Figuring Forms

Crochet Coral Reef by Margaret and Christine Wertheim and the Institute For Figuring, at the Museum of Arts and Design, NYC, 2017. Photo courtesy of MAD, by Jenna Bascom.

“To figure: to form or shape, to trace, to reckon or calculate, to represent in a diagram or picture, to ornament or adorn with a design or pattern.” Thus the Oxford English Dictionary defines the act of figuring, a word equally resonant in mathematics, science and art. Numbers are figures, as are scientific diagrams. Artists draw human figures, which are also becoming a locus of constant measuration as we count steps and calories to figure our physiologies. Textile makers weave patterned figures on jacquard looms; dancers spin cotillion figures across ballroom floors; literature is alive with figures of fun and speech, to say nothing of the farting figures in the margins of medieval manuscripts casting scatological comments on serious texts. As cognitive beings, we are continually figuring things out.

Although Western culture has long privileged symbolic modes of representation—the equations of physics, the DNA code of genetics, the algorithms and binary codes of computer science—formal relations thus described can often also be realized in concrete figurative forms. Fractals can be constructed out of business cards, platonic solids can be woven from bamboo sticks, tessellations can be cross-stitched, and the projective plane can be knitted. Even the logic underlying computation has analogs in two- and three-dimensional geometric models.

Not infrequently, abstract relations revealed by math and science may be modeled by material systems, opening up possibilities for tangible play with ideas. At the practice I’ve developed with my Institute For Figuring—co-founded with my twin-sister Christine Wertheim—we aim to create situations where people can experiment with symbolic codes via embodied play activities, thereby combining means of production frequently put in the category of “art” with modes of exploring knowledge usually affiliated with “science.”

The power of such figuring is witnessed in a project we do that uses handicraft to cast unexpected light on the foundations of geometry and processes of Darwinian evolution. In 1997, Cornell mathematician Daina Taimina discovered how to crochet models of hyperbolic space, an alternative to the usual Euclidean variety and an innovation that historically prefigured the mathematics underlying general relativity. Through domestic craft we can create structures long thought to be impossible, for geometers spent hundreds of years trying to prove that non-Euclidean surfaces couldn’t in principle exist. With a ball of yarn and a crochet hook we can render visible such pathologies as diverging parallel lines and triangles whose interior angles sum to zero degrees. Figuring with our fingers, craft becomes a gateway to the dreamlike abstractions of non-Euclidean space.

Nature meanwhile has been reveling in its possibilities since at least the Silurian age. Corals, kelps, sponges and sea-slugs, with their frilly crenellated forms, are variants of hyperbolic or ‘negative curvature’ surfaces. Though brainless and sessile, corals are capable of realizing in their bodies the geometric equivalent of a negative number, thereby raising questions about what it means to do and to know mathematics.

Nothing in the organic realm is mathematically perfect. Just as there are no true spheres in nature, but lots of sphere-like forms—eggs, sea urchins, planets—so living things only manifest wonky hyperbolic forms. And this too can be simulated with crochet. To move from Taimina’s geometrically perfect structures into a sim-ecology, we queer the code, deviating from, and embellishing on, her simple algorithm as we bring into being a taxonomy of crochet coral “species.” As life on Earth begins with simple cells and develops into ever-more complex forms, so our crochet forms capitulate a Darwinian transformation. There is now a crochet “tree of life.”

During the past decade the Crochet Coral Reef project has engaged over 10,000 people in a dozen countries all collectively contributing to a dynamically developing archipelago of simulated reefs. Handmade and code-based—an authentic digital technology—the Reef project constitutes a global-scale citizen-produced artwork, and an open-ended experiment in applied geometry and emergent algorithmic complexity. We crochet reefers not only take aesthetic inspiration from the living reefs we emulate, but together we enact processes underpinning their formation.

In the age of global warming, the Crochet Reef is of course also a response to the decimation of living reefs by climate change. On the night in 2005 that Christine and I started crafting our sim we joked to ourselves that if the Great Barrier Reef ever died out our reef would be something to remember it by. As I write here now from Australia that unthinkable prospect looms as a ghastly probability. Spawned from an alliance of art, science, and collaborative practice, this figurative simulation proposes a metaphor both monumental and tender: “We are all corals now.”


Margaret Wertheim

Margaret Wertheim is a writer and artist whose work focuses on the aesthetic and poetic dimensions of science and mathematics.