At eight o'clock in the morning, Jiang Yubai showed up on time. When he saw Lin Zhixia, he naturally held her hand 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."
And 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", please play it for me."
Jiang Yubai began to play "Autumn Whisper". He hadn't played 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 arms 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 floor-to-ceiling windows, and the gauze curtains filter down a piece of fine and fragmented green shadows, which happen 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 the dream I had last night.”
At this moment, he clenched her fingers, and his passion became even deeper.
Lin Zhixia did not give any response.
She jumped off the piano cover, her hands were numb, her legs were weak, and her mind was in chaos. She suddenly realized that many things could not be simulated by imagination alone. For example, she had read literary masterpieces from ancient and modern times, both at home and abroad, since she was a child, but she never understood why the clever protagonists often fell hard in the pursuit of love.
Now, she herself clearly tasted the strange feeling of being out of control.
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 still 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 extended a hand to her. She immediately took his hand, interlocking their fingers, and they went to the study.
The study room had good lighting, and rows of bookshelves stood tall, like a small library. The carpet was embroidered with delicate patterns, and on the long ebony table by the window was a computer and a stack of papers, and there were two ergonomic chairs with adjustable heights beside the table - these were obviously the seats for Jiang Yubai and Lin Zhixia.
Lin Zhixia sat down slowly and said in a very confident manner: "You sit down too. From now on, I am the teacher you hired."
"Teacher Lin." Jiang Yubai said.
Lin Zhixia nodded: "Yes, we should study in the manner of studying. When I tutor you, you should call me Teacher Lin, and don't change your words."
Jiang Yubai pushed the edge of the table, and the wheels of the chair 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 rich teaching experience."
The harder Lin Zhixia tried to act businesslike, the more Jiang Yubai wanted to cross 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 actually claimed that "your classmates' foundation is better than mine."
Was Jiang Yubai looking for her for tutoring, 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, the test points for each course are limited, 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. Some specific knowledge points were also marked under each major category. For example, the probability theory column included expectation and regression function, law large numbers and central limit theorem [1], and many other contents.
Lin Zhixia asked very responsibly: "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."
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. Since graduating from junior high school, she had never tutored him step by step 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. So he paused, pointed at the line of English, and whispered: "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 value a for each group. After standardization, a1, a2... .an will converge to a normal distribution."
She glanced at him: "The Central Limit Theorem is one of the most important theories in Probability Theory. We can continue to expand it..."
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 in a notebook and Lin Zhixia could add content next to it, so that they could fill in the gaps more efficiently.
Lin Zhixia recalled that she once used a feather to tease the kitten at Jiang Yubai's house. At this moment, all of Jiang Yubai's words turned into a feather and fell on her heart.
She held onto 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." Then he said: "I will give you a question. If you answer it correctly..."
"Is there a reward?" Jiang Yubai asked in her ear.
"I'll 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. Lin Zhixia not only did not show any rejection, but was also willing to play the game of "I will kiss you if you answer correctly" with him.
Jiang Yubai spread out a piece of draft paper and politely asked Teacher Lin to set the questions.
There was only one fountain pen on the desk, which was held by Jiang Yubai. Lin Zhixia took hold of his index finger and gently scratched it, and he immediately gave her the fountain pen. As long as you ignore his left hand around 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 sat on Jiang Yubai's lap to teach a class. Her mind was full of thoughts and imagination. How could she calm down and explain the questions to him
She asked a very simple question: “You noticed that samples from a Cauchy distribution do not apply the 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 thought for a moment and nipped all his unrealistic thoughts in the bud. He actually replied: "I'm sorry, Mr. 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 meticulously 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 pleasantly surprised.
Lin Zhixia thought that her teaching was very successful.
As Jiang Yubai's tutor, Lin Zhixia is dedicated to her job, fulfills her duties, and 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 hand around her waist, but he didn't even call her "Teacher Lin". Lin Zhixia thought he was very funny, and she couldn't figure him out, and all kinds of reactions were hard to predict.
Lin Zhixia sat sideways on his lap, hooked her hands around his neck, and stared at his Adam's apple.
Lin Zhixia has a strong and vigorous 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 moved closer to his neck, and the warm and subtle air flow brushed across his neck. He didn't speak, nor did he stop her.
When Jiang Yubai first started playing the "tutor role-playing game", he had many scene settings and dialogue modes. But now, he has transformed into a sculpture that accepts everything, quiet and self-sustaining, as if he is enshrined in a noble and holy temple.
Lin Zhixia found it more and more interesting and wonderful.
She gently kissed the bulge of his neck, as if touching a great switch. Jiang Yubai held the armrests of the chair tightly with both hands and called her again: "Teacher Lin."
So much fun.
Their role-playing game is still going on.
Lin Zhixia said carefully, "I... I didn't take the college entrance examination, and I wasn't good at biology..."
She was about to say, "You come and teach me biology," but Jiang Yubai interrupted her, "How can you be a tutor if you haven't taken the college entrance examination?"
As soon as this question was uttered, 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 turned the topic back to normal. 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 train of thought was 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 paper. He translated the English into Chinese and whispered a summary, as if he was treating the paper as a "Heart Purification Mantra". Lin Zhixia said, "Why don't you answer me? This is the teacher's order."