Robert J. Lang was born in Ohio and raised in Atlanta, Georgia. He received his degrees from the California Institute of Technology and Stanford University. Along the way to his current career as a full-time origami artist and consultant, he worked as a physicist, engineer, and R&D manager. During that time, he authored or co-authored more than 80 technical publications and 50 patents (awarded and pending) on semiconductor lasers, optics, and integrated optoelectronics. He is a Fellow of the Optical Society of America and Editor-in-Chief of the IEEE Journal of Quantum Electronics. Lang has been an avid student of origami for more than forty years and is now recognized as one of the world’s leading masters of the art.
Ivars Peterson: You became interested in origami when you were about six years old. When did your interest in mathematics arise?
Robert Lang: By high school. Without question it was because of Martin Gardner. A friend gave me some Scientific American magazines that had some of his articles, and that got me to check out his books. By that time, there were many collections of his columns, and that inspired me to do math. I became a voracious reader of anything mathematical.
By the end of high school I thought I would become a professional mathematician, but my first year of math at Caltech convinced me otherwise. When I took freshman calculus I said, “This isn’t as fun as I remember math being.” Years later I realized that what I really love is applied math, where the focus is on problem solving. But by that time I had changed to electrical engineering and ultimately physics and lasers. There were plenty of problems to solve in lasers.
An origami bowl by Robert Lang. Photos by Ryan Miller.
IP: Did you spend your entire undergraduate and graduate time at Caltech?
RL: I got my bachelors from Caltech in electrical engineering and then went to Stanford, thinking I would complete my Ph.D. at Stanford. But after I got my masters, I decided to go back to Caltech for my Ph.D. That’s when I switched from electrical engineering to applied physics.
IP: Were there any particular individuals or classes that helped set your direction?
RL: At Caltech, Donald S. Cohen taught the junior level applied math course, which was infamous for turning people into humanities majors. Cohen himself made it a terrific and inspiring experience for me. From then on, I took everything that Cohen taught in applied math, and this applied math background helped me when I came back as a physicist to focus on theoretical work.
IP: What was your thesis on?
RL: It had the title “Semiconductor Lasers: New Geometries and Spectral Properties.” My thesis advisor was Amnon Yariv, who is one of the big names in quantum electronics. Amnon had a very large group. I didn’t actually interact a lot with Amnon, but I interacted with those who were more senior to me in his group. Conversely, when I became more senior, I mentored the new students coming up. The student with whom I did my first paper was Kerry Vahala, who is now a professor at Caltech.
IP: After your Ph.D., you chose an industry/government lab route rather than an academic route.
RL: That was the big question. I had an offer from the University of Michigan and an offer from JPL [Jet Propulsion Laboratory], and one other offer. My supervisor at JPL argued that JPL offered the best of both worlds: the ability to do research and not too many of the headaches one would encounter in academia. I don’t know whether that was true, but it convinced me at the time.
After about four and a half years, I realized that, doing pure technology research at JPL, I was pretty far removed from the space missions, where all the excitement was. No one was going to put one of the lasers I was making onto a spacecraft. So I was open to being recruited when I got a call from what was then a small company called Spectra Diode Labs [SDL] in Silicon Valley. SDL was at the top of the field in research, so it sounded like a really good opportunity. I enjoyed it for the ten years I was there until I quit to do origami.
IP: What was happening to your origami at the time you finished your Ph.D.?
RL: Working at a place like Caltech was very invigorating and stimulating. So origami revved up to a much higher level in my life. I’d always tried to invent new things, but I really wanted to push the envelope and the state of the art. I started developing concepts that helped me design complicated things. My idea was that you could represent parts of a subject in the amounts of paper they would take up and that a circle was a good approximation of this. Finding suitable arrangements of circles could lead to potential origami structures.
I graduated and did a postdoc with a company in Germany in 1987. Because I was in a foreign country, I had a lot of time on my hands after work and spent a lot of it developing new origami designs and new techniques for origami.
IP: Were you already corresponding with people doing origami, or were you doing it on your own?
RL: I was doing it for myself. I had joined the Origami Society in the early 1980s and got their newsletter. But I didn’t actually meet any other folders until 1986 or so when I made a trip to New York and I was able to set up meetings with some of the big names in origami. That was interesting because they asked me to teach them something—that’s how origami people socialize. I showed them my dragonfly. It was way harder then anyone had expected, much more complex than was typical. That’s what got my name out a little bit. They said, “Whoa, where did this kid come from?” But I didn’t really start interacting with a lot of people until the early 1990s.
IP: What made you decide to give up lasers and do just origami?
RL: I made the decision to do just origami in about 2000, but the time wasn’t really right until the end of 2001. That was when I quit. The trigger was my book [on origami design]. By that time I had written six books of recipes, but what I’d had in mind since high school was a book on how to design origami. By the end of the 1990s I had a really good idea of what was going to be in this book, but if I was going to write it I needed a different model. All my other books were collections of recipes; they were short stories. This book was going to be a novel. It all had to hang together, and I had to think about it to the exclusion of everything else. That presented a very clear choice. I said, “If I’m ever going to write this book, I can’t be working fulltime on lasers.”
I finally decided that, even though I had a pretty successful laser career, anything I would do in the laser field someone else could do. But I felt that no one else could write the design book that I wanted to write. That triggered the change. There were some other factors, but that was the main one that forced the issue.
A fiddler crab. Image courtesy of Robert Lang.
IP: Your approach to origami design is mathematical or algorithmic, and that seems to open up new possibilities.
RL: When I started, there were only a few of us. Nowadays, anyone who designs complex origami uses algorithms and mathematics. Non-mathematicians might not recognize it as mathematics because the world has succeeded in teaching people a much narrower perception of what mathematics is than what it really is. Mathematics is the study of patterns and relationships, and the techniques we’ve developed for origami are ways of describing those patterns and relationships in very tangible, intuitive forms: geometric shapes, circles, polygons, packing problems, things that people can visualize. So when someone uses these techniques to design an origami model, their conception of math might be Greek letters and formulas. But they’re not using that; they’re drawing things, but drawing them according to a set of rules that are mathematical. That’s the only way to do a truly complicated origami design.
IP: What about the practical side of origami?
RL: The practical side comes up in two ways. People have discovered structures while doing origami art that have practical applications. The periodic crease pattern called the “water bomb base” shows up in Zhong You’s heart stent design. The woman who is working on it was familiar with that crease pattern from decorative origami.
The second way that [origami] has applications is that the tools we develop for understanding folding and designing specific folds can be applied, whether the end goal is an art piece or a practical object. An example of that is the famous airbag application, where the tool was the algorithm for flattening polygons for an origami insect, and that’s the same algorithm used for flattening the panels of an airbag.
IP: What about unfolding spacecraft?
RL: The spacecraft application came from a Japanese engineer who started by studying stress patterns, and that led him to folded patterns. If you stress a sheet, it doesn’t buckle smoothly; it buckles sharply along folds. That led him to discover periodic folding patterns, which then had application to the unfolding spacecraft.
The one I worked on with Livermore was a radial collapsing pattern. In this case, it was drawing upon knowledge of structures that already existed in the origami art world and understanding how to adapt those structures to apply to a very specific technological problem.
IP: Do you have a favorite origami construction?
RL: The last thing I’ve done is almost always it. To do a good job on something, you have to get passionate about it. I’m putting the finishing touches on a design right now for a turkey vulture that I really love. I’m working on it because I was inspired by the subject and I had an idea of an approach that I wanted to use to accomplish something new. That is important to me even if I do an old or existing subject. There has to be something new about the approach. I can see what I want this turkey vulture to look like, but I can also feel emotionally the response I want people to have when they see this folded object.
A turkey vulture by Robert Lang.
IP: Your origami constructions seem to require a lot of time, patience, and dexterity.
RL: It definitely takes time. I hesitate to say it takes patience because you don’t need patience for something you love doing. For me, going to a baseball game requires patience, so much so that I can’t make myself do it. But most of those 50,000 baseball fans love doing it. It’s the same for origami. it doesn’t require patience for me. It definitely requires dexterity.
IP: Do you have a wish list of things you want to construct?
RL: Absolutely. I’ve always got about twenty things in progress. Personally, I’d like to do better human figures. That’s an artistic goal, not a technical goal. It’s easy to do two arms, two legs, a head, and a body. It’s even easy to do fingers and facial expressions, but they all look very cartoonish, at least when I try it.
I’ve also been exploring curved folds. Even though people have been doing curved folding for a very long time, I feel like we’ve only scratched the surface of what’s possible.
On the mathematical side, I’ve been working with Erik Demaine for about four years on developing a very fundamental and rigorous definition of what a valid folded shape is from a mathematical standpoint. We all have a good intuitive definition of what a folded shape is, but we want to create a mathematical definition that is both rigorous and useful enough that you can then use it to prove the validity of various algorithms. There have been papers on algorithms in computational geometry; one has to appeal to intuitive notions at some point in most proofs, and we’d like to make it something more concrete.
And I have the goal to see origami, or folded-paper sculpture using the rules of origami, accepted in mainstream art. It has certainly made strides in recent years, but it’s not on the same footing yet as painting or sculpture.
Read About Robert Lang’s Distinguished Lecture