Christian Long

Ron Eglash: African Fractals

In TED Talks on May 12, 2010 at 9:44 pm
Reflection by TREVOR A.
Original TED page w/ speaker bio, links, comments, etc:

Ron begins his story in Germany in 1877 with a mathematician named Georg Cantor. Cantor decided to take a line, and erase the middle third of the line, and take the two resulting lines and bring them back into the same, recursive process, duplicating the number of lines from 2, to 4, to 16, etc. If this is done an infinite number of times, it makes an infinite number of lines with an infinite number of points in it, and Cantor realized that he had a set with a number of elements larger than infinity.
Then, in 1977, a French mathematician named Benoit Mandelbrot realized that if you use computer graphics with these shapes called fractals you end up with the shapes of nature. You get the shapes of human lungs, acacia trees, ferns, all these natural shapes, and, in fact, your entire body is covered with fractals. He then shows an example of natural recursion with a computer generated diagram of a leaf and its veins.
He then goes to the main point of his talk, the African fractals. He shows aerial view photographs of several African villages, and points out that each of them are made up of fractals. He then tells about his journey to find out more about this by traveling to Africa to ask about them. When he arrived at the palace of the chief there, he introduced himself as a mathematician who wanted to stand on his roof. He says that the chief was very cool, and upon arrival on the roof the chief told him that he knew exactly what he was talking about. “We knew about the rectangle within a rectangle, we know all about that”, the chief told him. Eglash shows more images of the village compared to the royal insignia, which, too, consists of a rectangle within a rectangle within a rectangle.
He goes through many different examples, explaining the significance of certain types of construction of these fractals before saying that there are three questions that may be sparked from this:
1. “Aren’t these scaling patterns just universal to all indigenous architechture?”  He states that he did several different tests on this, and concluded that this was not the case. He began to collect several aerial photographs of Native American and South Pacific architechture, and saw that only the African ones were fractal. He says that if you think about it, all different societies have different geometric design themes that they use in their architechture. The Native Americans used a combination of circular symmetry and fourfold symmetry, which is shown on their art, on their pottery, and on their baskets.
2. “Well, Dr. Eglash, aren’t you just ignoring the diversity of African cultures?” He responds to this by saying that “three times, the answer is no.” First, he believes that Africa is an artificial invention of first colonialism, and then oppositional movements, and that he agrees with Mudimbe’s book, The Invention of Africa. No, again, because a widely shared desuign practice doesn’t prove a unity of culture, and is “definitely not in the DNA.” And no a third and final time because the fractals have self-similarity, and are similar to themselves, but not necessarily similar to each other. Fractals are a shared technology in Africa, and you see very different uses of fractals there.
3. “Well, isn’t this just intuition? It’s not really mathematical knowledge. Africans can’t possibly be using fractal technology, right?”  To this, he says that it is true that some African fractals are just pure intuition, and when he asked people there what the method is for making these fractals, and why they do it, they simply responded by saying that they make it that way because “it looks pretty.” But then sometimes, that’s not the case. Sometimes there would be very sophisticated algorithms, and you’d see this recursive geometry, and argues that this is very conscious knowledge. He adds in that all over Africa you see this board game that here we call Mancala, where you see self-organizing patterns that are spontaneously occurring. He says that the people of Ghana, where he studied the game, would take these principles and use them strategically, reinstating that this is a very conscious knowledge.
He then talks about the most complex example of the algorithmic approach to fractals that he found in Africa, which he says was actually not in geometry, but in a symbolic code. This was Bamana sand divination, which is the same divination system found all over Africa. He says that the symbols of this code are very well preserved, and each symbol has four bits. You begin by drawing random lines in the sand, then you count off. If it’s an odd number, you put down one stroke, and if it’s an even number, you put down two strokes. He says they did this very quickly, but only did it four times, and he didn’t know where they got the other twelve symbols from, and they wouldn’t tell him even after he offered to pay them. They couldn’t tell him this because it was a religious matter, it wasn’t about the money. Out of desperation, he brought up the story of Georg Cantor in 1877. He told them all of his story and why he was in Africa doing what he was, and they got very excited after they saw the Cantor set. Afterwards, one of them took him through the initiation ritual for a Bamana priest. He had to sleep with a kola nut next to his bed, buried in sand, and he had to give seven coins to seven lepers before the initiation was complete. He finally revealed the secrets of the matter, and it turned out to be a pseudo-random number generator using deterministic chaos. He explains that when you have a four-bit symbol, you put it together with another symbol sideways. So then even plus odd and vice versa gives you odd, and even plus even or odd plus odd gives you even. Then you take this symbol and put it back there and you get a self-generating diversity of symbols. This was all very confusing to me. He says again that that they were truly using a kind of deterministic chaos in doing this.
Ron brings up the binary code’s history in Africa, showing how it originally came from the twelfth century, when Hugo Santalia brought the code from Islamic mystics to Spain, where it then entered the alchemy community as geomancy, or divination through the earth. Then different people adapted this method and used it in their own unique way until binary code was translated into the digital computer.
The final point that he makes is that the computers you see today, laptops, PDAs, all started in Africa. This really struck me by surprise. He presented the evidence, and told the entire story of how this came to be, but it just took me a minute to really take it in. I wondered how a place, a continent like Africa was the location of the beginnings of the computer. It blew me away completely.

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