At the Hyperbolic Earth Convention
by Zachery Brasier
part 1
United Flight 1333 banked over the miniature version of the Empire State Building. It soared over a volcano and a pirate ship. Its landing approach carried it over endless suburban tracts. Finally, it touched down, wheels screeching, at Harry Reid International Airport, arriving on time in sunny Las Vegas.
As it taxied across the tarmac, the three men sitting in row 25 leaned towards their window. They were the New Hampshire Committee for Geometric Truth. Jarod Saltman, mid-thirties, recently unemployed, was crowded by DP Vaughn, a man wearing sunglasses and a baseball cap. Liam Velculescu — unruly curls constantly moving under the overhead air conditioning vents — idly looked at the window while wearing his signature faraway look.
Jarod laughed and tried to push DP back, but he wasn’t budging. The man wanted to see the 737s with the red stripe. As their own Boeing swung around, the mysterious airplanes rotated into view.
DP whistled. “Hot damn, can’t believe they’re real.”
Jarod took out his phone and snapped a picture. “Janet Airlines. Welcome to Vegas, boys.” He looked over at Liam. “Can you see them?”
Liam sat up straight and nodded. After all these years of camaraderie between the three men, Liam still seemed unwilling to talk unless absolutely necessary.
It was a big moment for them, the first annual Hyperbolic Earth Convention. No longer regulated to the fringes of the internet, the Hyperbolic Earth theory was emerging into Real Life. Now their beliefs were getting official. Now things were getting serious.
Jarod had found out about the theory during one of his periodic bouts of unemployment. With nothing to do and not much to show for it on his LinkedIn, time was a bountiful luxury. Through algorithmically-maintained, AI-boosted paths, he stumbled upon the concept that Earth was not a sphere, as “science” would have you believe, or a flat circle, as the kooks theorized, but was in fact shaped like a saddle. The universe’s overall geometry was possibly this shape as well, so-called “negative curvature.” Why not the Earth?
What started as a semi-ironic attempt to stave off boredom became an all-encompassing fascination. Although the online groups were constantly getting booted from mainstream social media sites, they stayed together, clinging to life rafts in cyberspace and building their following. Finally, they reached a critical mass and scraped together enough money to rent conference rooms in Las Vegas, the city of dreams, the city of possibility, always ready to take your dollar as long as you weren’t winning more than the house.
There were only three Hyperbolic Earth theorists in New Hampshire, a far-flung chapter of the National Committee for Geometric Truth.
Jarod had never learned much about Liam Velculescu. They had connected on Discord, and all Jarod was ever able to pry from him was that he was some sort of disgraced mathematical wizard. That gave him credibility. His last name remained unpronounceable, the Romanian consonants never quite making sense to Jarod’s brain.
DP Vaughn was a construction manager with deep knowledge about all the ways the government was hiding the multifaceted Truth, geometric or otherwise. He was more apocalyptically-minded than Jarod, convinced that the end of the world — secular or religious, depending on the day — was just around the corner. He always dressed in what was called the “gray man” outfit in certain corners of the web: sunglasses, black hat, blue jeans, gray t-shirt. Supposedly, clothes like that made it impossible for the Feds to pick you out of a crowd, but to Jarod it seemed that such a bland style actually made one stand out more in a sea of individuality.
The jetway connected, the cabin opened, the passengers stood. “Keep your head on a swivel,” DP whispered as he reached for his overhead baggage. “Feds are definitely afoot.”
The other two nodded. As paranoid as DP could be, that was something to be serious about. The Flat-Earthers had clearly already been infiltrated; how else could one account for how many social media followers those people had? If Hyperbolic were not compromised from the beginning, some sort of federal plot would have to desensitize the public to the idea of alternative curvatures so that when the real truth — the hyperbolic truth — came around, they’d be primed to push it away. Clever stuff. Jarod tried to memorize the backs of all the heads he could see.
Out of the airplane and into the jetway, cold air conditioning was losing its battle to the June solar bake. Then to the concourse; in Vegas, it looked like a casino: advertisements everywhere, scantily-clad babes staring down at the recently deplaned, slot machines right there for those who just couldn’t wait. Jarod stopped to lose some quarters and won five bucks. When in Rome...
Saturated neon and chromed-out curves at baggage claim. Gaudy, exciting, otherworldly. A Cessna hung from the ceiling. Jarod didn’t know why, but the ostentatious decoration felt right for the setting. While they waited for the bags, he flipped through pictures he had taken of the horizon, trying to see if any of them bent up at the edges.
Liam saw what he was doing. “You wouldn’t notice the curve from the stratosphere. Gotta be higher up...” He looked heavenward.
Rental car claim, then out into the sun. The casinos slid by. Classics, ones you heard about from the Rat Pack days and the newer corporate ones: the pyramidal Luxor with its beam of light; the ambiguously themed Mandalay Bay; Trump Tower in the distance, the gold edifice to the dread name. The sun seemed much brighter than in New England, the sky seemed bigger, too. Weather apps showed that there hadn’t been a cloud for two weeks. High above, unseen, flying wing drones conducted reconnaissance training missions.
The conference was at the Aria, parking at the Bellagio, right next door. When they stepped out of the car and into the heat, they could hear Andrea Bocelli wobbling along to the famous fountain show. None of them had ever heard of the Aria and, in person, it was a strange sight. Designed with deconstructivist excess, the towers in the complex leaned at weird angles.
The New Hampshire Committee for Geometric Truth checked in, found their rooms, went out for drinks, lost money at the slots, lost even more money at poker, then went to bed ready for the first day of the first annual Hyperbolic Earth Convention.
* * *
The first full day started with breakfast and wandering through the casino. The gambling floor was sleekly modern in a strangely dated way, what one would have imagined the future would be like before the Great Recession hit. Too many saturated colors, too many strange curves.
The conference rooms were well off the main floor. Jarod opened the door to his own personal heaven. Around two hundred people had RSVP’d, and they were all milling about. Booths were everywhere, complete with T-shirts, movies and books. Jarod had never been in a place where he felt like he belonged, at least not one with so many people. It made him want to cry. Finally, he had found a community.
They registered and put on name tags. Before they could split up, a man with a very sharply defined power donut haircut stopped them with his hand out.
“John Smith,” he said, shaking each of the three men’s hands, “I actually saw you guys on the airplane, I remember your gray man outfit. Well done. Looks like you’re believers, too!”
“Do we know you?” DP asked flatly, looking over his sunglasses and adopting an inquisitorial tone.
“No, I said... I recognized you from the airplane. I didn’t know you were part of a Committee until you showed up here. Just trying to socialize.” He raised an eyebrow suspiciously.
“Which chapter are you from?”
“Worcester. In Massachusetts. Unfortunately it’s a one-man chapter, but I’ll find some other people to join me eventually. Nice to see some New Englanders here, too, though.”
“Good to meet you,” Jarod said, just to break the tension. “Um... see you around?”
John nodded, and the three snuck away.
“That’s the sort of thing I’ve been telling you about. Infiltration,” DP conspiratorially hissed when they were out of earshot. “Did you see him on the airplane? I know I didn’t.”
The other two shook their heads.
“I thought he was nice,” Liam offered. “Maybe a little awkward.”
DP pressed his lips thin. He pointed at his lenses, then around the room. “Eyes up, boys. Keep your wits about you.”
* * *
They decided to attend their first seminar together: “Projections of the Hyperbolic Earth,” presented by one Dr. Jeffries from a barely-accredited university. The NHCGT sat together, getting a good seat smack in the middle of the room.
As people shuffled in, Jarod caught a familiar face and elbowed DP. “Look who it is.”
“John Smith, huh? Interesting seminar for him to choose.”
It only got worse. The friendly Bay Stater took the row ahead of them. He waved and sat a few seats to their left. Not in their way, but rather close.
“Interesting seating choice, too,” Jarod mumbled.
Then the seminar began. A large screen slid down from the ceiling, and the lights dimmed. A projector snapped on and a slide show started. Liam got out a notebook and began writing.
Dr. Jeffries welcomed everyone and told them that, unlike some of the evidence they had seen online, mostly people taking pictures of horizons and trying to discern whether the curvature was unexpected, he was going to demonstrate how pictures from space showed evidence for the hyperbolic Earth.
A few boos and hisses erupted. People walked out. Space travel was still a contentious topic, with some hyperbolic Earth theorists believing that either outer space itself was not real or there was something preventing spacecraft from leaving the atmosphere.
Most did believe that space was real and travel through it was possible but that NASA was covering up the true geometry of the Earth. The shots from the spacecraft were only semi-genuine, manipulated to show the sphere.
A picture flashed on the screen. The shot was taken by the onboard camera of a space probe Jarod didn’t recognize. Over the wrinkly mylar and antennas, the disk of the Earth glowed. Wasn’t that supposed to be a saddle?
Dr. Jeffries was already fending off the concern: “Now I know that you might think this is a fake picture, and that’s why it shows a sphere. Why would I show this to you, then? Well, if you’ll remember Dick Malsen’s YouTube series on hyperbolic geometry, although negative curvature creates a saddle shape in abstract mathematical space, there is reason to believe that the Earth takes the shape of a projection of hyperbolic geometry, in which all points in hyperbolic space are mapped to the normal unit sphere we know. We would call this a Poincaré Sphere.”
Liam nodded sagely. Jarod was already getting lost.
The slides changed, now it was showing a strange drawing of a disk covered in fish, each one getting smaller as it approached the disk’s edge.
“This woodcut by M. C. Escher shows how hyperbolic geometry can be mapped in two dimensions. Notice how it seems to compress as it gets near the edges. And now...” The space image reappeared, but this time the Escher art was laid over it. “...we can see that as we look near the edges of the Earth we see a similar compression. Instead of a uniform sphere, it seems to ‘bulge’ near the middle...”
Jarod leaned over to DP. “Are you following this?”
But the gray man wasn’t paying attention, he was staring at Smith. “What’s up?”
DP leaned close to Jarod’s ear, close enough to smell the coffee on his breath. “Look at what our friend is writing. Do it discretely.”
Stretching his arms over his head, Jarod used the distracting movement to squint and glance at Smith’s notepad. He saw three names with notes. Theirs.
“Why write down our names?” Jarod asked.
“I think you know why.”
Liam shushed them and, for the next hour, Jarod nervously listened to an increasingly bewildering series of calculations involving things called hypercycles, geodesics, stereographic projections and tilings. He was starting to realize that he knew very little about the mathematics of the Earth. Or perhaps he wasn’t listening properly. He was mostly watching the back of Smith’s head.
When the seminar ended, they agreed to go separate ways and meet up at The Chandelier bar that evening. They would also look out for John Smith.
* * *
The Chandelier was pure consumer-grade opulence. The lounge was two stories tall, with swooping escalators making long journeys between the floors. In the middle was a gaudy, beautiful, disgustingly expensive modern art interpretation of the titular object. Instead of an inverted cone of tapering glass, this one was built from huge sheets of fake crystal parabolically climbing from the top of the central bar to the ceiling. It was reminiscent of a jellyfish, but one from a planet with a showgirl as the creator goddess.
Jarod caught sight of DP and Liam on the first floor, refracted and sparkling in the glass. Before he could take an escalator, who but John Smith materialized right in his face.
“Hey there sort-of-neighbor, what’d you think of the seminars?”
What’d he think? That the United States government was using counterintelligence techniques developed in wartime against its own citizens in an attempt to hide the geometric truth from them. Instead, he said, “Pretty interesting. Lots to think about.”
Smith raised an eyebrow. “’Lots to think about?’ That’s putting it lightly. I feel like my mind has expanded ten times as big.” He mimed his head getting larger, almost hitting a waitress, who scowled and spun away.
“Okay, well. Nice to see you again.” Jarod pointed at the escalator.
“Oh, sure.” The mysterious man stepped aside.
“Guess who just accosted me?” Jarod asked when he sat at the table.
“I saw it.” DP pointed upwards, a clear line of sight to the top of the escalator. “What’d he want?”
“Wanted to know what I thought of the seminars.”
DP nervously sipped at his appletini. “Suspicious. What’d you tell him?”
“That I thought they were interesting. Nothing else.”
“Good opsec.” DP, having removed his sunglasses, squinted and pursed his lips. “I don’t like this. Awfully convenient to be from Worcester and not from New Hampshire.”
Jarod ordered a whisky sour from a passing waitress. “Right. He doesn’t have to come up with a reason for us to not have come in contact with him. Close, but not suspiciously close. Why us, though? We aren’t big hitters.”
“Liam, got anything to add?” DP asked.
Liam shook his head. “I don’t know if it’s a good idea to be talking about this here.” The math wiz pointed to the bar. Sitting, Smith was in what seemed to be an intense conversation with a man in a black suit, a man whose facial features were so bland he’d be impossible to describe.
The hell? DP mouthed.
“Casual conversation for now,” Jarod suggested. Then he thought for a second, trying to figure out a secure, but innocuous place for them to talk. “Actually, I have an idea...”
An hour later, they were in the Venetian, riding in a gondola. It was a strange hotel supposed to be modeled after the famous Italian canals, but the painted sky and the too-small buildings made it feel claustrophobic. The canals were shallow, immaculately clean, filtered and chlorinated. Gondolas made loops through the watercourse, briefly emerging out into the real air before returning to their model city.
Vegas, as a whole, forced you to play along with the silliness, the artificiality of it all. But some of the hotels — the Venetian included — pushed it too far, and an attraction like the gondolas almost felt insulting, as if the casino itself was implying that you were kind of a mark if you enjoyed them.
Conveniently though, the gondoliers sang as they navigated the concrete waterways. Between the audio interference and the constant motion, it would be hard for someone to eavesdrop. Liam was given the task of watching the “shoreline” for anybody pacing their boat.
“Can you sing any louder?” DP asked.
“No,” the gondolier answered and returned to a flat rendition of “Beyond the Sea,” sung in Italian, naturally.
Copyright © 2026 by Zachery Brasier
