The Fitful Flog

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!

Our friend and unindicted co-conspirator, origamijoel, said that to me recently and it sounded immensely wise.

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.

Well, rather a left-handed apology, as the injury to him is largely imaginary and thoroughly unintentional, but an apology, nevertheless.

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.

We haven’t finished this yet, but we still wanted to tell you about it. It’s Kazuo Haga’s new book, Origamics: Mathematical Explorations Through Paper Folding (ISBN-13: 978-9812834898).

We’re no math head — anything above the most primitive forms of trig causes us anxiety and vague spiritual discomfort. That isn’t because we don’t enjoy the underlying principles of mathematics; it’s because mathematicians, ever since the late Renaissance, have insisted on divorcing number from distance and stacking abstraction upon abstraction until Hell won’t have it. We’re sure it’s all very interesting, if you can master the syntax — but that’s where we get off. We like geometry, not this airy-fairy chop-logic they teach in the schools.

So this books hits me where I live — I already knew the three Haga theorems from Kasahara’s books, Origami³ and the article on the Tanteidan site, but useful as they are, I can’t say I ever really understood where they came from or how they worked. The first few chapters work you through the reasoning behind the theorems and then delightfully extend them to silver rectangles — you know, A4 and its ilk. Nice, slow presentation, with a very personable narrator and the math remains within the world of the real. A very pleasant read.

Example: in the midst of discussing his third theorem, Haga comments:

I thought of this folding more than 10 years after the publication of Haga’s second theorem. My profession is biology, and for a while I concentrated on a new phenomenon in my field, and so I did not have time to play with those paper squares. I used to do paper folding while riding on the bus or train. I thought of this new way of folding while I was on a bus going from Tokyo station to Tsukuba Center. I did not notice I was talking to myself at that time, until some of the other passengers started staring at me. Suddenly, I felt embarrassed. Nevertheless, I was excited by my discovery and continued to look for relations as the bus proceeded.

I suppose we all like to read ourselves into any novel that comes to hand — as an inveterate bus folder, I found this little confession just delightful.

The middle of the book delves into distribution maps and this, of course, goes right by me.  Maybe I’ll get it the next time I read through. Tend to doubt it, though.

The last section is a wonderful fairytale about the King of Origami Land, who throws a wandering stranger into the dungeon for daring to fold rectangles instead of squares. The stranger is sentenced to starve in jail, unless he can fold his A4 into 17 equal sections. Won’t tell you how it ends, but it’s a rattling good story and not a bad reflection on the hegemony of the square-headed over today’s Origami Land.

The world needs more such math books.

Yesterday, I was at the Smith College Museum of Art, a lovely collection in a building of shocking hideosity, and they had a newish painting that caught my eye — it used a palimpsest technique that a friend of mine once used to good effect. One of the layers was a sketch of the Vitruvian man, a pretty obvious one, I thought, but it being a teaching museum, there was a placard right next to the painting, explaining who the Vitruvian man was. And that reminded me of something Mélisande* said a couple years back, about the feet being a heptagon’s edge apart.

So, I figured, why not? Make a palimpsest version of the Box of Seven Joys — you print it out, duplex. On my printer, that means I go and flip the paper around and run it through again. Your mileage may vary.

Crease Pattern

Missus oschene sees this and says, “That looks just like your physical therapy exercises on the refrigerator.” She’s right, it does, except that the physical therapy guy is wearing boxers and has a less rugged visage.

This is a video response to the Spiral Data Tato from whiteandfluffy701d, which has been on YouTube for a few months and somehow went right by me. A very nice production. (And, I should mention, detailed directions for this model can be had at Instructables.)

Also well worth noting is this, which I believe to be Fernando Sierra:

The way he scales up ideas and folding techniques is inspring.

There been times that I thought I couldn’t last for long
But now I think I’m able to carry on
It’s been a long, a long time coming
But I know a change gonna come, oh yes it will

This is a song that was released in 1964, shortly after Sam Cooke was killed (under strange and suspicious circumstances) in Los Angeles, California. Cooke had been a gospel singer who made the switch to pop and rock-and-roll at a time when it was considered egregiously wicked to use one’s talent for anything other than singing ad majorem gloriam dei. Sure glad he did. This song (and 1960’s Chain Gang) did as much to raise the national awareness as the lunch counter sit-ins did.

The song’s been much in mind, this past week. The electoral victory of Barack Obama is an epoch for this nation, the change that Martin Luther King, Jr. and Sam Cooke prophesied so long ago, a beautiful thing. Even those malefactors in the Republican party realized that — and promptly jumped on the bandwagon of grace-in-defeat. Well good for them — if lip-service is the best one can hope for, it’s best to have it up front.

Still, it leaves me playing games in my head. Obama was not elected because he’s a black man, but because he’s a good man who happens to be black and Americans are finally (kinda sorta) okay with that. What if he’d been Ojibwa or Mahican? Does American tolerance stretch that far? Maybe — I have my doubts. It’s nice to dream of a new world coming where a Traveller could become Taoiseach or where a Bukaru might lead the Japanese Diet or where the prime minister of Hungary just might happen to be a Rom. This could take a while, but it’s probably good to stay in practice, dreaming. In my lifetime, man has walked on the moon, the Boston Red Sox have won the series twice and a black man has been elected president. Yeah, we need to dream big and then a bit bigger.

When I dream, I tend to dream of curved surfaces and data streams — you don’t want to get inside this head, you really don’t. Lately, I’ve been dreaming of Golaseccan ceramics: one, because our friend, Mélisande*, was recently on vacation in North Golasecchistan and took some pictures at one of their museums:

and two, because we are journeying to South Golasecchistan in a few weeks, to attend the 26th convention of the Centro Diffusione Origami in Verbania, Italy. This is a big deal for me. I’ll take some pictures. (Somewhere, in my files, is a 30 year-old letter, announcing the founding of the CDO. Looked for it this morning, couldn’t find it. Ah, well, it’ll show up, things always do.)

(Did I mention, I just got back from San Francisco, California, where I attended a really nice retreat for Pacific Rim Origami? Jeremy Shafer described PRO as the origami Illuminati, which, so far, is the best description of the group I’ve heard. Nicest bunch of people you could ever want to hang with, tell you what. Bernie Peyton is a freakin’ prince.)

Anyhow, I’ve been working on folding shapes that these Iron Age beer glasses describe. This one, which surfaced in Pombia, has caught my attention.

I’ve been kicking around this idea for a while now, of modeling concave objects by sampling radii and then conceptualizing polygons of the same size, stacked up. If you made creases that described the curves made by the vertices of these polygons, you’d get a paper version of that shape. Something like this.

I suspect I’m missing some important pieces of this, but it is, as I observed above, important to keep dreaming big. ‘Cause I know, I know, a change gonna come.

Crease pattern for the Bicchiere Pombiese.