The numbers in the Kiswahili language form a decimal (base 10) number system. That is, all of the numbers are formed from the base of 10 numbers:
- moja ~ 1
- mbili ~ 2
- tatu ~ 3
- nne ~ 4
- tano ~ 5
- sita ~ 6
- saba ~ 7
- nane ~ 8
- tisa ~ 9
- kumi ~ 10
If we want to say eleven in Kiswahili we’d say kumi na moja which is literally 10 + 1. Twelve becomes kumi na mbili (10 + 2), and thirteen is kumi na tatu (10 + 3). Sixty is sitini (6 x 10) and seventy is sabini (7 x 10). The pattern is only broken where we find Arabic influence enter into the language.
The number system that the English-speaking world uses is also a decimal (base 10) number system. But not all number systems in the world are base 10. The Yasayama of the DRC have a base 5 number system. Their number system is based on the numbers:
- omoko ~ 1
- bafe ~ 2
- basasu ~ 3
- bane ~ 4
- lioke ~ 5
So in the Yasayama language, the word for six is lioke lomoko (5 + 1), the word for seven is lioke lafe (5 + 2), the word for eight is lioke lasasu (5 + 3), and so on.
The Yorùbá of Nigeria and Benin have a vegesimal (base 20) number system. The Khoisan of southern Africa have a binary (base 2) number system. In fact, on the continent of Africa, base 5, base 10, base 20, and base 2 are the most common number systems. But why are these number systems so common?
The base 5 and base 10 number systems likely evolved from our anatomy. Humans have 10 fingers – five on each hand – and thus base 5 and base 10. If we include our total number of fingers and toes then base 20 also makes sense. But what about base 2? Why was this a common number system in antiquity?
The 20,000 year old Ishango Bone – one of the world’s oldest mathematical artifacts – has been found to contain markings indicating an early binary number system. The classical mathematics of Nile Valley civilizations would later build upon this binary foundation. If other number systems that developed in Africa were related to our human anatomy, then could this also be true for the binary number system? The answer is a resounding ndio!
The binary number system is a system of doubling. It is the ones and zeroes of binary code that underlies modern computing. Think of the place values of our decimal number system: the one’s place, the ten’s place, the hundred’s place, thousands, ten-thousands, and so on. Where do these numbers come from?
1, 10, 100, 1000, 10000… are all powers of 10. That is:
100 = 1 (one’s place), 101 = 10 (ten’s place), 102 = 100 (hundred’s place), 103 = 1,000, 104 = 10,000
The 10 is the base of this number system. The binary system works the same way, except that the base is 2. So what are the place values in the binary number system?
- 20 = 1
- 21 = 2
- 22 = 4
- 23 = 8
- 24 = 16
- 25 = 32
These are all powers of 2! Therefore the “place values” of the binary number system are the one’s place, the two’s place, the four’s place, the eight’s place, and so on. We see that the place values are doubling: 1, 2, 4, 8, 16, 32, 64… A binary number system simply means doubling.
With that, can you guess what human biological function this relates to? Humans “double” by giving birth! The binary number system was born from the simple observation of our family ancestor tree.
There is 1 of us. Each of us has 2 parents, 4 grandparents, 8 great-grandparents, 16 great-great grandparents, 32, 64, 128, 256…We are all binary representatives of our family ancestor tree. The sequence 1, 2, 4, 8, 16… is known in mathematics as a geometric sequence with a common ratio of r = 2. This means that for each progressive generation we have twice the ancestors as the previous generation. How would you calculate the number of ancestors that you had in the generation 25 generations before the present? In Black Radical Algebra II we learn how to answer this question by finding the nth term of a geometric sequence using exponential equations.
In African philosophical understanding, numbers are understood to be symbolic and metaphorical.
Thus number is essential in the realization of the universe. Everything in the universe is assigned a number (or number of signs). In this way Amma used the principle of number to organize the creation. Indeed, the Dogon believe that the po will contain the entire universe conceived in Amma’s thought through the concept of number.
~Dr. Chukwunyere Kamalu, Word at Face Value
One number that is important in African cosmology is the number four, or as we call it, the fantastic 4. On the most basic level, the number four represents the the four elements (earth, wind, fire, water) and the four cardinal directions (north, south, east, west).
The fantastic 4 also relates to many traditional accounts of creation that we hear across the Continent that all seem to be attempting to tell some version of the same story… That is, in many traditional creation stories the original ancestors of human beings are described as beginning from four (or sometimes four pairs) of male/female twins.
We also see the fantastic 4 represented as four quadrants in the symbology of the ancient African world.
The fantastic 4 can be observed in traditional divination systems. Mẹ́rìndínlógún (literally “sixteen”) cowrie shell divination – used by Olórìṣà in the Yorùbá traditional religion – uses 16 cowrie shells: 16 = 42. Diviners of Ifá in the Yorùbá traditional religion use the ọ̀pẹ̀lẹ̀ divining chain or the ikin Ifá (sacred Ifá palm nuts) and the ọpọ́n Ifá (divining tray) to mark out one of 256 possible Odù Ifá signs. Each sign contains a number of verses and collectively they represent the ẹsẹ Ifá corpus – a collection of oral narratives that represent all possible scenarios and possibilities of human existence and interaction as well as the prescription to overcome any of life’s challenges. There are 256 odù signs: 256 = 44.
The Dogon of Mali have an alphabet and a divination system that is comprised of 266 signs. From Dr. Kamalu’s quote above, we know that in Dogon cosmology, Amma (the supreme being) organized the universe according to the concept of number. That is, Amma assigned everything in the universe one or more of the 266 signs mentioned earlier. For example, in Dogon cosmology the male number is 3 and the female number is 4. Together, their sum (7) represents life. The number 7 tends to hold special significance in traditional African religions.
The 266 signs that comprise the universe in Dogon cosmology are non-coincidentally similar to the 266 days between the conception and birth of a newborn child. Beyond that, the 266 signs of the Dogon actually break down further. There are two guide signs and eight master signs which serve as the keys to understanding the other 256 signs. Therefore it is: 2 + 8 + 256 = 266. This is not dissimilar to the 16 principle ojú odù of the Ifá (Yorùbá) system which are paired together to give birth to all of the 256 odù Ifá signs (256 = 162).
The Bamana of Mali use a system of divination that is also similar to the Ifá system. Bamana specialists perform their divination in the sand in a process known as cenda. The process of cenda divination begins with the specialist drawing four dashed lines horizontally in the sand.
The dashes are then paired together. If a row has an odd number of dashes then the result of that row is a single vertical mark. If the row has an even number of dashes then the result is a double vertical mark.
This is repeated four times in a recursive process that results in a total of 16 symbols (16 = 42) by the end. The 15th symbol is known as “this world” and the 16th symbol “the next world.” From there, the specialist dictates a narrative (reminiscent of the ẹsẹ Ifá oral narratives) from the symbols that addresses the original reason for the divination.
This is Afrikan math.