Cantor was defamed. Leopold Kronecker, a prominent mathematician and head of the mathematics department at the University of Berlin, said his ideas were a “grave disease,” infecting the discipline of mathematics. Kronecker accused Cantor of being a “scientific charlatan,” a “renegade” (is that so bad?), and, most extraordinarily, a “corrupter of youth.” The combined effect of all this and the realization that you could create a set whose number of elements were larger than infinity proved too much for Cantor to cope with. He had a breakdown and was swiftly dispatched to a sanatorium.
However, the idea didn’t entirely disappear with Cantor. In 1904, the Swedish mathematician Helge von Koch experimented with the incendiary concept, daredevil that he was! The difference now was that instead of subtracting lines, he added them together. As Ron Eglash explains, the result was a shape, or shapes, that shares the property of self-similarity: the part looks like the whole. It’s the same pattern on many different scales. Once more these new structures were looked upon with mistrust, dismissed as pathological, and pretty much consigned to the dustbin of mathematical history, until Mandelbrot in 1975. Or so the official history goes . . .
The ancient Greeks found infinity so potentially destabilizing that Aristotle redefined it. Infinity was to be understood as a limit one could tend toward but which must not be considered a legitimate object of inquiry in itself. Until the disruptive Cantor came along, this set the tone for the attitude of European mathematicians.
Yet in Africa a very different fractal landscape was unfolding. Eglash’s research reveals that the designs of African villages, which European colonial observers considered disorganized and thus primitive, were in fact anything but. It “never occurred to them that Africans might have been using a form of mathematics that they hadn’t even discovered yet.”16 Rather than the mud huts of African primitivism, Eglash discovers buildings not only constructed in ways that repeat patterns from the natural world but whose design demonstrates the mathematical and philosophical concept of infinity: “Recursive models: buildings within buildings, the same shape but decreasing in scale, down to minute models of spirit villages. And housed within those spirit villages are more spirit villages, which contain tinier spirit villages,”17 ad infinitum!
Fractal geometry in African Fractals: Modern Computing and Indigenous Design by Ron Eglash. It demonstrates the scaling in the cornrow style known in Yoruba as ipako elede.
From Ron Eglash, African Fractals: Modern Computing and Indigenous Design (Rutgers University Press, 1999)
Eglash discovers that fractal technology is evident across the continent, from sculpture to Yoruba idire cloth design or the kente cloth of Ghana, and that it is often at its most developed in the divination knowledge systems. Accordingly, the most complex example of an algorithmic approach to fractals that he finds is not in geometry but, as we saw, the symbolic code of Bamana sand divination. And, he explains, the symbols of the same divination system are found all over Africa, from the east to west coast. But what is of most interest for us is the frequency with which this evidence of fractals and concepts of infinity appears in traditional African hairstyles. In stark contrast to themes of criminality or lack of class, African cornrow styles showcase the mathematical concepts that are a part of everyday life across the continent.
Eglash describes the way in which even the humble ipako elade reveals the use of mathematical calculation. Ipako elade demonstrates conformal mapping, where the pattern is fitted along the contours of an already existing structure.18 Although adaptive scaling of this nature has less mathematical sophistication than some of the other braided styles, or the deterministic chaos of the Bambara divination system created from a binary code, it is important to include it nonetheless. By adapting the scale of a pattern to fit various forms, a number of aesthetic and practical effects can be achieved and, in the case of escaping slavery, it’s a practical application that might just save your life.
While conformal mapping exists where a pattern follows the contours of a preexisting object, Eglash cautions against interpreting this as the work of artisans who are strongly guided by concrete forms. To describe it in that way has echoes of the racist colonial discourse that purported that Africans lacked the intellectual capabilities of abstract thought. On the contrary, Eglash argues that “Adaptive scaling can also be seen in more abstract examples: global transformations in which space itself is distorted. This is a common operation in Western geometry, the most frequent example being a mapping between the plane and a sphere.”19 And we need look no further than the classic Yoruba hairstyle koroba (“bucket”) to see a plane design mapped onto a spherical surface.
Braiding is an embodied display of what the photographer Bill Gaskins calls “ancestral recall.” It operates as a bridge spanning spaces between the past, present, and future. Braiding is a tangible material thread connecting people separated by thousands of miles and hundreds of thousands of years.
Almost 10,000 miles away from Yorubaland is a Colombian town named San Basilio de Palenque. Founded some time at the dawn of the sixteenth century, the epic history of the Palenque is little known to the wider world. One of numerous palenques that once existed, San Basilio is the only one that remains today. It has a population of approximately 3,500 people and has been recognized since 2005 by UNESCO as a Masterpiece of the Oral and Intangible Heritage of Humanity. A style very similar to the Yoruba koroba can be found in the Palenque too, although the Colombian version goes by another name. According to folklore, la totuma is inspired by an organic vase like a calabash used by the indigenous people to drink water. Given koroba’s and la totuma’s roles as representing vessels that collect water, the historical meaning behind la totuma makes perfect sense. The inhabitants of the Palenque describe it as a hairstyle that reflected their experiences in the “continent that made us cry.” La totuma is a container for tears.
Palenque hairstyles are rich with meaning, and some of them have been no less than lifesaving. The founder of San Basilio de Palenque was a man named Benkos Biohó. He was a member of the royal family who ruled the islands off the coast of what is today Guinea-Bissau. In the 1590s Biohó was captured by a Portuguese slave trader before being “resold” numerous times throughout the 1590s.
Biohó was emphatically not about that life.
An early attempt at escape was cut short, but by 1599 our intrepid hero had escaped again, making his way into the marshy wetlands southeast of Cartagena in what is now Colombia. There, along with ten others, Biohó founded the Palenque, the first independent settlement in the entirety of the Americas. Even more remarkable is the fact that not only was it a free settlement, it was free and black, having been founded and entirely populated by Africans. Biohó’s army came to dominate all of the surrounding Montes de María region, and the extensive intelligence network he created helped thousands of enslaved people escape and find refuge in the Palenque.
One of the most remarkable tools of this intelligence network was the use of hair braiding. Hair was utilized as a form of mapping that would be unintelligible to the Spanish. Braided maps worked as a type of underground railway, but the emphasis was on hiding in plain sight. Women would encode important messages into their hair patterns; it was a means of communication for the enslaved, enabling them to share plans and eventually make their way to liberation and freedom in the Palenque. For example, the hairstyle “The Mother” is described as an “unequivocal sign that everything was planned”; “The women elaborated the hairstyle as a form of signal . . . So that the escape could happen in blocks of four slaves.”20