At eight o'clock in the morning, Jiang Yubai showed up on time. When he saw Lin Zhixia, he naturally held her and said to her, "I dreamed of you last night."
"What did I do in your dream?" Lin Zhixia asked curiously.
Jiang Yubai avoided answering. When he asked about Lin Zhixia's research progress, Lin Zhixia exposed him: "Are you trying to change the subject?"
He actually admitted: "Yes."
Lin Zhixia hugged his arm and continued to explore: "What did you dream about? Tell me quickly."
Jiang Yubai began to procrastinate: "Let's talk about it when we get to my house."
Just like that, Lin Zhixia followed him home.
They walked through the corridor and passed a concert hall with a grand piano in it. Lin Zhixia glanced at it and Jiang Yubai pushed open the side door of the concert hall.
Lin Zhixia followed him closely, like a little tail that couldn't be shaken off. She said, "I want to listen to "Autumn Whispers", play it for me."
Jiang Yubai began to play "Autumn Whispers". He hadn't touched a piano for more than two months and was trying to get the feel for it. He didn't open the huge lid of the grand piano, and the music played by his fingers sounded low and soft.
Lin Zhixia stood beside him and observed him.
His piano playing suddenly stopped.
He put his hands around Lin Zhixia's waist and lifted her up with a little more force. Her feet were hanging in the air, and she was a little scared, but she didn't struggle. She just asked him, "What do you want to do?"
Jiang Yubai asked her to sit on the piano cover. She asked back, "Will I break your piano?"
"You are so light," Jiang Yubai said, "it is impossible for you to get hurt."
Lin Zhixia thought to herself: I also weigh more than 40 kilograms.
There are lush trees in front of the French windows, and a fine patch of green shadows comes through the gauze curtains, which happens to be projected onto the pure black piano cover.
Jiang Yubai sat back on the piano bench and played the interrupted song with only his right hand. His left hand grasped Lin Zhixia's wrist. She watched him lower his head, kiss the back of her hand, and then kiss her fingertips.
He said, "This is what I dreamt last night."
At this moment, he clenched her fingers and his passion deepened.
Lin Zhixia did not give any response.
She jumped off the piano cover, her hands were numb, her legs were weak, and her thoughts were confused. She suddenly realized that many things could not be simulated by imagination alone. For example, she had read famous literary works from ancient and modern times, both at home and abroad, since she was a child, but she never understood why the smart and clever protagonists often fell hard in the pursuit of love.
Now, she herself clearly tasted the strange feeling of being unable to control herself.
Lin Zhixia's heart was beating as fast as a drum.
Jiang Yubai thought she would say a few words, but she was very quiet. He suspected that his actions were a bit abrupt. In order to break the silence, he suggested: "Let's go to the study to study."
Lin Zhixia quickly responded: "Okay."
Jiang Yubai stretched out his hand to her. She immediately held it, interlocking their fingers, and they went to the study.
The study room has good lighting, and rows of bookshelves stand tall, like a small library. The carpet in the room is embroidered with exquisite patterns. On the long ebony table by the window is a computer and a stack of papers. There are also two ergonomic chairs with adjustable heights next to the table - these are obviously the seats for Jiang Yubai and Lin Zhixia.
Lin Zhixia sat down slowly and said in a very assertive manner: "You sit down too. From now on, I am your hired teacher."
"Teacher Lin." Jiang Yubai said.
Lin Zhixia nodded: "Yes, we should study in a learning manner. When I tutor you, you should call me Teacher Lin and don't change your name."
Jiang Yubai pushed the edge of the table, and the chair rolled and slid, bringing him closer to Lin Zhixia: "Teacher Lin, have you taught other students?"
"Yes," Lin Zhixia spread out a textbook, "Don't worry, I have a lot of teaching experience."
The harder Lin Zhixia tried to act businesslike, the more Jiang Yubai wanted to go beyond the safety line of the "tutor-student" relationship. He said, "The students you taught before were probably your classmates, and their foundation was better than mine."
Lin Zhixia stared at him suspiciously.
In the fourth grade of elementary school, he often compared his grades with her.
After entering university, he even claimed that "your classmates have a better foundation than me."
Did Jiang Yubai ask her to tutor him, or was he playing a role-playing game with her?
Lin Zhixia's biggest hobby is role-playing. She was very interested and patiently said, "Don't worry. Each course has limited test points, but your potential is unlimited."
Jiang Yubai took out a course material and placed it in front of Lin Zhixia.
Lin Zhixia flipped through the book and saw that the last page of the table of contents listed the mathematical foundations needed for this course, including linear algebra, advanced mathematics, probability theory, and statistical methods. Specific knowledge points were also marked under each major category. For example, the probability theory column had Expectation and Regression Fun (expectation and regression function), Law of Large Numbers and Central Limit Theorem (law of large numbers and central limit theorem) [1] and a lot of other content.
Lin Zhixia asked in a particularly responsible manner: "Tell me first, what content do you not understand?"
Jiang Yubai picked up a pen and said, "I'm not sure. I don't understand something."
Lin Zhixia and Jiang Yubai had been deskmates for four years. She had taught him many times and even wrote a notebook for him to solve problems. After graduating from junior high school, she had never tutored him again.
She missed the old days.
She said more seriously: "Well, explain it to me again, starting from the first knowledge point..."
Jiang Yubai started with the "regression function". When he talked about the "central limit theorem", his pen fell on the table. He paused, pointed at the line of English, and asked in a low voice: "Teacher Lin, what is the central limit theorem?"
He doesn’t even understand the “central limit theorem”?
Lin Zhixia simply summarized: "This paper uses the most common expression of the central limit theorem. Suppose you have a distribution containing independent random variables. The number of random variables is finite, the mean is M, and the variance is D. You draw multiple groups of samples from this distribution, and take the mean a for each group. After standardization, a1, a2...an will converge to a normal distribution."
She glanced at him sideways. "The central limit theorem is one of the most important theories in probability theory. We can continue to expand it. You will find that samples from the Cauchy distribution do not apply to this theorem. Why?"
Jiang Yubai tapped the table lightly with his right index finger: "Teacher Lin."
"What's wrong?" Lin Zhixia blinked.
Jiang Yubai's voice was particularly pleasant: "Can you..."
"Um?"
"Sit on my lap."
Hearing his request, Lin Zhixia was stunned for a second.
Jiang Yubai explained his reasons. He said that Lin Zhixia was closer to him and he could hear more clearly. He wrote on the notebook and Lin Zhixia could add content next to it. In this way, they could check for omissions and make up for the gaps more efficiently.
Lin Zhixia recalled that she had used a feather to tease the cat in Jiang Yubai's house. At this moment, all of Jiang Yubai's words turned into a feather and fell on her heart.
She held his shoulders, stood up, and sat on his legs.
Before Lin Zhixia sat down, Jiang Yubai put his left hand around her waist, still holding a pen in his right hand. He politely reminded her, "We just talked about the Cauchy distribution, Teacher Lin."
Teacher Lin's breathing was disordered: "Yes, I remember." He then said: "I will give you a question, if you answer it correctly..."
"Is there a reward?" Jiang Yubai asked in her ear.
"I'll just kiss you." Lin Zhixia declared.
Last night, Jiang Yubai had a dream.
He not only dreamed about the scene in the piano room, but also dreamed about Lin Zhixia sitting on his lap. So far, his dream has come true. Not only did Lin Zhixia not show any rejection, she was also willing to play the game of "I'll kiss you if you answer correctly" with him.
Jiang Yubai spread out a piece of draft paper and politely asked Teacher Lin to give him a question.
There was only one pen on the desk, which was held in Jiang Yubai's hand. Lin Zhixia held his index finger and gently twisted it, and he immediately gave her the pen. As long as you ignore his left hand on her waist, he is a polite and good student.
Lin Zhixia wrote the probability density function of the Cauchy distribution on a piece of paper. Before she finished, Jiang Yubai asked her, "Are you still teaching me the central limit theorem?"
"Yes." Lin Zhixia let go of the pen.
It was the first time she taught a class while sitting on Jiang Yubai's lap. Her mind was full of thoughts and imagination. How could she calm down and teach him the topic?
She asked a very simple question: "You see that samples from a Cauchy distribution do not obey this theorem. Why?"
If Jiang Yubai answered correctly, Lin Zhixia would kiss him. She didn't set detailed rules, let alone an upper limit on the reward, which meant that Jiang Yubai could keep asking her for kisses - and what would happen next? He was afraid that he would be unable to control himself.
Jiang Yubai pondered for a moment and nipped all his extravagant thoughts in the bud. He actually replied, "I'm sorry, Teacher Lin, I haven't learned Cauchy distribution."
He said this with great sincerity.
Lin Zhixia believed it to be true.
She didn't expect Jiang Yubai's math foundation to be so weak.
She explained the Cauchy distribution in detail and mentioned that one of the constraints of the central limit theorem is that the mean and variance of the probability density function exist and are finite, so the Cauchy distribution does not apply to the central limit theorem[2].
Lin Zhixia added: "The result of group sampling from the Cauchy distribution and normalizing the mean..."
Jiang Yubai continued: "The result is not Gaussian distribution, but Cauchy distribution."
"Correct answer!" Lin Zhixia was delighted.
Lin Zhixia thought that her teaching was very successful.
As Jiang Yubai's tutor, Lin Zhixia is dedicated to her job, conscientious in her duties, and always keeps her word. She quietly turned her head and kissed his cheek.
Jiang Yubai remained silent, raised his chin slightly, and looked at the bookshelf in the distance. He tightened his hands around her waist, but he didn't even call her "Teacher Lin". Lin Zhixia thought he was very interesting, and she couldn't figure him out, and her reactions were unpredictable.
Lin Zhixia sat sideways on his lap, hooked her arms around his neck, and stared at his Adam's apple.
Lin Zhixia has a strong curiosity. Jiang Yubai has an Adam's apple, but she doesn't, so she wants to know what it feels like to have such a thing. She leans close to his neck, and the warm and subtle breath brushes against his neck. He doesn't speak, nor does he stop her.
When Jiang Yubai first started playing the "tutor role-playing game", he had many scenarios and dialogue modes. But now, he has transformed into a sculpture that accepts everything, calm and self-sufficient, as if he is enshrined in a noble and holy temple.
Lin Zhixia found it more and more interesting and wonderful.
She kissed the bulge of his neck gently, as if touching a switch. Jiang Yubai held the armrests of the chair tightly and called her again, "Teacher Lin."
So much fun.
Their role-playing game is still going on.
Lin Zhixia said carefully, "I... I have never taken the college entrance examination, and I am not good at biology..."
She was about to say, "You come teach me biology," but Jiang Yubai interrupted her and said, "How can you be a tutor if you haven't taken the college entrance examination?"
As soon as these words were spoken, Lin Zhixia was confused.
Lin Zhixia confidently told him: "Many of my undergraduate classmates were recommended for admission, and so was I."
Jiang Yubai finally changed the topic to a normal one. His tense nerves relaxed a little, and he did not lose his composure in front of Lin Zhixia. He wanted to have further contact with her, but fortunately he finally held back. He said calmly: "Teacher Lin, let's continue studying."
Lin Zhixia's thinking process is completely different from Jiang Yubai's. She asked him very directly: "How did you feel when I kissed you? Tell me, I want to know. I want to write your words in my diary."
Jiang Yubai spread out a thesis. He translated the English into Chinese and whispered a summary, as if he was treating the thesis as a "Heart Purification Mantra". Lin Zhixia said, "You still don't answer me. This is the teacher's order."
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