Last week I was lucky enough to attend a talk by Margaret Wertheim, in the art department at Pomona College. For those who don’t know her, Margaret is a science writer who has been engaged with the Crochet Coral Reef mathematical art project for over 17 years, along with her sister, artist Christine Wertheim. In this post I’ll share some of my take-aways from that talk, and use that as a springboard to share some of my own views on “Art” versus “Mathematical Art.”
The Crochet Coral Reef project builds on the work of Mathematician Daina Taimina, who was the first person to crochet models of the hyperbolic plane. For those unfamiliar with hyperbolic geometry, here’s all you need to know: In Euclidean geometry the circumference of a circle is proportional to its radius. In hyperbolic geometry, it’s longer. Thus, to crochet a model of hyperbolic geometry, you can start with a ring of stitches. Then, add a second row around it, but insert a few extra stitches to make the length of that second row longer than it would be than if you were creating a flat design. Then repeat. That’s it! As you work, you’ll find that the shape starts to curl up, much like a leaf of curly kale, or … many types of coral.
Each piece of “coral” can be used to demonstrate several features of hyperbolic geometry. For example, in the Euclidean plane, there is a unique line parallel to a given one, through a given point. In the hyperbolic plane, there are an infinite number. This is easy to see on a crocheted model of the hyperbolic plane.
The Crochet Coral Reef project extends Dr Taimina’s work by encouraging participants to deviate from the pattern for a perfect hyperbolic form. People who crochet “reef” forms are asked to vary the pattern to create ever more complex shapes. In this way, a whole ecology of different forms has been brought into being. Just as life on earth began with simple cells which gradually became more complex over time, so too the crochet reef has evolved into an increasingly diverse set of structures. Much like DNA, the building block of life, each one of these creations could be described by a formal algorithm or code: the code of the crochet pattern.
Those are the mathematical connections of the Crochet Coral Reef project. However, the project has so many more aspects to it! It’s a community project, crowdsourcing the work of thousands of people to make the individual elements that comprise each coral composition. The overwhelming majority of those people are female, and so it’s also a statement on women’s craftwork, while at the same time providing an experiential pathway into science and mathematics for women and girls. Each new form is a unique geometric structure, so in a very real sense the project is a kind of citizen-based exercise in applied mathematics, where participants are exploring a landscape of geometric possibilities.
As the world’s coral reefs are disappearing, the Crochet Coral Reef project is also a powerful statement about climate change. Some of the installations emphasize this by featuring pieces made from crocheting plastic materials, rather than yarn, or using a white material to raise awareness about coral bleaching.
The phrase “mathematical art” gets used in a lot of ways, but I don’t think I’ve seen a more appropriate project with this label than the Wertheims’. Most of the time it’s used to indicate some aesthetically pleasing form created with the aid of mathematics, or whose purpose is to illustrate some mathematics. Both categories tend to place the emphasis on the Mathematics, rather than the Art.
The word “Art,” as used by most Artists, is not the same as “art,” as a word just used to describe something someone might want to hang on their wall. “Art” with a capital “A” makes a statement. It is often understood best in a historical context, as part of a larger conversation of the Art community or society in general. A work of Art often tells a story. The entire purpose of this blog is to tell those stories about each piece I make. However, when talking to an artist, if I make the mistake of saying that I make “Art” (rather than “art”), the first question I always get is, “What is your work about?” The best answer I’ve come up with is “I explore ways in which mathematics can be used as a tool to make Art,” but I’ve never been satisfied with that. It’s more about process than purpose, which is the intent of the question. For example, here’s a 3D printed lamp I made several years back, reminiscent of many of the coral creations above, using a differential growth algorithm (described here). While it has many of the same aesthetic elements, it lacks any deeper connections.
In contrast, the Crochet Coral Reef project checks all the boxes. It has a strong connection to Mathematics, and it makes powerful statements about so many things. That’s not a criticism of more typical Mathematical Art (like mine), which often lacks such statements. Mathematical Art has tremendous value, in its own right. It just shouldn’t be understood to convey the same type of meaning/purpose that Art does. Perhaps it’s best then to say that the Wertheims’ work falls into two distinct categories: “Art” and “Mathematical Art.”
Thanks so much to Margaret Wertheim for sharing her images with me, and providing feedback about an early draft of this post! You can learn more about her work as a science writer and artist on her website. She also gave a wonderful TED talk back in 2009 that’s worth checking out. For those who would like to see more of the Wertheims’ Crochet Coral Reef project, I highly recommend their beautiful book Value and Transformation of Corals.
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