Chapter 27: Ten Minutes Between Classes

Eight o'clock sharp. The math teacher stepped into the classroom on the heels of the bell.

The chalk tapped out crisp sounds on the blackboard. Trigonometric functions. Sine. Cosine. Tangent. No greetings from the teacher—he went straight to drawing the unit circle. Coordinate axes. Radius. Angle. Projection. He spoke half a beat slower than the physics teacher, but the chain of logic bit down tight. The pace of teaching at the county high school waited for no one; knowledge points came down like parts on a conveyor belt, delivered section by section. If you failed to catch them, they dropped to the ground.

Lin Chen opened his math textbook. Chapter Three. Trigonometric functions. He opened a blank notebook. The pencil tip touched paper. He didn't copy the definitions. First he drew a table.

sin0° = 0. sin30° = 0.5. sin45° ≈ 0.707. sin60° ≈ 0.866. sin90° = 1. cos0° = 1. cos30° ≈ 0.866. cos45° ≈ 0.707. cos60° = 0.5. cos90° = 0.

He wrote very slowly. His fingertips were stiff with cold, and the muscle in the web of his hand ached from gripping the pen. Every ten minutes, he tucked his hands into his sleeves and pressed them against his ribs for thirty seconds. Body heat returned. Then he took them back out. Kept writing. No skipped lines. No missing angles. Three decimal places. Everything aligned. Like laying a wall. The joints between the bricks had to fit perfectly.

A boy in the front row turned and glanced back. His eyes fell on the dense rows of numbers in Lin Chen's notebook. He said nothing. Turned back around. Kept listening as the teacher explained the reduction formulas.

8:45. The bell rang for class to end.

The classroom came alive in an instant. Chair legs scraped across the terrazzo floor. Someone pulled out biscuits. Someone went to the corridor to get water. Someone gathered with others to compare answers. Lin Chen didn't move. He closed the math textbook and opened his physics workbook. He flipped to problem five. Pulley systems.

He stood and walked to the side of the podium. The physics teacher was organizing his lesson plans. The lid of his thermos was unscrewed, white steam rising out.

"Teacher." Lin Chen's voice was not loud.

The teacher looked up. His gaze swept over the coarse cotton shirt, washed pale from wear. He nodded. "What is it?"

"The force on a movable pulley. How do you count the rope segments? How do you calculate the tension?" Lin Chen handed over the workbook, opened to problem five. The diagram showed a fixed pulley, a movable pulley, a hanging weight, and a rope wound around three times.

The teacher took it, glanced at it, and didn't explain the theory. He simply drew lines on the diagram with a red pen. "The exam won't test complicated force analysis. Only standard models. Look at the movable pulley. Count the rope segments directly pulling on it. Three segments. So the pulling force is one-third of the weight. Add friction and the pulley’s own weight, and the real value is a little larger. Remember the rule of thumb: odd movable, even fixed. The number of segments determines how much effort is saved. Don't derive it yourself. Too easy to get wrong."

Lin Chen stared at the path traced by the red pen. His mind raced through the comparison. Last night's blind spot. Nailed shut with three sentences. He took out his pencil and wrote in the blank space of the workbook: Force on a movable pulley. Count the rope segments. Odd movable, even fixed. F = (G + G movable)/n. Exams don't twist it around.

"Got it?" the teacher asked.

"Got it," Lin Chen said.

"Go back and do the problems. Don't get stuck grinding on oddball questions. The monthly exam only tests basic models." The teacher screwed the lid back on the thermos and turned to leave the classroom.

Lin Chen stood there a moment longer. He put away the workbook, returned to his seat, sat down, and opened the ledger.

Day 7. 08:55. Physics blind spot: pulley-system tension. Cleared. Countermeasure: apply the standard model. Do not derive it myself. Progress: two weeks behind. Remaining blind spot: trigonometric application problems.

The pencil tip paused. He closed the ledger. The joints of his fingers were stiff. He laid his hands on his knees and slowly flexed them. Inside the Liberation shoes on his feet, the newly nailed soles pressed against the cracks in his skin. It hurt. But they could bear weight.

10:00. The second class ended.

A flood of students spilled into the corridor. Lin Chen didn't go to the water room. He sat in his seat and opened his math workbook, flipping to the trigonometric application problems. Problem one. Given one side and one angle of a right triangle, find the hypotenuse. He substituted into the formula. sin30° = opposite/hypotenuse. Hypotenuse = opposite/0.5. Calculation. Units. Answer sentence. He filled an entire page.

Problem two. A slope problem. He got stuck. The problem gave a slope angle of 15°. That wasn't in the table.

He set down the pencil. No anxiety. He opened the appendix of the textbook and looked up the half-angle formula. sin15° = sin(45° - 30°). He expanded it, substituted the values, and computed. The process was long. He wrote it out step by step, skipping nothing. Like disassembling a machine. Lay out every part, then reassemble it.

10:20. Finished.

He flipped to problem three. A combined physics-and-math problem. Inclined plane angle 37°. sin37° ≈ 0.6. cos37° ≈ 0.8. He substituted directly. Orthogonal decomposition. Set up the equations. Solve. The pencil tip drew smooth arcs on the page. The logic closed cleanly. No gaps.

The boy in the front row turned around, a sheet of scratch paper in his hand. "For problem three—you used the approximate values for 37°. Is that allowed on the exam?"

"The teacher said common angles can be substituted directly," Lin Chen said.

The boy nodded. "Fine. You're making up the basics fast. But don't get greedy. Just hold on to the basic points in the monthly exam."

"Mm," Lin Chen said.

The boy turned back around and kept working.

Lin Chen lowered his head, opened the ledger, and moved the pencil.

Day 7. 10:20. Trigonometric application problems, 1–3 complete. Blind spots: none. Progress: caught up one week. Funds: balance 1.96. Meal tickets remaining: 7 days.

The pencil tip paused. He crossed out Meal tickets remaining: 7 days and wrote beside it: Tomorrow's lunch: 0.15 (vegetables). Rice: 0.05. Target balance: 1.76.

He closed the ledger. The joints of his fingers were stiff. He laid his hands on his knees and slowly flexed them. The pain in the soles of his feet had already gone numb. His body felt hollowed out. But he didn't sit down. He put his hands on his knees and slowly worked them.

12:00 sharp. The dismissal bell rang.

The stream of students in the hallway surged toward the cafeteria. Footsteps crowded together. Voices stayed low. Lin Chen slung his canvas bag over his back, pushed open the door, and walked into the classroom of Senior Year One, Class Three.

The room was already more than half empty. The fluorescent tubes gave off a faint buzz. The air smelled of old books and sweat. He went to the window seat in the last row and sat down. He placed the canvas bag into the desk compartment and kept a hand on it.

12:15. Cafeteria.

A single-story red-brick building. A long line at the entrance. Above the service window hung wooden signs: Vegetables: 0.15. Meat: 0.40. Rice: 0.05. Soup: free.

Lin Chen stood at the end of the line. In front of him was a boy in a synthetic shirt, holding an aluminum lunch box. Behind him was a girl with a ponytail, head down reciting vocabulary words. He lowered his head and looked at his own canvas shoes. The uppers were split. The soles worn flat. The edge of the newly nailed-on sole had already started to curl up.

12:20. His turn.

"One serving of vegetables. One serving of rice." He handed over the meal ticket.

The cafeteria worker glanced at him. The ladle trembled once. A spoonful of cabbage, very little broth, went into the aluminum lunch box. Then a scoop of rice, packed down tight. Handed over. "Next."

Lin Chen took it. Thanked him. Turned away and walked to a long bench in the corner of the cafeteria. Sat down. Opened the lunch box. Steam rose out, carrying the earthy smell of cabbage. He picked up his chopsticks and ate very slowly. Chewed thoroughly. His stomach finally had something solid in it.

He didn't drink the soup. Soup filled the belly but didn't keep hunger away. He divided the rice in the lunch box into three portions. Ate one portion. Saved two. Wrapped them in oiled paper and placed them in his canvas bag. To eat before morning reading tomorrow. To eat at noon.

The numbers in the ledger had to fit perfectly.

12:40. He finished eating. Tidied the lunch box. Went to the sink. Rinsed it with cold water. Dried it. Put it back in the canvas bag. His movements were slow. But perfectly steady.

He went back to the classroom, sat down, opened the ledger, and moved the pencil.

Day 7. 12:40. Lunch expense: 0.20. Balance: 1.76. Meal tickets remaining: 6 days. Status: on target.

The pencil tip paused. He closed the ledger. The joints of his fingers were stiff. He laid his hands on his knees and slowly flexed them. Inside the Liberation shoes on his feet, the newly nailed soles pressed against the cracks in his skin. It hurt. But they could bear weight.

14:00. First afternoon period. Physics.

The teacher came up to the podium with his lesson plan under one arm. No self-introduction. He turned around and drew a pulley system on the blackboard at once. Chalk dust sifted down, settling on the old lesson plan at the edge of the podium.

"Force analysis. Pulley systems. Look at the board." He spoke fast, without pause.

Lin Chen opened a blank notebook. The pencil tip touched paper. He drew along with him. Fixed pulley. Movable pulley. Rope. Weight. Arrows. Labels. His wrist was steady. In his head he was comparing at top speed. Last night's blind spot, and the teacher's standard steps. They overlapped. Verified. Internalized.

14:30. The teacher began calling on students.

"Fifth row. The one in the gray sweater. Come up and draw the force diagram."

The boy stood and went to the blackboard. Chalk moved across it. His lines were messy. He labeled the rope segments wrong. The teacher said nothing, only tapped the board. "Movable pulley counted wrong. Pulling force calculated wrong. Draw it again."

The boy flushed red. He erased it. Drew again. Still wrong.

The teacher sighed. "Odd movable, even fixed. Count the ropes pulling on the movable pulley. Who'll come up and correct it?"

The classroom was very quiet. No one raised a hand.

Lin Chen put down his pencil and stood up. "Teacher. I'll try."

The teacher glanced at him, his eyes coming to rest on the coarse cotton shirt washed pale with wear. He nodded. "Come up."

Lin Chen walked to the board and picked up the chalk. No hesitation. First he drew the pulley system. Marked the weight. Drew the rope. Counted the segments. Three. Marked the direction of the pulling force. Wrote the formula. F = (G + G movable)/3. Set up the equation. Solved it.

Chalk dust sifted down and settled at the edge of the podium. His movements were slow. But perfectly steady. Straight lines. Clear labels. Closed logic.

He set down the chalk, turned around, and returned to his seat.

The teacher stared at the blackboard for three seconds, then nodded. "The steps are right. In the exam, write the given conditions, the units, and the answer sentence. Don't omit them."

"Understood," Lin Chen said.

The boy in the front row turned and looked at him, said nothing, and nudged his reference book half an inch in Lin Chen's direction.

Lin Chen lowered his head, opened the ledger, and moved the pencil.

Day 7. 14:35. Pulley-system logic fully understood. Blind spots cleared to zero. Progress: caught up one and a half weeks. Countermeasure: do integrated problems in evening study. Don't touch the final challenge question.

The pencil tip paused. He closed the ledger. The joints of his fingers were stiff. He laid his hands on his knees and slowly flexed them. The pain in the soles of his feet had already gone numb. His body felt hollowed out. But he didn't sit down. He put his hands on his knees and slowly worked them.

18:00. The preparatory bell for evening self-study rang.

The flow of people in the hallways began turning back. Footsteps grew heavier. Voices dropped lower. Lin Chen slung his canvas bag over his back, pushed open the door, and walked into the classroom of Senior Year One, Class Three.

More than thirty students were already seated. The fluorescent tubes gave off a faint buzz. The air smelled of old books and sweat. He went to the window seat in the last row and sat down. He placed the canvas bag into the desk compartment and kept a hand on it.

18:30. Evening self-study officially began.

The classroom was very quiet. Only the sound of pages turning and pencil tips scratching across paper. The boy in the front row had already spread open his workbook, with red-and-blue pencils and a ruler beside it. Lin Chen's gaze passed over it. Did not linger. Only remembered. The county kids had problem banks in their hands. The town kids had only the standardized county exam papers. The gap was not one of intelligence. It was one of training volume.

He opened the physics workbook. Integrated problems one through five.

Problem one. Basic model. He wrote. Problem two. Inclined plane plus pulley. He wrote. Problem three. Determining the direction of friction. He got stuck. The object was moving upward. The frictional force pointed downward. He marked it wrong.

He put down the pencil and took a deep breath. No anxiety. He opened the blank notebook and marked an X beside problem three, then wrote: Blind spot: direction of friction. Need to reinforce judgment by relative motion.

He stood and walked to the front row. Tapped on the boy's desk.

The boy looked up. "What is it?"

"Borrow your reference book. Half an hour. I'll return it." Lin Chen's voice was not loud.

The boy froze for a second, looked at his coarse cotton shirt washed pale from wear, and said nothing. He pushed over High School Physics Synchronized Guidance. "Don't dog-ear it. Don't write in it."

"Understood." Lin Chen took it. The book was thick, hard-covered, with smooth paper. He flipped to the table of contents, found Friction, and turned to the section. Read the definition. Read how to judge direction. Read the worked examples.

He went back to his seat and spread the book open. Compared it to the workbook. Problem three. Direction of relative motion. Friction acts opposite to the direction of relative motion. He understood. Picked up the pencil. Wrote the steps. Drew the diagram. Labeled it. Calculated.

19:00. Problem three finished.

He turned to problem four. Integrated force analysis. He wrote. Problem five. The challenge problem. He skipped it. Didn't force it. In the notebook he wrote: Challenge problem. Give it up. Hold the basic points.

19:30. He closed the workbook and pushed the reference book back to the front row.

"Thanks," he said.

The boy took it, flipped through it. No folded corners. No writing. He nodded. "You're making up the basics fast. But don't get greedy. Just hold on to the basic points in the monthly exam."

"Mm," Lin Chen said.

The boy turned back around and continued doing problems.

Lin Chen opened the ledger and moved the pencil.

Day 7. 19:30. Evening study progress: physics problems 1–4 complete. Problem 5 skipped. Blind spot: direction of friction. Patched. Countermeasure: memorize formulas in morning reading tomorrow. Ask the teacher during break. Don't drag it into the night. Funds: balance 1.76. Meal tickets remaining: 6 days.

The pencil tip paused. He closed the ledger. The joints of his fingers were stiff. He laid his hands on his knees and slowly flexed them. Inside the Liberation shoes on his feet, the newly nailed soles pressed against the cracks in his skin. It hurt. But they could bear weight.

21:00. Midway through evening study. Footsteps came from the corridor. A teacher on night rounds. Leather shoes on terrazzo, an even rhythm. Stopped at the door. Looked in. Said nothing. Turned and left.

Lin Chen's pencil did not stop. He finished his chemistry homework, opened the Chinese textbook, and moved on to classical prose. Encouragement of Learning. Recite. Write from memory. Misspelled characters. Correct them.

21:20. The bell rang for class to end.

The classroom filled with the sound of chairs shifting. Someone stretched. Someone packed a schoolbag. Someone complained in a low voice that there was too much homework. Lin Chen did not move. He put away the workbook and slipped it into the canvas bag. Pencil. Eraser. Ruler. Arranged in order.

He stood up, went to the back door of the classroom, picked up the bucket, went downstairs, to the water room, fetched water, wiped the blackboard, swept the podium, and took out the trash. His movements were slow. But perfectly steady.

21:40. Back to the dormitory.

Building Three, Room 402. The door was ajar. He pushed it open. Eight metal bunk beds. Upper and lower bunks. Someone was already asleep in the bed by the window, breathing evenly. He went to the upper bunk by the door. The bed board was pieced together from planks, dust gathered in the cracks. He set down the canvas bag, took out a washbasin, fetched water, and soaked his feet.

The cold water stabbed like ice. The cracks in the soles of his feet turned white from soaking, tissue fluid seeping out. He didn't touch them. Only soaked them. Three minutes. Dried them. Changed into clean gauze. Applied mercurochrome. The smell was sharp. He held his breath and spread it evenly. Wrapped them.

His movements were slow. But perfectly steady.

He lay down and closed his eyes. In his head he arranged the schedule. Tomorrow, 6:30. Morning reading. 7:00. Breakfast. 8:00. Class. One step, one footprint.

The wind outside had died. Moonlight shone across the cinder track. The chalk-written lane markers glimmered faintly in the dark.

The pencil tip paused. He set it down and closed his eyes.

Tonight. After lights-out. Problem five. The challenge problem.

He reached into the canvas bag and touched the half candle. The stiff cardboard wrapped around the wax had gone soft at the corners. He measured it once with his finger: three centimeters. Usable time: about forty minutes.

The plan had to be written plainly.

Stairwell corner between the third and fourth floors. Wait until the night-patrol footsteps pass. Light the candle with his back to the wind. Use the cardboard to block the flame. Finish the first two subquestions within forty-five minutes. If leather shoes sounded in the corridor, blow it out immediately.

He opened the ledger again and wrote very lightly:

Day 7. End. Progress: caught up one and a half weeks. Blind spots: cleared. Funds: 1.76. Status: alive.

The pencil tip paused. He drew another line under it.

Night task: challenge problem, first two subquestions. Tool: half candle. Risk: night patrol and footsteps at the stair mouth.

Footsteps came from the corridor, closer and closer. The teacher on night rounds. The beam of a flashlight swept across the crack of the door and stopped at the entrance.

"Go to sleep early. Don't be late for morning reading tomorrow." The voice was low and echoed.

"Got it," the boy in the lower bunk answered vaguely.

Lin Chen made no sound. He only pressed the ledger shut and slid the pencil under the pillow.

The footsteps receded. The flashlight beam disappeared at the far end of the hall.

He closed his eyes. In his head he arranged the route once more. Wait for the footsteps to pass. Third-floor corner. Strike the match. Forty-five minutes. First two subquestions. Extinguish at once if leather shoes sounded.

The wind outside had died. Moonlight shone across the cinder track. The chalk-written lane markers glimmered faintly in the dark.

One step, one footprint.