Monday, September 3, 2018

Lebomba & Ishango Bones: Mathematics in Ancient Africa

The continent that birthed mankind, Africa, has so many vast told, untold and under-told stories. For example, we are well versed about the Nile Valley civilizations including Kush, Nubia and Kemet (ancient Egypt).

The impressive edifices such as the pyramids, Sphinx, temples, monuments bear witness to the greatness and accomplishments of the people -- and not to mentioned the incredible scholarship on religion, science, medicine, cosmology, mathematics and philosophy that are still being deciphered.

Second, the ancient West African empires of Ghana, Mali and Songhai are well documented. Arguably, the most famous and wealthiest emperor is Mansa Mush from Mali. Musa is best known for his epic 1324-1325 pilgrimage to Mecca.

It is said that Mansa Musa was extremely rich and that he brought as many as 60,000 people along with him on his pilgrimage. He also brought camels loaded with gold. Mansa Musa must have made quite the impression during his trip with his large entourage and massive display of wealth. During his travels, Mansa Musa gave away and spent a significant amount of gold, but he also brought back a lot of new ideas to Mali. This included a number of scholars such as architects, poets, and teachers who helped to improve his empire. 


Oldest Mathematical Instruments

However, by way of archaeological and anthropological discoveries, we continue to learn how far back and deep into sub-sahara Africa the genesis of advanced human civilization dates. Incredible as it seems, thousands and thousands of years before Nile Valley civilizations there were the Lebomba Bone and Ishango Bone.

Lebomba Bone:


The Lebombo bone is one of the oldest mathematical artifacts known, a small piece of the fibula of a baboon, found near Border Cave in the Lebombo Mountains between South Africa and Swaziland. Discovered in the 1970s during excavations of Border Cave and dated about 35,000 B.C., the Lebombo bone is marked with 29 clearly defined notches. This suggests it may have been used as a lunar phase counter, in which case African women may have been the first mathematicians since keeping track of menstrual cycles requires a lunar calendar. Certainly, the Lebombo bone resembles calendar sticks still used by Bushmen in Namibia. source

Ishango Bone





The Ishango bone is a bone tool handle discovered around 1960 in the African area of Ishango, near Lake Edward. It has been dated to about 9,000 BC and was at first thought to have been a tally stick.

At one end of the bone is a piece of quartz for writing, and the bone has a series of notches carved in groups on three rows running the length of the bone. The markings on two of these rows each add to 60. The first row is consistent with a number system based on 10, since the notches are grouped as 20 + 1, 20 - 1, 10 + 1, and 10 - 1, while the second row contains the prime numbers between 10 and 20! A third seems to show a method for multiplying by 2 that was used in later times by the Egyptians. Additional markings suggest that the bone was also used a lunar phase counter.

The Ishango bone is kept at the Royal Institute for Natural Sciences of Belgium in Brussels. source


  


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