The god of wind who does the right thing.

It's smiling.

In the dementia worship of Li Zheng and Lin Yujing, he occasionally smiled spiritually, and then put himself into the next step of thinking.

He looked back several times and wanted to share some joy, but when he saw the looks of the two, he took it back and reluctantly continued his calculations.

This process is very similar to Li Zheng who wants to share the magic of solving the problem with Liu Xin.

Li Zheng has seen a lot of explosive academic ability, and he has also done some unbeatable geniuses.

But at this moment, he was still cowardly.

He has been galloping for many years, and friends in the circle appreciate his face and call him a god.

Physics friends call him that, he can pick it up.

Chemistry friends call him that, and you can pick it up.

Even biology and computers he hard-wired.

Only mathematics, as long as he sees the wind here, he is afraid that he will never be able to catch it.

Now the problem faced by the wind is really the "solution of the magic horn".

It is a mathematical topic that Li Zheng has worked hard to transform from physics papers.

In the title, he uses a way that almost talks to a computer, translating the electrical properties, electrons, and physical representations of two-dimensional graphene stacked together into a series of complex functions and matrices, just to clearly show them in front of the wind and let him have no distractions.

As for Li Zheng himself, if he were faced with the same topic, he might have been able to come up with the five solutions in the paper for a long time, but it would have been further expanded to eight? This is not a question of whether there is an idea or not, but that the idea of generating an idea will not be born at all.

After worshipping like this for about ten minutes, Gui saw that the wind actually pulled another pile of empty paper, smiled and shook his head.

"No, no, it's not an imaginary number, and imaginary numbers can only give a conventional solution......"

"Intuition...... Wrong?" asked Li Zheng weakly.

"My gut feeling is right, the tools are wrong, and your matrices are already equivalent to imaginary numbers...... We need to expand our theories......" Gui Jianfeng turned his head and raised his hand excitedly, "Quaternions! You've pushed me to this point, I like this question." ”

Li Zheng also stared, and after thinking for a long time, he remembered that there seemed to be such a thing, "Quaternion...... I remember it's a re-expansion of the imaginary part?"

"Well, the more complex but purer form of mathematics, the amount of computation has also accumulated, try to solve it before dark. Gui Jianfeng turned around and twisted his neck, panting and said, "If this doesn't work, you have to use eight yuan...... Accumulation and accumulation, even I have to work on it for a week...... I'm excited to say that......"

"Wait, you can take a break......"

However, at this moment, Gui Jianfeng could no longer hear Li Zheng speak.

At the moment he only talks to mathematics.

"Hmm......" Lin Yujing also dared to sigh at this time, and pulled Li Zheng and said, "I understand imaginary numbers, are they almost plural, what the hell is a quaternion?"

"Hmm...... It is a mathematical concept that has been proposed very early but has only had room for application in recent years. Li Zheng smiled, "You also have today!"

"My brain only records the knowledge that can be used, unlike you who remember all the scumbag knowledge. ”

"You don't understand this, knowledge is the source of inspiration. Li Zheng clenched his fists and said, "As long as I have enough knowledge, I may be able to combine two completely unrelated knowledge points at some point." ”

Li Zheng started his explanation.

Imaginary numbers are a subset of complex numbers, so the concept of "plural" is used more often when talking about this part.

The so-called plural is actually just middle school content, but most people will instantly lose their memory after learning that chapter, and they will never encounter this word again in their lives.

But for mathematicians, it is a tried-and-true tool, although mathematicians speak normally people can't understand, but they always say a sentence or two that makes people seem to understand what they don't understand, such as-

In the field of real numbers, the shortest path to connect two truths is through the field of complex numbers. 】

The so-called "seeming to understand" means that the words "connection", "shortest", and "path" are all understood.

But once you add the two things of "real number field" and "complex number field", it is impossible to understand.

At this time, the small lecture hall provided by Li Zheng for Liu Xin came in handy again, in fact, this sentence was only a figurative metaphor away from Liu Xin's understanding-

[The shortest path connecting any two points on the surface of the balloon is to pass through the inside of the balloon.] 】

Well, in fact, even if he says so, Liu Xin still doesn't necessarily understand.

Fortunately, there are not many samples like him in the human community.

If real numbers are numbers that can be felt intuitively, such as 1, 2, and 3, then complex numbers are numbers that cannot be felt intuitively, such as -1 under the root number, -2 under the root number, after all, in objective directness, it is never possible to find which number is squared equal to -2.

Here, the real domain is like the surface of the visible balloon, no matter how it curls and expands, it is still a two-dimensional plane, and the inside of the balloon, outside of the digital intuition, but the part that can exist in theory, is the complex number field.

It can be said that imaginary numbers add a dimension to mathematics, also known as binary numbers.

And what about the quaternions that the wind speaks of?

That's another ascending dimension to imaginary numbers......

At this level, it is already difficult to give an example that Liu Xin can understand.

As for the octabyte above this, human beings have not yet found a suitable application space, and it may already be knowledge outside this universe.

In the room, after Lin Yujing figured out the quaternions, she was also surprised: "Is it already so deep...... No wonder grandpa didn't catch us skipping class...... Find papers for Fengfeng every day to gnaw ......"

"Hmph. Li Zheng said disdainfully, "Seeing that I am thinking differently, my grandfather is an old scumbag." ”

Lin Yujing scolded with a smile: "You really have a chance to hack grandpa." ”

"Won't Grandpa hack me?"

"Hmm...... Still, it's okay......"

"Damn, I didn't hack me. ”

"Don't talk about grandpa, let's watch the wind. Lin Yujing looked at the back of Gui Jianfeng who sneered from time to time, and her expression gradually deepened, "Although the quaternion came a little suddenly, intuitively, I always feel that this direction is really right." ”

Li Zheng nodded frequently.

Guijianfeng's expansion of the mathematical dimension reminded him of the "two-dimensional quantum tunneling" in the system prompt.

In addition, he expanded the magic angle model to 3D and opened up the ambition of true superconductivity theory.

Once these are involved, it is impossible to give theoretical results from physical observations and experiments alone, on the contrary, only mysteries can be given, and more mysteries can be given.

Imagine if manned spaceflight preceded the theory of relativity.

Then in the space station, the astronaut who found that the clock was slowing down will be no less confused and shocked than the observer who found that "the wave turned into a particle" in the double-slit interference experiment.

At that time, the discussion of the nature of time, space, and energy was probably no less chaotic and psychedelic than the current state of quantum mechanics.

Of course, even in such a mess, it is good to conduct more, even if blind, experiments.

The more mysteries there are, the more research material is available for theories.

But this is only a process of accumulation, and all accumulation leads to only one result-

Use the weapon of mathematics to pass through the inside of a physical balloon.

Thinking of this, Li Zheng's eyes widened.

"Wonderful! I finally know why the middle school physics competition is held as a calculus competition for middle school students, the physics society has too long-term vision. ”

"In that case, let's make up a little bit about the quaternion. Lin Yujing rubbed her face and said, "Although I can't keep up with the wind, at least I want to see the content he made, and if you are idle, you will be idle, and you will go find the handouts!"

"Idle is idle?" Li Zheng frowned, "Shouldn't we take advantage of this rare leisure to have a relationship?"

"You're ...... again"

"Well, learning is our two-man ......"

On this day, Daddy Feng returned home three times.

The first time was at noon, and I thought they should go out to eat......

But when I saw that the three of them were in the house, they didn't say a word, and they each did their own questions......

I panicked.

Does my son's weekend socialization have to be expressed in math?

The second time was at two o'clock in the afternoon.

I'm still working on the problem, and I haven't touched the lunch money on the table at all.

The third time was at six o'clock in the evening, and Daddy Feng still tiptoed to the door to observe secretly.

This time it was slightly better, although the wind and the boy were still doing it, but the girl finally fell asleep.

Probably hungry......

Wait a minute...... Sleeping on your stomach can ...... But you just lay on that boy's lap so recklessly...... Still drooling......

Never mind...... See the Wind ...... It's time to grow up, too.

At this time, Li Zheng was also a little hungry after all, and found out about the return of Dad Feng.

"Ah, uncle, so ......" Li Zheng said hello and subconsciously looked out the window.

Seeing that night had fallen, he could only sigh.

It's always like this, learning the theory of relativity is happening all the time -

【Learning the Theory of Relativity】

[Once you start learning, time will flow faster]

[Time in learning = real time * under the root number (1 - (current learning speed??) /C??)) 】

Among them, C is 300,000 times the learning speed of Liu Xin, which is a constant cosmic constant.

With such a profound theory, Dad Feng naturally couldn't see it from Li Zheng's eyes, so he only smiled bitterly and pouted: "Whatever you want to eat at night, I'll make it for you." ”

"Ah...... This ......" Li Zheng looked at Guijianfeng embarrassedly, "How long will it take you?"

Gui Jianfeng still did not answer.

It's right to think about it.

His learning speed may have surpassed that of C.

In that case, the study of relativity would also dive into the complex realm, and his speed of time would become an imaginary number, independent of the universe, and a concept that existed only theoretically.

Come to think of it.

"Ah......" Li Zheng rubbed his head.

No, I'm thinking too much about this today, I'm afraid I'm going to go crazy.

For the first time, he wanted to end the day of study and take a good rest.

With a headache, Dad Feng had already brought two cartons of milk, handed him one box, and put the other box next to the head of Lin Yujing, who was sleeping on his stomach, that is, on Li Zheng's leg.

"The math is very painful, and the nutrition can't keep up, of course, it's a headache. Daddy Feng immediately stepped back, keeping a polite distance and smiled, "Actually, we met once before. ”

"Oh, sorry......" Li Zheng carefully weighed it, and it was indeed not impressive.

"When I was in the math national competition. Feng's father also took a carton of milk himself, and said with a smile while inserting a straw, "At that time, Fengfeng suddenly called and said that he was dying, and I immediately put down what I was doing and rushed over by high-speed rail, but when I entered your room, ......"

Dad Feng said, smiling and raising his hand: "The scene is exactly the same as today." ”

"!!" Li Zheng reacted at this time, "I remember, we studied all day at that time, and I didn't see the note you left until you left, which was very rude." ”

"Well, this is actually my third time coming back today. ”

“？？？”

"Haha, it's okay, that's good, and I want to thank you. Father Feng sucked the milk and smiled, "Since the National Competition, he has not been in a 'no' situation until now, it seems that he has found a new way, and it seems that he has become stronger." I thought he wouldn't be able to survive IMO, but he survived, thank you. ”

"I didn't actually do anything. Li Zheng rubbed Lin Yujing's head, looked at Gui Jianfeng and smiled, "If you don't say it, I got much more from him than I gave him." ”

"You are humble, I have checked, your experience and achievements are much stronger than the wind. Father Feng said and smiled at the sleeping Lin Yujing, "The result is also." ”

"Ha, ha. Li Zheng scratched his head with a dry smile, "I'm just greedy, in the core of mathematics, I am willing to use Guijianfeng as scratch paper." ”

"Your words should be modest, but I also understand......" Feng Dad shook his head and sighed, "You have learned so deeply that I can't even see my back...... I know I'm selfish, but if it's possible...... I actually...... Rather he was a healthy and ordinary person...... Even if it's stupid......"

Dad Feng said and hid his face sideways: "I'm sorry...... Well, whatever you want to eat, I'll prepare. ”

Li Zheng inevitably felt sour.

He had no doubt that the wind of return must be a treasure full of value for academics, and even for mankind.

But for the father and the family, this treasure is not worth mentioning in the face of health.

"You've done a great job. Li Zheng finished speaking, raised his hand and threw Lin Yujing aside, got up and patted Gui Jianfeng, "Don't forget it, just this time, cook for your father once." ”

"???" Seeing that the wind was stagnant, he stayed for a long time before scolding, "Take advantage of me again! I won't cook for you!"

The situation is a bit out of control.

Li Zheng hurriedly raised his hand and stabilized Feng Dad first: "Between familiar boys, being each other's fathers is a reasonable joke. ”

Then he looked at Lin Yujing, who rubbed his eyes and woke up and suddenly found Li Zheng as his father: "You continue to sleep yours." ”

finally caught the wind of returning: "You are good at calculating, your father didn't dare to come back after wandering outside for a day in order not to disturb us." Don't beep, take advantage of my Sakura Lake little master, and make a meal for your father. ”

"Ah......" Seeing that the wind was in a trance for a long time, he glanced at the sky outside, and then habitually looked at the small table on the right.

This habit has been around for a long time, and when he is hungry or tired enough to learn, that table will be filled with prepared meals without accident, so that it all seems to be a matter of course, like the laws of physics.

"It's fine. Dad Feng hurriedly wiped his eyes, "I'll do it, you continue to ......"

Before Gui Jianfeng could reply, he ushered in Li Zheng's angry glare.

"Ah...... It's still ...... this time" Gui Jianfeng had to rub the back of his head and get up, and said with a sideways face, "Let's do it today...... Li Zheng is a very good cook. ”

Dad Feng wanted to refuse again, but Li Zheng had already pushed it over: "You go outside to watch TV, see if I don't take us today...... Train us out of the wind. ”

It's hard to resist enthusiasm, plus Li Zheng is domineering, and Feng's father has no choice but to really watch TV.

Then he dragged the half-asleep Lin Yujing into the kitchen, and after asking about their favorite dishes, they sent Lin Yujing to purchase ingredients.

Li Zheng thought that Gui Jianfeng would complain about him, but when he saw Gui Jianfeng, he was even more serious than what he did, and he always tried hard to recall the taste that his father liked when cooking, and constantly reminded Li Zheng of the control of the ingredients.

Before eight o'clock, hot fish, meat, vegetables, and soup are served.

Feng Dad was full of praise, but his eyes were red and he stopped talking.

It's the same with the wind.

In the end, it became Li Zheng and Lin Yujing chatting hard.

"You give people a mouthful. ”

"Hmm...... I was so scared that I got a thorn. ”

"Well deserved. ”

"Really...... Hmm...... Stuck in the throat. ”

"Oh, I'll suck it out for you. ”

"It's okay, it's okay. ”

"Why do you still catch fish?

In this cycle of eating fish, the atmosphere finally eased again, and when he saw that the wind had snatched a piece of fish from under Lin Yujing's hand and sandwiched it into his father's bowl, he tilted his head and squeezed out the words in a very low voice.

"Dad...... Great work. ”

"Hey, what are you doing here. Dad Feng ate the fish with rice in one bite, with a smile on his face, "It's so delicious, it turns out that you have this talent." ”

"Not me...... The main thing is Li Zheng...... I'm much worse than him......" Gui Jian Feng said with his head bowed.

"Where?" Li Zheng glared, pointed to a large piece of strange-shaped "ginger shreds" on the fish with chopsticks, "This ginger shreds are cut by the wind, and they are very imaginative." ”

Feng Dad also floated, reached out and took the ginger shreds and chewed them into his mouth, nodding his head and saying: "Good, good, all good, this ginger shreds are the most delicious and cold wards." ”

It's a bit of a fight.

In order to alleviate the embarrassment, Li Zheng hurriedly sandwiched a lump of Lin Yujing: "Come on, eat ginger and drive away the cold." ”

"I don't ...... Hmmm......"

Seeing Lin Yujing being stuffed with ginger, the father and son also laughed and couldn't stop laughing.

In the end, taking advantage of the fact that the father and son watched the evening sports news together, Li Zheng left a note of "Let's discuss it tomorrow", and then pulled Lin Yujing and left quietly.

The bad news is that nothing has come of it today.

The good news is that we had a very happy day.

But Lin Yujing didn't.

She kept thinking about sleeping well......

Why did it fall to the ground?!