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Origins of African Abstract Mathematics |
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A first and natural display of the human mind's organization is a mental imagery production.
Next, learning "alphabet" type arithmetic leads to skills of concrete thinking concerning things made of matter--as by separating physical parts from physical wholes. Then through similarities derived from appearances comes the ability to group dissimilar things by their similarities (e.g. forming basketball teams by gender and height)--an advancement giving rise to Arts and to Inventions. After that is the development of the ability to do abstract thinking--and to elaborate let us look at the origins of the word "Calculate" (meaning "pebble"). Early Very Ancient Africans used mental imagery to keep up with a group of their puppies. To improve accuracy they put a pebble into an animal-skin sack to represent each puppy as it left the fold so as to tell, by checking the puppies returning at night against the pebbles, whether any had been lost. Each pebble represented the abstraction of "oneness" of each puppy--its numerical value. Similarly, in bartering goods stones were put into a sack to convey how much of something was owned. This was an abstract "figuring out" way to reduce negotiation problems--a process embracing "Forethought" (doing all the necessary planning before taking "calculated" risks).
As a result of applying these practices in various aspects of life; and of observing and touching mathematical type things in daily life; and of forming abstract relationships of things to each other and to nearby things, the ideas learned up to that point were easily and widely spread into all aspects of daily living. When problems of a more complex nature were faced that still required the application of numerical facts (as had been done in dealing with puppies) and with forethought needed to figure out things related to the abstractions obtained from foreknowledge, Africans instituted higher levels of abstraction--which went as high as fractions. A word used for this process of acquiring information out of lofty abstract realms is Foreknowledge (acquiring facts and information in an intuitive and perhaps instinctive manner).
To deal with such hard to describe foreknowledge information demanded the designing of concepts, symbols, or labels to stand for hazy isolated things in the real world and for the formation of thoughts and feelings about the things so named. To these ends the African equivalents of x's and y's and other abstract mathematical symbols were made from applicable numerical abstractions. Just as the word symbol "Dog" stands for a multitude of characteristics all dogs have in common, so do these symbols for abstractions. These symbols (that which stands in for and conveys the meaning of something less obvious) simplify the thoughts and the ideas involved in the maneuvering process of abstract principles. They get the job done (e.g. predict occurrences) because, by being based on agreed uniform principles (bottom-lines of Truth), their proper relationships are clearly understood by reasonable people. |
