The globe is round. That was the first thought in my mind this morning. It didn't burn itself into forty-foot-high flaming letters in a mountainside, but it seemed like a good and obvious sentence. Not yet out of bed, I turned this thought around a bit and wondered why I had been thinking it.
Globe-roundness had been pretty self-obvious for me ever since my first interaction with a globe as a child. Over the years, I'd heard about belief in flat Earth, in cosmic disks supported by elephants and turtles, and even about Time Cube, and for each challenger to the globe theory, I'd heard about empirical evidence which neatly disproves it.
Suddenly, I realized that I was not so sure of myself. Why was it that I was so uncertain in my thoughts? Surely I wasn't doubting the curvature of the Earth! And I knew what our planet looked like from outer space, too. This was all just another early-morning straggler left over from a dream, a vagabond tautology destined for the shower drain with all of its other companions.
I needed food. I walked out the door, considering whether all was right with the world and whether I had correctly inserted items into my pockets. Wallet, keys, phone, gloves. Hungry for knowledge but more hungry for hot dogs, I walked up to a street vendor.
"Hi!" I blurted. "Can you make me one with everything?"
He rolled his eyes and said, "It's called the Cosmopolitan Dog," as he tugged on some gloves and started assembling the delicate sausage-based structure.
"Okay, yeah, sorry," I muttered. As I sheepishly broke eye contact, a splash of color flickered on the edges. Blinking and focusing, I saw a most curious and fascinating projective map of the world. Like all projections, it would be inaccurate in some way, perhaps misrepresenting distance or area. I stepped closer.
It was a heptagon. A seven-sided regular polygon, with Antarctica and the South Pole in the center. Meridians leapt from the center, irregularly spaced, out towards the edges. Heptagonal latitudes radiated outwards across distorted continents and too-large or too-small oceans. I couldn't look away. The blatant and utter disregard for anything resembling accuracy was an artistic statement, striking me to my core, challenging my assumptions of what a map could even look like.
"Hey, I like your map," I said, eyes jumping between my new eye-candy and my food-provider. "What kind of projection is it?"
"It's just the Earth," he replied, shrugging and handing me my food.
I pulled out my card to pay, saying, "Of course, but I mean that the map itself is unusual, right? That's not a standard projection, is it?" I slowed down and added, "I'm just asking because I find it interesting."
He shrugged again. Somehow it seemed like a smaller shrug than before. "I'm not sure what you mean," he said. "That's the way it's always been."
"Okay? Thanks," I said, taking a bite and examining the strange map again. I supposed that asking a hot dog vendor for details on cartography was probably a little unreasonable, so I decided that I would figure out what kind of map this was on my own. I noted that the map's detail claimed it to be a "heptametric standard" projection. My hands were still busy with my messy meal, so I was temporarily limited to my own brainpower; nonetheless, I was certain that "heptametric" was a key word which would aid me in my search.
Ambling on, I decided to go to the library. Like the hot dog stand, it was neither a long nor unfamiliar walk, and I soon found myself no longer hungry for food, as I had finished eating, but thirsty for knowledge. Of course, I properly disposed of the remains of my meal in the proper receptacle as I climbed the library stairs and entered.
"Hello", I murmured to the librarian, automatically switching to sotto voce inside the quiet building. "I'm looking for a rare map."
"Well, let's see what we can find," she half-whispered, as she switched from a stern look to a smile and adjusted her glasses. Her fingers gently rattled a keyboard with preliminary queries. Even a librarian's typing is quiet. "What can you tell me about this 'rare map?'"
"It's called a, uh, h-heptam-m—" I stammered on the unfamiliar word.
"Heptametric?" she volunteered, then tittered. "That's funny!" Switching back to her serious face, she continued, "We have a selection of atlases, including standard heptametric maps." She gestured towards a corner. "Let me know if you have more questions. Thanks," she concluded.
I felt outsmarted somehow, but being outsmarted by a librarian seemed like a reasonable occurrence, so I chose not to worry about it. Instead, I went to the back corner and resumed my map quest. The first atlas I pulled out claimed to hold only heptametric maps, so I laid it out on a table and opened it.
It had to be a joke. I couldn't believe it. There, inside this atlas, was a succession of heptagons, each scored with the same bizarre lines, each showing off different features of the regions of the planet, like elevation or climate. I told myself not to panic and that surely this was just one atlas.
Ten minutes later, I was back at the librarian's desk, arms full of atlases, eyes full of suspicion and distrust, feeling like I might never be able to smile again. I gently laid the books on the counter with a mild pomf, earning a glare from a book-laden patron. "Hello, welcome back. Did you find what you were looking for?" she said, chirpy and carefree.
"They're all heptametric. They're all seven-sided. This has to be a joke. Where are the standard projection maps?" I hissed, perhaps more meanly than I had intended.
"I'm not sure I understand," she apologized. "Are you looking for a non-standard style of map?"
"I'm looking for Mercator," I said, trying hard not to raise my voice. "I'm looking for Mercator, and Gall-Peters, and the Waterman butterfly, and essentially I guess that I'm looking for a globe."
"A glob?" she replied.
"No, a globe," I repeated.
"Like these?" she asked, pinching and wiggling her ears with a endearingly irritating grin.
"I am looking for a spherical model of our planet. It usually comes equipped with mounts at the poles so that it can spin freely," I explained, wondering why I was allowing this librarian to toy with me.
"Sphere…ooh! Like 'globus!'" she exclaimed, earning her own glare from several buried-under-books library-goers. "Sorry, sorry." She continued, 'Globus' is Latin for 'sphere.' I didn't recognize it the first time. 'Globe' sounds like a neat word, though. So you're looking for a map that's wrapped around a ball?"
I considered. "Yes," I said, confident that I did, in fact, want very much at that moment to see a map wrapped around a ball and was starting to get very uncomfortable at the prospect of an educated person who had never seen one before.
"Then maybe you should go over to the university," she spoke conspiratorially. "I hear that they have a school of cartography."
"Thanks," I said. Suddenly I had a terrifying thought. "Um, I'm not sure how to say this, but the Earth is round, right?"
She tittered again, and smiling, said, "Yes, of course the Earth is round." Sighing with relief, I left, forgetting to put away the books that I had carried to her desk. I resolved that I would get to the bottom of this situation, whatever it was.
As I meandered to the university, I pondered how enticing it must have been for the ancients to come to the wrong conclusions. We knew that the world was flat at one point; it was only with the advent of sailing that we learned that it was round, and then that it was somehow circular by circumnavigation, and finally satellites confirmed once and for all that we definitely lived on a sphere. A "ball," as the librarian put it. Or an "ellipsoid," as a mathematician might say.
I am not too proud to admit that I got lost. I eventually got unlost and arrived at the school of cartography. Frowning at the heptagram inscribed on the front of the building, which was not burning with forty-foot-long lines of fire but nonetheless filled me with an absurd dread, I pushed open the doors and walked inside.
"Hello?" I called out. Surprisingly, the room on the other side of the doors was a broad atrium, with a high domed ceiling and bright lights illuminating a wide carpeted floor upon which dozens of cartographers were arranged in various states of discussion. Upon my inquiry, a few heads looked in my direction, a couple salutations were half-heartedly grunted, and an impeccable-looking couple strode over while waving.
"Hi!" they exclaimed together. Not in perfect unison, like twins, but more like a brother and sister who have always had a good relationship. She continued, "What can we help you with?"
An eternity passed. I wandered along a beach. The music of the spheres truly was divine. Perhaps, for a moment, I did know peace. I'm not sure; I don't remember.
"Hi," I burbled, feeling a mask drop down on my face, "I'm looking for information about the heptagonal standard map! What can you tell me about it?" I hoped that I did not look too much like a body snatcher.
He grinned wide, saying "Well, that's our entire field of study, isn't it!? The heptagonal, or heptametric, map became standard in the time period right after European colonization started, when many mapmakers were competing for popularity."
"So which of them came up with it?" I asked.
"We don't really credit any one person with the modern map, really," she explained. "It evolved incrementally, through the efforts of many different contributors. That's what gives it the robustness and reliability that lets humanity rely on it," she finished with a boast. I don't know whether she intended to look smug, but she looked smug. Maybe I was interpreting her attitude as smugness because I, myself, had been overly confident in my stance.
"Okay," I said, opening my mind and stance a bit, "I'd like to hear more. How does it all, um." I searched for a word in an empty palace across the sands of lost thoughts. "How does it all work?"
Their eyes sparkled. I wondered if "poor diction" was considered an acceptable cause of death, and if so, whether my family would be ashamed. I wondered if "overeager cartographers" would be any better.
"Let's go —" she squeaked.
"Yeah," he joined in.
"To the Big Room!" they gushed in unison. They then turned and started walking down a corridor. I decided to go for it, and followed."The Big Room," she called out, striding ahead of me, "is where we keep the Big Map, which is — oh, and you'll want these," she added, reaching out to snag some goggles off of a hook on the wall. Lobbing them at me, she grinned and continued walking. "Well, it's big."
"Thanks," I replied, catching the goggles. "The Big Map is big? What are the goggles for? Why don't you have any goggles?"
"Relax," he said, spinning around to power-walk backwards. The hallway started to open up into a reverberant tunnel. "They're just binoculars. You'll want them in order to see the fine details." Pretending to swoon slightly, he wilted, "The exquisite details!"
"Now you relax", she joked. Addressing me, she continued, "What you're about to see is the pinnacle of our school's efforts, and it tends to leave people speechless. We want you to be amazed and impressed, so we're talking it up a little."
"That," I blinked, "is remarkably honest."
"Thank you! We're scientists, after all," she justified. "Honesty is just part of how we do the scientific method."
We arrived.
They were not just telling jokes. The Big Map was quite large. Carefully mounted in the middle of the Big Room, which felt honestly more like a concrete silo than an actual display room, was a massive heptametric map, a few dozen meters tall, suspended by wires and struts. Electronics decorated its edges, blinking their lights, and the curvature of the Map caused the bright stark illumination of the room to gently shade its bedazzling surface.
The surface of the Map glistened and danced. Stepping closer, I approached the edge, where a concrete-and-rebar barrier indicated a supposedly-safe viewing distance. Remembering the binoculars, I held the dorky viewing lenses to my eyes, and beheld a fantasy of colors. The Map's surface was alive with superfine filaments which pulsed and buzzed with bright activity.
Zooming out slightly, I noticed the overlap with population centers and the relative dearth of threads crossing the oceans. "Travel routes?" I asked, trying to steady myself against the railing.
"Sure, airplanes, trains, busses, we have all of those mapped out," he explained as he came to stand beside me at the Map. I looked to my home and saw a familiar airport.
"And not just people, but also the flow of money and goods, and the spread of ideas and culture," she completed, standing at my other side and pointing to a massive flow of green and red.
"We even can track satellites. Look," he pointed to a blank patch of Antarctica. I held up the goggles again and saw a thin purple strand chasing out a chaotic knotted curve over the ice fields.
"This living map, the Big Map, is so great. I'm so glad that we can point to this and say, 'Yes, we made it, it's ours. We are great cartographers,'" he said.
"I can't deny that it's beautiful," I replied. "In fact, it's truly magical and possibly the most amazing piece of art I've ever seen."
The twin grins from either side of me silently indicated approval of my praise. But then I sensed a change. "Wait," she frowned, "you were going to follow that up with something not-so-nice, weren't you?"
"Is that okay?" I asked. "I came here in search of an answer to a question, and I worry that this question might be uncomfortable to you. However, I still want to respect you as scientists and thinkers, and I hope that you'll consider what I have to say." Why was I suddenly so formal?
"Why are you suddenly so formal?" she smirked.
I didn't know. "I don't know," I replied. "But I do know this: When I woke up this morning, I was convinced that the world is round."
"Yes," they both nodded, again in that not-quite-bizarre not-quite-unison.
Emboldened, I continued, "And…and also that the world is a globe; that is, the world is a sphere, and the world is round in the same way that a sphere is round." I finished my thought and awaited their response.
"Oh, okay, sure," she said, suddenly sassy. "This is a joke, right?"
"No, no!" I insisted, trying to wave my hands in some sort of manner. "I'm not joking, I'm not playing a prank, and I'm not trying to be a nuisance either. I guess I said something that you've heard before."
I heard an eye-roll from behind me. "You say that, but you also said 'globe,' and you can't not know what that means." he said, grumbling and rumbling.
"Okay, well, I just won't say the 'G'-word. Sorry," I apologized. "But it's spherical, right?"
"Ugh! That's just a stupid theory!" She groaned and stamped her foot, causing me to jump. "Spherical maps might be great if you're a greenfield postdoc with your head in the clouds and your butt in an ivory tower, but we're doing real-world work here!" Straightening up slightly, she pointed angrily towards the Map and intoned, "We have proven the ability of the heptametric model to work in all cases and do not need academics telling us how to make maps."
I started, then paused. She paused too, softening from her angry stance slightly. I wondered whether I really should open my mouth. Maybe, if I were to back away slowly, I could avoid losing any limbs.
While I was thinking, my mouth ran for it. "But aren't you two the academics? I'm just a guy who walked in off the street."
She was stunned. Unfortunately, I forgot to multi-target my quip, and he was just as quick. "Exactly! We are professionals. You have no idea of our theories other than the surface. You don't understand the real-world engineering concerns that go into cartography. The spherical model has never held up, and we know why, so there's no point going into —"
"Why‽" I interjected.
The hail started.
"There's no good way to project a sphere onto a plane," she exclaimed. Pointing at me, she recalled, "At best, you can preserve area or angles, but not both."
"The great-circle argument is fallacious as well," he chimed in. "While globe proponents insist that the shortest route between two locations is easily computable with great circles —"
"Exactly!" I blurted.
"But you're wrong!" he blurted back at me. "On land, there's the gradient of elevation; on water, trade winds; and in the sky, the Coriolis effect. Great circles are overly simplistic."
The rain cleared for a moment. "So how do you normally compute the distance between two points?" I asked.
Their simultaneous smirks were audible. "Oh, we wouldn't want to hurt your head with the details…" she teased.
"…Stochastic gradient descent…" he included.
"…Hamiltonian Monte Carlo…" she continued.
"It's all very complex and hard for us to explain; you need to have a background in statistical cartography before it all makes sense," he concluded.
"I might understand more than you think," I half-agreed, "But okay. I agree that your discipline is much more complex than I thought and I was being a little facile. Still, it sounds like there are corrections for real-world quirks in the heptametric model, right?"
"Sure, yeah," she cautiously nodded.
"And, really, that's to be expected in any model, since there are things like the jet stream," I ventured.
"I'm with you so far," he followed.
"So…why not use a corrected spherical model instead of a corrected heptametric model?" I finished. I wondered how contentious this would be. I felt that it was not an unreasonable proposal. "This way, the basic structure of the model is simple and easy to grok, and the corrections can still be computed."
The twins blinked. They exchanged a glance, blinked again, and she said, "That sounds like a very interesting project. It sounds too elegant and experimental to see much use, though."
"I see," I said. "Then I suppose that this is the end of my journey today."
He suddenly looked contrite. He said slowly and carefully, "I'm sorry that you had a tough time, but this is the way that maps work. Your ideas are interesting and maybe you could find a professor willing to take on you and your project."
They showed me out of the building. Along the way, she asked, "So how long have you been a follower of the school of globe-based map-making? You seem very into it!"
"I didn't know that there was a 'school of globe-based map-making,' to be honest," I honestly replied. "Nor did I realize that it's apparently heterodox. I've just always seen the world that way. Or at least the world makes so much more sense as a globe than anything else that it's hard for me to go back to any other mode of thinking."
"I'm not sure I understand," she admitted.
I explained, "I guess I know that, on one hand, the world must have been heptametric yesterday. Your amazing achievements —" I tried not to tear up while remembering the majesty of the Big Map! "— have shown that to be the case. But something clicked in my mind somewhere and now I can't help but see the heptametric model as flawed and clumsy," I sheepishly shrugged.
"What will you do now?" he asked.
"I'm going to build a globe. Maybe not a fancy globe, maybe not a pretty globe, and maybe not a perfect globe, but a globe. It'll spin on the polar axis and it'll show latitude and longitude and it'll have some great circles and I'll label the oceans and all of it. I'm going to build a globe," I resolved.
I went home and realized that I had no idea how to build a globe.