What an inspiration, someone to admire.
To have such a talent and no way to acquire
an education or a job or a life of his own.
To think what he could do and what he must have known!
He spent his life as a slave, I’m sure he wanted more.
I owe it to him not to waste or ignore
the chances that I’m given, opportunities galore.
I can be anything if I let my mind soar!9
Thomas Fuller was a mathematical prodigy, demeaningly referred to as Negro Tom, condemned to the limited existence of an eighteenth-century rural Virginia field hand, the property of an illiterate, uneducated white couple.
There is little incentive to uncover and preserve historic black achievement, so it remains crucial that legacies such as Fuller’s are recognized and his contributions remembered. Perhaps in this way we can, to some tiny extent, right these grave historical wrongs. A kind of historical Black Lives Matter or Say Her Name.
The closing lines of Thomas Fuller’s Columbian Centinel obituary are heartbreaking:
Had his opportunities of improvement been equal to those of thousands of his fellow-men . . . even a NEWTON himself, need not have been ashamed to acknowledge him a Brother in Science.
Who knows what groundbreaking discoveries Fuller would have made, what he might have invented? Instead he slaved away, a field hand imprisoned on a tiny farm in a racist backwater. The suppression of black genius has surely stunted society as a whole.
In the Western educational system, math is taught as something abstract, removed from everyday life. In contrast, African hairstyling culture is a place where math is unconsciously applied in each step of the process. In 1998 the mathematician Gloria Ford Gilmer conducted research in braiding patterns in New York and Baltimore.10 Gilmer and her assistants interviewed both stylists and clients about tessellations in box braids, brick and triangle-like patterns, a method of dividing the hair that determines its movement. The stylists in Gilmer’s study claim that they are not consciously mathematical, but the process of black hairstyling could not exist without multiple and complex calculations. Measuring the extensions necessary for uniform braids requires algebra, actual braiding itself uses geometry.
Impressed by the ability to create such immaculately uniform braided extensions or by the intricate designs and complex geometric shapes I have seen appearing on my own head, I have asked stylists how they do what they are doing with such astonishing precision. Not once has anybody specifically referenced mathematical calculation. Recently I posted a new style on Instagram. Shortly afterward I received an email asking me about it. The request was from a white designer: “I’m intrigued to know how the stylist divides the geometric sections with such straight parting lines between them? It’s a real work of art! I’d have to do a scale drawing or make a template before starting anything that geometrically complex and precise.”
When I next saw her, I asked my hairdresser how she had designed my previous style and, more generally, how she worked: “I design it as I’m going along. I just know. You’re the academic, you tell me how I know,” she quipped.
The type of knowledge she possesses might be understood as what the American artist and academic Nettrice Gaskins describes as belonging to “embodied memory institutions” or “technologies of the African past.” That this particular stylist is African-Caribbean demonstrates a connection that has been passed down over centuries, sustained across both oceans and time, a direct link back to a past that the European understanding of history describes as unrecoverable.
For Gaskins, cornrowing invokes other African practices that have survived the Middle Passage. She explains that braiding functions as another example of the “weaving or interweaving of cultures, identities, images, fabric and sound”11 that are not only a defining characteristic of African diasporic culture but operate as part of the pool of cultural resources. These constitute part of what sustained the descendants of those stolen Africans through the long dark centuries of exile in the West.
Although most commonly discussed in terms of music, Gaskins observes the same process in cornrowing hair. In fact, much of African cultural production, as well as that of its American descendants, is polyrhythmic. The “music theorist Adam Rudolph describes the weaving of threads or ‘thematic fibers’ in repeated patterns of rhythmic regularity and irregularity as polyrhythm.”12 If an algorithm is the process of following a set of rules to complete a procedure, it is not too much of a stretch to describe braiding as algorithmic. Thus Gaskins builds the case for cornrowing to be described as a technology:
Cornrows are created through braiding the hair very close to the scalp, using an underhand, upward motion to produce a continuous, raised row. Cornrows are often formed in simple, straight lines (rows), but they can also be formed in complicated geometric or curvilinear designs. In mathematical terms, the braiding of hair shows the formal possibilities of geometric variation. Hair braiding demonstrates an inclination for interrupting the expected line; braids are composed through juxtapositions of sharply differing units and abrupt shifts of form. Certain patterns are amenable or open to algorithmic modeling—but “amenable” need not connote the simple—a square is easier to simulate and repeat but the process of braiding, knitting or weaving these shapes into designs is more about complexity arising from simplicity. In other words, it is not the braid itself but the act of interweaving shapes that form the intricate patterns that unify the design. In mathematics and computing the algorithm is a step-by-step procedure for calculations. Algorithmic art is often referred to as computer generated art. However, traditional hair braiders do not use computers to make their calculation . . . Hair braiding is a technology.13
FRACTALS
“Rather than imposing an alien analysis from afar, [we should attempt to] allow the rich complexity of African culture, in all its global diversity, to enter into dialogue with nonlinear dynamics, complexity theory, and other mathematical and computational frameworks in which fractals occupy a central role.”14
Fractal braiding.
Fractals are the shape of the universe, patterns that repeat themselves at many scales. In addition to our organs, fractal shapes make up the world around us: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes are all fractal in design. Our lungs, our circulatory system, even our brain, all are fractal structures. We are fractal. But although we are made of fractals, most of us never think about them.
The Fractal Foundation defines these little bad boys as “infinitely complex patterns that remain the same regardless of scale, created by repeating a simple process over and over in an ongoing feedback loop.”15 Fractals are found throughout indigenous African design yet were only “discovered” by Europeans in 1975, when a Polish mathematician, Benoit Mandelbrot, invented the word.
Mandelbrot used the term to describe a large class of objects not immediately similar but sharing an internal and an external logic. In 1877 the German mathematician Georg Cantor had reignited the infinity debate in Western mathematics. Cantor drew a line and erased the middle third. He then took the two resulting lines and repeated the same recursive process. One line became two, and then four, and so on. This process can be carried out an infinite number of times. An infinite number of lines can be generated and each of these infinite lines would have an infinite number of points along it. Cantor’s work proved that the algebraic numbers are countable and that transcendental numbers are uncountable. This seemingly mundane fact is now standard in the mathematics curriculum, but at that time it was akin to heresy. The problem? Cantor had created (a deceptively simple) method for demonstrating the mind-blowing complexity of infinity. To represent infinity was seen as a direct challenge to God’s omnipotence and beyond the limits of social acceptability.