Chapter 388: Beyond time

Fengshen doing business.
Is smiling.
During the dementia worship of Li Zheng and Lin Yujing, he occasionally smiled spiritually, and then he threw himself into the next step.
He looked back several times and wanted to share some joy, but when he saw the expressions of the two, he took it back and continued his calculation helplessly.
This process is very much like Li Zheng who wants to share the magic of solving problems with Liu Xin.
Li Zheng has seen a lot of explosive academic abilities, and has also done some incredible geniuses.
But at this moment, he still persuaded.
He has been racing for many years, and his friends in the circle admire his face and say a word of grace.
He can pick him up if his physical friend calls him that.
Chemistry friends call him so, you can also pick up.
Even biology and computers are hard-wired.
Only mathematics, as long as the wind is here, he is afraid that he will never be able to catch it.
Now, the problem facing Jianfeng is really "the solution of the magic angle."
It is a mathematics topic that Li Zheng worked hard to transform from a physics paper.
In the title, he used a way of almost talking to the computer, translating the electrical properties, electrons, and physical display of two-dimensional graphene into a series of complex functions and matrices, just to show them clearly in the home. In front of the wind, let him have no distractions.
As for Li Zheng himself, if he is faced with the same problem, it may take a long time to get the 5 solutions in the paper, but further expand to 8? This is not a question of whether there are ideas or not, but that ideas that generate ideas will not even be born.
After ten minutes of worshipping like this, Gui Jianfeng pulled out another pile of empty papers and shook his head with a smile.
"No, no, it's not an imaginary number, and imaginary numbers can only give regular solutions..."
"Intuition...wrong?" Li Zheng asked weakly.
"The intuition is correct, the tool is wrong, your matrices are already equivalent to imaginary numbers... We need to do more theoretical expansion..." Gui Jianfeng turned his head and raised his hand excitedly, "Quadruple Count! You actually forced me to this point. I like this question."
"!!!" Li Zheng also stared. After thinking for a long time, he remembered that there was such a thing, "Quaternion...I remember it is a further expansion of the imaginary part?"
"Well, the more complicated but purer mathematical form, the amount of calculation has also accumulated, try to solve it before dark." Gui Jianfeng turned around and twisted his neck, gasping for breath, "If this doesn't work, just It’s going to be counted in eight yuan...and after accumulation, even if I have to do it for a week...that's pretty exciting..."
"Wait, you can take a break..."
But at this moment, Gui Jianfeng could no longer hear Li Zheng.
At the moment he only talks with mathematics.
"Um..." Lin Yujing dared not do it at this time, pulling Li Zheng and said, "I understand imaginary numbers, are they almost plural, what the is a quaternion?"
"Well... it's probably a mathematical concept that was put forward very early, but only applied space in recent years." Li Zheng smiled, "You have today too!"
"My brain only records the necessary knowledge, not like you remember all the scumbag knowledge."
"You don't understand, knowledge is the source of inspiration." Li Zheng clenched a fist and said, "As long as I have enough knowledge, I may be able to combine two completely unrelated knowledge points when I can."
Li Zheng started his explanation on this.
Imaginary numbers are a subset of complex numbers, so the concept of "plural numbers" will be used more often when talking about this part.
The so-called plural is actually just a middle school content, but most people lose their memory instantly after learning that chapter, and they will never encounter this word again in their lifetime.
But for mathematicians, it is a time-tested tool. Although mathematicians can't understand normal speech, they always say one or two things that make people seem to understand, such as-
[In the real number field, the shortest path connecting two truths is through the complex number field. 】
The so-called
understandable
means that the words "connection", "shortest" and "path" are understood.
But once the two things, "real number field" and "complex number field" are added, it becomes impossible to understand.
At this time, the small lecture room for supplementary lessons provided by Li Zheng for Liu Xin came in handy. In fact, the distance of this sentence made Liu Xin understand, only a visual metaphor-
[At any two points on the surface of the balloon, the shortest path connecting them is to pass through the balloon. 】
Well, even if you say that, Liu Xin still might not understand.
Fortunately, there are not many samples like him in the human population.
If real numbers can be felt intuitively, like numbers 1, 2, and 3 that exist exactly, then complex numbers are numbers that cannot be felt intuitively. Numbers like -1 under the radical sign and -2 under the radical sign, after all, in the objective directness, forever There is no way to find which number squared equals -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. The inside of the balloon is outside the digital intuition, but the part that can exist in theory is the plural. Domain again.
It can be said that imaginary numbers add a dimension to mathematics and can also be called binary numbers.
What about the quaternion mentioned by Jianfeng?
That is another upgrade of the imaginary number...
At this level, it is difficult to cite examples that Liu Xin can understand.
As for the octal numbers above this, human beings have yet to find a suitable application space, and it may already be knowledge outside this universe.
In the room, after Lin Yujing figured out the quaternion, she was also not surprised: "Is it so deep...no wonder my grandpa didn't catch us for skipping class..." I asked Fengfeng to find papers every day..."
"Huh." Li Zheng said with disdain, "When I see a change, my grandfather is a scumbag."
Lin Yujing smiled and scolded: "You really have a chance to black out your grandpa."
"Grandpa won't you black me out?"
"Um...also, okay..."
"Damn, specify that I will be blackmailed."
"Don't talk about grandpa, let's look at Fengfeng." Lin Yujing looked at Gui Jianfeng's sneered back, her expression gradually deepened, "Although the quaternion came a bit suddenly, intuitively, it always feels like This direction is correct."
Li Zheng nodded frequently.
Gui Jianfeng's expansion of the mathematical dimension reminded him of the "two-dimensional quantum tunneling" in the system prompt.
And then expanded the magic angle model to three dimensions, opening up the ambition of true superconductivity theory.
Once these are involved, it is impossible to give theoretical results only from physical observations and experiments. On the contrary, only mysteries and more mysteries can be given.
Imagine if manned spaceflight was born before the theory of relativity.
Then in the space station, the astronaut who found the clock slowed down will be no less confused and shocked than the observer who discovered that "waves have become particles" in the double-slit interference experiment.
At that time, the level of confusion and psychedelic in the discussion of the nature of time, space and energy was probably no less than that of quantum mechanics.
Of course, even in such a mess, it is good to conduct more, even blind experiments.
The more the mystery, the more the research material for the theory.
But this is only a process of accumulation, and all accumulation leads to only one result
Use mathematical weapons to pass through the physical balloon.
Thinking of this, Li Zheng's eyes stared.
"Wonderful! I finally know why the physics competition for middle school students should be organized as a calculus competition for middle school students. The Physics Society's vision is too long-term."
"In this case, let's just make up the content of the quaternion." Lin Yujing rubbed her face and said, "Although I can't keep up with the wind, but at least I want to see what he has made. Zhayou go find the handout!"
"Is idle?" Li Zheng frowned, "Should we not borrow this rare leisure time to have a relationship?"
"You are here again..."
"Well, learning is our double sport..."
On this day, Father Feng returned home three times.
The first time was noon, I thought they should go out to eat...
But seeing the three people in the room without saying a word, each doing questions...
Just panicked.
Does my son's weekend social activities need to be expressed in mathematics?
The second time was two o'clock in the afternoon.
Still working on the problem, I didn't even touch the lunch money on the table.
The third time was at six o'clock in the evening, and Father Feng walked to the door to observe in secret.
This time it was slightly better. Although seeing the wind and the boy were still doing it, the girl finally fell asleep.
Probably hungry...
Wait... it's okay to sleep on your stomach... but you just lie on that boy's lap so unscrupulously... still drooling...
Forget it... see the wind... it's time to grow up.
At this time, Li Zheng was finally hungry in a daze, and discovered the return of Father Feng.
"Ah, good uncle..." Li Zheng said hello, subconsciously looking out the window.
Seeing that night had fallen, he could only sigh.
It's always like this, learning the theory of relativity is everywhere--
【Learning Theory of Relativity】
[Once you start learning, the flow of time will become faster]
[Learning time=real timeunder the root sign (1-(current learning speed 2/C2))]
Among them, C is 300,000 times the learning speed of Liu Xin, and is a constant cosmological constant.
With such a profound theory, Dad Feng couldn't see it in Li Zheng's eyes. He just smiled bitterly and said, "What I want to eat at night, I will make it for you."
"Ah... this..." Li Zheng looked at Gui Jianfeng embarrassedly, "How long are you going to be? Can't we make another day?"
Gui Jianfeng still did not answer.
That’s right.
His learning speed may have exceeded C.
In that case, learning the theory of relativity will also dive into the domain of complex numbers, and his time flow will become an imaginary number, which will be independent of the universe and become a concept that exists only in theory.
Thought of this.
"Ah..." Li Zheng rubbed his forehead.
No, I've thought about it too much today, I'm afraid I'm going to be crazy.
For the first time, he wanted to stop the day of study and take a good rest.
With a headache, Dad Feng had already brought two boxes of milk, handed him one box, and the other box was placed on the side of Lin Yujing's head, which was Li Zheng's lap.
"Mathematical calculations are very painful. Of course I have a headache if I can't keep up with nutrition." Feng Dad stepped back, keeping a polite distance and smiled, "In fact, we've seen it once before."
"Oh? I'm sorry..." Li Zheng measured it carefully, but he didn't really have any impression.
"During the National Mathematical Competition." Dad Feng himself took a carton of milk, and smiled while inserting a straw. "At that time, Feng Feng called and said that he was going to be dying, so I immediately put down what I was doing and took the high-speed rail to go there. , But when I enter your room..."
Dad Feng said, smiling and raising his hand: "The scene is exactly the same as today."
"!!!" Li Zheng reacted, "I remembered that we had been studying for a whole day at the time, and it was very rude to see the note you left until you left."
"Well, this is actually my third time coming back today."
"???"
"Haha, it's okay, it's good, I also want to thank you." Father Feng sucked milk and laughed. "Since the National Competition, he hasn't been'not good' until now. It seems that he has found a new way. It also seems to have become stronger. I thought he could not survive the IMO, but he managed to survive. Thank you."
"I actually didn't do anything." Li Zheng rubbed Lin Yujing's head and looked at Gui Jianfeng with a smile, "If you don't say anything, I got much more from him than I gave him."
"You are humble. I checked. Your experience and achievements are much better than Jian Feng." Feng Dad said and smiled at the sleeping Lin Yujing, "The results are also."
"Ha, ha." Li Zheng smiled and scratched his head, "I'm just too greedy. In the core mathematics, I am willing to give Gui Jianfeng as draft paper."
"You should be modest, but I also understand..." Father Feng shook his head and sighed, "You have learned too deeply, I can't even see my back... I know I am selfish, but if it is possible, ...I actually...I would rather be a healthy and healthy ordinary person...even if he is a little stupid..."
Dad Feng said, turning sideways and hiding his face: "I'm sorry...well, I will prepare what you want to eat."
Li Zheng inevitably felt sour.
He has no doubt that Gui Jian Feng must be a treasure full of value for academics and even for humans.
But for the father and the family, this treasure is not worth mentioning in the face of health.
"You have worked hard." After Li Zheng said, he raised his hand and threw Lin Yujing aside, got up and patted it to see the wind, "Don't forget it, just this time, cook your father once."
"???" Seeing the wind stagnated, he murmured in a daze after a long delay, "It's taking advantage of me again! I won't cook for you!"
This situation is a bit out of control.
Li Zheng hurriedly raised his hand to hold Feng Dad first: "It is a reasonable joke to be fathers between familiar boys."
Then she looked at Lin Yujing, who was rubbing her eyes and woke up and suddenly found Li Zheng as father: "You continue to sleep with you."
Finally I caught the wind and said: "You are so cool, your dad, in order not to disturb us, did not dare to come back after walking outside for a day. Don't beep, take advantage of my little master Yinghu Lake, honor your dad to cook a meal Right."
"Ah..." After seeing the wind, he was in a daze for a long time, glanced at the sky outside, and then habitually looked at the small table on the right.
This habit has been for a long time. Once he is too hungry or tired to learn, the table will be filled with prepared meals without accident, so that all of this seems to be justified and exists like physical laws.
"It's okay." Dad Feng wiped his eyes quickly, "I'll do it, you continue..."
Gui Jianfeng greeted Li Zheng's anger before he could reply.
"Ah...this time..." Gui Jianfeng had to rub the back of his head and stood up, and said with his face sideways, "Let's do it today...Li Zheng's cooking skills are very good."
Dad Feng has to refuse again, and Li Zheng has already pushed over: "You can watch TV outside, and see if I will not teach us today... to train us Fengfeng."
The hospitality is difficult, and Li Zheng is overbearing, and Dad Feng had to really watch TV.
Then, dragging Lin Yujing, who was half asleep and half awake, into the kitchen, after asking about their favorite dishes, Lin Yujing was dispatched to purchase ingredients. Li Zheng listed the cooking steps and returned to the wind to make an overall plan. Arrangement, and finally the meeting started.
Li Zheng thought that Gui Jianfeng would blame him for troubles, but when he saw that Gui Jianfeng was more serious than what he did, he always tried hard to recall his father’s favorite taste in cooking, and constantly reminded Li Zheng of his control over the ingredients. .
Before eight o'clock, the hot fish, meat, vegetables, and soup are on the table.
Father Feng was full of praise, but his eyes were red when he praised him, and he stopped talking.
The same goes for returning home.
In the end, Li Zheng and Lin Yujing had a hard chat.
"You keep a mouthful of fish for people."
"Mmm... I was stabbed in fright."
"Deserve it."
"Really...well... stuck in the throat."
"Oh? Then I will help you it out."
"It's okay, it's okay."
"Why do you still catch the fish? Save the fish!"
In such a fish-eating cycle, the atmosphere finally eased again. Gui Jianfeng also just grabbed a piece of fish from Lin Yujing's hand and put it in his father's bowl, then tilted his head back and squeezed out the words in a very low voice. Come.
"Dad... worked hard."
"Hey, why are you doing this." Father Feng ate the fish with rice in one bite, with a smile on his face, "It's so delicious, so you have this talent."
"It's not me...mainly Li Zheng...I'm much worse than him..." Gui Jianfeng lowered his head.
"Where is it?" Li Zheng stared, and pointed at the strange-shaped "Jiang Si" on the fish with his chopsticks. "This Jiang Si is just imaginative."
Dad Feng is also floating. He stretched out his hand and grabbed silk and chewed it into his mouth. He couldn't help but nodded and said: "Okay, okay, all good, this silk is the best, and it's good for coldness."
This is a bit of a spell.
In order to alleviate the embarrassment, Li Zheng hurriedly gave Lin Yujing a tuo: "Come on, eat to get rid of the cold."
"I don't... uh..."
Seeing Lin Yujing being stuffed with Jiang, the father and son also laughed and kept laughing.
In the end, taking advantage of the effort of the father and son watching the evening sports news together, after Li Zheng left a note of [Discuss tomorrow], he pulled Lin Yujing away quietly.
The bad news is that there is no result today.
The good news is that I am very happy today.
But Lin Yujing did not.
She has been thinking about sleeping well...
Why did it fall to the ground? !