# The Ishango bone, a clue to archaeo-mathematics in antediluvian Africa

In the 1950s, the Belgian archaeologist Jean de Heinzelin completed a series of excavations near the village of Ishango, in what is now Congo, near the border with Uganda.

He found various tools dating back to the Paleolithic, such as chipped stones, as well as remains of human bones and ancient hearths (charcoal), but the most important object that was recovered was a baboon bone bearing three sets of engravings on three sides. At the top of the bone, just ten centimeters long, there is a quartz crystal set.

When the bone was subjected to carbon 14 testing it was discovered that it was carved 23 millennia before Christ.

Initially, not much value was given to the carvings, and it was thought that they were simple notches to count the number of people belonging to a tribe.

But then, carefully observing the carvings, we came to the conclusion that most likely, the carvings hide a mysterious encrypted code.

In the middle column the carvings, united in small groups are: 3 and 6; 4 and 8; 10; 5 and 5; 7.

In the two lateral columns, however, the groups are made up of 11, 21, 19, 9, and 11, 13, 17, 19 carvings respectively.

The archaeologist Heinzelin thought of a curious arithmetic game: according to him in the first lateral column there were numbers that could be obtained following this scheme: 10+1; 20+1; 20-1; 10-1. In the second column, however, there would be prime numbers from 10 to 20.

In 1972, the American journalist Alexander Marshack put forward the hypothesis that the Ishango bone represents a lunar calendar. This statement, however, is in conflict with the number of carvings. In the two lateral columns the sum of the engravings is equal to 60, while in the center column it is equal to 48 (the month of the lunar calendar is instead made up of just over 29 days).

To try to understand the logic of the ancient Ishango bone carvers we must consider that many African peoples used base 12 to count and not base 10, which is universally used today.

According to this logic, the groups of notches in the center column would be: 3+6=9 (12-3); 4+8=12; 10+5=15 (12+3); 5+7=12. The sums of the side columns (60) and the center column (48) are all multiples of 12.

In my opinion both the base 12 and the base 10 are used in the Ishango bone.

The ancient antediluvian mathematicians of Ishango used the bone as a sort of handbook: in the lateral column the dominant logic is 10 (10+1=11; 20+1=21;20-1=19;10-1=9), while in the central one the dominant logic it is 12 (3+6=9 (12-3); 4+8=12; 10+5=15 (12+3); 5+7=12).

The other column would actually report the prime numbers from 10 to 20.

Some linguistic studies of Nigerian people have proven that base 12 is predominant in the majority of ethnic groups. For example, in Biram culture, Nigeria, 1 is gwuini, 2=ba, 12=kurú, 13=kurú na gw gwuini (12+1), 14=kurú na v ba (14+2), etc.

These linguistic studies and also the discovery, in the mountains of Swaziland, of the so-called Lebombo bone, another artefact dated 33 millennia before Christ, which contains 29 carvings, suggest that the place where the Ishango bone was discovered was a irradiation of culture, not just mathematics and calendars.

For example, at the site of Shankeinab (Sudan), and Nagoda (Egypt), petroglyphs with carvings similar to that of Ishango, on base 12, were found.

Some researchers think that the site of Ishango was the place of origin of the Khoisan languages, which today survive in the Hottentots and Bushmen of Southern Africa. In fact, some internationally renowned scientists such as the Italian Luigi Luca Cavalli Sforza, have identified the Khoisan linguistic strain as one of the oldest in the world.

According to Cavalli Sforza, already 100 millennia ago HomoSapiens spoke the primordial language from which 4 languages initially originated: the language of the Pygmies, the embryo of the Nigerkordofanian languages (of the Bantu peoples), the proto Nilo-Saharan language (of the Nilotic peoples) and precisely the Khoisan, whose ethnic groups were decimated in the following centuries by the Bantu, and whose survivors are precisely Bushmen and Hottentots.

If further excavation work on the Ishango site definitively proved the Khoisan origin of the carved bone, an indication of archaic numerical knowledge on base 12, the influence of the original Khoisan culture on many African peoples would be proven, especially from a mathematical point of view.

YURI LEVERATTO