Africa Counts: Number and Pattern in African Cultures by Claudia Zaslavsky
BEST MATHEMATICAL HISTORY BOOK OF 2017 AWARD GOES TO: Africa Counts - Number and Pattern In African Culture.
I recall that in high school, I asked my history teacher how Africa developed mathematics, and he said that Africa never developed numbers and that they only could count in very basic ways with their fingers. WTF.
Claudia Zaslavsky’s book documents all the ways that math evolved in Africa and MORE IMPORTANTLY the two-way mathematical knowledge exchange between Africa and the West. Westerners treat their mathematical innovations as if it came ex nihilo. But the Greek upper class were educated in Egypt and adopted their numerical system that created the basis of scientific innovation in the Renaissance. The development of abstract numbers in Europe was not only influenced by Arabic and African math, but was built on top of it. So essentially, the Greeks don’t own the birth of math.
It’s often the case that Western systems are framed as rational, scientific, and precise and views while non-Western beliefs around numbers are seen as woo woo. Yet, Zaslavsky helps us break this down. For example, numbers often took on gender in Africa. The Pythagorean school of Ancient Greece also associated even numbers with gender - even with female and odd with male. African counting is connected to the body with numbers being communicated with hand gestures and measurements associated with body part. The British Measurement system is based on standardization of body parts - an inch is the top of the thumb knuckle, and an acre is based on the amount of land that a yoke of oxen can plow in 1 day.
I learned so many fascinating things. African numeration systems are quinary (5 is the primary base). The Yoruba have been counting to 1 million and beyond for much longer than the West. The Kikuya in Kenya developed mathematical perfect suspension bridges long before the West in the 20th cent - you can’t do that without math. Even though there are over a thousand plus languages on the entire continent, the words for 1, 2, 3, and 4 are similar for 50% of the continent covering multiple language groups. A unified systems of weights and measurement existed in Mali which contained some of the largest empires in the world, but of course unknown to the West.
And of course as the story goes, when European traders arrived in Africa, they actively depreciated local currencies, weakening local financial systems that created prime conditions for colonists to gain the upper hand.
Zaslavsky ends the book with a discussion on how slave trade and colonialism halted the potential development of sci. & tech in Africa.
I can't wait to follow up with 2 books I've had on my bookshelf for a long time, Ron Eglash's African Fractals: Modern Computing and Indigenous Design and Erica N. Walker's Beyond Banneker: Black Mathematicians and the Paths to Excellence.
"For many mathematicians, mathematics as a discipline originated in ancient Greece with the formulation of a logical system based on definitions, postulates and formal proved theorems. A more flexible definition—the British science writer, Lancelot Huogben calls it a “provisional formula”—is offered in his Mathematics in the Making: ‘Mathematics is the technique of discovering and conveying in the most economical possible way useful rules of reliable reasoning about calculation, measurement, and shape.” p 6
“The demands of commerce also dictated the degree of standardization of weights and measures. The villager with the longest arm sometimes set the standard for measuring cloth! Record keeping varied from knotted strings and notched sticks to the ritual of the annual census, carried out by indirect methods that circumvented the taboo on counting living creatures.” p 8
“The ability to observe and reproduce patterns, both numerical and geometrical, is of great important in Africa,…Cattle-herding folks have in their vocabularies dozens of words to describe their livestock on the basis of hide markings and dozes more to differentiate cattle by the shape of their horn. Each patten in weaving, in word carving, in cloth dying, has a special meaning. Numerical patterns are evidence in games,…” p 8
“The book concludes with the discussion of the disruptions caused by the slave trade and colonialism during the past five centuries, and their disastrous effect upon the potential development of since and technology in Africa.” p 8
"In Great Britain, there arose a school of anthropologists, led by E.B. Tylor, having a point of view based on their interpretations of the new doctrine of evolution. Their thesis was this: man evolved from a primitive to an advanced state during the course in many millennia. The white man had arrived at the highest level, in contrast to the “primitive savages” of “Darkest Africa,” who were still in the very early stages of evolution. Tylor’s Primitive Culture became a leading reference work for anthropologists, ethnologists, and even for writers of the history of mathematics. Using Tylor as his source, the mathematical history Florian Cajori wrote in 1896: “Of the notions based on human anatomy, the quinary and vigesimal systems are frequent among the lower races, while the higher nations have usually avoided the ones as too scary and the other as too cuprous, preferring the intermediate decimal system.”
“One must be extremely cautious about accepting the accounts of the inability of “primitive” people to count in higher denominations…The absence of counting words by no means indicates a lack of counting concepts, since the number concept and the designations for the numbers need not always coincide. One must consider the level of the economy, the practical need for arithmetic operations, etc.” p 14
“There is general agreement among anthropologists that in the evolution of counting, number was originally conceived in connection with the objects to be counted, and it was only at a much more advanced stage of development (like ours) that man conceived of number in the abstract. My experience as a mathematics teachers has taught me that most people in our own society still think of numbers in concert terms… I have found that most many people in modern society have difficulty in handling abstract numbers. …anthropologists Leslie A White…says ’the whole population of a certain region is embraced by a type of culture. Each individual is born into a pre-exiting organization of beliefs, tools, customs, and institutions. These cultural traits shape and mould each person’s life, give it content and direction. Mathematics, is, of course, one of the streams in the total culture.’ In every period of tie, in every geographical location, people inherit form their ancestors their ways of life. The resources available to the society in the form of materials, ideas, and human relationships determine the changes that take place in their institutions including their mathematics Great minds have their part in mathematical discovery, but they can operate only within th cultural setting in which they exist. In Africa, too, physical environment, inherited cultural resources, and the impact of external forces determined the nature and extent of mathematical development.” p 16
“In ancient Egypt, the flooding of the Nile River necessitated annual revision of the land. Private ownership of land and the ability to produce a surplus of commodities enabled the owners to exchange their products for their private gain or to store them for future use. Thus arose the need for a systems of weights and measures. Mathematical operations of addition, abstraction, multiplication, division, and the use of fractions are recorded in Egyptian papyri in connection with the practical problems of the society. Their multiplication and division by doubling developed into the doubling and halving called ‘depletion and mediation’ in medieval Europe…Western culture owes a great debt to Egypt and Mesopotamia. The ancient Greek have been regarded as the fathers of Western civilization. but many centuries before their time the Egyptian priests had developed a complete curriculum for the training of their members. This included philosophy, writing, astronomy, geometry, engineering, and architecture. Indeed, the upper class Greens completed their education by studying with Mesopotamian or Egyptian teachers. The Hellenic astronomers adopted the Egyptian civil calendar, the first of its kind in human history. .. The extensive Egyptian library’s were available to visitors. ..But intellectual stagnation had come to Egypt before the time of the Greeks. Compared with Mesopotamia, the commercial center of the ancient world, Egypt developed in isolation. Only a restricted upper class enjoyed the benefits of the small amount of supers wealth that this agricultural society could produce. Increasingly, the aristocrats appropriated this wealth for their private enjoyment and for the construction of magnificent monuments in the form of temple and tombs. The result was the virtual enslavement of the poor peasants and craftsmen The conflict among various dynasties of kings and between the royal and the priestly segments only weakened the whole structure of the state and led to further decline. ..What has happened to the enormous accumulation of literature, sincere, and technical achievements? Much has been lost; on the other hand, archeology is revealing to us how much has been assimilated and taken over by later societies…Hellenic science arose on the foundations of several thousands years of accumulated knowledge, and its influence was to be dominant from from India to Western Europe until the European Renaissance.” p 23-25
“The cultural interaction resulting from commercial contacts with other societies is a stimulus to scientific growth…One of the earlier spurs of mathematical development that we know took place in Mesopotamia, the crosswords of the ancient world, a center of unrestricted commercial activity. In a later era, the ancient Greeks, living in an atmosphere of freedom political and religious despotism, were perhaps the first to evolve a logical mathematical system. A thousand and more years later the Islamic world was the science of mathematical growth. The Arabs contributed original word, as well as translating the neglected manuscripts of the Greek mathematicians into Arabic, thus preserving them until they were reintroduce into Europe centuries later in their Arabic versions. The Arabs have been called “cultural middleman”; they traveled throughout Asia, north and east Africa and the Sudan region, and southern Europe, spreading the contributions of Indians, Chinese, Persians, Jews, Arabs, and Europeans to every region. Islamic science developed against a background of wide commercial contacts, flourishing cities, and official encouragement of its growth. In Europe, on the other hand, medieval Christendom was rooted in reverence of the traditional, and in reluctance to challenge the authority of the Catholic Church.
In 1202 Leonardo Fibonacci, on his return from his travels in the East, introduced Hindu numerals into Western Europe, but it took three centuries for the system to be widely adopted. Merchants in the growing cities of Italy were the firs to profit by this method of writing numbers. Now the rules of computation, hitherto a mystery to all except the most learned, were comprehensible to the average keeper of commercial accounts. At this time European universities were offering not much more than some arithmetic and a bit of Euclidian geometry, transited into Latin from Arabic.
Not only was there little progress in mathematics in Europe outside of the commercial centers but the subject was viewed with general suspicion by the Establishment. Among the crimes for which the Spanish Inquisition inflicted life imprisonment of death were the possession of Arabic manuscripts and the study of mathematics…’mathematicians were denounced as the greater of all heretic’ (Homer w Smith). It was the growth of the industrial class in most of Euopre, with its challenge to the existing order, which sparkers the gate age of mathematics. ” p 273-4
“Individuals in such a well ordered society do not seek wealth or social supriiorty that high create too great a departure from traditional tribal life. If cultural interaction is a requirement for invention, we can hardly expect to find scientific and mathematical inquiry in these isolated and tradition-oriented societies.” p 277
Marcia Ascher writes, ‘mathematical ideas are cultural expressions embedded within cultural contexts.” p 281
“All societies throughout the world and in all eras of history have developed mathematical ideas relevant to heir needs and interests.” p 281