In Susan Orlean's New Yorker profile of Robert J. Lang, a physicist who left physics for origami, she writes about how the ancient art of paper folding has changed more in the last 20 years than in its entire history.
Then a few people around the globe had the idea that paper folding, besides being a pleasant diversion, might also have properties that could be analyzed and codified. Some started to study paper folding mathematically; others, including Lang, began devising mathematical tools to help with designing, all of which enabled the development of increasingly complex folding techniques. In 1970, no one could figure out how to make a credible-looking origami spider, but soon folders could make not just spiders but spiders of any species, with any length of leg, and cicadas with wings, and sawyer beetles with horns. For centuries, origami patterns had at most thirty steps; now they could have hundreds. And as origami became more complex it also became more practical. Scientists began applying these folding techniques to anything—medical, electrical, optical, or nanotechnical devices, and even to strands of DNA—that had a fixed size and shape but needed to be packed tightly and in an orderly way. By the end of the Bug Wars, origami had completely changed, and so had Robert Lang. In 2001, he left his job—he was then at the fibre-optics company JDS Uniphase, in San Jose—to fold paper full time.Orlean's piece is fascinating but a bit hard to follow, because in typical New Yorker fashion, it's not meaningfully illustrated. Words alone don't do justice to Lang's original designs and the shapes they fold into.
That's why the Institute for Figuring's online exhibit, Mathematical Paper Folding Exhibit is a great place to visit in connection with the New Yorker article. You can actually see Lang's patterns and the paper creations they fold up into, like the paper lobster shown here. The site features features a number of examples of Lang's work, along with an in-depth interview by Margaret Wertheim.
There's a wonderful metaphorical resonance in the connection between these abstract, geometric patterns and the models of living things they generate, because it so beautifully symbolizes the way that Mother Nature uses intricate patterns of folding to structure the fundamental building blocks of life. We now know that proteins derive their properties as much from the way their molecules are folded as their actual chemical composition. The nature of protein folding is one of the things Wetheim discusses with Lang.
MW: One area in which I gather technical folding is proving useful is one of the major problems in biology. We know that with proteins often the most important thing about them is not the chemical composition, per se, but the shape they eventually fold up to.The site also has an extensive links section, including a link to Lang's very comprehensive website. Lang provides an extensive introduction to the technical aspects of origami, as well as a breathtaking portfolio of his work, including photos of a selection of his paper sculptures that have been cast in bronze.
RL: There’s both relevance and differences here, because paper folding is two-dimensional and a protein is roughly a one-dimensional shape, a linear chain with a bunch of joints in the chain. Protein folding is actually much more complicated than paper in that folds can happen only at certain angles and there are bits that stick together if you get them close. There are also other molecules jostling around that can knock the protein about as it’s folding. But the fundamental theory of folding is the same, and if you can develop general concepts that apply across dimensions—from one-dimensional to two-dimensional, and even higher-dimensional problems—then the results that you derive are going to be applicable to these very fundamental issues like protein folding and biological activity.
If you're looking for more information, this post at kottke.org weblog has a wealth of links in both the post and comments, along with instructions for making a little box out of Post-It Notes on your desk in about five minutes.