african fractals


Since the 1980s Ron Eglash has been documenting and studying the complex fractal systems evident in African braiding, architecture and social society. I believe this is worth sharing because in a time when there is a mad rush to equip Africans with computers and "technology", here we see the brilliant understanding that already exists in these communities for fractal math and binary systems and how that understanding is apart of the long-lived foundation of the social and spiritual make up of these communities.

"By looking at aerial-view photos -- and then following up with detailed research on the ground -- Eglash discovered that many African villages are purposely laid out to form perfect fractals, with self-similar shapes repeated in the rooms of the house, and the house itself, and the clusters of houses in the village, in mathematically predictable patterns.

. . ."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."
(Abstract Culture)

"The relationship between what we do as physicists today and the future that our work engenders is dialogical in the sense that not only do our present actions determine what our future will be, but we must be ever mindful of the impact of our present actions on the future... Through our moral responsibility and awareness of signals and trends, we in effect, 'listen' to what the future has to tell us." (Donnell Walton, Chair, National Conference of Black Physics Students 1995.)

While the temporal traditions of African societies were frequently cited by colonialists as evidence for primitive superstition, they appear today in quite the opposite context: mathematical analyses of traditional African designs, techniques and knowledge systems indicate a wide array of sophisticated indigenous inventions. Like Paul Gilroy's fractal Atlantic, Donnel Walton's invocation of African divination traditions- of listening to the future- is not only useful in its call for greater ethical responsibility, but also as a reminder fo the surprising links between traditional knowledge and modern science.

The modern binary code, essential to every digital circuit from alarm locks to super computers, was first introduced by Leibniz around 1670.

Leibniz has been inspired by the binary-based 'logic machine' of Raymond Lull, which was in turn inspired by the alchemists' divination practice fo geomancy (Skinner 1980). But geomancy is Clearly not of European origin. It was first introduced there by Hugo of Santalla in twelfth century Spain and Islamic scholars had been using it in North Africa since at least the 9th century, where it was first documented in written records by the Jewish writer Aran ben Joseph.

Geomancy is traditionally practiced by drawing patterns in the sand. It begins with four sets of random dashed lines. These are paired off (i.e. summed by addition module two), and the even/odd results recorded with two strokes or one stroke. Four of these binary digits represents one of 16 possible divination archetypes (ruler, travel, desire, etc.) Although the first four are generated by this random process, the following 12 are created by recursively applying the same pairing operation on the binary digits making up the four symbols (a process which can be seen in many other areas of African knowledge systems, c.f. Eglash 1995).

The nearly identical system of divination in West Africa associated with Fa and Ifa was first noted by Trautman (1939), but he assumed that geomancy originated in Arabic society, where it is known as ilm alraml ("the science of sand"). The mathematical basis of geomancy is however, strikingly out of place in non-African systems. Like other linguistic codes, number bases tend to have an extremely long historical persistence. The ancient Greeks held 10 to be the most sacred of all numbers; the Kabbalah's Ayin Sof emanates by 10 Sefirot and the Christian west counts on its "Hindu- Arabic" decimal notation.

In ancient Egypt, on the other hand, base 2 calculation was ubiquitous, even for multiplication and division, and Zaslavsky (1973) notes archeological evidence linking it to the use of doubling in the counting systems of sub-Suharan Africa. Kautzsch (1912) notes that both Diodorus Siculus and Oblian reported that the ancient Egyptian priests "employed an image of truth cut in halves."

Doubling is a frequent theme in African divination and many other African knowledge systems, connecting the sacredness of twins, spirit doubles, and double vision with material objects, like the blacksmith's twin bellows and the double iron hoe given in bridewealth. In a recent interview in Wired, Brian Eno claimed that the problem with computers is that they "don't have enough African in them". Eno was, no doubt, trying to be complimentary, saying that adaptive rhythm and flexibility is a valuable attribute of African culture. But in doing so he obscured the cultural origins of digital computing, and did an injustice to the very concept he was trying to convey. Take, for example, Henry Louis Gates' (1988, pp. 30) use of a recursive doubling description when discussing the relations between divination and sexuality in West African traditions:

The Fon and Yoruba escape the Western cersion of discursive sexism throught he action of doubling the double; the number 4 and its mul are sacred in Yoruba metaphysics. Esu's two sides "disclose a hidden wholeness," rather than closing off unity, through the opposition, they signify the passage from one to the other as sections of a subsumed whole.

The binary coding of traditional African knowledge systems, like that of their antecedents in modern computing networks, is neither rigid nor arhythmic; its beat is a heritage heard by those who listen to the future. (source)

Ron Eglash speaking at TED

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