Epsilons of Memories

Epsilon Camp, revisited 

 by Marcus

 

Part 1: for every e > 0

The sun was the cruelest thing in Saint Louis. It wasn’t like tropical Taiwan, where the sunlight is tempered a little by the constant storm clouds. It wasn’t like the deserts of Arizona either, where everything is just dry. In Saint Louis, the sun felt aggressive. Every ray of light was blasted directly into your face: bouncing off the water, or the glass windows of the skyscrapers, or even the metal of the Gateway Arch itself. I hated going outside in Saint Louis. That’s probably why I was so happy to stay inside and do math all day.

Saint Louis is where I first encountered Epsilon Camp, where they shove a bunch of ten-year-olds who can do algebra into a room for two weeks and gleefully watch over all the subsequent chaos. If you’ve been reading my blog for a really long time—as in, before it was Origami by Marcus II—you might remember some posts I made as a camp counselor there. But years before I was a counselor, I went there as a camper. It was that one fateful summer, on the campus of the Washington University of Saint Louis, that set me on the long, spiraling origami path that I’ve continued to walk ever since.

I don’t really have memories of Epsilon Camp in the early days. I have fragments of memories—epsilons of memories, if you will. My parents walking me into the central building on campus. Taking a lanyard with my name from a foldable plastic table. Spinning around in desperate circles trying to navigate the building. But I do clearly remember going to the introductory talk by the camp founder, Dr. George Thomas, explaining Epsilon Camp and why it was so special.

I did a little double take when I saw this elderly Indian man speaking at the front of the lecture hall in a very elderly-Indian-man accent and realized that yes, his name was George Thomas. That was the first of many surprising things about him. “Math comes from philosophy,” he said, really dragging the last word out. Philooooooosophyyyyyyy. This big, slightly crazed smile would show up on his face whenever he said it (he said it a lot). He drew a diagram of all the sciences up on the whiteboard: biology was based on chemistry, which was based on physics, which was based on math. But math, the purest of the intellectual disciplines, came from the human mind itself, and that made it special. Yes, I know that’s just a restatement of an xkcd comic. But back then, it blew our minds wide open.

 

Dr. George Thomas (from Epsilon Camp website)

 

Dr. Thomas discussed the life of Paul Erdös, the eccentric Hungarian mathematician, who coauthored so many papers that they invented a number—the Erdös number—that measures your distance from him by strings of successive collaborations. Erdös had an odd way of speaking English: among other things, he would refer to young children as “epsilons,” as the Greek letter e denotes very small quantities. The camp’s title was a direct homage to him. Dr. Thomas had never coauthored a paper directly with Erdös (his Erdös number was 2), but he spoke about Erdös like an old friend. One got the sense that a piece of Erdös’s spirit lived inside him, and he passed it down to us, the epsilons, in turn.

Dr. Thomas’s existence defied your expectations in more ways than one. A South Asian man in charge of a math camp would seem like a stereotype at first, but it actually isn’t. See, stereotypical Asians never love math. The stereotype is that we’re good at math because we work hard at it. To survive in the technocratic capitalist hellscape that is our country, everyone has to be good at math, so they can make all the AI chatbots and self-driving cars for the Elon Musks and Sam Altmans of the world to profit off of. Therefore, what better motivation to work hard at math than an entire race of people from halfway around the world that are better at it than you? But the genuine love of mathematics, that exists not for material gains but simply for its own sake, is never attributed to Asian people.

In the rare Hollywood films about people in love with math, from Good Will Hunting to A Beautiful Mind, they’re invariably white. (They’re also invariably men—a stereotype which Epsilon Camp only partially subverted—but that’s a topic for another essay.) To love mathematics so deeply that it becomes part of one’s soul, to transform it from work into play, is forbidden to Asians in the popular eye. But if you knew Dr. Thomas, you’d know otherwise. He lived and breathed math, and in those two precious weeks where we shared a lecture hall with him, we all did the same.

Here, I should explain the actual day-to-day structure of Epsilon Camp. Mornings were for breakfast, then the first class of the day. The first-years like me took Foundations of Logic; returning campers took Set Theory or Knot Theory. A lunch break followed, then we went to our second class on entirely different topics, like geometry or proving that 1+1=2 (don’t laugh—you go try and find a rigorous definition of what addition even is and then get back to me). After dinner was the really fun part: the end-of-day activities, where we’d get to blow off steam with any number of ostensibly math-based diversions. We could play with Zometools (a ball-and-stick geometric building kit), learn card games like poker, or my personal favorite: origami. You knew it was coming.

I got lucky heading into Epsilon Camp, considering that I’d just received a copy of Robert Lang’s Origami Insects II for my birthday and was eager to fold the ludicrously complicated models inside. (For those wondering, yes, it’s that copy.) But for the first few days, I didn’t even know origami was one of the activities. I’d go home and fold something fairly often, but I did that alone. After all, I always did origami alone. Why would that change at Epsilon Camp? I was in for one hell of a surprise.

I don’t quite remember how I found out about the origami group. Like I said, I only have epsilons of memories. But I walked into that activity room for the first time and my jaw dropped. All these other kids that I’d met at camp—doing origami! And not the basic stuff either: these kids were way beyond fortune-tellers and paper airplanes. They were taking on Tomoko Fuse and John Montroll, with the really advanced ones attempting Robert Lang and Satoshi Kamiya. The club even had a copy of Origami Design Secrets, which really blew my mind. But then again, where else but at Epsilon Camp would you find Origami Design Secrets, the most mathematical origami book ever written?

I quickly found a rhythm and a place among equals in the origami club. I say equals out of politeness; I knew I was the most skilled folder in the group. But raw skill didn’t actually matter in that community. We went on and on about box pleats and Huzita-Justin axioms and all these things only other folders would understand. It was our little universe that outsiders couldn’t enter, and it was the most glorious thing I knew.

I do have pictures of my origami bugs from that time. They’re kind of hilarious to look back on, given how poor the shaping is. But even with the limitations of kami, it’s clear that I was already exploring their expressive potential as much as I could. From an early age, I particularly adored the Longhorn Beetle, and that’s probably the best one in the set: 

 

 

 

 My most complete memories aren’t actually origami. Coming out of a class one day, we got a break from the angry, aggressive sun in the form of angry, aggressive rain. My friend and I stared out at the downpour, looked at each other knowingly, and sprinted back to the main hall as fast as we could. The sheets of water fell, soaking our clothes, as we shrieked in equal parts delight and fear. I stopped under the awning of the main hall, and my perfectly dry mother stood right there, shaking her head at me. She offered me a towel and I wrapped myself in it on the ride home, trying not to get the seat of the rental car drenched.

We were so incredibly brilliant; we were so utterly stupid.

 

Part 2: turning coffee into theorems

If the sun was the cruelest part of Saint Louis, the food was the cruelest part of Ogden, Utah. I don’t know what Joseph Smith was on when he founded Mormonism and said, “You know what would be a great idea for a religion? Constant green bean casserole and canned everything else!” I’m not exactly sure I want to know. The food on campus was out of the question. The nearest grocery store to this university was a thirty-minute drive away. But perhaps the most ridiculous thing was the complete lack of coffee.

Ever seen the musical The Book of Mormon? There’s one scene where the protagonist has a dream where he’s in hell with Jeffrey Dahmer, Hitler, and Johnnie Cochran. He’s also at one point tortured by two dancing coffee cups, an image that’s going to stick in my mind forever because it perfectly described the attitude the school had during Epsilon Camp. There was not a single cup of coffee to be found on campus whatsoever. Not even at the Starbucks. To say this didn’t sit well with a bunch of math professor parents would be the understatement of the decade. Immediately, they erupted in protest. So many complaints were made to the school staff that after a couple of days, they gave up and put a coffee machine back in the cafeteria. To think of the things that can awaken a revolutionary consciousness in mathematicians.

But as hilarious as the Great Coffee Revolution was, it mostly happened in the background. Several years had passed since I had last been to Epsilon Camp, and my younger sister was now planning to attend. I was going with the rest of my family and didn’t have many of my own plans besides hanging around awkwardly. But as always, I brought my origami books with me. In the years since I’d last been to Epsilon, I’d done something pretty significant with origami: started a blog. If nothing else, I could probably fold something good enough to post within the next two weeks.

As the start of camp drew closer, I didn’t expect much interesting stuff to happen. I certainly didn’t expect it when Dr. Thomas reached out and asked if I wanted to lead the origami activity. I’m sorry, what? Several of the end-of-day activities were led by parents, and apparently, the person who had done it over the last few years had declined to come back. Now, Dr. Thomas needed to find someone else experienced enough with origami to lead the activity—and guess who had decided to show up that year?

Not many people know that in the academic world, official structures of all kinds are quite flexible. Professors will write journal articles locked behind paywalls but will also upload them to places like arXiv for free. Lab safety regulations are taught in school as if they’re absolute and fixed, but in practice many of them vary according to a laboratory’s specific circumstances. In that spirit, why couldn’t I simply become an origami teacher? In the early days of Epsilon Camp, nothing was set in stone. So there I was, appointed as the activity lead, and that was it. Once again, Dr. Thomas defied your expectations.

My plans were immediately upended, in the best way possible. The first order of business was a quick trip to the closest Barnes & Noble for more origami books. The second was to rework my entire schedule around the fact that I was now working for Epsilon Camp in a semi-official capacity. In exchange for leading the origami club, I also had to be a teacher’s assistant for Set Theory, helping wrangle the kids into place during their classes. Thus a routine began: like Bruce Wayne and Batman, I was a billionaire philanthropist TA by day and a caped vigilante origami teacher by night. (This analogy kind of falls apart when you remember that TA’s aren’t even remotely close to being rich.)

I had gone out of my way to buy extra origami books, but it turned out that I hardly needed to: the kids practically fought over my copy of Montroll’s Classic Polyhedra Origami, which I should have predicted. I always viewed the artistic and technical halves of origami as equally relevant, so I wanted to make models that involved detailed shaping. But these kids didn’t quite think the same way, so they were always going to go for the most mathematical designs possible. Perhaps I thought I could make them care a little more about the artistry behind origami, but that would have taken time—and a lot of experience that I didn’t have yet.

There was one curious exception, a boy in the group who had a little more vision than the rest. One evening, he came up to me and asked if he could borrow my copy of Origami Insects II. Surprised, I let him. While the rest of the club fought over the shiny foil paper, he went to work on Robert Lang’s layered sink folds and unusual landmarks. Like myself so many years earlier, he was working with less-than-ideal materials, and the results reflected that. Still, we chatted away multiple evenings in the origami room, as equals in that space. Skill didn’t matter in that space, but neither did age; we saw ourselves in each other, different as we were.

At the end of my first week there, an idea struck me: what if I wrote a blog post about origami at Epsilon Camp? My blog mainly consisted of pictures at that point, and I had never written about my experiences with the origami community (not that I had many). So I started a series: intending to become the next Math with Bad Drawings, I wrote up four posts detailing my experiences at camp. Two of them were just recaps of various events, but the third and fourth were proper explanations of the mathematics of origami, like how to do angle trisections. They were a hit with my tiny audience, and I thought to myself: I’ve got this. My blog’s going to go viral one day, just you wait.

The old Epsilon Camp posts don’t exist anymore, after an incident where I backed up my blog improperly—and for the sake of my own vanity, I’m a little bit grateful. The writing is stilted, the revelations pitifully basic. Yet all the same, I can trace a direct line from my present-day writings back to my first few posts about camp. My official job may have been teaching origami, but the kids at camp taught me just as much about origami in return. They opened up a new avenue for my blog, where I searched for a deeper knowledge of origami beyond just creating models. In that one room on an unused college campus, where we sat and shared paper together, I was transformed. Once as student, once as teacher, always as part of something larger than myself.

 

Part 3: delta x

Compared to the first two, my third summer at Epsilon Camp was more of an evolutionary experience than a revolutionary one. That didn’t make it any less meaningful, of course. I was invited back to be the origami teacher, again, and I had all sorts of ideas on how to make it even better than last time. Of course, I’d spent an entire year thinking about this exact subject, so I was more than prepared. I brought more of John Montroll’s polyhedra books, knowing that Epsilon kids connected with geometry. I got different types of paper for the different projects that they liked, such as modulars. All was going according to plan.

The biggest difference, though, was the events. Last year, as the activity lead, I mostly sat back and folded for my own purposes, letting the kids do what they wanted largely on their own. That was the origami activity I had grown up with. But this year, I made it my job to organize the inaugural Epsilon Camp Paper Airplane Competition. What better draw for the origami club, I figured, than a chance to step up and prove yourself in a test of your origami skills? And against all odds, it actually worked.

In the days after I announced the paper airplane competition, the origami activity was abuzz with activity, as kids from other activities flocked to compete. Paper airplanes were thrown. Paper airplanes were picked up, had their noses straightened out, and were thrown again. Probably contributing to the excitement was the knowledge that I myself would be competing. Want a good motivation to join the origami activity? Imagine beating the activity lead at his own contest! Trust me when I say nothing motivates a ten-year-old like a chance to inflate their own ego.

Unbeknownst to them, I had a hidden weapon: the secret wisdom of the ancient Japanese. Well, actually, it was publicly available wisdom, and it came from just one Japanese guy, and he was only slightly less ancient than the invention of airmail. But in principle, I’m still right. In his book Origami from Angelfish to Zen, Peter Engel published a lengthy interview with Akira Yoshizawa, who famously made thousands of models consisting mostly of animal forms. But less famously, Yoshizawa also enjoyed making paper gliders. Furthermore, as he revealed to Engel, he had devised a test for them:

“And for the gliders I learned aerodynamics…. I have more than a hundred kinds, and I’m quite strict with them. Take a piece of paper fifty centimeters [about 20 inches] square. Wet it, make it into a ball, tie it with thread, squeeze it tight. When it dries it becomes hard, like a ball made of wood. Now, if you throw it, it will go quite far. But my gliders must go farther than that or they might as well not be gliders.”

So for my own entry, I constructed a modified version of Yoshizawa’s test: crumple up a piece of letter paper into a ball and throw it as hard as I could. I still maintain that this is the single funniest thing I’ve ever done. Kids would ask me, “what’s your paper airplane going to look like?” and I just smiled at them. They had no clue what was coming.

When the day came, the results were basically what I expected. Most of the airplanes lost to the crumpled-up ball. But not all of them! The insect kid was no longer attending camp, but there was always one quiet girl who spent all her time making Tomoko Fuse polyhedra in the back of the room. Out of all the paper airplane contestants, she understood the assignment and made a proper plane. And that was the only one that beat the test. Yoshizawa would be proud. Personally, I was just a tad disappointed, because the crumpled-up ball was now a slightly worse punchline. But when it comes to math there’s always someone better than you, and I had long since learned to revel in those moments. Especially at Epsilon Camp. 

 

My second place winning design (recreation), after A. Yoshizawa

With all this new material on my hands, what better to do than write about it? And indeed, the Epsilon Camp blog series returned. Unfortunately, it took a little longer this time: the last post came out almost a month after camp had ended. Perhaps this was the first sign of something I realized years later: I can’t write according to a deadline. It doesn’t seem to matter how simple or how complicated an essay is. If I set a specific length of time and try to get something out by the end of it, the result just feels hollow. My writing unfolds (pun absolutely intended) sporadically, over a period of weeks or even months. Uncoupling myself from a schedule allowed me to dive deeper and bring real thought to my blog posts.

My series only consisted of three parts, but I tried to say more than I had the previous year: I included some of my reflections about what it meant to be a teacher, and the value of connecting with younger generations. To my surprise, these got an even bigger response than the previous year’s posts, to the point where teachers at my own school complimented them. Since when had I connected with non-folders through my blog? That was further proof to me that origami had real emotional power, and that writing about origami could be a genuine form of self-expression. Once again, that lesson would become more and more true as I turned further to writing over the years.

On the last day of camp, I managed to squeeze in one more event: a showcase containing everyone’s models from our two weeks together. The whole camp oohed and aahed over the things we’d constructed, from polyhedra and animals to even some of the airplanes. After the ending ceremony we got yearbooks, and I chased down all the origami regulars, getting a signature from each one of them. Saying goodbye provoked a lot of feelings: dreading going back to school, laughing over the airplane competition, regretting all the events I hadn’t made time for. But I knew deep down that it didn’t matter, because I would be back. I just knew I would do things bigger and better next year.

So, as fate would have it, I didn’t.

 

Part 4: that this margin is too small to contain

Like everything else in the world, my plans for another summer of Epsilon Camp were rudely derailed in 2020 when a certain pandemic shut everything down. I did plenty of origami during lockdown, of course. With all that time on my hands, I continued my experiments with paper and made blog posts at a record pace. I even started writing proper essays about origami, distilling my numerous thoughts on the art into written form. Over time, the essays grew longer and more complex, until they almost fully subsumed my blog. The COVID-19 pandemic was truly a renaissance for Origami by Marcus. But for me it was also the end of Epsilon Camp.

By the time lockdown was lifted, my sister was too old for Epsilon Camp, so my biggest reason to go there had ended. My old do-it-on-the-side attitude would no longer cut it. So it was over. No goodbyes, no speeches, nothing. The blog posts I would have written, the events I would have planned, the people I would have met–all gone. Most of the kids I had gotten to know over the last two years I never saw again.

Maybe that’s the reason I left math behind. During my Epsilon Camp days, I had always wanted to be a math major; when I finally did go to college, I chose chemistry instead. It’s not like I completely gave up math (if you’re any sort of STEM major, you’re going to use at least a little). But all the same, math used to be my whole life. I did math competitions and took advanced math classes and, indeed, went to math summer camps. With the end of Epsilon Camp, all of that slowly fell away. The most substantial bits of math that I have now are my memories, and even those are fading.

G.H. Hardy once said, “Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. Immortality may be a silly word, but probably a mathematician has the best chance at whatever it may mean.” I don’t actually think this is true. Isn’t mathematics more than theorems we read in old textbooks? What about an old Indian man’s waxing over his love of Paul Erdös? What about the joy of hearing angry parents demand coffee? The exhilaration of silly paper airplane competitions where no one is trying to do well? My favorite parts of math are the small ones, the moments of community and connection­–and those are also the parts of math that get forgotten the fastest. No textbooks bother to record them.

Now might be a good time to discuss Fermat’s Last Theorem, a math problem so famous it got referenced in an episode of Star Trek. Its origin story is almost as famous: Fermat hardly thought anything of the theorem. He scribbled it in the side of an old algebra book, alongside a comment that every mathematician knows by heart: “I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.” I ask you this: How many marvelous things in mathematics are too big for the margins? How much of the mathematical experience does the world never glimpse, thanks to academic elitism?

Mathematics is so often treated as a detached, otherworldly enterprise, separate from messy human things like emotion or culture or, god forbid, politics. Math lovers exalt these qualities. Math haters condemn them. But neither side seems to grasp–never mind question–the deeper assumption underlying both. In case I haven’t been obvious enough, it’s complete nonsense! If math was as detached from humankind as humans seem to think it is, none of this essay would even exist. I write about Epsilon Camp as a deliberate act of remembering, a final attempt to prove that mathematical culture is just as bountiful and diverse as any other part of our culture. For every Archimedes there is a boy who loves Robert Lang insects. For every Fermat there is a girl who loves paper airplanes. The smallest figures in the world of mathematics, the epsilons, are the ones who give it true meaning. Those are worth just as much as any theorem or proof or textbook.

Dr. Thomas’s wisdom (or perhaps Randall Munroe’s) comes back to me all these years later: in contrast to the rest of the sciences, math is the one discipline that springs directly from the human mind itself, which makes it the most abstract of them all. Yet doesn’t that also make math the most human of all the sciences? Within math is contained all of our humanity–our loves, our fears, the deepest truths about ourselves. Some may scoff at this statement for being overly sentimental. But I dare you to find a single person who actually attended Epsilon Camp that disagrees with me.

Then the claim that math is beautiful on account of being “cold and austere” gets it completely backwards. Math is beautiful precisely because of its warmth and its humanity. And yes, to be human is to be mortal, to know that all things must die. The truly human parts of mathematics, the parts I want to remember the most, cannot escape mortality either. So I am at peace with the end of my time at Epsilon Camp. And if my memories must fade as well, so be it. They are like epsilons in their own way: always tending towards zero, leaving us with smaller and smaller pieces of them, never vanishing entirely.

Maybe that’s the real meaning behind origami at Epsilon Camp. Paper is delicate, fragile, ephemeral. Origami models are so easily swept away by the currents of time. Yet these qualities do not diminish origami; on the contrary, its short lifespan is precisely what makes origami beautiful. Origami, then, strikes deepest at the very meaning of the camp. I spent a total of six weeks at Epsilon Camp, long since passed on. Those brief moments are now forever consigned to the margins, where all living things must someday go. But they refuse to rest. They continue to grow, larger and larger, until the margins are finally too small to contain them.

 

Dedicated to Dr. Thomas, and all the epsilons, everywhere