My IQ has been increasing year by year.

Chapter 290 Common Things

Chen Zhuo stood in front of the blackboard without speaking immediately.

He looked at the solid vortex that Allen had drawn in chalk, representing the inward collapse, and then glanced at the nonlinear tensor product that Sam had pointed out.

The physical collapse.

A black hole of computing power.

These two towering mountains stood firmly in front of us, completely blocking the road that had just begun to take shape.

Chen Zhuo turned his head, his gaze sweeping over the groove below the blackboard.

He reached out and picked up the half of the white chalk he had just put down.

He neither refuted Sam nor argued with Allen about the physical phenomenon of vacuum decay.

Chen Zhuo turned around, and the tip of the chalk landed next to the red vortex that Alan had drawn.

He planned to try the most conventional method of repair in mathematics.

Since the mesh will collapse when taking the limit, we can use the homology tool in algebraic geometry to forcibly add a layer of constraint on the outside.

He wrote down a symbol representing the coherent group.

David leaned against the pillar, watching Chen Zhuo's movements without saying a word.

Sam didn't laugh either.

In academic deduction, no one would laugh at a brain that is trying to solve a problem.

Sam just stared at the line of equations that Chen Zhuo had written down.

After watching for a while, he turned around, walked to the empty table where they had been standing, and reached out to grab a piece of paper.

He then pulled a pen from the pocket of his hoodie.

Sam took the paper and pen, walked back to the blackboard, and stood next to David.

He placed a napkin in his left palm, held a ballpoint pen in his right hand, and began writing rapidly on the paper.

The ballpoint pen left tiny dents on the rough paper, and in some places even tore the paper a little.

Sam wrote quickly, silently muttering a few parameters to himself.

Chen Zhuo finished writing the first line of constraints on the blackboard, paused for a moment, and then began writing the second line.

He attempted to use the intersections of algebraic cycles to firmly nail down the collapsing grid nodes one by one into the multidimensional space, like driving nails into a hole.

Sam put down his pen.

He glanced at the somewhat messy characters on the napkin, gave a slight smirk, and handed the napkin to David next to him.

David took the somewhat tattered tissue and glanced down at it.

Look here.

Sam tapped the last line of the equation on the tissue with the tip of his pen, lowered his voice, and spoke in a volume that only the two or three of them could hear.

Allen also came over to take a look.

"To satisfy the homophonic group constraint he just added."

Sam looked at David, his tone carrying a helpless certainty.

"He wrapped another layer of tensor outside the original matrix."

Sam looked up at Chen Zhuo, who was still writing on the blackboard.

"When the grid is not shrinking, the dimension of this variable is N^2," Sam said.

"Now, with this coherence constraint, once the mesh starts to take the limit towards the center, the matrix variables will skyrocket to 2^N in order to prevent the relative positions of those nodes from collapsing."

David looked at the derivation on the napkin, his brows slowly furrowing.

"The exponential explosion has begun."

Sam pressed the pen, and the tip retracted into the pen holder.

"With each line of constraints he writes, the dimension of the variable doubles. Once he locks the entire grid, the volume of this matrix will be greater than the number of atoms in the entire universe."

Allen sighed beside him.

"I told you, the rules of physics aren't so easy to circumvent."

Chen Zhuo wrote half of the third line.

The chalk tip stopped on the blackboard.

A half-finished Greek letter remained there, unfinished.

He didn't hear Sam and David whispering behind him.

But the moment he wrote down that half-line equation, his brain automatically figured out the logic that followed.

He calculated that inflation rate.

Using conventional algebraic patching techniques to fill this spinless physical grid comes at the cost of an infinite expansion of computing power.

If you rob Peter to pay Paul, the wall will still collapse eventually, just in a different way.

Chen Zhuo stood quietly in front of the blackboard, looking at the two and a half lines of white chalk writing he had just put on it.

He didn't have the resentment that comes with a genius being slapped in the face by reality.

They didn't grit their teeth and insist on banging their heads against this dead end.

He lowered his hand from the chalk.

Chen Zhuo turned around and searched in the blackboard tray, but couldn't find the blackboard eraser.

He simply raised his right hand, placed the back of his hand on the blackboard, and forcefully erased the two and a half lines of equations he had just written.

He wiped away the two lines of algebraic constraints that were trying to salvage the situation.

He turned his head and looked at the three people standing behind him.

There was no look of frustration on his face, only a calm that came from objective verification.

"Sam is right."

Chen Zhuo looked at Sam, his voice gentle and factual.

"This path is blocked."

He threw the remaining half of the chalk back into the trough and dusted off his hands.

"Conventional algebraic repair is indeed a black hole of computing power. The further you write, the faster the matrix expands, and it's unstoppable."

Chen Zhuo answered frankly.

David looked into Chen Zhuo's still clear and calm eyes, and a feeling he couldn't quite describe suddenly arose in his heart.

Often, what prevents a person from moving forward is not a lack of intelligence, but the inability to accept their own failures.

But the Asian boy in front of me overturned his hard work with such decisiveness that there wasn't the slightest bit of hesitation.

This absolute rationality was even more unfathomable than the complex algebraic matrices he wrote on the blackboard.

"Alright."

David stepped forward and patted Chen Zhuo on the shoulder twice.

"It's already terrifying enough that they've explored the area to this extent. Even if you call Edward Witten here tonight, he'll be scratching his head while staring at this blackboard."

David turned his head and waved to Sam and Allen.

"Let's go back to our seats. If we keep standing here staring at the blackboard, nobody's going to get any sleep tonight."

After a high-intensity mental battle, deep exhaustion follows.

Chen Zhuo did not look back at the blackboard.

He turned around and followed the three of them, walking back through the tavern's passageway to the innermost, secluded corner.

There were fewer people in the tavern than before.

Some college students who have classes or need to clock in tomorrow morning have already checked out and left.

The deafening rock music on the old jukebox in the corner has ended, replaced by a slow, slightly languid blues saxophone tune.

The four of them sat down again at the rectangular table.

The things on the table were the same as when they left.

Allen's half-glass of dark beer sat there quietly, the white foam on top long gone, the liquid appearing somewhat cloudy.

The last bit of ice in the glass of soda in front of Chen Zhuo had completely melted, and water droplets slid down the glass, gathering into a small puddle on the table.

As soon as Allen sat down, he leaned back in his chair, tilted his head back, and vigorously rubbed his face with both hands.

"Damn high-dimensional topology."

Alan's voice came through his fingers, thick with a nasal tone.

"I swear, I won't touch anything related to manifolds this weekend. I'm going to lie on the beach on Long Island for two days."

Sam crumpled the napkin covered in calculations into a small ball, tossed it into the middle of the table, then picked up his beer and, ignoring that it was flat, gulped down half of it.

"If I had known this thing would be so torturous, I should have gone into database architecture when I was choosing my major at MIT. At least there I would only have to deal with those stupid clients, not this kind of unreasonable exponential explosion."

The atmosphere at the table became somewhat subdued, but not oppressive.

It's all too common in their circle to spend months or even years on a project only to find it's a dead end.

No one will be discouraged just because they hit a wall in front of the blackboard tonight.

They simply felt tired.

Chen Zhuo sat in his seat.

He did not complain.

He picked up the glass of soda water on the table, took a sip, and found that the room-temperature water no longer had that stimulatingly cold feeling. As it slid down his throat, it tasted rather bland.

David twirled the glass in his hand, listening to blues music, seemingly trying to relax the tension in his mind.

"Actually, Chen's line of thinking tonight is very similar to a solution we abandoned in the lab last month."

David looked at the crumpled napkin in the middle of the table and slowly opened his mouth.

"We were also trying to use Ricci flow to deal with singularities on three-dimensional manifolds, just like the situation Chen just encountered. Once a singularity appears, the curvature tends to infinity."

David sighed.

"Richard Hamilton was stuck on this problem for more than a decade. Our group tried to use a local geometric excision method to remove the singularity and then suture it back up surgically."

Sam glanced at David.

"And the result?"

"The curvature boundary after stitching was completely uncontrollable."

David shrugged.

"Just like the computing power black hole Chen mentioned earlier, as long as you try to precisely describe and control that singularity, mathematical tools will completely collapse in the face of infinity."

Allen put down his hands that were rubbing his face, picked up the flat beer, and took a sip.

"Your math is just too rigid."

Allen leaned back in his chair, staring at the ceiling.

"You always try to find a perfectly fitting equation for every change in the universe, and once you can't find one, you think it's the end of the world."

David smiled and did not refute.

He turned his head to look at Allen and casually asked a question following the topic.

"Since you think we math students are too rigid, what about you physics students?"

David pointed to the red circle that Chen Zhuo had drawn on the blackboard to represent the collapse.

"Chen's grid just now collapsed into a black hole because it had no spin. This can't be calculated mathematically, so what about in the real physical world?"

David picked up his glass and looked at the Harvard postdoctoral fellow in high-energy physics.

"What exactly is the state of the true singularity at the center of a black hole? Have you physicists calculated it using your non-linear methods?"

This question was asked casually, just a casual chat among colleagues at a dinner party to pass the time.

Sam looked at Allen.

Chen Zhuo was looking at the ripples in the water in the cup when he heard the question, so he raised his gaze slightly and looked at Alan.

When Allen heard David's question, his hand holding the cup froze in mid-air.

He suddenly gave a self-deprecating laugh.

"Figure it out?"

Allen shook his head and put the cup on the table.

"That's bullshit."

Allen's answer was crude and direct.

"Do you think physics can handle infinity? When a star collapses, its mass becomes infinitely concentrated, and its volume shrinks infinitely, the equations of general relativity will still fail at the center of a black hole."

Allen tapped the table twice with his finger.

"With infinite curvature and infinite density, at that point, time stops and space ceases to exist. If you try to apply any existing physical equations to it, the results will all be meaningless and absurd data."

"So what are you going to do about it?" David asked, somewhat curious.

"We can't just leave it there and ignore it, can we?"

"Don't care? How could we not care?"

Allen tugged at the slightly wrinkled collar of his shirt.

"The physicists' method is very simple."

Allen looked at David and uttered a word that was extremely basic in modern physics, but seemed very meaningful at this moment.

Planck length.

Chen Zhuo paused slightly in the hand holding the soda water.

"We introduced the Planck length as a fundamental limit in physics."

Alan didn't notice Chen Zhuo's subtle movements. He leaned back in his chair and continued to explain in a tone that was both casual and somewhat helpless.

"In our understanding, there is no meaningful physical scale in this universe that is smaller than the Planck length; it is the bottom line of all physical laws."

Allen held up two fingers, gesturing to indicate an extremely small distance.

"As a star collapses and matter is squeezed toward the center, we use equations to calculate its evolution, and keep calculating and calculating."

Allen's fingers slowly moved closer together.

"However, when it shrinks to the Planck scale..."

Allen's fingers stopped; he didn't close them any further.

"Let's stop."

Allen looked at the people at the table.

"We're not going to calculate any further because once we reach that limit, the concept of continuous spacetime becomes meaningless. Quantum gravity takes over everything, and we don't have a perfect theory of quantum gravity at all right now."

"so."

Allen spread his hands, striking an extremely bachelor pose.

"We draw a line directly at the Planck length and treat the singularity inside that line as an absolute black box."

Allen picked up the flat beer.

"We don't care what's inside the black box, or how big it is; we only deal with the physical phenomena outside the black box."

Allen took a sip of his drink.

"This is how physicists avoid risks. If I can't calculate it, I won't force it. I draw a bottom line for myself, and when I reach that line, I just close my eyes."

There was a few seconds of silence on the table.

The sound of a blues saxophone echoed through the pub, carrying a unique husky quality.

After hearing Allen's words, Sam suddenly snorted coldly.

"So you physics students aren't that different from us coders."

Sam leaned forward and placed his hands on the table, crossed.

"When faced with an unsolvable deadlock, it all boils down to the same logic."

David looked at Sam.

"What do you do when your computer gets stuck? Unplug it?"

"That's slightly more civilized than unplugging the power cord."

Sam pursed his lips.

He pointed to the napkin on the table that he had crumpled into a ball.

"Just like the matrix Chen just wrote, if you ignore it, as the grid shrinks, the dimensions explode exponentially, and the final result is a memory overflow, the system completely crashes, and all the previous calculation data is lost."

Sam glanced at Chen Zhuo.

"In computer science, if we know that a variable will approach infinity under certain extreme conditions, leading to such devastating consequences, we would never be foolish enough to add more memory to the server in an attempt to support that infinity."

Sam tapped the table.

"We'll write some code."

Sam's eyes revealed a cold logic characteristic of programmers.

"A piece of code called 'exception handling'."

Sam looked at the people at the table and explained this basic operation that is most common in programming.

"In the underlying logic of the program, we set a limit or a critical value in advance. When the algorithm runs, the variables start to expand and keep approaching that critical value."

Sam made a gesture of swinging a knife downwards.

"As long as it dares to cross that line."

"Crack."

Sam added a sound.

"The exception handling mechanism will be triggered immediately, and the program will automatically interrupt the thread that is causing the infinite loop, forcibly truncating it."

Sam spread his hands.

"Then, the system will pop up an error window, telling you that there is a problem here, but..."

Sam emphasized his words.

"The system itself will not crash, the server is still running normally, and other data remains safe."

Sam leaned back in his chair, picked up a few cold fries from the table, and stuffed them into his mouth.

"Computer logic is just so unreasonable. I can't solve that infinity, and I can't calculate that infinity, but as long as I set up exception truncation, that infinity will never be able to kill my system."

The lights in the tavern seemed to flicker.

Allen and Sam's words intertwined on this small table.

The Planck length in physics is a black box and will not be calculated further.

Computer error handling: truncation, error reporting without crashing.

Whether it's high-energy physics studying the origin of the universe or computer science studying virtual algorithms, when faced with the "infinity" that represents destruction and collapse...

None of them chose to, like mathematicians, relentlessly work on it, try to patch it up, or attempt to fill that bottomless pit with rigorous equations.

They're all just giving up.

In their own ways, they drew a line on the edge of the cliff, then turned away, refusing to take another step forward.

Chen Zhuo sat opposite Allen and Sam.

He was still holding the glass of soda water that had long since run out of ice.

He didn't interrupt their conversation.

He listened quietly.

Listening to Allen talk about the limits of physical laws, and listening to Sam talk about forced truncation in code.

Chen Zhuo's gaze fell on the unremarkable surface of water in the glass.

But the calm in his eyes had subtly changed without him realizing it.

His gaze, which had been somewhat unfocused due to the failure of algebraic repair, was now gradually refocusing.

Planck length.

Abnormal truncation.

These two terms, belonging to other disciplines and imbued with a strong sense of pragmatism, were like two faint matches lit in the darkness of his mind.

Chen Zhuo slowly put down the soda water glass in his hand.

He simply sat there quietly, his posture unchanged, but David keenly sensed that the air around Chen Zhuo seemed to freeze for a moment.