N-M Chapter 57 The Meeting of the Four Gods—How come I, the developer, didn't know about it?
Chapter 57 The Meeting of the Four Gods—How come I, the developer, didn't know about it?
"I've considered it."
Lu Feng took the whiteboard marker and started a new line next to the equation of motion.
"If the linear density of the rod is not uniformly distributed along its length, for example, if ρ(x) = ρ₀(1 + αx/L), then the position of the center of gravity is no longer simply L/2."
The pen tip drew an integral symbol on the whiteboard.
"The centroid coordinates x_c = ∫₀ᴸ xρ(x)dx / ∫₀ᴸρ(x)dx need to be recalculated, and the moment of inertia also needs to be rewritten as I_rod = ∫₀ᴸ x²ρ(x)dx."
He paused for a moment, expanded the integral, and within three lines calculated the expression for the center of gravity with the α parameter and the corrected moment of inertia.
"After substituting into the equation of motion, the expression for the natural frequency will have an additional correction term for α. When α approaches zero, the entire formula degenerates into the result of the uniform rod mentioned earlier."
Put the pen cap back on and put it back in the chalk tray.
Zheng Tiancheng stood in front of the whiteboard and pushed up the frame of his glasses.
There was silence for about five seconds.
"You've covered the general case as well."
He picked up the roster on the podium, flipped to the Lu Feng line, and ticked it next to it.
"Let's call it even."
The classroom erupted in whispers. Several male students majoring in automation in the front row turned around and stared intently at Lu Feng's retreating figure as he walked to the back.
"No way, he even mastered the generalization of non-uniform mass distribution in a flash?"
"Is this still a freshman physics class? Why do I feel like I'm listening to a graduate thesis defense?"
"Didn't you notice? He didn't look at the textbook at all, and he didn't even make any drafts."
Lu Feng walked to the last two rows and sat down in the empty seat next to Zhang Wei.
"Brother..." he said in a low voice, "I've actually become the Six-Eared Macaque."
Lu Feng pulled out a chair, sat down, and glanced at him.
"How do you resemble me?"
Zhang Wei was speechless for a couple of seconds after hearing that, then chuckled and leaned closer, lowering his voice.
"Hey kid, don't get too cocky. If you push me too far, I'll use your photo to find someone online. When they come knocking on your door, you'll be sorry."
Lu Feng picked up the water glass on the table and slowly unscrewed the cap.
"Don't bend down like that."
On the podium, Zheng Tiancheng tapped the table, a crisp sound silencing all the noise in the classroom.
"Quiet."
All three hundred people shut up.
Zheng Tiancheng placed his hands on the edge of the podium and scanned the audience.
"You all saw Lu Feng's explanation just now. A rod, a small ball, and a flexible hinge support—seems simple, right?"
He turned around and patted the lines of derivation on the whiteboard.
"But this thing involves knowledge points that cover rigid body mechanics, vibration theory, differential equations, and even the elastic modulus in mechanics of materials."
"Many students find physics boring and think it's useless."
He paused for a moment, and the corners of his mouth turned up slightly.
"But think about it, what was the basis for the design of every joint and the selection of parameters for every motor in that exoskeleton that Lu Feng put together in the competition last month?"
"It's all thanks to these things on the blackboard today."
Lu Feng inwardly thought, "You know something I, the developer, don't even know?"
Zheng Tiancheng picked up the remote control and turned to the first page of the PPT.
"Alright, enough chit-chat, let's begin the lesson. Today's topic happens to be related to the problem we just discussed, which concerns the rotation of a rigid body around a fixed axis."
He turned and wrote the chapter title on the whiteboard, chalk dust falling in a flurry.
"Turn to Chapter 4, Section 2 of your textbook and follow along."
Lu Feng opened his textbook, his gaze sweeping over the formulas and definitions he already knew by heart. The university physics curriculum was hardly a warm-up for him.
He was pondering how to make the most of this hour and a half when a crisp notification sound suddenly flashed through his mind.
The icon for the public chat channel is jumping.
Sender: Bernhard Riemann.
[Bernhard Riemann]: @Lufeng, could you come over here for a moment? I've encountered an obstacle in the derivation and need to discuss it.
Lu Feng glanced at the podium. Zheng Tiancheng was writing the definition of moment of inertia on the whiteboard with his back to the students, the chalk making a scratching sound.
Zhang Wei was lying on the table, already fast asleep.
No one in the front row turned around.
The timing was perfect.
Lu Feng held the textbook up in front of him, closed his eyes, and silently recited "enter the shared space" in his mind.
The field of vision switched instantly.
The noise of the lecture hall vanished completely. The pure white dome unfolded overhead, and that familiar, boundless space came into view.
But today's scene is different from the past.
Three people were sitting around the conference table.
Newton sat on the left, holding a half-eaten apple in one hand and drawing auxiliary lines on the table with chalk in the other.
Tesla sat on the right, his suit jacket draped over the back of the chair, his shirt sleeves rolled up to his elbows, his fingers flying across a virtual circuit diagram.
Riemann stood in front of the huge blackboard in the center, holding a piece of chalk in his left hand and his right hand in his pocket. His thin shoulders were slightly hunched, and he looked like he wanted to speak but was a little hesitant.
"Here they come." Newton looked up first, nodding to Lu Feng with his chin.
"Hurry up, Mr. Riemann has been waiting for you for ages." Tesla didn't even look up, finishing drawing the last connection on the circuit diagram with his finger.
Lu Feng walked to the conference table and pulled out a chair.
"Mr. Riemann, where is it stuck?"
Riemann turned around, his blue eyes flashing with that unique light, a mixture of shyness and focus.
"It's a functional equation about the Zeta function."
He raised his hand and pointed to a spot on the blackboard.
"I have verified the idea you proposed last time, which uses Dirichlet features to transform commutative number theory problems into problems of noncommutative operator algebras. The logic is completely self-consistent."
His voice gradually stabilized, and once he entered the realm of mathematics, his social anxiety and restraint automatically disappeared.
"But I encountered a problem when constructing the spectral triples."
He picked up the chalk and wrote an operator expression on the blackboard.
"The kernel space dimension of this Dirac operator D differs from the zero-order of the Zeta function I expected by a constant offset."
Newton put down the apple, wiped the juice off his fingers, stood up, and walked to the blackboard.
"I took a look, and this offset is related to the boundary conditions of the Hilbert space you defined."
He took another piece of chalk and added a line below Riemann's formula.
"If we replace L²(R) with L²(R/Z), that is, define the operator on the quotient space, the boundary condition becomes periodic, and this constant offset should be eliminated."
Riemann stared at the line of formula that Newton had added and rubbed his fingers together.
"Periodic..."
He turned to look at Lu Feng, his expression questioning.
Clearly, the three of them had developed a tacit understanding during this period of working together. Riemann was responsible for proposing the mathematical framework, Newton provided intuitive suggestions for correction from the perspectives of mechanics and geometry, and Lu Feng was ultimately responsible for judging whether the overall direction was feasible.
As for Tesla, although he wasn't particularly fond of pure mathematics, his occasional analogies from the perspective of electromagnetism often opened up unexpected avenues of thought.
Lu Feng walked to the blackboard and stared at the two lines of formulas for more than ten seconds.
"Sir Newton was on the right track, but the quotient space L²(R/Z) will introduce new symmetries, and the spectral triples need to be modified accordingly."
He picked up the chalk and wrote down the revised plan in the blank space next to him.
"I suggest introducing a cutoff function to control the divergence in the high-frequency part while preserving the periodic boundary conditions."
After writing down the three lines of formula, he stepped back half a step so that Riemann could see the whole picture.
Riemann leaned closer, his eyes scanning the lines of formulas back and forth three times.
A faint blush rose on her thin face—the color of excitement.
"The introduction of the truncation function...can indeed solve both the divergence and offset problems at the same time."
He turned around, grabbed the chalk, and quickly began to verify and deduce on the other side of the blackboard. The range of his wrist rotation increased, and chalk dust fell down in a flurry.
Tesla leaned back in his chair, crossed his legs, and stared at the increasingly dense formulas on the blackboard, muttering something under his breath.
"The three of you math guys together are more of a headache than my bunch of superconducting coils."
Newton glanced back at him.
"Your pile of coils almost blew up the lab last week. Who's more of a headache?"
"That was just a minor accident during energy release!" Tesla sat up straight, looking unconvinced.
Choosing the order of the truncation function is crucial. If it's too high, the accuracy will be insufficient; if it's too low, the computational cost will explode.
Riemann's writing speed suddenly slowed down. He stopped in front of a certain integral sign, tilted his head and thought for a few seconds, then started writing again, changing the way he wrote.
Lu Feng looked at the transformed integral and his lips twitched slightly.
Riemann used an extremely ingenious substitution technique to transform the infinite series that originally required numerical approximation into a closed form that could be analytically summed.
Only Riemann himself could have come up with such a thing.
Lu Feng memorized this technique and planned to write it down on a draft paper as soon as he got back.
The true value of summoning top talents lies not in having them do your work, but in drawing inspiration from geniuses through face-to-face interactions.
After writing the last equal sign, Riemann put down the chalk and took two steps back.
On the entire blackboard, a complete scheme for constructing spectral triples was clearly formed.
All four people stared at the blackboard at the same time.
"Nuclear space dimension... and zero-point order..." Riemann's voice was so soft it was almost inaudible, his gaze sliding over the last line of the equation word by word.
"They've reached an agreement."
Newton picked up the half apple again and took a big bite.
Tesla whistled.