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.
What you say you don’t see is that you are the one blowing the sky now.
Okay, okay, I'll let you finish all the good and bad words alone.
"Old Duan, look, how well written this is!"
Principal Lin also did not forget to take Duan Yongming to enjoy it together.
"That's it?"
Duan Yongming was too lazy to chat with him here, he was busy doing other things.
"There are so many things here, and if we just change them so rashly, it will probably be a little difficult for the students to accept it."
Principal Lin thought for a while.
"I will divide it according to the degree of acceptance and implement it in three stages. If possible, arrange it. It will take three weeks for students to gradually adapt."
Principal Lin is not without something.
Without something, can he really bring the Longjiang Experiment to a level that is on par with Longjiang No. 1 Middle School?
The internal education reform of Longjiang Experiment.
For now, only Duan Yongming and Lin Dong know that Lin Dong needs to rely on his own experience as a principal to make an evaluation and judge whether the final transformation is feasible.
He said that he was the person who knew the Longjiang experiment best in the school, and he was not exaggerating.
but.
After Xu Qingshan handed this material to Duan Yongming, he didn't think about it again.
Even if a small class in Qingbei is formed later, he will bring a few classmates he has selected there, and then occasionally take them with him.
But this kind of thing is mutually beneficial.
Xu Qingshan now has the qualifications to guide these top students in the Longjiang Experiment. He can also continue to consolidate his ability in exam-oriented education while using new methods of guidance.
Other times, he would devote himself entirely to probability theory.
Xu Qingshan is really interested in probability theory now.
In fact, probability theory can be traced back to the ancient Greek period and the Spring and Autumn Period and the Warring States Period.
Although Aristotle was engaged in philosophy, 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 contingency is an event that has no obvious cause or regularity.
This may sound simple.
But the big one is coming.
Our ancestors directly created the "Book of Changes" based on this distinction and connection between necessity and accident.
The Book of Changes has been circulated for thousands of years and is still the subject of research by many people.
Those engaged in philosophy study the Book of Changes, those engaged in mathematics study the Book of Changes, those engaged in theology also study the Book of Changes, and even those engaged in meteorology also study the Book of Changes.
Guys like Xu Qingshan who don't know what they are doing are now holding a copy of the "Book of Changes" in their hands.
"No, Shan'er, don't you want to read mathematics? Why do you see Zhouyi going there?"
Ye Xincheng watched Xu Qingshan flipping through the ancient book that looked like a magic book, and then looked at the mathematics paper in his hand.
He suddenly felt that the gap between him and Xu Qingshan was no longer just about studying.
"I study probability theory. Isn't it normal to read the Book of Changes?"
Seeing that Ye Xincheng was puzzled, Xu Qingshan could only take some time to explain to him.
"Here, take a look at this picture."
Xu Qingshan moved the book in front of Ye Xincheng and showed him the Bagua picture.
"I can't understand."
Ye Xincheng's eyes were dim and he couldn't tell which one was which and what it was for.
"Just don't understand."
Xu Qingshan pointed at this picture and said.
"The sixty-four hexagrams corresponding to the Bagua Diagram in the Book of Changes are one of the symptoms of our country's exploration of random phenomena in the early civilization."
"These sixty-four hexagrams are composed of six lines. Each line has two states: yin and yang. It is divided into yang and yin."
"The ancients used the method of throwing three copper coins to randomly generate the state of six lines to form the final hexagram, and then combined the lines of the Book of Changes and the stems and branches of time to divine the development process and results of things."
"This is actually a method of simulating random phenomena and random processes by tossing a coin. It is essentially a special kind of probability."
Xu Qingshan said this.
Ye Xincheng seemed to understand.
After hesitating for a moment, he finally asked his curious question.
"So is Zhouyi's fortune telling accurate?"
Xu Qingshan glanced at Ye Xincheng speechlessly.
"You'd better do your math paper."
but.
Xu Qingshan's use of Zhouyi to study mathematics did not last long, because it was just a trace of human civilization's preliminary understanding of probability theory.
Ye Xincheng watched Xu Qingshan put the "Book of Changes" back on the table, and then took out another "Probability Theory".
He was doing the questions, but out of the corner of his eye he could always catch a glimpse of the cover of the "Theory of Probability".
A little itchy.
"Then probability theory has existed thousands of years ago?"
Xu Qingshan heard Ye Xincheng's question and put down the book in his hand.
This guy has so many problems.
But thinking about the Feynman learning method, I just happened to explain it to him and see how well I mastered it.
"If it is probability theory in a narrow sense, it should start from the classical probability of the 17th century." "The real beginning of probability theory is currently recognized as coming from gambling."
Xu Qingshan closed the book and said seriously.
"gamble?"
Ye Xincheng also put down his paper and opened his eyes wide as if he was hearing something horrifying.
"It started out because of a bet. In 1654, when the French mathematician Blaise Pascal and the French lawyer Pierre Fermat were writing letters and chatting, they talked about a bet, and then the two people discussed Questions arose about this bet.”
"Actually, the question is very simple, that is, what should we do and how should we bet to win more money."
Xu Qingshan's popular science opened Ye Xincheng's horizons.
Even he, who doesn't really like mathematics that much, found it interesting and enjoyed it.
"So, then entertainment is really the ladder that promotes human progress?"
"If you insist on saying that, I agree."
Xu Qingshan smiled while listening to Ye Xincheng's imaginative theory.
“In this conversation about gambling, Blaise Pascal and Pierre Fermat introduced for the first time in history the concept of mathematical expectation, expected value.”
"Is this the mathematical expectation we use when doing probability and statistics questions in mathematics now?"
Ye Xincheng felt that knowledge entered his head in a strange way.
"Yes, you will know from the English translation. In fact, mathematical expectation is a weighted average of the possible results of a random event, which is used to measure the average outcome of the event."
"Theoretically, as long as the number of events is large enough, the final result will inevitably tend to the desired 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 even went to the casino to try it, which was euphemistically called practical testing. Actually just go out and make some extra money.”
Xu Qingshan smiled.
He suddenly remembered that he had seen the news in his previous life. There was a gambling team composed of mathematicians and computer experts from famous schools. They went to Las Vegas to perform various calculations, and unexpectedly won a lot of money and ran away. In the end, they were blacklisted by the casino. .
So.
Is being a betting dog the final destination of a mathematician?
Hearing this, Ye Xincheng narrowed his eyes and looked at Xu Qingshan.
"I said, Shan'er, why don't you learn this probability theory to the highest level, and then we'll 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 really only play math games with you?"
Ye Xincheng scratched his head and smiled, but then he reacted.
"No, I was born before you."
"When I say you are young, I don't necessarily mean your age."
Xu Qingshan said disdainfully.
Ye Xincheng glanced down subconsciously, becoming angry with shame.
"you!"
"You're anxious, it seems you guessed it right."
"I don't."
"Oh, let me continue."
Xu Qingshan's calm reply made Ye Xincheng grind his teeth.
"Actually, there are quite a few people who study probability theory because of gambling."
"In 1657, the German mathematician and physicist Christian Huygens wrote "On Calculation in Gambling."
"You also wrote a book specifically on gambling?"
Ye Xincheng was speechless.
"Does this count as betting on dogs to promote the development of a subject?"
"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 and the multiplication theorem. The addition theorem states that when two events are mutually exclusive, the sum of their probabilities is equal to the sum of their respective probabilities; the multiplication theorem states that when two events are independent, they occur simultaneously. The probability of is equal to the product of their respective probabilities.”
"Actually, the so-called mutual exclusion and independence can be understood as the difference in time order. Mutual exclusion means that they cannot occur at the same time, and independence means that they can occur at the same time."
"Like the intersection and union of sets and the coverage of geometry that we learned, think about it, is there a concrete consistency in mathematics?"
Xu Qingshan finished.
Ye Xincheng's eyes widened and he thought about it carefully.
"It's true."
"Of course, so sometimes clarifying abstract concepts and concrete representations can better help us learn mathematics well."
"Don't think that you won't have to worry about mathematics in the future if you study materials. You won't be able to escape any advanced mathematics or line generation by then."
Xu Qingshan slightly threatened Ye Xincheng.
Ye Xincheng frowned.
"I just like to do experiments."
"For experiments, you just kill them and don't bury them. Don't you need to analyze the experimental data after the experiment?"
Xu Qingshan exposed Ye Xincheng's dream of escaping.
"Okay, then I'd better learn high school mathematics first. But, is what you just talked about probability theory? Is it actually quite fun 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 this look.
"This is just classical probability. It is a prerequisite theory of probability theory. It can be regarded as setting a basic framework for probability theory."
"The really interesting probability theory is yet to come."
(End of chapter)