43: Chapter 43 Machining

For the entire rest of the day, Jiang Lin did not touch his phone again.

Sitting in front of his desk, he frantically flipped through the linear algebra textbook and Quantum Mechanics lecture notes on hand, filling those three pages of correction notes with dense text.

He used up a dozen sheets of draft paper.

He pushed and re-pushed the commutation relations of various operators on paper, and solved and re-solved the characteristic equations until he felt the blood vessels in his temples throbbing wildly, his head swelling, and the symbols in his vision beginning to double, feeling dazed before finally stopping to rub his brow hard.

Unknowingly, the time had reached past nine o'clock in the evening.

Outside the window, the city had long been lit up by neon lights, and the rapid sound of car horns came from the main road from time to time, exuding the prosperity and hustle and bustle of modern society.

Jiang Lin leaned against the back of his chair, staring blankly at the ceiling.

The abstract concepts about infinite-dimensional Hilbert spaces in his mind gradually faded away.

No matter how beautiful Quantum Mechanics was, it was still just something on paper.

Yet in the Wasteland, he had to face not only the blackboard, but also survival.

What he needed was not just formulas, but also the means to turn theory into reality.

Soon, he straightened his body, picked up his phone, clicked on that familiar chat box, and sent his second question.

This time, he did not ask about Bell's inequality, nor the many-worlds interpretation, nor the eigenvalues of angular momentum.

He typed: "Teacher Lu, I am truly sorry to disturb you again. Besides theory, I have another question related to experiments that I would like to consult you about."

"If under very low-cost, or even one might say crude conditions, one wants to do some basic Physics measurements, for example: using the phone's recording function to measure the period of a simple pendulum, using low-cost sensors bought online for dozens of yuan to record temperature and humidity changes, and using some plastic tubes and lenses to build a simple device to observe light intensity. Under such circumstances, what is the blind spot most easily ignored by self-taught learners?"

"When I was tinkering with these things myself in the past, I always habitually listed the formulas first and drew the data processing tables all pretty. But when actually hands-on making those small devices, I always felt that the sources of error were very chaotic, and the data drifted wildly. Many times I didn't even know whether the problem lay in a flaw in the measurement method itself, or simply because my device was too unstable. I'd like to hear your perspective from a professional angle."

After sending this passage, he thought about it, and incidentally attached the experimental process of measuring the gravitational acceleration g with a simple pendulum that he had done himself.

This question carried a strong Wasteland aura.

But it was also the predicament he had to face every day during those forty years.

The first day passed, and Professor Lu Zhixing did not reply.

The second day also passed, and the chat box remained quiet.

Jiang Lin did not feel anxious; the other party had no obligation to reply to him instantly.

He continued to read books, continued to derive formulas, and occasionally went out to wander the streets, feeling the hustle and bustle of mortal life.

Until late at night on the third day.

Jiang Lin had just finished taking a shower and was wiping his hair with a towel when his phone screen suddenly lit up.

A message had arrived.

This time's reply was much shorter than when they discussed Quantum Mechanics previously.

"Your question is closer to Physics experiments."

"Many people think that experiments are an appendage of theory, that you first have a pretty formula, and then take a bunch of things to verify it. In fact, that is completely wrong."

"In low-cost measurements, what self-taught learners most easily ignore is never whether the formula was written correctly, nor even how poor the sensor's precision is, but the measurement chain."

"How the sample is placed, what materials the device is fixed with, whether the relative position of the sensor can maintain absolute repetition across multiple operations, whether the surrounding environment has undergone covert changes, whether calibration with standard parts was performed before reading, whether the recording format and timestamp are seamlessly consistent... It is these trivial details seemingly unrelated to Physics principles that ultimately determine whether the string of numbers you obtain has any significance for comparison."

"Take the experiment you mentioned of measuring gravitational acceleration g with a simple pendulum; the formula is so simple that even a junior high school student knows it. But when you actually start doing it, all the troubles are outside of Physics: where exactly is the pendulum length calculated from, how to measure it accurately, whether the suspension point is stable, whether it will undergo minor displacement as it swings, whether the swing angle is strictly controlled within a small-angle range, and whether the phone lens you use for recording is mounted on the exact same three-dimensional spatial coordinates every time? Is the plane of the swing strictly perpendicular to the optical axis of the phone lens, and will the support bracket of the entire simple pendulum produce resonance and shaking when it swings?"

"If you cannot even control these, there is only one result: you think you are comparing two sets of data measured at different times, but in reality, you might be comparing two completely different experimental setups."

Looking at the last sentence, Jiang Lin thought of his days in seclusion in the Wasteland last time, and the experiments he had done.

When doing experiments, he was actually very cautious in his heart.

He also thought he had reached the absolute limit of what a self-taught learner and a survivor could achieve.

He had even felt complacent about it, feeling that he still maintained a noble and rigorous spirit in desperate straits.

But now, Professor Lu Zhixing had used just a single sentence, like a crowbar, to pry open that perfectly disguised lid, revealing the riddled and dilapidated interior.

Was he really comparing the gravity of the Wasteland and Earth?

When that nylon rope was subjected to tension, did the internal fibers truly undergo no minute elastic deformation?

After the stone swung fifty times, did that knot tied to the steel bar truly not slip even on a millimeter scale?

Just how large was the error in his so-called estimated pendulum length?

Did that hand of his holding the phone to record truly never experience slight shaking?

If the suspension point was changing, if the pendulum length was changing, if the lens was shaking...

Then what he calculated was not the gravitational acceleration of the Wasteland at all.

At this thought, a layer of cold sweat seeped out of Jiang Lin's back.

He didn't immediately deny that 9.79 in the Wasteland.

Under specific precision requirements, that number still had its survival reference value.

But this was also the first time in all his life that he truly and soberly realized: the credibility of that data built on crude conditions was as thin as a piece of window paper that would break at a single poke.

It wasn't that his formula derivation was wrong.

It wasn't that his mathematical foundation was no good.

Rather, his device and his hands were too crude.

On the screen, Professor Lu Zhixing's message popped up again, seemingly unsatisfied, as if he wanted to completely poke through this layer of window paper.

"Nowadays, many people have a misconception: whenever they talk about doing experiments, they think of buying the most expensive data acquisition cards and using the most advanced software to fit curves. But many people forget that the primary task of an experiment is a complete set of physical means to make the observed object stably appear and the measurement conditions repeatable. Without repeated positioning at the physical level and without rigid connections, no matter how pretty your data processing algorithm is, and no matter how close the fitted R-squared is to 1, you are simply using a set of flashy mathematical tools to process a bunch of pretty noise."

Jiang Lin put down the towel, walked to the desk, picked up a pen, and heavily wrote four characters on the draft paper.

[ Repeated Positioning ]

Just at this moment, Professor Lu Zhixing's last passage popped up right after.

"If you are really interested in measuring things yourself, don't rush to buy high-precision sensors on Taobao; first try to make a simple, stable support bracket."

"The requirements are not high: it can fix the phone without sagging, and can hang a pendulum line without shaking. The most crucial thing is that you can dismantle it into parts, then reassemble it back, and try your best to ensure that after every assembly, the positions of the phone and the suspension point are exactly the same as the last time."

"If you can achieve this step purely by hand, you should have a brand-new understanding of the two words 'error'."

After reading this passage, a strong urge surged in Jiang Lin's chest, and he immediately wanted to type a reply saying he had been instructed.

But he held back.

What is obtained from paper is ultimately shallow.

No matter how thorough Teacher Lu's words were and no matter how profound the analysis was, that was still someone else's experience.

Jiang Lin, who had tumbled and struggled in the Wasteland for decades, knew better than anyone that understanding a principle ten thousand times was not as profound as messing it up with one's own hands once.

Jiang Lin pulled open the drawer, took out a new draft notebook, and wrote six characters.

[ Reassembly Error Test ]

Then, he drew a table below and began listing the test items.

First, the vertical distance from the center of the phone lens to the plane of the pendulum line.

Second, the absolute length from the suspension point to the center of mass of the pendulum bob.

Third, the angle between the optical axis of the phone and the plane of the swing.

Fourth, the positions of the left and right feet of the bracket base relative to the edge of the desk.

Fifth, the maximum drift amount of the above parameters after disassembly and reassembly.

After writing the fifth item, he paused, and at the very bottom of the table, heavily added another line of words.

[ Test Purpose: Not to measure the gravitational acceleration g, but to test whether the exact same set of apparatus can return to its state from the previous second. ]

Jiang Lin stood up and began collecting materials.

Ten minutes later, a pile of objects appeared on the desk.

An old aluminum alloy phone tripod with a ball head.

A spring phone clamp forcibly dismantled from a selfie stick.

A roll of transparent fishing line with a wire diameter of 0.8 millimeters.

Several regularly shaped M8 hexagonal nuts.

A thirty-centimeter-long steel straightedge.

A two-meter-long small tape measure.

A newly printed sheet of A4 grid paper.

A vernier caliper.

With the items gathered, Jiang Lin began building his optical platform.

He spread out the tripod and placed it on the desk, with the three rubber foot pads stepping on the tabletop, fixed the phone clamp on the ball head, and tightened the screws.

Using transparent tape, he pasted that sheet of A4 grid paper flatly onto the wall, smoothing out the four corners with his hands to ensure no air bubbles swelled up.

This piece of paper would serve as the two-dimensional reference background coordinate system of the entire system.

Then, he horizontally pressed the steel straightedge under several thick reference books, with the edge of the straightedge protruding a section past the desk edge.

The fishing line hung down from the cold metal edge of the straightedge, and the lower end was tied with a dead knot around two hexagonal nuts to serve as the pendulum bob.

The setup was complete.

Jiang Lin pulled over a chair and sat down, beginning his first calibration.

He wedged his phone into the clamp and turned on the camera.

First, he slightly adjusted the ball head by hand so that the pendulum line in the screen image fell as much as possible in the center of the grid.

Next, he exited the camera and opened the phone's built-in compass and spirit level app, carefully checking the inclination angles of the phone body on the X-axis and Y-axis.

The phone's built-in spirit level could only serve as a rough reference, and the sensor itself had not been calibrated either.

But at this stage, he didn't even have a better angle-measuring tool, so he could only temporarily treat it as a somewhat unreliable ruler.

After doing all this, he picked up the vernier caliper and tape measure, and began recording the first set of parameters.

Jiang Lin closed one eye, trying his best to make his line of sight perpendicular to the scale to avoid visual parallax.

For the distance from the lens to the plane of the pendulum line, he could only roughly measure it along the desk with a tape measure, and then use the steel straightedge to correct the position of the pendulum line's projection.

Distance from lens to pendulum line plane: 36.8 centimeters.

Suspension point to pendulum bob center of mass: 50.2 centimeters.

Base left foot to desk edge: 12.4 centimeters.

Base right foot to desk edge: 11.9 centimeters.

Phone pitch angle: approximately -2.0 degrees.

The five lines of numbers falling on the draft paper looked very neat.

This system was far better than that simple pendulum he had set up back then in the Wasteland Stone House using a nylon rope and a stone.

If it were just to finish a school assignment, record a video and do a simple Physics demonstration, this set of things could be used completely, and could even fit a seemingly very pretty sine curve.

But Jiang Lin didn't even click to record video, nor did he flick those two nuts; he just quietly looked at it for a minute, then reached out his hand and dismantled it without hesitation.

The phone was pulled out of the clamp.

The three latches of the tripod were opened one by one, the aluminum alloy tubes retracted, and it folded up.

The ball head screw was loosened, and the pendulum line was untied.

The steel straightedge was pulled out from under the books.

Everything returned to zero, leaving only that sheet of grid paper on the wall acting as the background.

The measurement platform that had looked passable just moments before turned back into a pile of scattered parts.

Jiang Lin glanced at the wall clock and waited for a full three minutes.

These three minutes were enough to make muscle memory blurry, enough for the force of the wrist twisting the ball head to be forgotten, and enough for the three-dimensional spatial afterimage of the previous apparatus to dissipate from his mind.

"Begin reassembly."

He softly said to himself, then relying on memory, grabbed the tripod again.

He pulled open the leg tubes and flipped the latches.

He tried to place the three foot pads of the tripod onto those faint dust marks on the desk.

The straightedge was pressed back under the books, the line hung down again, and the phone was clamped back on.

Trying his best to follow the feel of the first time, he tightened every joint.

Assembly completed, Jiang Lin once again picked up the caliper and tape measure for the second recording.

While measuring, he filled in the numbers in the table, his face as gloomy as water.

Distance from lens to pendulum line plane: 37.6 centimeters.

Suspension point to the center of mass of the pendulum: 50.0 cm.

Left foot of the base to the edge of the table: 12.1 cm.

Right foot of the base to the edge of the table: 12.3 cm.

Mobile phone pitch angle: about -3.5 degrees.

Jiang Lin looked at this second freshly baked batch of numbers.

The distance differed by 0.8 cm, the pendulum length differed by 0.2 cm, the base position was off by a few millimeters, and most absurdly, the phone's pitch angle changed directly by 1.5 degrees.

He didn't frown, nor was he angry, because this result was within his expectations.

Rubber foot pads are elastic; pressing hard versus placing gently results in different contact areas on the table surface.

The table edge is curved, and if the angle at which the tape measure leans against it is slightly crooked, the reading will differ by a few millimeters.

He put down his pen and disassembled it once again.

This was the third reassembly.

This time he deliberately controlled the force of placing the tripod, and the tape measure was attached tighter.

When the data came out, the lens distance miraculously returned to 36.9 cm, with a difference of only 1 mm.

However, he did not feel relieved.

Because when he turned on the phone camera, he could tell with the naked eye that the angle between the plane of the pendulum string and the lens in the frame was off.

The lines on the grid paper turned into slightly tilted slanting lines on the screen.

He leaned closer to the setup, took the flashlight of his phone, and illuminated each joint for a long time.

The light beam swept across the pan-tilt head, swept across the phone clamp, and finally landed on the edge of the steel ruler extending beyond the table surface.

He found that the problem was not with the lens, but with the suspension point.

That 0.8 mm fishing line was not hanging down from a fixed, enclosed hole.

It was simply wrapped around the edge of the steel ruler, barely maintained by the friction of the ruler and the gravity of the nut itself.

The edge of the steel ruler looked flat, but from the microscopic perspective of Physics, when a line rests on a right-angle edge, every time it is placed back, the tangent point of the line on this tiny right angle will undergo random slippage.

It might have slipped just a little bit, less than a millimeter.

But even this tiny amount was already a non-negligible change for a pendulum length of 50 cm.

Its plane of oscillation was thus forcibly twisted by a tiny angle.

Find the problem, then solve the problem.

Fourth reassembly.

Jiang Lin tried to stick an extremely narrow positioning marker on the edge of the steel ruler using a small piece of black electrical tape.

Then he carefully wedged the fishing line at the edge of the tape.

The effect was indeed a bit better, and the randomness problem of left-right slippage was alleviated.

However, a new problem followed.

The tape had thickness, and its material was also soft.

When the gravity of the two iron nuts pulled the fishing line to swing, the fishing line would act like a knife, cutting bit by bit into the soft edge of the tape under the tiny tangential force generated by each swing.

The suspension point was still moving.

And it was also slowly sinking in an imperceptible way.

It was fundamentally not a geometrically fixed and immovable point.

Fifth reassembly.

Jiang Lin replaced the suspension point with a small iron clip with a strong spring, clamped it to the edge of the ruler, and let the line pass through the ring of the iron clip's metal handle.

Metal to metal.

Is it hard enough this time?

Wrong.

The problem turned back to the elastic rebound of the opening part of the spring clip.

If clamped too tightly, the nylon fishing line was directly flattened by the metal, changing the wire diameter and altering the internal stress distribution.

If clamped slightly looser to protect the line, after the heavy object swung a few times, the smooth nylon line would slide invisibly to the naked eye inside the slick iron inner wall of the clip.

Sixth reassembly.

Jiang Lin abandoned the suspension point and turned his attention back to fixing the camera angle.

He found that even if he precisely clamped the phone near the exact same scale line of the pan-tilt head every time, as long as he finally tightened the knob used for locking, the angle would definitely change.

This is a common defect of all threaded mechanisms, known in mechanics as lateral torque and thread backlash.

When you tighten a screw clockwise, the inclined plane of the thread engagement generates an irresistible lateral torsion force.

This torsion force would forcibly push the sphere inside the pan-tilt head, causing a slight displacement.

This is why, even though you hold the bubble level with your hand and adjust it, as soon as you release your hand, or as soon as the knob is tightened, the bubble immediately drifts off.

The magnitude of the rebound was not large, perhaps only a few tenths of a degree.

Yet placed in the field of view of the lens more than thirty centimeters away, this meant that the grid paper in the background had already shifted by two or three squares.

The plane of the pendulum string in the frame was no longer the same plane as the previous second.

Jiang Lin finally stopped the actions in his hands.

The table on the desktop had unknowingly been filled with a full six rows.

The data in each row was very clean.

And the error each time could definitely not be considered absurd.

If this piece of paper were handed to a student at school who was just muddling through and not very rigorous, the other party might even think the data was unbelievably good, wave their hand and say: "Almost there, it can be used, throw it into the software to run a least squares, and the R-squared will definitely look great."

Yet Jiang Lin leaned back in his chair, quietly looking at those almost there values, knowing it clearly in his heart.

"Almost there" is the biggest problem in experimental Physics.

He had witnessed firsthand how the setup he built with his own hands irreversibly turned into a completely different setup with every disassembly and reassembly.

The pendulum length of the first setup was 50.2, accompanied by the non-linear deformation of the rubber.

The pendulum length of the second setup was 50.0, accompanied by the structural distortion of the pan-tilt head under stress.

The suspension point of the third setup suffered from slippage due to friction failure.

The tape of the fourth setup produced soft creep at the level of material mechanics.

[You think you are comparing two sets of data, but in fact you might be comparing two different setups.]

Professor Lu Zhixing's words, like a grand bell, once again struck a huge echo in his mind, making his scalp tingle with numbness.

Jiang Lin lowered his head, his gaze sweeping across the parts on the table.

This pile of things had the luster of metal and the chamfers of industrial products, looking very much like the real deal.

Yet they still could not answer that most rustic Physics problem.

After taking it apart, how do you ensure that it can return to its original position seamlessly?

Jiang Lin picked up his phone and typed a reply to the private message.

"Teacher Lu, I made a simple simple-pendulum filming setup, and the result was disastrous."

"The biggest problem is not how to film with a mobile phone, nor what software to use for point extraction and analysis later, but it all crashed and burned on fixing and reassembling. After I disassembled them, it was completely impossible to restore them to the roughly identical state from ten minutes ago. Even if it's just a slight misalignment invisible to the naked eye, the field of view and suspension point change completely."

"This problem, I actually vaguely realized it when making things in the past, but I had been deceiving myself by trying to use mathematical magic like measuring multiple times and taking the average to cover it up. I never regarded it as a basic link in the measurement chain that must be tightly locked at the physical level."

The message was sent out, and Professor Lu Zhixing replied extremely fast, as if the other party wasn't sleeping at all, but holding a cup of coffee, smiling in front of the phone screen, waiting for him to hit a brick wall.

"Very good, this is the first lesson of experimental Physics."

"You have already touched the edge of that iron door. Many people study up to a PhD, spending their whole life spinning around outside the door with mathematical formulas, thinking that as long as the derivation is correct, that is Physics."

"You must remember, a good experimental sense, the awe of the real resistance of the material world, many times, grows out from the hands, not imagined out of thin air from the brain."

"If you have the chance, don't just read books, go touch real machining. Even if it's just the most basic filing flat a piece of iron, drilling a hole, tapping a thread. When you personally turn a rough lump of iron into a standard part with a dimensional accuracy of a few tenths of a millimeter, your understanding of the entire measurement system and the two words 'error' will also undergo a heaven-and-earth overturning change."

Jiang Lin looked at these lines of words on the screen and silently put down his phone.

Then, under the light of the desk lamp, he spread open his hands and looked at them carefully.

This was a pair of a youth's hands, with fair and rosy skin, distinct knuckles, and besides a thin callus on the middle finger of the right hand, there were no other marks.

But in the memories of the Wasteland, these hands were not like this.

His hands would swing an entrenching tool, turning over the red earth baked hard as stone by radiation.

Would lift heavy stones and pile up wind-blocking walls.

Would mix mud and broken grass, repairing the drafty holes in the walls.

Yet that was a pair of surviving hands struggling purely to stay alive.

Not a pair of hands capable of measuring the universe and exploring microscopic truths.

He indeed knew how to make things.

But he couldn't make anything precise and reliable.

"So, machining?"

Jiang Lin stared at his palm prints and muttered to himself.

Then the question came, what is machining?

Half an hour later.

On a video website on his computer, following various keywords, he found a video.

An internal training and teaching video from a vocational college with touching video quality, almost zero view count, and no bullet comments.

[Electromechanical major benchwork basic skills teaching: standard action demonstration of sawing, filing, drilling, and tapping]

Benchwork?

Of course he had heard of this word before.

But it was just a noun existing in the Labor Day reports of Xinwen Lianbo.

In Jiang Lin's mind, this word had always been vague, even carrying a bit of stale engine oil scent.

Like some rough craft of the last century that was extremely distant from modern Gaokao, from elegant theoretical Physics, and from college courses sitting in bright classrooms.

But after some understanding, he realized that this was not a backward craft, but one of the foundations of modern industrial precision training.

The ability to use a hand drill to make a hole unbiasedly without any power tools.

The ability to use a hacksaw to steadily saw a curved iron bar straight.

The ability to use a tap to purely manually tap an internal thread in a piece of metal that could stably engage with a bolt without obvious deviation or stripped teeth.

Jiang Lin took a deep breath, feeling the blood in his entire body rushing to the top of his head.

Clicked on that training video.

The picture was really unclear, with old-fashioned snowflake noise.

In the video, an old master craftsman wearing deep blue work clothes stood in front of a heavy green bench vise, holding a flat file in his hand.

The old master spoke in a resonant voice with a heavy accent towards the camera: "All of you remember this, filing is not asking you to take a file and blindly rub it on a lump of iron."

"Your body must stand firm, your back straight, your wrists locked, your force application even, apply force when pushing, be light on the return stroke, absolutely no dragging or hesitation, otherwise the file teeth will be ruined."

"On this platform, eyes will deceive you, and hand feel will deceive you. If you think it's flattened, that's self-deception. In the end, you have to rely on this square, measuring tools, and the light-penetration method to speak. Clamp it on, face the light and look; if the light cannot pass through, that is what's called flat."

Jiang Lin stared at the black iron block tightly clamped in the bench vise on the screen, without blinking an eye.

In the video, there were no complex partial differential equations.

No dazzling matrix derivations.

No beautiful function graphs of the Schrödinger equation.

The master held the wooden handle and front end of the file with both hands, leaning forward slightly, with his center of gravity pressed low.

"Swish—"

The file pushed across smoothly and forcefully.

Accompanied by the harsh yet rhythmic metal friction sound, fine silver-white iron filings, like snowflakes in early winter, fell down rustling from the rough metal surface, dropping onto the oil-stained workbench.

That piece of low-carbon steel material originally covered with scale underwent a transformation bit by bit under the master's hundreds of pushes and pulls of the file.

From the naturally cooled rough state, it began to become flat and smooth, revealing the dense texture inside the metal.

It was crossing macroscopic chaos, approaching bit by bit towards that perfect plane in the geometric sense.

Jiang Lin watched motionlessly like this for over an hour.

At one point, he felt that harsh friction sound was more pleasant than any music in the world.

After watching, he turned off his phone, returned to the desk, opened a new page of the draft notebook, and picked up his pen to write down.

[Fifth Wasteland Preparation Plan: Basic Metal Machining and Mechanical Resetting Ability]