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[Isaac Newton]: Everyone, why is there always a significant discrepancy between the speed of sound I calculate based on Boyle's Law and the results I actually measure in the gallery of the Royal Society? [Galileo Galilei]: @Isaac Newton, what are your initial conditions? Have you considered the air's humidity, temperature, and even wind direction? If the error isn't large, could it be due to the precision of your instruments? [Isaac Newton]: No, the value I calculated is 979 ft/s, but the measured value is 1142 ft/s. That's a full 16% difference! This absolutely cannot be explained away as mere 'error.' It's as if God has hidden some variable within the air... Jiangcheng Seventh Middle School, Senior Year, Class (2). Li Dong sat in the back of the classroom, looking at the group chat messages on his phone and shaking his head helplessly. 'These guys are way too into their roles...' He stuffed his phone under a textbook and looked again at his math test, on which he had only scored an 87. The test was out of 150 points, with 90 being a passing grade. Once again, he had failed to cross the passing threshold. A glorious defeat—my ass! The phone under his textbook vibrated twice. It was a WeChat group he had joined a month ago called the "Cyan Dragon Study Group." Back when he had just started his senior year, Li Dong had resolved to change his ways, feeling he couldn't keep slacking off. To get into a decent university, he had searched all over the internet for study groups, hoping to find a few academic aces who could guide him and let him experience the atmosphere of striving for Qingbei. Instead, he had stumbled into this group by mistake. The group only had a dozen or so members, but their IDs were more impressive than the last, and their avatars more vintage than the next. Besides the [Isaac Newton] and [Galileo Galilei] who had just spoken, the member list also included names like [Gauss], [Faraday], and even an [Einstein] who had been lurking for what felt like an eternity. They were all the legendary figures from the black-and-white photos hanging in history books. This wasn't a study group at all; it was clearly a large-scale rehabilitation center for people with eighth-grade syndrome. He had originally thought the group would discuss things like predicting trends in past exam questions. But what did he get instead? They didn't spend all day discussing college entrance exam math problems. Instead, it was all wave-particle duality of light, the derivation of the mass-energy equivalence equation, the 3n+1 conjecture, and the like. Li Dong recognized every word individually, but when strung together, they were complete gibberish to him. 'A bunch of posers.' Li Dong was already in a bad mood today, and watching this group of people act out their roles so seriously only irritated him more. Newton was here asking about the speed of sound. What was next? Was that Faraday guy going to put on a show and touch a live socket with his bare hands? Just as he was about to leave the group, his eyes scanned over Newton's message again. 'Calculated value 979, measured 1142...' Even though Li Dong was a slacker, he was still familiar with those two names. Newton was the guy who sold apples with Jobs. And Galileo, well, he was the guy who dropped things from a tall tower. He'd learned about them in his textbooks. 'If you're all going to role-play, then I'll play along.' Li Dong switched out of WeChat and opened "Douzhi AI." He typed into the input box: "Why was there an error in Newton's calculation for the speed of sound? Why is the actual measured value higher than the calculated value?" Just two seconds later, a large block of text popped up. Li Dong glanced at it. It was filled with words he didn't understand at all, like "thermodynamics" and "adiabatic compression," but he couldn't be bothered to care. He just copied and pasted it. [Senior Year Grind]: @Isaac Newton, you might have gotten one thing wrong. The propagation of sound in air is an adiabatic process, not an isothermal one. So, you need to include the adiabatic index in your calculation, or there will definitely be a discrepancy. As soon as the message was sent, the group suddenly fell silent. Galileo, who had been discussing with Newton whether wind speed was affecting the measurement, also went quiet. One second, two seconds, ten seconds... Li Dong felt a strange sense of unease. 'What's going on? Did the AI get it wrong?' Just as Li Dong was about to retract the message and pretend nothing had happened, that Newton guy finally spoke up. [Isaac Newton]: An adiabatic process? Do you mean to say, sir, that no heat is exchanged during this process? [Isaac Newton]: How is that possible? Air is a fluid. Vibrations must be accompanied by compression and expansion. How could there be no heat conduction? Could you please elaborate, sir? What is this "adiabatic index"? Li Dong looked at the screen and raised an eyebrow. 'Oh, so he's really getting into it, huh?' He switched back to Douzhi AI and typed: "Explain the adiabatic index in detail and its application in calculating the speed of sound." This time, however, the normally responsive AI lagged and then displayed a conspicuous red exclamation mark. [Network connection timed out. Please try again.] "Damn it!" Li Dong cursed under his breath and quickly tried again several times. This time, there was no error message, but the answer that appeared was full of complex calculus formulas and a jumble of Greek letters that looked like gibberish, things like gamma = C_p / C_v, and partial differential equations. Li Dong tried a few more times, asking the AI for a simple explanation, but it started spouting nonsense, jumping from quantum mechanics to advanced theories in fluid dynamics. You have to remember, this was early 2022, a time when AIs frequently hallucinated. 'This artificial idiot!' Li Dong started to get anxious. Meanwhile, in the group chat, Newton also seemed to be getting anxious. [Isaac Newton]: @Senior Year Grind, Sir? Are you still there? If you could elaborate, I would be most grateful! Li Dong had no interest in such verbal thanks, but the problem was, he was only halfway through his act. He couldn't just back down now, could he? Li Dong gritted his teeth, his mind racing. He tried his best to extract anything he could understand from the AI's answer. Since he couldn't explain the complex principle, his only option was... to act profound! [Senior Year Grind]: The mechanical velocity of sound propagation is far greater than the molecular velocity of heat transfer. After sending that, he felt it wasn't quite enough. To cover up his own uncertainty, he added another line. [Senior Year Grind]: Figure the rest out yourself. One must not become lazy in their studies. After sending that message, Li Dong felt like a true educator. The group fell silent once again. Just as Li Dong was waiting for a response, he felt the light above him suddenly dim. Li Dong stiffly raised his head and saw his math teacher, Old Yang, his face etched with disappointment. Old Yang's voice wasn't loud, but the surrounding students could still hear him. "You're on your phone day in and day out. You should reflect on why your math score is so terrible." Old Yang shook his head and walked back to the teacher's desk, his hands clasped behind his back. A few suppressed snickers came from the students around him. Li Dong's face flushed bright red. The sense of superiority he'd felt from posturing in the group chat vanished in an instant. Jiangcheng Seventh Middle School was, to be honest, a very average school. The students' grades here were generally not very good. The college acceptance rate was frankly embarrassing; last year, only a little over 100 seniors met the minimum score for an undergraduate program, and over 70 of them were art students. Here, the teachers had only one requirement for their students: just don't disturb others. That was why Old Yang turned a blind eye to students bringing their phones to class. After all, a student quietly reading a novel was much easier to manage than one who talked during class. Li Dong watched Old Yang's retreating back, feeling a pang of guilt. The truth was, Li Dong studied quite hard, often staying up late to grind through practice problems. But some things really just came down to talent. He was the type who studied hard, but his grades remained stubbornly mediocre. If he were at a top-tier high school, he might be able to get into an ordinary Tier 1 university by giving it his all. But here at Seventh Middle School, his ceiling was probably an ordinary Tier 2 university, and even that would require him to work himself to death. It was a matter of educational resources, and a matter of fate. 'Whatever, I'm not going to think about this anymore.' Li Dong sighed, ready to put his phone away and take a good look at his test corrections. Just then, the phone in his palm vibrated twice more. He glanced at it subconsciously. [Isaac Newton]: @Senior Year Grind, Sir, are you saying that the essence of heat conduction is the motion of molecules? And not caloric fluid? Li Dong read the line and thought the guy was just way too deep into his character, still rambling on about "caloric fluid" at a time like this. 'I can't be bothered with you. Whatever, think what you want.' He decided to ignore the group and focus on his studies. Just as he was about to lock the screen, [Isaac Newton]: Your idea is very novel. Although it subverts my previous understanding, my intuition tells me you are correct. I will verify it. Thank you for providing this line of thought. Immediately after, a red packet suddenly appeared on the screen. [Isaac Newton has sent you a direct red packet] A red packet? The instant the red packet appeared, Li Dong's finger had already tapped on it. However, what he received wasn't a few yuan and jiao, but... [You have received Isaac Newton's thanks.] [Item Acquired: Concentration +1] [Description: This is a token of gratitude from a titan of science.] [When he thought, the world stood still. He was once so focused that he threw his pocket watch into boiling water instead of an egg.] [Now you will experience this same Concentration, powerful enough to pierce through to the truth.] [Duration: One hour (can be activated at any time)] Li Dong froze. Before he could even react, a blue option box appeared out of thin air in front of him: [Use Now: Yes/No]. 'For real?' His finger lightly tapped "Yes." A countdown timer immediately appeared before his eyes... 59:59 59:58, 59:57, 59:56... Li Dong swallowed, looking back at the "Cyan Dragon Study Group" in disbelief. [Isaac Newton]: I hope to receive your guidance again in the future. A jolt of electricity shot up from the base of his spine to the top of his skull. This... Could it be that this group wasn't for role-playing? Could it be that those people weren't just playing scientists, but were actual scientists? So, a moment ago... did he really just lecture Newton, telling him "one must not become lazy in their studies"? RRRRRING. The class bell rang. Old Yang stood at the podium, frowning at the test papers in his hand. "Our class did very poorly on this month's exam!" His voice was tinged with exhaustion. "The highest score in our class was only a 109! I honestly can't believe that not a single person managed to break 110!" Most of the students below lowered their heads in shame. "Especially the final bonus question, which involved derivatives and proving inequalities. Out of fifty students in the class, not a single person got it right!" Old Yang sighed, then waved his hand in resignation. "Alright, take out your papers. Let's start with the first multiple-choice question." Given set A = {x | x² - 2x - 3 Normally, when Li Dong saw a problem like this, combining sets and function domains, his brain would just short-circuit. His logical reasoning had always been weak, making these kinds of questions his worst nightmare. But things were different now. He had Concentration +1. The moment he saw the question, the world around him seemed to freeze. All background noise vanished. All he could hear was Old Yang's voice, as if it were in slow motion. "This question tests your understanding of set operations and the domain of logarithmic functions…" As soon as he heard this, long-forgotten knowledge points in his mind flew toward him like iron filings drawn to a magnet. He could even clearly recall that this topic was on page 12 of the Compulsory 1 textbook from the first semester of his first year. He had even accidentally left a ballpoint pen mark on the bottom-left corner of that page. He also remembered a similar variation on page 24 of the *Five-Year Gaokao, Three-Year Simulation* workbook he'd done last month. He had gotten it wrong back then because he forgot that 'a' could be inclusive. All the knowledge points arranged themselves in his mind. The process wasn't fast, but he genuinely understood the problem now! x²−2x−3 Set B is x > a. Since A ⊆ B, the interval (−1, 3) must fall completely within (a, +∞) on the number line. Therefore, a ≤ −1. While Old Yang was still at the blackboard drawing a number line to explain, Li Dong had already moved on to the next question. It was a question about graphical transformations of trigonometric functions. Li Dong had no idea how to solve this one. The knowledge points in his memory weren't enough to tackle it. Normally, he would have gotten frustrated and skipped it, but not now. Because he could quickly pinpoint the exact, crucial piece of knowledge he was missing. He wasn't sure what "symmetrical about the origin" meant for the analytical expression of a sine function. 'Does it become an odd function, −sin(x)? Or does the phase simply become kπ?' He quickly jotted it down in his error correction notebook. Li Dong had never experienced a feeling like this before. Even for problems he couldn't solve, he could find a direction for his efforts. 'Is this how top students see the world?' Before he knew it, the bell to end class rang. "Alright, that's all for this class." Old Yang never dragged out his lessons, which was one of the things his students liked most about him. But Li Dong was wailing internally. 'Don't go!' For the first time ever, he hated the sound of the bell. He hadn't had enough. If only Old Yang would teach for another ten minutes... no, even five minutes would be great! He had just started to get a handle on an analytical geometry problem about deriving the eccentricity of an ellipse, but he hadn't fully grasped it yet. He really wanted to rush up and stop Old Yang. 'Teacher, please, just give us a little more!' But reason stopped him. If he dared to do that, he would be instantly ostracized by his classmates. So, Li Dong just glanced at the countdown timer in the upper-right corner. Fifteen minutes left! 'Can't waste it!' He frantically started rummaging around for the blind spots he had marked in his correction notebook during class. "Found it! Elective 2-2, page 34!" Li Dong exclaimed in a low, excited voice. Normally, his mind would wander after just a glance at such a tedious mathematical derivation. But now, every symbol seemed to be dancing for him, and every line of the formula showcased the beauty of logic. 'I have to figure this out! I have to master this topic right now!' Just as he was completely engrossed in working through the formula, a large, chubby hand patted his shoulder. "Dongzi! Stop pretending. Come on, I've got something cool to show you, a movie I just downloaded…" Li Dong whipped his head around. A chubby-faced guy was holding up a phone, smiling slyly. "Liu Liang!" "Go watch it by yourself! I need to study!" The air fell silent for two seconds. Liu Liang stared at Li Dong as if he were an alien. "No way, Dongzi. You're done for. You've caught the study bug!" Li Dong ignored his teasing. 13:10 'Time is ticking away. Every second of this Concentration is priceless!' "Don't bother me, I'm deriving a formula." Li Dong once again immersed himself in the world of mathematics. Seeing that he was actually studying, Liu Liang didn't pester him further. Besides, this wasn't the first time Li Dong had claimed he was going to study; he'd revert to his old self in three days, tops. The surrounding noise was blocked out once more. Li Dong seized the last ten-plus minutes. Facing one knowledge point after another, he took them down one by one, scoring a triple kill. The geometric meaning of a derivative, the chain rule for composite functions, the method for identifying extreme points—all mastered! At that moment, the blue countdown timer finally hit zero. The math formulas that had seemed so friendly and lovely just a moment ago suddenly became hideous. "It's… over already?" He looked at the sunlight outside the window, feeling as if a lifetime had passed. The efficiency of that short hour of studying was higher than his past week… no, his past month combined! A never-before-seen light glinted in Li Dong's eyes. 'If I could maintain this state of Concentration… forget just a regular Tier 1 university, I'd even have a shot at Qingbei!' Unfortunately, it was a one-time thing. However… He subconsciously pulled out his phone and looked at the WeChat group named "Cyan Dragon Study Group." This was his only chance to change his fate! The following English class was excruciating for Li Dong. Li Dong's foundation in English was actually much better than his math; he could usually score around 110. But after experiencing that truth-piercing Concentration, his current learning efficiency made him feel like he was wasting his life. He would memorize vocabulary only to forget it, then memorize it again. He could understand the grammar, but he'd still get the questions wrong. This way of studying made him desperately miss the red packet sent by that guy named "Isaac Newton." He finally managed to endure until school let out in the afternoon. There were two hours until the evening self-study session, time for the day students to go home for dinner. Li Dong was a boarding student, so he didn't need to go home. He hastily ate some rice in the cafeteria and returned to the classroom to ponder a serious question: how could he swindle… oh, no, get another red packet from those legendary scientists? He even tried playing red packet games with the group members. But the chat group prompted him: [This activity has been detected as unrelated to "academic discussion." Please adopt a proper attitude toward learning.] Just as he was staring blankly at the screen, feeling at a complete loss, his phone suddenly vibrated. A new message popped up. Li Dong quickly tapped it open. [Isaac Newton]: Following the line of reasoning you suggested, Your Excellency, I just conducted an experiment in my laboratory. I found a discarded bronze cannon barrel, bored into it forcefully with a dull drill bit, and immersed the entire apparatus in water. If heat were a substance, then the amount of bronze shavings produced would be finite, and the heat released should also be finite. But! Guess what happened, Your Excellency? Li Dong could feel Newton's excitement. [Isaac Newton]: The water boiled! As long as I keep drilling, the water keeps boiling! Heat is generated ceaselessly! This proves that heat is not some kind of fluid substance at all, but a form of motion! The vigorous motion of molecules! Thank you for your guidance, Your Excellency. The fog that has puzzled me for years has finally lifted today! Reading this series of messages, the corner of Li Dong's mouth twitched. 'Isn't this the experiment that the Earl of Lennford or Joule did?' 'Newton, are you stealing the thunder from your successors?' However, the instant Newton sent that last message, lines of semi-transparent text appeared above his phone screen: [System Announcement: Inspired by you, group member "Isaac Newton" has developed the embryonic form of the "kinetic theory of heat" 150 years ahead of schedule.] [The technology tree of Parallel Universe #1666 is deviating…] [Congratulations. As the "mentor" who triggered this butterfly effect, your Group Leader authority has been unlocked.] [Attribute Panel opened.] Before Li Dong could react, a transparent panel appeared before his eyes: Host: Li Dong Identity: Cyan Dragon Study Group Leader (Probationary) [Core Attributes] Concentration: 0 (The average level for a normal person. The slightest disturbance will break your focus.) Logic: 0 (Your cerebral convolutions might be a bit smooth. A slightly roundabout problem can easily throw you off.) Memory: 0.1 (Your only praiseworthy attribute. You can probably remember the name of the prettiest girl in the class next door, but that's about it.) [Special Reward] For altering the course of history, you have received a feedback reward: Concentration +0.1 Li Dong was completely stunned by words like "parallel universe," "tech tree deviation," and "butterfly effect." He never imagined that just by casually showing off, he'd actually caused a parallel universe's tech tree to deviate. 'This feeling... it's like I'm God, casually plucking a string and making the whole world tremble.' Li Dong swallowed and shifted his gaze to his attribute panel. [Concentration: 0.1] 'Wait, what the hell is 0.1?' Li Dong wore a constipated expression. Attributes with decimals? How was he supposed to work with that? Suddenly, a flash of insight struck him. 'Wait!' 'The effect of that red packet Newton just sent was [Concentration +1].' 'If that red packet represented Newton's Concentration, then…' 'Newton is 1, and I'm 0.1…' Li Dong started chuckling foolishly. 'That's Newton we're talking about! The legend who casually invented Calculus just to calculate planetary orbits!' 'Even if I only have one-tenth of his… here at Jiangcheng Seventh Middle School, wouldn't I just dominate?' Still excited, Li Dong turned his attention back to the group chat interface. 'Um... I already kicked open the door to thermodynamics for you. Isn't there some other show of appreciation?' Li Dong stared at the screen, waiting for a long time. The group was silent. Forget a red packet; there wasn't even a sticker. 'This Newton… he's not one of those scumbags who uses you and then tosses you aside, is he?' Just as Li Dong was about to proactively ask for a red packet, someone in the group finally spoke. [James Joule]: @Isaac Newton, Sir! Your experiment is absolutely astounding! I followed your line of thinking, using a paddle wheel to stir water in a bucket and measuring the change in water temperature. The results perfectly verified that heat is the motion of fine particles! [James Joule]: In this process, mechanical work was converted into heat! It's simply a work of God! By the way, a chemist here, a Mr. Dalton, seems to have mentioned a concept called the "atom." I believe that's what you meant by molecule, correct? [James Joule]: Thank you so much, Sir Newton! If it weren't for you, I don't know how much longer I would have wandered, lost in the erroneous "caloric theory"! Looking at these lines of text, Li Dong was taken aback for a moment. 'Joule?' 'He's another legend—a man who, like Newton, has a unit of measurement named after him.' Newton's reply came quickly. [Isaac Newton]: @James Joule, no, you are thanking the wrong person. I was merely guided by another. [Isaac Newton]: The one who truly discovered all this is @Cramming for Exams. He is the one who showed me the correct path. You should be thanking him. 'Look at that! Just look at that!' 'That's the magnanimity of a true master! Unlike certain advisors who, for the sake of... ahem…' Since these great minds wanted to thank him, Li Dong certainly wasn't going to be modest. 'No need to be so formal. Since we're all so familiar with each other, how about sending a red packet to show your appreciation?' [System Notification: This behavior has been detected as unrelated to "academic discussion." Please adopt a proper attitude toward learning.] 'Damn it!' Li Dong fumed helplessly, but he quickly calmed down. 'Asking for a red packet directly didn't work, so I'll have to try another way.' 'If I can't get a material reward, I'll just have to fleece them for some knowledge!' 'This group is filled with the most brilliant minds in human history. If I could get them to give me some pointers on my studies…' With this thought, Li Dong immediately took action. [Cramming for Exams]: It was nothing, really, not worth mentioning. However… I've run into a small problem recently. [Cramming for Exams]: I have a nephew who is about to take a very important exam, but he's a bit slow and has always struggled with math. I was just trying to explain a problem to him, and after a long time, it still wasn't clicking. [Cramming for Exams]: I was wondering if any of you have some good study methods that could help my poor, slow nephew? Li Dong's persona as a master couldn't possibly be ignorant of high school math, so he would ask on behalf of his "nephew"! The trick worked like a charm. Newton replied quickly. [Isaac Newton]: Since he is your nephew, his aptitude cannot be too poor. Why don't you post the problem for us to see? Li Dong was overjoyed. 'Getting Newton to be my tutor? Can any of those cram schools even compare?' Li Dong quickly flipped open his math test paper and found the final, killer problem that had stumped the entire class. [Given the function f(x) = e^x - ax - 1 (where a is a constant). If f(x) ≥ 0 holds true for any x ≥ 0, find the range of values for the real number a.] Li Dong replaced the "e" in the problem with "the base of the natural logarithm" and swapped the term "derivative," which Newton might not understand, for "fluxions," a concept from Newton's era that he would comprehend. Then, he sent it. [Cramming for Exams]: This is the problem. How does one determine the bounds of the constant in this fluxion? Less than two seconds after the message was sent… [Isaac Newton]: The answer is a ≤ 1. Li Dong waited a bit. He was still expecting Newton's derivation process. A minute passed, but Newton said nothing more. Li Dong grew a little anxious and continued to ask. [Cramming for Exams]: Um… could you be a little more detailed? My nephew is a bit slow; he won't understand just by looking at the answer. Is there a specific derivation process? [Isaac Newton]: ??? [Isaac Newton]: Process? Isn't it self-evident? What process is needed? Li Dong suddenly realized he'd made a mistake. He was asking Newton! Who was Newton? He was the monster among geniuses who, in his twenties, went back to his rural home to escape a plague and, out of sheer boredom, casually invented Calculus, discovered universal gravitation, and developed spectrum analysis! This was like asking Bolt to teach you how to run. Bolt would just say, "You hear the gunshot, and then WHOOSH, you just dash to the finish line, right?" A mere mortal could never learn that way! Just as Li Dong thought his "fleecing" operation was about to end in failure, the man named Joule appeared again. [James Joule]: Ahem… Um, Sir Newton, you may be overestimating the thinking speed of an ordinary person. [James Joule]: @Cramming for Exams, I can deeply sympathize with the problem your nephew is facing. I am of dull aptitude myself, so I understand the pain of your brain just not getting it. Li Dong's eyes lit up. 'That's right! Joule!' 'Joule came from a family of brewers. He hadn't received much formal higher education; he taught himself mathematics to solve physics problems.' 'This kind of self-taught master must have a study method that works for him!' So Li Dong hurriedly typed in the group. [Cramming for Exams]: Mr. Joule! You're too modest! I was wondering if you had any insights you could share? [James Joule]: If not for your insights, I wouldn't have been able to so quickly determine that heat is the motion of molecules. Since your nephew is having trouble with his studies, I will share my own learning method. [James Joule]: Although these clumsy methods are not worth mentioning in front of Sir Newton, for someone with a weak foundation, they might help build a solid base. Then he sent a document to the group. Li Dong immediately opened it, and the contents of the document appeared in his mind. The first point was Breakdown and Mastery. This meant breaking down concepts into the smallest possible units. Master one unit at a time: memorize definitions, derive formulas, and solve ten practice problems of the same type with perfect accuracy before moving on to the next concept. The second point was Review and Quantify Errors. Generally, people make mistakes for three reasons: they forgot the formula, they miscalculated, or they had no idea how to approach it. Therefore, if you get the same type of problem wrong twice, you must stop and relearn that entire unit from the beginning, which brings you back to the first point. The third point was Connect and Transfer Methods. The science subjects are all interconnected. While studying, you should often think about whether a method can be applied to other subjects. For example, finding the maximum or minimum value in math is the same process used in physics kinematics. The conservation principles in chemistry are the same as the conservation of energy in physics. Once you open up your mind, you'll naturally find clues to solving those difficult problems you couldn't do before. In truth, this method wasn't complicated. It wasn't that the average person couldn't think of it, but very few could actually follow through. It was like a multiple-choice question. If hard work isn't guaranteed to pay off, would you still persevere without hesitation? Most people would probably give up halfway. But if someone told you that as long as you follow their method, you are guaranteed to succeed, far more people would be willing to grit their teeth and persevere. Now, with Joule's endorsement, Li Dong had made up his mind. He would follow this method step by step. With this method, plus the attribute boosts he could get at any time… Li Dong felt like he was about to take off. Just as Li Dong had finished thanking Joule and said he would have his nephew try it… The bell for evening self-study rang. The classroom door was pushed open, and Old Yang walked in, carrying the stack of test papers he hadn't finished going over. "Everyone, quiet down!" "Take out your test papers. We're picking up where we left off this afternoon!" "And Li Dong, stop hiding your phone under your book. You think I can't see it?" Li Dong quickly stuffed his phone into his pocket. The whole class erupted in laughter. At the front of the class, the chalk in Old Yang's hand tapped against the blackboard. TAP, TAP. "Problem 18, solid geometry. This was a freebie! How many times have I gone over this? Establish a three-dimensional Cartesian coordinate system! Find the normal vector! Why can't you all remember? Huh? On a simple question like this, over a dozen of you still didn't get any points?" He was lecturing with great enthusiasm, but the eyes of at least half the students below were glazed over. Only a few students in the front rows were still taking notes. As for the students in the back rows... Old Yang's gaze fell on Li Dong's seat. Old Yang had always had a pretty good impression of Li Dong. The kid wasn't the sharpest, the type for whom it was hard to get things to 'click,' no matter how you taught him. But his saving grace was his diligence. But today, Li Dong was acting exceptionally strange. Since the start of class, the kid had been doing God knows what, constantly scribbling all over his test paper. You might think he was correcting his mistakes, but Old Yang was only on problem 18, and Li Dong was already working on the final bonus question. 'Has he just completely given up?' Old Yang sighed to himself. In an environment like Seventh Middle School, once a student gives up on themself, there's nothing a teacher can do to pull them back. Old Yang shook his head and went back to explaining the test questions. However, what Old Yang didn't know was that the Li Dong he saw as having given up on himself... ...was, at that very moment, frantically berating himself thanks to his Concentration +0.1. 'You idiot...' Li Dong stared at the steps he'd taken to solve the problem, wishing he could go back in time and slap himself twice. 'The need for monotonicity analysis was so obvious. Why did I take the logarithm of both sides? Was I just trying to make things harder for myself?' It felt like a Challenger-tier player looking back at their Bronze-league gameplay—it was nothing but mistakes. He still couldn't see the answer at a glance like those academic aces, but he could clearly identify his mistakes and see the correct path forward. While Old Yang was going over the test, Li Dong had already reviewed all the problems he'd gotten wrong at the beginning of the exam. The thrill of solving the problems was so intense he couldn't stop. 'This feeling... It's not as good as that freak Newton's Concentration +1, but for a failure like me, it's more than enough!' Li Dong gloated internally and turned his gaze to the final bonus question on the test. [Given the function f(x) = eˣ − ax − 1 (where a is a constant). If f(x) ≥ 0 for all x ≥ 0, find the range of values for the real number a.] Newton had already provided the answer to this question: a ≤ 1. But he hadn't shown the derivation. In the past, Li Dong definitely wouldn't have been able to derive the answer on his own. But now, riding this wave of intense focus, he suddenly remembered the "Deconstruction + Basic Looping" method from the study guide Joule had shared. 'Deconstruct the problem... Holds true for all x... which means the minimum value must be greater than or equal to 0...' 'Find the minimum value... take the derivative... f′(x) = eˣ − a...' In less than five minutes, Li Dong was staring at the final derived result on his scratch paper, a ≤ 1. He was completely stunned. 'I... solved it? Just like that?' He patted his cheeks in disbelief. This test might have been made by the school and wasn't especially difficult, but this was still a bonus question. 'I solved it just like that?' 'Was it just easier because I was working backward from the answer? Or is this +0.1 Concentration really this powerful?' Li Dong felt terrifyingly capable. 'Deconstruction + Basic Looping...' Li Dong muttered the phrase to himself and began rummaging through his school bag. He'd always considered "dihedral angle" problems in solid geometry his weak spot. Since Joule said to break problems down into their smallest components, he'd start by practicing how to find the "normal vector." 'Book Two... Where did Book Two go...' He was so excited that his movements were a little too rough as he searched. The noise was particularly jarring in the quiet classroom. At the front of the room, Old Yang finally lost his patience. He had just asked if anyone had solved the bonus question, but not a single student had volunteered to answer. And then there was Li Dong, making all that noise and causing a scene. "Li Dong!" The furious shout made the entire class jump. Everyone's head snapped toward Li Dong in the back row. Li Dong, who had his head buried in his bag looking for a book, instinctively looked up with a bewildered expression. "Huh? Here!" "Li Dong, if you feel you've already completely mastered this problem and don't need my lecture, then come up here and show everyone how it's done." "If you haven't solved it, then stop messing with your bag and pay attention!" Old Yang pointed to the blackboard behind him. He was just trying to get Li Dong to pay attention; he didn't actually expect him to come to the board and solve the problem. The surrounding students all ducked their heads, afraid Old Yang would turn his fury on them next. Liu Liang, in the next seat, nudged Li Dong with his elbow and whispered. "Dongzi, you're toast. Old Yang's making an example out of you." But thanks to his enhanced Concentration, Li Dong's thought process had become incredibly... linear. His brain was still contemplating a better way to apply Joule's study method. His interpretation of Old Yang's tirade went something like this: Information received: The teacher is calling me. Directive analyzed: Go to the blackboard and solve the problem. Operation executed: Okay, I'll go solve it. As for Old Yang's true intentions and the difficulty of the question... all of that was filtered out by the +0.1 Concentration. "Oh, okay." Li Dong agreed, then stood up and started walking to the front of the class. He walked up to the blackboard as if in a daze. Seeing that he had actually come up, Old Yang was momentarily stunned. He then turned to address the class in a grave tone. "Class, I know this question is difficult. But it's been a while now, and not one of you has even tried to think it through. You're all just waiting for me to give you the answer..." He was still speaking when he noticed the students looking as if they'd seen a ghost. He was just about to turn and see what was happening. But then he saw Li Dong walk past him, coming down from the blackboard. Old Yang was dumbfounded. 'What on earth is with Li Dong today?' he thought. 'He seems completely out of it. Did he just come up here to immediately go back down?' Just as he was about to give Li Dong a proper scolding, he heard a student in the front row exclaim. "Oh, so that's how you do it!" "'That's how you do what'?" Startled, Old Yang instinctively followed the student's gaze to the blackboard behind him. [If a ≤ 1, then f'(x) = e^x - a ≥ 1 - a ≥ 0. The function is monotonically increasing, and the minimum value f(0) = 0, which satisfies the condition.] [If a > 1, the local minimum is f(ln a) = a - a ln a - 1. Since this value is always less than 0 when a > 1, it does not satisfy the condition.] [Final Conclusion: a ≤ 1] Old Yang's eyes widened as he stared at the solution on the blackboard. This... How is this possible? Had it even been a full minute between Li Dong walking up to the board and walking back down? After his initial shock, Old Yang quickly regained his composure, but his brow furrowed even more deeply. He checked the work from top to bottom. It was all correct. But Li Dong had skipped many steps. On an actual exam, he would've definitely lost points for that. But for someone who understood the problem, those steps were trivial; they would fill in the gaps mentally. Li Dong's derivation, therefore, looked more like a set of guiding notes than a full solution. This kind of abbreviated solution might be plausible coming from an academic ace, but from Li Dong—a student who regularly failed math—it was utterly unbelievable. Therefore, Old Yang felt no sense of pride. Instead, he was even more disappointed. 'No wonder the kid was on his phone all afternoon,' he thought. 'He must have found the original question online and memorized the answer!' Old Yang was bitterly disappointed, frustrated that his student wasn't living up to his potential. 'So what if he failed this one monthly exam? Does he really need to resort to this to save face? He's only fooling himself!' "Fine. Well written," Old Yang said, nodding expressionlessly at Li Dong, who had returned to his seat. He didn't intend to put Li Dong on the spot in front of the whole class. But the other students knew Li Dong's usual standard. There was no way he could have solved that problem so quickly. Whispers began to spread among some of the students. "He must have looked up the answer online." "Definitely. I saw him on his phone just a minute ago." Only one person, a girl in the front row, was sizing up Li Dong with a look of shocked suspicion. Her name was Misha. She was the academic representative for their class and had scored a 109 on this very test. She hadn't been able to solve this problem, so she had secretly looked it up on her phone. The standard online solution used the parameter separation method, which was a very complicated process. But the method Li Dong had written on the board... ...was completely different from the online answer! 'Did he come up with that himself?' Misha chewed on her pen, a flicker of curiosity in her beautiful, fox-like eyes. Just then, Old Yang, after a moment's hesitation at the front of the room, called out to Li Dong again. "Li Dong, come back up here for a second." Li Dong stood up, looking confused. "Teacher Yang?" "Since you have such a good grasp of this problem, it must mean you have a profound understanding of derivatives and inequalities." Old Yang picked up an eraser and, with a couple of quick swipes, cleared a space on the board. "As it happens, I have a variation of that problem right here. The difficulty is close to that of a bonus question on the actual college entrance exam." As he spoke, he wrote a new problem on the board: [Given the function f(x) = e^x - a ln(ex), if f(x) ≥ 0 holds true for all x in the interval (0, +∞), find the maximum value of a.] After he finished writing, Old Yang handed the chalk to Li Dong. He wasn't deliberately trying to make things difficult for Li Dong. It was just that this kind of vanity, once indulged, was bound to happen again. He didn't want this once-diligent student to start down the path of cheating just for a bit of ridiculous pride. He even held on to a tiny, almost impossible shred of hope. 'But what if he can actually solve it?' "Go on, Li Dong. Give it a try." Li Dong looked at the problem on the blackboard with a strange expression. He turned to look at Old Yang, a hint of confusion on his face. "Teacher Yang." "Hm? What is it? Find it too difficult?" Old Yang sighed internally. 'So he can't do it after all?' Just as he was about to give Li Dong an easy way out... "No," Li Dong said, pointing to the blackboard. "This problem is essentially the same as the last one. How about you give me a different one?" He genuinely wanted a problem he didn't know how to solve so he could master a new concept. Old Yang was left speechless. Even his good temper was starting to fray. "Then by all means, solve it and show me!" 🔥Click Here To Read On👉

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[Isaac Newton]: Everyone, why is there always a significant discrepancy between the speed of sound I calculate based on Boyle's Law and the results I actually measure in the gallery of the Royal Society?