Chapter 2: Welcome to 1960

If life could be chosen again, Lin Ran would absolutely not choose to spend the last day of 2019 stargazing at Cherry Springs State Park.

He was merely trying to find a place around his pitched tent to relieve his urgent need to urinate, only to encounter a strange light gate, and out of excessive curiosity, he approached to see what it was.

And then? Then there was no then.

When he regained consciousness, everything within sight was pitch black.

Lin Ran did not doubt whether he had gone blind, because compared to the loss of vision, the disappearance of hearing, touch, taste, and smell was even more chilling.

No matter how he tried to open his eyes, he could not feel their existence.

There was only empty darkness around him, and silence and emptiness gradually emerged in his heart.

No! There was a light; Lin Ran could feel a flame-like light in the distance constantly devouring the darkness.

Although he didn't know what the light was, his intuition told him that once the light completely devoured the darkness, his consciousness would be devoured along with it.

Countless thoughts flashed through his mind: "Could it be that I am stargazing, and the stars are also gazing at me? Have I been kidnapped by aliens?"

Lin Ran already regretted it. If he had known it would be like this, even staying in his rented room or reading literature in the library to spend the last day of the 2010s would have been much better than his current situation.

If consciousness disappears, the mild result is becoming a vegetable, and the severe result is death.

From the initial clutter in his mind, as time passed, the distracting thoughts in his brain were rapidly disappearing, leaving only endless pain and torture. Lin Ran completely understood why being locked in a dark room was a top-tier torture.

Both the environment he was in and the crisis of his consciousness about to disappear were enough to make Lin Ran hover on the verge of collapse.

"No! I cannot die just like this. If I am finished, I feel like my mother won't be able to go on living either." As an only child from a single-parent family, Lin Ran knew very well what he meant to his mother.

"No, consciousness cannot stop the spread of the flames!"

"Thinking doesn't work either!"

"What on earth can stop the flames from spreading?"

Lin Ran was terrified; he didn't even need to wait for the flames to devour his consciousness, his own negative emotions were enough to devour him.

"No, I have to find something to do, otherwise I will go crazy or become a fool," Lin Ran thought.

As an outstanding graduate of the School of Aeronautics and Astronautics at Jiao Tong University and a current doctoral student in computer science at Stony Brook University, State University of New York, Lin Ran's so-called finding something to do was to dig out the knowledge in his mind and review it.

"Using GraphAI to solve various problems, including partial differential equations, bioinformatics, quantum physics, materials science, etc..." A computer science PhD was a huge field, and GraphAI was a new branch under this behemoth.

Lin Ran actually had a strong interest in aerospace. As for why he didn't choose aerospace, it was because it was impossible for a Cultural Huaguo person to apply for an American aerospace project, let alone a PhD with a scholarship.

So in the end, he gave up his ideals and the distance for the sake of survival. Whether staying in the US or returning to Cultural Huaguo after getting a computer science PhD, the prospects and expectations were far beyond working in aerospace in Cultural Huaguo.

It was just that the GraphAI direction was a huge pit, which he hadn't expected.

"Design and Manufacturing, Automatic Control Principles, Aerodynamics, Engineering Thermodynamics, Comprehensive Russian, Aircraft Design..." These were all Lin Ran's professional compulsory courses.

That's right, Russian was too; he only had English in his freshman year, while Russian spanned his three years from freshman to junior year.

From the textbooks to the content of the professors' lectures and the exercises he had done, they all emerged in his mind one by one. Compared to the topics he was working on now, aerospace-related content could make his heart calmer and offset some of the fear brought by the darkness.

"Functions, limits, derivatives, integrals, multivariable calculus..."

"Mechanics, thermodynamics, electromagnetism, optics, modern physics..."

"History of aerospace development, aircraft types, principles of aerospace technology..."

Course after course presented itself in Lin Ran's consciousness, and the content that was about to be forgotten was reawakened. Lin Ran felt that if he had been this serious in the past, his GPA would not just be in the top five of his grade; it would definitely be the top one.

The once difficult and boring Russian courses became exceptionally interesting at this moment. Even if he sat in the first row of the classroom and was washed by the professor's splashing saliva, Lin Ran would be willing.

"I can only hope that this will be *Всякая беда – к лучшему приводит*."

This Russian sentence means "a blessing in disguise."

After breaking down and chewing over all his university courses from beginning to end, Lin Ran discovered that he was undergoing some strange changes.

More and more details forgotten in the past, fragments that he hadn't noticed in class, were being awakened, and his brain's computing power was becoming stronger and stronger.

While the flames were devouring the darkness, it seemed they were also tempering his thinking.

It was just that the trend of the flames constantly spreading had not changed; he could even feel the heat, which was enough to show how close the flames were.

"If life really ends like this, then dissipating in the ocean of knowledge seems not bad."

If his brain in the past was just an X86 computer, then now it was at the supercomputer level. High-order determinants, large-scale linear equations, linear equations with parameters, etc. —these types of problems that required massive calculations in linear mathematics could be quickly solved by him just by mental arithmetic.

Time cycled back and forth in the process of pain, thinking, and recalling.

Lin Ran discovered that not only had his brain ability made great progress, but his concentration, which had been weakened by smartphones, had also made a qualitative leap. The time he could sustain thinking about problems was getting longer and longer, and the time he could enter a flow state was getting longer and longer.

"If I could return to the real world, I would definitely be a top-tier genius!" Lin Ran thought, but the premise was that he had to be able to go back.

After rearranging the past content, Lin Ran finally turned his attention back to the topic he was currently working on: "Using Artificial Intelligence to Solve the N-S Equations."

The reason why it was said that GraphAI was a huge pit was because this direction was very new; being able to do everything also meant being able to do nothing.

After Professor Samuel's team at the University of Washington published a paper titled "Data-driven discovery of partial differential equations" in 2017, AI solving equations began to enter the public eye.

Lin Ran also jumped into this pit.

What Professor Samuel did before was artificial intelligence solving partial differential equations, and he did the same, but the N-S equations were just the top-tier ones.

The N-S equations, one of the top problems in the field of mathematics, were mathematical problems on par with the Riemann Hypothesis and the Goldbach Conjecture.

If a general analytical solution to the N-S equations could be found, aircraft design could find the optimal shape under various conditions, wind power generation would no longer be garbage power, wind power could be mentioned in the same breath as photovoltaics and nuclear power, and car shapes could find the optimal aerodynamic effect...

Simply put, if a general analytical solution to the N-S equations were found, all real-world application problems involving the flow of air, liquids, and solids would have an optimal solution.

Even if the Nobel Prize or the Fields Medal weren't given to you, scientists around the world would protest collectively.

This was also one of the few top mathematical problems that, once solved, would have the most significant impact on the real world.

However, what Lin Ran was doing sounded intimidating, but using artificial intelligence to solve the N-S equations was actually not finding a general solution at all; it was just doing some minor work, finding solutions under some specific conditions. The difficulty was reduced from finding a needle in a haystack to finding a needle in a bowl.

"It's just that I only have a brain now, no computer?"

Lin Ran used his limited foundation in higher mathematics to deduce the formulas in computational fluid dynamics.

From the numerical method of finite difference method in the textbook, he deduced high-order finite difference methods, compact finite difference methods, and adaptive finite difference methods.

From the finite element method, he deduced mixed finite element methods, discontinuous finite element methods, and isogeometric analysis finite element methods.

At the moment of deducing the result, Lin Ran felt the spread of the flames slow down. "Could it be that I need to stop the flames from spreading by expanding the boundaries of knowledge?"

"What conditions must be met to completely extinguish the flames?"

"Could it really be completely solving the N-S equations?"

From the finite volume method, he deduced high-order finite volume methods, unstructured finite volume methods, and dual-time-step finite volume methods.

When losing the five senses, mathematics became the only source of aesthetic beauty.

Moving toward the N-S equations bit by bit:

"If we assume that an ideal flow appears on a two-dimensional plane, then I can obtain the precise velocity field and pressure field by adding certain boundary conditions..."

"For the viscous laminar flow of fluid between circular pipes or parallel plates, the precise solution where the flow velocity presents a parabolic distribution can be solved..."

The flames were constantly being burned backward.

From plane Couette flow to Poiseuille flow, from circular pipe Hagen-Poiseuille flow to Taylor flow between rotating concentric cylinders...

The sudden start of a plate or circular pipe, the flow near an oscillating plate or rotating disk, the two-dimensional or axisymmetric stagnation point flow rushing toward a plate...

When the fluid inertial force is much greater than the viscous force, the N-S equations can be divided into two regions to solve. In the outer region, it is a uniform flow, and in the inner region, the horizontal derivative term of the viscous term of the N-S equations is ignored, so a similarity solution can be obtained...

Predecessors built an incomparably exquisite mathematical building. In the past, Lin Ran could only peek at one corner, but now he could not only see the whole picture, but also see what other mathematicians could not see. He realized that he really might be able to add a floor named N-S equations to the entire mathematical building.

Lin Ran was moving toward the general solution of the N-S equations bit by bit.

"How long has this been? I seem to have found the general precise analytical solution to the N-S equations!"

After verifying the general solution with various N-S equations, Lin Ran felt that he had really done it. Just relying on a foundation of fluid mechanics to solve the N-S equations was much more exaggerated than using martial arts techniques to become a true immortal, Lin Ran thought.

Although there were no big shots to verify it, no public to witness it together, no human world to cheer for it, and no Nobel honor to crown him, he still knew that he had persisted through endless years by relying on thinking about unprecedented ultimate problems, without becoming an idiot or losing his sanity. His soul was cheering for him, and his spirit was applauding for him.

"If Old Wang, who taught me advanced mathematics, knew, he would definitely feel that his life was without regrets, being able to teach a student who solved the N-S equations problem."

Before he could be happy, the spreading flames were devoured by the darkness, and then the pitch black finally collapsed bit by bit, and a colorful world slowly emerged before his eyes.

"Where did this bring me?"

Whether it was the vehicles roaring past on the road, the attire of the surrounding pedestrians, or the large "1960" lettering on the crystal ball that caught his eye the most.

All were telling Lin Ran an incomparably precise piece of information: Welcome to 1960.

"The neon ball marked with 1960 is 46.2 meters away from me. The temperature in the air at this time is about 15% higher than the Cherry Springs State Park where I was before. Judging from the direct sunlight angle, the approximate time point, and the surrounding environment, I am afraid I am still within the scope of Niuyuezhou..."

The classic red styling behind him and the English letters "TELEPHONE" were telling him that this was a telephone booth.

The vehicles passing in front of him were like slow motion; every license plate number was engraved in his mind.

Lin Ran felt that if a bullet were to strike him now, he could see through its trajectory and dodge it.

Countless information exploded in his mind like fireworks. The evolution of his brain and body was secondary; Lin Ran realized that his biggest gain at this moment was: "The Door."

"To be precise, it is that I can shuttle between all the doors I have passed through. All doors are my anchor points, and that white light circle helped me create a door to a parallel space-time in 1960, which is the telephone booth behind me.

I only have one door in 1960 now, but I have countless doors in 2020?"

The doors he had walked through in the past emerged in Lin Ran's mind one by one.

In the cold wind of New York, Lin Ran gritted his teeth and stood at a newsstand, freeloading on the day's New York Times, trying to figure out the situation.

"In 1957, the Soviet Union successfully launched the world's first artificial Earth satellite, Sputnik 1, which marked humanity's entry into the space age..."

"On January 1, 1958, the European Economic Community and the European Atomic Energy Community were officially established..."

"In 1958, Jack Kilby of Texas Instruments in the United States invented the integrated circuit..."

"Sir, 10 cents for the New York Times New Year Special Edition."

Putting down the newspaper, he continued to stand on the residual snow in front of the newsstand. On the billboard next to him was a blonde woman puffing on a cigarette, and the slogan below, "Camel cigarettes, doctors love to smoke too!", was covered by snow for half of it.

In the public telephone booth behind him, a young man in a tweed suit was shouting into the receiver: "Those hicks in Houston don't understand orbital calibration at all!"

Lin Ran looked back and saw the young man wearing a silver NASA badge on his chest, the glass covered in mist.

By the time Lin Ran came back to his senses, he had already arrived in the lobby of a cafe next to the telephone booth, with a cup of hot water on the table. The blonde, blue-eyed waitress at the bar saw Lin Ran look up and gave him a friendly smile, while sitting opposite him was the young man from the telephone booth just now.

"Sir, you mentioned orbital calibration just now. I think I might be able to provide you with a little help." ===== CHAPTER 3 =====