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.

“Our Deepest Fear” by Marianne Williamson

I really liked this poem “Our Deepest Fear” which was read by Nelson Mandela during his presidential inauguration speech in 1994.  I also particularly liked the rendition by this year’s South Africa’s Got Talent Botlahle, an 11 year old South African girl, who is a great poet.  Enjoy the poem itself, and Botlahle’s rendition.

Our deepest fear is not that we are inadequate.
Our deepest fear is that we are powerful beyond measure.
It is our light, not our darkness that most frightens us.
We ask ourselves, Who am I to be brilliant, gorgeous, talented, fabulous?
Actually, who are you not to be?
You are a Child of God.
Your playing small does not serve the world.
There is nothing enlightened about shrinking so that other people won’t feel insecure around you.
We are all meant to shine, as children do.
We were born to make manifest the glory of God that is within us.
It is not just in some of us; it is in everyone.
And as we let our own light shine, we unconsciously give other people permission to do the same.
As we are liberated from our own fear, our presence automatically liberates others.

Marianne Williamson – A return to love

Kente Cloth: An Ashanti Tradition dating Centuries back

Kente scarf
Kente scarf

Have you ever seen those beautiful bright multicolored scarves worn on graduation day by thousands of African Americans and African students across the United States?  Those scarves are usually hand-woven, bright, and multicolored, worn to represent the membership to a Black sorority, fraternity, or to just an African student organization at the different colleges and universities.

Well, those scarves are made from a material commonly known as Kente cloth, which originates from the Ashanti people of Ghana and Cote d’Ivoire.  The Ashanti people used to (and still do) hand weave these bright multicolored clothes for their kings and noblemen.  The tradition of kente cloth is said to have been developed in the 17th century, and stems from ancient Akan weaving techniques dating as far back as the 11th century AD (this is one of Africa’s textile tradition).  Kente cloth is known as nwentoma (meaning woven cloth) in Akan language, and is a type of silk, cotton, or rayon fabric made of interwoven cloth strips which is native to the Akan/Ashanti ethnic group of Southern Ghana (and also Cote d’Ivoire).  It is woven on a wooden loom, which produces a band about 10 cm wide; several bands will then be sewn together to make a larger cloth.  The elaborate patterns arise from the mixture of different weaving techniques applied to the same band of cloth.  The quality of the fabric, and weaving indicates the rank of the person, the best being reserved for the kings.  It is worn by men as a toga, and by women as upper and lower wrappers.  The art of weaving kente is passed down only to males, from generation to generation.  The main center of weaving kente is around the Kumasi region of Ghana.

Kente cloth
Kente cloth

An Ashanti legend has it that two friends who had gone hunting in the forest came across a giant spider (the famous Ananzé) who was weaving her web.  They were so amazed that they stayed welded in place for two days, contemplating the spider at work.  When they returned from hunting, they imitated the animal and wove a cloth out of raffia.  This is how was born the first kente which was offered to the king.  The Asantehene (king) was so amazed by the beauty of the present, that he elevated the weavers to the rank of royalty, and they became the king’s exclusive tailors.  The clothes woven for the king were each unique, and whoever tried to reproduce them was severely punished.

Kente is an Akan royal and sacred cloth worn only in times of extreme importance and is the cloth of kings and nobility, before finding its way into bags, and scarves sold around the globe nowadays.  In Akan culture, the different colors and intricate patterns used in the weaving do have traditional meanings.

White: is the color of purity, innocence, spirituality, and peace (mental, collective, and interior).  Very small amount are found on the kente (sometimes just the threads are white).  White has a divine and sacred character;

 Paramount chief Nana Akyanfuo Akowuah Dateh II in Kumase,Ghana (Photograph by Eliot Elisofon,1970, National Museum of African Art).
Paramount chief Nana Akyanfuo Akowuah Dateh II in
Kumase, Ghana (Photograph by Eliot Elisofon,1970,
National Museum of African Art).

Yellow: is the color of gold, and symbolizes preciousness, royalty, wealth (financial, spiritual, intellectual, etc), and fertility.  It is associated with the earth’s generosity.  This color is strongly represented in the kente, because the king, who wears it during public gatherings, embodies all these virtues: gold, royalty, wealth, high status, glory, spiritual purity.  Yellow, just like the sun’s rays, also reminds of divine goodness.

Black: is the color of bereavement, and darkness, but also of mystery and secrecy.  It is mostly used in initiation and purification ceremonies.  It is an ambivalent color representing both obscurantism, and spiritual elevation; it is thus both feared and revered.  Its discrete presence in kente reminds that noblemen are first and foremost the guardians of the throne.  Black also represents maturation and intensified spiritual energy;

Blue: reminds of the big spaces: the sea and the sky.  It symbolizes elevation, communion, humility, patience, and wisdom.  The king and noblemen have perfect control over their environment.  Blue is the color of peace, harmony, and loveIt is sometimes associated with yellow or white, or red, to represent wealth and power which are founded on spirituality, and which bring tranquility, and balance, and constitutes a strong guarantee of stability for all powers;

Green: is the symbol of life, growth and harmony.  Green reminds of the forest, the trees, birth, and youth.  It is also linked to vegetation, planting, harvesting, growth, and spiritual renewalJoined with blue and yellow on a kente, it completes the meaning of the clothing which expresses wealth and nobility founded on humility, humanism, and balance.

Other less common colors are:

A Kente cloth was offered to Michael Jackson during his enthronement as prince of Krindjabo (Côte d’Ivoire).
A Kente cloth was offered to Michael Jackson during his enthronement as prince of Krindjabo (Côte d’Ivoire).

Grey: healing and cleansing rituals, and is associated with ashes;

Brown: is the color of mother earth, and is associated with healing;

Pink: mostly worn by women, is associated with the female essence of life: sweetness, tenderness, calmness, pleasantness;

Purple: is associated with feminine aspects of life, and is mostly worn by women;

Red: political and spiritual moods, bloodshed, sacrificial rites, and death;

Silver: serenity, purity, joy, and is associated with the moon;

Continue reading “Kente Cloth: An Ashanti Tradition dating Centuries back”

Freedom at last? 12 high political figures freed in Côte d’Ivoire

Affi N'Guessan (Source: Le Nouveau Courrier)
Affi N’Guessan (Source: Le Nouveau Courrier)

Freedom at last for 12 high political figures in Côte d’Ivoire.  These were members of the FPI, Laurent Gbagbo‘s who had been detained without any hearing for the past 2 years.  This is a sign that truth and justice always wins.  I have translated here a speech by Pascal Affi N’Guessan, one of the detainees and once prime minister of Côte d’Ivoire.  This was published on the website of Le Nouveau Courrier. For the audio and integral text, go to Le Nouveau Courrier. Thank goodness for this… and let us keep fighting for freedom and true democracy (not the one manufactured by the IMF, in Europe or the US, but what will work for us).


Président Laurent GBAGBO
Président Laurent GBAGBO

I would like to, before giving any speech, first greet you and thank you wholeheartedly.  If we can stand here today in front of you, don’t be fooled. There are no three explanations. There are no two explanations. There is only one explanation. It’s your engagement, it is your determination, your strength, it is your rejection of an unfair situation that was made in Côte d’Ivoire which explains why we can stand before you today. This explains why yesterday other comrades were released. This explains why yesterday Bê Diabaté and other comrades […] have been released. And it is this mobilization which will explain tomorrow’s  normalization in Côte d’Ivoire, the release of all our comrades who are still detained, the return from exile of all our comrades who were forced to flee their own country, and the return to us of President Laurent Gbagbo.

… The original project [Ouattara regime] is not to let the FPI exists as a political party. The ambition nurtured by those who came to power under the conditions that we know is not to reinstate democracy. It is not to let a party as powerful as the Ivorian Popular Front party exist. (…)

Cote d'Ivoire
Cote d’Ivoire

Dear Comrades, you defeated the odds. You have proven that the Ivorian Popular Front (FPI) was intractable. You have proven that the Ivorian Popular Front was a spirit. You have proven that the people of Côte d’Ivoire did not want to backtrack. And its course is determined to be democracy, to be progress, to be freedom. And it is because our opponents have realized this fact, because we have imposed this reality, that we stand here today in front of you.

Today is a day of rejoicing. A day to celebrate this milestone in our struggle. That is why it may be too risky to go further. But know that we do not have three programs, we do not have two programs, we have one program. And this program is the program of the people of Côte d’Ivoire. And this program are the aspirations of the people of Côte d’Ivoire. And this program is to resolve all the problems that prevent this country from becoming a modern and prosperous country. This is our program!

We’re here to straighten out. As the old of Ménékré says it, “twisted politics”, we are here to rectify. Continue reading “Freedom at last? 12 high political figures freed in Côte d’Ivoire”

Why the name: Lusaka?

Map of Zambia
Map of Zambia

Today, I will be talking about Lusaka, the capital of Zambia and its largest city.  The actual location of the city of Lusaka corresponds to that of a village which was named after its chief Lusaaka, and which was located at Manda Hill, near the current site of the Zambian National Assembly building.  In the Nyanja language, Manda means graveyard.

Zambian flag
Zambian flag

The area was expanded by British settlers in 1905 with the building a the railway. Due to its central location and its position on the railway at the crossroads between the Great North Road and Great East Road, Lusaka is chosen to replace Livingstone as the capital of the British colony of Northern Rhodesia (Southern Rhodesia being today’s Zimbabwe) in 1935.  With the fusion of the Northern Rhodesia (Zambia) with Southern Rhodesia (Zimbabwe) and Nyasaland (Malawi) in 1953, Lusaka became the center of independentist movements amongst the educated elite, which eventually led to the creation of the Republic of Zambia.  In 1964, Lusaka became the capital of the newly independent country Zambia, with the country’s first president being Kenneth Kaunda.

Lusaka is not only the capital of the country, but also the capital of the province of Lusaka, which is the smallest and the second most populated of the nine provinces of Zambia.


Today, Lusaka is one of the fastest-developing cities in Southern Africa.  It is the centre of both commerce and government in Zambia and connects to the country’s four main highways heading north, south, east and west, including the famous Cairo Road which is a section of the Great North Road and was so named because it is a link in Cecil Rhodes‘ then dream of a Cape to Cairo Road through British colonies in Africa.  The city is also located at an altitude of 1300 m above sea level.  English is the official language of the city, but Nyanja, and Bemba are commonly used as well.

In recent years, Lusaka has become a popular urban settlement for Zambians and tourists alike.  Check out the map of city of Lusaka, or the newspaper Lusaka Times to get more news about this great city whose name hails from that of a local king.  Enjoy the video below about the city of Lusaka.

When Lion could Fly


LION, it is said, used once to fly, and at that time nothing could live before him.  As he was unwilling that the bones of what he caught should be broken into pieces, he made a pair of White Crows watch the bones, leaving them behind at the kraal whilst he went a-hunting.

But one day Great Frog came there, broke the bones in pieces, and said, “Why can men and animals live no longer?”  And he added these words, “When he comes, tell him that I live at yonder pool; if he wishes to see me, he must come there.”

Lion, lying in wait (for game), wanted to fly up, but found he could not fly.  Then he got angry, thinking that at the kraal something was wrong, and returned home.  When he arrived, he asked, “What have you done that I cannot fly?”  Then they answered and said, “Someone came here, broke the bones into pieces, and said, ‘If he want me, he may look for me at yonder pool!”‘  Lion went, and arrived while Frog was sitting at the water’s edge, and he tried to creep stealthily upon him. When he was about to get hold of him, Frog said, “Ho!” and, diving, went to the other side of the pool, and sat there. Lion pursued him; but as he could not catch him he returned home.

From that day, it is said, Lion walked on his feet, and also began to creep upon (big game); and the White Crows became entirely dumb since the day that they said, “Nothing can be said of that matter.”

South African Folk Tales, by James A. Honey, 1910, Baker & Taylor Company.