Posted by: Dr. Y. | August 29, 2013

The Ishango Bone: Craddle of Ancient Mathematics

Ishango Bones

Ishango Bones

Today, I would like to talk about the Ishango bone, or rather the first evidence of a calculator in the world.  Named after the place where it was found in the Democratic Republic of Congo (DRC), the Ishango bone is what is called a bone tool or the craddle of mathematics.  Dating as far back as 22000 years ago, in the Upper Paleolitic era, the Ishango bone is a dark brown bone which happens to be the fibula of a baboon, with a sharp piece of quartz affixed to one end for engraving It is the oldest attestation of the practice of arithmetic in human history. 

The Belgian geologist Jean de Heinzelin de Braucourt uncovered the bone buried in layers of volcanic ashes on the shores of Lake Edward in the Ishango region in DRC, near the border with Uganda.  The Ishango bones are actually two (2) bones of baboon, 10 to 14 cm long, with several incisions on each faces.  The smallest of the two bones was the first to be exposed at the Royal Belgian Institute of Natural Sciences in Brussels; it carries several incisions organized in groups of three columns.

The location of Ishango

The location of Ishango

The left column can be divided in 4 groups, with each group possessing 19, 17, 13, and 11 notches.  The sum of these being 60.  Those are the 4 successive prime numbers between 10 and 20.  This constitutes a quad of prime numbers.

The central column is divided in groups of 8.  By an approximate count, one can find (in the parenthesis, is the maximum number): 7 (8), 5 (7), 5 (9), 10, 8 (14), 4 (6), 6, 3.  The minimal sum is 48, while the maximal sum is 63.

The right column is divided into 4 groups, where each group has 9, 19, 21, and 11 notches.  The sum of these 4 numbers is 60.

The second bone has not been well-studied.  However, we know that it is composed of 6 groups of 20, 6, 18, 6, 20, and 8 notches.

The Ishango bones with their notches and the numbers

The Ishango bones with their notches and the numbers

The first bone has been subject to a lot of interpretation.  At first, it was thought to be just a tally stick with a series of tally marks, but scientists have demonstrated that the groupings of notches on the bone are indicative of a mathematical understanding which goes beyond simple counting.  In fact, many believe that the notches follow a mathematical succession. The notches have been interpreted as a prehistoric calculator, or a lunar calendar, or a prehistoric barcode.

Jean de Heinzellin was the first to consider the bone as a vestige of interest in the history of mathematics.  For instance, he noted that the numbers in the left column were compatible with a numeration system based on 10, since he saw that: 21 = 20 + 1, 19 = 20 – 1, 11 = 10 +1, and 9 = 10 -1.  These numbers are also prime numbers between 10 and 20: 11, 13, 17, 19.

The Ishango bones

The Ishango bones with the notches

Some other scientists such as the Belgian physical engineer proposed that the bones were probably a slide rule. While Alexander Marshack has indicated that the bones could refer to the oldest lunar calendar on earthClaudia Zaslavsky thinks that the author of the Ishango bone must have been a woman following the lunar phases to calculate her menstrual cycle.  However, the second bone completely rules out the lunar calendar theory, and favors more the numeration system.

All said, it is amazing to realize that there were mathematicians 20,000 years ago on the African continent.  It is so great to realize that my ancestors, on the shores of Lake Edouard, were actually brilliant scientists playing with prime numbers.  Whether it was a woman calculating her menstrual cycle, or some brilliant tribe astronomer, it feels so good to know that the paleo-mathematicians of Ishango already knew prime numbers.  They were a great civilization long before the pharaohs of Egypt. Thus, in reality, the Ishango bone is the oldest table of prime numbers in the world. To read more, check out Mathematicians of the African Diaspora,, the Prime Glossary, and Wolfram Mathworld.


Responses

  1. […] >via: https://afrolegends.com/2013/08/29/the-ishango-bone-craddle-of-mathematics/ […]

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  2. Brilliant. Having been trained in both Prehistory and Anthropology, the analysis of this find scotches two widely held misapprehensions in one grand sweep: that Paleolithic man’s intellect can be equated with the simplicity of his toolkit, and that African cultures are in some way inferior. Let’s hear a big cheer for the ingenuity of humankind that evolved in, and dispersed from the Great Rift – because that means all of us.

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  3. […] https://afrolegends.com/2013/08/29/the-ishango-bone-craddle-of-mathematics/ […]

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  4. […] bones were being used for counting the menstural cycle. However in the website that I was using (https://afrolegends.com/2013/08/29/the-ishango-bone-craddle-of-mathematics/ ) there were a part saying: ‘’Claudia Zaslavsky thinks that the author of the Ishango bone must […]

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  5. […] 1. Samori Toure: African leader and Resistant to French Imperialism 2. ‘Love Poem for My Country’ by Sandile Dikeni 3. ‘My Name’ by Magoleng wa Selepe 4. ‘Femme Noire/Black Woman’ by Leopold Sedar Senghor 5. The Ishango Bone: Craddle of Ancient Mathematics […]

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  6. Actually, very few mathematicians looked at it, and the fact that they do not agree should make us suspicious. Olivier Keller has written an article which should temper the enthousiasm:
    https://www.bibnum.education.fr/sites/default/files/ishango-analysis.pdf
    The big problem here is : “what you desire to see, you will see”. You desire to see higher mathematics? Then your mind will make you see it, even if it is not there.

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  7. […] https://afrolegends.com/2013/08/29/the-ishango-bone-craddle-of-mathematics/ […]

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  8. […] I do not believe that the online aspect of record keeping is a bad thing, it is probably our biggest asset with record keeping in our current era. Technology may change drastically over time, but the the only thing that has fundamentally changed about the internet has been the speed, use and apparatus on which to access it. Additionally, whenever researchers have come across some kind of medium that has information, if they want it badly enough, they are usually able to figure it out (like the Ishanago Bone https://afrolegends.com/2013/08/29/the-ishango-bone-craddle-of-mathematics/) […]

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    • Thanks for reblogging this article.

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  9. Nice way to explain everyone one that what are ISHANGO BONES
    Good work!!

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  10. wow

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  11. Although I think that this is a outstanding find, the people of Ancient Kemet stated that they come from this area of Africa.

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  12. […] Los Huesos de Ishago (que son dos), de aproximadamente 22,000 años, fueron encontrados en la República Democrática del Congo, un enorme país en África Central, por cierto no muy democrático. Los Huesos de Ishago van más allá de simples marcas y se consideran la primera calculadora de la historia. Estos dos huesos parecen seguir una sucesión matemática, hacen referencia a números primos, y su uso específico es un misterio, algunos dicen que siguen un ciclo menstrual asociado a la luna y otros que es un sistema numérico–astronómico completo (más información aquí). […]

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    • Gracias por reblogging.

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      • So blacks possessed mathematics twenty thousand years ago, while at that time whites in Europe and the uk were crawling on their hands and knees eating their own excrement! The evil tragedy is, when whites eventually came in to contact with mathematics they would come to use it to count African slaves as they were boarded on to ships bound for America and Europe. its a fucking disgrace.

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      • Exactly Steve.

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  13. Good job, just stop of the iceberg for any further information, feel free to contact us about any question of your own choice.

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