My IQ has been increasing year by year.

Chapter 285 Lessons from Others

The midday sun shone through the glass windows of the hotel room, casting a square patch of light on the carpet.

The room was quiet. Chen Zhuo sat at his desk, head down, a pen in his hand.

Several sheets of draft paper were scattered on the table, covered with densely written calculations.

This is an excerpt of some materials he copied back from the Harvard Library this morning, titled "The Fundamental Definition of Lattice Gauge Field Theory".

He ignored the physics background information about quarks, gluons, and the strong interaction.

His gaze skipped over the long text descriptions and landed directly on the mathematical formulas in the middle.

Chen Zhuo rewrote the continuous gauge field as a group element defined on the discrete grid lines.

Next, he forcibly replaced the integral symbol in the original continuous space with the summation of discrete lattice points.

After writing this line, he stopped and looked at the structure on the paper.

This is a mathematical framework that was forcibly invented entirely to circumvent infinity.

Physicists devised this method when faced with integrals that were impossible to calculate in continuous space.

Chen Zhuo didn't delve into the physical meaning behind this set of tools, nor did he care what particles it corresponded to in reality.

He simply broke down the matrix structure and algebraic relationships of this tool, line by line, and memorized them.

The continuous micro-business model has become a difference, and the points have become a summation.

The outline of the bridge seemed to be starting to emerge, but it was still very blurry.

Chen Zhuo glanced at the alarm clock on the table; it was 1:10 PM.

He put down his pen, gathered the several sheets of draft paper on the table, and stacked them together. He opened a drawer and took out the sheets of paper he had marked with black dots at the Harvard Science Center yesterday, placing them aside with the draft paper.

He didn't plan to take the old papers with him when he went out.

Chen Zhuo took a brand new notebook.

This notebook is a size larger than a regular notebook, with a hard cover and light blue grid lines.

He had just bought this when he passed by the stationery store that morning.

He put the new notebook in his bag, took a pen, then picked up the pass Pierre had given him, pushed open the door, and went out.

The Boston afternoon sun was a bit glaring, but the wind was still cool.

Chen Zhuo followed the path on campus and turned towards the building complex on the other side.

A dozen minutes later, a building appeared in front of us. There was no conspicuous sign at the entrance of the building, only a bronze plaque embedded in the wall next to the door.

Jefferson Physics Laboratory.

The architectural style here is completely different from that of the mathematics department.

The lobby of the science center in the mathematics department is filled with sofas and round tables, and the walls of the corridors are covered with blackboards, on which people are writing and drawing at any time.

But it's not here.

The corridors of Jefferson Laboratory were somewhat dimly lit, with rows of closed doors on both sides, each bearing warning signs indicating high voltage or laser.

Occasionally, one or two people would walk by from the other end of the corridor, hurrying along without looking at each other.

Chen Zhuo followed the signs on the corridor wall.

The pass Pierre gave me indicated that the meeting room was at the far end of the second floor.

He went up the stairs to the second floor and pushed open a half-closed door.

Inside is a small tiered conference room.

It's not very big; it can probably accommodate fifty or sixty people.

Rows of benches extend downwards in a tiered fashion, with a small lectern at the bottom and two sliding blackboards hanging on the wall.

The seminar hadn't officially started yet, but there were already thirty or forty people inside.

Unlike the atmosphere at the math department, where everyone was dressed in suits and ties and seemed ready for anything, the people here were all dressed very casually.

Some people were wearing faded plaid shirts, some were wearing oversized old coats, and some were simply wearing short-sleeved T-shirts with logos of unknown bands.

A few people in the front row were gathered together, loudly arguing about the error rate of some experimental data, while some people in the back row were flipping through newspapers or eating half-eaten sandwiches.

Chen Zhuo took the pass and walked down the passageway.

He stopped in an empty seat on the side of the third-to-last row.

Next to me sat a white guy with messy hair, wearing a gray hoodie, looking down at a book on his lap, twirling a pen in his hand.

Chen Zhuo pulled out a chair and sat down.

The commotion wasn't loud, but the boy next to him still looked up at him.

The boy's gaze lingered on Chen Zhuo's young face for a second before settling on the clean table in front of him.

"undergrad?"

The boy asked casually, his tone somewhat lazy.

Chen Zhuo turned his head, looked at the other person, and smiled gently.

"No," Chen Zhuo replied.

The boy stopped writing, closed the book on his lap, the cover of which bore the large characters "Quantum Field Theory".

He glanced at Chen Zhuo's attire.

"A math major?"

The boy raised an eyebrow.

I guess so.

Chen Zhuo nodded.

The boy chuckled and leaned back in his chair.

"What a rare guest."

The boy put his hands behind his head.

"These past few days, haven't you math department students been at the science center listening to reports on that Poincaré conjecture? I heard it's driving people crazy."

"It's quite tiring."

Chen Zhuo followed up with a sentence.

"So you came here to clear your head?"

The boy pursed his lips.

"But you might be disappointed. Today's lecture is about topological evolution in string theory. The old man on stage is known for his wildly imaginative lectures. You math students will probably want to punch him if you listen to him."

"It's nothing, I'm just listening casually."

Chen Zhuo placed the notebook flat on the table.

The boy glanced at the thick notebook, then at the grid lines printed inside.

"Bringing such a thick notebook, and you say you're just listening casually."

The boy muttered something, opened his book again, and stopped talking.

Chen Zhuo did not explain.

He took a pen out of his pocket and turned to the first page of the grid notebook.

On the white paper, only fine light blue lines intertwine to form countless tiny squares.

Chen Zhuo placed the pen next to the paper, crossed his hands on the table, and quietly looked at the podium in front of him.

It was exactly 2 PM.

The side door at the front of the conference room was pushed open.

A unkempt man with graying hair walked in.

He looked to be in his sixties, wearing a wrinkled suit with the two pockets bulging from being filled with too many things.

He wasn't wearing a tie, and the top two buttons of his shirt were undone.

He held a mug in his left hand and a piece of chalk between his right.

The buzzing conversation in the conference room quieted down a little, but it didn't completely fall silent; a few people were still whispering in the back row.

The old professor didn't seem to mind the casual atmosphere.

He walked up to the podium, placed the mug he was holding on the edge of the lectern, and then went directly to the blackboard.

There was no opening statement, no self-introduction, and no slideshow was shown.

The old professor turned to face the audience.

"Today we'll discuss the topological changes of strings in spacetime evolution."

The old professor spoke, his voice loud and clear, carrying an undeniable confidence.

He turned around and drew an arc on the blackboard with chalk.

"In the most basic case, we can regard the trajectory of a string sweeping through spacetime as a two-dimensional curved surface, which we call the world surface."

The chalk drew a cylindrical shape on the blackboard.

The old professor drew quickly, and his lines were somewhat messy, completely different from Zhu Xiping's meticulous handwriting on the blackboard.

Chen Zhuo sat in the back row, looking at the cylinder.

"When this string moves smoothly through spacetime, everything is fine, and we can calculate its effect using continuous integration."

The old professor wrote an integral symbol next to the cylinder, followed by a series of physical quantities.

"but."

The old professor squeezed the chalk in the middle of the cylinder with force.

He drew a shape on the blackboard that looked like someone was being choked, with the cylinder becoming extremely narrow in the middle.

"If the topology of spacetime changes, such as space tearing apart, or multiple dimensions curling up together."

The old professor used chalk to make a heavy dot on this extremely fine spot.

"Here, a singularity will appear."

A solid white dot appeared on the blackboard.

The old professor turned around and looked at the students and researchers below the stage.

"Continuous spacetime diverges at this point."

He pointed to the white dot.

"The curvature becomes infinite, the metric tensor becomes invalid, and all those beautiful continuous calculus formulas you learned before become useless here."

Chen Zhuo leaned back in his chair, his eyes fixed on the white dot on the blackboard.

This is essentially the same problem that Zhu Xiping encountered in the Poincaré conjecture.

Zhu Xiping was dealing with the topological breaks that occur in the evolution of manifolds.

Yesterday morning, Chen Zhuo personally witnessed Zhu Xiping pull down three blackboards in a lecture hall at Harvard.

Zhu Xiping spent a full forty minutes writing down countless complex partial differential equations, using extremely rigorous logic to set a limit on the convergence rate near this singularity.

Chen Zhuo looked at the old professor on the stage, wondering how the physics department would deal with this thing.

The old professor picked up his mug and took a sip of coffee.

"If you go to the science center across the street, ask your colleagues in mathematics."

The old professor put down his cup and pointed out the window.

Several people in the audience laughed.

"They will tell you that major surgery is needed here."

The old professor shook his head.

"They would write hundreds of pages of equations to prove that the limit converges under certain conditions. They would do everything they could to patch up the hole and make the manifold smooth again."

The old professor turned around and looked at the singularity on the blackboard.

"But we don't have that time."

He put down the chalk in his hand.

Under the watchful eyes of everyone in the audience, the old professor picked up a blackboard eraser from the lectern.

He walked up to the blackboard and aimed the eraser directly at the white dot representing the singularity.

Smear it hard.

No equations were set up, no limits were found, and no convergence conditions were proven.

The singularity that mathematicians believed would take ten years to fill was completely erased from the blackboard in less than a second by a worn-out eraser.

After erasing, a large blank space appeared in the middle of the originally continuous cylindrical shape.

The old professor threw away the blackboard eraser and picked up the chalk again.

He didn't draw a new smooth curve in that blank space.

He flicked his wrist, drawing crisscrossing straight lines on the blackboard.

A horizontal line.

A vertical line.

Within seconds, a perfectly square grid was crudely placed over the original location of the singularity.

The grid lines divide the originally continuous space into individual square grids.

The continuous lines have disappeared, replaced by discrete intersections.

The old professor turned around and patted the chalk dust off his hands.

"Continuous integrals cannot be calculated here."

The old professor looked down at the audience, his tone as calm as if he were stating a truth.

His fingers tapped on the grid on the blackboard.

"So we break down spacetime and put it into a discrete lattice."

The meeting room was quiet; everyone was used to this simple and direct method of deduction.

Chen Zhuo sat in the back row, his gaze fixed on the grid.

"Don't worry about whether the limit is strictly continuous at this point."

The old professor's voice echoed in the conference room.

"Don't bother with those mathematical proofs of existence."

The old professor took the chalk and slammed it down on the nodes of the grid several times.

"As long as the mesh is dense enough, and the distance between nodes approaches the Planck length."

The old professor turned his head and looked at the students below the stage.

"If the results obtained from the test match the observations of the gravitational field and the experimental data, then it is correct."

As soon as those words were spoken...

Something seemed to suddenly light up deep within Chen Zhuo's pupils.

If it conforms to observation, then it is correct.

There's no need to worry about whether the limit is strictly continuous.

This kind of skipping step, which seems full of loopholes and completely illogical to mathematicians, is actually a perfectly legitimate and standard practice in the physics department.

Mathematicians strive for an absolutely flawless process, even if the final conclusion is utterly useless.

Physicists, however, want results.

As long as the result works, they dare to step on even the scaffolding made of mud, as long as the process is effective.

Chen Zhuo looked at the rough grid on the blackboard.

Last night in his hotel room, he was trapped by the enormous chasm that needed to be proven that the discrete mesh could perfectly converge back to the original topology.

In the eyes of physicists, it simply does not exist.

The bridge is broken?

Then don't worry about whether it's broken or not, just jump over it on the rubble.

Chen Zhuo realized that he had indeed been suffering from the kind of fastidiousness that mathematics professionals have, just as Pierre had said. He wanted to be perfect from the very first step.

But he forgot that before building a magnificent structure, what is often needed first is a crude scaffold.

Chen Zhuo did not copy the equations about energy fields and spin that the old professor later added to the blackboard.

He doesn't need those physical shells.

All he needed was this simple and direct action.

Chop the pieces into small pieces.

Chen Zhuo lowered his head, his gaze completely focused on the pages in front of him.

With his pen, he steadily drew black dots along the light blue grid lines printed on the notebook.

These dots represent broken manifolds.

The old professor on the stage was still talking eloquently about the quantum fluctuations of strings in a grid.

The old professor's voice gradually faded into the distance and was eventually completely filtered out by Chen Zhuo.

With a slight flick of his wrist, he drew a line connecting the two black dots.

Physicists have defined gauge fields on the wires.

Chen Zhuo doesn't need a regulated field.

Next to the line, he wrote a mapping symbol from algebraic geometry.

Since physicists dare to run experimental data on this grid.

Then he dared to build the framework of Hodge's conjecture on this grid using pure algebraic matrices.