Age 13
The announcement arrived like a chalk line across the board, simple and straight. Dr. Li dusted her hands after wiping the board clean, then turned back to the class and said a visiting researcher was opening a small modeling competition for undergraduates. Three weeks, one prompt, written report, optional code appendix. Teams limited to two. The winning pair would receive a quiet letter of recommendation and a modest grant to cover books. She said it like it was routine, a small note between gradients and divergence, then she wrote the prompt in four compact lines and underlined it once.
Predict the spread and stabilization of a phenomenon in a constrained environment.
Define the phenomenon.
Justify the constraints.
Build a model.
Defend it.
No examples. No guardrails. The chalk dust settled as if that were the only way it could be asked.
Paige didn't look at me right away. She kept writing until the board filled again and the lecture moved on. When class ended and chairs scraped and the room filled with the soft noise of people leaving, she capped her pen and finally turned. Her expression was thin and steady, like a tight wire.
"Two," she said.
I nodded. We didn't shake hands on it. We didn't need to.
That afternoon, Dr. Asher, a visiting research fellow from a university in Illinois, introduced himself during Professor Kim's lab. He spoke in brief, measured sentences, the kind that come from long hours in front of whiteboards instead of windows. His project was simple: build a predictive model that could survive scrutiny. No metaphors, no shortcuts. He said that if we were going to build anything at all, it had to withstand someone trying to break it. I liked him immediately.
Paige and I took the first copy of the guidelines as we left. In the hallway, she tapped the page with one finger.
"Constrained environment," she said. "If we pick something too big, we drown."
"Keep it small then," I said. "Keep it clean."
In the cafeteria we found a corner table that smelled faintly of burnt toast and wiped plastic. Paige pulled a notebook from her bag and drew a square.
"We need walls," she said. "Something with edges."
"Dorm floors," I said. "People, not particles. Move, pause, collide. We can measure."
Her mouth tilted at the corner. "You want to model freshmen."
"Behavior is a phenomenon," I said. "So is boredom. So is hunger at seven p.m. on a Tuesday when the pizza runs out."
She laughed more with her eyes than her mouth. "All right," she said. "Let's try it. Population starts at low density, ramps to high, stabilizes after a resource constraint. We can define the resource as food slots, time, or seating."
"And movement rules," I said. "People take the path of least resistance until it's crowded, then they divert. We can set probabilities for diversion based on observed congestion. Add a crumb of psychology to keep it honest."
She wrote fast. I watched her letters grow cleaner the further she went, the way handwriting improves when someone stops noticing it. She asked how many nights I could watch the cafeteria without going insane. I said three, maybe four, if we rotated shifts. She said she would take early evenings; I could take late. Neither of us mentioned the rest of our classes. The semester moves like water around anything you put in the stream if you stack the stones correctly.
That night I ran the perimeter of campus before the air cooled too much. The path along the lawn was uneven, the lamplight thin. I counted ten breaths in, ten out, kept my stride even, and let the clatter of the day fall away. The project sat in the back of my mind like a clean line waiting to be drawn. When I reached my building I took the stairs two at a time and stopped at the landing to stretch until my heartbeat slowed. When my pulse matched my breathing, I went inside and started a page of notes.
We began with definitions. Paige wanted the system to be comprehensible at a glance. I wanted it to be unbreakable. We compromised: a simple grid for the cafeteria floor, entrances marked as sources, the serving line as a resource, tables as sinks. Agents moved by probabilistic rules that shifted with local density. We disagreed for ten minutes about whether agents should remember past congestion. She argued for simplicity, I argued for realism, and we finally wrote a small parameter that could be set to zero or one. It fit like a hinge.
Observation came next. For three nights we watched patterns. People clustered at the entrance and then split into two currents, toward food or toward friends. When the line grew long, some sat first and waited for it to thin, others left and returned later, and a small number cut diagonally in a narrow stream that only existed when noise rose above a threshold. Paige recorded time stamps; I drew quick maps with arrows and tiny numbers to mark counts. We didn't talk much. We moved our pens. When the staff closed early on the second night because of a shipment delay, the whole system changed shape in less than five minutes. Demand doesn't wait for permission.
We worked in the library until lights-out most nights. The math fell into place first. Conservation equations for people in the room. Transition probabilities between states. A steady state if arrivals and departures were balanced. We kept the interior honest by building in random shocks, small breaks in the flow when a tray spilled or a chair scraped loud enough to make people look up. The simplest systems ignore noise and call it elegance. The ones that last admit the mess.
On the fifth day we started coding. I built a bare simulation in C, the kind that looks ugly but runs fast. Paige sat beside me and traced the rules with her finger while I typed, checking that every conditional matched what we'd written. She caught two mistakes before I compiled. When we pressed run, the terminal printed a neat line of numbers, then a second, then a block of output that started to look like something we could believe. The grid filled and thinned. Currents formed and dissolved. When we mapped density over time the curve rose and flattened, wobbled when we added noise, then stabilized again. It was only a shadow of the real room, but it behaved. We both stared at the screen longer than necessary. It is a rare satisfaction to see an idea make the smallest promise and keep it.
In class that week, Dr. Li asked three people to present problem solutions at the board. I watched her eyes as they spoke and wondered if she could see the structure of their thoughts the way she sees the structure of a proof. Afterward, she looked in our direction for a second too long and said, without pointing, that anyone leaning on shortcuts would be found out by the algebra. I felt the warning slide through the room and settle somewhere near my spine. I like warnings when they are earned.
At night I stayed to the routine. Push-ups, slow holds, stretching until the muscles in my legs released the heat of the day. Control, not strain. The body is just another system under constraint. If you keep it honest, it stays out of the way of the mind. When I sat down again, the numbers greeted me like a metronome, steady as breath.
By the second weekend the draft report was six pages and growing. Paige wrote the introduction with clean, unadorned sentences that named the problem and the environment without apology. I wrote the model section like a set of instructions, each paragraph a step in assembly. We listed assumptions and cut three that weren't necessary. We added one we could defend. When we hit the discussion, we argued quietly over a single adverb for five minutes, then deleted the sentence and replaced it with a figure. The figure carried more weight.
We tested edge cases until the code squeaked. Zero entrances. Infinite arrivals. Obstacle in the center. Door held open by a propped chair. Corrupted resource stream when the serving line closed early. In one run the system fell apart; in another, it self-organized into strips of motion like a zebra pattern at the edge of the grid. Paige laughed under her breath at the stripes and then immediately scolded herself for it. "Science," she said, and I could hear her smile when she said it.
On Monday, Professor Kim asked for a preview of the competition projects. He said it the way people ask if your car will make it to the next town on a thin tank of gas. I showed him the density plots and the steady-state analysis. He skimmed the code, ran a finger along a brace, and asked why we seeded the random generator with the same value each time.
"Repeatability," I said.
He shook his head. "That's for us. Give the fellowship guy noise. He'll trust you more if he can't predict the run and still sees the same shape."
We switched the seed to the system clock that afternoon and reran everything. The curves wobbled differently but stabilized to the same plateau. Paige wrote one sentence that said so and moved on. We didn't narrate. We just showed.
By the third week, the project reached the part of the arc where hours go quiet. The outline is built, the structure holds, and the work becomes the movement of polishing joints and tightening screws until everything is flush. Paige grew sharper at the edges, the way she does when she wants to outrun her own limits. Her questions came faster. Her pencil tapped more often. Once, in the library, I saw her look away from the page and stare at the window like it might hold a different kind of answer. I offered to take the analysis section she had claimed. She shook her head. "I can do it," she said. I didn't push. I respect friction when it isn't wasting heat.
The night before the deadline, we printed the report to proof on paper. The library smelled like ink and dust and winter coats. I held the pages while Paige read aloud in a low voice, catching missing words, redundant phrases, a section header that mirrored the one before it too closely. We crossed out, rewrote, reflowed paragraphs until the pages felt light in my hands. When she finished the last line, she set the stack down and exhaled as if remembering how. I watched her shoulders settle from their raised position back to their natural angle. She closed her eyes for a breath and opened them again with the calm that comes after a storm you prepared for and still weren't sure you would avoid.
We walked to the lab to attach the appendix and package the files. The monitors glowed tired light in the dim room. I zipped the code with a readme that explained how to run the simulation and reproduce the plots. Paige checked the figure captions one last time and found a typo in the axis label. She corrected it without comment. We named the archive with the format requested: team name, project title, date. We hadn't agreed on a team name. She typed Cooper Swanson because the underscore looked crowded. I didn't object.
When we hit send, the progress bar crawled. The machine fan clicked twice and steadied. The screen flashed a small message that said submission received at 23:41. Outside the lab, the hallway was empty. A vending machine hummed to itself next to the locked lounge. I became aware of the weight in my shoulders and stood straighter until it left.
We didn't celebrate. Paige doesn't celebrate. I don't either. We walked halfway back to our dorm building together and stopped at the point where our paths split.
"Good work," she said.
"You too," I said.
She tucked a stray hair behind her ear, nodded once, and headed into the cold.
In my room the air felt thinner, as if the heater had finally caught up. I set my bag down and sat on the floor while my heartbeat reminded me I hadn't moved in hours. I went through the routine slowly, letting each hold last longer than usual, stretching the muscles until they were warm. The silence that follows a completed task is different from ordinary quiet. It's not emptiness. It's a cleared field.
I took a short run down the stairs and back up again, not for exercise but to reset the system. On the landing I paused with my hand on the rail and looked through the narrow window at the dark courtyard. A single figure crossed the path and disappeared behind the next building. Somewhere a door slammed, and echoes stacked for a second like folded paper and then fell.
On my desk the notebook waited. I wrote two lines:
Systems obey rules until people bend them.
If the model can forgive the bend and still hold shape, it is worth more than a beautiful proof.
The next morning, the day felt ordinary again. Dr. Li lectured about flux and wrote an integral that looked like a river over smooth stones. Professor Kim assigned a small compiler exercise we were expected to break and then fix. The campus buzzed with the usual chatter about grades and sleep and who had found which classroom. Paige and I sat through the day as if nothing had happened and everything had.
In the afternoon, I returned to the cafeteria without a notebook. I wanted to see if the room still looked like our model. People formed the same currents. The line thickened and thinned on its own schedule. In the corner a table scraped and half the heads turned; the flow shifted by a degree and then corrected. I watched long enough to feel the diagram settle behind my eyes and then left. It isn't good to stare at your own answers too long. You start to mistake the map for the ground.
That night, routine again. Push-ups, holds, breathing. A page of problems for Li. A page of code for Kim. Normal is a practice. I like practice.
I didn't think about whether we would win. That wasn't false modesty. It was an accurate description of the part of me that prefers net results to medals. The letter would help later. The grant would buy books. But the thing of value had already occurred in the three weeks it took to make a set of rules that could withstand a pair of young people trying hard not to be wrong. The world is full of things that look right under calm skies and split the first time they meet weather. Ours bent a little when it needed to and kept its shape.
Before I turned off the lamp, I opened the code one last time and read through the header. It felt like looking at my own handwriting in a mirror. Then I closed it and let the room go dark. My mind recited breath counts without needing to keep time. Outside, a late train passed somewhere far away, the sound low and steady, and I imagined a straight line of cars sliding through the night toward a place that would be there whether the train arrived on time or not.
In the morning, I would wake, and the system would start again. That's enough for now.
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