How crochet helps mathematics and the Great Barrier Reef

Photograph of crocheted coral (image by Margaret Wertheim (cc:by))

The art of crocheting provides a model for understanding both complex math and environmental threats to coral reefs.

This story was originally covered by PRI's Studio360. For more, listen to the audio above.

When a grandmother crochets a baby blanket or an oversized sweater, few people realize that the simple handicraft could be a tool for modeling a complex geometric concept. It could even increase public awareness of hazards to ocean life.

Hypothetical worlds, or spaces, are the foundation of many complex mathematical fields, including one called hyperbolic geometry. This geometry was essential to Einstein's theory of relativity, and is used by scientists in planning space missions. Mathematicians had never been able to create a physical model of the theoretical space that hyperbolic geometry operates within until 1997, when Daina Taimina realized that crocheting held the key.

Here's the science, in a nutshell: If you look at a knit scarf, you'll see that it has parallel lines running vertically down its length. If someone started adding more and more stitches horizontally between each line, the scarf would have a ruffle at the end. In the ruffle, the parallel lines of the scarf are moving farther and farther away from each other as they do on a hyperbolic plane. This is an image that many mathematicians can't fully visualize without being able to touch and see it.

Taimina describes the first time a colleague saw one of her crocheted models: "He was looking at this hyperbolic plane and suddenly he said 'Oh! That's how it looks like!' It just shows how somebody really needs something tactile to visualize."

The crocheted models of hypothetical worlds are being used to raise awareness about very real, and very threatened, coral reefs. When Margaret Wertheim, a science instructor, and her sister Christine, started crocheting their own hyperbolic models, they noticed that if they varied the pattern slightly, the results looked a lot like sea life.

Their discovery led to the creation of an educational exhibit, "The Crochet Coral Reef." Their exhibit has traveled to art galleries and museums around the world, offering workshops on crochet, threats to coral and hyperbolic space. While coral reefs in the ocean keep shrinking, the Wertheims' crocheted reef keeps expanding, as attendees crochet additions to the traveling installation. This arts-and-crafts project has taken math and science concepts out of a potentially anxiety filled classroom and into a warm social setting.

Unfortunately, grandmotherly crochet has become a controversial tool in the mathematical community. Margaret Wertheim believes the controversy stems from veiled sexism. "I think it's related to gender, she says. "I thought it would be less of a gender imbalance, but it turns out, you know, handicrafts are still primarily seen as women's activities. But within the context of doing this feminine handicraft, one is also engaging in our workshops with one of the most difficult areas of mathematics, issues about marine biology, global warming, ocean acidification."

PRI's Peabody Award-winning "Studio 360 with Kurt Andersen" from WNYC is public radio's smart and surprising guide to what's happening in pop culture and the arts. Each week, Kurt Andersen introduces you to the people who are creating and shaping our culture. Life is busy -- so let "Studio 360" steer you to the must-see movie this weekend, the next book for your nightstand, or the song that will change your life.

More PRI's "Studio 360"