I have long wondered whether it was possible to create Art that expressed the beauty of science at a deep level. Most of the Art I’ve seen celebrating science has lain strictly at the surface – mostly, images of scientific concepts that happen to have aesthetically attractive representations. Fractals, various spirals based on the Golden Mean, microscopic images of cells, and so on. These are OK, I guess; they help make science more approachable, and they definitely demonstrate that science-y things can also be pretty things. But they don’t get at the true beauty of science, which for me is conceptual beauty, the sheer elegance of the rules underpinning the way the world is put together. I have never, for example, seen a work of Art that really expressed how elegant Maxwell’s equations, or the Pythagorean theorem, really are. Not their truth, or their usefulness, but their elegance: The simplicity and power with which they express their underlying truth.
It may sound odd to non-mathematicians or non-scientists to talk about beauty in a profession that is supposedly dedicated to truth, but the beauty of the truth, of the rules underpinning how the world works, is what gets most of us into the game. Particularly, it’s what gets mathematicians into the game. Because mathematicians work with abstractions rather than messy data, and because much of mathematics has no obvious application to the real world, mathematicians are in some sense the poets of the scientific world, seeking truth and elegance for their own sake rather than for any specific application. (This is, like most sweeping statements, an overgeneralization, but one with a reasonable degree of truth to it.)
The great mathematician G.H. Hardy, in his book A Mathematician’s Apology (one of my favorite books about the philosophy of mathematics), said this about mathematics, Art, and beauty:
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. A painter makes patterns with shapes and colours, a poet with words…The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics….
It would be quite difficult now to find an educated man quite insensitive to the aesthetic appeal of mathematics. It may be very hard to define mathematical beauty, but that is just as true of beauty of any kind—we may not know quite what we mean by a beautiful poem, but that does not prevent us from recognizing one when we read it.
I’m not going to try to give a rigorous definition of mathematical beauty – it would be an interesting exercise, and Wikipedia takes a stab at it, but it would be kind of like trying to explain being in love to someone who’s never experienced it. Louis Armstrong once said, “If you have to ask what jazz is, you’ll never know.” Mathematical beauty is somewhat similar.
Nonetheless, it exists, but it’s a conceptual beauty, and trying to render it in physical form is hard. Really hard. In fact, I wasn’t even sure it was possible. It’s something I’ve always wanted to do, but couldn’t figure out how because I’d never seen it done.
Until someone told me about Figuring Fibers. Figuring Fibers is a compilation of articles that demonstrate mathematical principles using fiber arts in a deep, thoughtful manner. It’s unique in that it’s written with mathematical rigor, yet is readable by the sufficiently bold layperson, and each article covers a deep, interesting mathematical idea and then demonstrates it/extends the idea using a fiber art technique. Crochet, knitting, quilting, sewing, and beading/embroidery are all used in the book. (No weaving, alas, but perhaps a future volume?). This is no mere crocheting of a Moebius strip or knitting a 3D rendition of a Klein bottle; this is creating fractals, extending the Chinese Remainder Theorem to knitting contexts, and proving hyperbolic geometrical theorems through quilting. I mean, this stuff is cool. Way cool. As in, I had continuous nerdgasms for three days cool. (Okay, okay, TMI, but you know what I mean. 🙂 )
Figuring Fibers is definitely not your “Quilt in a Weekend” type fiber book, and it is not for those easily intimidated by mathematical notation. In fact, I opened it, looked inside, saw subscripts and superscripts and phrases like “Triply periodic polyhedra in Euclidean Three-Dimensional Space” and nearly shut it again. But I didn’t, and I’m very glad I didn’t. If you are mathematically educated enough to read Scientific American, and if you are willing to put some time and effort into understanding the concepts, you can skip over the more technical bits and still get 90% of what the authors are saying. There are definitely places where you’re going to get lost – at least, for awhile. And there are places where you’re going to have to go back and forth until you get it. But it is possible to skim over those parts and still appreciate how devastatingly cool (did I mention devastatingly cool?) the concepts and the art are. Yes, I was a math major, but I haven’t cracked a math text in 25 years, and I still think this was an amazingly enlightening read, both for the mathematical beauty and the knowledge that it is possible to combine Art and mathematics in a deep, beautiful way. (Plus, I now have a new favorite phrase: “The Borromean Rings are Hyperbolic: Proof by Quilt”! OMG, I’m in love.)
Figuring Fibers is edited by Carolyn Yackel and Sarah-Marie Belcastro and published by the American Mathematical Society; it is available through Amazon but is (at least for now) available much more cheaply on the American Mathematical Society website. It is the third book in a series; I haven’t yet read Making Mathematics with Needlework or Crafting by Concepts, but you can bet they’re on my reading list now!