The annual spawning season begins on Australia’s Great Barrier Reef after the full moon in late October and November each year. Coastal coral species, where water temperatures are warmer, spawn first, followed by the main event, offshore coral species. Last year, this spectacle of nature was discovered in the wool of his two new colonies of crocheted coral reefs, a long-running collaborative art of craft and science now housed in the Schloss Museum in Linz, Austria, and the Carnegie Museum of Art in Pittsburgh. It coincided with breeding.
To date, approximately 25,000 weavers (“reefers”) have created a global archipelago of more than 50 coral reefs. It is both an ode and a plea to the marine rainforest ecosystem, which is under threat from climate change. The project also explores mathematical themes, as many living coral reef organisms biologically approximate the strange curvature of hyperbolic geometry.
Within the realm of two dimensions, geometry deals with the properties of points, lines, figures, and surfaces. The Euclidean plane is flat, so it has zero curvature. In contrast, the surface of a sphere exhibits a constant positive curvature. At every point, the surface bends inward toward itself. And a hyperboloid exhibits a constant negative curvature. At every point, the surface curves away from itself. Reef life thrives on hyperbole, so to speak. The curved structure of corals maximizes nutrient uptake, and the nudibranchs navigate through the water with frilly flanges.
In her work, marine forms are modeled in crochet to look like the real thing. A bit like Monet’s water lilies, crocheted corals are an abstract representation of nature, said Christine Wertheim, an artist and writer now retired from the California Institute of the Arts. Dr. Wertheim is the artistic driving force behind the project, which she created with her twin sister, Margaret Wertheim, who is a Science writer responsible for the scientific and mathematical elements and management. The Australian Wertheim family, who live together in Los Angeles, separated Mother Her Leaf from her living room months ago in 2005.
A crochet reef exhibition usually has two main components. The Wertheims offer pieces from their collection, which they have crocheted over the years, as an anchor of sorts. It also incorporates works by selected and accomplished international contributors. One is a “bleached reef,” reminiscent of corals stressed by rising ocean temperatures. Another is a “coral forest” made of thread and plastic, lamenting the debris contaminating coral reef systems.
Then, in response to an open call, a wide range of volunteers put together a pageant of individual specimens gathered at the Satellite Reef, directed by a team of local curators under the guidance of the Wertheim family. The Wertheims liken this hive mind to a friendly iteration of the Borg in “Star Trek: The Next Generation.” All contributors are credited.
The largest satellite reef to date was assembled in 2022 at the Frieder Burda Museum in Baden-Baden, Germany, with around 40,000 coral fragments from around 4,000 contributors. The Wertheim family calls this the Sistine Chapel of crocheted reefs (documented in fancy documents) exhibition catalog). However, the exhibits at the Linz Castle Museum, which is dedicated not only to natural science but also to art and culture, are reminiscent of the work of the painter Giuseppe Arcimboldo. Wertheim said his collage portraits made from depictions of fruits, vegetables and flowers are “fantastic, foreign, and also very diverse,” interesting and clever.
The Lindt Satellite Leaf is made up of approximately 30,000 pieces put together by 2,000 crocheters. As the exhibition text states, the various parts take colorful inspiration from traditional Austrian “craftsmanship,” and the vast, glowing coral walls are reminiscent of artist Gustav’s Klimt. But in the Wertheim family’s view, the crochet coral project proves that great art is not always created by lone geniuses, but also by communities. They pointed out that in the art world this is a radical idea, but in science, large-scale collaborative projects and papers have been published. thousands of authors It’s not unprecedented.
Primitive bamboo crafts
Scientifically, the Lindt exhibit has special symbolism. Because, as the story explains, this region was previously occupied by an “ancient pristine sea filled with coral,” the ruins of which can still be found in Upper Austria’s basins and the Alps. I can.
The mathematical side of this story intersects (at a distance) with research by applied mathematician Shankar Venkataramani and his students at the University of Arizona. They use an idealized model to Studying hyperboloids in nature. “It’s all around us,” said Dr. Venkataramani. Consider curly kale being everywhere. “The question is, why is it all around us?” The textbook benefit of evolutionary theory is that it helps optimize processes such as circulation and nutrient absorption, he said. His group’s research has shown additional benefits, such as giving organisms a structural “sweet spot” that is neither too rigid nor too flexible, allowing them to “move and change shape with a small energy budget.” There is.
When Margaret Wertheim, who studied mathematics, physics and computer science at university, learned about hyperbolic geometry, she thought it was “a little ridiculous.” She accepted the principle more on the basis of her faith than on understanding it. Still, she said, through crochet models, “you can learn very deeply what hyperbolic structure is. I think it has a very powerful educational effect.”
feel the frills
It was only a quarter of a century ago that it was discovered that you could use a crochet hook to create looped hyperboloids. Daina Taimina, now a retired mathematician from Cornell University, made this discovery while preparing a geometry course. “I needed to feel it,” Dr. Taimina said. His research with the Wertheims in the early to mid-2000s planted the seeds for their reef project (and his professional book “Field guide to hyperbolic space”) and Dr. Taimina’s outreach workshops and shows (and her own book, “Hyperboloid crochet adventure”).
Even further back in 1868, Italian mathematician Eugenio Beltrami built a parchment model of a hyperboloid and rolled it up to create a negative surface called a pseudosphere (which he did). A century later, mathematician William Thurston developed a similar idea on his own using paper and tape.
Dr. Taimina came across the crumbling paper version in 1997 at the workshop of her partner David Henderson, a mathematician at Cornell University. Dr. Henderson learned model making techniques from Dr. Thurston. On the spot, Dr. Taimina began building something more flexible and durable for her own courses. When she tried knitting it, the result was too squishy and unwieldy. Crochet proved to be the perfect medium. Dr. Taimina devised a simple algorithm that increases the number of stitches by a constant ratio of N+1. For example, N=6. Crochet 6 eyes, crochet the 7th eye and increase it to 2 eyes to 1. Repeat, row by row.
“You can experiment with different ratios, but not with the same model,” she warned in the article.mathematical intelligence She wrote it with Dr. Henderson. “You only get a hyperboloid if you always increase the number of stitches by the same proportion.”
Dr. Taimina also joined Dr. Henderson, who passed away in 2018, as a co-author on the revised edition of his book “.experience geometryIn it, he explained his belief that “mathematics is a natural and deep part of human experience, and that meaningful experiences in mathematics are accessible to everyone.”
The Wertheim family adopted a similar vision at their nonprofit organization, the Figuring Institute. The nonprofit organization’s projects are motivated by the belief that people can play with and aesthetically appreciate mathematical ideas, and thereby gain understanding of them.
As a scientifically trained Margaret, her instinct was to follow Dr. Taimina’s algorithm to the end. But Christine’s artistic sensibility was to break her rules and go wild. For example, crochet several rows and she increases every third stitch, then she switches every fifth stitch, then she switches every second stitch. The result is not a perfect hyperbola because the pieces do not have regular curvature.
For the Wertheim family, embracing that irregular ruffle was the moment the crochet reef project was born. Unstable algorithms have produced wild taxonomies, zoological seascapes of living things that more closely emulate the geometrically unusual curvatures of their real-world biological counterparts.
pattern of change
Recently, another incarnation of crocheted coral emerged from a pond of creativity organized by the Carnegie Museum of Art in Pittsburgh, known for its three rivers. The Allegheny and Monongahela rivers join to form the Ohio River, which flows into the Mississippi River. It flows into the Gulf of Mexico, where corals spawn after the full moons of July and August. Curated by Alyssa Velasquez, curatorial assistant for decorative arts and design, the show will exclusively feature satellite leaves made by 281 community crocheters.
Velazquez said the Wertheims’ project draws inspiration from and democratizes the fiber art movement, which was driven largely by women, including Sheila Hicks, Tau Lewis and Marie Watt. . As the (mostly) women gathered together to piece together loops of yarn, Velasquez observed conversations taking place. Memories of time spent on local waterways, recycling habits, and opportunities to knit something other than baby boots. She said the company represents “creative possibilities for environmental dialogue and new ecological actions” and evokes imaginative and concrete patterns of change.
