Every digital circuit in the world started in Africa.

Ron Eglash, TEDTalks

I came across this TED talk when I was researching random numbers for a recent blog post. The speaker is Ron Eglash, a mathematician with an interest in fractals (scaling patterns), and an important point to make:

When Europeans first came to Africa, they considered the architecture very disorganized and thus primitive. It never occurred to them that the Africans might have been using a form of mathematics that they hadn’t even discovered yet.

Eglash describes African fractals as a shared technology with many applications. He then traces the roots of modern computing back to the system of Bamana sand divination, a system of self-generated variety.

The divination begins with four hurriedly drawn rows of dashed lines: You count off the pairs, and record if each row contains an even or odd number of dashed parts.

A single vertical line is used to represent odd (one stroke); double vertical lines represent even (two strokes). The outcome is a column of vertical lines, e.g.:

This process is repeated three more times, generating the initial four symbols. From then on, the system is self-generating. The initial outputs are paired and counted off to generate the next two symbols, e.g.:

Each output is used as the input in the next operation over multiple iterations, producing a total of sixteen symbols (see all the steps here), but “a maximum-length pseudorandom number generator using their initial four symbols will produce 65,535 symbols before it begins to repeat.” (Ref.)

Out of Africa: Eglash goes on to explain how, in the twelfth century, this technology traveled from Africa to Europe, and later informed German mathematician Gottfried Wilhelm Leibniz’s binary code, which led to George Boole’s Boolean algebra, which led to John von Neumann’s digital computer.

Ron Eglash: The fractals at the heart of African designs (2007)