A woolly exploration of hyperbolic space and biology

"Crochet Coral and Anemone Garden" with sea slug by Marianne Midelburg. Photos © The IFF by Alyssa Gorelick.

"Crochet Coral and Anemone Garden" with sea slug by Marianne Midelburg. Photos © The IFF by Alyssa Gorelick.

Kate:  Can I use my grandmother’s crotchet hooks to explore hyperbolic space and the science of evolution? A collaborative science/art project created by Queensland sisters Margaret and Christine Wertheim invites people to do just this. The Crotchet Coral Reef Project, is an initiative of the Institute for Figuring (IFF) founded by science communicator Margaret and Art philosopher Christine to promote science communication to audiences who don’t follow mainstream science media (which is most people!).

The reef project was inspired by the work of mathematician Dr Daina Taimina who discovered that she could crotchet a manipulable physical model of hyperbolic geometry. The concept of hyperbolic space emerged as 18th century mathematicians grappled with the realization that there are spaces (such as curved planes) where parallel lines do not stay the same distance apart but instead curve away from each other. While mathematicians could grasp the concept it has been difficult to visualize. A keen crotcheter, Dr Taimina discovered that with a pattern of increasing the number of stitches in each row she could create a crotchet surface that represented a theoretical quality of hyperbolic space. The crenellation and ruffles of the resulting crotchet surface reflected the hyperbolic quality of exponential expansion away from any point. Dr Tamina’s models were in fact the first models of hyperbolic space.

When Margaret Werheim, learnt of Dr Tamina’s crotchet models she noticed that grouped together they bore an undeniable resemblance to coral. Margaret and Christine invited people through the IFF website to contribute to a crotchet coral reef that drew responses from around the world, including an invitation from The Andy Warhol Museum to an exhibition exploring artist’s responses to global warming.  This led to invitations to other exhibitions and spawned ‘satellite reefs’ around the world. Coral reefs have now been created in cities across North America, Europe and Australia (the Sydney Powerhouse recently exhibited a crotchet reef). The project expanded and morphed way beyond the initial vision of the Wertheim sisters drawing collaboration from diverse crotcheters around the world.

The exciting evolution of the project reflects another of its educative aspects. The process of coral crotchet involves repetition of a small set of steps. Small changes to the underlying pattern, combined with variation due to quality of yarn and tightness of stitch results in the possibility of endless varieties of crotchet organisms. Sometimes seemingly insignificant changes have resulted in surprising results. Thus the expanding taxonomy of the crotchet coral reef also gives insight into processes of evolution in the natural world where a wondrous variety of species has resulted from minor modifications in genetic coding. Further insight into biology comes from the anatomy of the coral creations. Hyperbolic geometry turns out to be the underlying geometry of many living organisms. For stationary filter feeders like corals it is a very beneficial form because it maximizes surface area in a limited volume. Maximizing surface area is beneficial for many life forms and hyperbolic geometry can also be found in kelps, sponges, sea slugs, land plants and seed pods. A sister project to the crotchet reef is a crotchet cactus garden.

I connected with this project on different levels. I was attracted to idea of continuing a tradition of feminine handicraft while contributing to a collaborative project highlighting a contemporary problem – the threats facing coral reefs. As an ecologist, I was fascinated by the way the crotchet process and hyperbolic geometry gives insight into biological processes. However I also found myself enjoying learning about hyperbolic mathematics more broadly, which was definitely a surprise. So the coral reef projects demonstrated to me the power of science/art collaboration to engage wide audiences and to communicate science in novel ways. The surprising answer to my question? Yes I think I can use my grandmother’s crotchet needles to explore mathematics and evolution.

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