When Origami and Mathematics Collide: Interview with Origami Artist, Engineer, and Physicist Robert J. Lang
This week’s interview is with origami artist and engineer, Robert J. Lang. For the first fifteen years of his career, Robert worked as a physicist, engineer, and R&D manager, both at NASA and in Silicon Valley. Outside of his day job, he spent his nights and weekends pursuing his curiosity and building a reputation in an area he’d been passionate about since childhood…origami.
For a long time, origami was just that, a hobby for nights and weekends, until Robert was confronted with an idea he couldn’t quite shake. He had a bigger vision for a book that felt like something only he could write (and that would require full-time devotion). With the dot com boom changing the company he worked for and Silicon Valley, Robert decided that it was time to go all in on origami.
The intersection of mathematics and origami is where Robert has found a niche that has propelled him forward over the past 20+ years. His understanding of the mathematical underpinnings of origami has allowed him to develop unique designs that have been exhibited at places such as the Museum of Modern Art in New York and the Carrousel de Louvre in Paris. In addition, his ability to use that understanding, speak engineering language, and use engineering tools has enabled him to develop applications for origami in areas such as space and industrial design. As Robert says on his website, he is “...a pioneer of the newest kind of origami—using math and engineering principles to fold mind-blowingly intricate designs that are beautiful and, sometimes, very useful.”
In the interview, we spoke about his path as well as:
Focusing on what’s next (and not making 5 and 10-year plans)
How an obsession with solving problems propels him forward
Enjoying the process vs pursuing being great
Getting unstuck
The importance of finding a niche
The origami applications he’s working on in the space industry
What’s next for him
Note: The following interview has been lightly edited for clarity and length. While every effort has been made to preserve the integrity of the conversation, please be aware that the quotes may not be verbatim but reflect the essence of the dialogue.
You had a very long-term career as an engineer before you went all in on origami. What led you to make the leap?
Origami had been my passion since childhood. Although for most of my life, I viewed it as a hobby completely separate from my career and day job as an engineer and physicist. In a way, doing both of those things is what prepared me to be able to make that change to full-time origami.
I was doing laser physics first for JPL, which is part of NASA, and then for a company in Silicon Valley. I was with them for about 10 years and progressed up the management ranks of the company as it grew from a small company to a big company. 2001 rolled around and it started heading towards being a small company again (or at least, a much smaller) company again. That was the famous dot com bust. So it was a good time to think about trying other things.
Throughout the whole period of professional laser research, I had been developing my origami activities, career, and reputation. I had written by that time about 6 books about origami, but all working nights and weekends. Throughout that time I'd had a bigger vision for a book. It was different from what people were writing and what I'd been writing. Instead of writing collections of recipes like “Here's how to fold 30 different things,” I wanted to do a book that taught people how to design their own unique origami. I’d come to the conclusion that writing the book required full-time devotion. Writing recipe books was like writing a collection of short stories. You could work on it during the weekend, set it aside, and then come back to it. The book I was picturing was more like writing a novel where you had to hold all the characters in your mind the entire time. I came to the conclusion that I'd never get that book written unless I was working on it full-time. That crystallized the choice. Do I continue down the laser career and probably never write the book? Or do I write that book which means doing something different career-wise? I was having success in my laser career, but there are lots of laser physicists in the world who could do what I was doing. But I really didn't think there were any other origami people who could write the book I wanted to write, and I felt like it needed to be written and out there. So that was what really made the decision.
I decided to take time off from lasers and work full-time on this book. I still needed to make ends meet so I pursued all the professional origami opportunities I'd had to turn down when I had a full-time day job. I set up a website and began to give talks and lectures about the things I was doing. By the time I finished the book, all those other things had grown to become a kind of a full-time job in itself, and that full-time job was a lot more fun than the management job I’d been doing previously. So I said, “Well, it's time to decide what's next, and what's next is going to be continuing to do this.” That’s basically what I’ve been doing for the past twenty years. What's been interesting about it is that the mix of activities has changed over that time. There have been a lot of changes in technology, in the way people create artwork, in the art markets, and so forth. In a way, I've been fortunate that as one area of the origami business has wound down, others have been winding up to take its place. I’ve been quite lucky that this ebb and flow of different types of work has averaged out to be pretty steady, gainful employment.
You made the switch having built a strong foundation of experience and reputation in the origami world. That said, I imagine your day-to-day changed pretty substantively. You were no longer working in a managerial role in a company and, instead, were writing a book and engaging with all these different activities. What was it like for you to build out this new career? Were there moments where you experienced self-doubt and a lot of uncertainty? Or did it feel like it evolved more naturally and organically?
It was more of the latter. As long as I know what to do next, I don’t worry too much about what’s going to happen after that. We hear about people saying, “Well, I've got this long-term plan. Here's my 5 year plan. Here's my 10-year plan, 15-year plan.” I think it's probably a good thing that I never made one. I'm not saying that’s the case for everyone. In my case, I had no idea what I was going to be doing long term, but I knew what I was going to be doing today, tomorrow, and for the next few weeks. After a while, I could start to see the pattern that new things and new opportunities would come along often enough that I didn't ever get to the point where I was sitting twiddling my thumbs, saying, “What do I do now?” I always had something to do next, and I recognize that in itself is being pretty lucky. I know a lot of people who are setting off on this entirely new path get to that point over and over, where work isn’t coming in and they have to confront: What do I do now? One of the things that helped me avoid that in my career and lay the groundwork is that I have always spent time working on things just out of curiosity. I solved problems just because they looked interesting or designed origami figures because the Muse said this would be a good thing to design. I built up a reservoir of designs and ideas I could draw upon when something new came up that was different than what I’d done before.
One of my favorite quotes has become my guiding principle. The quote is from Louis Pasteur and he said, “Chance favors the prepared mind,” meaning that you can’t predict what's going to come along in the future. That's the chance part. But if you’ve prepared your mind and learned a lot about a lot of different areas, you can recognize opportunity when it comes along and know how to get started. That has helped me tremendously. I’ve lost track of the number of times that someone has come to me with a problem, and I’ve realized I've got some expertise to devote to it that I didn’t even know I would need.
That reminds me of something you wrote about pursuing careers in origami. You said, “90% of the practitioners are starving artists. Another 9% get steady work and make a living at it; and 1% get to be famous. A lot of the time, the difference between the 9% and the 1% is nothing more than luck, or being in the right place at the right time (and having that “prepared mind,” of course). So I would suggest not setting your sights on the 1%, but rather, aim to be one of those who get steady work. To do that, you can make sure your education is contributing; learn the standards of business; strive to produce quality work, whatever it is; and be ready when the 1% chance comes along. Even if it never comes, you will have had a great time.”
I encounter a lot of people who in the course of trying to have a prepared mind will easily get discouraged with questions like: Why isn't it happening yet? Why haven't I had more success by now? What do you think helps to cultivate a prepared mind and stay the course?
I'm not sure it's something that I can tell a person to turn on. If I get an idea, I get a little bit obsessive about it. I think that’s a recipe for success for lots of people in vastly different fields. I think your devotion to solving a problem, creating artwork, or pursuing an idea helps you brush aside the little barriers that come up, as opposed to seeing a barrier and saying, “Oh, that’s going to be too hard. Now what do I do?”
This literally came up in the last week with a project I'm working on with Brigham Young University. I'm writing code to design folding structures for space and the software package I've used for decades is crashing. It's not that my inputs are wrong. It's that the software package itself is crashing. I could give up on that avenue, but I really want to get that thing working so I found another software package that claims to specialize in this sort of calculation. I’m now figuring out how I can make this one talk to that one by writing a script that uses a new programming language I've never used before. So I need to learn that program language, and that’s what I’ve been doing the last few days. That’s a lot of stuff I’ll have to do, but I want to solve the problem so I’m going to do all those things. I think that drive is key. I don’t know how you get that drive. Maybe I was born with it or developed it over time.
I wonder if this will land with you. One thing that separates a lot of great athletes is learning how to fixate on exactly what they can control. If you're an elite golfer, you're not spending time fixating on whether or not you’re going to win the masters. You're asking yourself, “Did I practice my swing 1,000 times this week?” or whatever the relevant metric for your game is. It sounds like what you’re saying is really honing in on what it takes to be great at something.
I think it’s a little bit different. When I say I love being an expert at origami, what I mean is that I love to fold. I’ve folded for tens of thousands of hours and in doing so I've gotten good at it, but it's not because I wanted to become good at it. I folded because I loved folding, and I think there's something that plays there. I don't remember who the basketball player was who would spend hours doing free throws. If his motivation was, “I want to be great at free throws,” he’d probably lose motivation pretty quickly. But if it’s loving the process of honing the ability to make those shots, you can spend hours doing it. The getting good at it comes from that.
You've written about how a lot of innovation happens on the edges. Your career is certainly a testament to that. I think one thing that can be terrifying about the edges is there's a lot that you don't know. How has your relationship with that uncertainty changed over time? How do you approach problems where you have no idea what the answer will be?
I’m going to fall back on the way my friend, Professor Erik Demaine, a professor at MIT, put it because I think he hit the nail on the head. When you’re intrigued by a problem, which by its nature is uncertain, whether it’s math, computer science, or origami, you don't know how to solve it so you're going to nibble at the edges until you see a path, and then try to complete your path to the answer. Once you’ve solved it, at that moment, you know something that no one else in the universe knows, and there’s a dopamine hit when you realize that. As Erik says, “Then you want more of those hits.” So you go on to the next problem and the next one after that. That’s just curiosity-driven research. I think an awful lot of progress has happened because of that.
One thing I encounter a lot with my clients is the concept of feeling stuck; that feeling of, “I don’t know where to go from here.” Do you ever encounter that feeling? If so, what helps you get unstuck?
1 million times a day.
Well, I mean little “stucks,” and then there are bigger “stucks.” I’m lucky that in most cases I’m not under such time pressure that I can put it aside for a few hours or a day. Very often a day is all I need. I go for a hike most mornings before I go to work, just as exercise, and it's pretty common that while I'm doing that two-hour hike, the solution to the previous day’s “stuck” pops into my mind on the hike. Then I immediately want to get home and get back to my desk because now I know what I need to do. To turn that experience into more general advice: put the problem aside for a little while, let your subconscious chew on it for a bit, and then come back to it.
Looking back on the past twenty years and this big second chapter of your career, what would you say to a young person at a similar precipice?
One of the things is to figure out what your niche might be, not necessarily what it will turn out to be. It's this whole idea of what comes next. What is something that sets you apart from the crowd? In my case, especially in that first decade from 2000 to 2010, what set me apart was that I could speak engineering language and use engineering tools to describe origami solutions. There were lots of other origami artists who could come up with folded things, but not many could build a computational model of the folding that an engineer could then bring into their CAD program or talk about the second-order effects of things like mass, stiffness, strain, and other things that are really important to product design but are not things that play a quantitative role in origami. That gave me unique opportunities that I wouldn’t have been able to capitalize on as a pure-play origami artist or a pure-play engineer. Similarly, I would urge people to look for how they can combine some skills in different fields to address a unique set of customers or opportunities.
You mentioned that throughout your career, you've adjusted to a lot of changes in your industry. What have you found keeps your creativity alive? Where do you go to find inspiration and to continually cultivate that sense of curiosity?
There are two buckets. Clients come to me and bring problems or constraints that wouldn’t have occurred to me to work on. It forces me to go solve some new problems or learn some new things. For example, I've had clients who have wanted me to fold something from a very unique, unusual material and that's what led me down the path of finding ways to fold fabric, wood, veneer, metal, mesh, and polymers. All things that behave very differently from paper. That set of creativity comes from being presented with problems that require creativity for their solutions.
The other part is just that sort of pure curiosity-driven thing that comes up when you solve one problem, and then you see several new problems that you couldn’t even think about or wouldn’t have even considered until you’ve solved that first problem. Then you realize, “Oh, now I can make headway on these other problems that I hadn't even thought of attacking because I have a new way of approaching them.”
What are some of the frontiers of origami that you're exploring right now that you're most excited about?
One I’m most excited about on the engineering side is folding with thick materials, meaning materials that are thick enough that you can’t treat them as if they have no thickness. When you’re folding tissue paper, it’s so thin that you can ignore the thickness. But for a lot of real-world applications, especially space applications, the thickness is significant. If you're making an antenna, there are electronics on its surface and things like chips, so you need to take that into account in the design of the pattern. For quite a few years, I’ve had an interest in developing techniques and specific folding structures that work even with arbitrarily thick materials. That's what I'm working on right now. As soon as we hang up, I'm going to go back to coding on one of those problems.
On the art side, I’d say its folding designs where the crease pattern itself, the pattern of folds on the paper, is elegant. For about 20 years, when I exhibit origami at a museum or in an exhibition, I will exhibit the finished piece as well as the unfolded pattern. I collaborate with an artist in Santa Fe named Kevin Box. When we do metal sculptures of origami, people buy the metal versions of origami, but they also buy metal versions of the unfolded pattern to see the pattern because it’s beautiful. So I’m interested in making origami where the creases that went into it are also aesthetically pleasing.
Do you feel like you have to differentiate who you are as an artist from who you are as an engineer or does it all mesh together?
Everything is a mixture. When I create art, I use engineering techniques to accomplish my artistic goals. When I'm doing engineering, a lot of my gut instinct is driven by aesthetics. I strive for an elegant solution to the engineering problem. I think you'll find lots of engineers who will tell you that elegance is important in their design process. Elegant design often turns out to be the best design in purely practical dollar terms with the fewest parts, fewest ways it could go wrong, easiest to troubleshoot, and those kinds of considerations.
Many people I interview for the No Directions blog have created lives that are uniquely theirs in terms of how they live, work, and build their lives. What does the life that is uniquely yours look like today? What are you building towards?
What’s next for me is I’m going to solve some interesting problems, and I'm going to create what I hope are some beautiful objects and have a really good time doing both. I just expect that is going to continue for the foreseeable future.