Origami chaine operatoire

The New Yorker has a nice profile of origami artist (and physicist) Robert J. Lang. My print edition of Discover had a profile of Lang earlier this year, which has become an online feature complete with illustrations.

The New Yorker story sort of leads with a dog-bites-man "well-groomed artist" story. People tend to forget that the original "Renaissance men" were skilled practical chemists (pigments) and physicists (optics) as well as painters and sculptors. There is always a long series of steps involved in the creation of art, steps that require collecting special resources, creating and manipulating technology, and bringing observations into a conceptual framework.

For this last step -- the conceptualization -- origami has lately become the province of mathematics:

He would have liked to have folded insects, but, in those years, bugs, as well as crustaceans, were still an origami impossibility. This was because no one had yet solved the problem of how to fold paper into figures with fat bodies and skinny appendages, so that most origami figures, even television characters and heads of state, still had the same basic shape as the paper cranes of nineteenth-century Japan. Then a few people around the globe had the idea that paper folding, besides being a pleasant diversion, might also have properties that could be analyzed and codified. Some started to study paper folding mathematically; others, including Lang, began devising mathematical tools to help with designing, all of which enabled the development of increasingly complex folding techniques. In 1970, no one could figure out how to make a credible-looking origami spider, but soon folders could make not just spiders but spiders of any species, with any length of leg, and cicadas with wings, and sawyer beetles with horns. For centuries, origami patterns had at most thirty steps; now they could have hundreds. And as origami became more complex it also became more practical. Scientists began applying these folding techniques to anything -- medical, electrical, optical, or nanotechnical devices, and even to strands of DNA -- that had a fixed size and shape but needed to be packed tightly and in an orderly way.

This progression is illuminating. At first, thirty steps or less -- and yet, this was a hundreds-of-years-old art form. The constraints were learning (mastering the basic techniques of folding and progressively more difficult combinations of steps) and innovation (extremely high probability of failure in objects of greater than this complexity).

Additionally, we may consider that aesthetic considerations coming from Japanese culture have driven some constraints (beauty, simplicity).

These cultural constraints themselves are process-dependent. If it were very easy to have made more complicated patterns, the value of simplicity might have been less apparent; on the other hand, the existence of an aesthetic of simplicity tends to constrain artists from experimentation with more complex forms.

Here, the artists begin with a raw material (paper) that is highly standardized is shape and form (flat, usually square) and originally, all origami was made on plain white paper. This has changed so that an endless variety of colors and textures are now used, but the starting point is still a uniform flat piece of paper.

With successive steps, there are many more ways to go wrong than to go right, and these compound as the piece becomes more complicated. Even the simplest folded crane has a high element of non-obviousness about it. No one on earth could fold an insect as recently as thirty years ago.

Simplicity may be a design feature. It may equally result from limited information -- either because information transfer is limited or because the information quantity increases too rapidly for efficient

The problem has been to devise a method for finding longer pathways to more complex shapes in an exponentially increasing sea of jumbled-looking possibilities. Lang is famous in large part because he developed software to help the process. As the Discover article makes clear, the software doesn't solve all the problems, it just narrows the possibilities. Still, this provides a light at the end of the tunnel for many complex designs -- the designer can at least know that there is a way, even if it is going to take some doing to figure it out.

At the same time, information transfer between origami artists has massively intensified. The New Yorker article lays out a short history of the art form, which blossomed during the mid-20th century as paper-folding was included in elementary school curricula, and popular magicians like Harry Houdini published books on the topic. The blossoming of more and more complex origami forms during the 1990's was made possible by international organizations and competitions -- effectively providing incentives for high-stakes exploration of folding-spaces. As people spent more time on origami, they found new ways to support themselves, from publishing instructional books to consulting with NASA on ways to fold solar panels. In short, origami became a skilled trade with multilevel professional communications.

So, if we ask the question, "How did this change in technology come about?", there are at least three answers. First, origami was adopted broadly outside the culture of its origin, causing new aesthetics to be applied to its products. Second, the incentives for innovation greatly increased, causing people to spend more time exploring folding pathways with high failure rates. Third, new search strategies and communication strategies increased the acquisition and transfer rates of information between origami artists.

With these changes, a group of artists following a broad but shallow tradition made a transition to a rich and deep field of possibilities, but a field increasingly constrained by a few important pathways widely shared among them. The essential methods for creating the narrow-appendages shared by insects, animals and human forms are a key example. Once these techniques were worked out, they were shared, subjected to subsequent alterations, and transmuted into legs, antlers, and horns.

(As an aside, the fact that magicians were an important part of this transition is characteristic of the same changes occurring in the field of illusion. The vast increases in complexity of equipment and processes, and their proliferation into more and more "unique" tricks has

How can you not love this?

In fact, origami as therapy has its proponents in 1991, at the Conference on Origami in Education and Therapy, a mental-health professional presented a paper detailing her origami work with prisoners. "The most rewarding of experiences," she wrote, "was that of observing the effect that Origami had on psychopathic killers."

(via Gene Expression)