Posted by: Dale Griffiths Stamos
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How do coral reefs, geometry, crochet, and environmentalism come together? Well ask Margaret and Christine Wertheim, Australian twin sisters who are two of our profile subjects in RenWomen: What Modern Renaissance Women Have to Teach Us About Living Rich, Full Lives. These two sisters are each exceptional in their own fields. Margaret is a trained physicist, mathematician, computer scientist, and has pursued successful careers in science writing, and public speaking. Christine has a PhD in literature, is a poet, critic, performer, museum curator, and teaches creative writing and critical studies at the California Institute of the Arts.
But they have also created an amazing synergy by bringing their various skills together to found the Institute for Figuring, “The mission of the Institute of Figuring,“ explains Margaret, “is to engage people with science and mathematics by looking at the poetic and aesthetic dimensions of these fields.” And there is no better example of this kind of synthesis than their Project Coral Reef, a project which, as the IFF website explains: “resides at the intersection of mathematics, marine biology, handicraft and community art practice, and responds to the environmental crisis of global warming and the escalating problem of oceanic plastic trash.” Whoa! How you may ask, does it do all that?
It began with the discovery in 1997 by Cornell mathematician Daina Taimina, that through crochet, one could create a model of a mathematical structure many mathematicians thought was impossible to model. This structure is a non-Euclidean geometry called hyperbolic space, and crochet is the perfect vehicle for demonstrating its strange crenulated properties.
For years, mathematicians had been trying to model hyperbolic geometry on computers, but with no success. When Margaret was asked by TED interviewer, K. L. Mulholland, why this was, she explained: “We are moving into the age of being able to simulate more and more things on computers and we are coming to realize how mind-bogglingly complex the world is which we are trying to simulate. The fall of a handkerchief in the wind is hard to simulate, and yet the handkerchief does it effortlessly. In some sense, the handkerchief knows something; it can do something that our best computer engineers can’t do.”
The sisters met Daina in 2003. As Christine explains it: “She'd been crocheting [her models] for six or seven years, and she was using them in her classes at Cornell. Daina's models looked a certain kind of a way. Daina and Margaret were very interested in making them mathematically perfect. But I'm not that kind of person, so I started playing. Using pink wool and fluffy wool and sparkly wool… I changed the recipe somewhat. They were still essentially hyperbolic, but not perfectly so.
“And then I just had a pile of them on the coffee table, and I said to Margaret, ‘It looks like a coral reef!’ Because I wasn't doing them perfectly, and because I had embedded them in pink and orange and fluffy, I made them look like organic things which also made them look like corals.”
It turns out that corals are essentially hyperbolic. There are also other things in nature that share this geometry as well, such as lettuce leaves, cactuses, and sea slugs. “There was a theorem among mathematicians,” Margaret comments wryly, “that you couldn't have models of this geometry in the physical world. They could not see that natural structures around them were doing this. And I once asked some mathematicians, why didn't they realize it? And their brief answer was ‘I guess there aren't many mathematicians out there looking at sea slugs.’”
The Australian twins, having been brought up near the Great Barrier Reef, also saw their reefs as environmentally relevant. They are concerned about how, due to the influence of global warming, coral reefs are dying out worldwide. As Margaret explained in the Ted Talk she gave in 2009: “Corals are very delicate organisms, and they are devastated by any rise in sea temperatures. It causes these vast bleaching events that are the first signs of corals being sick. And if the bleaching doesn't go away -- if the temperatures don't go down -- reefs start to die.”
Well the twin sisters’ coral reef went viral. First asked to fill a small room with their reef at the Andy Warhol museum, they were subsequently commissioned to fill larger and larger gallery spaces. And what started as a two woman endeavor expanded into community projects across the globe involving over 7000 people (predominantly women.) Margaret says: ““One of the reasons that the reef project has been so successful and gone on so long is that it engages so many women about science.” And what these reefs demonstrate is something so many women already intuitively know: Knowledge is not just something abstract. It is a hands-on experience!
For years, mathematicians had been trying to model hyperbolic geometry on computers, but with no success. When Margaret was asked by TED interviewer, K. L. Mulholland, why this was, she explained: “We are moving into the age of being able to simulate more and more things on computers and we are coming to realize how mind-bogglingly complex the world is which we are trying to simulate. The fall of a handkerchief in the wind is hard to simulate, and yet the handkerchief does it effortlessly. In some sense, the handkerchief knows something; it can do something that our best computer engineers can’t do.”
The sisters met Daina in 2003. As Christine explains it: “She'd been crocheting [her models] for six or seven years, and she was using them in her classes at Cornell. Daina's models looked a certain kind of a way. Daina and Margaret were very interested in making them mathematically perfect. But I'm not that kind of person, so I started playing. Using pink wool and fluffy wool and sparkly wool… I changed the recipe somewhat. They were still essentially hyperbolic, but not perfectly so.
“And then I just had a pile of them on the coffee table, and I said to Margaret, ‘It looks like a coral reef!’ Because I wasn't doing them perfectly, and because I had embedded them in pink and orange and fluffy, I made them look like organic things which also made them look like corals.”
It turns out that corals are essentially hyperbolic. There are also other things in nature that share this geometry as well, such as lettuce leaves, cactuses, and sea slugs. “There was a theorem among mathematicians,” Margaret comments wryly, “that you couldn't have models of this geometry in the physical world. They could not see that natural structures around them were doing this. And I once asked some mathematicians, why didn't they realize it? And their brief answer was ‘I guess there aren't many mathematicians out there looking at sea slugs.’”
The Australian twins, having been brought up near the Great Barrier Reef, also saw their reefs as environmentally relevant. They are concerned about how, due to the influence of global warming, coral reefs are dying out worldwide. As Margaret explained in the Ted Talk she gave in 2009: “Corals are very delicate organisms, and they are devastated by any rise in sea temperatures. It causes these vast bleaching events that are the first signs of corals being sick. And if the bleaching doesn't go away -- if the temperatures don't go down -- reefs start to die.”
Well the twin sisters’ coral reef went viral. First asked to fill a small room with their reef at the Andy Warhol museum, they were subsequently commissioned to fill larger and larger gallery spaces. And what started as a two woman endeavor expanded into community projects across the globe involving over 7000 people (predominantly women.) Margaret says: ““One of the reasons that the reef project has been so successful and gone on so long is that it engages so many women about science.” And what these reefs demonstrate is something so many women already intuitively know: Knowledge is not just something abstract. It is a hands-on experience!
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