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Fractals, Complexity, and Connectivity in Africa

Written by sankofa

– By Ron Eglash and Toluwalogo B. Odumosu

The question “What mathematics from Africa?” can be seen as a conflation of two

pertinent, related questions. First, “What mathematics?” Second, “What Africa?”

Answering these will enable us to more fully explore the subject of our inquiry.

The first question “What mathematics?” is of course nonsensical as a statement. What we are really trying to ask, is “What do we mean by mathematics?”. Is our mathematics a verb or a noun? It is important to ask this question as there are many different understandings of what mathematics actually is, and controversy surrounds any effort to try and define mathematics. A comprehensive look at the question of the nature of mathematics is beyond the scope of this paper, and we will consciously delimit our discussion of mathematics to mathematics as practice – by which we refer to systematic material and symbolic understandings of quantity and logic. A simple example of what we mean by mathematics as practice can be seen in architecture. For example, much of New York City is laid out as a grid, which may be seen as a collection of rectangles. It also includes an ordinal dimension in that streets can be numbered. For the inhabitants of a built environment, the very obviousness of certain patterns can make them invisible. We don’t realize that we are surrounded by the shapes of Euclid – circles, rectangles and triangles, etc. – because we don’t have built fractal structures to contrast them with. As we will see, fractal geometry not only illuminates the underlying structure

of African designs, but also helps us see the cultural-boundedness of our own

mathematical practice.

Most people engage in mathematical exercise unknowingly everyday. Determining change in financial transactions is just one of the many abilities that require mathematical sensibilities. Time and space are also mathematically delimited as we all refer to our clocks for local time and unconsciously resolve the mathematical relationship between seconds, minutes and hours. The argument can easily be made that mathematics is all around us. This point must be fully understood as we proceed to discuss mathematics from Africa.

The second question, “What Africa?” alas may not be as easily resolvable. In our opinion, the term Africa is used as a placeholder for all things relating to that particular continent. For example, we often hear phrases similar to “she visited Brazil, Mexico, London and then Africa.” – thus conflating the continent of Africa with countries (Brazil and Mexico). The continent of Africa is the second largest in the world and is geopolitically comprised of many countries, cities and people groups. The critical position that we must strive to recover is that of difference (Appiah 1992; Eglash 1999). Africa is not homogenous; either culturally, or politically, or even architecturally. It could be convincingly argued that there is no singular “African” identity (though some would add that one is evolving).

Similarly, to speak about an “African” mathematics is to oversimplify a very complex phenomena. While our discussions oscillate around an “African mathematics” we must emphasize that at best, we are describing a subtle family resemblance across multiple cultural streams.

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