Volume 1 Chaos Comes Chapter 8 High School Girls and Attractors
The scenery of the North China Plain is actually a boring combination of woods, farmland, greenhouses and villages. I looked at it for a while, then took out my phone and opened the social software, and noticed a chat box that hadn't said a word after adding a friend.
The other person’s profile picture is a lake blue Mandelbrot set.
I took a deep breath and typed five words.
"Are you home yet?"
After sending the message, I immediately deleted the chat box and looked out the window, not daring to face the embarrassing situation of the other party not replying.
Ten seconds later, I heard a clear prompt tone.
It was my mother who asked me where I was.
I chatted with her for a while, and the bumpy train made me a little dizzy, so I put my phone down temporarily.
Ten seconds later, another reminder tone sounded. I was about to open my phone and tell my mom that I didn't want to talk anymore.
"I'm home now, and I'm shopping with my bestie."
How should I continue the conversation in this situation? It would be great if I had a conversation dictionary.
"I'm still on the train and will be home soon. When I get home, I'll show you our New Year's Eve dinner."
"Okay, I just had an egg cake."
The picture sent to me showed a thick golden pancake wrapped in cream, and I stared at the hand holding it for several seconds. The knuckles were long, and the nails were painted in cold white and dotted with small flowers.
"It looks delicious. Is it sweet?"
"There are sweet and salty ones. I like the ones with sugar and sesame."
“Is it cold in Chengdu now? What should I wear?”
"It's OK, about the same as late autumn in the north? It's just too humid and I feel uncomfortable."
After a while, I received a photo on my phone.
In the picture, Ai Bishui has long hair draped over her shoulders and is wearing a light-colored beret. She is wearing a black and white skinny sweater on her upper body, a burgundy pleatless skirt on her lower body, a tweed coat with white horn buttons on the outside, and flesh-colored leggings under the skirt.
The girl is standing in front of a dark gray brick wall, holding a light gray short cotton jacket, with her side face facing the camera.
This is very different from the huge down jacket before. For the first time in my life, I had a negative view of the northern winter. Then I enlarged the picture and silently clicked save.
"It's so beautiful!" The words were typed out before rationality even came into play.
"Let's continue shopping. We can talk later when we have time."
The content of the days during the New Year is always the same. It is nothing more than going to my grandparents' house to cook New Year's Eve dinner together, visiting relatives and friends to receive red envelopes, accepting compliments from others after saying the name of the school, and satisfying my parents' vanity.
This year is a little different. In between helping the elders with their work, I have been working on deriving formulas from the book given by Teacher Jie. This probably made my relatives feel a little weird.
"Chengcheng, I heard from your mom that you were very good at physics in college. Why don't you teach your sister about physics before dinner is over?"
On the afternoon of New Year's Eve, my third aunt was peeling oranges on the sofa in front of the TV. She turned to me who was staring at the snow scene outside the window and said something.
The "sister" she mentioned was her daughter, my cousin Fang Xue, who was in her second year of high school. When she was talking, the girl with twin ponytails had just come back from setting off firecrackers with her uncle and was taking off her boots at the entrance.
She is a very delicate girl, and has always been clean and neat. When she was young, she often heard relatives praise her for looking like a doll. This statement seems to be a fixed combination used by people of that era to describe beautiful girls.
Fang Xue made an extremely reluctant expression when she heard what my third aunt said. Although she knew it was not directed at me, she still felt a little uncomfortable. She was always compared to me by her third uncle and aunt since she was a child. I guess she has PTSD now.
Actually, her grades in school are pretty good, although still slightly worse than mine.
"Why talk about physics on New Year's Day? Xiaoxue and Chengcheng, come over and watch TV together." My grandma seemed a little unhappy.
"It's okay, grandma. Xiaoxue and I will come out for dinner in a while." At this time, the sofa in the living room was already full of people, and I really wanted to escape from this smoky and noisy environment.
My grandparents' house is a medium-sized three-bedroom, two-living-room house, which was a common unit housing in that era. Every Chinese New Year, they would clean up the remaining two bedrooms and give them to me and my parents to stay in temporarily.
We walked into the room that my grandmother had reserved for me and closed the door, but we could still faintly hear the elders outside the room talking loudly about the international situation. The small desk in the room was already filled with books and documents I brought from school, as well as a pile of draft paper with various symbols written on it.
"Fang Cheng, what do you study in the physics department in college?" She stopped calling him brother since junior high school.
"Normally, freshman learns general physics, which is mechanics, heat, and optoelectronics; sophomore learns the four major mechanics; and after junior year, some subdivisions begin. I'm not at that stage yet."
In fact, there are many people in our school who have completed the senior year courses in their sophomore year, and some people have even almost learned them in high school. But I'd better not put pressure on my younger sister.
"Besides that, I have to take several math and programming classes every semester. Oh, and there are also various physics experiments. Those classes are useless and waste time..."
After all, scientific research experiments and laboratory classes are two different things.
"Emmmm, I don't understand." Fang Xue sat down on the bed and kicked my knee with her bare feet.
"Tsk, don't touch me with your feet after taking off your shoes. You're making my pants smell."
When she heard that, she suddenly raised her legs up, and the soles of her feet almost hit my nose.
I stood up, rolled up the draft paper and threw it at her head, but was blocked by the pillow. After a long fight, we finally returned to our study posture.
"You bully your sister all day long. Do you behave like a brother?" She said while panting and imitating my grandmother's tone.
"What was your total score on the final exam?"
I'm ready to end this pointless bickering and go straight to checkmate.
She ignored me, stood on tiptoe, walked over me while I was sitting on the chair, and reached for the book open on the table. I immediately stepped back.
"You're not a kid anymore, stop having physical contact with me. What will your parents think if they see you?"
"Psycho." She fiddled with the English book in her hand, trying to read the words on the cover. "Bring...inside..."
“Nonlinear Dynamics & Chaos”
"What do you mean?"
“This is the classic textbook on chaos theory, written by Strogatz.”
I don't know how to translate his Chinese name.
"What are wontons? Is it physics? Why are all the drawings in the book function graphs?"
I didn't intend to tell her the cliché story about butterflies in the Amazon rainforest, so I just opened my laptop and typed a few words.
"Lorenz...system...attractor..."
"What is this? It's so beautiful."
On the screen is the Lorenz attractor in the phase space (x, y, z). Bright blue stripes of varying thicknesses densely outline a butterfly-like shape, with a delicate and exquisite beauty similar to that of a mechanical watch.
The Lorentz here is the American Edward Norton Lorentz, who is not the same as the well-known Dutchman Hendrik Anton Lorentz who proposed the Lorentz transformation.
"You have learned derivatives, right? You are already in the second year of high school." I took a piece of draft paper and wrote down the three equations of the Lorentz system.
"These three equations form something called a 'dynamical system'. If we want to study how the three values x, y, and z change with time t, we need to plot their trajectories in the (x, y, z) space, which is called the phase space."
She obviously didn't understand, and sat cross-legged with the book on her feet. I took this opportunity to take the book away. After all, it was borrowed from the teacher, and it would be troublesome if she damaged it.
"This is...math, I guess. It feels like solving equations."
"Three equations with four independent variables cannot be solved. We can only describe the trajectory of point P (x, y, z) with respect to time t." I raised the book and sniffed it from a distance, but there was actually no smell.
"Your feet are the ones that stink!" She tried to sit up and kick me, but I grabbed her feet with one hand and held her in place.
A soft cat meow came from not far away, and a round tabby cat flew out of the closet. It was our pet Buster, who had been sleeping in the closet since she came to grandma's house.
It seems we just woke her up.
Buster jumped lightly onto the bed and coiled between Fang Xue's thighs. I took the opportunity to release my hand that was pressing on Fang Xue.
"If this bedroom is the phase space, you can think of it as a butterfly shape displayed on the computer above our heads. This butterfly is floating in the air like a cloud of mist, and it is the attractor of the Lorentz system.. "
"Why can it float?" Fang Xue fiddled with Buster's white claws.
"This is determined by the form of the equations themselves. You can imagine point P (x, y, z) as a ping-pong ball. If we throw the ball from anywhere in the bedroom, it will always fall into the butterfly, just like being caught by an invisible hand."
The kitten began to purr and her attention was no longer on me.
"For a system that exhibits 'chaos', it is unpredictable where the ping-pong ball will appear in this attractor, and as time passes it will keep spinning in it forever..."
The discussion among the elders outside died down as we both heard footsteps at the bedroom door and hurried back to our sitting position together at the desk.
It was my third aunt who opened the door. She must have come to ask us to go out for dinner.
"The New Year's Eve dinner is ready! Oh, you guys are studying so hard. Fang Xue, put on your socks quickly to avoid catching a cold. By the way, Cheng Cheng, teach your sister about 'electromagnetic induction', she just can't learn it..."
While eating the New Year’s Eve dinner, I stood on a bench and took a panoramic photo of the table, and sent it to Ai Bishui without delay.
