Just turned over a new leaf and became a wise and intelligent student

Chapter 110: Using the Book of Changes to Study Mathematics (13)

"As expected of Qingshan!"

Principal Lin held the folder in his hand and muttered to himself.

Duan Yongming pursed his lips.

The one who said he didn't want to watch it is you, but now you are the one who is praised to the sky.

Okay, okay, I’ll let you say all the good and bad things by yourself.

"Look, Lao Duan, this is so well written!"

Principal Lin did not forget to pull Duan Yongming to appreciate it together.

"So that's it?"

Duan Yongming was too lazy to chat with him, he was busy doing other things.

"There are so many things here. If we just change them rashly, it might be difficult for students to accept it."

Principal Lin thought about it.

"I will divide it into three phases according to the degree of acceptance. If it is feasible, I will arrange it and give students three weeks to gradually adapt."

Principal Lin also has something to offer.

Without something like that, could he really bring Longjiang Experimental School to the same level as Longjiang No. 1 Middle School?

Regarding the internal educational reform of Longjiang Experimental School.

For now, only Duan Yongming and Lin Dong know the answer. Lin Dong needs to make an assessment and judgment based on his experience as a principal to determine if the transformation is feasible.

He said that he was the person who knew Longjiang Experimental School best in the school, and he was not exaggerating.

but.

After Xu Qingshan handed the materials to Duan Yongming, he no longer thought about what happened here.

Even if a small class of Peking University and Tsinghua University was formed later, he would bring a few of his selected classmates with him and teach them occasionally.

But this kind of thing is mutually beneficial.

Xu Qingshan is now qualified to guide the top students of Longjiang Experimental School. He can also continue to consolidate his abilities in exam-oriented education while using new guidance methods.

The rest of the time he would devote himself entirely to probability theory.

Xu Qingshan is indeed very interested in probability theory now.

In fact, probability theory can be traced back to ancient Greece and the Spring and Autumn Period and the Warring States Period.

Although Aristotle was a philosopher, he did pay attention to the difference between necessity and contingency.

Aristotle believed that necessity is an event that occurs according to causes and regularities, while chance is an event that occurs without apparent causes or regularities.

This sounds simple enough.

But the big one is coming.

Our ancestors directly created the "Book of Changes" based on the distinction and connection between necessity and chance.

The Book of Changes has been passed down for thousands of years and is still the subject of study for many people.

Philosophers study the Book of Changes, mathematicians study the Book of Changes, theologians study the Book of Changes, and even meteorologists study the Book of Changes.

A guy like Xu Qingshan, who doesn't even know what he is doing, now has a copy of the "Book of Changes" in his hand.

"No, Shan'er, you are here. Didn't you want to study mathematics? Why did you end up studying Zhouyi?"

Ye Xincheng watched Xu Qingshan muttering in a mysterious manner as he flipped through the ancient book that looked very mysterious, and then looked at the math paper in his hand.

He suddenly felt that the gap between him and Xu Qingshan was no longer just about study.

"I'm studying probability theory, so isn't it normal for me to read the Book of Changes?"

Seeing that Ye Xincheng was puzzled, Xu Qingshan had no choice but to take some time to explain it to him.

"Come, take a look at this picture."

Xu Qingshan moved the book in front of Ye Xincheng and asked him to look at the Bagua diagram.

“I don’t understand.”

Ye Xincheng's eyes were blurry and he couldn't tell which was which or what it was used for.

"Just don't understand."

Xu Qingshan pointed at the picture and said.

"The sixty-four hexagrams corresponding to the eight trigrams in the Book of Changes are one of the representations of random phenomena explored in the early days of Chinese civilization."

"These sixty-four hexagrams are composed of six lines, each of which has two states, yin and yang, and is divided into yang lines and yin lines."

"The ancients used the method of throwing three copper coins to randomly generate the state of the six lines to form the final hexagram, and then combined the hexagrams of the Book of Changes and the stems and branches of time to predict the development process and results of things."

"This is actually a method of simulating random phenomena and random processes by tossing a coin, which is essentially a special kind of probability theory."

Xu Qingshan talked about this.

Ye Xincheng seemed to understand but not quite.

After hesitating for a moment, he asked his curious question.

"So is Zhouyi fortune-telling accurate?"

Xu Qingshan glanced at Ye Xincheng speechlessly.

"You should do your math test."

but.

Xu Qingshan's use of the Book of Changes to study mathematics did not last long, because it was just a tracing back of human civilization's initial understanding of probability theory.

Ye Xincheng watched Xu Qingshan put the "Book of Changes" back on the table, and then took out another book on "Probability Theory".

He was doing the questions, but his peripheral vision always caught a glimpse of the cover of the book "Probability Theory".

I feel a little itchy.

"So probability theory has existed for thousands of years?"

Xu Qingshan heard Ye Xincheng's question and put down the book in his hand.

This kid has so many problems.

But thinking about the Feynman learning method, I just told it to him to see how much I have mastered.

"If we are talking about probability theory in a narrow sense, we should start from the classical probability in the 17th century." "It is generally recognized that the real beginning of probability theory came from gambling."

Xu Qingshan closed the book and spoke seriously.

"gamble?"

Ye Xincheng also put down the paper and opened his eyes wide as if he was listening to something horrifying.

"It all started with a bet. In 1654, French mathematician Blaise Pascal and French lawyer Pierre Fermat were chatting over letters when they talked about a bet. Then the two of them started discussing the issue of the bet."

“In fact, the problem is very simple, that is, what should we do and how should we bet to win more money.”

Xu Qingshan’s science popularization broadened Ye Xincheng’s horizons.

Even he, who actually doesn't like math that much, found it interesting and listened with great interest.

"So, entertainment is really the ladder that promotes human progress?"

"If you insist, I agree."

Xu Qingshan listened to Ye Xincheng's imaginative theory and smiled.

"In this conversation about gambling, Blaise Pascal and Pierre Fermat introduced the concept of mathematical expectation, expected value, for the first time in history."

"Is it the mathematical expectation that we use when we are doing probability and statistics problems in mathematics?"

Ye Xincheng felt that knowledge entered his head in a strange way.

"Yes, you can tell from the English translation that mathematical expectation is actually a weighted average of the possible outcomes of a random event, which is used to measure the average outcome of the event."

"In theory, as long as the number of events is large enough, the final result will inevitably tend towards the expected result."

"So by calculating mathematical expectations, Blaise Pascal and Pierre Fermat were able to solve the probability problems involved in various gambling games. At that time, they went to the casino to try it out, under the guise of practical testing, but in fact they went to make some extra money."

Xu Qingshan smiled.

He suddenly remembered that he had read in the news in his previous life. There was a gambling team composed of mathematicians and computer experts from prestigious universities. They went to Las Vegas, made various calculations, and won a lot of money and ran away. In the end, they were blacklisted by the casino.

so.
Is being a gambler the ultimate destiny for mathematicians?
When Ye Xincheng heard this, he narrowed his eyes and looked at Xu Qingshan.

"I say, Shan'er, why don't you learn probability theory to perfection, and then we can go..."

"Don't even think about it."

Xu Qingshan rolled his eyes at Ye Xincheng.

"You are still young and don't understand the dangers of the world. Do you think casinos are really just playing math games with you?"

Ye Xincheng scratched his head and smiled, but then he reacted.

"No, I was born earlier than you."

"When I say you are young, I don't necessarily mean your age."

Xu Qingshan said disdainfully.

Ye Xincheng subconsciously glanced down and became angry.

"you!"

"You are anxious. It seems that you guessed it right."

"I do not have."

"Oh, let me continue."

Xu Qingshan's calm response made Ye Xincheng grit his teeth.

“In fact, many people study probability theory because of gambling.”

"In 1657, German mathematician and physicist Christian Huygens wrote a book called On Calculation in Gambling."

"And he wrote a book specifically about gambling?"

Ye Xincheng was shocked.

"Does this count as gamblers pushing a new direction for the development of a discipline?"

"That certainly doesn't count."

Xu Qingshan replied.

“Because gambling itself is a mathematical problem, it naturally attracts attention. This book begins to systematically study probability theory.”

"Huygens proposed the addition theorem, which states that when two events are mutually exclusive, the sum of their probabilities is equal to the sum of their individual probabilities; and the multiplication theorem, which states that when two events are independent, the probability of their simultaneous occurrence is equal to the product of their individual probabilities."

"In fact, the so-called mutual exclusion and independence can be understood as different time sequences. Mutual exclusion means that they cannot happen at the same time, while independence means that they can happen at the same time."

"Like the intersection and union of sets and geometric covers that we learn, think about it, is there a concrete consistency in mathematics?"

Xu Qingshan finished speaking.

Ye Xincheng opened his eyes wide and thought about it carefully.

"It's true."

"Of course, so sometimes clarifying abstract concepts and concrete representations can help us learn mathematics better."

"Don't think you don't have to worry about math because you're studying materials science. You won't be able to escape advanced math and linear algebra when the time comes."

Xu Qingshan threatened Ye Xincheng a little.

Ye Xincheng looked worried.

“I just like doing experiments.”

"You're doing an experiment, you just kill people and don't bury them. Don't you need to analyze the experimental data after the experiment?"

Xu Qingshan shattered Ye Xincheng's dream of escape.

"Okay, then I'd better learn high school math first. But, what you just talked about, is that probability theory? It seems quite interesting and not complicated?"

“Not complicated?”

Xu Qingshan raised his eyebrows and looked at Ye Xincheng with eyes full of pity and love.

Ye Xincheng felt like a three-year-old child under such a gaze.

"This is just classical probability, which is a prerequisite for probability theory and provides a basic framework for probability theory."

"The really interesting probability theory is still to come."

(End of this chapter)