"Go on. If the grid method is a dead end, then step outside of it."
Li Jianming didn’t even look up.
"Don’t waste your foundation in mathematics."
Chen Zhuo nodded.
"Good luck with your defense, Senior."
As Chen Zhuo walked past Wu Tao, he patted him on the shoulder.
Wu Tao raised the stapler in his hand and gave it a wave.
"I’ll take all the luck I can get."
He pushed open the door and stepped into the hallway.
The wind outside seemed to have grown colder, but Chen Zhuo’s mind felt unusually clear.
Li Jianming’s words were like a seed that had already taken root somewhere deep in his mind.
But he was still missing something.
A physical anchor that could bridge the gap between this highly abstract, pure mathematical theory and the engineering data of the real world.
By the time Chen Zhuo got back to his dorm, it was almost dark.
The dorm room door was ajar.
He pushed the door open, and a thick smell of scraped metal and machine oil wafted out.
Wang Dayong was sitting at his desk, his back to the door.
Several old newspapers were spread across his desk. In the center lay a fist-sized, silver-white aluminum alloy component.
Wang Dayong held a coarse, half-round file, slowly grinding the edges of the metal block.
SCRAPE... SCRAPE...
The sound of the metal file scraping against the aluminum block was rhythmic. With every movement, fine, silvery dust drifted down onto the old newspapers.
Chen Zhuo entered the dorm and casually closed the door behind him.
He walked over to his chair, sat down, twisted open the water bottle on his desk, and took a sip.
His gaze was unfocused, resting quietly on Wang Dayong’s back.
Wang Dayong worked with intense focus. Every few scrapes, he would stop, pick up the metal block, and hold it close to the desk lamp, squinting to carefully examine the curve of the edge.
After a few seconds, he would put it down, change his angle, and continue filing.
SCRAPE... SCRAPE...
The sound was monotonous and repetitive.
Chen Zhuo watched for a while.
"Dayong."
Chen Zhuo spoke.
Wang Dayong didn’t stop what he was doing, nor did he turn his head.
"Huh? You’re back? Eaten yet?" Wang Dayong asked.
"Not yet."
Chen Zhuo screwed the cap back on the bottle.
"Is that for a class project?"
"Yeah."
Wang Dayong stopped filing and wiped the sweat from his face with a towel hanging around his neck.
"It’s a component that has to be polished entirely by hand. The precision requirement is pretty high—I have to create a smooth, curved surface. This aluminum block is really soft. If I press the file even a little too hard, the whole thing’s ruined."
Chen Zhuo leaned back in his chair.
"How do you know if you’re filing it correctly?" Chen Zhuo asked.
Wang Dayong turned around, still holding the aluminum block.
"I just follow the blueprint."
"Do you measure every single millimeter with a caliper?" Chen Zhuo looked at him.
Wang Dayong laughed and set the file down on his desk.
"How could I? I’m not a CNC machine. If I measured it millimeter by millimeter, I’d never get it done this month."
Wang Dayong reached into a messy pile of tools on his desk and pulled out a greasy sheet of A4 paper.
He handed the paper to Chen Zhuo.
"Here, look. This is the entire blueprint."
Chen Zhuo took the blueprint.
The paper was thin. It didn’t have the dense grid of dimensional annotations or the hundreds and thousands of coordinates that Chen Zhuo had expected.
On it, a parabola was drawn with a simple black line.
And next to this curve, a very short algebraic equation was quietly printed:
y = ax^2 + bx + c
In the bottom-right corner of the blueprint, a tolerance range was specified.
"See?"
Wang Dayong walked over and pointed at the curve on the paper.
"The designer didn’t draw thousands of points for me to match on the blueprint. They just drew one line and gave me a quadratic equation."
Wang Dayong picked up a cup from the desk and gulped down half of it.
"When I’m working, I just keep the general shape of this equation in my mind. As long as I make sure the start and end points are within the tolerance range of the coordinate system, and I just follow the feel of it, the curve in the middle comes out naturally. It’s a whole, not a collection of points."
The dorm room was silent.
Chen Zhuo sat in his chair, holding the grease-stained blueprint.
His gaze was fixed on the very short algebraic equation.
An equation with only a few letters.
No redundant grid.
No endless coordinate nodes.
With just these few simple symbols, it perfectly and precisely defined the entire shape of the parabola on this two-dimensional plane.
The lump of dough Li Jianming had drawn in his office that afternoon and the parabola on the blueprint before him slammed together in Chen Zhuo’s mind.
’The designer didn’t draw points.’
’Because points aren’t needed.’
’The equation itself *is* the shape.’
Chen Zhuo’s breath caught, and his pupils contracted slightly.
The thick fog in the depths of his mind—a fog named "physical grid"—was violently churned up by this simple quadratic equation.
He remembered the forty million grid cells in the School of Physics computer lab.
He remembered the server that had crashed to a blue screen.
’If a complex parabola can be perfectly described in its entirety by an extremely simple algebraic equation...’
’...then what about the massive, three-dimensional curved surface of a high-speed train’s nose?’
’No matter how complex the nose is, its surface is still, in essence, a continuous geometric manifold.’
’Why do I have to follow the intuition of physics and chop this smooth, complete whole into tens of millions of fragmented grid points?’
’Why must I make the computer calculate the boundary conditions for the wind blowing over these tens of millions of fragments?’
’This is so stupid.’
’It’s like trying to solve calculus with an abacus.’

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