African Math Origins

So I tracked down one of the folks who makes these things this guy in Molly just outside of Bomico I asked him how can you make him fractal fence? Because nobody else is and his answer was very interesting He said well if I lived in the jungle I would only use the long rows of straw because they're very quick in the very cheap doesn't take much time doesn't take much straw He said but wind and dust goes through pretty easily Now the tight rows up at the very top They really hold out the wind and dust but it takes a lot of time and it takes a lot of straw because they're really Really tight Now he said we know from experience That the farther up from the ground you go The stronger the wind blows right it's just like a cost benefit analysis and I measured out the lengths of straw Put in a log log plot got the scaling exponent and almost exactly matches the scaling exponent for the relationship between wind speed and height in the wind engineering Hamper So these guys are right on target for for a practical use of Scaling technology The most complex example of an algorithmic approach to fractals that I found was actually not in geometry it was in a symbolic code And this was a bomb in a sand divination and the same divination system is found all over Africa You can find in the east coast as well as the west coast and often the symbols are very well preserved So each of these symbols has four bits. It's a four-bit binary word You draw these lines and sand randomly And then you count off and if it's an odd number you put down one stroke and if it's even number you put down two stroke And they did this very rapidly And I couldn't understand where they were getting they only did the randomness four times I couldn't understand where they were getting the other 12 symbols And they wouldn't tell me they said no, no, I can't tell you about this I said well look I'll pay you you know you can be my teacher and and I'll come each day and pay you So that's not a matter of money. This is a religious matter and finally under desperation I said well let me explain George cancer in 1877 and I started explaining you know why it was there in in Africa And they got very excited when they saw the cancer set and One of them said you know, I think I can help you out here and so he took me through the initiation ritual for a Bombin of priest and of course I was only interested in the math so the whole time you kept shaking you said going you know I didn't learn it this way but I had to sleep with a cold in that next to my dad buried in sand and give seven points to seven lepers and so on and Finally he he revealed the the truth of the matter and It turns out it's a suit around a number generator the using deterministic chaos When you have a four-bit symbol you then put it together with another one sideways So even plus odd gives you odd odd plus even gives you odd Even plus even gives you even odd plus odd gives you even it's a dish in modular too Just like in the parody bit check on your computer and then you you take this symbol and you put it back in So it's a self-generating diversity of symbols. They're truly using a kind of deterministic chaos in doing this Now because that's a binary code you can actually implement this in hardware what a fantastic teaching tool that should be in African engineering schools and the most interesting thing I found out about it was Historical in the 12th century a Hugo Sontalee abroad it from Islamic mystics into Spain And they're it entered into the the alchemy community as Gilmancy the the the divination through the earth This is a geometric chart drawn by For the for a King Richard the second in 1390 Leibnitz the German mathematician talked about Gilmancy in his dissertation called decominatoria and He said well instead of using one stroke and two strokes let's use a one and a zero and we can count by powers of two Right ones and zero's the binary code George bull took livenets his binary code and created bullying algebra and John von Neumann took bullying algebra and created the digital computer So all these these little pda's and and laptops every digital circuit in the world Started in Africa and I I know Brian you know says there's there's not enough African computers, but you know I don't think there's enough African history in Brian, you know So let me in with just a few words about Applications that we've we've found for this and you can go to our website the applets are all free They just run in the browser any button in the world can use them the National Science Fundations broadening participation in computing program recently was a grant to make Programme a bull version of these design tools so so hopefully in three years anybody We able to go on the web and create their own simulations of their own artifacts We focused in the US on on African American students as well as Native American Latino We found statistically significant improvement with children using this software in the mathematics class in comparison with with a control group that did not have a software So it's really very successful Teaching children that they have a heritage that's about mathematics that it's not just about singing and dancing We've started a pilot program in Ghana. We got a small sea grant just to to See if folks will be willing to work with us on this and we're very excited about the future possibilities for that We've also been working in design. I didn't put his is name up here at my colleague Cari and in Kenya has come up with this great idea for using a fractal structure for postal address In villages that have fractal structures because if you try to impose a grid structure Postal system on a fractal village it it doesn't quite fit Bernard Shumiet Columbia University has been issued using this in a design for a Museum of African art David Hughes at High-state University has written a primer on Afrocentric architecture in which he's he's used some of these fractal structures and finally I just wanted to point out that this idea of self-organization As we heard earlier, you know, it's it's in the brain It's in the the the the it's in Google search engine Actually the reason Google was such a success is because they were the first ones to take advantage of the self-organizing properties of the web It's in ecological sustainability. It's in the developmental power of entrepreneurship the ethical power of democracy It's it's also in some bad things self-organizations why the AIDS virus is spreading so fast and if you don't think the capitalism Which is self-organizing can have destructive effects you you have an open your eyes and now so we need to think about As as as was spoken earlier the traditional African methods for doing self-organization These are robust algorithms These are ways of doing self-organization of doing entrepreneurship That are gentle better egalitarian so if we want to find a better way of doing that kind of work We need look only no farther than Africa to find these robust self-organizing algorithms. Thank you