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Unfolding origami's secrets

Artist Robert Langhopes to demystify the ancient art

Robert J. Lang says origami is like music. If that's so, he writes its symphonies.

Lang, who comes to the Massachusetts Institute of Technology this week to give a series of lectures and workshops on the art and theory of origami, combines a firm grounding in mathematics with a refined aesthetic sense to create dazzling, elegant works out of a single sheet of paper: a swooping owl, a horned beetle, a stunningly detailed fish complete with scales. The process, he says over the phone from his California home, is not unlike what composers do, taking known rules of composition and using them to achieve their own artistic goals.

What's different about origami, though, is that although the art is hundreds of years old, its theory has only started to be understood.

''For many years, by far the vast majority of origami participants were just performers," Lang says, not composers; they followed instructions to replicate others' designs, rather than creating their own. But in the last 10 to 15 years, he says, many more have started to compose their own works, and ''the techniques for design or for composition have started to become known."

Lang, who began his career as a physicist and engineer, then became a full-time origami artist three years ago, is one of the art's leading theorists; he has presented several technical papers on origami mathematics and was the first Westerner invited to speak to the Nippon Origami Association's annual meeting. When he discusses the theories he has developed, he says, ''it feels similar to teaching the rules of musical composition: what are chords; what is a tonal progression; if you want to get a particular effect, here are codified ways of doing that."

Both in a talk for general audiences (tonight at 7) and in a more specialized one for mathematicians (Monday at 11 a.m.), Lang will discuss his ''tree theory," which shows practitioners how to develop a folding pattern for any ''treelike" form -- a shape with one axis and branches, which could be anything from a lizard with arms, legs, tail, and head to a six-legged insect to, yes, a tree -- by mapping it onto a stick-figure diagram.

It's in discussing that theory that Lang's host at MIT, the MacArthur Award-winning professor Erik Demaine, grows particularly animated.

''It helps a lot to have some theory in how paper can be folded -- how to use paper in an efficient way," says Demaine. Part of Lang's time here will be spent in continuing a project he has already begun with Demaine: to expand the tree theory to encompass even more shapes -- and, ultimately, to develop a theory for constructing any shape from a single, folded sheet of paper.

''In some sense, we're shooting for the moon," Demaine says. ''We know mathematically that anything is possible. Now it's just a question of doing it artistically and elegantly."

In his own work, Demaine mostly sticks to the theoretical side of origami, which, he explains, ''fits into a broader set of problems, geometric folding." But that theory can also have practical applications: ''foldable structures that can get very small and then very large later on," which can be useful, for example, in deploying a telescopic lens in space or in designing more efficient airbags for cars. In nanomanufacturing, Demaine says, developing efficient ways to fold protein strands could lead to new ways to fight disease.

Lang has worked on such practical applications himself, particularly a prototype of a space telescope that, with a lens 100 meters across, would be about 40 times larger than the Hubble.

And far from feeling conflicted about moving from art to science and back again, he says, he finds it energizing.

''I love shifting gears completely, from art to math, which is very formal, abstract, and almost unrecognizable, and to engineering, which is certainly not art, but neither is it really math," Lang says. ''That switching gears is fun, and I think it also keeps the creative juices flowing in both categories. I very rarely have an inspiration when I'm sitting down at my desk to do an origami design. The inspiration happens when I'm doing something else, and then it's a question of whether I can get back to my desk quickly enough to get it done."

He also gets inspiration from the kind of informal competition that Demaine calls ''the insect wars."

That grew, Lang says, out of a small group of people who particularly like to design origami insects and are good at folding complex structures.

''For years, insects were considered the pinnacle of design," Lang says, because their long, skinny legs were particularly challenging to fold in an elegant way. So, at origami conferences, ''one year, people would bring their new beetle design, and you'd admire it, but you'd kind of be thinking, 'How can I top that?' So the next year, it would be a beetle with long antennae. Then a beetle with wings outstretched. Then it was a horned beetle. So you start scouring entomology journals for beetles with more horns, the most horns. Eupatorus gracilicornus -- I'm quite familiar with it." Indeed, there's a specimen, in dark brown paper, on his website,

Lang will share some of his secrets with ''advanced folders" in a workshop Tuesday night. ''I think the advanced workshop will be really inspirational for the advanced folders, but there are not many of those," Demaine says, a little wistfully. ''It definitely takes many years to become an advanced. I'm closer to a high intermediate folder."

But Lang will also be demonstrating techniques to ''anyone who can learn to fold paper," Demaine says, in a novice workshop on Saturday that he says is filling up fast. And Lang speaks with just as much enthusiasm about that workshop as about the rarefied stratum of advanced ''computational geometry" where he and Demaine spend much of their time.

''One of the beauties of origami as a culture is that it encompasses all levels, and there's this tremendous feeling of community and commonality among the participants," Lang says. ''At a conference, you'll see a 6-year-old teaching a 60-year-old how to fold something. It's wonderful -- the friendliness, the level of sharing, and the feeling that anyone can do anything. You can probably do more than you think you can."

To register for Robert J. Lang's novice workshop, Saturday from 2 to 4 p.m, or advanced workshop, Tuesday from 7 to 9 p.m., e-mail Erik Demaine at For information, call 617-253-2341.

Louise Kennedy can be reached at 

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