How Does Africa Count?
By “Awake!” correspondent in Nigeria
A FOREIGNER traveling through the continent of Africa during the eighteenth century was undoubtedly impressed with the seemingly endless variety of peoples and cultures. Communication was accomplished by means of numerous highly developed and complex languages. But even more startling, perhaps, was the fact that the peoples were good mathematicians. Some of their methods of calculating are still being used today.
In the eighteenth century the Hausa city of Katsina in northern Nigeria was a center of learning, where Muhammad ibn Muhammad specialized in numerology. However, for most of the sub-Saharan tribes, counting was and is simply a part of their way of life.
How They Count to Twenty
Consider the Yoruba, Ibo and Efik languages of Nigeria and the Gun language, which is spoken in Dahomey. Each language has its peculiar number system and each system is interesting and practical.
Although in the Yoruba, Gun and Ibo languages the numerals from one to 10 each have individual names, there are many dissimilarities in their counting methods. To a large extent, 20 is the basic unit in both Yoruba and Ibo. On the other hand, 40 is more often used as a base in Gun. In Yoruba and Gun, numerals continue to have individual names up to 15, but then the Yoruba language completes the rest of the teens by subtracting from 20. However, in Gun this is done by adding to 15.
In counting from 11 to 19, the Ibos add their units to 10; but the Efiks have a totally different system, using 5 as their basic unit in counting up to 20. Thus the number 6 in Efik is 5 + 1, 11 is 10 + 1, 16 is 15 + 1, and so on. This means that the numerals one to 5 and 10, 15 and 20 all have individual names. Beyond 20 each system employs seemingly complicated ways of designating the numerals. A look at each language should prove interesting.
Up, Up and Beyond Twenty
As we have already seen, the Yorubas make use of 20 as their basic unit. Thus the numerals 20, 200 and 400 have individual names. Other decimal units (progressing by tens) are established by multiplication of 20 or 200, and subtraction of 10 or 100 as required. Thus 60 is expressed by three 20’s, and 50 is expressed as three 20’s minus 10. Of course, the expressions designating these numerals are contracted into single words in each case. The intermediate numbers between decimal figures are expressed by adding units up to 5 and subtracting units beyond 5. Thus 24 is expressed as 20 + 4, while 28 is expressed as 30 − 2. The number 565 is expressed, (200 × 3) − (20 × 2) + 5.
In contrast to the Yorubas, the Ibos, the Efiks and the tribes that speak Gun do not make use of subtraction in expressing their numerals. The Ibos, employing the basic numerals of 20 and 400, establish their large decimal numerals by multiplication and addition. Thus 50 is expressed as two 20’s plus 10 (20 × 2) + 10, and 300 is expressed as fifteen 20’s (20 × 15).
How would you like trying to express 1,000? It is simple; just say: “nnu-abua na ogu-iri” (two 400’s and ten 20’s). Or 1,000,000 is expressed as: “nnu-nnu-isi na ogu-nnu-ise” (400 × 400 × 6) + (20 × 400 × 5). These expressions are perfectly understood by the Ibo villagers.
The system employed by the Efiks is somewhat different. We have already seen that, below 20, 5 is the basic unit. All the decimal numerals that are multiples of 20, up to 100, have individual names. The intermediate decimal numerals are formed by adding 10 to the lower numeral. Thus 50 is expressed as 40 + 10.
It appears that 100 used to be the highest numeral that had a vernacular name. Figures beyond that were expressed as multiples of 100. Now, however, the word “tosin” is used to express 1,000, apparently a corruption of the word “thousand.” Also, the English word “million” is used.
East African Methods
The Malagasy people of the large island of Madagascar off the east coast of Africa are thought to have migrated from the Malayan Peninsula more than two thousand years ago. Thus their language is of Malayan origin, and their system of counting dates back to centuries before they left Malaya.
In this system all units from one to 10 have individual names. Numerals from 11 to 19 are expressed as 10 plus the appropriate units. The decimal numerals up to 90 are expressed as multiples of 10, such as “telopolo” (30, or three 10’s). The numerals 100 (“zato”), 1,000 (“arivo”), 10,000 (“alina”), 100,000 (“hetsy”) and 1,000,000 (“tapitrisa”) all have specific names. “Tapitrisa” literally means “end of figures.” Other decimal numerals are obtained by multiplication, as in English, such as “telo arivo” (3,000), “telo alina” (30,000, or 3 × 10,000), and “hetsy tapitrisa” (100,000 × 1,000,000).
The Malagasy people express their numerals backward, and compound figures can become veritable jawbreakers. Try pronouncing 1,569,753 in the Malagasy language: “telo amby dimampolo amby fiton-zato sy sivy arivo sy enin-alina sy dimy hetsy sy iray tapitrisa.” Remember that the numerals are expressed backward, so that it literally means: 3 + 50 + 700 + 9,000 + (6 × 10,000) + (5 × 100,000) + 1,000,000.
On the mainland, the majority of languages spoken in East, Central and South Africa belong to a family of languages that has been given the name Bantu. One of these languages, Swahili, which is reputed to be one of the twelve principal languages of the world, has been modified and affected by other languages, such as Arabic. So we find, for example, that 6, 7 and 9 are designated by Arabic words. All the units have individual names, and the numerals above 10 are formed by adding the units to 10. Twenty and all the other decimal numerals up to 100 have their own name, as does 1,000; but multiples of 100 are expressed by multiplication and addition. Thus 999 is expressed as “mia tisa tisini na tisa” (literally, “hundreds nine, ninety and nine”).
The Cinyanja-speaking peoples have specific names for their units from one to 5 and for the decimal numerals 10, 100 and 1,000. The other units from 6 to 9 are expressed as 5 + 1, and so on. The numbers from 11 to 15 are expressed as 10 + 1, and so on, while 16 to 19 are expressed as 10 + 5 + 1, and so on. A system of multiplication and addition is used in establishing the designations for all the large numerals. Thus 30 is expressed as 10 × 3, and 600 as (5 + 1) × 100. So people in Malawi have quite a mouthful in saying, for example, 66: “makumi asanu ndi limodzi mphambu asanu ndi limodzi” (10 × [5 + 1] + [5 + 1]).
It can readily be appreciated why not only many Cinyanja-speaking persons but also those using other vernacular languages in Africa have adopted the European words for numbers in their everyday speech. So in Nigeria one can hear a man speaking fluent Efik but using English words for numbers, whereas in neighboring Dahomey Fon-speaking persons will often use the French words for numbers.
Practical Systems
The different systems of counting of the tribes in the sub-Saharan civilizations have been well suited to their way of life. A further look at the methods employed by the Yorubas of Nigeria will illustrate this.
Over the centuries, their civilization placed emphasis on trading, and their medium of exchange was the cowrie shell. Buying and selling thus involved the counting and exchanging of large quantities of shells. This explains why the establishing of numbers by subtraction is preferred in their system. They counted their “money” by drawing off groups of five shells in order to establish heaps of 20’s and 200’s. Then to arrive at intermediate numbers they would subtract the few extra ones from the overall total. This minimized the motions involved in counting.
Numbers denoting fractions, order and frequency all have their expressions in the sub-Saharan languages. Some tribes make use of suffixes or prefixes in naming such numbers, while others employ complete expressions or phrases in order to express the idea. In the Swahili expression “kasa robo” (1/4), the literal translation is “less a quarter.” One and three quarters (“mbili kasa robo”) is literally “two less a quarter.”
In African cities up-to-date systems of currency have replaced the use of cowries and manillas or metal bracelets, also once used as a medium of exchange. However, the older complex systems are still widely used in the villages, and even those who cannot read or write in any language are able to accomplish impressive feats of mental arithmetic. Yes, Africa does count in a wide variety of ways and with real skill.