Chapter 13 - Structure
Chapter 13 - Structure
Two years had passed since the announcement of the Hodge Conjecture, and the public had already drifted away from the name Yoon Siwoo.
For the first few months, every media outlet talked about Siwoo's name, and people were ecstatic that an eight-year-old boy had solved a Millennium Prize Problem.
But the world moved on to other stories faster than expected.
New political scandals broke, economic news filled the screens, and sports finals and celebrity divorce articles snatched away people's attention.
It wasn't that the name Yoon Siwoo had vanished, but it had naturally been pushed to the back of the public's daily life.
However, mathematicians in academia still read his papers, and drawings modifying his structures still remained on the MIT math department chalkboards.
Still, that was academic business, and Yoon Siwoo's daily life was far more ordinary than that.
Waking up in the morning, eating, going to MIT, playing games with students, and stopping by the lab if necessary.
His parents had also gotten quite used to life in America now.
Hyejin greeted the neighbors naturally, and Taesik, caught up in the fun of watching baseball, laughed while talking about starting pitchers with MIT staff.
The two no longer followed Siwoo around all day.
They had gotten somewhat used to Siwoo moving on his own, and Siwoo, too, had gotten used to the gazes that treated him specially.
Just like that, Yoon Siwoo had turned ten years old before he knew it.
The MIT student lounge was noisy even after lunchtime, and Siwoo sat in the middle of it, holding a game console.
At first, the students found Siwoo difficult to approach, but as time passed, they got used to it.
Yoon Siwoo in front of a chalkboard was uncomfortably quiet and scary, but Yoon Siwoo in front of a game console was just a 10-year-old kid.
"Lost again."
Yoon Siwoo said, looking at the screen.
"It was okay until the middle this time."
"Is that supposed to be comforting?"
"It's not comfort, it's a fact. The early movements weren't bad, but you threw away too many paths you could have taken in the late game."
"You see all that while playing a game?"
"I don't see everything. But I can see which way the flow is leaning. Even when there seem to be many options, in reality, there are often only a few left."
The student next to him laughed.
"Easy to say, but it's frustrating for the person on the receiving end."
"It might be frustrating, but the result of that last round was already decided from the middle."
"That makes it even more frustrating."
Yoon Siwoo kept looking at the screen while hearing the laughter.
The finished game screen still had the traces of where the characters had moved just moments ago.
To a normal person, it was just a past play, but to Siwoo, it strangely looked like lines.
He could see where they were blocked, where they turned back, where it was empty, and from which moment the opponent's options had dwindled.
At first, he thought it was because he played a lot of games, but when he thought about it, it wasn't just a simple matter of skill.
The students probably thought they made different judgments, but in reality, they were just moving within the structure the map allowed.
Even if it looks like they are choosing freely, when the structure narrows, choices flock to similar places.
This wasn't just about games.
"Let's play one more."
"Sure."
The game started again, and this time, three students were determined to corner Yoon Siwoo.
One blocked the front, one went around the back, and one cut off the resource points.
It was pretty good in the beginning, but as time passed, the same thing happened again.
The students' movements gradually flocked in one direction, the space to escape dwindled, and Siwoo was always standing in the necessary position first.
Eventually, the victory sign popped up on the screen again.
"Oh, seriously! This makes no sense."
"Yoon, are you actually playing the game?"
Siwoo put down the controller.
"I am playing the game. But games, in the end, are just moving within a structure."
"Structure again?"
"It's true. There's a map, there are paths, there are places that are blocked, and there are places to turn back. People think they move freely, but in reality, they move within the range the structure allows."
The student tried to retort but shut his mouth.
At that moment, Siwoo's gaze stopped on the screen, and the movement paths from the previous round came to mind again.
The paths the characters took overlapped with something else.
The scene of cars flocking at an intersection, the flow of batted balls changing depending on defensive positions at a baseball stadium, and even the spatial structure he had been holding onto when solving the Hodge Conjecture two years ago.
They were completely different things, but they were strangely similar.
Siwoo stopped for a moment after seeing that. He was looking at the game screen, but it wasn't a game.
The students used different strategies, cars drive on roads, baseballs fly over the stadium, and the points of mathematics move within an abstract space.
The names are all different, but the essence was similar.
There is movement, and there is a structure that allows or blocks that movement.
Many of the things people call 'skill' might actually be the difference in who saw the structure first.
If so, the reason I win at games is probably not because my reaction speed is fast, but because I see the structure first.
Siwoo pulled a napkin from the table, and his pen moved.
The game map was drawn, and the characters' movement paths were connected with lines.
On the second napkin, a road was drawn.
An intersection where cars flock, blocked roads, and alleys to turn back were marked.
On the third napkin, a baseball stadium was drawn.
Defensive positions, batted ball directions, and the runner's movements were connected.
On the fourth napkin, the structure used to prove the Hodge Conjecture two years ago was drawn.
A student asked.
"Are you doing math while playing a game?"
"It's more of a verification than math."
"Verifying what?"
"Whether things that look different can actually have the same structure."
"Why verify that?"
"Because I saw it."
He took out a new napkin, and this time, he drew a circle.
Small dots were marked inside the circle, and lines were connected between the dots.
At first, it looked like a simple pattern, but the lines became denser, and the flow split and then gathered back into one.
"What is it this time?"
Siwoo couldn't answer right away.
Thoughts were connecting in his head, and completely different scenes were tied into a single line.
People move, cars move, balls move, game characters move, and electrons move too.
If they move, there is a path, and if there is a path, there is a structure.
If you look at the reason electrons lose energy only as a phenomenon, it's called resistance.
But from the perspective of structure, it looks a little different.
It's not that the electrons are strange; it's that the path is strange.
Because the path bends, collides, scatters, and has to turn back, it loses energy.
Then, what if you make the path properly in reverse?
If you can create a structure where electrons don't have to turn back, an arrangement where they don't have to collide, and a path where the flow doesn't break, where does the resistance come from?
Siwoo's hand stopped.
"...Electrons were losing their way, too."
"What?"
"It's not that the electrons are weird, it seems the structure is weird. If you make the path properly, there's no reason to turn back."
"Suddenly electrons?"
"I'll go to the lab."
"You're going now?"
"Yes. I think I need to see this now."
Siwoo opened the lab door alone.
Siwoo took the napkins out of his bag and spread them on the desk.
Game map, road, baseball stadium, Hodge structure, and the atomic arrangement drawn last.
He stared at them for a long time, then picked up a marker.
At first, he transferred the drawings from the napkins, and the electron flow moves from one side to the other.
In a general arrangement, the flow bends, collides, and scatters. He didn't erase those points.
Because if he erased them, he wouldn't know why it was blocked, so he drew a different structure next to it.
The alignment method used in the Hodge Conjecture was included.
Back then, it was a structure used to match the threshold of mathematical space, but now it was being used to match the path of electrons.
Standing in front of the whiteboard, I felt a bit strange.
This didn't feel like forcing something new.
It was closer to the feeling of discovering a path that already existed.
People tried to find superconductors as a phenomenon.
They looked for which material resistance disappears in, at what temperature it appears, and under what conditions it is maintained.
But what I am looking at is not a phenomenon, but a structure.
If I create the path for electrons to pass through first, wouldn't the phenomenon follow? It was similar when I solved the Hodge Conjecture.
People tried to cross the wall, but I looked at the point where the standard was misaligned, not the wall.
If it's the same this time, the problem might not be the electron, but the standard of the space the electron passes through.
The marker moved, and the atomic arrangement changed.
The crystal structure was redrawn, and the electron flow continued without turning back.
The line, which was thin at first, gradually stabilized.
Siwoo started calculating.
One line, two lines, three lines; the formula got longer, but it didn't get complicated.
As unnecessary paths disappeared, it became simple.
Siwoo stopped in the middle and looked at the structure again.
It was strangely natural.
If it were a forced structure, it would have to creak somewhere.
But this structure didn't creak, as if I had just discovered a path that had been there from the beginning.
Finally, I overlapped the alignment standard of the Hodge structure exactly.
The flow closed in an instant, and the formula stopped. It was strange.
It closed too quickly. At first, I thought it was a mistake.
I tried approaching it in different ways, but the result was the same.
I turned on the computer and ran a simple simulation.
I stared at the monitor and stopped.
[0]
At first, I thought it was an error and changed the conditions, but the result was the same.
I went back to the front of the whiteboard and slowly wrote under the last line.
[Resistance = 0]
I stared at that sentence for a long time.
Resistance disappears, and energy is not lost.
Heat is not generated, and electrons do not stop.
This is not a simple efficiency improvement.
I could tell that much.
Siwoo sat in the chair, and his head was strangely calm.
When too big a result comes out, emotions follow late.
"...This makes no sense."
Although he said that, Siwoo knew.
It's not that it makes no sense, it's just that it hadn't been seen until now.
If you try to find a phenomenon, you have to wait for coincidence, but if you look at the structure, you can create a path.
The path the electrons lost, if you open that path, there was only one name.
"...Superconductor."
Siwoo took a picture of the whiteboard, thought for a moment, and sent an email to Jonathan.
The title was short.
[Request for structure verification]
The body wasn't long either.
[Strange results came out in the electron flow]
[Please check in the morning]
Even after pressing send, Siwoo didn't move for a while.
He briefly wondered if it was something that could wait until morning, but soon packed his bag.
It was still a formula, and experiments were needed.
Samples were needed, and someone to verify it was needed.
Before turning off the lab lights, he looked at the whiteboard one last time.
[Resistance = 0]
"If the structure is right, a path is created."