The Lebombo Bone: The Oldest Mathematical Artifact in the World

Lebombo bone_2
The Lebombo bone

Have you ever heard of the Lebombo Bone? It is even older than the Ishango bone. It is indeed the oldest known mathematical artifact in the world. Discovered in the 1970s in Border Cave, a rock shelter on the western scarp of the Lebombo Mountains in an area near the border of South Africa and Swaziland (now Eswatini). The bone was found on the Eswatini side, and dates from 35,000 BC. It consists of 29 distinct notches that were deliberately cut into a baboon’s fibula.

The bone is between 44,200 and 43,000 years old, according to 24 radiocarbon datings. This is far older than the Ishango bone with which it is sometimes confused. Other notched bones are 80,000 years old but it is unclear if the notches are merely decorative or if they bear a functional meaning.

According to The Universal Book of Mathematics, the Lebombo bone’s 29 notchesmay have been used as a lunar phase counter, in which case African women may have been the first mathematicians, because keeping track of menstrual cycles requires a lunar calendar.” However, the bone is clearly broken at one end, so the 29 notches may or may not be a minimum number. In the cases of other notched bones since found globally, there has been no consistent notch tally, many being in the 1–10 range. The Lebombo bone resembles a calendar used by the early men of the area, coming from the San clans of Namibia; this way of making tallies is still used by the San people today.

 

Lebombo Ishango bones
Top image: Lebombo bone. Bottom: Ishango bone with prime numbers engraving (J.D. Loreto and D.H. Hurlbert Smithsonian)

According to The Universal Book of Mathematics, the Lebombo bone’s 29 notches “may have been used as a lunar phase counter, in which case African women may have been the first mathematicians, because keeping track of menstrual cycles requires a lunar calendar.” However, the bone is clearly broken at one end, so the 29 notches may or may not be a minimum number. In the cases of other notched bones since found globally, there has been no consistent notch tally, many being in the 1–10 range. This resembles a calendar used by the early men of the area, coming from the San clans of Namibia. These represent the earliest unambiguous evidence for modern human behavior. An article in the Proceedings of the National Academy of Sciences (PNAS) on recent archaeological discoveries, “Early evidence of San material culture represented by organic artifacts from Border Cave, South Africa” , has shown that bone tools were already present 75,000 years ago and were used in San culture.

To anyone who ever doubted it, Africa is indeed the cradle of humanity… and women (if it is indeed a lunar tool) were quite advanced mathematicians 35,000 years ago, using calculators to make lunar calendars!

 

Happy 2015!

Fireworks
Fireworks

Precious readers, may the year 2015 be the year of all great conquests, achievements, success, and greatness. I would like to express my sincere gratitude to all those who visited my blog, and to all future visitors. 2014 was a beautiful year: the number of subscribers on Afrolegends.com has tripled, the number of visitors on the blog has doubled, the article Burkina Faso was cited by TIME Magazine online, while the article La SAPE was cited by The Guardian, and many articles were reblogged on multiple sites. For 2015, I wish you wonders without borders, peace, grace, and love.

Happy 2015 (Illustration by Osee Tueam, for Dr. Y, Afrolegends.com)
Happy 2015 (Illustration by Osee Tueam, for Dr. Y, Afrolegends.com)

Here were the top posts of 2014. Keep trusting, reading, sharing, and liking.

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

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.