By Last year an LA gallery exhibited a paper model of the Menger sponge, a curiosity of geometry that resembles a Rubik’s Cube eating itself from the inside out. It took 66,048 business cards, nine years, and hundreds of folders to make. The show was set up by the Institute for Figuring, an organization tickled by big, brainy concepts expressed through everyday objects. On October 13 the IFF brings its latest exhibit to the Cultural Center: a 40-foot-long (and growing) crocheted model of the Great Barrier Reef that doubles as a model of hyperbolic space. The Chicago reef’s colors are as shocking as the ones in undersea photos of the real thing–hot pink, Bakelite orange, ice blue, and white in spots to show how the reef “bleaches” and dies. The project has been likened to the AIDS Memorial Quilt–both a form of collective protest and a tribute to life that’s being destroyed.

The IFF was founded in 2003 by Margaret and Christine Wertheim–twin sisters from Queensland, Australia–and according to its Web site is “dedicated to the poetic and aesthetic dimensions of science, mathematics and the technical arts.” It organizes exhibits and lectures (recent talks were on “the mathematics of paper folding” and “the physics of snowflakes”) around LA, where Margaret, a science writer, and Christine, a professor of critical studies at CalArts, are now based. In 2005 Margaret Wertheim heard about a breakthrough in geometry involving crochet; the sisters immediately wanted to make an IFF project out of it.

The discovery concerned non-Euclidean geometry. Euclidean geometry has been around since about 300 BC, when the Greek mathematician Euclid wrote what remains the best-selling math textbook of all time, Elements. It includes five short statements about basic geometry. The first four, which concern the nature of straight lines, circles, and right angles, are easy to swallow and universally considered mathematically sound. But the fifth, “parallel” postulate is trickier. It says that if you’ve got a straight line and a point outside that line, you can draw exactly one straight line through that point that won’t ever collide with the first line–no more, no fewer. Mathematicians realized that number five held up only if you stayed on the Euclidean playing field–that is, as long as the plane on which the lines were drawn was flat. If space itself was curved, there might be zero or hundreds of lines through a given point parallel to another line.

By the 19th century mathematicians were imagining space that grows exponentially; they called it hyperbolic space. An infinite number of lines could be drawn through a point in hyperbolic space that would never touch the first line, since the space between them was always growing.

It’s a complicated theory to ask someone to envision, like trying to explain an Escher print without having one handy. In the 1970s mathematicians starting using 3-D paper models folded like origami to show hyperbolic space, but the models were difficult to make and too delicate to be practical.

In 1997 a Cornell math researcher named Daina Taimina made the connection between hyperbolic space and one of her hobbies, crochet. Taimina grew up in Latvia in a family full of crafty women and has been an avid crocheter all her life. She knew that hyperbolic space is supposed to “ruffle up” along its outer edge–the edge constantly grows from a given point and crinkles as it spreads, like the edge of a lettuce leaf. Taimina crocheted a tight circle of loops using a simple chain stitch. She added a longer row around it, and then a longer one around that. When the circle got wide enough, its edge started to ruffle. There was nothing special about the method she used; it’s an old crochet technique called “increasing.” Crocheters know they can get a tight ruffle by adding lots of stitches with each new row, or a loose wave with just one or two extra stitches each go-round.

If you took one of Taimina’s crochet models of hyperbolic space and stitched onto it the components of Euclid’s fifth postulate–a straight line and a point outside of it–you could stitch any number of lines through the point that would never intersect with the original line; you need just two such lines to disprove the postulate. The secondary lines look curved when viewed from above, but folding along them proves they’re perfectly straight. Taimina’s discovery is what mathematicians had been hunting–a physical model of hyperbolic space, one that could be folded this way and that without falling apart.

When the Wertheims learned about Taimina’s work, they immediately thought of the reef forms off the coast of Queensland where they grew up. In Taimina’s geometric shapes, they saw wispy kelp, columnlike sea anemones, and bunchy corals. Thanks to global warming and pollution, scientists had predicted the Great Barrier Reef would be gone in another 30 years. On the IFF’s Web site, the Wertheims posted instructions on how to crochet a model of hyperbolic space and invited crafters everywhere to send in their own pieces in homage to the reef.

In the spring the Wertheims contacted the organizers of the Chicago Humanities Festival about exhibiting the Hyperbolic Crochet Coral Reef. Over the last several months, the Jane Addams Hull-House Museum has organized locals to crochet small pieces to be added to contributions the IFF has already received and is still soliciting from people around the world for upcoming shows. All summer there were gatherings–at the museum, yarn shops, schools, and in crocheters’ living rooms–where (mostly) women stitched their individual pieces into a subreef. The Hull-House Museum sits on the UIC campus in the former home of Jane Addams and Ellen Gates Starr, founders of the Hull House settlement for working-class women. “Addams believed that every member of society needed to vote, but that it was also important for every member to contribute to the ‘cultural capital’ of society,” says Catherine Chandler, a museum staffer. She says the subreef includes the work of more than 100 crocheters and expects that when it’s joined with the IFF’s reef, the exhibit won’t even fit in the Cultural Center’s Chicago Rooms. If there’s overflow, the museum will host a smaller exhibit.

Arcadia Knitting, run by sisters Kathy and Sharon Kelly in Edgewater, donated yarn and hosted a crochet circle. Kathy Kelly says the project relieved many crocheters’ closets of the “pound of love,” or heap of too-bright or too-weird yarn remnants that never fit into new projects. “On the coral reef, it turns out, shocking pink is a natural color,” she says. “And, I don’t want to sound like a yarn snob, but these hyperbolic forms respond better to the cheap, squeaky acrylic. People were able to use up all the crazy stuff they had.”

In some places Jewel and Dominick’s bags were used instead of yarn, both to recycle and to protest the Great Pacific Garbage Patch–roughly three million tons of trash, much of it nonbiodegradable plastic, trapped at the center of the North Pacific Gyre.

Cheryl Rogers, a life coach, grandmother, and lifelong Stony Island resident, was leading a summer-camp crochet circle made up of fourth- to seventh-grade girls from Phoebe A. Hearst Elementary, near Midway, when she found out about the Chicago Reef Project. “The first day of camp, they were literally crying. They wanted to quit. They threw their needles across the room. And they kind of segregated themselves, into blacks, Mexicans, and Puerto Ricans. Somewhere around the third or fourth week, they started sharing stitches. They started laughing. Then they started sitting in one big group.”

Rogers took them to a Chicago Reef Project workshop at the Cultural Center in August, where Margaret Wertheim showed slides of the work in progress. “The girls had brought their hooks and they were sitting there duplicating what they were seeing in the PowerPoint presentation. On the bus back to school they all sat in the back, starting their contributions for the reef. They called me to the back because they really wanted to talk about the environment. One girl said she had been proud that her family recycles, but now that she thought about it, if they stopped using plastic altogether, there wouldn’t be a need to recycle. By this time, camp was over. So I said, ‘Let’s meet one more time.’ I bought yarn from Wal-Mart one afternoon the next week and headed to the school. There was no one there but the cleaning crew, getting ready for school to open. The whole building was empty. Then the girls came in and they were all carrying bags of contributions they had made at home. When we put them all on the table, it was stacks and stacks and stacks. These were girls who had never heard the words ‘crochet’ or ‘coral reef’ in their lives.”

Hyperbolic Crochet Coral Reef

Sat 10/13 through Sun 12/16, Chicago Cultural Center, 78 E. Washington, 312-744-6630. F

Art accompanying story in printed newspaper (not available in this archive): Jon Randolph (crocheters), the Institute for Figuring/Alyssa Gorelick (garden).