You have to compare. So you can get a little distance from things. Like Laika. She really must have seen things in perspective. It’s important to keep a certain distance.

That’s what Ingemar says in one of my favorite movies, Mitt liv som hund.  It came to mind this past winter when the news reminded me that it was forty years ago, Christmas eve, that Apollo VIII cruised around the moon and sent back photos of our little blue earth. At the time, this seemed perfectly natural to me, that astronauts should be floating around in lunar orbit, reading Bible verses to those of us left crawling on the planet’s face. On the other hand, the clusterfuck in Vietnam also seemed perfectly natural to me — kids normalize things right out of the box and then spend the rest of their lives wondering why the box looks so funny.

It also reminded me of a Christmas eve I spent in København some years back, hanging with this obscure Danish sculptor, Berthel Thorwaldsen. It was crazy cold in Denmark that year, crazy cold and damp in ways that just don’t obtain in the New World and every time one complained about it, one was handed a glass of the medicinal extract of caraway. A dose of that would cause a sensation of warmth for thirty seconds, followed by a couple hours of temporal and spatial distortion and a very vivid delusion that the universe was constructed entirely of stale pumpernickel. Don’t know if one can say this really helps — not in the way, say, that throwing a turf on the fire might.

So, somewhere in the conversation, I said, “Your problem, Berthel, is that you’re Danish and obscure….”

“My problem,” he responded with a snarl, “is that I’m surrounded by barbarians.”  It was just me there in the pub — double vision is another side-effect of the medicinal extract of caraway. I was, to be fair, dressed as a barbarian — just the way I dressed in those days.  I tried again.

“An artist should always challenge his medium….”

Berthel slammed his fist on the table and threw me a malevolent sidewise glance. “You presume to speak to me of medium, yankee Visigoth? Let me tell you about medium: clay is the birth; plaster the death; and marble the resurrection.”

“But I work in paper, ” I said, “a developable surface….”

“Clay, life; plaster, death; marble, immortality! That’s it!”

Then he fell asleep, face down in a plate of sauerkraut and I had a hell of a time getting us back to his studio. Pretty freakin’ cold in there, too. Was there a peat shortage that winter? Certainly, there was no shortage of caraway seeds.

It’s so very easy to lose one’s perspective. Berthel, bless him, he’s dead now and presumably has gotten some of his back, but mine comes and goes with the shocking irregularity of a PVTA commuter bus on a Thursday evening. Whenever Eric Gjerde and I talk, after an hour or so, one of us is always sure to say, “For God’s sake, it’s just a piece of paper!” And we will hold that gnostic flash in our consciousness for a New York minute and then immediately return to our wonted obsessions.

Origami is a damned strange way to create art and one must never forget that. Even the odder of the outsider artists will look at origami models and say, “Pshaw, blood, what’s that about?” Origami is outside the mainstream of the art world and beyond the fringes of the backwaters — that’s okay.

A lot of it is medium — however lovely the paper, it remains an aggressively, heroically ephemeral choice. Every piece you fold is, to some extent, condemned to the slow burn of Time as soon as you put the final shaping to it. You can use the best paper and coat it with resins and polymers and put it beneath a bell jar inside a columbarium in a cathedral close, but still, the clock has started. And that’s okay, too — origami is a viral art and depends as much on the transmission of the idea as it does on the medium. The paper will perish — how should it not? — but the idea can live on in a very real and interesting way, not unlike the barbarian concept of immortality through glory.

Which brings me to ellipses. What, you were thinking it was only my prose style that was elliptical? Folding ellipses is like folding circles, but from a slightly different perspective — they force you to focus on the foci and that can be a little disorienting. But give it a try. I like the silver ellipse, myself– it has a ratio of one to the square root of two, just like A4, and this makes finding the foci particularly easy.

Here is a Rolling Box, which is made from a 2:1 ellipse. This is just a variation of the Box of Rox, which chungdha points out, is not an entirely new shape. (Indeed, shortly after he told me that, I saw an interesting lamp packaging thing, using a similar shape.) I like this one a lot — it’s pretty close to cylindrical, so it rolls nicely, and it also stands up in this slanty way. Here, try it out: a crease pattern.

Photo and hand by Andrew Hudson

Just a note to alert our readers to another publication well worth a visit and a read: Origami Weekly began publication earlier this year and has been warmly received by the greater folding community. It is the ambitious project of two young men out West, Andrew Hudson and Jared Needle, to publish diagrams on a weekly basis. And we’re not talking six-step penguins and duckies — this ain’t Origami for Eejits. In announcing their intention, Jared said:

Why, you say? Short answer: we’ve grown tired of folding the same “classic” models, and thought we’d spice it up a bit. Long answer: we’re looking for exposure, not only for ourselves, but also for the other folders that we’ll be featuring. We’re trying to freshen up the world of the advanced origami folder, while at the same time giving us a challenge and some extra experience. There is a lot of untapped talent in the amateur origami world, and it’s about time someone took notice!

Of course, it is somewhat lacking in grace for us to point at their blog the same week that they publish diagrams from your sometimes less-than-humble narrator, but if we allowed the knowledge of our native bumptiousness to curb our pen, hell, we’d never say anything at all. We will mention that the week before, the intrepid duo published the first ever (to our knowledge) CP of a Joel Cooper mask — go find that in the mainstream origami press!

Readers there may be who remember the Zhoubi Bowl — a CP appeared in these pages, oh, eons ago and some who saw it wished they had some diagrams to it. This week, Origami Weekly speaks to that desire. Read, mark, learn and inwardly digest. Then subscribe — we anticipate good things to come.

That’s my old friend, Catullus, who often wrote in hendecasyllabics, that is, an eleven syllable line. Here, he’s saying, To whom shall I give this pretty little blog entry? To you, gentle reader…

It occurred to me the other day that twist stars, such as the nine- and ten-pointed models I written about before, probably have an Al Gore Rhythmic method to them. So I thought about it a while and decided that there is.

Briefly, choose a regular polygon. Then choose a regular polygram to fold inside it. (There are very sharp ones and very dull ones — I like the middle ones, myself.) Now, fold another polygram inside the smaller polygon you just created, connecting not the corners, but the midpoints. This forms yet a third polygon in the middle. Make a tato from that smallest polygon, fold in and squash the pleats. That’s it.

Can’t quite visualize it? That’s okay, I made a slide show for a hendecagram twist star. (Or the detail view, if you prefer a slower approach.) Before you click over, you might want to print and cut out a hendecagon.

There’s nothing all that profound about these — they’re just pretty and look good in the window when the sun comes through. The method is extensible, but who knows how far? There are lots of regular polygons and a whole lot more polygrams.

Indiscipline

I do remember one thing.
It took hours and hours but…
by the time I was done with it,
I was so involved, I didn’t know what to think.
I carried it around with me for days and days…
playing little games
like not looking at it for a whole day
and then… looking at it.
to see if I still liked it.
I did.

I repeat myself when under stress.
I repeat myself when under stress.
I repeat myself when under stress.
I repeat myself when under stress.
I repeat…
The more I look at it,
the more I like it.
I do think it’s good.
The fact is…
no matter how closely I study it,
no matter how I take it apart,
no matter how I break it down,
It remains consistent.
I wish you were here to see it.

I like it!

(That’s a song by King Crimson which I’m tempted to embed here, but do not, for fear of alienating the uninitiated. It’s on Discipline, if you want to check it out.)

This is a tato that Claudine Pisale handed to me at the CDO convention in Verbania. She said it had been given to her by a Japanese neighbor and that she couldn’t see how it was done. (The version she gave me had pencil marks on it, from where she had copied the landmarks over.) She thought it traditional. The tricky part, said Claudine, is that there were no folds across the central square of the design.

Emma, who teaches math at Milano U., figured out a solution, but unfortunately, I don’t remember what it was — I was more than a little jet-lagged.

In the pocket of my wool waistcoat, I’ve carried the model and pulled it out, odd times, to take a whack at solving it. I came up with several solutions, but after a week or so, I’d trash them and start over. For one thing, I kept going at it with a shell on my head. Convinced that the offset was arbitary, I kept trying to mirror arbitrary angles. Got pretty good at it, too. But it wasn’t right. Eventually, I got out a ruler and a calculator and figured out it was done with fractions. Once I had that, I used Fujimoto’s method to mark the fractions on the edge of a square. Eccolo!

This is kind of crazy sophisticated for traditional. If any of you out there in TV land know anything about this model, I’d love to hear it.

Fold one for yourself — diagrams.

This is Nathan Austin, after a long night of working on a tessellation. We’re sure many of our readers know this feeling. Nathan is a film director, an occasional poet (that is, he writes nonce verse, not poems every so often), and an alumnus of the College where I work. We met a couple years back. (The photo is by Andy Tew, a talented young photographer, an alumnus, who works for the College. He’s also quite tall and has been known to pour milkshakes on people’s heads, so I hope he doesn’t mind my using it.)

What happened was that I had to go over to the Campus Center and drop off something. As I walked by the reception booth, I noticed half of a curved stellated tetrahedron, pinned to the bulletin board.

Further up the wall, I spied Eric Gjerde’s spread hexagons, folded from a stock certificate, and I thought to myself, “Hmm, there is some young person hereabouts of remarkable taste and abilities.” I asked the young woman working the booth and she said Nate, who worked the night shift, had folded them. “It’s really boring at night,” she explained.

I checked my visitor logs and found that, indeed, late at night, this blog was sometimes visited by someone with a Mac notebook and a College IP address.

The next time I walked through the campus center, I saw a young man in the booth, tessellating away, so I introduced myself. Nate was a little surprised. We chatted.

Some months later, Nate called me up and wanted to meet to talk folding. So we met at the Dirty Truth, a marvelous pub downtown, and spoke about a short film Nate had in his head, a movie about a girl and a tessellated dress. What did I know of such things? So, I told him about Eric and Christiane and Joel and Jane and of course, Polly — he knew most of the names already, but was impressed that we all knew each other. He described the plot to me — sounded fascinating.

That was a year ago. Yesterday, I received an email from Nate with this photo.

The actress is Emma Jaster, also an alumna. I met her briefly, when she was working in our Theater department. (All new employees are required to speak with me for thirty minutes — discourages the faint-hearted from applying, I like to think.)

Nate will tell you the rest:

So, I was on the bus the other day, cheerfully folding away and rocking out to an old Bowie/Eno song and got to thinking about culture. The song was ostensibly about culture, you see — Bowie says:

It’s not as truly hostile about Americans as say “Born in the U.S.A.”: it’s merely sardonic. I was traveling in Java when the first McDonald’s went up: it was like, “for fuck’s sake.” The invasion by any homogenized culture is so depressing, the erection of another Disney World in, say, Umbria, Italy, more so. It strangles the indigenous culture and narrows expression of life.

Really? This seems a rather incongruous expression of outrage for a rock-and-roll musician. Rock-and-roll is not exactly a culturally pure idiom — certainly not the kind Bowie has pursued all these years — nor is it a genre particularly averse to propagation.

One can imagine oneself, sitting in the McD’s in Jakarta, pushing a PaNas Special around the plate with a plastic fork, watching the local students though the glass, protesting something strikingly nongermane, and hearing this song on the radio. Rock-and-roll gets around — that’s what it does. Rock-and-roll is a little, you know, American that way. Perhaps David was dabbling more in the ironic here than the sardonic.

A lot of culture entities have spent too much time in the blender, were you asking me. Musical theater. Ballet. Haute cuisine. Don’t get me started on free verse. But you know, it’s not all that difficult to avoid cultural forces you don’t approve of. Say, someone offers you tickets to the ballet. You reply, sir, ballet is a decadent art form, deleterious to the common good, fostering inhuman ideals in its followers and deforming the feet of its practitioners. Yeah, you will still have to take the tickets and sit there for three hours, but you will definitely be off the list for the cast party. Count it as a victory and move on.

And what has this to do with origami? Well, origami comes with all sorts of cultural baggage: the foreign name, the missionary zeal of its adherents, the Sadako mythology, the seemingly endless number of penguin models…and there’s the internal culture, as well. Modern origami has developed all sorts of cultural norms and squirrelly values in the past few decades, things you don’t find out about until after you’ve been converted by the zealous missionaries: the square thing, the no-cuts/no glue thing, the cult of the creative genius, the antiquarian reverence for diagrams, and most of all, the hegemony of the power of 2. Think about how many models involve dividing by 2 and then by 4 and again by 8…and your angles, there? How many are 90° and 45° and then to 22½° and 11¼°? Why? Sure, it’s simple, but it’s clearly not the only way to go. You can make simple and intermediate models from other numbers, but none or few ever do. Listen up, all you protest kids, 1/2ⁿ is the white bread of paperfolding. You can live on white bread, but why not challenge your palate a bit? Here, try a nice tasty seven.

First, mark the halves on the top and bottom edges.

Then mark the quarters on the upper left and lower right.

Fold from the quarter marks to the corners.

Now, make a diagonal crease and note where it crosses the creases you just made.

Fold horizontals and verticals through those crossings. You’ve found the 3/7 and 4/7 on this square. (This is all from Kazuo Haga, by the way. Did you read his new book, yet?)

Fraught with possibilities, I hear you say? Go for it. It’ll give you something to do with the program at the ballet. Or you can fold up the tray liner at the Jakarta McD’s, while you’re waiting for the students to move on.

Being a boxy kind of guy, I made a box out of it, and yes, I used nothing but 1/2ⁿ angles here. Have a crease pattern.

I’m pretty sure that the Javan and Umbrian cultures are sufficiently vital to put up with a little competition, especially if it’s from something as bland as hamburgers and Mickey Mouse. Me, I’d like to hear this song done by a gamelan, wouldn’t you?

Though the most credulous of men, I have trouble believing many things. For instance, I don’t believe an Airbus A320 can float. Just took one from Madrid to Milan and I don’t really believe they can fly, either. It’s morning on Inauguration Day and I don’t believe those cynical criminals will actually step down on schedule. Fortunately, the world does not rely on me for magical thinking.

Happy Inauguration Day!

Joel is a soft-spoken man with an air of affable gravitas and he often says things that strike me as being immensely wise. It’s just his way. When we were sitting on the concrete on 27th Street this past June, Joel said, “Try the hummus, it’s very good.” And it was — but then I thought, Does he mean the hummus Jane just got at the store? Or does he mean the Hummus of Life? I nodded. Yes, the Hummus of Life is good, but what does this make the pita chips? Truth? Amity?

Such thoughts are difficult for me — casual introspection is a two-edged blade and as such, is illegal in Massachusetts.

This  is a tato box I made, using some of Nakao Takeda’s ideas about kaki self-locks. A certain Swiss miss (no, not that one) reminds me today that I shouldn’t get bummed out to find I didn’t actually invent the lightbulb. Who invented what is always somewhat up in the air. (Nikola, am I right?) And art is not, after all, a freakin’ contest — we’re all just trying to spread the joy. Sometimes, that takes time. Sometimes, it takes thinking other people’s thoughts — it’s okay, they always come out differently. Here’s a crease pattern.

Did I mention that Joel has an Etsy shop? Well, I probably should then and the prices are darned reasonable. (Without Bacchus and Ceres, Venus gets a little chilly, tell you what.)

Anyway, there I was, sitting on the concrete with Joel and Jane, munching and folding and thinking, Yes, yes, the Kalamata olives are the bitterness and the richness of our Western heritage. The Medjool dates represent the sweetness of the opinions in the Babylonian Talmud or maybe they’re Omar Khayyám’s algorithms…. And then some zaftig young ladies in Brasilian football jerseys walked by, hooting and whooping. Was it for the world cup or for gay pride? I forget, but either way, I got distracted.

In the grand scheme of things, the pita chips are probably ourselves, but you know, the Hummus of Life is so very garlicky, that we should all eat it or none of us should.

This is a tato box:

by which I mean, an origami box with radial symmetry and a closure the resembles that of a tato, a traditional Japanese purse. In the past year, I think I’ve made dozens of these: different number of sides, curved, straight, slanted…. My colleague, Mélisande*, has created as many more, using a rather different construction method. The tato box is a good design to play with and we’ve certainly had a lot of fun with it.

This past week, I began to find that these boxes existed in the commerical world — they were being sold in galleries in New York and being used to hold gift cards for a largish dealer of ladies’ nether garments. For a while, being a vain creature, I imagined that these folks were modifying some of my designs — except that they weren’t. Twenty years ago, Kunio Ekiguchi, a Japanese author who writes about gift wrapping, published a design for a twelve-sided tato box in this book. He called it Chrysanthemum Box. The boxes I was seeing were manufactured versions of this and an eight-sided variation. That which is done is that which shall be done: and there is no new thing under the sun. (Including that last line.)

The boxes I’ve folded in the last year are not descended from Mr. Ekiguchi’s — just found out about him — but they sure look as though they might have been. The resemblance is accidental, but that doesn’t mean it doesn’t exist or that the resemblance might not have grieved Mr. Ekiguchi.

Such duplication of effort is not exactly a new thing in origami, particularly with the more geometric models. And the fact that someone else already trod these same paths should not stop us from following them where they lead — but it is meet and right to mention those we now know to have been there before us, like Mr. Ekiguchi. (And Lai Chen-Hsiang from Taiwan, too, who has made similar boxes with a different closure method.)

This said, the crease pattern for the seventeen-sided model above and another for the seven-sided model below.

An idea I had, early one morning — a trompe-l’œil tato box, very impure.

A magician, perhaps, could work up some patter for collapsing the box, but it would be far beyond my talents.

Whist is an old game — I learnt when I was in school — all I remember is that the rules were strange, arbitrary and I was terrible at it. That, and you were dealt 13 cards at the beginning of the hand. Horatio Hornblower supported himself between the wars by playing whist — that was before I knew him.

Here’s a crease pattern — print it back-to-back and cut out along the edge of the cards. Ooh, concave edges and so impure! Relax, you can take a shower later.

Big shout out to David Bellot, who made the SVG cards used here.

Update:

I think this is more engaging as a curved box. Here the crease pattern for that.