Into Unscientific

"."

Looking at Ye Duzheng who had been waiting for a long time.

Xu Yun was only slightly taken aback, then quickly nodded and said:

"Okay, Director Ye has instructions, how dare I, a little soldier, refuse to follow?"

Ye Duzheng waved his hands quickly when he heard the words:

"Hey, Comrade Han Li, you're joking."

Then he looked around, pointed to a stone table under the shade of a tree and said:

"Comrade Han Li, why don't we go there for a chat. There are chairs and the sun is not too bright."

Xu Yun had no objection.

At the same time, at the moment when he looked away from Ye Duzheng.

He couldn't help but glance at the middle-aged man standing beside Ye Duzheng.

This person looks about forty or fifty years old and is plainly dressed.

The hair on the forehead is sparse, the apple muscles are conspicuous, and the teeth are slightly buckled.

Do not know why.

Although Xu Yun didn't recognize this person's identity, he always felt that the other person was vaguely familiar.

If nothing else.

This should also be a famous person.

However, the other party's appearance is not so clear that Lu Guangda and Lao Guo can recognize their identities at a glance, so Xu Yun can only temporarily suppress this feeling back to the bottom of his heart.

Anyway, when we are going to chat next, Ye Duzheng should introduce the identity of the other party.

The stone table was only less than 30 meters away from where they were, and it could be seen that this was a place specially chosen by Ye Duzheng.

Come prepared.jpg.

Then the few people walked for a while, and soon came to the stone table.

Ye Duzheng first blew the dust on the stool with the strange man, brushed off the fallen leaves, and sat down straight down.

After being seated.

Ye Duzheng coughed lightly, patted the shoulder of the middle-aged man beside him, and introduced to Xu Yun:

"Comrade Han Li, let me introduce you. This is my friend from Yanjing, Comrade Qian Yi."

"He is the workshop supervisor of the base boiler factory. He is currently in charge of some projects related to water heating. Today, he will drop by and come out with me for a walk."

Qian Yi?

Hear the name.

Xu Yun's eyebrows under the bandage raised heavily.

Mentioned long ago.

Today's ordinary workers in Factory 221 may not be so mysterious, but the scientific researchers basically use pseudonyms.

So from the moment I knew I came to Factory 221.

Xu Yun had a very firm consciousness in his heart:

After hearing a person's name, first suspect that it is a fake name.

And the middle-aged man in front of him, Xu Yun, was vaguely familiar, so it was obviously impossible for him to be an unknown person.

In other words.

Qian Yi must also be a pseudonym!

However, most people's pseudonyms generally do not change their surnames, that is, most of the other party's surname is Qian.

etc!

Surname Qian?

Think here.

Xu Yun stayed on the opponent's plump apple muscles and hairstyle for another two seconds, and a guess suddenly popped up in his mind.

Could it be that this is.

Academician Qian Bingqiong among the three coins?

Then Xu Yun quietly looked at "Qian Yi" for a few more times, and became more and more sure of his judgment.

After all, this apple muscle and hair volume are really representative.

This is a real big guy.

Qian Bingqiong is one of the most important instigators of Huaxia's nuclear industry, and he is also one of the earliest members of Huaxia's academic department—a later academician. His wife He Zehui is also a well-known female academician.

Done.

Speaking of the famous three coins in later generations, many people often think that Qian Bingqiong, Qian Weichang and Qian Xuesen are related by blood.

But in fact, these three money are not father and son brothers, they are just branches of the same surname.

For example, Qian Bingqiong's branch is Huzhou Qian's.

Mr. Qian Xuesen belongs to the Hangcheng Qian family.

Mr. Qian Weichang's is Liangxi Qian's.

Among them, the Liangxi Qian family also produced the father and son Qian Jibo and Qian Zhongshu. Counting the local neighbors, there were a total of dozens of Chinese academicians-this is really not an exaggeration.

For example, Qian Zhonghan, Qian Linzhao, Qian Lingxi, and Qian Yitai are all direct descendants or offshoots of the Qian family in Liangxi. If they write out all their names, it is estimated that some idiot author will be scolded for hydrology.

alright.

The line of sight returns to reality.

At this moment, Qian Bingqiong was sitting beside Ye Duzheng with a smile on his face, and he really looked like an ordinary boiler worker or just a passerby.

So Xu Yun had no choice but to pretend he didn't know anything and nodded to Qian Bingqiong, which was regarded as a greeting.

After the formalities are over.

Xu Yun turned his gaze to Ye Duzheng again, and asked him hesitantly:

"Director Ye, I don't know why you came to see me today."

Ye Duzheng was silent for a moment when he heard the words, then sighed slightly, and said:

"Comrade Han Li, to tell you the truth, I came here specially to clear up your doubts."

Xu Yun blinked:

"Confused?"

Ye Duzheng did not directly explain the reason, but first raised a question:

"Comrade Han Li, my mentor is Carl Gustav Rossby. I wonder if you have heard of this name?"

"Rosby?"

Xu Yun blinked and recalled:

"The one who studies atmospheric turbulence and boundary layer theory? The Rossby radius is also very famous, but I can't remember whether it's from Germany or Sweden."

It's a coincidence.

As a non-meteorological physics practitioner, Xu Yun only knows three or five meteorologists—of course, excluding Chinese seniors like Ye Duzheng and Zhu Kezhen.

And among these three or five people, there happened to be Rossby.

After all, this big guy introduced wave theory into meteorology, and he belongs to a famous physicist in modern meteorology.

In a sense.

His fame is almost as famous as Piekenis.

In addition, the Rossby radius is also a very well-known physical concept, which has a wide range of extensions in later generations.

"That's right, it's him, a Swede."

Ye Duzheng raised his brows, and seemed a little pleased that Xu Yun had heard about his mentor:

"Rosby's mentor is also one of the proposers of numerical weather forecasting, and has worked in MIT and the University of Chicago."

"Ten years ago, he returned to Stockholm and became the director of the Meteorological Center at Stockholm University. He died of illness four years ago."

That's all.

The color of memory in Ye Duzheng's eyes receded slightly, replaced by a complicated look:

"Mr. Rossby has always believed that the atmosphere above our heads is a random system. The so-called solution to the atmospheric wave equation is actually just an approximate solution rather than an exact solution."

"This is also a fairly mainstream view in the world at present, and even for a long time, I also uphold this attitude."

"but."

Speaking of which.

Ye Duzheng couldn't help but look at Xu Yun, let out a foul breath, and said:

"But after Comrade Han Li helped me build that model, I feel more and more that this theory is not correct."

"I always feel that the atmospheric system is not completely random, but another very mysterious situation that can be mastered by calculation."

"What's more, I did an experiment a few days ago."

Xu Yun was startled again, subconsciously asked:

"What experiment?"

Ye Duzheng pondered for a moment, then picked up his briefcase from his side.

He rummaged through it a few times, quickly took out a black notebook, and handed it to Xu Yun:

"Comrade Han Li, take a look at this."

After realizing that Xu Yun might not have the ability to pick up heavy objects, Ye Duzheng deliberately turned the notebook to the page he wanted to display.

Xu Yun lowered his head for a few glances, then raised his head in surprise:

"Director Ye, is this the simulation result of two weather data?"

"Yes."

The expression on Ye Du's face was very solemn, pointing to the data above, he explained:

"To be precise, this is the simulation result of two sets of extremely small difference data."

"The circulation field parameter of the first data is 1.14514, and the parameter of the second data is rounded to 1.1452 by me. The remaining 19 sets of data are all the same."

"However... it's such a small difference, but the final derivation results are far apart by hundreds of thousands of miles."

"The former will have clear weather in seven hours, while the latter will have a torrential rain three hours later."

Ye Duzheng himself didn't notice it.

When he said this, his fingers were trembling a little.

In fact, as early as a week ago, that is, the night when the data model was derived, Ye Duzheng had talked with Tao Shiyan about some things.

At that time, he even named his guess, Taisu System.

But at that time, Ye Duzheng was more inclined to conjecture, without much actual evidence to support it.

What prompted him to have this idea was not data or phenomena, but a weather model he built with the help of Xu Yun, which had never been done before.

However, just a few days ago.

An accident happened.

At that time, in view of the great contribution made by the Meteorological Center in weather forecasting, the superior department offered to reward the members of the Meteorological Center materially.

After reporting the rewards to the group.

Ye Duzheng suddenly made a request out of nowhere:

He personally does not need any rewards, but only hopes that the capital can free up a small part of the computing power of the 104 computer to help him simulate the calculation results once, and only one parameter will be changed in the whole derivation process.

After evaluation, the superior department thought that this request was not too much, so they allowed machine 104 to cooperate with him to do a simulation.

However, unexpectedly

The results obtained by the two initial parameters of 1.14514 and 1.1452 are as different as the hair volume of Zhu Shimao and Chen Peisi!

This result also alarmed Mr. Zhu Kezhen in the capital, so Mr. Zhu changed his mind and intercepted the parameters from the middle part to modify the simulation.

Although the modification of non-initial parameters this time still has some changes in the results, the degree of difference is far from that of the first time.

In other words.

The model constructed by Ye Duzheng is extremely sensitive to the initial conditions.

At the same time, this sensitivity is not completely random, but a more complex discrete state—otherwise, Zhu Lao's experimental results should be equally biased.

Think here.

Ye Duzheng couldn't help taking a deep breath, and said to Xu Yun:

"Comrade Han Li, you are very familiar with the principles of weather Doppler radar, and you are more knowledgeable about weather data than I am."

"So I came to you today to ask you one thing, what is the state of our atmospheric system?"

"Is it extremely precise, or is it completely random? Or is it some kind of approximation that is infinitely close to precision?"

"."

Looking at Ye Duzheng with a puzzled expression on his face.

In Xu Yun's heart, he couldn't help feeling a strong surprise.

If the weather Doppler radar is the backhand he considered when he was in the damper.

Then Ye Duzheng's situation at this time was completely out of his expectation, and it could even be said to be far out of his control.

At least Xu Yun would never think of it anyway.

Ye Duzheng actually skipped over the numerical weather forecast and ran directly to .

Chaos system!

That's right.

Chaos system!

well known.

The cognition of the world in the modern physics community is in a progressive state, and the version is constantly being optimized and updated.

First of all, Einstein's theory of relativity broke Maverick's absolute space-time view.

Then the creation of quantum mechanics revealed the randomness and uncertainty of the movement of microscopic particles.

The third stage is the present period.

That is, the study of randomness in the deterministic framework leads to the .

chaos theory.

Chaos theory was first proposed in 1963, some time before now.

At that time, meteorologist Edward Norton Lorenz established a simplified weather model to simulate weather conditions.

This model uses a total of 12 parameters to represent basic meteorological characteristics, such as air pressure, temperature, etc., which is much simpler than the 20 parameters Ye Duzheng used at this time.

during one simulation.

In order to ensure the accuracy of the data, Lorenz decided to rerun part of the program.

But to save time.

He didn't run the model from scratch, but from some point in the middle of the run as a starting point.

Students who are familiar with numerical operations should know it.

The program remains unchanged, and the initial point is from the result of the previous operation.

So in theory, no matter how many times you run it, the final result will be the same.

But this time it was different.

At that time, the results of Lorenz's second run were quite different from the last one, and the deviations were irregular.

It's as if the result came from a completely different program.

After careful inspection at the earliest, Lorenz found that he had simplified a data by two decimal points during the transcription process.

It is such a slight deviation that leads to completely different operating results.

In the end, Lorenz proposed the famous chaos theory in 1963, the most representative of which is the sentence of the butterfly effect:

"A butterfly in the Amazon rainforest of South America, with an occasional flap of its wings, can cause a tornado in Texas two weeks later."

Of course.

One thing that needs to be explained is

The original meaning of this sentence is not to say [butterfly wings caused a storm].

but

[The causes of the storm are so complex that we need to know the wings of each butterfly to be able to predict this outcome. 】

The emergence of chaos theory has completely pushed the physics world to another direction.

Think here.

Xu Yun couldn't help but took a deep breath, and made a decision in his heart.

Although Ye Duzheng's situation was not what he expected, Edward Norton Lorenz did not have any conflicts with Xu Yun.

But how can there be any reason to shirk such a good thing delivered to your door?

So Xu Yun pondered for a moment, and quickly said to Ye Duzheng:

"Director Ye, to tell you the truth, the situation you mentioned has actually been thought about by some people in the Fenglingyueying Club."

"By the way, Director Ye, I don't know if you have heard the story of the prime minister of King Shekhan of India, Sisa Ban Dail, who counted the grains of wheat?"

Ye Duzheng blinked, and quickly gave the answer:

"Of course I've heard of it."

King Shehan rewarded the wheat.

This is a well-known mathematical allusion.

Students who played chess in their previous lives should know this.

Legend has it that the inventor of chess was Sisa Ban Dail, the prime minister of ancient India. The king at that time was Shekhan, and the world called him King Shekhan.

King Shehan was very fond of chess, so he asked Dail what reward he wanted.

Dail left a classic sentence handed down from generation to generation:

[Please put 1 grain of wheat on the first grid of the chessboard, 2 grains on the second grid, 4 grains on the third grid, and 8 grains on the fourth grid. That is, each grid in the next order The number of grains placed on top must be a multiple of the number of grains in the previous grid until the last grid, which is the 64th grid, is full, so I am very satisfied].

King Shehan agreed to this request, but in the end he found that if Dail's calculation was followed, he would have to pay for the entire kingdom's grains of wheat for the next 2,000 years

Then Xu Yun paused, and said to Ye Duzheng:

"Of course, we have no way of distinguishing whether this story is true or false, but we can see a truth from it."

"That is, if there is a small error δZ0 in the initial conditions of a dynamical system, then in its evolution process, this deviation changes within time t to appear an evolution function."

Say it.

Xu Yun picked up the pen with some difficulty and wrote down a function:

|δZ(t)||δZ0|eλt.

Then Xu Yun drew a horizontal line under λ, and continued:

"I call this λ the Lyapunov index, which represents the degree of sensitivity." (Note: Lyapunov was born in the 19th century, but the Lyapunov index will only be proposed after the chaotic system is established)

"If it's negative, we see that the initial bias gets smoothed out during evolution—meaning it's insensitive to initial conditions, and extremely sensitive otherwise."

"And in a general dynamical system, its evolution can always be described by such a differential equation, that is, d/dtX=f(X)"

Looking at the contents written by Xu Yun eloquently.

Qiao Caihong, who has been [0v0] since leaving the interest group, couldn't help scratching her hair.

oops.

My head is a little itchy, it seems like I'm going to grow my brain

Actually.

What Xu Yun described to Ye Duzheng is exactly the well-known feedback system and index divergence in later generations.

This is also the conceptual mathematical entry point for one of the few chaotic systems.

Of course.

Later generations also have some Mandelbrot sets and multifractal patterns, etc., but these all require computer assistance.

After a while.

Looking at what Xu Yun wrote, Ye Duzheng had a faint flash of understanding:

"...I seem to understand a little bit, Comrade Han Li, the basic principles of the atmospheric system actually conform to the logic of determinism?"

"That's right."

Xu Yun felt slightly relieved when he heard this, and nodded vigorously:

"This system is not refuting determinism, but because the deterministic equations have unpredictable phenomena, which makes this system worth exploring."

"It's a theory based on determinism, with determinism leading to unpredictable outcomes—a very important concept."

In Xu Yunlai's later life.

There are often two misunderstandings about the concept of chaotic systems.

One is that the existence of a chaotic system refutes knowlism or determinism, and is a concept with quantum uncertainty.

This is actually a very outrageous mistake.

A chaotic system refers to being unknowable within a certain period of time, not uncertain, and it does not conflict with determinism itself.

At the same time, chaos theory is a purely mathematical mechanism, while quantum uncertainty is a physical mechanism - there is chaos in classical dynamics, but there is no chaos in pure quantum mechanics.

more importantly.

Chaos implies the butterfly effect and the fractal structure of phase space, requiring nonlinear dynamics.

The definite state in quantum mechanics can only be described in Hilbert space, which is a linear state.

As for the second misunderstanding?

It is that the chaotic system is often inexplicably related to 'philosophy', and eventually goes further and further away.

For example, when you talk about it, you will get involved in the definition of Taoism. It means that Tao gives birth to one, one gives birth to two, two gives birth to three, and three gives birth to all things.

Then I will give you a WeChat at the end, add it to tmd to sell sandalwood

Xu Yun has always worried that Ye Duzheng will fall into these two traps by mistake, which will cause Ye Duzheng to face extremely serious research barriers in the future, and may even become Li Huowang mentally.

Therefore, from the very beginning, he tried hard to instill in Ye Duzheng the concept that chaos theory is a purely mathematical mechanism.

"Comrade Han Li."

Just when Xu Yun explained to Ye Duzheng almost.

Qian Yi or Qian Bingqiong, who had been silent all this time, suddenly spoke:

"Comrade Han Li, according to what you say, our world is actually nonlinear for the most part?"

"So, isn't there too few problems that linear equations and linear programming can solve?"

Hearing Qian Bingqiong's words.

Xu Yun couldn't help but glanced at him.

Then forcibly suppressed the excitement of seeing the boss, shook his head calmly, and explained:

"Amount of money, Comrade Qian Yi, right? Not necessarily."

"At least in my opinion, a linear system is actually an 'optimal linear approximation' to a nonlinear system."

"It preserves the most important qualitative properties of nonlinear systems, such as stability or instability, that is, topological properties of dynamical systems."

"According to the theory of differential topology, nonlinear systems on smooth manifolds that can be linearly approximated are common."

Say it.

Xu Yun picked up the paper and pen again and began to write slowly.

well known.

Broadly speaking.

"Linear system" means a system whose solution satisfies the principle of linear superposition, namely:

F(x_1+x_2+x_3+)=F(x_1)+F(x_2)+F(x_3)+

This F cannot simply be understood as just a function form that can be written explicitly, but should be regarded as a mapping.

in short.

A linear system corresponds to a linear map.

The form of the linear system referred to in the field of nonlinear research of ordinary differential equation dynamical systems is often like this:

\\frac{dX}{dt}=A\\cdot X where X=[x1,x2,x3,.]T.

And A is a constant matrix, then this is a linear ordinary differential dynamical system.

The nonlinear system, which is different from it, is the system that cannot be represented by the above-mentioned equations.

For example, some are second-order, third-order, and higher-order systems, or formally the items in the matrix A are related to the items of X.

Of course.

Nonlinear systems also include nonlinear systems in partial differential equations.

For example, a system with a diffusion term that can form a Turing Pattern.

But on the other hand.

The Koepka-Smale theorem mechanism in differential topology guarantees a dense case:

Locally stable manifolds after local linearization at the operating point.

The corresponding linear system will have a stable subspace εs and an unstable subspace εu, which are respectively tangent to the corresponding manifold.

That is, to a certain extent.

Nonlinear systems can be treated approximately as linear systems.

"."

after awhile.

Qian Bingqiong digested Xu Yun's thoughts, frowned and said:

"But even so, Comrade Han Li, not all nonlinear systems can be approximated by linearization?"

"Or it is necessary to approximate the nonlinear system to linear, and a large amount of calculation must be completed?"

"That's right."

Xu Yun nodded bluntly and said affirmatively:

"If you want to optimize the approximation as much as possible, you must complete a lot of calculations-this is the same as the exhaustive method."

"And to do that, you have to rely on another tool."

this time.

Qian Bingqiong was silent for a longer time before he said slowly:

"You mean the computer?"

Xu Yun took a deep breath, and quietly clenched his hands into fists under the table:

"Yes, computers, I personally think that this direction is one of the most important trends in the future."

"Even saying that the 21st century will be the century of computers."

Qian Bingqiong's pupils shrank suddenly.

As the founder of Huaxia Atomic Energy Science, Qian Bingqiong is not proficient in computers due to professional limitations.

But his mastery of the big picture is far beyond anyone's reach.

So during the whole conversation, he realized one thing:

If the world is truly nonlinear.

Then the basic logic of scientific development in the future is to approximate nonlinear things into a linear state.

This so-called 'thing' could be the weather,

may be theory,

may be economical,

may also be

technology and military.

And if so.

So the computer that Xu Yun mentioned is indeed an essential and important direction.

"A computer?"

Looking at Qian Bingqiong whose face was constantly changing, Xu Yun was also very nervous.

This is a hole he dug temporarily.

【The world is non-linear】.

This is a truth that was only discovered after the chaos theory was proposed.

Notice.

Again:

This is not a philosophical topic, but a mathematical concept.

It just sounds a bit philosophical.

Nonlinear research appeared in the 1960s, and did not officially enter the development stage until the end of the 1970s.

This concept has directly promoted the development of many fields, the most representative of which is

Computer Industry.

The financial chaotic systems, neurological chaotic systems, and meteorological chaotic systems of later generations are all supported by computers.

Therefore, after Ye Duzheng raised the question of chaos theory, Xu Yun immediately thought of this layer:

I had already planted the line of industrial software with Sun Junren at the beginning, and if I planted the seeds of computers today.

That picture is so beautiful.

And to know.

At this moment, Qian Bingqiong was sitting opposite to him!

A boss who is fully capable of understanding the concept he said, realizing this value, and passing it on to the decision-making level!

If the upper echelons really start to pay attention to computers

Damn.

The world seems to have changed a bit

But that's okay.

The one being strengthened is the rabbit. Who doesn't want their country to get better and better?

Xu Yun even wished that Rabbit could come up with Gundam as soon as possible. Everyone drove the first model machine, and showed what it means to have a good style in front of some houses that don't have a house!

So for a while.

All three people at the scene were lost in thought, only Qiao Caihong, who was at the side, felt dizzy.

However a few seconds later.

woo woo woo——

On a telegraph pole not far from them, a horn suddenly sounded a shrill siren.

See this situation.

Stone table.

Ye Duzheng, Qian Bingqiong and others suddenly changed their expressions, and suddenly turned their heads to look in a certain direction.

Qiao Caihong also recovered from the expression of o.O in an instant, and grabbed Xu Yun's wheelchair:

"Comrade Han Li, there is a situation! Let's go!"

Note:

It's brother donkey's birthday, everyone go to the character card and like it.