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Was the Wealth of Nations Determined in 1000 B.C.?
Abstract We assemble a dataset on technology adoption in 1000 B.C., 0 A.D., and 1500 A.D. for the predecessors to today’s nation states. We find that this very old history of technology adoption is surprisingly significant for today’s national development outcomes. Although our strongest results are for 1500 A.D., we find that even technology as old as 1000 BC is associated with today’s outcomes in some plausible specifications
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viola75 - There is a reason why you are the first person to disseminate this particular study - think about that for a moment - until you posted it, no one had heard about it.
That is because this study is what is called a "White Boys Dreaming" study.
To be more precise, it is pure nonsense.
"White" Europe was built on the theft of other peoples property and technology, no bogus study will change that.
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If someone has the ability to steal technology and develop the technology so that it is stronger than it was originally, then the one who stole it had more mastery of the technology than the one that originated it.
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This is the frightening truth that Afronutcases are afraid to admit.
quote:Originally posted by the lioness: If someone has the ability to steal technology and develop the technology so that it is stronger than it was originally, then the one who stole it had more mastery of the technology than the one that originated it.
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^If the originating society was still intact, then that would be true. But the originating societies were not brought down by superior societies or technologies. Quite the contrary, they were brought down by illiterate Barbarians (please read White people).
But your argument speaks to my original reply. The thread is about the bogus proposition that Europeans INVENTED superior technologies.
My reply simply spoke to the White mans NEED to lie.
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Mike simple question, What was the race of the people who invented the computer you are typing on...who's language are you typing in?? The White man or the black man???
Posts: 8804 | From: The fear of his majesty had entered their hearts, they were powerless | Registered: Nov 2007
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quote:Originally posted by Mike111: ^If the originating society was still intact, then that would be true. But the originating societies were not brought down by superior societies or technologies. Quite the contrary, they were brought down by illiterate Barbarians (please read White people).
But your argument speaks to my original reply. The thread is about the bogus proposition that Europeans INVENTED superior technologies.
My reply simply spoke to the White mans NEED to lie.
Mike if all these literate nerdy black people were up in Europe and they produced some albinos who came to be known as white people how did they become illiterate barbarians?
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quote:Originally posted by Mike111: ^If the originating society was still intact, then that would be true. But the originating societies were not brought down by superior societies or technologies. Quite the contrary, they were brought down by illiterate Barbarians (please read White people).
But your argument speaks to my original reply. The thread is about the bogus proposition that Europeans INVENTED superior technologies.
My reply simply spoke to the White mans NEED to lie.
Mike if all these literate nerdy black people were up in Europe and they produced some albinos who came to be known as white people how did they become illiterate barbarians?
according to Mike111.com whites are Indian Albinos who inhabited Central Asia and invaded Europe killing the black euros like the Greeks..
step your game up in Mike111's scholarship...girl.
BTW, what happened to your Michelle Obama avatar pic...let me guess the CIA told you to take it down huh Michelle??
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according to Mike111.com whites are Indian Albinos who inhabited Central Asia and invaded Europe killing the black euros like the Greeks..
step your game up in Mike111's scholarship...girl.
according to Mike111.com whites are Indian Albinos who inhabited Central Asia and invaded Europe killing the black euros like the Greeks..
well than where did the Indians come from before they were in India and how and why did a certain group of Indian albinos become illiterate and take over the world? Let us assume they and all people came from Africa originally. I guess the albinos of India just lied their way to the top. For some reason their lies didn't work that well on other Indians. So they moved to Europe and told all the literate blacks of Europe that they were gods and the literate blacks somehow forgot their books, became dumb and fell for it.
makes sense
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in 15oo a.d apart from the gun, what technologys did they have in europe which wasnt in africa?
Posts: 142 | From: england sw | Registered: Aug 2010
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according to Mike111.com whites are Indian Albinos who inhabited Central Asia and invaded Europe killing the black euros like the Greeks..
step your game up in Mike111's scholarship...girl.
according to Mike111.com whites are Indian Albinos who inhabited Central Asia and invaded Europe killing the black euros like the Greeks..
well than where did the Indians come from before they were in India and how and why did a certain group of Indian albinos become illiterate and take over the world? Let us assume they and all people came from Africa originally. I guess the albinos of India just lied their way to the top. For some reason their lies didn't work that well on other Indians. So they moved to Europe and told all the literate blacks of Europe that they were gods and the literate blacks somehow forgot their books, became dumb and fell for it.
makes sense
??? Why are you asking me, this is Mike's theory...its on his website..
Posts: 8804 | From: The fear of his majesty had entered their hearts, they were powerless | Registered: Nov 2007
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quote:Originally posted by viola75: in 15oo a.d apart from the gun, what technologys did they have in europe which wasnt in africa?
Viola - Don't allow Sub-Saharan's to bullsh1t you.
Whites want to bullsh1t you into believing that they were everywhere, and they invented everything. Because that masks the true fact that they were insignificant.
Sub-Saharan's want to bullsh1t you into believing that they had NO technology, in order to explain why the White man was able to so easily conquer and colonize Africa.
The fact is that the Gun, and every other technology was available to them. Their problem was simply "Stupidity".
Even before that (70 A.D.), another Egyptian "Heron of Alexandria" invented the steam engine and the Windmill.
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quote:Originally posted by Mike111: Here is the history from the same source that you used (Wiki). See if you can figure it out.
The Battle of Ain Jalut (or Ayn Jalut, in Arabic: عين جالوت, the "Spring of Goliath") took place on 3 September 1260 between the Egyptian Mamluks and the Mongols in Palestine, in the Jezreel Valley, not far from Ein Harod.
from the same link as Mike posted...seems he left out that the Mamluk part??? HMMM..
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Jari - I know that you are not very bright. But I don't think that even YOU would suggest that "Slaves born to serve as Soldiers" i.e. the Mamluks, invented the Gun???
I'll go you one better: where or when, was ANY soldier, the inventor of his weapon.
Damn Boy, take your head out!
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Mike, I'm still not clear on how whites were able to take over. If blacks invented things like the gun and whites copied it they would be on equal footing. How did the whites become dominant in battle? But further these barbarian whites only had the ability to copy things, blacks the true inventors, would be inventing new things while whites were still copying their old inventions. Therefore blacks should have won because they would have been one step ahead all the time. In addition we, the blacks, would have been coming up with new battle strategies all the time while whites were predictable because they just copied our old strategies. You haven't explained how they got the advantage.
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you know he is going to dig deep in the annals of computer, internet, and technology and find the most obscure invention indirectly tied those three that is attributed to a black man, and use that as proof that the Black man invented the computer and net, hello Al Gore! (LOL)
quote:Originally posted by Just call me Jari: Mike simple question, What was the race of the people who invented the computer you are typing on...who's language are you typing in?? The White man or the black man???
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HAHAHAHAHAHAHAHA!!!!!!!!! Sarcasm at its finest!
quote:Originally posted by the lioness: Mike, I'm still not clear on how whites were able to take over. If blacks invented things like the gun and whites copied it they would be on equal footing. How did the whites become dominant in battle? But further these barbarian whites only had the ability to copy things, blacks the true inventors, would be inventing new things while whites were still copying their old inventions. Therefore blacks should have won because they would have been one step ahead all the time. In addition we, the blacks, would have been coming up with new battle strategies all the time while whites were predictable because they just copied our old strategies. You haven't explained how they got the advantage.
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there is shrewdness in the sarcasm. She caught you good w/that one bruh. I got to give her that credit, she made mince meat out of your thinking process.
quote:Originally posted by Mike111: Lioness - I know that you are not clear, never have you been.
Interestingly, Gigantic thinks "Dimwittedness" is Sarcasm.
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Mike Remember, these are the same people who in 1876 had to rely on an African slave to create and inoculate them against smallpox. While 1800s White America (or England) had never seen a smallpox inoculation, African tribes had been inoculating themselves for 100s of years.
Once the African slave produced the serum and inoculated the slave owner and his family, the slave owner's neighbors bum rushed his home burnishing torches and pitchforks yelling insanely; "Witch craft!!! Burn the heathens!"
Did anybodys other than the TS actually read the study
Was the Wealth of Nations Determined in 1000 B.C.?
I haven't gotten to it yet. If you put the titel in google you can also get an HTML version from the "quick view" version.
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MK - It must be all the "Meth" White people are doing - their children sure are coming out stupid.
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They've ALWAYS come out stupid. These are the same people who called Marco Polo a liar when he returned to England and told them of the wonders of China. These are the same people who drove dirty nails through each others brains performing what they called, brain surgery. The same people who in the 1900s played at brain surgery and cut out people's Pineal glands not understanding how vital it is to life. These people are so psychologically damaged they'd rather murder those best equipped to cure their psychosis than be healed.
Mike, all those Anti-Psychotic and depression drugs (and sexual dysfunction drugs as well) you see being pushed on TV specifically target these whites and their mental illnesses. Proving; A vital Pineal gland is a terrible thing to waste.
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quote:Originally posted by MelaninKing: They've ALWAYS come out stupid. These are the same people who called Marco Polo a liar when he returned to England and told them of the wonders of China. These are the same people who drove dirty nails through each others brains performing what they called, brain surgery. The same people who in the 1900s played at brain surgery and cut out people's Pineal glands not understanding how vital it is to life. These people are so psychologically damaged they'd rather murder those best equipped to cure their psychosis than be healed.
Mike, all those Anti-Psychotic and depression drugs (and sexual dysfunction drugs as well) you see being pushed on TV specifically target these whites and their mental illnesses. Proving; A vital Pineal gland is a terrible thing to waste.
MK what race invented the computer you are typing on?? Who language are you speaking and typing in?? Whose civiliation, laws and constitution are you abinding under, you are a Moor right, whats wrong with Morocco?? Why live with the white man??
Mike seems to be unable to answer this??
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quote:Originally posted by Mike111: Jari - I know that you are not very bright. But I don't think that even YOU would suggest that "Slaves born to serve as Soldiers" i.e. the Mamluks, invented the Gun???
I'll go you one better: where or when, was ANY soldier, the inventor of his weapon.
Damn Boy, take your head out!
The Mamluk Sultanate was a regime composed of mamluks who ruled Egypt and Syria from the mid-1200s to the early 1500s. By the time of the fall of the Ayyubids, most Mamluks were Kipchak Turks.[2] While Mamluks were purchased, their status was above ordinary slaves, who were not allowed to carry weapons or perform certain tasks. Mamluks were considered to be “true lords,” with social status above freeborn Egyptians.
The word mamluk means “one who is owned.” The term was originally applied to boys from Central Asian tribes who were bought by the Abbasid caliphs and raised to be soldiers. The same practice was adopted by the Fatimids, an Ismaili dynasty based in Tunisia that conquered Egypt in 969 and founded Cairo as its new capital.
When Salah ad-Din (Saladin to the West), the son of a Kurdish general, supplanted the Fatimids and founded the Ayyubid dynasty in 1174, he formed the Mamluks into a distinct military body. Since the Ayyubids were strangers in Egypt, they likely felt more comfortable with the support of their fellow foreigners.
Slave traders bought the children of conquered tribes in Central Asia, promising them security, discipline and the possibility of great fortunes. Mamluk boys then endured several years of rigorous training in horsemanship and archery. They were used both as royal bodyguards and to offset the dominating influence of the Arab military in the state. Not to be confused with ordinary slaves, the Mamluks were members of an elite military corps—a kind of proto-Foreign Legion or a knighthood of Islam. In 1254, the Mamluks revolted against the Ayyubid ruler and one of their own—a Turk named Aybak—married Shagar al-Durr, the wife of the murdered sultan: The Mamluks had accomplished the rare feat of transforming themselves from slaves to masters.
Power in the Mamluk realm was not based on heredity. Every Mamluk arrived in Egypt or Syria as a slave- soldier. The young men were converted to Islam and worked their way up the ranks on merit alone. Every commander of the army and nearly all of the Mamuk sultans started life in this way. The result was a succession of rulers of unbounded ambition, courage and ruthlessness.
After the Mamluks made themselves masters of Egypt and Syria, they continued the tradition of recruiting foreigners for their military. Agents were sent to buy and import boys from Central Asian tribes, chiefly Circassians, Turkomans and Mongols. Mamluks looked on their Egyptian-born sons as socially inferior and would not recruit them into regular Mamluk units, which only admitted boys born on the steppes.
This constant influx of new blood prevented the dynasty from decaying from within as a result of less-capable princes ascending to the throne, but it also made for turmoil at the top: While some Mamluk sultans ruled for a decade or more, the average length of rule was only five years. As an autocratic military caste, [/b]the Mamluks ruled with considerable harshness, imposing heavy taxes and holding all political and military power. They did employ the native-born population in civil posts; such persons often achieved high rank and honors in the civil administration.[/b] In contrast to their harsh reputation as rulers, the Mamluks also bequeathed an astonishing legacy of artistic achievement. Much of the glory of medieval Cairo still visible today is the result of Mamluk patronage.
The Mamluks ruled Egypt until 1517, when Cairo fell to the Ottoman Turks whose artillery and firearm skills far surpassed that of the Mamluks who, as consummate horsemen, disdained such novelties. The Ottoman ruler, Selim i, ended the Mamluk sultanate but did not destroy the Mamluks as a class; they kept their lands, and Mamluk governors retained control of the provinces and were even allowed to keep private armies.
In the 18th century, when Ottoman power began to decline, the Mamluks were able to win back an increasing amount of self-rule. In 1769 a Mamluk leader, Ali Bey, proclaimed himself sultan and declared independence from the Ottomans. Although his reign collapsed in 1772, the Ottoman Turks still felt compelled to concede increasing measures of autonomy to the Mamluks and appointed a series of them as governors of Egypt. The last great charge of the fabled Mamluk horsemen took place on July 17, 1798, when Napoleon Bonaparte’s modern army shattered the Egyptian cavalry at the Battle of the Pyramids. Their power as an elite class ended in 1811 when Muhammad Ali, an Albanian Turk who had wrested control of Egypt from the Ottomans in 1805, invited several hundred prominent Mamluks to dinner in the Cairo Citadel. After diner, as the Mamluk notables and their entourages made their way to one of the fortress’s lower gates, Muhammad Ali’s troops massacred them all, a violent final chapter for a dynasty whose rulers rose from slavery to control much of the Middle East.
By 1492 A.D, Christopher Columbus had discovered the "New World" (it had a 100 million people)
In the 19th century alone over 50 million people left Europe for the Americas. The local populations or tribes, such as the Aboriginal people in Canada, Brazil, Argentina, Australia, and the United States, were usually far overwhelmed numerically by the settlers.
BTW Dumbass, didn't I already school you on whose language we speak?
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quote:Originally posted by Mike111: ^Damn you Albino MFs are stupid!!!!!
WHO MOVED IN ON WHOM ASSHOLE?????
By 1492 A.D, Christopher Columbus had discovered the "New World" (it had a 100 million people)
In the 19th century alone over 50 million people left Europe for the Americas. The local populations or tribes, such as the Aboriginal people in Canada, Brazil, Argentina, Australia, and the United States, were usually far overwhelmed numerically by the settlers.
BTW Dumbass, didn't I already school you on whose language we speak?
What does this have to do with the Mamluks??
Posts: 8804 | From: The fear of his majesty had entered their hearts, they were powerless | Registered: Nov 2007
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quote:Originally posted by Mike111: ^Damn you Albino MFs are stupid!!!!!
WHO MOVED IN ON WHOM ASSHOLE?????
By 1492 A.D, Christopher Columbus had discovered the "New World" (it had a 100 million people)
In the 19th century alone over 50 million people left Europe for the Americas. The local populations or tribes, such as the Aboriginal people in Canada, Brazil, Argentina, Australia, and the United States, were usually far overwhelmed numerically by the settlers.
BTW Dumbass, didn't I already school you on whose language we speak?
Also if Whites invaded can you please show us the Laws, the Civilization and the Constitution of the black Indians??
Also did you not say that Blacks invented all the Weapons and Tech..How did the whites Sail navigate and destroy the Blacks in the Americas if blacks are the True inventors why did they not invent weapons to destroy whitey...Mike M.K said blacks invented Smallpox Vaccince...Why did the Black Aboriginal Americans not utilize the Small Pox Inoculation from their African borthers??
Posts: 8804 | From: The fear of his majesty had entered their hearts, they were powerless | Registered: Nov 2007
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^What, you write so much stupidness that you can't remember what you wrote only ten minutes ago?
Just call me Jari quote: Who language are you speaking and typing in?? Whose civiliation, laws and constitution are you abinding under, you are a Moor right, whats wrong with Morocco?? Why live with the white man??
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quote:Originally posted by Mike111: ^What, you write so much stupidness that you can't remember what you wrote only ten minutes ago?
Just call me Jari quote: Who language are you speaking and typing in?? Whose civiliation, laws and constitution are you abinding under, you are a Moor right, whats wrong with Morocco?? Why live with the white man??
Also did you not say that Blacks invented all the Weapons and Tech..How did the whites Sail navigate and destroy the Blacks in the Americas if blacks are the True inventors why did they not invent weapons to destroy whitey...Mike M.K said blacks invented Smallpox Vaccince...Why did the Black Aboriginal Americans not utilize the Small Pox Inoculation from their African borthers??
Posts: 8804 | From: The fear of his majesty had entered their hearts, they were powerless | Registered: Nov 2007
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quote:Originally posted by Mike111: Quote: "If Whites Invaded"
You're not stupid, you're sick.
Damn you MFs are fuched-up!
Also did you not say that Blacks invented all the Weapons and Tech..How did the whites Sail navigate and destroy the Blacks in the Americas if blacks are the True inventors why did they not invent weapons to destroy whitey...Mike M.K said blacks invented Smallpox Vaccince...Why did the Black Aboriginal Americans not utilize the Small Pox Inoculation from their African borthers??
Is this your admission of defeat??
Maybe M.K can answer..
Posts: 8804 | From: The fear of his majesty had entered their hearts, they were powerless | Registered: Nov 2007
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quote:Originally posted by the lioness: If someone has the ability to steal technology and develop the technology so that it is stronger than it was originally, then the one who stole it had more mastery of the technology than the one that originated it.
Some people are indeed better at lying, stealing and killing people and then pretend to be these great civilised humanitarians. This is what we should teach our children: steal, lie, cheat at exams; if you want to succed in life!
But I was asking myself how long historical events can and/or should influence us today.
Posts: 5454 | From: Holland | Registered: Aug 2008
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So who did they steal the combustion engine and plane from?
quote:Originally posted by Egmond Codfried: Some people are indeed better at lying, stealing and killing people and then pretend to be these great civilised humanitairians. This is what we should teach our children: steal, lie, cheat at exams; if you want to succed in life!
But I was asking myself how long historical events can and/or should influence us today.
quote:Originally posted by Just call me Jari: Mike simple question, What was the race of the people who invented the computer you are typing on...who's language are you typing in?? The White man or the black man???
I want to start my story in Germany, in 1877, with a mathematician named Georg Cantor. And Cantor decided he was going to take a line and erase the middle third of the line, and take those two resulting lines and bring them back into the same process, a recursive process. So he starts out with one line, and then two, and then four, and then 16, and so on. And if he does this an infinite number of times, which you can do in mathematics, he ends up with an infinite number of lines, each of which has an infinite number of points in it. So he realized he had a set whose number of elements was larger than infinity. And this blew his mind. Literally. He checked into a sanitarium. (Laughter) And when he came out of the sanitarium, he was convinced that he had been put on earth to found transfinite set theory, because the largest set of infinity would be God Himself. He was a very religious man. He was a mathematician on a mission.
And other mathematicians did the same sort of thing. A Swedish mathematician, von Koch, decided that instead of subtracting lines, he would add them. And so he came up with this beautiful curve. And there's no particular reason why we have to start with this seed shape; we can use any seed shape we like. And I'll rearrange this and stick this somewhere -- down there, OK -- and now upon iteration, that seed shape sort of unfolds into a very different looking structure. So these all have the property of self-similarity: the part looks like the whole. It's the same pattern at many different scales.
Now, mathematicians thought this was very strange, because as you shrink a ruler down, you measure a longer and longer length. And since they went through the iterations an infinite number of times, as the ruler shrinks down to infinity, the length goes to infinity. This made no sense at all, so they consigned these curves to the back of the math books. They said these are pathological curves, and we don't have to discuss them. (Laughter) And that worked for a hundred years.
And then in 1977, Benoit Mandelbrot, a French mathematician, realized that if you do computer graphics and used these shapes he called fractals you get the shapes of nature. You get the human lungs, you get acacia trees, you get ferns, you get these beautiful natural forms. If you take your thumb and your index finger and look right where they meet -- go ahead and do that now -- -- and relax your hand, you'll see a crinkle, and then a wrinkle within the crinkle, and a crinkle within the wrinkle. Right? Your body is covered with fractals. The mathematicians who were saying these were pathologically useless shapes? They were breathing those words with fractal lungs. It's very ironic. And I'll show you a little natural recursion here. Again, we just take these lines and recursively replace them with the whole shape. So here's the second iteration, and the third, fourth and so on.
So nature has this self-similar structure. Nature uses self-organizing systems. Now in the 1980s, I happened to notice that if you look at an aerial photograph of an African village, you see fractals. And I thought, "This is fabulous! I wonder why?" And of course I had to go to Africa and ask folks why. So I got a Fulbright scholarship to just travel around Africa for a year asking people why they were building fractals, which is a great job if you can get it. (Laughter)
And so I finally got to this city, and I'd done a little fractal model for the city just to see how it would sort of unfold -- but when I got there, I got to the palace of the chief, and my French is not very good; I said something like, "I am a mathematician and I would like to stand on your roof." But he was really cool about it, and he took me up there, and we talked about fractals. And he said, "Oh yeah, yeah! We knew about a rectangle within a rectangle, we know all about that." And it turns out the royal insignia has a rectangle within a rectangle within a rectangle, and the path through that palace is actually this spiral here. And as you go through the path, you have to get more and more polite. So they're mapping the social scaling onto the geometric scaling; it's a conscious pattern. It is not unconscious like a termite mound fractal.
This is a village in southern Zambia. The Ba-Ila built this village about 400 meters in diameter. You have a huge ring. The rings that represent the family enclosures get larger and larger as you go towards the back, and then you have the chief's ring here towards the back and the chief's immediate family in that ring. So here's a little fractal model for it. Here's one house with the sacred altar, here's the house of houses, the family enclosure, with the humans here where the sacred altar would be, and then here's the village as a whole -- a ring of ring of rings with the chief's extended family here, the chief's immediate family here, and here there's a tiny village only this big. Now you might wonder, how can people fit in a tiny village only this big? That's because they're spirit people. It's the ancestors. And of course the spirit people have a little miniature village in their village, right? So it's just like Georg Cantor said, the recursion continues forever.
This is in the Mandara mountains, near the Nigerian border in Cameroon, Mokoulek. I saw this diagram drawn by a French architect, and I thought, "Wow! What a beautiful fractal!" So I tried to come up with a seed shape, which, upon iteration, would unfold into this thing. I came up with this structure here. Let's see, first iteration, second, third, fourth. Now, after I did the simulation, I realized the whole village kind of spirals around, just like this, and here's that replicating line -- a self-replicating line that unfolds into the fractal. Well, I noticed that line is about where the only square building in the village is at. So, when I got to the village, I said, "Can you take me to the square building? I think something's going on there." And they said, "Well, we can take you there, but you can't go inside because that's the sacred altar, where we do sacrifices every year to keep up those annual cycles of fertility for the fields." And I started to realize that the cycles of fertility were just like the recursive cycles in the geometric algorithm that builds this. And the recursion in some of these villages continues down into very tiny scales.
So here's a Nankani village in Mali. And you can see, you go inside the family enclosure -- you go inside and here's pots in the fireplace, stacked recursively. Here's calabashes that Issa was just showing us, and they're stacked recursively. Now, the tiniest calabash in here keeps the woman's soul. And when she dies, they have a ceremony where they break this stack called the zalanga and her soul goes off to eternity. Once again, infinity is important.
Now, you might ask yourself three questions at this point. Aren't these scaling patterns just universal to all indigenous architecture? And that was actually my original hypothesis. When I first saw those African fractals, I thought, "Wow, so any indigenous group that doesn't have a state society, that sort of hierarchy, must have a kind of bottom-up architecture." But that turns out not to be true.
I started collecting aerial photographs of Native American and South Pacific architecture; only the African ones were fractal. And if you think about it, all these different societies have different geometric design themes they use. So Native Americans use a combination of circular symmetry and fourfold symmetry. You can see on the pottery and the baskets. Here's an aerial photograph of one of the Anasazi ruins; you can see it's circular at the largest scale, but it's rectangular at the smaller scale, right? It is not the same pattern at two different scales.
Second, you might ask, "Well, Dr. Eglash, aren't you ignoring the diversity of African cultures?" And three times, the answer is no. First of all, I agree with Mudimbe's wonderful book, "The Invention of Africa," that Africa is an artificial invention of first colonialism, and then oppositional movements. No, because a widely shared design practice doesn't necessarily give you a unity of culture -- and it definitely is not in the DNA. And finally, the fractals have self-similarity -- so they're similar to themselves, but they're not necessarily similar to each other -- you see very different uses for fractals. It's a shared technology in Africa.
And finally, well, isn't this just intuition? It's not really mathematical knowledge. Africans can't possibly really be using fractal geometry, right? It wasn't invented until the 1970s. Well, it's true that some African fractals are as far as I'm concerned just pure intuition. So some of these things, I'd wander around the streets of Dakar asking people, "What's the algorithm? What's the rule for making this?" and they'd say, "Well, we just make it that way because it looks pretty, stupid." (Laughter) But sometimes, that's not the case. In some cases, there would actually be algorithms, and very sophisticated algorithms. So in Manghetu sculpture, you'd see this recursive geometry. In Ethiopian crosses, you see this wonderful unfolding of the shape.
In Angola, the Chokwe people draw lines in the sand, and it's what the German mathematician Euler called a graph; we now call it an Eulerian path -- you can never lift your stylus from the surface and you can never go over the same line twice. But they do it recursively, and they do it with an age-grade system, so the little kids learn this one, and then the older kids learn this one, then the next age-grade initiation, you learn this one. And with each iteration of that algorithm, you learn the iterations of the myth. You learn the next level of knowledge.
And finally, all over Africa, you see this board game. It's called Owari in Ghana, where I studied it; it's called Mancala here on the east coast, Bao in Kenya, Sogo elsewhere. Well, you see self-organizing patterns that spontaneously occur in this board game. And the folks in Ghana knew about these self-organizing patterns and would use them strategically. So this is very conscious knowledge.
Here's a wonderful fractal. Anywhere you go in the Sahel, you'll see this windscreen. And of course fences around the world are all Cartesian, all strictly linear. But here in Africa, you've got these nonlinear scaling fences. So I tracked down one of the folks who makes these things, a guy in Mali just outside of Bamako, and I asked him, "How come you're making fractal fences? 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, and they're very cheap. It 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 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 it on a log-log plot, got the scaling exponent, and it almost exactly matches the scaling exponent for the relationship between wind speed and height in the wind engineering handbook. So these guys are right on target 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 Bamana sand divination. And the same divination system is found all over Africa. You can find it on 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 in the sand randomly, and then you count off, and if it's an odd number, you put down one stroke, and if it's an even number, you put down two strokes. 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." And I said, "Well look, I'll pay you, you can be my teacher, and I'll come each day and pay you." They said, "It's not a matter of money. This is a religious matter."
And finally, out of desperation, I said, "Well, let me explain Georg Cantor in 1877." And I started explaining why I was there in Africa, and they got very excited when they saw the Cantor set. And one of them said, "Come here. I think I can help you out here." And so he took me through the initiation ritual for a Bamana priest. And of course, I was only interested in the math, so the whole time, he kept shaking his head going, "You know, I didn't learn it this way." But I had to sleep with a kola nut next to my bed, buried in sand, and give seven coins to the seven lepers and so on. And finally, he revealed the truth of the matter. And it turns out it's a pseudo-random number generator 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 addition modulo 2, just like in the parity bit check on your computer. And then 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 it'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, Hugo of Santalla brought it from Islamic mystics into Spain. And there it entered into the alchemy community as geomancy: divination through the earth. This is a geomantic chart drawn for King Richard II in 1390. Leibniz, the German mathematician, talked about geomancy in his dissertation called "De Combinatoria." 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 zeros, the binary code. George Boole took Leibniz's binary code and created Boolean algebra, and John von Neumann took Boolean algebra and created the digital computer. So all these little PDAs and laptops -- every digital circuit in the world -- started in Africa. And I know Brian Eno says there's not enough Africa in computers; you know, I don't think there's enough African history in Brian Eno. (Applause)
So let me end with just a few words about applications that we've found for this. And you can go to our website, the applets are all free; they just run in the browser. Anybody in the world can use them. The National Science Foundation's Broadening Participation in Computing program recently awarded us a grant to make a programmable version of these design tools, so hopefully in three years, anybody'll be able to go on the Web and create their own simulations and their own artifacts. We've focused in the U.S. on African-American students as well as Native American and Latino. We've found statistically significant improvement with children using this software in a mathematics class in comparison with a control group that did not have the software. So it's really very successful teaching children 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 seed grant, just to see if folks would be willing to work with us on this; we're very excited about the future possibilities for that.
We've also been working in design. I didn't put his name up here -- my colleague, Kerry, in Kenya, has come up with this great idea for using fractal structure for postal address in villages that have fractal structure, because if you try to impose a grid structure postal system on a fractal village, it doesn't quite fit. Bernard Tschumi at Columbia University has finished using this in a design for a museum of African art. David Hughes at Ohio State University has written a primer on Afrocentric architecture in which 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, it's in the brain. It's in the -- it's in Google's search engine. Actually, the reason that 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 also in some bad things. Self-organization is why the AIDS virus is spreading so fast. And if you don't think that capitalism, which is self-organizing, can have destructive effects, you haven't opened your eyes enough. So we need to think about, 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, that are 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.
quote:Originally posted by Just call me Jari: Mike simple question, What was the race of the people who invented the computer you are typing on...who's language are you typing in?? The White man or the black man???
Show me the computer patent and the photo of the original in Africa..please.
I want to start my story in Germany, in 1877, with a mathematician named Georg Cantor. And Cantor decided he was going to take a line and erase the middle third of the line, and take those two resulting lines and bring them back into the same process, a recursive process. So he starts out with one line, and then two, and then four, and then 16, and so on. And if he does this an infinite number of times, which you can do in mathematics, he ends up with an infinite number of lines, each of which has an infinite number of points in it. So he realized he had a set whose number of elements was larger than infinity. And this blew his mind. Literally. He checked into a sanitarium. (Laughter) And when he came out of the sanitarium, he was convinced that he had been put on earth to found transfinite set theory, because the largest set of infinity would be God Himself. He was a very religious man. He was a mathematician on a mission.
And other mathematicians did the same sort of thing. A Swedish mathematician, von Koch, decided that instead of subtracting lines, he would add them. And so he came up with this beautiful curve. And there's no particular reason why we have to start with this seed shape; we can use any seed shape we like. And I'll rearrange this and stick this somewhere -- down there, OK -- and now upon iteration, that seed shape sort of unfolds into a very different looking structure. So these all have the property of self-similarity: the part looks like the whole. It's the same pattern at many different scales.
Now, mathematicians thought this was very strange, because as you shrink a ruler down, you measure a longer and longer length. And since they went through the iterations an infinite number of times, as the ruler shrinks down to infinity, the length goes to infinity. This made no sense at all, so they consigned these curves to the back of the math books. They said these are pathological curves, and we don't have to discuss them. (Laughter) And that worked for a hundred years.
And then in 1977, Benoit Mandelbrot, a French mathematician, realized that if you do computer graphics and used these shapes he called fractals you get the shapes of nature. You get the human lungs, you get acacia trees, you get ferns, you get these beautiful natural forms. If you take your thumb and your index finger and look right where they meet -- go ahead and do that now -- -- and relax your hand, you'll see a crinkle, and then a wrinkle within the crinkle, and a crinkle within the wrinkle. Right? Your body is covered with fractals. The mathematicians who were saying these were pathologically useless shapes? They were breathing those words with fractal lungs. It's very ironic. And I'll show you a little natural recursion here. Again, we just take these lines and recursively replace them with the whole shape. So here's the second iteration, and the third, fourth and so on.
So nature has this self-similar structure. Nature uses self-organizing systems. Now in the 1980s, I happened to notice that if you look at an aerial photograph of an African village, you see fractals. And I thought, "This is fabulous! I wonder why?" And of course I had to go to Africa and ask folks why. So I got a Fulbright scholarship to just travel around Africa for a year asking people why they were building fractals, which is a great job if you can get it. (Laughter)
And so I finally got to this city, and I'd done a little fractal model for the city just to see how it would sort of unfold -- but when I got there, I got to the palace of the chief, and my French is not very good; I said something like, "I am a mathematician and I would like to stand on your roof." But he was really cool about it, and he took me up there, and we talked about fractals. And he said, "Oh yeah, yeah! We knew about a rectangle within a rectangle, we know all about that." And it turns out the royal insignia has a rectangle within a rectangle within a rectangle, and the path through that palace is actually this spiral here. And as you go through the path, you have to get more and more polite. So they're mapping the social scaling onto the geometric scaling; it's a conscious pattern. It is not unconscious like a termite mound fractal.
This is a village in southern Zambia. The Ba-Ila built this village about 400 meters in diameter. You have a huge ring. The rings that represent the family enclosures get larger and larger as you go towards the back, and then you have the chief's ring here towards the back and the chief's immediate family in that ring. So here's a little fractal model for it. Here's one house with the sacred altar, here's the house of houses, the family enclosure, with the humans here where the sacred altar would be, and then here's the village as a whole -- a ring of ring of rings with the chief's extended family here, the chief's immediate family here, and here there's a tiny village only this big. Now you might wonder, how can people fit in a tiny village only this big? That's because they're spirit people. It's the ancestors. And of course the spirit people have a little miniature village in their village, right? So it's just like Georg Cantor said, the recursion continues forever.
This is in the Mandara mountains, near the Nigerian border in Cameroon, Mokoulek. I saw this diagram drawn by a French architect, and I thought, "Wow! What a beautiful fractal!" So I tried to come up with a seed shape, which, upon iteration, would unfold into this thing. I came up with this structure here. Let's see, first iteration, second, third, fourth. Now, after I did the simulation, I realized the whole village kind of spirals around, just like this, and here's that replicating line -- a self-replicating line that unfolds into the fractal. Well, I noticed that line is about where the only square building in the village is at. So, when I got to the village, I said, "Can you take me to the square building? I think something's going on there." And they said, "Well, we can take you there, but you can't go inside because that's the sacred altar, where we do sacrifices every year to keep up those annual cycles of fertility for the fields." And I started to realize that the cycles of fertility were just like the recursive cycles in the geometric algorithm that builds this. And the recursion in some of these villages continues down into very tiny scales.
So here's a Nankani village in Mali. And you can see, you go inside the family enclosure -- you go inside and here's pots in the fireplace, stacked recursively. Here's calabashes that Issa was just showing us, and they're stacked recursively. Now, the tiniest calabash in here keeps the woman's soul. And when she dies, they have a ceremony where they break this stack called the zalanga and her soul goes off to eternity. Once again, infinity is important.
Now, you might ask yourself three questions at this point. Aren't these scaling patterns just universal to all indigenous architecture? And that was actually my original hypothesis. When I first saw those African fractals, I thought, "Wow, so any indigenous group that doesn't have a state society, that sort of hierarchy, must have a kind of bottom-up architecture." But that turns out not to be true.
I started collecting aerial photographs of Native American and South Pacific architecture; only the African ones were fractal. And if you think about it, all these different societies have different geometric design themes they use. So Native Americans use a combination of circular symmetry and fourfold symmetry. You can see on the pottery and the baskets. Here's an aerial photograph of one of the Anasazi ruins; you can see it's circular at the largest scale, but it's rectangular at the smaller scale, right? It is not the same pattern at two different scales.
Second, you might ask, "Well, Dr. Eglash, aren't you ignoring the diversity of African cultures?" And three times, the answer is no. First of all, I agree with Mudimbe's wonderful book, "The Invention of Africa," that Africa is an artificial invention of first colonialism, and then oppositional movements. No, because a widely shared design practice doesn't necessarily give you a unity of culture -- and it definitely is not in the DNA. And finally, the fractals have self-similarity -- so they're similar to themselves, but they're not necessarily similar to each other -- you see very different uses for fractals. It's a shared technology in Africa.
And finally, well, isn't this just intuition? It's not really mathematical knowledge. Africans can't possibly really be using fractal geometry, right? It wasn't invented until the 1970s. Well, it's true that some African fractals are as far as I'm concerned just pure intuition. So some of these things, I'd wander around the streets of Dakar asking people, "What's the algorithm? What's the rule for making this?" and they'd say, "Well, we just make it that way because it looks pretty, stupid." (Laughter) But sometimes, that's not the case. In some cases, there would actually be algorithms, and very sophisticated algorithms. So in Manghetu sculpture, you'd see this recursive geometry. In Ethiopian crosses, you see this wonderful unfolding of the shape.
In Angola, the Chokwe people draw lines in the sand, and it's what the German mathematician Euler called a graph; we now call it an Eulerian path -- you can never lift your stylus from the surface and you can never go over the same line twice. But they do it recursively, and they do it with an age-grade system, so the little kids learn this one, and then the older kids learn this one, then the next age-grade initiation, you learn this one. And with each iteration of that algorithm, you learn the iterations of the myth. You learn the next level of knowledge.
And finally, all over Africa, you see this board game. It's called Owari in Ghana, where I studied it; it's called Mancala here on the east coast, Bao in Kenya, Sogo elsewhere. Well, you see self-organizing patterns that spontaneously occur in this board game. And the folks in Ghana knew about these self-organizing patterns and would use them strategically. So this is very conscious knowledge.
Here's a wonderful fractal. Anywhere you go in the Sahel, you'll see this windscreen. And of course fences around the world are all Cartesian, all strictly linear. But here in Africa, you've got these nonlinear scaling fences. So I tracked down one of the folks who makes these things, a guy in Mali just outside of Bamako, and I asked him, "How come you're making fractal fences? 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, and they're very cheap. It 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 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 it on a log-log plot, got the scaling exponent, and it almost exactly matches the scaling exponent for the relationship between wind speed and height in the wind engineering handbook. So these guys are right on target 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 Bamana sand divination. And the same divination system is found all over Africa. You can find it on 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 in the sand randomly, and then you count off, and if it's an odd number, you put down one stroke, and if it's an even number, you put down two strokes. 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." And I said, "Well look, I'll pay you, you can be my teacher, and I'll come each day and pay you." They said, "It's not a matter of money. This is a religious matter."
And finally, out of desperation, I said, "Well, let me explain Georg Cantor in 1877." And I started explaining why I was there in Africa, and they got very excited when they saw the Cantor set. And one of them said, "Come here. I think I can help you out here." And so he took me through the initiation ritual for a Bamana priest. And of course, I was only interested in the math, so the whole time, he kept shaking his head going, "You know, I didn't learn it this way." But I had to sleep with a kola nut next to my bed, buried in sand, and give seven coins to the seven lepers and so on. And finally, he revealed the truth of the matter. And it turns out it's a pseudo-random number generator 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 addition modulo 2, just like in the parity bit check on your computer. And then 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 it'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, Hugo of Santalla brought it from Islamic mystics into Spain. And there it entered into the alchemy community as geomancy: divination through the earth. This is a geomantic chart drawn for King Richard II in 1390. Leibniz, the German mathematician, talked about geomancy in his dissertation called "De Combinatoria." 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 zeros, the binary code. George Boole took Leibniz's binary code and created Boolean algebra, and John von Neumann took Boolean algebra and created the digital computer. So all these little PDAs and laptops -- every digital circuit in the world -- started in Africa. And I know Brian Eno says there's not enough Africa in computers; you know, I don't think there's enough African history in Brian Eno. (Applause)
So let me end with just a few words about applications that we've found for this. And you can go to our website, the applets are all free; they just run in the browser. Anybody in the world can use them. The National Science Foundation's Broadening Participation in Computing program recently awarded us a grant to make a programmable version of these design tools, so hopefully in three years, anybody'll be able to go on the Web and create their own simulations and their own artifacts. We've focused in the U.S. on African-American students as well as Native American and Latino. We've found statistically significant improvement with children using this software in a mathematics class in comparison with a control group that did not have the software. So it's really very successful teaching children 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 seed grant, just to see if folks would be willing to work with us on this; we're very excited about the future possibilities for that.
We've also been working in design. I didn't put his name up here -- my colleague, Kerry, in Kenya, has come up with this great idea for using fractal structure for postal address in villages that have fractal structure, because if you try to impose a grid structure postal system on a fractal village, it doesn't quite fit. Bernard Tschumi at Columbia University has finished using this in a design for a museum of African art. David Hughes at Ohio State University has written a primer on Afrocentric architecture in which 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, it's in the brain. It's in the -- it's in Google's search engine. Actually, the reason that 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 also in some bad things. Self-organization is why the AIDS virus is spreading so fast. And if you don't think that capitalism, which is self-organizing, can have destructive effects, you haven't opened your eyes enough. So we need to think about, 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, that are 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.
posted
"Show me the computer patent and the photo of the original in Africa..please."
i think his point is there wouldnt be any of the stuff now like computers planes physics etc if europeans didnt borrow the binary code fom africa,
Posts: 142 | From: england sw | Registered: Aug 2010
| IP: Logged |
quote:Originally posted by Just call me Jari: Mike simple question, What was the race of the people who invented the computer you are typing on...who's language are you typing in?? The White man or the black man???
Show me the computer patent and the photo of the original in Africa..please.
I want to start my story in Germany, in 1877, with a mathematician named Georg Cantor. And Cantor decided he was going to take a line and erase the middle third of the line, and take those two resulting lines and bring them back into the same process, a recursive process. So he starts out with one line, and then two, and then four, and then 16, and so on. And if he does this an infinite number of times, which you can do in mathematics, he ends up with an infinite number of lines, each of which has an infinite number of points in it. So he realized he had a set whose number of elements was larger than infinity. And this blew his mind. Literally. He checked into a sanitarium. (Laughter) And when he came out of the sanitarium, he was convinced that he had been put on earth to found transfinite set theory, because the largest set of infinity would be God Himself. He was a very religious man. He was a mathematician on a mission.
And other mathematicians did the same sort of thing. A Swedish mathematician, von Koch, decided that instead of subtracting lines, he would add them. And so he came up with this beautiful curve. And there's no particular reason why we have to start with this seed shape; we can use any seed shape we like. And I'll rearrange this and stick this somewhere -- down there, OK -- and now upon iteration, that seed shape sort of unfolds into a very different looking structure. So these all have the property of self-similarity: the part looks like the whole. It's the same pattern at many different scales.
Now, mathematicians thought this was very strange, because as you shrink a ruler down, you measure a longer and longer length. And since they went through the iterations an infinite number of times, as the ruler shrinks down to infinity, the length goes to infinity. This made no sense at all, so they consigned these curves to the back of the math books. They said these are pathological curves, and we don't have to discuss them. (Laughter) And that worked for a hundred years.
And then in 1977, Benoit Mandelbrot, a French mathematician, realized that if you do computer graphics and used these shapes he called fractals you get the shapes of nature. You get the human lungs, you get acacia trees, you get ferns, you get these beautiful natural forms. If you take your thumb and your index finger and look right where they meet -- go ahead and do that now -- -- and relax your hand, you'll see a crinkle, and then a wrinkle within the crinkle, and a crinkle within the wrinkle. Right? Your body is covered with fractals. The mathematicians who were saying these were pathologically useless shapes? They were breathing those words with fractal lungs. It's very ironic. And I'll show you a little natural recursion here. Again, we just take these lines and recursively replace them with the whole shape. So here's the second iteration, and the third, fourth and so on.
So nature has this self-similar structure. Nature uses self-organizing systems. Now in the 1980s, I happened to notice that if you look at an aerial photograph of an African village, you see fractals. And I thought, "This is fabulous! I wonder why?" And of course I had to go to Africa and ask folks why. So I got a Fulbright scholarship to just travel around Africa for a year asking people why they were building fractals, which is a great job if you can get it. (Laughter)
And so I finally got to this city, and I'd done a little fractal model for the city just to see how it would sort of unfold -- but when I got there, I got to the palace of the chief, and my French is not very good; I said something like, "I am a mathematician and I would like to stand on your roof." But he was really cool about it, and he took me up there, and we talked about fractals. And he said, "Oh yeah, yeah! We knew about a rectangle within a rectangle, we know all about that." And it turns out the royal insignia has a rectangle within a rectangle within a rectangle, and the path through that palace is actually this spiral here. And as you go through the path, you have to get more and more polite. So they're mapping the social scaling onto the geometric scaling; it's a conscious pattern. It is not unconscious like a termite mound fractal.
This is a village in southern Zambia. The Ba-Ila built this village about 400 meters in diameter. You have a huge ring. The rings that represent the family enclosures get larger and larger as you go towards the back, and then you have the chief's ring here towards the back and the chief's immediate family in that ring. So here's a little fractal model for it. Here's one house with the sacred altar, here's the house of houses, the family enclosure, with the humans here where the sacred altar would be, and then here's the village as a whole -- a ring of ring of rings with the chief's extended family here, the chief's immediate family here, and here there's a tiny village only this big. Now you might wonder, how can people fit in a tiny village only this big? That's because they're spirit people. It's the ancestors. And of course the spirit people have a little miniature village in their village, right? So it's just like Georg Cantor said, the recursion continues forever.
This is in the Mandara mountains, near the Nigerian border in Cameroon, Mokoulek. I saw this diagram drawn by a French architect, and I thought, "Wow! What a beautiful fractal!" So I tried to come up with a seed shape, which, upon iteration, would unfold into this thing. I came up with this structure here. Let's see, first iteration, second, third, fourth. Now, after I did the simulation, I realized the whole village kind of spirals around, just like this, and here's that replicating line -- a self-replicating line that unfolds into the fractal. Well, I noticed that line is about where the only square building in the village is at. So, when I got to the village, I said, "Can you take me to the square building? I think something's going on there." And they said, "Well, we can take you there, but you can't go inside because that's the sacred altar, where we do sacrifices every year to keep up those annual cycles of fertility for the fields." And I started to realize that the cycles of fertility were just like the recursive cycles in the geometric algorithm that builds this. And the recursion in some of these villages continues down into very tiny scales.
So here's a Nankani village in Mali. And you can see, you go inside the family enclosure -- you go inside and here's pots in the fireplace, stacked recursively. Here's calabashes that Issa was just showing us, and they're stacked recursively. Now, the tiniest calabash in here keeps the woman's soul. And when she dies, they have a ceremony where they break this stack called the zalanga and her soul goes off to eternity. Once again, infinity is important.
Now, you might ask yourself three questions at this point. Aren't these scaling patterns just universal to all indigenous architecture? And that was actually my original hypothesis. When I first saw those African fractals, I thought, "Wow, so any indigenous group that doesn't have a state society, that sort of hierarchy, must have a kind of bottom-up architecture." But that turns out not to be true.
I started collecting aerial photographs of Native American and South Pacific architecture; only the African ones were fractal. And if you think about it, all these different societies have different geometric design themes they use. So Native Americans use a combination of circular symmetry and fourfold symmetry. You can see on the pottery and the baskets. Here's an aerial photograph of one of the Anasazi ruins; you can see it's circular at the largest scale, but it's rectangular at the smaller scale, right? It is not the same pattern at two different scales.
Second, you might ask, "Well, Dr. Eglash, aren't you ignoring the diversity of African cultures?" And three times, the answer is no. First of all, I agree with Mudimbe's wonderful book, "The Invention of Africa," that Africa is an artificial invention of first colonialism, and then oppositional movements. No, because a widely shared design practice doesn't necessarily give you a unity of culture -- and it definitely is not in the DNA. And finally, the fractals have self-similarity -- so they're similar to themselves, but they're not necessarily similar to each other -- you see very different uses for fractals. It's a shared technology in Africa.
And finally, well, isn't this just intuition? It's not really mathematical knowledge. Africans can't possibly really be using fractal geometry, right? It wasn't invented until the 1970s. Well, it's true that some African fractals are as far as I'm concerned just pure intuition. So some of these things, I'd wander around the streets of Dakar asking people, "What's the algorithm? What's the rule for making this?" and they'd say, "Well, we just make it that way because it looks pretty, stupid." (Laughter) But sometimes, that's not the case. In some cases, there would actually be algorithms, and very sophisticated algorithms. So in Manghetu sculpture, you'd see this recursive geometry. In Ethiopian crosses, you see this wonderful unfolding of the shape.
In Angola, the Chokwe people draw lines in the sand, and it's what the German mathematician Euler called a graph; we now call it an Eulerian path -- you can never lift your stylus from the surface and you can never go over the same line twice. But they do it recursively, and they do it with an age-grade system, so the little kids learn this one, and then the older kids learn this one, then the next age-grade initiation, you learn this one. And with each iteration of that algorithm, you learn the iterations of the myth. You learn the next level of knowledge.
And finally, all over Africa, you see this board game. It's called Owari in Ghana, where I studied it; it's called Mancala here on the east coast, Bao in Kenya, Sogo elsewhere. Well, you see self-organizing patterns that spontaneously occur in this board game. And the folks in Ghana knew about these self-organizing patterns and would use them strategically. So this is very conscious knowledge.
Here's a wonderful fractal. Anywhere you go in the Sahel, you'll see this windscreen. And of course fences around the world are all Cartesian, all strictly linear. But here in Africa, you've got these nonlinear scaling fences. So I tracked down one of the folks who makes these things, a guy in Mali just outside of Bamako, and I asked him, "How come you're making fractal fences? 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, and they're very cheap. It 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 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 it on a log-log plot, got the scaling exponent, and it almost exactly matches the scaling exponent for the relationship between wind speed and height in the wind engineering handbook. So these guys are right on target 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 Bamana sand divination. And the same divination system is found all over Africa. You can find it on 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 in the sand randomly, and then you count off, and if it's an odd number, you put down one stroke, and if it's an even number, you put down two strokes. 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." And I said, "Well look, I'll pay you, you can be my teacher, and I'll come each day and pay you." They said, "It's not a matter of money. This is a religious matter."
And finally, out of desperation, I said, "Well, let me explain Georg Cantor in 1877." And I started explaining why I was there in Africa, and they got very excited when they saw the Cantor set. And one of them said, "Come here. I think I can help you out here." And so he took me through the initiation ritual for a Bamana priest. And of course, I was only interested in the math, so the whole time, he kept shaking his head going, "You know, I didn't learn it this way." But I had to sleep with a kola nut next to my bed, buried in sand, and give seven coins to the seven lepers and so on. And finally, he revealed the truth of the matter. And it turns out it's a pseudo-random number generator 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 addition modulo 2, just like in the parity bit check on your computer. And then 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 it'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, Hugo of Santalla brought it from Islamic mystics into Spain. And there it entered into the alchemy community as geomancy: divination through the earth. This is a geomantic chart drawn for King Richard II in 1390. Leibniz, the German mathematician, talked about geomancy in his dissertation called "De Combinatoria." 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 zeros, the binary code. George Boole took Leibniz's binary code and created Boolean algebra, and John von Neumann took Boolean algebra and created the digital computer. So all these little PDAs and laptops -- every digital circuit in the world -- started in Africa. And I know Brian Eno says there's not enough Africa in computers; you know, I don't think there's enough African history in Brian Eno. (Applause)
So let me end with just a few words about applications that we've found for this. And you can go to our website, the applets are all free; they just run in the browser. Anybody in the world can use them. The National Science Foundation's Broadening Participation in Computing program recently awarded us a grant to make a programmable version of these design tools, so hopefully in three years, anybody'll be able to go on the Web and create their own simulations and their own artifacts. We've focused in the U.S. on African-American students as well as Native American and Latino. We've found statistically significant improvement with children using this software in a mathematics class in comparison with a control group that did not have the software. So it's really very successful teaching children 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 seed grant, just to see if folks would be willing to work with us on this; we're very excited about the future possibilities for that.
We've also been working in design. I didn't put his name up here -- my colleague, Kerry, in Kenya, has come up with this great idea for using fractal structure for postal address in villages that have fractal structure, because if you try to impose a grid structure postal system on a fractal village, it doesn't quite fit. Bernard Tschumi at Columbia University has finished using this in a design for a museum of African art. David Hughes at Ohio State University has written a primer on Afrocentric architecture in which 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, it's in the brain. It's in the -- it's in Google's search engine. Actually, the reason that 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 also in some bad things. Self-organization is why the AIDS virus is spreading so fast. And if you don't think that capitalism, which is self-organizing, can have destructive effects, you haven't opened your eyes enough. So we need to think about, 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, that are 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.
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Ad Hominen attack wont get you no where niether will specuation. Again I am not denying the fractals might have impacted but the fact remains Europeans developed the computer, this is a known fact Im not going to play games here...Show me the Computer the machine IN AFRICA developed by Africans..Using your logic the Africans in Timbuctu "Borrowed" or Needed Arabs to teach them Mathmatics and Science found in the manuscripts.
Posts: 8804 | From: The fear of his majesty had entered their hearts, they were powerless | Registered: Nov 2007
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