23 February 2010

Self-Organization: Fractals in the Heart of Africa

I'll bet there are a couple of readers out there wondering if I really am an anthropologist given all the stuff about technology and professional development I've been posting lately.  I haven't forgotten, I've just been a bit side-tracked.

Royal palace, Logone-Birni, Cameroon (Musee de l'Homme, Paris)

This morning I received an interesting email that brought together a few subjects near and dear to me - Africa, indigenous knowledge, and fractals.  "Fractals?" you say.  Yes.  Fractals.  They are everywhere in nature, art, architecture, and even, as I will discuss, African society.

Queen Anne's Lace - Daucus carota - More images at WebEcoist

The email came from a listserve for folks interested in indigenous knowledge that is based at Penn State - ICIK.  It seems that in June 2007, Dr. Ron Eglash, an ethnomathematician gave a TED talk and someone in the forum found it, sent it to the co-director of ICIK, and she (Dr. Audrey Marezki) posted it round to the listserv.

Eglash's talk started out with some background about the history of fractal math in Europe and what exactly fractals are.  "Pathological curves" are one definition used by mathematicians, but really they are self-organizing systems/patterns.  Each part looks like the greater whole - a property of self-similarity, where recursion continues into infinity.  He then went on to talk about African architecture, art, and social organization.  His work, beginning with a Fulbright to explore why African villages and towns, used fractal math to organize, shows that while some of the use is unconscious, much of the use of fractal mathematics in Africa is deliberate.  And the village layout patterns are repeated in the clustering of houses and organization of rooms within homes.  Fractal algorithms even appear in the seasonal cycles of religious ceremonies, funeral ceremonies, and spirit/ancestral houses.

“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, Designers 421

Eglash then moved on to discuss fractal math used in the game Mancala, wind screens made in West Africa for desert winds, and the origin of binary code in Bamana Sand Divination.  Yes, even the humble code that allows me to produce this blog finds its origins in Africa.  According to the talk, explorers carried the Bamana Sand Divination to Moorish Spain where it was picked up by alchemists and incorporated into their geomancy divination practices.  Later, Leibonitz derived binary code from geomancy.  If you watch the video I've posted below, you will see that Eglash makes the story far more interesting with inclusion of giving out gold to 7 lepers and sleeping with a kola nut.

Dr. Eglash ends with a discussion of how this knowledge is being applied in American classrooms - encouraging black students to connect to their mathematical roots - and how the robust, self-organizing algorithms found in indigenous knowledge could be applied to finding solutions to many of the African continents' problems.

More links:

Eglash, R.  2008.  Bamana sand divination: recursion in ethnomathematics.  American Anthropologist 99(1): 112-122.

Eglash, R. 1999.  African Fractals: Modern Computing and Indigenous Design.  Rutgers University Press.

TED Profile on Ron Eglash with the link to the original video talk.

Ron Eglash's African Fractals homepage.
  • Link to CDST page with teaching applets (cultural design and math).

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