Rubik’s cube, Dyson’s sphere, Maslow’s pyramid, etc.—the list goes on: standard shapes imbued with meaning or purpose and named after their creators. It’s one of the surest, easiest ways to attain immortality; you’re not inventing something new, just taking an existing shape and slapping your name on it. I’m determined to join the ranks of Rubik, Dyson, Maslow, et al by getting a shape to bear my name. But what shape?
First, I need to know what shapes there are. I pay a visit to the Science Museum, conveniently next door to my apartment building, and ask the woman at the front desk if they have an exhibit on shapes. She sends me to the gift shop’s children’s book section, where I find a board book laying out the usual suspects (circle, square, triangle, etc.); a picture book with more advanced shapes (rhombus, trapezoid, hexagon, etc.); and a pop-up book with three-dimensional shapes (sphere, cube, pyramid, etc.). While some of these shapes are already spoken for, I’m still overwhelmed with options. Which to choose? I shouldn’t pick one just on a whim. For my name shape to be famous, I’ll need to pick a shape that captures the imagination of the public and/or gives it meaning and/or purpose (i.e. addresses problem that needs solving). To get a clue in that direction I’ll have to take those questions directly to the public with market research. But I’m hungry, and have already made good progress anyway. Time for a break and a meal.
I hop on the subway—what the English call the “tube”—and as I’m riding it to my favorite pub I think: tube! I should add that to my list. But is a tube a shape? No. A shape has to be complete, closed on all sides. A tube is a cylinder with its ends cut off. A tube, at best, connects shapes—but isn’t a shape itself. Ah, but here I am, still thinking about shapes! I’m supposed to be taking a break! If I keep this up, I’ll burn myself out in no time. After missing my stop and doubling back, I make my way to my favorite pub, Trudy’s, where I’m one of the few original regulars. I’ve been coming every single day since it opened—last Friday, I believe. I swing through the heavy wooden doors, say hello to my fellow patrons, and then plonk down on my seat at the bar.
“The usual?” says Trudy.
“You bet,” I say. “Long day.”
With shapes still on my mind when my order arrives a few minutes later, I look at my usual meal through a different lens. My wine glass filled with pinot noir mixed with Diet 7Up: a bowl shape (half a sphere) sitting on a stem shape (a cylinder) connected to a disk-shaped base (a circle). My cheesy penne with crusty croutons and canned clams is served on a plate (a circle), and my many individual penne are tubes. But a tube isn’t a shape, I remind myself. I have to stop thinking about tubes!
“Did you say something about tubes?” says Trudy, noticing I’ve been thinking out loud this whole time.
“Oh, um,” I say, thinking of a cover story so that I don’t have to explain the whole thing. “I could use a tube for my drink.”
“You mean a straw?” she says, plopping it into my glass, fizzing it up.
“That’s the word,” I say, snapping my fingers in recognition as the spherical bubbles lift the tubular straw to the surface of my drink. “A straw is a tube.”
“Thank god for tubes!” says Trudy.
“But they’re not shapes,” I say, quietly, to myself, jabbing my fork (cylinder with four cones) into a penne.
A shape has to be complete, closed on all sides. A tube is a cylinder with its ends cut off. A tube, at best, connects shapes—but isn’t a shape itself.
After finishing my meal I take a long walk home, reflecting on my day, exhausted but excited for the task ahead. When I get back into my apartment, my common-law spouse Bianca is already asleep. Wonderful Bianca, always supportive and kind, catching her Zs as beautifully as ever. I quietly slip into bed and kiss her on the forehead.
“Happy anniversary,” I say to her.
“In two days,” she mumbles.
“Right,” I say.
“How’s the shapes thing coming?”
“Terrific so far, Bianca.”
“Have you packed for the trip yet?”
“Yes,” I say, which reminds me that I have to pack for our upcoming anniversary trip. I rest my head on the pillow and begin to drift off to slumberland as visions of anthropomorphic shapes dance in my head.
I wake up the next morning energized for market research! After downing a cold brew and gobbling a quick brekkie I grab a clipboard and race out the door to start asking the public what their favorite shape is and what problems in their life need solving.
This starts off a bit rocky. In my haste, I forget to bring a pen and paper, and so the only way to record responses on the clipboard is to carve them directly into the particle board backing with my keys. I also realize that I’ve forgotten to get dressed after breakfast and am still wearing just my bathrobe. I’d be more successful at this with paper, pen, pants, and a shirt, but I still manage to get a ton of responses. The problem: everyone says their favorite shape is a tube! Every single person! I try arguing with them that a tube isn’t a shape, but that only seems to strengthen their resolve. Even when I ask them for a backup shape, they refuse to provide one. This just proves yet again that you can’t change the public’s mind once it’s already made up. Begrudgingly, I accept tube as my chosen shape.
Now, what to do with the tube that will make it my own? I was hoping my second question—what’s a problem in your life that needs solving?—would yield results. But the results are all over the map. Turns out, people have lots of problems, including some big ones, and for the life of me I can’t figure out how a tube or tubes will fix them. I duck into a cafe to do some brainstorming. I order a half-caff-coff, grab a seat by the window, and take a deep sip. I imagine the trip the liquid takes through my body: down my tubular esophagus, through my tubular intestines, out my tubular urethra, and then, after flushing, down the tubular pipes. After twenty minutes of sipping, the barista comes by with a fresh carafe and asks if I’d like a top up. As he’s pouring, I think of something.
“Hey, wouldn’t it be great if there were tubes coming from the coffee machine that went to the ceiling and then dropped down at each table, so that you could refill each person’s coffee without having to get up?”
The barista thinks about it for a second.
“Just one more thing to clean at the end of the day,” he says.
He’s right. It’s a bad idea. All the tube ideas I thought of at the cafe—tube bed, tube computer monitor, tube through the earth as a shortcut for spaceships—are also bad. I’ll need outside help to come up with a new way to look at tubes, ideally from some kind of shape expert. I plan to make a quick stop at home to get dressed and then set out to find one.
And what better place to find an expert than the University? I find the contact info of Doctor Jorge P. Hernandez, a professor in geometry, and call him to set up a meeting. He tells me he only meets with prospective students, which gives me an idea: I lie and tell him I’m a prospective student. He tells me to come right over. I ride my bike to a brutalist rectangular prism on campus and lock it up to some circular metal hoops. Professor Hernandez’s fourth-floor office is square, decorated with cut-outs and models of shapes of all shapes and sizes scattered on various shelves and some dangling from wires on the ceiling. He also proudly displays his geometry degrees on his wall, leading me to believe he knows the names of all the shapes surrounding him. The Professor is unsurprisingly a bookish man in his late forties; he’s wearing a beige button-up shirt underneath a sweater vest (sweater without arm tubes), half-circle glasses are perched on his nose, and a triangular gray goatee covers the lower half of his elliptical head.
“Hmm . . .” says Professor Hernandez, leaning back in his chair and stroking his goatee after I explain my mission and what brought me to him. “The quest for a new shape has eluded geometers for millennia. I myself am among those who have felt the pull to discover one, though I have never succeeded, sadly.”
“Well I’m not looking for a new shape, necessarily,” I say. “Could just be a new way of looking at an old shape, or something new you can do with one. Anything I can stick my name in front of.”
“Hmm . . .” says the Professor again, leaning back and chin-stroking again. “This too is fraught with peril.”
“Peril?” I say. “You mean like . . . cursed?”
“No, not cursed.”
“Oh, phew!” I say, wiping sweat from my forehead. “Just what I’d need—a curse!”
“What I mean is it’s not easy. I’ve seen colleagues driven to monomaniacal obsession over the search.”
“So you’re saying there’s no hope?”
“Well, not that there’s no hope. It’s happened before, after all. One of the biggest innovations in shapes over the last century was to look beyond our traditional three dimensions—and into the fourth dimension. Harold Coxeter did some incredible work with fourth-dimensional analogues of three-dimensional shapes, including what we call the fourth-dimensional hypercube, or the tesseract. Unfortunately, Coxeter didn’t have the foresight to name it after himself, which is why we don’t call it Coxeter’s Cube. He regretted that the rest of his life. Every geometer I know dreams of having a new shape named after them.”
“A fourth dimensional analogue of three-dimensional cube, eh?” I say. “Could you do that with any 3D shape?”
“What about a tube?”
“A fourth-dimensional tube?” says the Professor. “A fourth-dimensional tube . . .” he repeats, quieter this time, trailing off. Suddenly he goes silent. He puts his hand on his chin, leans back, furrows his brow, and his eyes start starting back and forth. Then, seconds later, he scrambles to find a pad of paper and then furiously starts scribbling something down. After fifteen minutes, I clear my throat and say “Professor?” to get his attention.
“Huh?” says the Professor, startled. “Oh, right, you. Um . . . no, a fourth-dimensional tube is a stupid idea, I’m afraid. Very stupid. I’d forget about it if I were you. Anyway, I’m quite busy, as you can imagine, working on something . . . um . . . completely unrelated. Now, if you’ll excuse me—”
“I was hoping just for a few more minutes of your time—”
“No! I’m sorry, but I can’t spend all day listening to silly ideas from strangers wearing bathrobes!”
Realizing I never did make the trip home to get dressed, I stand up, close my bathrobe and fasten it tight, then thank the professor for his time and go back home.
The next morning, I grab the newspaper off the front step and see in big bold letters the front-page headline “NEW SHAPE ANNOUNCED.” I spit out a thick mist of cold brew. At first I think maybe I’ve been transported into the future, and that I’m reading the yet-to-come headline of my own new shape. Incredible! How far ahead have I skipped? I look down at my hands to see how much older they look before thinking that if I was sent into the future I’d look the same age and everyone else would look older. But this theory is mooted when I read the date on the top of the paper, which is the day after I went to bed. I jump below the fold to read the article:
Professor Jorge Hernandez yesterday announced the introduction of a new shape, a fourth-dimensional tube. The International Society of Geometers as well as the entire scientific community has hailed the announcement as a major breakthrough and are calling the new shape “Hernandez’s tube” . . .
When Bianca wakes up and walks into the kitchen, she can tell something’s wrong. After being together for ten years as of today, she’s developed a sixth sense about my moods, no matter how subtle the signs. In this case, I happen to be weeping uncontrollably, pounding my fists on the table and shouting “WHY, WHY, WHY!”
“Something wrong?” says Bianca, softly.
I slide the newspaper across the table to her.
“Oh dear,” she says, reading it. “This is just like when Higgs took your idea for a new boson.”
At the mention of that, I dive my head into my hands.
“There, there,” she says, rubbing my back. “Ugh, the timing of this couldn’t be worse! I hope this won’t ruin our anniversary trip!”
Our anniversary trip? Our anniversary trip! She’s right—I can’t let this sour our long-planned tenth anniversary vacation to Maui! That wouldn’t be fair to Bianca! I turn my frown upside-down, pack my bags, and then we’re out the door, on the tube to the airport, checking in, buckling up, and then, after a quick emergency landing in San Diego due to what the pilot calls an “unplanned wing detachment event,” our newer, better plane lands on the tarmac of Hawaii’s second-largest island.
The resort is wonderful. Everyone is so nice and accommodating and the weather is out-of-this-world. After we get our keys, Bianca and I take a quick jet-lag nap then share an outdoor shower on our back patio (with ocean view!). All the negative vibes I had in the morning have completely vanished.
The quest for a new shape has eluded geometers for millennia.
But things change at our opening night luau. As I’m taking a bite of my kalua pua’a, I look across the floor and see him: Professor Jorge Hernandez. He’s here at our resort. I try to ignore him; let bygones be bygones. But he must’ve seen me too because a minute later there’s a tap on my shoulder and that bygone has become very much a hellohere.
“May I get you a drink?” he asks.
I smile at Bianca to let her know I’m okay, and she gives me a nod to let me know I can go ahead and accept the offer. I get up from the table and start walking with the Professor towards the bar.
“I didn’t expect to see you here,” says the Professor. “You’re not stalking me, are you?”
“I’m here on a long-planned tenth anniversary vacation with my common-law spouse, Bianca.”
“How’s the trip been?”
“I see you’ve taken advantage of the complimentary bathrobes.”
“They’re very soft,” I say, stroking the robe.
We reach the edge of the pool, so I take my bathrobe off, revealing my bathing suit (it’s always good to be prepared at these resorts), then the Professor and I slip in and start swimming toward the swim-up bar.
“What are you doing here?” I ask, switching from breast-stroke to side-stroke so I can face him. Professor Hernandez sighs, and, since he’s doing the backstroke, is careful not to sigh in some water.
“There was a lot of pressure on me when I unveiled the new shape. Interviews, photographs, congratulatory phone calls from celebrities. Sure, the attention was nice—but it was a lot to handle, and I wasn’t ready for it. Be careful what you wish for, right? I needed an escape. When the Nobel money came through, I called my travel agent and said ‘spin your globe, stick your finger on a spot, and then send me there,’ and after she put her finger on Antarctica six times in a row, I said, ‘enough—how about Hawaii?’ and here I am.”
“I can’t say I feel sorry for you,” I say.
“Two beers,” says the Professor.
“Huh?” I say.
“I was talking to the bartender.”
(We’d reached the swim-up bar.)
“Listen,” says the Professor, grabbing his plastic cup of beer and taking a sip, “I’d like to apologize to you. I shouldn’t have acted the way I did. I’ve done a lot of thinking the last little while, and I realize what I did back then was wrong. People change with time.”
“It was yesterday.”
“If I could rewind all the way back then, I’d change things.”
“Could you call the International Society of Geometers and explain the situation to them? Maybe give me the credit, or even just share it?”
“Wish I could. But the Society has two unbreakable rules: no double-names and no take-backsies. Sorry.”
“No big deal,” I say. I say it reflexively, since that’s what I always say when somebody says “sorry” to me. But I mean it this time. Maybe it’s the serene location, maybe it’s the warmth of the pool, maybe it’s the island beer, but I feel at peace with the whole thing. “What’s there to be upset about?” I add. “I’m just glad that people know about the tube now, and I hope there’s a way it can help people solve their problems.”
We cheers our cups and drink the rest together, chatting and joking around like we’re old friends. Eventually, we get out of the pool and say our goodbyes. I rejoin Bianca and we go take a nighttime stroll on the beach, underneath the moon (looks like a crescent but is actually a sphere) and the stars (spheres but far away). With our fingers (cylinders) intertwined as we walk in the sand, I feel a profound sense of love for Bianca and gratitude that I get to spend my life with her. Above us, we see a meteor (ovoid) streak across the atmosphere (sphere), leaving a three-dimensional tube of particles in its wake. We stop to kiss the most wonderful kiss we’ve ever had, and then I take one last look at the shooting star, close my eyes, and make a wish: that I’ll never think about shapes again.