Math geek as artist: Robert Lang’s origami

Robert Lang at work on an American flag. Via Wikimedia Commons

Here’s a fascinating little video, plus some additional thoughts about art, science, and creativity below. This is so much more than folding little paper cranes. Robert Lang talks about the intersection of art and mathematics, and shows how “problems that you solve for aesthetic value only, turn out to have an application in the real world.” Not to mention some mind-blowing designs.

Lang’s eighteen-minute TED talk is fast paced, lively, and funny. Here are some highlights:

People think they know what origami is, but it’s gone way beyond the simple toys and cranes. But no matter how complex it is, the common theme to it is “folding is how we create the form.” Though it’s hard to believe when you see his work, everything Lang shows is made from a single sheet of paper, no cuts.

Origami has been around for centuries. “You’d think that everything that could be done has been done long ago, but that’s not the case.” What changed? Math — specifically its application to complex problems of origami. This has revolutionized the art, allowing for complex, 3-D designs that were considered impossible before.

Lang says, “The secret to productivity in many fields, including origami, is letting dead people do your work for you. Because what you can do is take your problem and turn it into a problem that someone else has solved and use their solution.”

Lang explains four simple laws that encapsulate all of origami’s possibilities. Just four laws — yet they can produce vast complexity.

Art alone would justify the effort, but it turns out that origami has real-world applications… and here not only is Lang blurring art and math, but art becomes engineering as well. He describes a proposed space telescope with a lens 100 meters in diameter, a heart stent, and automotive airbags. In each case engineers need something small for transport that becomes large for use — and each problem is solved by an origami design that began as art.

In origami as in mathematics, “problems that you solve for aesthetic value only, turn out to have an application in the real world.”

A few thoughts in response:

Just four simple laws to produce vast complexity and beauty? Yes, this is something we find again and again in nature. Lang mentions the laws of quantum mechanics, which are (and I’ll take his word for it) simple enough to state, though their implications are so vast that only specialists can begin to comprehend the field. Another example he doesn’t mention: natural selection is a relatively simple algorithmic process which, over evolutionary time, produces a planet-full of biological “design.” Or fractal images. Or weather. It turns out that one of nature’s great surprises (and here’s your dose of awe for today) is that complexity can have surprisingly simple roots.

Second, I love the way Lang transgresses the boundaries the separate art, math, and engineering. I think “arty” people often think that the math and science people aren’t creative, or that art is about instinct and passion while math and science exist in the barren land of Just the Facts, Ma’am. But in fact, the best creative environments seem to be those in which people get out of their cultural and professional silos and learn from people in other fields.

And that’s one reason, by the way, why I — a writer and editor — devote most of my blog to art, music, science, and nature, and rather little to writing about writing. Because what I’m really blogging about is what we can do to cultivate the kind of mind from which to write and create. I don’t know if Robert Lang is a writer, but I think he’d understand that.


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