29: Chapter 29 The Physics Autopsy Report

Advanced Mathematics in the morning, General Physics in the afternoon.

For the past five years, every afternoon, Jiang Lin had been tormented by mechanics, thermodynamics, and electromagnetism.

However, once Physics goes deeper, its underlying framework is entirely Mathematics.

When he hadn't thoroughly chewed through Advanced Mathematics in the past few years, looking at General Physics felt like looking through a layer of frosted glass.

When encountering differential equations, he could only half-guess and half-memorize them.

When encountering multiple integrals to calculate moment of inertia or electric flux, his calculations were stumbling and halting, and most of the time he knew what was done without knowing why.

When encountering line integrals and surface integrals, it felt even more like seeing a group of ghosts wearing white lab coats; clearly every symbol was recognized, but when linked together, only oppression remained.

Relying on the grit-it-out spirit polished during those nine years in the third Wasteland, he swallowed those Physics derivations containing calculus whole without chewing.

Swallowed it had been.

But the digestion was not good.

Many things in the past few years had merely been forcefully crammed into his brain.

Much like a person who had been starving for a long time, facing a table of dishes, regardless of whether they could be chewed thoroughly, desperately swallowing them into the stomach first.

Surviving was already not bad; how could one still care about texture, nutritional structure, or digestion and absorption?

Now, the first stage of Advanced Mathematics has completed its closed loop.

Those mathematical roadblocks that once spanned across the Physics formulas finally seemed to have reached a time when he could personally tear them down flat.

Therefore, the so-called autopsy today was not testing freshly baked unknowns.

He was going to use the calculus scalpel, which was already basically taking shape, to dissect the university Physics he had forcefully learned alive over the past five years from beginning to end.

Let's see where real meat grew and where it was just bloated fat.

Where he muddled through by memorization back then, and where he actually never truly understood from the very beginning.

Jiang Lin opened the number one hard drive and clicked on the [02 General Physics] folder.

Inside quietly lay several different versions of classical mechanics textbooks, including the domestically common "Mechanics" and the first volume of the Berkeley Physics Course.

If someone asked Jiang Lin in his senior year of high school which part of Physics he studied best,

he would definitely answer without hesitation: kinematics and Newtonian mechanics.

That was precisely the source of his confidence in scoring a full 100 marks in the Jiangcheng First Mock Exam.

Whatever uniform acceleration linear motion, whatever horizontal projectile and inclined projectile motion, whatever circular motion.

As long as given an initial velocity and a force-bearing situation, the three-dimensional sandbox in his brain could instantly run out the complete trajectory of the object.

Whatever formula applied to whatever model had long since turned into muscle memory after grinding tens of thousands of questions.

But the opening of university textbooks did not have those routine formulas summarized for solving problems.

There were only two dry lines of definitions.

[ Velocity v = dr / dt ]

[ Acceleration a = dv / dt = d ² r / dt ² ]

Jiang Lin recalled his mood when he first saw these two formulas five years ago in the Stone House of the Wasteland.

At that time, his mind was full of high school mathematical and physical thinking, and he only felt that university textbooks were putting on airs.

Isn't velocity just the displacement change divided by time?

Wouldn't using that capital triangle Δ from high school suffice? Why must it be made into the limit form of calculus, practically like translating human speech into alien language.

But Jiang Lin, who had experienced the beatings of Advanced Mathematics for five years, looked at these two formulas again today, and goosebumps instantly popped out.

A sense of transparency like eating a ginseng fruit crawled all the way up his spine.

High school Physics had always been spinning around in a greenhouse artificially and carefully pruned.

Why in high school problems did cars always undergo uniform acceleration motion?

Why in horizontal projectile motion was the gravitational acceleration forever a constant g?

Why was air resistance changing with velocity never considered?

Why were all forces so obedient, either constant or linear, or simply giving you an image to let you piece together the answer using area?

Because once acceleration changes, once force continuously changes with time, position, or velocity, that set of algebraic formulas pieced together with Δ in the hands of high school students completely crashes.

High school Physics pretended the world was linear, uniform, and composed of constants.

But the Real World never follows such rules.

A gust of wind blows past, and the wind force is changing at any time.

A car steps on the accelerator, and the engine's output power changes with the rotation speed.

Even gravity, in the process of a rocket launching into the sky, will change with height.

Facing this world undergoing nonlinear changes every single moment, that set of high school tools was like a plastic toy shovel.

And now, placed before Jiang Lin was a heavy-duty excavator.

[ Velocity v = dr / dt ]

This was the derivative he spent a massive amount of time chewing through.

The derivative is not where I am right now.

The derivative is how I am leaving the present.

No matter how complex your motion is, no matter how many bends your trajectory takes, as long as you chop time fine enough, down to that instant approaching zero, the rate of change of position is velocity, and the rate of change of velocity is acceleration.

This is the true description of Physics.

Jiang Lin turned to the next page.

Newton's Laws of Motion.

On high school textbooks, Newton's Second Law was written clearly in black and white, F = ma.

An object's acceleration is directly proportional to the net external force it receives and inversely proportional to its mass.

Jiang Lin casually wrote F = ma on the LCD erasable board, then stared at it.

Over these five years, he had re-recognized this formula countless times.

University textbooks mercilessly pierced through the window paper of high school.

The more general expression of Newton's Second Law is that the rate of change of an object's momentum with respect to time is equal to the net external force acting on the object.

Namely: F = dp / dt.

If the object's mass is constant, p = mv.

Then F = d(mv)/dt = m(dv/dt) = ma.

That F = ma worshiped as an ironclad rule by countless students in high school textbooks is essentially a simplified form under the premise of constant mass.

Jiang Lin looked at this line of derivation, and a very complex feeling suddenly arose in his heart.

High school Physics did not lie to him.

But high school Physics indeed hid a massive amount of premises.

Just like a teacher writing a bridge on the blackboard, but not telling you that underneath this bridge there are actually densely packed piers.

The bridge looks very simple.

But if one truly wants to know why it doesn't collapse, one must crawl under the bridge to look at the structure.

He subconsciously wanted to treat m in p = mv as a variable as well, directly expanding it into:

F = m(dv/dt) + v(dm/dt).

Just as the pen tip wrote halfway, Jiang Lin stopped again.

He stared at that line of formulas for a long time, then gently scraped the LCD board with his fingernail, wiping away the second half.

"Incorrect."

He said in a low voice.

Variable mass problems cannot be so lazy.

A rocket is not a simple particle whose mass changes.

The combustion gas ejected by the rocket leaves the system carrying momentum, and there is momentum exchange between the main body and the jet. If one truly wants to handle it rigorously, they must treat the rocket and the ejected combustion gas together as a system, and then calculate momentum conservation and momentum flux.

The reason why rockets are rarely touched in the high school stage is not because Physics cannot solve them, but because that is no longer simple F = ma.

What it leads to behind the scenes is variable mass systems, the Tsiolkovsky rocket equation, and engineering mechanics and propulsion theory.

Jiang Lin did not continue expanding downwards.

He had not reached that level yet.

But he already knew that he could no longer be like the past few years, rushing to apply a formula the moment he saw it, and feeling complacent upon deriving a seemingly beautiful result.

Physics is not a symbol game.

Every formula has boundaries.

Every simplification has a price.

He suddenly realized that the most dangerous part of his past few years was not not understanding formulas.

But rather trusting formulas too eagerly.

Formulas are not incantations.

Formulas are merely a contract; one must first see clearly the conditions written when it was signed.

This was the biggest difference between him and five years ago.

He from five years ago only wanted to know the answer.

He of now began to know where one cannot answer blindly.

"This is the true Physics engine."

Jiang Lin said in a low voice.

Over the next few days, Jiang Lin, like a harsh forensic pathologist, plunged headfirst into the abyss of mechanics.

With Advanced Mathematics as this sharp scalpel, the difficult points that used to choke him were now readily solved.

Work done by a variable force?

In the past, he could only calculate constant force, or calculate the trapezoid area in the F - x image.

Now he directly goes to definite integrals.

W = ∫ F(x) dx.

Even if the force changes into all sorts of patterns with position, once the integral sign covers it, it can be dissected bit by bit.

The relationship between conservative force and potential energy?

In the past, he rote-memorized that gravity doing positive work decreases potential energy, and elastic force doing positive work decreases elastic potential energy.

Now he understood that the negative gradient of potential energy is the conservative force.

F = - ∇ Ep.

A partial derivative operator bucked the underlying logic of force and energy seamlessly together.

He even used differential equations on the draft board to fluently derive the falling motion under air resistance.

This was a stubborn illness that he half-understood in the previous few years.

Assuming air resistance is proportional to velocity, f = - kv.

The equations of motion of the object are:

mg - kv = m(dv/dt).

This is a typical first-order linear ordinary differential equation.

If Advanced Mathematics wasn't learned well, seeing this equation would only leave one staring blankly.

But Jiang Lin of now skillfully separated variables and integrated both sides.

dv / (mg - kv) = dt / m.

The derivation process flowed rapidly on the LCD board without any sluggishness.

Soon, he derived the analytical expression of velocity changing with time.

v(t) = (mg / k) [1 - e ^ (-kt / m)].

When t approaches infinity, e to the negative infinity power approaches zero.

Then the terminal velocity:

vmax = mg / k.

This of course was not a universal model for all falling bodies.

Jiang Lin quickly added a sentence beside it: low speed, small scale, viscous drag approximation.

Real raindrops, gravel, and bullets, when moving at high speeds in the air, resistance is often closer to the velocity squared term.

But this did not prevent this model from becoming his first key to understanding terminal velocity.

Physics is not applying a formula to the entire world, but first judging whether this formula can be used.

"Satisfying!"

Jiang Lin leaned against the stone chair and let out a long breath.

Advanced Mathematics was no longer a bunch of abstract symbols existing to torture people; they had turned into the sharpest knife, cutting open the epidermis of physical phenomena and clearly picking out the flesh and bones inside for him to see.

Mathematics is the language.

Physics is the story.

In the past, he had always been listening to others tell stories with poor translations.

Today, he was finally able to read the original work without any obstacles.

This feeling was simply intoxicating.

Unconsciously, the dark red sun of the Wasteland had already sunk down.

The light in the Stone House was too dim to see characters clearly.

Jiang Lin, restless from extreme quietness, pushed open the wooden door and walked out.

The cold air poured into his lungs, making his feverish brain sober up a little bit.

He wrapped his military coat tighter around himself and walked to the edge of his two-hundred-square-meter farmland.

Most of the potatoes had already been harvested, and a portion of late-maturing varieties still remained in the ground.

The Soybean stalks swayed in the wind, making a fine, rustling sound.

He squatted down on the field ridge, looking at this Wasteland in the darkness before him.

In the past when he looked at the wind, it was just wind.

Looking at sand, it was just sand.

But tonight, when the wind carrying sand and dust roared past from the side of the dried-up riverbed, Jiang Lin not only heard the sound of the wind, but also saw the transfer of momentum.

The wind gave velocity to the sand.

Under the action of air resistance, the sand underwent variable acceleration motion, ultimately impacting the wall surface.

Within an extremely short time dt, the sand handed over momentum dp to the wall, generating an impact force F.

This was why the walls in the Wasteland would be weathered into that state.

Countless grains of sand, countless tiny dp / dt, over the long years, like countless invisible miniature carving knives, forcefully sliced and diced the hard concrete into a riddled mess.

The world had not changed.

The Wasteland was still that desolate, dead-silent place full of acid rain and toxins.

Jiang Lin was no longer a victim who could only passively endure the torment of the environment, and could finally use the perspective of Physics to deconstruct this world.

In the following time, Jiang Lin completely fell into this crazy autopsy and reconstruction.

After the mechanics review was completed, he killed his way toward rigid body mechanics.

This was yet another domain that locked high school students outside the door.

High school Physics only studies particles, treating all objects as a point with mass but no volume.

But in reality, objects have shapes and can rotate.

Moment of inertia, angular momentum, torque.

In the past few years, he had suffered immensely here.

Moment of inertia I is not a simple constant; it is closely related to the object's shape, mass distribution, and the position of the axis of rotation.

In the past, when he encountered problems calculating moment of inertia, he would directly flip through books to check tables, remembering that a disk is 1 / 2mR², and a sphere is 2 / 5mR².

Now?

Jiang Lin threw all the tables in the book aside.

Calculate the moment of inertia of a uniform disk?

[part:gemini-3.6-flash]

He skilfully wrote out the double integral in polar coordinates, with the integration variable going from 0 to R and the angle from 0 to 2π, integrating outward layer by layer.

Calculating the moment of inertia for a cone?

He went straight to a triple integral, expanding the volume element dV in cylindrical coordinates, executing the calculation as cleanly and decisively as chopping vegetables.

For the first time, he truly felt that those tedious multiple integration techniques in Advanced Mathematics had transformed here into his most practical abacus.

Every successful integration meant he had accurately grasped an object's mass distribution in space.

Spring of the sixth year.

A rare moderate rain fell over the Wasteland.

Acid rain pattered on the roof of the Stone House, trickling along the drainage gutter into the water pit with a rhythmic dripping sound.

Jiang Lin did not go out to work.

He sat at the stone table, tackling another major peak in General Physics.

Vibrations and waves.

In high school, simple harmonic motion was taught by hanging a spring, giving it a pull, and letting it bounce back and forth.

The formula was: x=Acos(ωt+φ).

As for how this formula came about, high school teachers usually offered a mysterious smile.

"Just memorize it, everyone. The Gaokao won't test the derivation."

Jiang Lin could derive it himself now.

A spring oscillator, restoring force F=-kx.

According to Newton's Second Law:

m(d²x/dt²)=-kx.

Rearranging it:

d²x/dt²+(k/m)x=0.

This was a classic second-order linear homogeneous differential equation with constant coefficients.

He had learned how to solve this equation in Advanced Mathematics: find the characteristic equation, solve for the complex roots, and apply Euler's Formula.

At the final step of the derivation, the cosine formula that his high school teacher had told him to memorize by rote naturally flowed from the tip of his pen.

Not only that, but he also incorporated damping.

The real Wasteland had air resistance; a spring could not oscillate forever.

After adding the damping term -γ(dx/dt), the equation became:

m(d²x/dt²)+γ(dx/dt)+kx=0.

In the past, seeing this equation would give him a massive headache.

Now, he smoothly wrote down the characteristic equation and solved it.

Depending on the damping coefficient, he clearly observed three completely different Physics scenarios.

Underdamping: complex roots. The object oscillates back and forth while its amplitude decays exponentially.

Overdamping: two distinct real roots. The object cannot even complete a single oscillation, slowly creeping back to the equilibrium position as if stuck in mud.

Critical damping: two equal real roots. The object returns to the equilibrium position at maximum speed without oscillating.

Jiang Lin stared at the mathematical plots of these three solutions and pondered for a moment.

Isn't this the exact mechanism behind car shock absorbers?

If a shock absorber is underdamped, the car will bounce up and down endlessly after hitting a bump.

If it is overdamped, the damping is too stiff and the chassis recovers too slowly, making passengers terribly uncomfortable.

Of course, real automotive suspension doesn't blindly chase mathematical critical damping.

Comfort, grip, vehicle posture, spring stiffness, and tire feedback all require compromise.

But at least at this moment, Jiang Lin saw for the first time that the real and complex roots in a mathematical equation truly translated into jolts, dizziness, and a sense of safety for people in the Real World.

Jiang Lin thought for a bit and wrote a line on his scratchpad.

[The real and complex roots in mathematical equations dictate the comfort of automobiles in the Real World.]

Another chunk of the barrier between Physics and reality shattered before him.

This rare spring rain lingered for several days before finally stopping.

Jiang Lin rubbed his sore eyes and closed the laptop.

Having just derived the equations for simple harmonic motion, the string of oscillation in his brain was still humming.

Knowledge gained from books alone remains shallow.

Physics isn't mathematics; while mathematics can be purely deduced through logic behind closed doors, Physics is an experimental science.

It must withstand the test of Real World measurement.

Jiang Lin pushed open the wooden door and walked outside the Stone House.

The Wasteland air was still dry, laced with a faint metallic scent of rust.

The dark red Wasteland stretched infinitely beneath a hazy grey sky, while several dilapidated load-bearing walls stood silently on the horizon like giant skeletons forgotten by time.

Jiang Lin bent down, picked up a dark red pebble from the ground, weighed it in his hand, and threw it hard into the distance.

The pebble traced a parabola in the air and struck the hard dirt dozens of meters away, kicking up a small puff of dust.

Jiang Lin's gaze followed that parabola to the ground.

For some reason, a very basic yet extraordinarily critical question popped into his mind regarding this world.

"What is the acceleration of this stone as it falls?"

In the Real World, any high school student knows that the standard gravitational acceleration g is approximately 9.8 m/s².

But he wasn't on Earth right now.

He was on a planet countless light-years away from Earth, or perhaps in a parallel world of a completely different dimension.

What if this planet's mass was far greater than Earth's, or its radius was entirely different?

Taking a step back, what if the Gravitational Constant G of this universe wasn't even the same value as in the Real World?

A cold sweat suddenly broke out across Jiang Lin's back.

The five hard drives he had brought with him were packed with the accumulated fruits of human Physics.

Every day, like an ascetic monk, he derived formulas inside the Stone House.

If the underlying physical laws of this Wasteland differed from Earth's, wouldn't the entire system of General Physics he was studying be nothing more than scrap paper here?

It would be like taking a manual written for Earth's chess rules to play Go on the Wasteland.

A guaranteed loss.

"I must measure it."

Jiang Lin turned and dashed back into the Stone House.

Knowledge gained from books alone remains shallow; to truly understand, one must practice.

Having studied Physics for so long, he couldn't remain stuck in armchair theorizing on scratchpads.

Rummaging through his backpack, he pulled a roll of nylon parachute cord out from the bottommost pouch.

This cord was designed for outdoor use, offering exceptional toughness and relatively low elasticity.

Next, he found a tape measure.

Under crude conditions, the method with the smallest margin of error for measuring gravitational acceleration was the simple pendulum experiment.

Grabbing an entrenching shovel, Jiang Lin ran to the ruins west of the camp and searched for nearly half an hour before finally chipping off a piece of high-density, relatively rounded metallic ore—slightly smaller than a fist—from underneath a collapsed concrete pillar.

"You'll do."

"Perfect for a pendulum bob."

Returning to the Stone House, Jiang Lin began assembling his crude Physics setup.

It was windy outside, which would cause severe air resistance interference; it was best to conduct the experiment indoors.

Fortunately, he had expanded the Stone House to fifteen square meters with a height over two meters, providing plenty of space.

He brought over stones to stand on and tied one end of the nylon parachute cord securely to the row of thick rebar acting as load-bearing roof beams.

To the other end of the cord, he fastened the ore tightly with knots.

Then, using the tape measure, he carefully measured the length.

From the suspension point on the rebar all the way to the ore's center of mass.

"98.5 centimeters... No, better round it to a nice whole number for easier calculations."

He slightly adjusted the knot and measured three times to ensure the distance L from the pivot to the center of mass was precisely controlled at around 1.00 meter.

As for the stopwatch, Jiang Lin pulled out his old phone and opened a stopwatch app.

"Phew, all set."

Jiang Lin stood by the stone table and took a deep breath.

He knew the formula for the period of a simple pendulum by heart:

T=2π√(L/g).

The period T equals 2 multiplied by pi π, multiplied by the square root of the pendulum length L divided by the gravitational acceleration g.

Working backward, as long as he measured the oscillation period T, he could calculate the gravitational acceleration of this Wasteland planet:

g=4π²L/T².

Jiang Lin gently pulled back the piece of metallic ore.

To satisfy the approximation conditions for simple harmonic motion, the displacement angle couldn't be too large; he estimated and kept the release angle within 5 degrees.

He didn't start counting at the lowest point.

While the lowest point was easy to observe, each pass through it represented only half a period.

If every pass through the lowest point were counted as a full oscillation, the calculated data would be off by a factor of two.

So he chose a clumsier yet far more reliable approach.

Timing started from the left release point.

He originally thought of timing from the highest point on the left, but quickly rejected that idea.

The highest point seemed easy to spot, but the bob moved slowest there, making visual judgment prone to hesitation.

The most reliable method was watching for the exact moment the bob crossed the lowest point moving in the same direction.

Only each pass through the lowest point from left to right counted as one full period.

"Three, two, one, release."

Drawn by gravity, the metallic ore carved a tiny arc, dropping down past the lowest point, swinging over to the right peak, and then reversing direction.

There and back.

Returning to the left.

That was one complete, full oscillation.

Jiang Lin kept his eyes fixed on the bob each time it returned to the lowest point, his concentration razor-sharp.

"Twenty-eight."

"Twenty-nine."

"Thirty."

When the bob returned to the lowest point for the 30th time, Jiang Lin decisively hit the stop button.

He glanced at the numbers on the screen:

60.25 seconds.

Divided by 30, the average period T for a single full swing was roughly 2.008 seconds.

Jiang Lin knew better than to rely on a single data set, so he didn't rush to calculate.

He stretched his stiff shoulders and pulled the bob back once again.

Repeating the exact same process, he completed five consecutive sets.

The five sets of recorded data were:

60.25 seconds.

60.18 seconds.

60.31 seconds.

60.22 seconds.

60.28 seconds.

Averaging these five sets together gave an average total time of 60.248 seconds for 30 complete oscillations.

Thus, the period for a single oscillation was:

T=2.0083 seconds.

With the data in hand, Jiang Lin set the ore on the floor, turned around, plopped back down at the stone table, and grabbed his LCD writing tablet.

He began his calculations.

L=1.00 meter.

T=2.0083 seconds.

π set as 3.14159.

g=(4×3.14159²×1.00)/(2.0083²).

g≈39.4784/4.0333.

g≈9.788 m/s².

Jiang Lin stared at this number for a long time before crossing out the trailing decimal places.

He couldn't make it look too pretty.

The tape measure lacked precision, the cord had slight stretch, the ore was not an ideal point mass, the pivot had friction, and the phone stopwatch carried human reaction error.

Under such experimental conditions, writing down a figure like 9.788 wasn't rigor.

That was false precision.

In the end, he simply noted down on his logbook:

[g≈9.79 m/s², margin of error around the 1% order of magnitude.]

This result was virtually identical to Earth's gravitational acceleration.

Looking at the numbers on the board, Jiang Lin felt a strange, tingling sensation surge up his back.

The tingle rushed right up his spine to the back of his head, causing him to shudder involuntarily.

This wave of awe felt far more profound than solving a hundred Physics problems correctly.

He stood up and walked outside once more.

He looked at the red dirt everywhere, at the distant greyish-black ruins, at the dried-up riverbed.

The scenery here was completely different from Earth.

There was no sign of life, a sulfurous reek lingered in the air, and the sky remained perpetually dark red.

Yet at this moment, Jiang Lin felt this desolate Wasteland become immensely familiar.

"At least on this scale, gravity closely resembles Earth's."

He spoke very slowly.

He no longer rushed to extrapolate a single statement to infinity as he had in earlier years.

A crude simple pendulum experiment could only prove that local gravitational acceleration was close to Earth's.

It could not prove that all physical constants in this world were identical to Earth's.

Nor could it prove that the fundamental laws of the entire universe possessed zero discrepancies.

Yet this was already important enough.

An apple here would drop with an acceleration of approximately 9.8 meters per second squared.

This meant that the overwhelming majority of classical mechanics knowledge stored on his hard drives remained applicable here.

It meant that no matter how desolate or mysterious the Wasteland was, it was not a fantasy realm ruled arbitrarily by magic or supernatural forces.

It was a world that could be measured.

As long as it could be measured, it could be compared.

As long as it could be compared, it could be modeled.

As long as it could be modeled, it could be understood.

This was the first true Physics experiment Jiang Lin had performed on the Wasteland.

Simple and unrefined.

Yet for the first time, he truly understood why university-level General Physics placed such immense emphasis on experimentation and measurement.

Physics wasn't conjured out of thin air from formulas on a blackboard.

It grew out of measuring the Real World.

Every measurement—even one laden with significant error—was humanity attempting to speak to the universe using the language of reason.

On his paper notebook, he solemnly flipped to a fresh page and penned four words at the top.

[Wasteland Experiment].

[part:gemini-3.5-flash-lite]

He meticulously recorded the time, location, materials used, raw data, calculation process, and error analysis of the pendulum experiment.

At the very bottom of the page, he wrote the following concluding remarks.

[Sixth year of the Fourth Wasteland Calendar, the local gravitational acceleration was measured to be approximately 9.79 m/s².]

[The error is relatively large, but it is sufficient to show that near the local surface, the gravitational acceleration is close to that of Earth.]

[Combined with previous long-term life experience, the classical mechanics model at low-speed macroscopic scales can continue to be used for the time being.]

After writing these sentences, Jiang Lin put down his pen.

He looked at it for a long time.

Then he gently let out a breath.

Afterwards, Jiang Lin entered the autopsy phase of the thermodynamics section.

This was the part he had learned the most confusedly in high school.

What ideal gas law.

What first law of thermodynamics.

What internal energy, what temperature, what pressure.

In high school, he had never understood why macroscopic gas pressure and temperature could be combined with a few simple letters.

In the past few years in the Wasteland, when he studied this part, he had also swallowed it whole without digesting.

But after college Physics opened the door of statistical mechanics to him, everything changed.

What is pressure?

It is not an abstract concept.

Instead, it is the macroscopic average effect produced by countless microscopic gas molecules crazily bombarding the container walls like headless flies and transferring momentum.

What is temperature?

It is a sign of the average kinetic energy of the random thermal motion of a large number of gas molecules.

Jiang Lin drew a huge square box on the LCD board, and inside it drew countless small dots representing gas molecules.

Following the train of thought in the textbook, he started calculating from the collision of a single molecule.

Calculating the momentum it delivered upon hitting the wall.

Calculating the time it took to travel back and forth between two walls.

Then, introducing the probability density function, he used calculus to superimpose the collision effects of countless molecules.

Derived to the end, that familiar equation of state impressively appeared on the paper.

Jiang Lin stopped his pen, feeling his brain a little hot.

From the microscopic motion of a single particle, using statistical laws and calculus, he forcibly derived the macroscopic pressure.

Macroscopic and microscopic met on the bridge of statistical laws.

This was the charm of Physics.

Using the most basic microscopic assumptions to deduce the performance of the entire macroscopic world.

But what truly made Jiang Lin fall silent was not the ideal gas law of state.

But the second law of thermodynamics.

Entropy.

When this word first appeared in the textbook, he only felt it was abstract, feeling it was like some concept invented to torture students.

But when he truly understood "the entropy of an isolated system does not spontaneously decrease", Jiang Lin suddenly raised his head and looked at the Wasteland outside the Stone House.

The Wasteland was entropy increase.

Walls would weather, steel would corrode, wood would rot, ditches would silt up, farmland would harden, and order would disintegrate bit by bit in the wind and sand, acid rain, hot and cold cycles, and time.

Everything he had done in the past few years was essentially the opposite.

Piling scattered stones into walls.

Sifting barren soil into farmland.

Composting decaying plant residue into fertilizer.

Channeling runoff water into water storage pits.

Organizing a chaotic life into a survival system that could operate repeatedly.

He had always thought he was farming, building houses, and surviving.

Until this moment did he understand that he was frantically creating a small local low-entropy zone in a huge entropy-increasing Wasteland.

And the cost was solar energy, food, physical strength, tool wear, time, and his repeatedly discharging greater disorder to the outside world.

He had not defeated the second law of thermodynamics.

He was just like all life forms, relying on the brief process of energy flowing through himself to barely maintain a bit of order amidst the chaos of the universe.

This was the autumn of his sixth year in the Wasteland.

Several mountains of mechanics, vibrations and waves, and thermodynamics had been shoveled flat by him with the engineering shovel of calculus and statistics.

But Jiang Lin did not rush to cheer.

Because General Physics still had the last and hardest bone.

Electromagnetism.

That afternoon, Jiang Lin finished his work in the farmland and returned to the Stone House covered in mud and dust.

He washed his face and opened the autopsy section of the electromagnetism textbook.

Coulombs law, electric field, Gauss law, electric potential.

These terms were seen every day when doing problems in the third year of high school.

But in college Physics, they changed into a much more complicated outfit.

Calculating electric fields in high school always meant calculating point charges, or infinitely large uniformly charged flat plates.

Calculating electric fields in college meant calculating a charged straight line, a charged ring, and a charged hemispherical shell.

Integrals were everywhere.

Using the idea of calculus, the charged body was cut into countless infinitesimal charge elements dq, then the tiny electric field dE generated by each dq was calculated, and finally integrated along the geometric shape of the object.

If it was a line charge, a line integral was used.

If it was a surface charge, a surface integral was used.

If it was a volume charge, a volume integral was used.

In the past few years, Jiang Lin had suffered a lot in multivariate integration, and calculating the electric field distribution was simply like torture.

But now, having practiced multiple integrals and curve and surface integrals for a long time in Advanced Mathematics, he finally ushered in the most satisfying output here.

He spent a full week calculating the electric field distribution and electric potential distribution of various strangely shaped charged bodies clearly with integrals.

Then, he encountered that thing that made his heartbeat accelerate.

The integral form of Maxwells Equations.

This group of formulas, hailed as the most beautiful in human history, was quietly printed on the pages.

Gauss law for the electric field.

Gauss law for the magnetic field.

Faraday electromagnetic induction law.

Ampere-Maxwell law.

Four equations encompassed the mysteries of all macroscopic electromagnetic phenomena in the universe.

But what truly made his scalp tingle was the understatement at the back of the textbook.

Using the Gauss formula and Stokes formula, Maxwells Equations can be rewritten from the integral form to the differential form.

The flux passing through a closed surface becomes the divergence at every point in space.

The circulation along a closed curve becomes the curl at every point on the surface.

Jiang Lin stared at the two words divergence and curl for a long time.

He suddenly realized that electromagnetism was not studying pushing and pulling between a few charges across a distance.

What it truly studied was how space itself was rewritten by sources, and how it responded to this rewriting at every local point.

This reminded Jiang Lin of how, in the third Wasteland, in order to understand lenzs law of electromagnetic induction, he had drawn force analysis diagrams in his tent for a whole day.

At that time, he felt that electricity and magnetism were two completely different things, only occasionally influencing each other.

But Maxwells Equations told him with the most frigid mathematical language.

Electric fields and magnetic fields were simply the two sides of the same coin.

Changing electric fields produce magnetic fields.

Changing magnetic fields produce electric fields.

They excite each other alternately in a vacuum, embrace each other, and then propagate outward at the speed of light.

This was electromagnetic waves.

This was light.

Jiang Lin suddenly turned his head and looked outside the small square window of the Stone House.

The dark red light of the setting sun was slanting across the stone table.

This light, which had crossed countless light-years, penetrated the thick clouds and suspended particles of the Wasteland, and finally fell on the floor of the Stone House, was essentially a symphony of electric and magnetic fields in space.

He sat in front of the stone table and did not move for a long time.

The romance of Physics reached its peak at this moment.

It was not romantic leisure written in poetry.

It was writing the underlying order of the universe with the most rigorous mathematical symbols.

The winter of the sixth year.

The Wasteland ushered in the first wave of cold snap.

Jiang Lin warmed himself by the fire pit and temporarily closed the electromagnetism textbook.

This huge and complex corpse of Physics, after nearly a year of repeated dissection and verification by him, finally had its first layer of skeleton examined out by him.

Most of those formulas that he used to remember by swallowing them raw now had a solid calculus base.

He took out the logbook of the time capsule and solemnly wrote on the latest page.

[General Physics, calculus backbone, the first round of autopsy completed.]

After writing this sentence, Jiang Lin instinctively wanted to add a sentence afterwards.

[All mathematical logic has been connected.]

But as soon as the nib touched the paper, he stopped again, thought for a moment, put down the pen, and reopened the computer.

He clicked on the second half of the textbook volume on Vibrations and Waves.

There was a section of content there that he had never fully understood.

Multi-degree-of-freedom systems.

Two spring oscillators coupled together.

Three mass blocks connected in a row.

Even a whole string of atoms vibrating in a crystal lattice.

When it was a single oscillator, he could write a second-order differential equation and then solve it using methods from Advanced Mathematics.

But once the oscillators became two, three, or even countless, the equation was no longer a single line.

Instead, it was a net.

Every variable pulled at another variable.

Every degree of freedom was entangled with other degrees of freedom.

He tried to write starting from the simplest two mass blocks.

The mass block on the left had a displacement x₁, the mass block on the right had a displacement x₂, and a spring in the middle tied them together.

The equations were quickly written out.

But problems also appeared immediately.

The first equation contained not only x₁ but also x₂.

The second equation contained not only x₂ but also x₁.

The two degrees of freedom were like two wet threads intertwined together.

Of course he could forcibly eliminate them using the substitution method.

Forcible calculation was not impossible.

But the textbook did not do so.

The textbook wrote them into matrices.

Then it told him that what was truly to be found was not where a certain mass block was at the moment, but how the entire system naturally wanted to vibrate.

Matrices, eigenvalues, eigenvectors, normal modes.

Jiang Lin stared at those words for a long time.

He obviously understood every differential symbol.

Obviously knew where the restoring force of the spring came from.

Obviously could already derive the equations of motion for a single oscillator.

But when two oscillators were coupled together, he suddenly realized that he could no longer see this system.

It was not that he could not solve a certain problem, but that he could not understand it from a structural perspective.

The book said that the coupled equations should be written in matrix form.

The book said that the characteristic frequencies of the system should be found.

The book said that each eigenvector corresponded to a normal mode.

Separated individually, he recognized all these words.

Linked together, however, they were like a thick wall, lying coldly in front of him.

Jiang Lin suddenly realized that Advanced Mathematics had given him a sharp knife.

This knife could cut open continuously changing flesh and blood.

It could handle velocity, acceleration, variable force work, electric field distribution, and thermal motion statistics.

But when Physics truly went deeper, it relied on more than just changes.

It also needed to see structure.

How many degrees of freedom were in a system.

How these degrees of freedom were coupled.

How to decompose mixed motions into mutually independent modes.

How to find the skeleton that truly dominated the systems behavior from a pile of entangled equations.

That skeleton was not called calculus.

That skeleton was called Linear Algebra.

Jiang Lin lowered his head, looking at the sentence he had just written in the time capsule logbook.

[General Physics, calculus backbone, the first round of autopsy completed.]

He indeed had no qualification to add all mathematical logic has been connected afterwards.

Because ahead lay an even deeper skeleton, quietly lying in the dark, waiting for him to open the coffin.

Jiang Lin was silent for a moment, and at the very bottom of that page, he added another line of words.

[Next stage: Linear Algebra.]

[Objective: Understand multi-degree-of-freedom systems, matrix equations, eigenvalues, eigenvectors, and normal modes.]

After writing the last word, he closed the logbook.

Outside the Stone House, the cold wind of the Wasteland swept across the Wasteland, whipping up fine sand and dust.

Inside the Stone House, the light from the fire pit reflected on his face, flickering.

Jiang Lin looked at the string of unfamiliar yet familiar words on the computer screen.

He suddenly smiled.

After gnawing on Advanced Mathematics for a few years, calculus finally internalized into a tool.

But when he truly wanted to walk into the depths of General Physics, he quickly hit the next wall.

Without Linear Algebra, he could only forcibly calculate even the vibrations of multi-degree-of-freedom systems.

Let alone understanding.