Africa Counts

Number and Pattern in African Culture

By Claudia Zaslavsky

Chicago Review Press Incorporated

Copyright © 1973 Claudia Zaslavsky
All rights reserved.
ISBN: 978-1-55652-350-2

Contents

FOREWORD TO THE 1999 EDITION,
FOREWORD TO THE 1973 EDITION,
PREFACE TO THE 1973 EDITION,
SECTION 1 THE BACKGROUND,
1 African Mathematics?,
2 Historical Background,
SECTION 2 NUMBERS — WORDS, GESTURES, SIGNIFICANCE,
3 Construction of Numeration Systems,
4 How Africans Count,
5 Taboos and Mysticism,
SECTION 3 NUMBERS IN DAILY LIFE,
6 The African Concept of Time,
7 Numbers and Money,
8 Those Familiar Weights and Measures!,
9 Record-Keeping: Sticks and Strings,
SECTION 4 MATHEMATICAL RECREATIONS,
10 Games to Grow On,
11 The Game Played by Kings and Cowherds — and Presidents, Too!,
12 Magic Squares,
SECTION 5 PATTERN AND SHAPE,
13 Geometric Form in Architecture,
14 Part I: Geometric Form and Pattern in Art,
15 Part II: Geometric Symmetries in African Art, By D. W. Crowe, with Original Drawings,
SECTION 6 REGIONAL STUDY: SOUTHWEST NIGERIA,
15 History of the Yoruba States and Benin,
16 Systems of Numeration,
17 Significant Numbers,
18 Time-Reckoning,
19 Markets and Currency,
SECTION 7 REGIONAL STUDY: EAST AFRICA,
20 History of East Africa,
21 Spoken and Gesture Counting,
22 Number Superstitions,
23 East African Time,
24 Wealth Means Cattle — and Other Livestock,
SECTION 8 PAST AND FUTURE,
25 Pure Mathematics in Africa,
26 Update: Twenty-Five Years Later,
APPENDIX,
ACKNOWLEDGMENTS,
CHAPTER REFERENCES AND NOTES,
BIOGRAPHICAL NOTES,
Marianne Schmidl,
D. W. Crowe,
Frank E. Chapman, Jr,
BIBLIOGRAPHY,
INDEX,
MAPS,
Africa Today,
Peoples Discussed in the Text,
Africa: Geographic Features and Ancient Cities,
Old Sudanic Kingdoms,
Distribution of Numeration Systems in Africa,
Sixteenth-Century States of the Nigerian Region,
Eastern Africa: Countries and Peoples,

CHAPTER 1

AFRICAN MATHEMATICS?

Before the time of Newton, mathematics and science had little impact on the daily lives of people. Since then mathematics and technology have worked hand in hand to bring about radical innovations in our life style. In an "advanced" country like the United States, the greatest portion of the federal budget is now spent on products whose existence depends on higher mathematics — military hardware and equipment for space travel. People are constantly being urged to purchase more cars, more electronic devices, more material goods manufactured by precisely designed machinery. The computer has taken over many jobs of office workers, technicians, factory operators and teachers. Technology, made possible by mathematics, has become the new god and the possession of its products the goal of life. Yet, the ways of this new god remain as mysterious to the uninitiated citizen of the modern world as were those of the ancient deities.

To the average person, mathematics is a subject that deals with numbers in counting and the computations of elementary arithmetic. I have had my students tell me, "I could do the proof all right, but I made a mistake in the math. I added two and three, and got six!" So, when I tell people that I am doing research in African mathematics, they often ask: "How do Africans count — like us?" I posed this question to two young colleagues, one from Kenya and the other from Tanzania. "How do you count in your own language?" They looked at me in surprise, and replied, "Just as you do here in the United States!" Nowadays school children in most of the world write Hindu numerals (popularly called "Arabic") — truly universal symbols.

The Sociomathematics of Africa

For many mathematicians, mathematics as a discipline originated in ancient Greece with the formulation of logical systems based on definitions, postulates and formally proved theorems. A more flexible definition — the British science writer, Lancelot Hogben calls it a "provisional formula" — is offered in his Mathematics in the Making (page 9): "Mathematics is the technique of discovering and conveying in the most economical possible way useful rules of reliable reasoning about calculation, measurement, and shape."

The last part of Hogben's provisional formula describes the subject matter of this book; it deals with "calculation, measurement, and shape." It would be difficult to discuss "discovery", since few records exist. "Conveying" was accomplished chiefly by word of mouth and by example, from one generation to the next. "Useful" is the key word; I shall deal with mathematics entirely from the point of view of its applications, and not as an abstract body of thought.

It is true that Africans, to our present knowledge, have only recently begun to participate in the development of pure mathematics; possible reasons will be suggested in the concluding chapter. But mathematics is in evidence in many aspects of African life. This book is concerned with the "sociomathematics" of Africa — the applications of mathematics in the lives of African people, and, conversely, the influence that African institutions had upon the evolution of their mathematics.

Geographically, this study is confined to that part of Africa which lies south of the Sahara, an area comparatively isolated from the Mediterranean, Europe, and Asia. We are concerned with a vast region extending nearly four thousand miles from north to south and over four thousand miles from east to west. Within these boundaries exist a variety of cultures and a corresponding diversity of mathematical developments.

The development of a number system depends upon need. In a small, self-contained economy in which all or most of the necessities of life are produced within the community — typical of large sections of Africa — there is little need for an extensive reckoning system. The names of numbers are frequently connected with the objects to be counted, just as we have special names for certain sets — flock, herd, brace, etc., dating back from a pastoral or agricultural society. Gesture-counting is especially necessary in the market place, where people speaking various languages gather to exchange goods. It may be customary to use beads, shells, nuts, or pebbles (the word calculate is derived from calculus, Latin for pebble) as media of exchange or counting materials, and to arrange them in sets, thus giving rise to special words.

Systems of numeration range from the few number words of some San peoples, who have been pushed into the least hospitable areas of the continent by advancing black and white populations, to the extensive numerical vocabulary of nations having a history of centuries of commerce. A characteristic of African counting is a standardized system of gestures to accompany, or even replace, the number words. The gesture languages show as much variety as the spoken ones.

Mystical beliefs about numbers are many and varied. Certain numbers are deemed to have special significance, favorable or unfavorable. In Chinua Achebe's novel Arrow of God the medicine-man counted the cowrie shells "carefully on the ground as a woman would before she bought or sold in the market in groups of six. There were four groups and...