AFROCENTRIC CULTURE BY DESIGN: Why study the history of Mathematics in Africa S. of the Sahara?

Friday, April 16, 2010

Why study the history of Mathematics in Africa S. of the Sahara?

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Why study the history of mathematics in Africa south of the Sahara?

There are many reasons which make the general study of the history of mathematics both necessary and attractive (see e.g. Struik, 1980). There exist important additional reasons which make the research on the history of mathematics in Africa south of the Sahara indispensable.
African countries face the problem of low 'levels' of attainment in mathematics education. Math anxiety is widespread. Many children (and teachers too?) experience mathematics as a rather strange and useless subject, imported from outside Africa. One of the causes thereof is that the goals, contents and methods of mathematics education are not or not sufficiently adapted to the cultures and needs of the African peoples, as stresses the first Secretary-General of the AMU Commission for Mathematical Instruction (Eshiwani, 1979, 346; cf. Eshiwani, 1983; Jacobsen, 1984). Today's existing African educational system is "unadapted and elitist" and "favours foreign consumption without generating a culture that is both compatible with the original civilization and truly promising" (Ki-Zerbo, 1990, 4; cf. El-Tom on mathematics education and the selection of élites, 1984, 3).

The delegates to the Vth Conference of Ministers of Education and those Responsible for Economic Planning in African Member States declared that educational policy should be designed to "restore to their rightful status the African cultural heritage and the traditional social and human values that hold potential for the future " (MINEDAF,1982, 41). The mathematical heritage of the peoples of Africa has to be valued and African mathematical traditions should be 'embedded' into the curriculum (Cf.e.g. Ale, 1989; Doumbia, 1984, 1989b, Gerdes, 1985a, 1986a, 1986b, 1988d, 1990c; Langdon, 1989, 1990; Mmari, 1978; Njock, 1985; Shirley, 1986a, 1986b). And as this scientific legacy of Africa south of the Sahara is little known, research in this area constitutes a challenge to which an urgent response is necessary (Njock, 1985, 4). Also African-Americans and minorities of African descent all over the world feel the need to know their cultural-mathematical heritage (Campbell, 1977; Frankenstein & Powell, 1989; Zaslavsky, 1973, etc.; Ratteray, 1991). More generally, both in highly industrialised and in Third World countries it is becoming more and more recognised that it is necessary to multi-culturalise the mathematics curriculum in order to improve its quality, to augment the cultural confidence of all pupils and to combat racial and cultural prejudice (cf. e.g. D'Ambrosio, 1985a; Ascher, 1984; Bishop, 1988a, b; Joseph, 1987; Mellin-Olsen, 1986; NCTM, 1984; Nebres, 1983; Zaslavsky, 1989a, 1991).

Broad conception of 'history' and 'mathematics'

Most histories of mathematics devote only a few pages to Ancient Egypt and to northern Africa during the 'Middle Ages´. Generally they ignore the history of mathematics in Africa south of the Sahara and give the impression that this history either did not exist or, at least, is not knowable / traceable, or, stronger still, that there was no mathematics at all south of the Sahara (cf. Lumpkin, 1983; Njock, 1985). "Even the Africanity of Egyptian mathematics is often denied" (Shirley, 1986b, 2). Prejudice and narrow conceptions of both 'history' (cf. Ki-Zerbo, 1980, General Introduction) and of 'mathematics' form the basis of such (eurocentric) views (cf. Joseph, 1987, 1991).

At the 17th International Congress of Historical Sciences, Humphrey (1990, 4) stressed that "Any narrow definition of science in modern terms would make it difficult for us to understand its origins and the variable forms it has taken in different cultures". In the case of mathematics, authors like Ale, D'Ambrosio, Ascher & Ascher, Bishop, Doumbia, Gerdes, Njock, Shirley and Zaslavsky consider 'mathematics' as a pan-cultural phenomenon and propose a broad conception, including counting, locating, measuring, designing, playing, explaining, classifying, sorting...

Pioneer study

Zaslavsky's ' Africa Counts ' is a pioneer work in the area of the history of mathematics south of the Sahara. She offers her book as "a preliminary survey of a vast field awaiting investigation" (1973a, vi). Her task was not an easy one: in face of "the inadequacy of easily accessible material... ", she had to search "the literature of many disciplines - history, economics, ethnology, anthropology, archaeology, linguistics, art and oral tradition - ..." (1973a, vi).
She used a broad perspective on mathematics; her study deals with, what she calls, the 'sociomathematics' of Africa: she considers "the applications of mathematics in the lives of African people, and, conversely, the influence that African institutions had upon the evolution of mathematics" (1973a, 7). The concept of sociomathematics may be considered a forerunner of the concept of ethnomathematics. It is ethnomathematics as a discipline that studies mathematics (and mathematical education) as embedded in their cultural context - the (development of) different forms of mathematical thinking which are proper to cultural groups, like ethnic, professional, and age groups.

For the (possible) relationships between ethnomathematics and the history of mathematics, see (in general) D'Ambrosio (1985b) and (in the case of Africa) Shirley (1986b) and Gerdes (1990e).
The application of historical and ethnomathematical research methods has contributed, as will be shown, to the knowledge and understanding of the history of mathematics in Africa, or, at least, of some further mathematical elements in African traditions, in addition to the information gathered in ' Africa Counts '.

The beginnings

Zaslavsky presented as early evidence for (proto-)mathematical activity in Africa a bone dated at 9000-6500 B.C., dug up at Ishango (Zaire). The bone has what appear to be tallying marks on it, notches carved in groups. The bone's discoverer, De Heinzelin, interpreted the patterns of notches as an "arithmetical game of some sort, devised by a people who had a number system based on 10 as well as a knowledge of duplication and of prime numbers". Marshack, on the contrary, explains the bone as early lunar phase count. Their views, summarized in (Zaslavsky, 1973a, 17-19), are reproduced recently in (Fauvel & Gray, 1987, 5-7). Later, the dating of the Ishango bone has been reevaluated, from about 8000 B.C. to 20,000 B.C. (Marshack, 1991). Zaslavsky (1991b) raises the question "who but a woman keeping track of her cycles would need a lunar calendar?" and concludes that "women were undoubtedly the first mathematicians!".

Bogoshi, Naidoo & Webb report in 1987 on a still much older "mathematical artefact": "A small piece of the fibula of a baboon, marked with 29 clearly defined notches, may rank as the oldest mathematical artefact known. Discovered in the early seventies during an excavation of Border Cave in the Lebombo Mountains between South Africa and Swaziland, the bone has been dated to approximately 35000 B.C.". They note that the bone "resembles calendar sticks still in use today by Bushmen clans in Namibia" (1987, 294).
A research project looking for numerical representations in San (Bushmen) rock art has recently been started by Martinson (University of the Witwatersrand, South Africa). From the surviving San hunters in Botswana - "the oldest pattern of life found in the world today..." - , Lea and her students at the University of Botswana have collected information. Her papers describe counting, measurement, time reckoning, classification, tracking and some mathematical ideas in San technology and craft. The San developed very good visual discrimination and visual memory as needed for survival in the harsh environment of the Kalahari desert (Lea, 1987, 1989, 1990a, 1990b).

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The middle and upper reaches of the Niger River have played an important role in West African history. This area in Western Sudan was a base for the camel caravan routes crossing the Sahara to the Mediterranean, while a black nation is reputed to have existed there from around the 3rd or 4th centuries A.C.
The Mali Empire flourished in the 13th century, with the city of Timbuktu on the banks of the Niger River as an intellectual, artistic and religious center. The Songhai Empire reigned in the 15th century, followed notably by the Bambara Kingdom in the 17th and 18th centuries. From the latter half of the 16th century, Mali experienced a period under Moroccan control in its north party.
In the 19th century the French army advanced into the region, making Mali a part of French West Africa from 1898 to 1960. Mali became an autonomous republic within the French Community in 1958, formed the Mali Federation with Senegal in April 1959, and gained independence in its own right on September 22, 1960.

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ALKEBULAN-CENTRIC

KEMETIC SCIENCE - The Master Keys to the Study of Ancient Kemet~ 1. Cultural Antiquity and Continuity Starts in Pre-Dynastic Times and Go to 640 A.D. We must remember this when reading or listening to presentations about Kemet. Even those who eventually conquered Kemet adopted its culture. 2. Older is Better. The older architecture is superior to the later works. It's as if the art and discipline was forgotten with time. 3. The Entire Orientation of the Ancient Kamites is Southern. Word for face and South, right and West, left and East, North and back of head are respectively the same. 4. The Origin of the Kamites is Southern. 5. Leadership is Southern. The main leadership that ruled ancient Kemet always came from the South 6. All Invasions Were Destructive. No one donated culture to ancient Kemet. 7. Arabic Migration Mixes with Nubian People in the Kemetic Valley at and After the Time of Muhammad. Arabic people come in from Syria and Assyria in large numbers for the first time as the first large population of settlers after Muhammad. And with Islam, you have the first change in the fundamental culture of Kemet. 8. Science Generated Religion. The ancient Kemetic people got religion by studying aspects of nature. Nature, when viewed systematically, represents "God" anywhere you look. If you keep seeing the same patterns and rules repeated over and over again in nature, you suddenly realize that there is something bigger that you can't grasp that is behind all this. Therefore, you study yourself into religion. The religion that the Kemetic people developed through study is the same religion that others borrowed from the ancient Kamites without study. Science generated religion, it generated philosophy, and it generated general culture (religion was not Sunday). 9. There is No Dualism in Kemetic Culture. Dualism in interpretation philosophically or culturally is a western phenomenon. (Example, Kierkegaard: It's got to be either this or that). The priest was a scientist. No split between a person searching truth through one means and a person seeking it through another. No split between science and religion, the sacred and the secular. ~ (From a lecture given by Dr. Asa G. Hilliard, III, a.k.a. Nana Baffour Amankwatia

Professor Cheikh Anta Diop (1923-1986)

In His Lab , At the University of Dakar. An outstanding Historian, Egyptologist, Philosopher, and Chemist, ---“In this chapter I hope to demonstrate that the origin of the civilization of Egypt (khem) was black African, specifically Ethiopian or Anu . . . The history of Black will remain suspended in air and cannot be written correctly until African historians dare connect it with the history of Egypt. In reviewing Egypt’s beginnings, we find an advanced civilization already intact from the earliest Dynasty. This fact has perplexed historians down through the ages. Common sense dictates that if Egypt began fully mature, then its civilization must have originated elsewhere . . . . [Herodotus] The ‘Father of History’ was told that the first man to rule Egypt was Min, who lived so long ago that Egypt was still under water: ‘in (Min’s) time the whole country, except the district around Thebes, was marsh, none of the land below Lake Moeris, was then showing above water. To this place from the sea [Nowe] is seven days passage up the river . . . . Cheik Anta Diop, The African Origin of Civilization: Myth or Reality (originally published Nations Negres et Culture) 1955 - (Published in English in 1974)

QUEEN NZINGA - Warrior Queen - (1583-1663)

In the sixteenth century, the Portugese position in the slave trade was threatened by England and France. As a result, the Portugese shifted their slave-trading activities to the Congo and South West Africa. Mistaking the title of the ruler (ngola) for the name of the country, the Portugese called the land of the Mbundu people Angola—the name by which it is still known today. Here, the Portugese encountered the brilliant and courageous Queen Nzinga, who was determined never to accept the Portugese conquest of her country. An exceptional stateswoman and military strategist, she harassed the Portugese until her death, at age eighty. She became renowned for the guerilla tactics she employed for resisting the technologically superior Portugese army. She was a brilliant strategist and, although past sixty, led her warriors herself. Never surrendering, she died on December 17, 1663. Her death accelerated the Portugese occupation of the interior of South West Africa, fueled by the massive expansion of the Portugese slave trade.

QUEEN TIYE - 1415-1340 BCE

Born in Nubia, Queen Tiye was the Great Royal Wife of Amenhotep III, mother of Amenhotep IV (later known as Akenhaton), and mother-in-law of Nefertiti. Highly prestigious during the reign of both her husband and son, she exerted her influence as queen consort and queen mother of Egypt over a fifty-year period. In addition, she shaped Egyptian fashion and altered the prevailing view regarding royal women. Married at an early age, her husband fiercely admired her and displayed his love lavishly by building temples and massive statues where she sits by him as an equal, a feat unparalleled in that time; dedicated a number of shrines to her; and even created a monumental artificial lake for her. She was glorified by her husband as "... The most praised, the lady of grace, sweet in her love, who fills the palace with her beauty, the Regent of the North and South, the Great Wife of the King, the lady of both lands..." Wielding her power and taking charge at this juncture in the nation's history, she used her political influence and astute decisions to maintain Egypt's authority. She averted key national crises by becoming Secretary of State when her husband's physical and mental powers deteriorated with age; and redirected political decisions to her attention when her son Akenhaton neglected his political duties while preoccupied with his religious innovation (named the Heretic King, Akenhaton was the first ruler in recorded history to believe in monotheism).

ANCIENT BLACK CHINESE

The Africans or blacks that founded civilization in China were often called li min "black headed people" by the Zhou dynasts. This term has affinity to the Sumero-Akkadian term sag- gig-ga "black headed people". In northern China the blacks founded many civilizations. The three major empires of China were the Xia Dynasty (c.2205-1766 B.C), Shang/ Yin Dynasty (c.1700-1050 B.C) and the Zhou Dynasty.The Zhou dynasty was the first dynasty founded by the Mongoloid people in China called Hua (Who-aa). These li min are associated with the Chinese cultural hero Yao. The founders of Xia and Shang came from the Fertile African Crescent by way of Iran. According to Chinese legends the first man Pan Gu, used a hammer 18,000 years ago to make man. The skeletal remains from southern China are predominately negroid. (Chang 1964, p.70) The people practiced single burials.

MANI TRIBE IN THAILAND

The Chinese legends designate various culture heroes as the inventors of various aspects of Chinese civilization. The Chinese term for emperor is Di. Huang Di (Yellow Emperor), is the Chinese culture hero credited with introducing boats, carts 'chariots, the bow and arrow, ceramics, wooded houses and writing.Chinese civilization began along the Yellow river . Here the soil was fertile and black Chinese farmers grew millet 4000 years ago, and later soybeans. They also raised pigs and cattle. By 3500 B.C., the blacks in China were raising silkworms and making silk.

AFRICA'S OLDEST KNOWN BOAT

8000 years ago, Nigeria. "Africa's oldest known boat" the Dufuna Canoe was discovered near the region of the River Yobe. The Canoe was discovered by a Fulani herdsman in May 1987, in Dufuna Village while digging a well. The canoe’s “almost black wood”, said to be African mahogany, as “entirely an organic material”. Various Radio-Carbon tests conducted in laboratories of reputable Universities in Europe and America indicate that the Canoe is over 8000 years old, thus making it the oldest in Africa and 3rd oldest in the World. Little is known of the period to which the boat belongs, in archaeological terms it is described as an early phase of the Later Stone Age, which began rather more than 12,000 years ago and ended with the appearance of pottery. evidence of an 8,000-year-old tradition of boat building in Africa throws cold water on the assumption that maritime transport developed much later there in comparison with Europe. Peter Breunig of the University of Frankfurt, Germany, an archaeologist involved in the project, says the canoe’s age “forces a reconsideration of Africa’s role in the history of water transport”. It shows, he adds, “that the cultural history of Africa was not determined by Near Eastern and European influences but took its own, in many cases parallel, course”

AFROCENTRIC CULTURE BY DESIGN

Friday, April 16, 2010

Why study the history of Mathematics in Africa S. of the Sahara?

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