Magazine article UNESCO Courier

Words, Gestures and Symbols

Magazine article UNESCO Courier

Words, Gestures and Symbols

Article excerpt

Africa has a rich variety of traditional counting methods

MANY hundreds of well-structured numeration systems were invented in Africa south of the Sahara whose peoples, like those elsewhere in the world, learnt through the ages that it is very difficult to count and calculate if one uses a completely new, different word or symbol for each quantity--that is, for each number. These systems include spoken numeration systems, gesture counting systems, and symbolic systems that use body parts or objects to represent numbers.

The most common way to avoid having to invent completely new words for different numbers has been to compose new number words out of existing ones by using the arithmetical relationships between the numbers concerned. This principle can be seen in many African spoken numeration systems.

In the Makhwa language spoken in northern Mozambique, for example, the words thanu (5) and nloko (10) are dominant in the composition of number words, and constitute the bases of the system of numeration. The expression for 6 is thanu na moza (5 plus 1), and 7 is thanu na pili, (5 plus 2). To express 20, people say miloko mili (tens two or 10 times 2), and 30 is miloko miraru (tens three).

The most common bases in Africa are 10, 5 and 20. Some languages such as Nyungwe, which is spoken in Mozambique, use only base 10. Others like Balante in Guinea-Bissau use 5 and 20. Verbal numeration in the Bete language of Cote d'Ivoire uses three bases: 5, 10 and 20. Fifty-six, for instance, is expressed as golosso-ya-kogbo-gbeplo, that is "20 times two plus 10 (and) 5 (and) 1". The Bambara of Mali and Guinea have a 10-20 system in which the word for 20, mugan, means "one person", while the word for 40, debe, means "mat", referring to a mat on which husband and wife sleep together--and jointly they have 40 digits.

The Bulanda (West Africa) use 6 as a base so that 7 is expressed as 6 + 1, 8 as 6 + 2, and so on. The Adele count koro (6), koroke (6 + 1 = 7), nye (8) and nyeki (8 + 1 = 9). Among the Huku of Uganda the number words for 13, 14, 15 are formed by the addition of 1, 2 or 3 to twelve. Thirteen, for instance, is expressed as bakumba igimo (12 plus 1). The decimal alternatives, 10 + 3, 10 + 4 and 10 + 5, were also known.

One advantage of using a low number such as 5 as the basis of a spoken numeration system is that it may facilitate oral or mental calculation where the answer has not been memorized. For instance, 7 + 8 would be (5 + 2) plus (5 + 3). As 2 + 3 = 5, one finds as answer 5 + 5 + 5, 10 + 5, or 5 multiplied by 3.

* The duplicative principle

A particular case of the use of addition to compose number words is the situation where both numbers are equal or where one of the two is equal to the other plus one. For instance, the Mbai count from 6 to 9 in the following way: mutu muta (3 + 3), sa do muta (4 + 3), soso (4 + 4), and sa dio mi (4 + 5). The Sango of northern Zaire express 7 as na na-thatu (4 + 3), 8 as mnana (4 + 4) and 9 as sano na-na (5 + 4). One possible reason for using the duplicative principle to compose the number words between 6 and 9 is that it may make it easier to do mental arithmetic, in particular duplication operations. For instance, to obtain the double of 7, one has to add, if one has not memorized the answer, 4 + 3 and 4 + 3. As 4 + 3 + 3 = 10, the answer becomes 10 + 4. In sub-Saharan Africa, there is a strong tradition of mental calculation, and oral and mental multiplication often were (and sometimes still are) based on repeated duplication.

In several African languages subtraction, as well as the additive and multiplicative principles, has been used to form number words. In the Yoruba language of Nigeria, for example, 16 is expressed as eerin din logun meaning "four until one arrives at twenty". The Luba-Hemba people of Zaire express seven as habulwa mwanda ("lacking one until eight"), and nine as habulwa likumi ("lacking one until ten"). …

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