Mathemagical Chapter 1: Equations in Meditations
“Close your eyes and focus on the sensation of being. Visualize where you want to be, separate, above, and aware of all your cares and worries. And let the transformation occur.”
Even in my head, Bhante Dokan’s words sounded wrong.
I uncrossed my legs and stretched them, dejected. Yes, learning the secrets of the universe wasn’t supposed to be easy, and I didn’t really expect it to be. Still, some part of my brain mocked me, saying, “You skipped grad school for this, Sarah?”
Magic was real, and it had somehow failed to be a game-changer.
Of course, when magic first broke onto the scene, everyone was going nuts. When you see a guy floating in mid-air in front of James-freaking-Randi, you know it’s gonna go viral. The physicists went ballistic, trying to figure out how the levitation worked. Unfazed, the monk, Bhante Dokan, continued to perform, over and over again, under test conditions.
He had hundreds of thousands of students signed up in just a few days. You had the terminally ill, the filthy rich, and the scientists all thinking that this miracle would somehow solve their problems. But Bhante Dokan’s monastery was small, and no one knew how applicants were selected. The applications rolled in, regardless.
I was still in school at that time, doing my undergrad in applied philosophy. Don’t get me wrong— I was just as caught up in this levitation stuff as the rest of the world, but I didn’t think it’d actually be teachable. So when some reporters who had gotten an exclusive to the monastery reported that the effect could be replicated among the students, I got very, very interested in the potential for impact.
I mean, I probably wouldn’t have made that much of a difference in trying to solve morality, but now here was this whole, untapped field that might overthrow centuries of established fact. Sure, I’d have to invest some time learning and I might fail, but I might also be able hack physics. Excited, I felt like there was something deeper, something more fundamental, to be discovered here.
I’d seen my friends like Andre and Jing-Soo make it big on their risky endeavors, from launching satellite startups to managing hedge funds. Maybe this was my chance to try my chances.
And it was an uncrowded field. For all the hype Bhante Dokan drummed up, the vast majority of his students went away, disappointed that learning levitation took “real effort”, as Dokan said. Filled with grandiose dreams of breaking the laws of physics, I sent in my application.
Two days later, I got a reply— I was in.
One week later, I was in the mountains, sitting in a half-lotus position (the full-lotus is excruciatingly painful), focusing on my breathing.
Three months had since gone by, and I could easily flow into the detached state of awareness that characterized mindfulness. Yet, I still couldn’t float.
I grit my teeth. In my mind’s eye, I could still see Bhante Dokan’s effortless levitation. When I had first arrived here, he had showed me the same demonstration as he had on television:
Bhante Dokan simply rose up and hung there in the air, about a meter above the ground.
“There really is no trick to it!” I said, moving a full circle around him. I’d already gotten confirmation from a million news articles, sure, but seeing it in person had been still been astounding.
“Nothing but understanding the body in relation to the universe,” he said, “for you are but a single point.”
“Right,” I said. “But, how?”
“By imagining myself moving through space and time, a translation across dimensions,” he said, slowly floating down.
Which obviously explained nothing.
Bhante Dokan was, in no uncertain terms, a little crazy. The guy had just decided one day to leave his accounting job and practice meditation. It didn’t help that he spoke in a New Age style and ran his monastery like a cult. Thankfully, I’d had prior experiences with charismatic speakers. But I still had to hang on to his every word just like everyone else—he was the only one who could consistently float, after all.
I had hoped the other students might have had some more helpful tips. I’d sought out a few, the ones who had actually managed to float, if even a little, under Bhante Dokan’s tutelage, and asked them for advice.
Rachel, who had been a sales director, was willing to talk to me.
“I can usually get it after a long while of concentration,” she said. I sat down on a cushion to watch.
After a few hours, she slowly rose a few inches. I gasped again; after months, levitation still got me every time. Rachel held the pose for around ten seconds, and then dropped back to the ground.
“So what’s going on? Are you really just imagining yourself moving up, like Bhante Dokan says?” I asked.
“A little. It’s like I’m this box, you know, and I’m putting in my desire to rise, and it’s coming out from my top,” she gestured to her head, “and it pulls me upward.”
“So it goes through this box?” I asked. “That’s all?”
“Yeah, like the box— that’s me— transforms my desire into reality. In and out,” Rachel said.
“Okay, I think I’m going to go back and try this again on my own. Thanks,” I said.
Uncrossing my legs from the half-lotus, I drank some water. There had to be some link I was missing here. All the advice I’d gotten had a ring of truth to them, something that united them in some grand way.
But I just wasn’t seeing it.
I got back into position, and I tried to lighten my mind. The worries and fears came back again, haunting me. Had I really made the right choice coming here? What if I failed? I really began to regret the Fermi estimate I’d made, which promised me a high-risk, high-reward opportunity.
It looked like I’d be losing out on this gamble.
Cracking open an eye, I saw another student, Kevin, who got a few inches of airtime for a brief instant.
We had arrived here at around the same time. What was he doing right that I wasn’t? Was I just not cut out for this? Did magic self-select for some “magic” gene? What was going on here?
“Ow!” he said, landing with a slight thud. “I’m okay, guys!” he said to everyone.
Right. He wasn’t hurt.
Weirdly enough, that little realization carried me back. I popped out of the cycle of regret I had in my brain. I had a reason for coming here. Here, more than anywhere else, I thought I might make a difference.
I bit my lip. I had came here to solve levitation (and then hopefully solve everything else). I’d already made my decision, and I’d already known I’d feel conflicted. And I’d precommitted to powering through, all the same. If I hadn’t received new information, it was stupid to keep ruminating.
“But don’t you have new information? You now know you really suck at this,” my brain said.
“I committed to an entire year. I’m sticking to it,” I said to myself.
I let the thought hang for a moment, and then I exhaled.
My thoughts slowly returned to my breathing.
“It’s like some function of my body I have control over,” Kevin had later told me, “I’m just applying it to myself, letting it propel me up.”
“Right,” I had said.
“Don’t worry, you’ll get it eventually,” Kevin had said.
Like he was one to talk. He could only float a few inches and only got it right about once a week.
That had been one month ago.
“This shouldn’t be this ridiculously hard!” I said, jamming my eyes closed. Anger might not have been conducive to mindfulness. I didn’t care.
For all of Bhante Dokan’s mumbo jumbo about finding one’s place in the universe, levitation was very easy to describe mathematically: It was a simple translation in the y-direction. A stupid, basic function— “f(x) = x + N”
Why couldn’t levitation be that simple?
I focused on the sheer simplicity of it, how obviously easy it was to describe the concept of floating upwards. My thoughts honed in, imagining myself moving along an imaginary axis, ever upwards.
It was a curious feeling, focusing on translation as the basis for my meditation.
I held the feeling of myself upward and my other thoughts faded away. A calm blankness had spread itself over my head, dulling my usually speeding brain.
It felt… right. I felt the pressure from my cushion fade. The wind whipped around me, and it really did feel like I had left some part of myself behind. I was the function, and it acted on me.
“Sarah!” came Bhante Dokan’s voice.
My eyes flew open.
Confusion hit immediately. Was Bhante Dokan always this short? Why did— my thoughts clicked into place.
“I’m floating,” I said, finding myself about a few meters off the ground.
“Indeed,” said Dokan, “recall that you are the point, moving through space and time.”
“I’m floating!” I exclaimed.
Everyone turned to me and clapped. I’d probably asked all of them for help at some point.
The realization of all my hopes seemed to crystalize in that one moment I hung in the air. The math, that was what I had needed.
With that, I didn’t worry about getting down. Closing my eyes, I imagined myself again along the same axis, applying a translation downward. In my head, I could see the function f(x, y, z) = y – 1 actually applied to myself.
I was the point, and I was moving through space and time.
And then I was back down on the ground.
The elation. The wonder. The insanity. The twisted sense of it all. I was so incredibly ecstatic I didn’t sleep that night. I walked around the grounds in a mental rush, periodically testing my newfound levitation abilities, floating up and down. I was a wizard.
An actual, rule-defying master of the universe.
And, oh, the twisted sense of it all. My mental metaphor for mastering magic via meditation was math, magnificent math. Math was the key to magic. Magic ran on math. The universe ran on math.
The implications stretched out before me. I filled two notebooks to the brim with my theorizing, all hastily scribbled.
“Your progress today was very impressive, Sarah. We must talk talk more of this later, Bhante Dokan had said after I had floated down.
Did he realize the true implications of what he was teaching here? How much did he know? I shivered in my revelry.
As the night dragged on, though, I finally slept, and my dreams were incomprehensible, filled with swirls of abstract entities my mind could not contain.
Waking up, my thoughts felt incredibly lucid.
Magic is a shortcut to applying math in the real world.
Bhante Dokan had talked about focusing on oneself in his lectures, and all the other students had followed suit. I didn’t realize it then. In hindsight, though, what was going on was painfully obvious. In my mindfulness trance, I had been applying a function to myself.
I had specified a point in the universe— me, and I had specified the translation function to be applied.
But what if—what if I applied the function to something else?
Getting out of my cot, I ventured outside to find a secluded area of the monastery. I finally settled for the zen garden to the far left of the property. Sitting down, I stared intently at a small pebble in front of me.
In my mind, I saw its coordinates, relative to its surroundings, in three-dimensional space. I visualized the function f(x, y, z) = y + N. Opening my eyes, I kept the position and function in mind.
Mentally, I adjusted the value of N. The pebble silently moved up about one meter. Then down. Then back up. I let the pebble drop back down.
I tried the same levitation procedure with a larger rock. No problem.
From N = 1, N = 2, N = -1, N = -2; ; up, down, up, down.
I took a deep breath, steadying myself. My prospects at gaming the universe suddenly seemed a lot brighter.
I felt like Magneto, except suddenly everything seemed within my grasp.
Everything? Everything everything?
“How far is the range on this?” I said aloud. Could someone move something halfway across the Earth? What if someone ridiculously stupid tried to move us into the Sun?
The realization hit me, a full-body shock.
“Oh man,” I said, sweating. It wasn’t even just the range. Could I move individual air molecules? Did this mean someone could invisibly assassinate anyone—by suffocating them with mindfulness?
I wasn’t sure I wanted to know.
I leaned back, in massive worry. Yes, there was probably some huge potential for perpetual energy here, or some other physics hack. But I’d probably also just discovered the greatest potential threat to the entire universe.
All because mathematical functions applied to real-world objects. I thought about translation and frowned. Something was off.
“Ugh,” I said aloud.
Because Dokan had only ever demonstrated levitation, I originally only thought about functions in terms of transformation of position. But mathematical functions went way beyond that. There were twists, turns, pulls, inversions, and more. And that was just transformations…
Translations were only the tip of the iceberg.
What if someone tried to instantiate a Platonic solid in real life, a sphere? What would that even mean? What about something even more ridiculous, like the Ackermann function or the Halting Function?
“Goddamn magic,” I said.
This was going to be a long day.
My steps were slow as I walked to Bhante Dokan’s office.
Earlier, I had, very carefully (and very discreetly), tried to break apart a rock my tearing it apart from different directions. Concentrating on three different sections of the rock, I breathed in and tried to move it.
The rock had only shifted in the direction of one of the functions. I’d repeated the procedure with my shirt. Once again, it didn’t tear apart. Oddly enough, it looked like magic only worked on “things” from a human perspective.
I groaned as I opened the office door. Thankfully, this meant that it would probably be hard to kill someone internally. It also raised lots more questions about what was going on when I used magic.
What possible reason could there be for magic only working on things that were “fundamental”, like rocks and shirts (but not individual shirt fibers), from a human’s ontology?
The room was bright and a little warm.
Bhante Dokan was seated at a normal office desk. His balding hair framed the top of his lined face.
“Bhante Dokan,” I inclined my head. “We need to talk about a lot of things.”
“Indeed,” he said. “Have a seat.”
During the slow walk to Dokan’s office, I’d tried to make a plan for how to handle the possible end of the world. That had been, perhaps understandably, incredibly difficult.
My brain had also not been cooperative, instead saying things like, “Hey Sarah, let’s hope we don’t go crazy at some point. Because, you know, we can literally end all sentient life if we have a bad day.”
So I hadn’t really done any Death Note-level scheming. Still, there was one very obvious thing that seemed like a very good idea, no matter what I planned to do in the future.
“Bhante Dokan,” I began, “with all due respect…”
I paused, choosing my words.
“With all due respect, I actually think that continuing to teach meditation could be incredibly dangerous.”
Dokan frowned. “Dangerous, Sarah? How could you say that? You’ve seen the results. You’ve experienced it firsthand! What I’m teaching here has incredible potential.”
“No, you don’t understand. There’s a…a level deeper than what you’ve taught us. And anyone who improperly stumbles upon it could be incredibly bad. Like, actual cataclysmically bad,” I said.
I was trying hard not to give specifics; telling anyone about the mathematical analogy promised to be absolutely stupid.
“Cataclysmically bad? And you’ve stumbled upon this level?” asked Bhante Dokan. There was a slight smile on his lips. “What might this level be? What could be so dangerous?”
So he didn’t know. Or he was pretending. If he actually didn’t know, though, then I’d need evidence.
“Erm, I don’t exactly know if I can explain,” I said, “yes, that sounds incredibly suspicious, but, erm…”
“Can you share the reasons for your worry, Sarah?” he asked.
I shook my head, “I can’t really give specifics. That, too, would probably be dangerous.”
Dokan was obviously the most experienced practitioner here. If I gave any inkling that meditation had greater potential than he thought, any misguided action on his part would be fatal.
“Are you sure you cannot say?” he asked. “Even if it is vague feelings, I may be able to help.”
“No, I really, really can’t,” I said.
Bhante Dokan sighed.
“Don’t worry too much about it then, Sarah. Sometimes, memories from past lives mix into ours when we start cultivating mindfulness,” he said, guessing wrongly at the source of my worry.
His dismissal dropped the weight of everything back on my shoulders.
My brain spoke again: “Hey Sarah, you’re really not doing too well. Haven’t you forgotten that if you fail to convince Dokan here, he’ll continue to teach magic of potentially apocalyptic proportions? You know, including creative people?”
As usual, my brain was snarky but correct.
“Wait, I can explain better! Just let me think,” I said, closing my eyes.
I swept through several ideas, all risky. I rejected one idea immediately and thought for a few breaths. I had to win. The least risky option I thought of was still not great. But I needed to keep moving forward. There was no right move, but there was a path ahead.
I took it.
“Okay, I’ll show you,” I said, deciding.
“Really?” asked Dokan. “What do you plan to do?”
“The meditation you’ve taught, if used incorrectly, can be used to harm others,” I said.
Dokan’s eyes opened wide.
“Like this,” I said, focusing the function on Dokan.
In a second, I lifted him up from his seat and lowered him back into his chair, unharmed. Bhante Dokan yelped.
“Wow, good thing he didn’t explode. That would have been messy,” my brain said. Given the weird ontological focus for the targeting system for magic, I hadn’t been entirely sure it was going to work fine on another human.
“Wh-what just happened?” he asked. “You…just lifted me up?”
“Do you see now?” I asked. “That’s why this is so dangerous! I obviously won’t give any specifics, but I think anyone who learns meditation might be able to do this.”
“Oh dear,” said Dokan.
“If someone with malicious intent discovered this, why they might drop people off skyscrapers or cliffs! We need to be very, very careful!”
I left out the part about cosmic destruction. One step at a time, I reminded myself.
“Oh dear, oh dear, oh dear,” Dokan said. “You should have told me the moment you suspected this.”
I merely nodded. I guessed his statement was merely rhetorical, seeing as I actually had come over and told him immediately.
Bhante Dokan was silent for a minute. An actual minute; I watched the second hand make a full revolution on my watch. I breathed in our out, watching Dokan’s pupils move.
At last, he spoke:
“I fear, Sarah, that you are right. I will not ask you for how you did such a thing. This knowledge, as you rightly say, appears incredibly dangerous. Know that I now share your worries,” he said.
“So we’ll close down the school?” I asked.
A spasm flitted across his face. Bhante Dokan tensed for a moment.
“Yes,” he said, “we cannot risk loosing such dangerous knowledge upon the world, whatever that may be.”
I could see how it hurt him; yet, he still stayed sensible.
“I’m surprised you’re so reasonable,” I said. Ugh, why did I say that aloud?
“Mindfulness is intended to bring tranquility, Sarah. As fervent as I may sometimes seem, it may do you well to remember that other people can also be competent,” he said.
We made plans to close down the school.
Three days later, everyone had left.
Bhante Dokan, in his normal passionate style, had stressed the importance of never practicing magic again. I had mingled about the students as they left, and thanked Rachel and some others, stressing how important it was that we should move on, in light of Bhante Dokan’s words.
Dokan had tears on his face. He had seen me looking and had slowly nodded.
I nodded back.
“Great going,” my brain said, “this school was his hope for helping everyone out. And you destroyed it.”
“Shut up,” I told myself. “This was much, much better than our first plan. Anyway, any emotional damage you feel now doesn’t even compare to what’s at risk.”
I knew the stakes had been high. Still, it was frightening how easily murder had leapt to the mind. My internal paranoia had been on high-alert since my chat with Dokan. I was letting all these potential world-ending threats back into the world with what—a stern warning not to show off?
But I hadn’t been able to bring myself to take that final, cold step.
Dokan and I had decided stick together while we thought more about how to move forward. It was also quite dangerous to leave the only actual teacher of magic unsecured.
“We’ll need to pack too, Bhante,” I said to him.
“Of course, Sarah,” he said, wiping an eye.
Telling pretty much the truth, I’d convinced him that things were indeed dire. But I had no idea how to proceed. What was the best thing to do now?
I was going to try really, really hard to figure this out.