Before we begin, I'd like to briefly apologize.
School has been taking up quite a bit of my time. This happens every year: I do a bunch of origami over the summer, get a good schedule going, and then September hits and I forget that this blog even existed.
These days, I try to stick to one model per month, with the occasional written post in between those monthly models. This was supposed to be completed by the end of August. So... yeah. I hope, however, that this post was worth the wait.
I'll get back to normal blog posts after this; however, in addition to folding new things, I'll also post older models. The time during which I can fold isn't always consistent, but that won't stop me from making content.
And with that, here's an essay on origami and stuff!
Part One: An Actual Introduction
Is origami an art or a science?
If you're like most people, this question probably seems silly. Origami is an art, obviously.
In origami, the artist folds a piece of paper, typically a square, to create some type of visual artwork. A folder uses paper as a medium for creation, as a blank canvas for drawing paper sculptures. Origami takes creativity, imagination, discovery--all deeply artistic concepts--and produces something like this scorpion. Is it even a question, really? How could origami be anything but an art form? (After all, what is this--an art blog or a science blog?) The history of origami is a history of artistry: in ancient Japan, "samurai warriors exchanged gifts adorned with noshi, good-luck tokens of folded paper and strips of abalone or dried meat. Shinto noblemen celebrated weddings with glasses of sake wrapped in male and female paper butterflies representing the bride and groom" [1]. From its inception, origami has been used as a decoration, as a visual showpiece, as an art. Origami is an art. Obviously.
And that's one view of origami, sure. But let me introduce you to another view.
In this view of origami, origami is transformed from an art into a science. In origami, the scientist folds a piece of paper to reveal hidden patterns within the universe. Folded paper is pure geometry, full of shapes, angles, and tessellations. Paper is a tool for scientific and mathematical discovery, not merely a showpiece to be put on display in a museum. Take a look back at the scorpion from the previous paragraph--but this time, look deeper, at the crease pattern. This may look like a bunch of colorful, meaningless nonsense, but it's quite possible to make sense of: it's the result of a hexagonal tiling, in which polygons have been placed to signify flaps, which later form legs and claws. If you need proof, look closely at the lines--they're all at angles that are multiples of 30 degrees. This scorpion requires creativity, and imagination, and discovery--all those good artistic concepts--but they have been flipped into profoundly mathematical concepts, used to create a highly mathematical origami design.
Mathematical origami is everywhere these days: in space, used in solar panels [2]; in car airbags, which need to be stored flat and expand quickly in the event of an emergency, and in the classrooms of MIT, which has a class on the geometry of folding taught by expert folder Erik Demaine (incidentally the youngest professor in MIT's history; he started teaching at 20). Perhaps mathematical origami is even older than this, originating with the geometric paperfolding traditions of the Spanish Moors. (We'll get to this later.) Even folders regarded as origami artists, like Robert Lang and Satoshi Kamiya, make extensive use of mathematics in their models.
I don't know about you, but origami is starting to sound an awful lot like a science to me.
So which is it? Could it be both? Is that even possible?
Part Two: A Union of Two Worlds
Let's take a look at the history of origami: paper was invented in China, and soon spread to surrounding countries, such as Japan. With the invention of washi--handmade Japanese artisanal paper--origami soon became a frequent pastime among Japanese nobility. (Paper was, of course, expensive back then: only the rich could afford to pursue origami.) Throughout the years, a small collection of traditional models was discovered, occasionally expanded on, and passed down through the generations. Even to many non-folders, this will not seem too hard to believe.
But the Japanese were not the only ones to develop origami. Paper was, at the time, an exciting new technology, and it quickly spread west through trade, where Middle Eastern and European nations eagerly accepted it. Soon, paper spread to a certain group of North African Muslims, the Moors. (If you've ever read Shakespeare's Othello, the titular character is a Moor--now you know what that means.) Simultaneously, Moorish populations in Spain developed paperfolding. Though the Moors were widely expelled during the Spanish Inquisition, folding--or papiroflexio, in Spanish--remained, and large paperfolding communities exist in Spanish-speaking countries to this day.
The Moorish tradition of paperfolding could hardly have been more different from the Japanese one. The Japanese folders depicted animals and everyday objects, and often used cuts to produce extra points. (It is easy to forget that the "no cutting" rule is actually a very modern restriction[3].) Japanese origami reflected the aesthetics of other Japanese arts: simplicity, subtlety, and minimalism. The Moors, on the other hand, had little use for wishy-washy artistic concepts.
It is easy to forget that Islam was an incredible source of mathematical knowledge during the Middle Ages, with Islamic scholars revolutionizing fields such as geometry and trigonometry (and outright inventing algebra). Moorish folding reflected a vast knowledge of geometry, experimenting with the symmetries and other properties of the folded square. In a sense, today's folding solar panels and airbags are the direct descendants of the papiroflexio experiments of the Moors.
The modern origami landscape is a result of the cross-pollination of these two worlds. Today's origami models require satisfying the demands of both artists and scientists. In the words of the folder Peter Engel: "[An origami model] must be anatomically accurate-a Western demand, not a Japanese one-and yet suggest more than it shows. It may employ folding techniques that are unexpected, but never arbitrary, and whose logic may become clear only when the entire figure has been completed."[1]
Part Three: Crossing the Divide
Let's take one more look at Islamic folding [4] and one of its more peculiar properties. The Moors were expert geometers, and their folding reflected this. But origami, like all Islamic art, was constrained by the rules of Islam itself: in particular, a complete ban on depictions of real-life objects [5]. It wasn't simply that Islamic folders didn't enjoy folding representational artwork--in accordance with their religion, they couldn't.
Let's take a small detour for a moment: The year was 1936. A young Dutch artist was touring around southern Europe, seeking inspiration. While in Spain, he came across the Alhambra: a Moorish palace decorated with the intricate geometric tilings that Islamic artists are so well known for. Fascinated, he began incorporating geometry into his work, producing impossible shapes and tessellations.
That artist's name, in case you're wondering, was M.C. Escher. Intrigued by Islam's ban on "images," he wrote the following words years after his journey:
"What a pity it was that Islam forbade the making of 'images.' In their tessellations they restricted themselves to figures with abstract geometrical shapes. So far as I know, no single Moorish artist ever made so bold (or maybe the idea never dawned on him) as to use concrete recognizable figures such as birds, fish, reptiles, and human beings... I find this restriction all the more unacceptable because it is precisely this crossing of the divide between abstract and concrete representations, between 'mute' and 'speaking' figures, which leads to the heart of what fascinates me above all in the regular division of the plane."
Let's focus on that last part: it is precisely the crossing of the divide between abstract and concrete representations which makes the regular division of the plane fascinating. The Moors believed that origami was to be pursued solely as a geometric, abstract art. Escher found this idea repulsive. To shun any attempt at artistic realism was pointless, contradictory. The entire purpose of art, especially geometric art like tessellations, was to try and create realistic-looking images, as difficult as it may have been.
Escher was referring to drawings and tessellations, but his beliefs can also be applied to origami. By making origami, a folder challenges themselves to create art that is both mathematically elegant and aesthetically pleasing. From Escher's point of view, then, origami is defined by its acceptance of art and mathematics, simultaneously, and it is enriched by incorporating both of them into itself.[6]
This is unusual, to say the least. Math can't mix well with art, can it? One is cold, calculating, and strict. The other is energetic, creative, full of life. The two couldn't be more different from one another.
But, like yin and yang, things that seem to be complete opposites can have a surprising amount in common.
Part Four: Explanations
So what makes science and art distinct from one another? On the surface, this question seems so trivial it is hardly even worth mentioning. But similar concepts unite the two disciplines: a constant search for patterns, a love of beauty and elegance, and an endless need for creative thinking. Besides the subject matter, there's quite a bit in common between the two. What, then, is the answer to the question?
The main divide between art and science seems to be that between discovery and creation. We discover science; we examine the world for the patterns it has created and bring them to the eyes of other humans. On the other hand, we create art: we make the patterns ourselves, and present them as uniquely our own. Discovery exposes ideas that exist regardless of the observer [7], while creation is inherently bound to the creator and their mind. If Da Vinci had never been born, could the Mona Lisa exist? Without Picasso, would someone else have created Cubism? I don't think so; such is the nature of art. By contrast, parallel scientific discoveries are almost comically frequent: Newton and Leibniz simultaneously invented calculus, and the three chemists Carl Scheele, Joseph Priestley, and Antoine Lavoisier all discovered the element oxygen.
The question, then, of "Is origami an art or a science?" can therefore be rephrased as, "Is origami discovered or created?" The answer, as I hope I have made clear in the previous paragraphs, is "both."
Why is this so? I believe this is due to the nature of origami as an art medium. There are also a massive number of restrictions on folded paper in comparison to more popular art forms like wood, stone, or canvas. In painting, one starts with a canvas and uses a brush to add various colored paints. In carving or woodworking, one starts with a piece of wood or stone and uses a chisel to carve out the undesired parts. In either case, one has a medium and a tool which shapes that medium. But in origami, the medium is the tool.
Any type of art is created: an artist has a unique vision, and shares that vision with the world. But in origami, any vision an artist can have is already there, in the paper itself. Therefore, just as they are created, origami artworks are discovered. To my (admittedly somewhat limited) knowledge, this is unique among art forms.
As a folder, I feel privileged to call myself an artist and a scientist, simultaneously. In the popular perception, the two are often considered separate. But in places like origami, the divide becomes muddled and difficult: "Somewhere in the accumulation of folds, absolute rigor gives way to beauty, and mathematical discovery yields to artistic creation." [1]
Part Five: Conclusions
I'm going to wrap this up with help from the great master, Akira Yoshizawa.
I've been referencing Peter Engel a few times throughout this essay. In truth, he inspired me to write this through his book, Origami: From Angelfish to Zen. The book is unique in that part of it is like a traditional origami book, with models, diagrams, and instructions. But the first half largely ignores actual models, instead being a discussion of the creative process, as well as the art, science, and history of origami.
If you're interested in learning more about origami, I can't recommend this book enough. There is so much more I wanted to discuss in this essay, but the things he's written about origami would... fill a book. I had to say it.
One of the sections in his book is a meeting with Yoshizawa himself, in which Yoshizawa discusses the influences on his work, such as Zen Buddhism. The interview is full of profound quotes, but one in particular stands out to me. Towards the end of the interview, Yoshizawa-san gives Engel the following words:
"There are two ways to the Zen style of living. One is to know the space around you, to know the world, and accept it. The other way is to know yourself, your feelings and what's inside you....If you know yourself and at the same time love nature and the people around you, the two ways of Zen will be united." [1]
Hmm... I wonder if this was a metaphor for origami. Knowing the world around you (a metaphor for science and discovery) and knowing yourself (a metaphor for art and creation), at the same time? Yoshizawa-sensei was certainly a wise person. I'll let you interpret that however you like.
In the end, I guess the question "Is origami an art or a science?" doesn't say so much about origami as it does about art and science.
Wow. That was a long post, and I don't think I'll do anything like this again. But you never know... I hope you enjoyed this, and I'll see you next month!
Oh, and if you're still around, here's an octopus from Angelfish to Zen:
Subject: Octopus
Designer: Peter Engel
Paper: 30x30 cm. foil paper
Sources and endnotes
1. Origami: From Angelfish to Zen, by Peter Engel.
2. Tony Grecius, "Solar Power, Origami-Style." https://www.nasa.gov/jpl/news/origami-style-solar-power-20140814
3. Jeremy Shafer, "Origami Purism." http://www.barf.cc/jeremy/origami/BOOK/essays/origami_purism/origami_purism.htm
4. I faced a bit of a dilemma on whether to call it "Spanish folding" or "Islamic folding." On one hand, as far as my research suggests, paperfolding was not ubiquitous to all Muslims, just the ones living in the Iberian peninsula. On the other hand, "Spanish folding" refers to not just mathematical folding, but also representational papiroflexio produced outside Islam's ban on such figures. That's an important distinction, and therefore, I went with Islamic folding.
5. How strictly Islamic artists had to follow this rule varies. Muslim religious authorities in different regions and time periods had different opinions on the subject, and a few Muslim paintings of humans and animals exist. This practice of aniconism existed to prevent the creation of idols, so all paintings were either highly stylized or clearly shown in submissive positions so it was clear they were not being worshiped. The most strictly prohibited thing in Islamic art was, obviously, the depiction of God (if you ever see someone folding an origami God, please let me know).
6. Here's another, similar quote from Escher: "Science and art sometimes can touch each other, like two pieces of the jigsaw puzzle which is our human life, and that contact may be made across the borderline between the two respective domains."
7. A related quote from Neil Degrasse Tyson: "The great thing about science is that it's true whether you believe in it or not."
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