Chapter 31: Medium and Scale

Six-thirty. The alarm did not ring. Lin Chen woke on his own.

His eyelids were heavy. His head felt stuffed with wet cotton. His breath still carried the night’s cold. He sat up. Beneath the gauze, the crack in the sole of his foot throbbed. The pain was clear. Not sharp. But constant. Like a fine thread tied to the ends of his nerves. He felt for the canvas bag by the bed. Ledger. Pencil. He crossed out yesterday’s plan and wrote: Day 11. 06:30. Objective: find the journal. Funds: 1.56. Meal tickets: 0.32. No bus. Walk.

He washed his face with cold water. A thin crust of frost rimmed the metal basin. The towel was coarse. It scraped across his cheeks and took the sleep with it. He put on his Liberation shoes. The edges of the soles had already been flattened down. He kept the split in his foot away from the pressure point, leaned his weight forward, pushed open the door. The corridor floor was terrazzo, worn smooth and glossy along the edges. Morning light slanted in from the window at the far end and fell across the duty roster on the wall. He walked close to the wall, avoiding the pooled water between the tiles. In his mind he arranged the schedule. Building Three to the washroom. Fifty meters. Walking. Two minutes. Washing up. Five minutes. Back to the dorm. Get the lunch tin. To the cafeteria. Ten minutes. Six-fifty. Classroom. Morning study.

Wind swept over the cinder track, lifting scraps of ash. His fingers froze stiff. The joints turned dry and sluggish. He tucked his hands into his sleeves and rubbed them alternately. He could not stop. If he stopped, his body heat would fall fast. In his head he did the accounts. Balance: 1.56. Meal tickets for four days. Sixty cents a day. Four days, 2.40. That left 0.32. 0.32. Not enough for a new pencil. Not enough for a bottle of mercurochrome. He could only save it. For emergencies. He slipped a hand into his pocket and touched the half candle. One and a half centimeters left. Burning time: about fifteen minutes. He took it out and set it in his palm, weighed it lightly. Light. But enough. Fifteen minutes. Enough for one final big problem. Enough for one pass of verification. Enough to check the symbols once.

Seven o’clock. The warning bell for morning study rang.

The flow of people in the corridor began to turn back. Footsteps grew heavier. Voices dropped. Lin Chen swung the canvas bag onto his back, pushed open the door, and walked into Class 3, First Year.

More than thirty students were already seated. The fluorescent tubes gave off a faint hum. The air smelled of old books and sweat. He went to the back row by the window and sat down. He put the canvas bag into the desk compartment, one hand resting on it, opened his physics workbook to Problem Ten, and reviewed the solution from last night. The logic was clear. The steps complete. He picked up his pencil and wrote in the blank space: Core of the final problem: critical state. Maximum static friction. Simultaneous equations.

Eight o’clock. The class bell rang. The iron striker hit the brass bell. The sound was dull, echoing.

Old Li, the physics teacher, walked in with a stack of test papers in his hand. Chalk dust clung to his cuffs. He set the papers on the lectern and clapped his hands.

“Quiet.” His voice was not loud. The room fell silent at once.

“Today we’re covering critical-state problems.” Old Li turned and drew an incline, a pulley, a light rope on the blackboard. Chalk scraped against slate with a harsh sound. “The key is to find the invariant. Force analysis is the skeleton. Mathematics is the flesh. This problem was adapted from a provincial competition. The original is in issue four, 1998, of the teaching reference. If you get the chance later, go look it up. It helps with the way of thinking.”

Lin Chen’s pencil tip stopped. Issue four, 1998. The clue was confirmed. Not rumor. He lowered his head and looked at his notebook. He broke the teacher’s boardwork into three columns: given conditions, hidden conditions, target of the solution. He underlined with pencils of different colors. Blue for what was given. Red for what was implicit. Black for the target. Color to separate. Structure to layer logic. Not memory. Structure.

A boy in the front row turned around and lowered his voice. “Old Li brought up the teaching reference again. He loves pulling problems from there. That incline-friction problem you worked on last night—you got the direction right. But he may change the type. He’ll switch static friction to kinetic friction. Then add a spring.”

Lin Chen nodded and said nothing. He put half an eraser into his pencil case beside the half he already had. Two erasers. Different shapes. Same hardness. Enough. He opened the workbook to the spring model, drew the force diagram. Hooke’s law. F = kx. Equilibrium position. Maximum compression. He set up the equations. Checked them. Symbols. Units. No mistakes. He copied the steps into his notebook of wrong answers and wrote beside them: Critical point: velocity zero. Acceleration maximal. Elastic force balanced against the component of gravity.

Ten o’clock. The break bell rang.

The crowd poured out of the classroom. Lin Chen ran against the flow, toward the school gate. Eight hundred meters. Eight minutes. He adjusted his breathing, lowered his center of gravity, avoided the standing water. At the gate there was the guard booth, the iron bars. He showed his student card. The guard waved him through. County Xinhua Bookstore, on Cross Street. A red-brick building. A poster for the Xinhua Dictionary pasted inside the glass display window. He pushed open the door. The wind chime rang. Heat mingled with the smell of old paper. Behind the counter, an elderly clerk in reading glasses sat reading the newspaper. Lin Chen went straight to the teaching aids section. The shelves were tall. Dust lay thick. He stood on tiptoe and ran his fingers across the spines. Secondary School Physics Teaching Reference. Arranged by year. 1997. 1998. He pulled one free. The cover had yellowed. He opened to the table of contents. Issue Four. The contents page was creased. He scanned quickly. Third article: “A Teaching Discussion of Critical Conditions in Inclined Plane Pulley Systems.” Author: Li Jianguo. Old Li himself. His heartbeat quickened. But his hands stayed steady. He turned to the article. Diagrams. Formulas. Derivation. It overlapped with the calculations he had done last night, but it was more systematic. He noted the key pages. Fourteen to seventeen. He could not buy it. He could not afford it. He could only read. Standing by the shelf, he quickly copied down the core formulas and the way the auxiliary lines were drawn. Pencil scratching on scrap paper, a dry rustle. The clerk looked up at him once and said nothing. When he finished, Lin Chen closed the journal and put it back in place. Lined up square. Edge flush. Then he turned and left.

He ran back to the classroom. The bell rang just as he arrived. He sat down, pressed his breathing back under control, opened the scrap paper, and broke down the copied method. Compared with his own. The difference was this: he had used isolation; the reference used the whole-system method plus virtual displacement. The whole-system method was faster. But it required spatial imagination. He closed his eyes and built the model in his head. Pulley. Light rope. Inclined plane. Changing angle. Triangle of force vectors. Rotation. Superposition. It clicked. He opened his eyes and added to the notebook of wrong answers: Whole-system method first. Virtual work as support. Critical point: rope tension equals zero. The handwriting was neat, not hurried.

The afternoon classes—chemistry, mathematics, study hall—cut time into pieces and spliced it back together. Hunger burned in his stomach. He drank two mouthfuls of free soup and pressed it down. Blood had seeped through the gauze on his foot and stained the edge red. He did not change it. Changing the dressing cost money. It cost time. He adjusted the way he sat, shifted his weight onto his left foot, held the right one slightly off the ground, rocking it faintly to ease the pressure. The boy in the front row turned around. “You look pale. You okay?” Lin Chen shook his head. “Low blood sugar. I’ll be fine in a bit.” The boy handed him half a compressed biscuit. “Brought it from home. Eat something.” Lin Chen took it and thanked him. He did not eat it. He put it into the canvas bag. Tomorrow morning, with hot water, it would get him through till noon.

Evening study. Eighteen-thirty. The classroom was full. Fluorescent lights. Humming. Lin Chen finished his homework and checked the time. Twenty-one hundred. Thirty minutes until lights-out. He packed up and counted. Half candle. One and a half centimeters left. Stiff cardboard. Matches. Pencil. Eraser. Ruler. Into the bag. Zipper shut. Twenty-one-thirty. Lights out. Corridor dark. Footsteps. Sounds of washing. Lin Chen waited. Counted to one hundred. The noise thinned. He pushed open the door and walked close to the wall. Stairwell. Between the fourth and fifth floors. Strong wind. Damp air. He crouched down, unfolded the cardboard as a windbreak, struck a match, lit the candle. The flame steadied. He opened the past exam paper. Timed session. Forty-five minutes. Only the final problems. First: conveyor belt. Second: composite field. Third: incline and pulley. Whole-system method. Set up equations. Solve. Mass ratio. Check. Symbols. Units. Logic. No mistakes. He looked at his watch. Forty-one minutes. Four left. Review. Blow out the flame. Pack up. His fingers were numb with cold. The joints stiff and dry. He stood. His knees cracked. He walked back to the fourth floor, pushed open the door. The dormitory was quiet. Even breathing all around.

He sat down, took off his shoes, unwound the gauze. The edges of the crack had gone white. The fluid had dried. A scab had formed. He applied mercurochrome. A sharp sting. He held his breath. Rewrapped it. Lay down. Closed his eyes. Arranged the schedule. Tomorrow. Morning study. Breakfast. Class. Noon rest. Evening study. Back to the dorm. Wash up. Sleep. One step, one imprint.

He felt for the ledger, opened it, moved the pencil. Day 11. 22:15. Stairwell calculations. Progress: 3 final physics problems completed. Whole-system method mastered. Time used: 41 minutes. Status: on target. Gap: funds 1.56. Meal tickets 0.32. Tomorrow: monthly exam.

The pencil tip paused. He closed the ledger. His fingers tightened. The page edges curled. He pushed it down to the bottom of the bag and held it there. In the corridor, footsteps. A flashlight beam swept across the crack of the door and stopped. “Sleep early. Monthly exam tomorrow. Don’t be late.” The voice was low. “Got it,” the boy in the lower bunk answered. Lin Chen said nothing. He rested his hands on his knees and slowly flexed them. The pain in his foot had gone dull and numb. His body felt hollowed out. But he did not sleep. Outside the window, the clouds were breaking. Moonlight cold. Puddles reflecting light. Wind rising.

He reached into his pocket and touched the notice. Warm. Curled. He unfolded it and read it once. Reporting in. The time had passed. The rules remained. One step, one imprint. No disorder. He folded it, put it away, tightened his fingers. The edge of the cloth bag pressed into his palm. He closed his eyes. His breathing steadied. In his head he arranged the schedule. Tomorrow. Six-thirty. Morning study. Seven. Breakfast. Eight. Monthly exam. Twelve. Noon rest. Eighteen-thirty. Evening study. Twenty-one-thirty. Back to the dorm. Wash up. Sleep. One step, one imprint.

The wind outside slipped through the gaps and gave a low whine. Far off came a faint roll of thunder, muffled and heavy, like something massive crossing through the clouds. Rain was coming. The temperature would drop. The monthly exam papers would be handed out tomorrow. If the ink met water, it would blur. He slipped his hand into the inner pocket against his body and felt the spare pencil there. The lead had been sharpened to a fine point, wrapped in oil paper against the damp. He took it out and placed it beside the pillow. His fingertips ran over the barrel. The wood was rough. But solid. Tomorrow. Eight o’clock. Examination room. Seats assigned by student number. He was in the second-to-last row, by the window. Windy there. He would need to press the canvas bag against the corner of the desk to block the draft.

He closed his eyes. His breathing steadied. In his mind he kept arranging the time. One step, one imprint. But in the wind, besides the smell of earth, there was also the faintest trace of disinfectant drifting from the direction of the town clinic. He opened his eyes. His gaze fell on the ledger by the bed. The paper pale in the dark. He reached out, found the pencil, and drew one very faint line across a blank page.

Day 11. End. Progress: caught up by three weeks. Blind spot: redox medium. Funds: 1.56. Status: alive.

The pencil tip paused. He set it down. Closed his eyes.

Tomorrow. Eight o’clock. Monthly exam.