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African Abstractions in Mathematics |
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The purpose of the discussions to follow is to acquaint Black students with the fact that Mathematics was originated by their brilliant Primitive (the first humans) African, Very Ancient African, and Ancient African Ancestors and from Mathematics has sprung all fields of study.
The point is for Black youth to become aware of the historical significance of African contributions and realize the same sparks which produced this genius have been transmitted to them.
The "Mathematical Abstractions" story starts with it arising from simple "Picture Thinking." It is not hard to imagine that the very first reaction of Primitive Africans who encountered a thunder storm or eclipse of the sun was instant Magical Thinking. Such fantasy mental pictures supposedly explained happenings of things seen but with them having no idea how or why. Meanwhile, certain problems appeared that required being handled by Trial-and-Error methods--the trying of many possible solutions, one by one, until the correct or satisfying one appeared. Success from having solved that problem enabled them to use Reasoning by Analogy—comparing solved and familiar problems as a starting point to deal with difficult situations suddenly faced but never seen nor heard of before. Overtime, Primitive Africans encountered more complex Effects they could see but not solve by prior Trial-and-Error problem-solving successes. Still, those prior successes from Trial-and-Error and from Reasoning by Analogy (comparing the unfamiliar with the familiar) were partly workable in the present situation. The transference of what was successful served as a spring-board to jump into the new problem.
Once inside the problem they used the tool of Abstractions (“away from the physical”). To explain, Paleolithic (c 60,000 BC) drawings on African caves showing hunting scenes with dogs and records on Egyptian monuments (6500 BC) are of slender greyhound, short-legged terrier, and hundreds of different breeds of African dogs. But despite their different shapes, functions, usages (e.g. pets, guard, sacred), and habits, the broad and deep insight of Very Ancient Africans shows by their ability to mentally extract partial similarities of like features out of these hundreds of dogs--a process called Abstraction--to give the African equivalent of the name "Dog." The word "Dog" (an idea, a concept) is a shorthand word making discussions about them possible--and also about all dogs to be seen later or not; about dogs in dreams; and about dogs yet to be born. Similarly, by early Africans extracting from a tough problem partial similarities of like features from the unlike essential parts and simply ignoring the differences enabled them to use what was extracted to see proper abstract relationships of similarities to each other; see proper fits of certain abstracts into the whole; see how different proper fits could lead to a solution; and see how the best fit led to proper judgments about the issue at hand. Math works like this because it is a language of abstract components. |
