From small town scholar to chief scientist

Chapter 251 "The Mathematical Principles of Zhouyi"

In fact, just before Zhouyi released the news, the School of Mathematics of Shangjing University even advertised its good geomantic omen in the official blog.
It is a courtyard house with unique and unimaginable advantages.

As a result, as soon as the news of Zhouyi was released, countless netizens went to Beijing University one after another,

Ask Shangjing University what you think.

In the past, the domestic mathematics circle was divided into six major schools, Shangjing, Chinese Academy of Sciences, Shangjing Normal University, Aurora, Nankai and Shanda.

But after Qiu Chengtong returned to China, the Qiu Chengtong Mathematical Science Center basically dominated the family.
In other words, Beijing University and the Chinese Academy of Sciences can talk to them a little bit,
The introduction of Fields Medal winner Effie Germanov by SUSTech also had a certain influence.

Up to now, Zhou Yi himself is the founder of Yuzhou Advanced Research Institute,
Then the entire Great Xia Kingdom School of Mathematics can only have new top five born.

The strongest must be the Yau Mathematical Sciences Center of Shuimu University, followed by the Yuzhou Advanced Research Institute.

Next are the Chinese Academy of Sciences, Shangjing University and South University of Science and Technology.

However, in the long run, the potential of Yuzhou Advanced Research Institute must be greater than that of Shuimu University Qiu Chengtong.

However, from the perspective of outsiders, especially those outside academia,
The Department of Mathematics of Shangjing University is still unique.

So many netizens asked the Department of Mathematics of Shangjing University what they thought of Zhou Yi's speech.

What else can they think, just wait and see the joke.

Originally, they didn't want to meet Zhou Yi head-on, but it was a coincidence that they bumped into each other.

[Why does Shangjing University give me a feeling of gloating? 】

[Nonsense, can Shangjing University take pleasure in other people's misfortune?Can you not be angry that the golden generation I have cultivated so hard has been poached by Zhou Yi? 】

[The above is right, Zhou Yi is Qiu Chengtong's apprentice, and the relationship between Zhou Yi and Qiu Chengtong is very good,
Can the Mathematics Department of Shangjing University be unhappy to see that the Yuzhou Institute for Advanced Study is now in such a turmoil? 】

[That's right, the Department of Mathematics of Shangjing University is probably jumping for joy now. 】

[Professor Zhou said that he will give an explanation, but he doesn't know what the explanation is, looking forward to the reversal. 】

[I really want to see Beijing University being slapped in the face by Professor Zhou Yi.Doing academics can still be related to Fengshui, it is simply a joke in the world. 】

[Indeed, metaphysics is still talked about in academics, why do we believe in science? 】

[One thing to say, the poor location of Chongqing Higher Court is probably the biggest impact on enrollment. 】

[Princeton University is still in a small town?Go there to study for a few years, and then you can live in a big city for the rest of your life,

I think this kind of choice should be a good choice. After all, people who can get high scores in the exam are geniuses, and they mature much earlier than ordinary people. 】

[Yes, after studying for 8 years, you will definitely become a leader in the industry in the future, there is no doubt about it. 】

People who eat melons on the Internet are looking forward to the follow-up of Zhouyi, waiting for the confrontation with Shangjing University.

But Zhou Yi didn't bother to reply to some of Aite's own comments.

After sending it out, Zhou Yi said to everyone in Yugao Court:

"Let's leave, everyone. I have enough confidence to beat the entire metaphysics world and make them recognize me as the new generation's patriarch."

Seeing that Zhou Yi was so sure, everyone couldn't say anything else, and said one after another:

"Okay, let's leave Professor Zhou first, and wait for your good news."

Zhou Yi said:

"it is good."

After they left, Zhou Yi started taking drugs and watching "Zhou Yi".

"The enhanced version of the focused capsule drawn in the lottery was used in the right place to learn "Book of Changes".

Anyway, this thing must be the best to use on the cutting edge. "

In two days, Zhou Yi read Zhou Yi thoroughly.

I have to say that "Book of Changes" is indeed a subject of great wisdom.
The mathematical knowledge used is comprehensive, and it is all mathematical knowledge developed after the 16th century.
It even involves a lot of modern mathematical knowledge.

Zhou Yi murmured alone in the room:

"It's no wonder that the people who studied the "Book of Changes" in the past are all masters of mathematics, and it basically contains mathematical knowledge.

If the knowledge of branches of mathematics such as group theory can be used, it can be further derived, and the so-called rumors about the bad geomantic omen of Yugaoyuan will be self-defeating. "

Zhou Yi closed his eyes and meditated for half an hour, then dictated in the room:

"Write the introduction first, and Chapter 11.1 is called "Summary of Mathematics Research of Yi Scholars in the Past Dynasties"."

Combining the conclusions of famous historical figures to demonstrate the development of mathematics in "Book of Changes",

Obviously it is more convincing, so Zhou Yi put this chapter in Chapter 1.

Masters of Yi studies in all dynasties have tirelessly studied mathematics in order to study "Book of Changes".
You disciples and grandchildren dare to say that "Book of Changes" does not require strong mathematical knowledge?
Is it to deceive the master and destroy the ancestor?

Zhou Yi's move directly put himself in the strongest position.

Once these people realize that mathematics has revolutionized the "Book of Changes", it is difficult to say whether "Zhouyi" is metaphysics or mathematics.

Next, Zhou Yi began to describe the development of mathematics in Zhou Yi,

Start with the relationship between set theory and "Book of Changes".

Zhou Yi began to say:
"Set theory is the foundation of modern mathematics, and it not only penetrates into various fields of mathematics, but also penetrates into many fields of natural science and social science.

German mathematician Cantor (G. Cantor, 1845-1918) first proposed the concept of set, and he published a series of papers on set theory between 1872 and 1897, laying the foundation for set theory. "

Zhou Yi first explained the origin of set theory, and also prepared for the next one. Zhou Yi continued to say:

""Xi Ci" said: 'Fangs gather together, and things are divided into groups.'

The 'class' and 'group' mentioned here are very close to the concept of 'set' in mathematics.

It will be more convenient, clear and precise to describe many propositions in the study of Yi Xue in the language of set theory, which will help reveal the essence of the problem.

This chapter first introduces some basic concepts of set theory, and then explains the relationship between Yi-learning problems and some basic concepts in set theory. "

Then Zhou Yi divided this big chapter into four subsections to narrate.

"Definition 2.2.3:
Let A_1, A_2, ..., A_n.It is a set of n, take element α_1 in A_1, take element α_2 in A_2, ... take element α_n in A_n,

Make an ordered n-element group (a_1, a_2, ..., a_n,), which is called an n-element sequence group of the set A_1, A_2, ..., A_n. A_1, A_2, ..., the set of all n-grams of A_n:

D={(a_1, a_2,..., a_n)丨a_1∈A_1, a_2∈ A_2,...,a_n∈A_n}
It is called the Cartesian product of the sets A_1, A_2, ..., A_n, and is written as:
D=A_1*A_2**A_n.

Special case: If A_1=A_2=...=A_n=A, then D is called the n-fold Cartesian product of A.

A subset R of A_1*A_2**A_n is called a relation of sets A_1, A_2,..., A_n.

Many concepts in the study of Yi Xue are closely related to the concept of the relationship of sets.

Let's just give an example, I believe all Feng Shui masters must be very familiar with it.

This should be Example 2.2.1.

The ancient book "Xi Ci" said: "There is Tai Chi in Yi, which produces Liangyi. Liangyi produces four images, and four images produce eight trigrams." '

He also said: "The gossip is in a row, and the image is in it. Therefore, it is important, and the line is in it." '

Let us leave aside the philosophical meaning of these words.

But from the point of view of set theory, Yi Gua set can be regarded as the Cartesian product of some other sets.For example:
Let A={1, 0} be the set of "two instruments", and make the double Cartesian product of A:
B=A*A={(1), (1), (1), (0)}
In this way, we can get a set of 'four images'.

Take the triple Cartesian product of A:
C=A*A*A={(1)(1)(1)(1)(1)(0) )(1)(0)}
Will get a 'gossip' set.

Then if we do the 6-fold Cartesian product of A, we can get the set of Yi Gua.

The process here is relatively simple and single, and readers are advised to prove it confidently. "

Zhou Yi left a piece of homework, after all, he wants to be the originator of this direction, so how can he do without leaving homework?

Let this group of metaphysics teachers experience the pain of mathematics students.

The pain of proving the problem.

Zhou Yi took a sip of water, moistened his throat, and continued:
"If we start from the set B of the "four images" and make the triple Cartesian product of B, we can also obtain a set of Yi Gua.

D=B*B*B.

Similarly, we can also start from the set C of "eight trigrams" and make the Cartesian product of C and C, and we can also get a set of easy hexagrams,

Due to the limited time and the relatively simple steps here, it is left as an exercise.

Then, we conduct further analysis, and the Yi Gua set D can also be regarded as some other forms of Cartesian products.

But the time is limited, and the process is relatively simple, leaving it as an exercise for the majority of Yi-learning enthusiasts. "

In each chapter, Zhouyi uses examples from "Zhouyi" or other ancient books as examples or exercises,
For this group of Yixue enthusiasts, when the time comes, this group of people can't do it, so they have to obediently beg themselves.

How many people are there who know both easy learning and mathematics?
Even after these people make it, can they still have their own authority?

You have to ask yourself.

The Book of Changes has already been calculated, and most of the entire metaphysical world will have to come to ask for themselves.

After finishing Chapter 2, the relationship between Zhou Yi and set theory, Zhou Yi started to write Chapter 3,

The relationship between Zhouyi and Boolean algebra.

Before each major chapter, Zhouyi must first write about the relationship between the mathematical knowledge involved and the "Book of Changes",

Otherwise, it would be impossible to attract this group of people who tirelessly study metaphysics.

"Boolean algebra arose first in the study of the laws of logical thought.

The British philosopher Boole (G. Boole, 1815~1864) used mathematical methods to study the laws of the relationship between sets and sets. His research work later developed into an independent branch of mathematics.

With the development of electronic technology, Boolean algebra has been widely used in automation technology and electronic computer technology.

A Boolean vector is an array of two numbers of 0 and 1 arranged in a certain order. It is widely used as a mathematical model to describe things with several factors, and each factor has two opposite states.

We will see that each hexagram of the Yi Gua set is a Boolean vector, and the Yi Gua set itself is a Boolean algebra.

Therefore, in this chapter I will introduce the first knowledge about Boolean vectors and Boolean algebra,
Introduce the relationship between Boolean vectors and Boolean algebra and easy learning. Before introducing these two concepts, first introduce the concept of operation. "

In this chapter, there is also a lot of content. In three sections, Zhou Yi once again left a lot of exercises.

Zhou Yi couldn't express his anger by not leaving exercises to insult their IQs.

Only by leaving the exercises can they know what the gap is. Zhou Yi had a flash of inspiration. Is there a better way for them to ask themselves?
But I couldn't think of it for a while, so I started the inner cylinder at the back.

Immediately afterwards, Zhou Yi started writing Chapter 4.

The relationship between Zhouyi and group theory.

First of all, it is the connection between the group theory and "Book of Changes".

"Group is an extremely important concept in modern mathematics. It was introduced in 19 by Galois, a young French mathematician in the 5th century, when he was studying the solution of algebraic equations of degree five or more.

Groups have very important applications in various branches of mathematics and in many theoretical and technical sciences.

For example, the Lorentz group in the theory of relativity and the Lie group in quantum mechanics are commonsense tools in modern science. Today, group theory has developed into a difficult branch of mathematics.

We will see that after properly defining the operation of the Yi Gua Set A, the Yi Gua Set A becomes a commutative group, which is isomorphic to the addition group modulo 2.

Therefore, it is of course possible to apply the basic knowledge of groups to the study of Yi Xue.

This chapter first introduces the basic concepts of groups, then proves that Yi Gua set A is a group, and discusses some properties of Yi Gua groups and their applications in the study of Yi studies. "

Zhou Yi continued:

"Theorem 4.1.2:

Suppose H is a non-empty subset of group G, and the necessary and sufficient condition for H to be a subgroup of G is: for any two elements a, b of H, there are ab^(-1)∈H.

The proof process is skipped here, because many mathematical foundations of group theory have been explained before,

I believe that with the level of the masters, it is already clear that practice makes perfect, and this simple proof should be a piece of cake.

Let's look at a few examples.

Example 4.1.1: ..

Example.
Example 4.1.3:

Because the inverse of the element a of the Yi Gua group is a itself, a^, =a.

Therefore, according to Theorem 4.1.2, to verify whether a certain subset H of Yi Gua group A is a subgroup of A, it is enough to verify that when a, b∈H, ab^(-1)=ab∈H .

That is, it only needs to verify that the multiplication of H to A is closed.

According to this, some interesting subgroups of A can be verified.

H_1={dry}={1, 1, 1, 1, 1, 1 } is the first-order subgroup of A (a finite group with several elements is called several-order group).

H_2={Qian, Kun}={(1, 1, 1, 1, 1, 1), (0, 0, 0, 0, 0, 0)} is the second-order subgroup of A.

The fourth-order subgroup of A and the eighth-order subgroup of A are left here as exercises for readers to practice due to limited time.

I believe that your wisdom must be no problem. "

After Zhou Yi finished talking about Chapter 4, he took another sip of water and checked the time. It was already three o'clock in the morning.

Zhou Yi smiled bitterly and said:
"I'm going to stay up all night again, but I can't finish writing even if I stay up all night. At most, I can finish "Zhouyi" and number theory, "Zhouyi" and combinatorial theory.

As for the "Book of Changes" and the theory of probability, the application of mathematics in the study of the Book of Changes will be discussed later. "

Zhou Yi rubbed his head, then continued to talk to Peony.

If it weren't for Peony's high intelligence, she could help write papers and typesetting,

A book of 100+ pages is simply impossible to write.

I saw Zhou Yi chanting:

"In Chapter 1, we talked about the concept of congruence in Qin Jiushao's "Yan Gua Fa Wei" and "Da Yan Zhi Shu" in "Zhou Yi·Xi Ci".

The concept of congruence is one of the most fundamental concepts in number theory.

The content of the traditional Yi Xue is the so-called image, number, reason, and accounting.Therefore, there are many places involving number theory in "Book of Changes", such as the number of heaven and earth, the number of divination, and the number of river maps.

However, most of the numbers are relatively simple.This chapter only introduces the relationship between the concept of congruence and Yi-learning.

In particular, the divining method in "Book of Changes·Xi Ci" involves many data;

2 for 'divide into two', 1 for 'hang one',

4 in 'Butterfly with Four', 3 in 'Three into Yao'.

For these data, Yi scholars have always regarded them as a mystery, can they be changed?
Why is the 'Number of Dayan' 50?
But its use is "nine out of forty" and so on.

These are long-standing unresolved issues in the study of Yi Xue.

I discuss these issues further in Chapter 8. "

I wrote until dawn, Zhou Yi really didn’t want to write anymore, because I was too sleepy,

It doesn't make any sense to write it all out.

The current five and a half chapters have been able to explain many issues.

Originally, Zhouyi planned to finish writing "Zhouyi" and number theory, "Zhouyi" and combinatorial theory, but now it seems unnecessary.

As long as people who study metaphysics are not stupid, they will carefully figure out the meaning of it,
Once you understand the profound meaning of it, you will learn from the masters of Yi studies in the Song Dynasty, and try to innovate and recreate the "Book of Changes".

For example, Shao Yong's "Huangji Jingshishu", "Tianyuanshu", "Siyuanshu" and so on.

The seemingly fantasy name is actually a study of mathematics or easy-to-learn content.

Many authors of fantasy fairy tale novels have taken it for secondary creation.

As for the content at the back of the book, Zhou Yi was going to break a chapter and ask them to update it by themselves.

Otherwise, it would be too cheap to write it out casually.

Zhou Yi felt that he was a well-known mathematician anyway, how could he do things that were too cheap?
If this group of people who study metaphysics don't blow themselves up to the sky, the content of a section of Zhou Yi will not be updated.

Moreover, Zhouyi specifically focuses on why Dayan's number is 50, but its use is "nine out of forty".

Can't this group of people kneel and sing conquest?
After finishing writing, Zhou Yi began to think about how to name it.

The formulation of this book will explode the entire metaphysical world.

As we all know, "Book of Changes" was created by absorbing the essence of "Lianshan Yi" and "Guizang Yi".

And the book "Book of Changes" was absorbed by Confucianism, Taoism, Buddhism and other schools of thought, so this book is very important for the declining schools of thought.
It must be a groundbreaking innovation.

After thinking about it again and again, Zhou Yi simply called it "The Mathematical Principles of Zhou Yi".

Hey, this "Book of Changes" is a pun here.

It's so beautiful, Zhou Yi thought proudly.

There was no written content, Zhou Yi still wrote a table of contents.

The relationship between "Book of Changes" and combination theory, the relationship between "Book of Changes" and probability theory, and the application of "Book of Changes" in Yi studies.

Before each missing chapter, Zhou Yi still made a description,
For example, the relationship between "Book of Changes" and combinatorial theory,

[Combinatorial mathematics is an ancient subject, a branch of mathematics that is still flourishing today. Its main research content is counting and configuration.

For example, using the two symbols of Yang Yao "One" and Yin Yao "One", take 6 symbols in order each time and arrange them into a hexagram. How many different hexagrams can be arranged in total?
This is a typical combinatorial counting problem.

Another example is "Xi Ci" which says: "The river produces maps, Luo produces books, and the sages follow them." After simplifying Luo Shu into "Nine Palace Maps",

It is equivalent to filling the 1 numbers 2, 3, 4, 5, 6, 7, 8, 9, and 9 in a 3*3 square, so that the three rows, three columns and two diagonal lines The sum of the three numbers is equal.

This is a typical configuration problem. Graph theory is a branch of mathematics separated from combinatorics in recent decades, and has been vigorously developed with the needs of computing technology.

For the sake of time, I will not write more here, and I will write when I am happy. 】

Combination theory is also widely used in today's computers, not to mention easy to learn.

For example, the relationship between "Book of Changes" and probability theory:

[Probability theory and mathematical statistics are a science that studies the regularity of random phenomena, and it is an important and active branch of mathematics.

The ancients regarded "Book of Changes" as a book of divination, and used Yi hexagrams for divination. When divination, a hexagram must first be obtained through a fixed procedure.

But which hexagram is obtained is not known in advance, and it is a random phenomenon.

Therefore, to study "Book of Changes", you must understand some basic knowledge of probability theory.

This chapter mainly introduces the relevant knowledge of classical profiles, especially the Bernoulli (Bernoulli, 1654-1705) profiles that are closely related to the ancient "Dieyarrow Cheng Gua".

But due to time reasons, I will not write it now. 】

Probability theory is closely related to robot learning, and Ding Jian is mainly researching this direction now.

And it's already eight o'clock in the morning, and many marketing accounts have already started making videos.
The copywriters are already in place, and there are all kinds of copywriting.

It depends on the results behind.

　Happy New Year, brothers and sisters!
　　
　
(End of this chapter)