Volume 1 Chaos Comes Chapter 13 Under the Sky
Unlike last year, my discomfort with the crowded campus after the start of the semester has completely disappeared, and I am actually looking forward to seeing my classmates. I still don’t understand the reason for this change.
The course that Mr. Xie mentioned earlier is scheduled for the third and fourth periods on Wednesday and Friday afternoons, in the only remaining classroom in the old physics building. Many famous physicists have come out of this classroom in history, and now it is mainly used as a discussion room for the Institute of Complex Systems.
The first class of this semester was packed with people. I arrived ten minutes early according to the experience of my seniors, but was still squeezed into a corner. When I entered the room, I took a deliberate look and saw Ai Bishui sitting by the wall next to the window, concentrating on typing on her laptop.
I had just sat down and taken out my notebook from my bag when Teacher Xie walked up to the podium, looking very energetic. He said with a serious expression that I had never seen before:
"Let me first emphasize the course requirements: one homework assignment per week, closed-book exams at the midterm and final, and no course papers."
The classroom, which had been a little noisy just now, suddenly became silent.
Teacher Xie held up the textbook he had asked me to look at earlier and said, "We will cover chapters one to five of this book in the four classes this week. I hope everyone has reviewed it in advance."
By the second class, there were only about ten people left in the classroom, and in the third class, Ai Bishui and I were the only undergraduates left. Teacher Xie didn't seem to care about the rapid decrease in students, and he didn't slow down his lectures at all.
"The main scientific object studied in this course is called 'complex dynamical system', or complex system for short. Simply put, it is to examine the laws governing the evolution of a series of interacting objects over time. This is a topic with a long history, dating back to the discussion of differential equations by Henri Poincare in the 19th century."
“Complex systems in nature consistently have four states.” He drew a diagram of the structure in black and white.
According to students who have taken his classes, this old professor never used PPT in his lectures. No matter how many formulas he had to explain, they were all handwritten on the blackboard.
"The first is an ordered state, which involves a system with periodic motion. The best example is a solid lattice. In this state, all molecules can be uniformly described by the same formula, and the system itself is in a definite state."
I sat in the middle of the fourth row in the classroom, while Ai Bishui sat in the second row by the window. She always sat by the window during class. She was wearing the same white sweater as when we met at school last year, and was writing something on the computer like when we first came to class, but it didn't seem to be about the course.
"The second is a self-organized critical state, in which each component of the system is connected by a simple interaction mechanism. There are many examples of self-organization in nature, such as earthquakes, sand piles, fish and bird flocks, and even human social networks. This is a very common structure."
"The third state is the chaotic state. In this state, the system is generally unpredictable, but this unpredictability is not completely random. There are also many examples of chaotic systems in nature, such as three-body systems, smoke and dust spreading in the air, atmospheric movement, and liquid turbulence. This is also the main research direction during my doctoral studies."
There was no atmospheric movement in the classroom at this time, and everyone present was taking notes quietly. After all, there was no book to refer to for the homework of this course, and it could only be done if one truly mastered the content taught in class.
"The fourth type is a true random process, such as Brownian motion or the flight of ideal gas molecules. The components that make up the system do not interact with each other, and we cannot track the behavior of individual components. In this case, the behavior of each element that makes up the system is truly unpredictable."
Teacher Xie filled the blackboard with writing and then turned to face us.
"These four types of dynamical systems have exactly the same underlying mechanisms. In other words, we can use the same equation to continuously obtain four states of the same system. This is the unified theory of complexity, or CUTs for short, which is also the main content of this course."
During the entire class, Teacher Jie did not even glance at the handouts. He was so focused on this lesson that it was already very late when the get out of class ended.
The sunset glow on the edge of the clouds gradually faded, indigo slowly dyed the sky, and the sun sank below the horizon.
After class that day, I secretly observed Ai Bishui. Even she would be tired.
Sure enough, this time she did not go to Teacher Jie to discuss for a while as she did before. Instead, she stretched, opened the window and took a deep breath.
I put on my cotton jacket, put away the notebook filled with notes, pushed aside the polluted air and walked towards her position.
"Are you going to the library after dinner?"
Spring is still far from arriving in this city. The hot air coming out of my mouth instantly condenses in the biting cold wind from the window, and turns into a white mist and dissipates.
"Well... I won't go. I'm a little tired today. I'm not going to have dinner either. I might go back to the dormitory, listen to some music, and then go to sleep."
She put her index finger under her chin and thought for a while, then began to put the things on the table into her schoolbag.
"Well... can we walk together for a while..."
We're just walking back to the dormitory area together, there should n't be any problem, just don't run into anyone we know.
"Okay, what do you want to discuss? Is it about the course?"
I used to discuss problems and homework with her often, and I could feel that although she didn't attend the class, her understanding was much deeper than mine.
"Just... can I chat? I don't think it's good to keep asking you questions..."
"Hmm... that's fine, chatting can help change your mind. Is there anywhere you want to go?"
I had planned three locations: the hill with the observatory next to the physics building, the stone boat in the lake in the center of the school, and the small courtyard with stone slabs behind the main library. These three scenes flashed through my mind for a moment, and finally my frontal lobe decisively chose the one closest to me.
"Then let's go to the observatory. It's on the way back to the dormitory."
We walked through the withered flower beds and climbed the stairs, and in a few minutes we reached the top of the slope. I walked behind Ai Bishui, secretly admiring her silhouette against the lights of thousands of houses.
"The scenery here is pretty good! It's my first time coming up here at night."
The sky was getting dark, with only a few clouds in the dark blue background. The lights on the viaduct were like falling stars, flowing slowly under the shadow of the tall buildings.
"Thousands of miles of floating clouds roll over the green mountains..."
I muttered to myself at the view before me.
"A lone moon floats in the middle of the blue sky."
The voice in my ear continued the second half of the sentence.
"The lonely moon over the blue waves and the clear river."
"The Big Dipper is scattered and Chang Gengming is bright."
I searched the sky in front of me, trying to find a constellation to continue the conversation.
"It's a pity that the Milky Way cannot be seen in this season..."
"Venus is so bright tonight, right there!"
I looked in the direction her finger pointed and felt my ears getting a little hot.
"The city's light pollution is too serious. I can only find Orion now." Ai Bishui sat down on the lawn and let her schoolbag rest against her knees.
"Yes, Betelgeux is the brightest." I also saw three stars connected together.
The seven stars of the Orion constellation illuminate the night sky, and the two shoulders, two feet and three are the waist. The three stars are also the belt of Orion.
"I feel like the names of ancient constellations are all very cool. The Ape sounds much more advanced than Orion."
"It's probably because of the unfamiliarity, but it does sound nice."
I searched for the names of the stars in my mind: Bi Yue Wu, Kui Mu Lang, Xu Ri Shu, Yi Huo She...
Unfortunately, none of them can be seen now. Even the bright Big Dipper is only faintly visible under the bright lights of the city.
"I found Beidou, I should be able to see Xinyue Fox..."
I remembered that I had memorized the poem "Lisheng Duiyun" when I was a child: The two stars of Niu and Nv are on the left and right of the river, and the two stars of Shen and Shang are in the west and east. These are probably the few constellations that can be seen clearly with the naked eye in early spring.
I glanced at Ai Bishui. She seemed to be thinking about something and didn't look at me.
There was a subtle pressure in the air, which suppressed my desire to continue. We sat on the top of the hill, silently admiring the night sky of the distant city.
There was a commotion in the sky, and the stars slowly opened their eyes.
