from The Institute for Figuring’s interview with Robert Lang, “a pioneer in the emerging field of computational origami, a branch of mathematics that explores the formal properties and potentialities of folded paper.”
[Margaret Wertheim]: 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.
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.
MW: It reminds me of another branch of mathematics– knot theory. In the late nineteenth century, mathematicians and physicists became interested in how many different ways were there to tie a knot. And it’s turned out in the late twentieth century that some physicists believe knot theory might explain the nature of subatomic particles. Mathematicians seems to have this way of taking what seem to be unbelievably trivial things and developing from them incredibly powerful abstract techniques. Do you think paper folding may one day have some relevance to our understanding of fundamental physics?
RL: Whenever you’re developing new mathematics, there’s always that possibility. The hallmark of these sorts of surprise applications is that they always turn out to have been a surprise. There is a great example of this that is close to origami. In technical origami when we’re designing complicated forms like many-legged insects, we use a technique called “circle packing” which basically asks the question how can you efficiently pack a bunch of circles into various shaped containers. Now over the years mathematicians have also studied how to pack spherical objects into higher-dimensional spaces and how close a packing you can get. Well, it turned out that in 24 dimensions there is a particularly dense packing. That sounds about as irrelevant an idea as you can get, except it turns out that 24-dimensional packing gives a very dense compression algorithm for sending data. So using this 24-dimensional sphere packing result has become the basis for developing a very efficient code for 24-bit binary words. Now, who would have predicted that?
