Friday, April 18, 2008


Ishango Bone

Math history books do not provide a lot of information about maths from the African continent. Though references have been made to the fact that the study of mathematics had its origins in Ancient Egypt and Babylonia, often people ignore the fact Egyptian mathematics is in essence a part of the African continent history.

In 1960, Professor Jean de Heinzelina Belgian geologist discovered a small animal bone in Ishango, a small African fishing village on the border of Zaire and Uganda. The small bone was inscribed with marking that is thought by some to represent numbers. It was originally thought to be between 6,000 and 9,000 years old. However, it was recently re-dated and found to be around 25,000 years old. At first glance the Ishango bone is said to resemble a simple writing tool. It is 10 cm long, and at one end is embedded with a piece of quartz thought to be for engraving and tattooing.

Though the engravings on the bone resemble tally marks, various details have led some researchers to suggest that the Ishango Bone is some kind of a mathematical table.

"For example, along one edge the number of notches in each group is a prime number (prime numbers are divisible only by themselves and one; e.g., 1, 3, 5, 7, 11, 13, 19, etc.) Coincidence? Perhaps. But then, there are three separate rows of notches, and the total number of notches in each row is a multiple of twelve. Another coincidence? Maybe. But along one row, the notches in adjacent groups appear to be related by a factor of two: 3 notches in one group and 6 in the next, then 4 followed by 8, then 10 and 5. A crude multiplication table? Or another coincidence?"


"Most histories of mathematics devote only a few pages to Ancient Egypt and to northern Africa during the 'Middle Ages´. Generally they ignore the history of mathematics in Africa south of the Sahara and give the impression that this history either did not exist or, at least, is not knowable, traceable, or, stronger still, that there was no mathematics at all south of the Sahara. In history, to Europeans, even the 'Africanity' of Egyptian mathematics is often denied or suffers eurocentric views of conceptions of both 'history' and of 'mathematics' form the basis of such views."

Prime numbers or menstrual calendar?

Claims that the Ishango Bone is the oldest table of prime numbers have been challenged by several critics. Further microscopic examination by various researchers allude to the fact that the markings engraved on the bone represented a six-month lunar calendar. Which raises then the question who but a woman keeping track of her cycles would need a lunar calendar?

Other critics are of the view that the mathematical claims for the Ishango bone are exaggerated.
"They suggest that, as there are only 4 numbers on the left hand column of the bone, it may be just a simple coincidence that all of these are prime numbers. The most compelling aspect of their argument is the fact that there is no evidence of the knowledge of prime numbers before the Classical Greek period, at least 10,000 years later.
" Source: Simonsingh

Ishango Bone now lies in the Royal Institute for Natural Sciences of Belgium in Brussels, and can only be seen on special requests.



William Tennis said...

The Ishango Bone is similar to other bones with engraved converging lines like the Bones of Bilzingsleben of 23.5 degrees mimiking the arc made by the Sun in its oscillation from solstice to solstice. Contact me for a full description of a Solstice Calendar and how to identify one

william Tennis said...

The angle the Sun makes from solstice to solstice is 47 degrees.

Term Papers said...

Such a nice post, it is really interesting..