the lunar month, and for this reason the bone is often presented as a calendar; but it is broken, and we do not know how many notches it originally had.
The Ishango bone nonetheless remains an extraordinary find. It shows that, thousands of years ago, someone was carving organised and repeated marks on an object meant to be kept. Whether they were counting days, moons, prey or something else, those notches bear witness to a mind capable of abstraction and record-keeping. The lunar hypothesis is legitimate and suggestive, provided it is presented for what it is: a hypothesis.