http://www.ted.com/index.php/talks/view/id/198
So… Ron Eglish, a mathematician, went to Africa. There, he said to chiefs and children, “Hello, I am a mathematician, and I would like to stand on your roof” in bad and broken French. From the rooftops, he saw in reality what he had seen in aerial photographs, that many African village designs are based in fractals. He also discovered that much of sub-Saharan African culture is rooted in fractals, right into the nitty-gritty of spirit houses and mask-making. Mancala, the board game played throughout much of Africa, is also rooted in fractal mathematics and pattern recognition. And then Eglish discovered, and was initiated into, Bamana sand divination.
In Bamana sand divination, a suppliant draws a series of lines in sand. The oracle or priest performs a pseudo-random number generation routine in order to turn the suppliant’s lines into one of hundreds of patterns based on a four-item sequence. These patterns are indicated with either a single line, or a pair of lines. The technique was described in a book by Islamic mystics and scholars in Timbuktu, who passed a copy of the work on to mystics and scholars at Salamanca, in Spain.
When the Christians conquered Salamanca in the late 1100s or early 1200s, copies of the book fell into Christian hands. King Alfonso the Wise, famous for having quipped “Had I been present at the beginning, I would have given our Lord God some useful hints for the better ordering of Creation,” arranged for Spanish and Jewish translators to work in concert with each other; the Jew translated from Arabic to the local Spanish dialect, and the Spaniard translated from dialect to Latin.
The book on African sand divination, now named Geomancy, eventually found its way to a printer’s office, and from there to a bookseller’s shop, where a German named Gottfried Willhelm Leibnitz eventually bought and read it. He used it as the basis for an essay on a new kind of mathematics, titled De Combinatoria. This essay, when read by George Boole, became the basis of Boolean algebra. Which mathematics, when combined with the work of another fellow named Von Neumann, and another guy working for the Brits in World War II, Alan Turing, became the basis for the machine you are using to read these four short paragraphs.
Holy cow. Binary mathematics and fractal mathematics are African.
