There is a distinguished history of abstruse higher mathematics becoming suddenly practical without warning, the protestations of pure mathematicians like G.H. Hardy notwithstanding. Factoring large prime numbers, for example, is critically important to secure encryption, while multidimensional sphere-packing generates crucial insights into data compression. Now knot theory is popping up in an unlikely place: creating a practical quantum computer. Read about it here in Science News: Knotty Calculations: Science News Online, Feb. 22, 2003. The prose in this article has an uncanny resemblance to science fiction claptrap.
Depicted in space-time, these paths can intertwine to form what mathematicians describe as a braid. If the particles are so-called anyons, it’s possible to recapture information about a braid by measuring physical properties of the anyons after the motion ceases. This process may open the door to a completely new type of computer that calculates by using braids.
Um… sure, but then again I believed in cold fusion for a while, too. Anyway, the key insight here is in the push-pull of mathematical association with a real-world phenomenon. If the physical world can “solve a problem” that would take a million years to solve on a computer, then why not work backwards? Set up a physical counterpart to a math problem, watch what happens, and save a million years by interpreting the results mathematically. My physicist friend Dan, who spent years working on complicated integrals working out the interaction between particle beams at the Stanford Linear Accelerator, said one day: “After a while you start to think of an accelerator as a way to solve really hard integrals.”
It calls to mind one of my favorite quotes from the (applied) mathematician Stan Ulam: “It is still an unending source of surprise for me to see how a few scribbles on a blackboard or on a sheet of paper could change the course of human affairs.”