bull moose
flight of folds
euthysanius beetle
acoma pot
artist

Origami Connections, with apologies to James Burke (1997)

In 1992, I left my job researching lasers at NASA's Jet Propulsion Laboratory in Pasadena and moved to a small company in San Jose called SDL, which designs and manufactures a wide variety of the type of laser called a "semiconductor laser." San Jose is in the heart of Silicon Valley and is full of high-tech gadgetry. When one arrives at the San Jose airport, one of the first things one sees in the terminal is a complex assembly of wire, motors, gears, bells, balls, and boxes; it is a "kinetic sculpture" that is in constant motion as balls go up and down ramps, whirl around spirals, and bounce off boxes, all the while emitting a euphonious mixture of plinks, dings, whirs and plops. This sculpture and a much larger one in downtown San Jose were designed and built by an artist named George Rhoads, who has developed a considerable name in the field of modern sculpture. Although known in the art world for his kinetic sculptures, Rhoads is a man of many talents, and in the 1950s and 1960s, he was one of the foremost origami designers in the world.

Rhoads is probably best known in the origami world for his Elephant, a model which was introduced to the world through a photograph in Harbin's Secrets of Origami (which is where I also learned of his artistic endeavors) and through instructions in Sam Randlett's Best of Origami. Rhoads's Elephant was a remarkably sophisticated design and provided an inspiration for a generation of folders, myself included. For example, the technique of unwrapping layers from a blintzed structure, used to great effect in the Elephant, is one I used in several of my early models, including my first Cicada, which I invented during a summer job at Hughes Research Laboratories. I was so proud of it I gave one to my office mate, a fellow summer student named Phil Mitchell, before delving into what was to become the field of my graduate research and my eventual profession, semiconductor lasers. During graduate school, I pursued origami alongside lasers, publishing laser articles in Applied Physics Letters and Journal of Quantum Electronics and publishing origami models in the FOCA Annual Collection, British Origami Magazine, and a short-lived journal of origami, The Origami Collection, which, during its brief lifetime, was published by a graduate student at the University of Utrecht in The Netherlands. Remember these names.

Back to the present: Some ten years after graduating I had joined SDL and I and my co-workers began working on a new type of laser, called a MOPA, that turned out to be a revolutionary advance in the field of optics and semiconductor lasers (or so we said in our press releases). However, we found that we were not the first to work on this type of MOPA. Back in the late 1980s, two guys named Steve and Andy had developed and patented a very similar creature before going on to new endeavors. While Steve's new endeavors continued to include lasers, Andy eventually decided he didn't care much for optics any more; he quit his job to go to law school. Lawyering didn't occupy him fully, so he also decided to start a publishing company with his brother. Andy Montroll and his brother John named their company "Antroll," and their first book was written by John, called Origami Sculptures. Their third was a collaboration between John and me, Origami Sea Life, which went into its third printing just about the time our (SDL's) MOPA laser hit the marketplace.

In my career, as in graduate school, origami and lasers occupied my attentions in alternate amounts. After starting work on the MOPA at SDL, I was invited to go to Japan to talk about origami and to meet the Japanese folding community. Among the people I met was Masao Okamura, who had made a study of nested crane patterns folded from slitted squares that were described in the Japanese classic Sembazuru Orikata. Okamura-san was intrigued by a model of mine, which I called "Generations"; it was a series of nested flapping birds folded from a single uncut square. We got to talking and Okamura-san mentioned that he knew of a Lang in Japan; as a boy, he lived down the street from one Hiroyoshi (Roy) Lang, who he remembered over the years because of the Western name.

Roy Lang and I aren't related, at least not by family; but Roy did grow up to be a scientist and his work appeared in scientific journals in the 1970s and 1980s, which you may find indexed by his name, "R. Lang." This was unfortunate for me because Roy's field of research was semiconductor lasers and feedback — which at the time was perilously close to my Ph.D. thesis topic of coupled-cavity semiconductor lasers. To make matters worse, we published in the same journals, and to put it bluntly, Roy was famous and I was not. To avoid confusion, I began to use my middle initial in all my publications — "R. J. Lang" — a practice I continue to this day, even in my origami world, where Roy, fortunately, has yet to venture.

A distinguishing feature of Roy Lang's and Robert Lang's laser work was that while we both studied noise processes in lasers, I looked at a special type of noise in semiconductor lasers known as "1/f noise." This type of noise is of long-standing interest in the physical sciences and is found in many physical systems, so it had already received a great deal of study by the time I starting looking at how it affects semiconductor lasers. In fact, some of the pioneering work in the field was done by one of the big names in physics earlier in this century, a fellow named Elliot Montroll, who named two of his sons Andy and John.

While in Japan, I visited several folding groups, and during one of these visits, I was designing new models by doodling circles inside a square. This is a technique I had developed and used for several years, and my scrawls caught the eye of several people who recognized the doodles. It seems I wasn't the only one using circles to design origami and through these doodles I made the acquaintance of Toshiyuki Meguro, who had developed his own circular doodles — not to mention his own flying beetles, spiny sea urchins, and a whole host of other point-rich designs. We exchanged ideas, and I combined my own ideas, concepts I learned from Meguro, and a numerical technique used in optics called "nonlinear constrained optimization" to write a computer program that designs origami bases, which I posted on the Internet.

The globe-girdling network known as the Internet owes its existence to several entities, not least of which is Xerox's Palo Alto Research Center, or PARC, which designed the networking scheme called Ethernet that connects many of the Internet's computers. Xerox PARC is famous for developing a wide assortment of technologies: some got away scot free, like the graphical user interface used in Macintosh and Windows computers; some continue to bring royalties to Xerox, like Ethernet; and some were spun off into startup companies, like the semiconductor laser group that in 1983 formed a company, Spectra Diode Laboratories — which in 1992 changed its name to SDL and hired a paperfolder-cum-physicist to work on MOPAs.

While many of its technologies have been exported elsewhere, PARC continues to do world-renowned research in computer science. One of the pioneers of the field called "computational geometry" is a PARC researcher named Marshall Bern, who, having learned a bit about origami, decided to address the issue of the difficulty of solving certain origami-related problems in computer science. Bern and his colleague Barry Hayes showed that the problem of assigning mountain and valley creases to an existing crease pattern was in a class of difficulty known as "NP-hard," which essentially means that as the number of creases increases, the problem rapidly becomes too hard to solve with finite computing resources. A good-sized chunk of theoretical computer science relates to what problems are, or are not, NP-hard. Proving that crease assignment was NP-hard was a significant, i.e., publishable, accomplishment in computing circles. Wanting to see how it played in origami circles, Bern sent a copy of his paper to a number of paperfolders, one of which happened to be me.

As it turns out, the origami computer program I posted on the Internet falls in the area of computational geometry, and wanting to see how it played in computational geometry circles (and in the spirit of "turnabout's fair play"), I sent it to Marshall. He encouraged me to submit a paper to a computational geometry conference, which I did. It still had to be accepted, however. At the review session, (I subsequently learned) there was some controversy over accepting the paper, since origami was rather far afield from most of the other papers submitted to the meeting. However, my paper was supported by two of the big names in the field, one being Bern; the other big name, it turned out, was a professor at the University of Utrecht, Mark Overmars, who as a graduate student had been the publisher of The Origami Collection.

So the paper was accepted and in mid-1996 I went to Philadelphia and presented it. The talk went over well, computational geometers being as susceptible as anyone to the charms of origami. Afterward I was approached by one whose name tag read Joe Mitchell. Joe was not entirely unfamiliar with origami; it seemed that for the better part of the past decade, Joe had displayed on the dashboard of his car a paper cicada, given to him by his brother Phil, who acquired it the summer he shared an office at Hughes Research Laboratories with the guy who had folded it.

After the meeting I had a few hours to kill and I chose to kill them at Philadelphia's Franklin Museum of Science, where I ruminated on the connections between my science life and my origami life — and wrote the first draft of this article. While doing this, I was serenaded by a series of clinks, plinks, and plops, which emanated from a contraption near my seat, a large assembly of wires, motors, and balls. It was, of course, a kinetic sculpture, yet another from the hands of George Rhoads, the guy who started both my origami career and this article; one of which I will bring to a close.