Xiao Yu watched quietly, and the child Luka was still writing slowly.
"I heard that Masters No. 3 and No. 4 are conducting research in this area. I have seen them on TV. They are so powerful. It seems that no matter what the problem is, there is no difficulty for them. That's the only way they can be so powerful.
Only by being a good person can you become the master's right-hand man, and only then can you get such great honors as No. 3 and No. 4."
"When I grow up, I must become a scientist and move my parents to the Paradise. I also want to have my own independent laboratory in the Eternal Kingdom and become a scientist like No. 3.
A great person like No. 4."
The Luca child put down his pen, and at the same time, the teacher's voice came from the podium: "Okay, everyone put down their pens, it's time to hand in the papers."
Several Lucca children stood up, followed their respective positions, collected all the papers, and handed them to the podium. After the teacher announced that class was over, all the Lucca children ran out laughing.
After entering the classroom, Xiao Yu was still staring blankly here.
At this moment, Xiao Yu's mind was filled with turmoil.
Xiao Yu thought of a way, a way that was very likely to succeed.
"Möbius strip? Möbius strip?"
Just like the child Luca said, the method of making a Möbius strip is very simple, so simple that a child of a few years old can just find a piece of paper and make it. But the Möbius strip contains
The truth is not simple.
When I was on earth, there was a widely circulated joke about the Zen master. It said that a young man went to consult the Zen master and asked why there was sadness in addition to joy in the world. The Zen master asked the young man, and asked him,
Is there any paper in the world that only has the front side and no back side?
In this joke, the young man brought a People's Daily, but was directly KO'd by the Zen Master.
Of course, this is just a joke, even if you have seen it. But in the world, there really is paper with only one side, and that is the Möbius strip. Just do it yourself, tear a piece of paper, turn one end 180 degrees and connect it with
Merge the other end. Then use your finger to follow the Möbius strip in a circle, and you will understand why it has only one side.
In other words, there is no distinction between inside and outside of a Möbius strip. This is a very important point.
Suppose the two-dimensional world is regarded as a piece of paper, and a circle is drawn on the paper. This circle becomes a cage in the two-dimensional world. In the two-dimensional world, you will have no way to escape from the circle. Because it
There are no flaws. This circle is like a sphere in the three-dimensional world. If you are imprisoned in a sphere, you naturally have no way to get out unless you pass through a higher dimension than this world.
If you want to break through the blockade of a circle in the two-dimensional world, you can achieve your goal through the third dimension. If you want to break through a sphere in the three-dimensional world, you can achieve your goal through the fourth dimension.
But the Möbius strip provides another way, which is to break through the blockade without passing through a dimension higher than this world. In the two-dimensional world, you can distort the space to
The circle becomes a Möbius strip, because the Möbius strip has no distinction between inside and outside. As long as you walk a certain distance and then flatten the space, you will unknowingly get out of the blockade.
In the two-dimensional world, you can break through a circle through the Möbius strip. So, is there a way to break through a sphere in the three-dimensional world?
After all, the Möbius strip only applies to two-dimensional space, and in the two-dimensional space, the Möbius strip cannot exist. It can only be produced in a three-dimensional world that is one dimension higher than it.
So, is there something similar to a Möbius strip that can break through a three-dimensional sphere without passing through the fourth dimension?
The answer is that such a thing exists, and that is a Klein bottle.
Suppose you have a vase without a bottom, and then you extend the mouth of the vase, bend it downward, let the mouth penetrate the body of the bottle, enter the inside of the bottle, and place the mouth where the bottom of the bottle is, it becomes
A three-dimensional world of Klein bottles.
The Klein bottle is an upgraded version of the Möbius strip. The Klein bottle manufactured according to the above method is only a simplified version of the three-dimensional world. The real Klein bottle cannot be truly manufactured in the three-dimensional world, as
A Möbius strip cannot really be created in a two-dimensional world.
The mouth of a real Klein bottle does not need to penetrate the bottle body to connect to the bottom of the bottle. Because it is a product of the four-dimensional world, it is actually connected to the bottom of the bottle through the fourth dimension.
Like a Möbius strip, a Klein bottle has no distinction between inside and outside. In other words, if you are inside a Klein bottle, you just need to go straight forward without breaking through any blockades.
Walking outside, similarly, if you are outside the Klein bottle, you can also walk inside the bottle without any hindrance.
"Mobius strip, Klein bottle!" Xiao Yu muttered these two terms silently in his mind, and began to calculate quickly without realizing it.
If you want to create a Klein bottle, you must meet the following two conditions. First, you must have an extremely deep understanding of four-dimensional space, and second, you must be able to create a true four-dimensional space.
Xiao Yu cannot create a four-dimensional space, but there is a four-dimensional barrier next to Xiao Yu.
Then, there are only the following two points left for Xiao Yu to solve. The first is the ability to bend three-dimensional space. Xiao Yu has basically possessed this ability through research on super-light navigation. The second is what is needed to bend space.
Huge energy, Xiao Yu also obtained this ability through in-depth research on element decay technology.
So, what is missing? Nothing is missing.
Xiao Yu began to get excited, and Xiao Yu felt keenly that he had found the truly right direction.
This method is consistent with all of Xiao Yu's inferences.
The four-dimensional barrier is indeed so strong that it cannot be destroyed by a fourth-level civilization. The Klein bottle can be overcome by not destroying the four-dimensional barrier.
Only Xiao Yu himself can master it, and the rest of the fourth-level civilizations cannot master the fourth-dimensional space, which is not accessible to the fourth-level civilization. Through getting along with Taihao during this period, Xiao Yu gained some relevant knowledge of the four-dimensional space.
Only then did he have the ability to make Klein bottles.
"The Klein bottle is very likely to be the key to unlocking the four-dimensional barrier... Then, let's start trying." At this moment, Xiao Yu made up his mind.
Xiao Yu took one last look at the signature on the top of the pile of test papers that had been put away on the classroom podium. He remembered the name of the Luca child deeply in his mind, and then withdrew his energy.
"If you really break through the four-dimensional barrier through the Klein bottle method, then you will become the fourth Lucca person with a title, and you will become Lucca No. 5."
Xiao Yu murmured to himself, and immediately summoned all Lucca scientists to start a discussion in the auditorium.
Every Lucca scientist participating in the meeting had a worried and haggard look on their face. Obviously, during this period, they did not think of other solutions, and none of them had a good rest.
"Master, I wonder why you summoned us here?" Luca No. 3 asked.
"I have a guess." Xiao Yu replied, "I seem to have found a way to break through the four-dimensional barrier."
"Well? What method? What method?" Luca Three asked eagerly.
"Klein bottle." Xiao Yu said a very brief word.
There was a moment of silence in the auditorium. It seemed that the four words "Klein bottle" had supreme magic power, which could shock all the people of Lucca and make them unable to extricate themselves.
"Klein bottle? Klein bottle? This kind of thing full of contradictions, can it really... help us?" After a long silence, Luca Three finally said this with some difficulty.
The Klein bottle is indeed a thing full of contradictions. Its contradiction lies in that it cannot be truly manufactured in the three-dimensional world. But it is precisely these contradictions that gave Xiao Yu a breakthrough in the three-dimensional world.
A sphere approach.
"Don't forget, since you can break through the blockade of a two-dimensional circle in the two-dimensional world through a Möbius strip, why can't you break through a three-dimensional sphere in the three-dimensional world through a Klein bottle?
The blockade?”
Xiao Yu replied.
The auditorium fell into silence once again. Obviously, the Lucca scientists were thinking nervously.
"Theoretically, well, I mean, just in theory, it is completely feasible to break through the four-dimensional barrier through a Klein bottle. However, the problem is, how do we create a Klein bottle full of contradictions?
Because? We are in a three-dimensional world after all." Luca 4 said.
"We have element decay technology that can provide energy, we have super-light navigation technology that can bend space, and we also have a four-dimensional barrier that can provide us with a fourth dimension, allowing us to move the mouth of the Klein bottle without passing through the bottle body.
It can be connected to the bottom of the bottle, why can't we make it?" Xiao Yu asked rhetorically.
"Okay, it sounds reasonable." Luca Three said hesitantly, "Anyway, this method is worth trying."
"Of course." Xiao Yu said, "We only have this one way left. If this method works, we can break through the four-dimensional barrier. If this method doesn't work, we have no other way but to wait to die.
"Then, let's start fighting. I need your help to calculate the curvature and find a way to make a Klein bottle..." (To be continued...)
ps: Please vote for me! I'm a little busy these days. Rainbow will work hard to code words tomorrow or the day after tomorrow, and try to add more!