When origamist Peter Engel, who trained as an architect, visited the origami master Akira Yoshizawa, he asked the master whether he’d folded dinosaurs. Yoshizawa replied, “All of them! Tyrannosaurus rex. Iguanodon. Triceratops. Brontosaurus. Stegosaurus. I’d show them to you, but they’re in the attic.” (Folding the Universe: Origami From Angelfish to Zen (1989), p. 33.) There! In my mind, I’ve justified this post, and I do return to ancient creatures at the end.
In the middle of the 20th century, Yoshizawa almost single handedly remade origami, creating new models more complex than had been seen heretofore and in staggering numbers. So it was no wonder that Engel described his visit in terms appropriate for an acolyte gaining audience with a high priest. It was a religious experience. Ultimately Yoshizawa was not alone in breaking through the traditional boundaries that had contained origami. For what might be labeled the origami revolution of the mid- to late-20th century, Yoshizawa not only broke through traditional barriers to show what was possible, but he also played a central role in codifying the symbols and notations used to record folds in origami instructions. This powerful development enabled paper folders to follow instructions regardless of the language they spoke. And so the revolution spread.
In the revolution, origami crossed myriad boundaries and is still crossing them: from the relatively abstract to the very concrete (particularly objects from natural history), from the simple to the extremely complex, from the artistic to the practical, from art to mathematics and back to art, from the stasis of tradition to a state of rapid, continuous evolution.
Much of my writing for this blog has sought to cross lines that normally compartmentalize the amateur from the professional, the collector from the scientist. I have tried to move beyond visceral reactions to fossils and other aspects of natural history to explore the all-important backstory. It’s in the traversing of such boundaries that the context becomes broader and richer, and, concomitantly, the original object more meaningful.
As for origami, I am just a dabbler, decidedly an amateur, capable of only creating simple figures (from cootie-catchers to cranes, but not much beyond). My frustration level rises markedly as the number of steps in a pattern grows, and it’s in those lengthy instructions that the true richness of the art form lies. Despite my inability to cross the boundary into the complex, I find origami endlessly fascinating.
Origami (from the Japanese for to fold and paper) dates back centuries in Japan, though similar art forms appear to have emerged independently elsewhere. Given the stability in designs over much of origami’s existence, the potential for making figures from folding a single sheet of paper would seem to have been exhausted. Then a flowering occurred. Traditional instructions of a limited number of steps blossomed into ones with hundreds of steps. As physicist Robert J. Lang, one of the key players in this revolution, wrote in his The Complete Book of Origami: Step-by-Step Instructions in Over 1000 Diagrams (1988), “The detail in complex folds can be astounding, for the artists of the modern era have carried origami to unprecedented heights of realism and complexity.” (p. 1.)
The revolution involved many things. Even more than by the ability to chronicle instructions in a near-universal language (see Yoshizawa above), the revolution was fueled by rigorous mathematical analysis of the patterns of creases and folds recorded in the paper from the action of origami creation. As writer Beth Jensen noted in her profile of Lang for Smithsonian Magazine (Into the Fold: Physicist Robert Land Has Taken the Ancient Art of Origami to New Dimensions, June 2007), “Lang and others use analytical geometry, linear algebra, calculus and graph theory to solve origami problems.” Technology has a role to play as well. Lang wrote a computer program that can generate the crease and fold patterns needed to fashion complex figures. Another program can then derive the various sequence of steps that might be needed to create such models. These programs don’t do all of the work. Indeed, as Lang has observed, although parts of origami can be captured by equations, “the artistic aspect will never be captured in equations.” (Jensen, Into the Fold.)
Art to mathematics back to art as the paper folder strives to inch closer to the essence of the organism being depicted.
For more on Lang, I highly recommended the article by Susan Orlean titled The Origami Lab: Why a Physicist Dropped Everything for Paper Folding, The New Yorker, February 11, 2007, and Lang’s TED Talk of February 2008. The Mitsubishi car commercial he runs in the middle of the talk is worth the price of admission.
As I’ve noted, for some, the appreciation of origami borders on (and perhaps embraces) a religious fervor. In Folding the Universe, Engel begins his exploration of the connections of origami to nature, science, and, indeed, life, by quoting artist M.C. Escher. Escher was quite taken by the patterns in the tiles decorating the Alhambra. Applying these patterns to figures from nature was, he believed, a “crossing of the divide between abstract and concrete representations” (as quoted in Engel, p. 3). The theme of crossing divides underlies Engel’s book, and it’s at the heart of his fascination with the art form. Taking a single sheet of paper and transforming it into a object calls on the folder to cross a divide. As Engel would have it:
Crossing the divide is a spiritual act. . . . In the paper, as in the primordial cosmic soup, chaos yields to order, formlessness to form, darkness to light. (p. 5)My appreciation doesn’t rise to such heights, but that concept of crossing boundaries or lines attracts me. As I've already stated, my folding fails to cross the line that separates simple, relatively abstract representations of nature from complex near approximations of reality. For the former, here are several of my origami pieces created by following very simple, long-established patterns. Lest they be too abstract or crude, they are a mouse and a duck.
In contrast, a post-revolution creation by Fumiaki Kawahata appears below.
(This image was taken from Wikimedia Commons and purports to be in the public domain and licensed under the Creative Commons Attribution 2.0 Generic license.) []
Origami has crossed from the artistic to the practical. Lang, in his TED Talk, considers an aspect of this process. Origami, by developing techniques for folding and compressing a sheet of material into a particular shape, has generated approaches that are applicable to real world concerns. How, for example, can one efficiently and effectively pack an airbag into the dashboard of a car? Origami has contributed to solving that challenge, as it has to addressing the problem of folding a stent for transport through a blood vessel until it reaches the place where it can be unfolded and do its job. Origami has also been involved in development of ways to get the broad array of a telescope into space when, to reach space, it has to fit within the relatively narrow confines of a spacecraft’s cargo hold.
The trail of ancient animals leads from Yoshizawa to Lang, from those that would fit comfortably (probably in small boxes) in the attic in Yoshizawa’s house to a life-size Pteranodon that majestically soars in the high, far reaches of the ceiling in the Dawson Gallery of McGill University’s Redpath Museum. The latter is one of Lang’s “monumental origami” creations. Such origami is described on Lang’s website.
One of the characteristics of origami is that it embodies a contradiction: how can such an intricate, detailed object come from a single uncut square? Monumental origami takes that contradiction and expands upon it. Conventional, bread-box-sized-or-smaller origami challenges the observer: is it possible from a single sheet? Monumental origami makes the same challenge, but adds the element of size to the mix.The Pteranodon was a flying reptile that flew the skies of the Cretaceous (possibly from about 72 to 89 million years ago). Though in some Pteranodon species, the wingspan stretched to more than 23 feet, the span in the model that Lang made for the Redpath Museum comes in at merely 16 feet. Here it is in all its glory:
(This image is reproduced with the generous permission of the Redpath Museum and appears on its website.)
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