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Chapter 60 Klein Bottle

Yifan sat in the office and read books all day. At 5 o'clock in the evening, Chen Lei, who had just booked a recruitment seat from the talent market, came back and said, "I'm off work and can leave."

"Oh," Ivan responded verbally, but was not ready to leave.

He was doing a topological experiment in space. In Chen Lei's view, Yifan was staring at the computer screen in a daze.

Chen Lei knew that Yifan had been reading college books all the time, mostly in mathematics and physics. At first, he thought that this was just a way for him as the boss to hide it, but after observing him for a while in the morning, he didn't think so.

No matter how you look at it, Chen Lei could not connect the nerd in front of him with money laundering.

"Then I'll leave first. Remember to lock the door when you leave and put the key here. Remember to come and open the door early tomorrow." Chen Lei said, putting the key to the door next to Ivan.

Ivan raised his hand and said he knew.

After Chen Lei left, Yifan locked the door of the guard room, and looked around with the space eye, making sure no one paid attention to him, and silently recited the "New Space Hand" he just designed.

However, the complexity of this new magic is only half the original, and half of this is saved is not because Ivan made any improvements to the magic, but because he deliberately omitted part of it.

So, this is a "incomplete hand of space".

If you are a person who has just come into contact with magic, such unformed magic cannot be cast, but for Ivan, this is not a big problem. The entire magic of the Space Hand is not complicated. For example, the original Space Hand is like a person learning to eat. A newly born baby has not learned to chew. They can only instinctively swallow the food. However, as an adult, it is easy to master this skill. Although it is chewing and swallowing when eating, once you want to carefully savor a food, you can deliberately refine the chewing process, or even not eat it.

Ivan was chewing on his hand of space. He had never thought of doing detailed research on his magic before. Wizards are often keen on studying magic that seem to be more powerful and more practical. They are studying the principles of magic, and they are also very representative, such as space connections and other sustainable. The hand of space is a very basic entry-level magic. The structure of its own is very simple, just like learning 1+1=2 in mathematics. No one cares how this process is obtained.

People who really care about are often those who study mathematics to the end.

Ivan's experiment this time was an ordinary rubber balloon, which was a long balloon that looked like a caterpillar after it was blown up. The color of the balloon was yellow.

Ivan blew the balloon all over, and the balloons bulged, and then Ivan tucked the buttons tightly with a thin plastic rope.

Then I used the focus of my experiment - "The Hand of Incomplete Space".

A gentle "pop" sound came from the air. Ivan felt a burst of air blowing across his face, and the balloon instantly faded. Ivan carefully checked the place where the rope was tied, and the rope was still there.

The air just now was the gas inside the balloon.

Ivan saw that the balloon had been made into a twisted number "8". He checked it with his naked eyes and the balloons had been connected from beginning to end. Where the balloon intersected with him, Ivan saw that the end of the balloon seemed to have reached into the center of the balloon, but he did not find any damage there.

He pulled the end and the balloon seemed to be pulled out as if a chain was pulled out, but the balloon itself became nervous, as if he pinched a piece of the rubber to pull the other end, but the rest of the balloon had become tighter except for the part he had pinched.

Ivan found the air inlet at the beginning and began to blow in. As he guessed, the balloon could not be damaged at all, but no matter how he blew it, it couldn't be bulged, just as if there was a ghost in demand that stole all the air in the air.

Ivan knew that his experiment was successful, and the balloon in his hand should be strictly speaking, a real "Klein bottle".

Clay flask is a concept conceived in topology, and its specific concept was expanded with reference to the Mobius belt.

The Mobius belt is a special curved surface formed by rotating one hundred and eighty degrees at one end of a paper bag and then pasting it to the end. It has a distinctive feature, that is, there is only one side, and there is no right or wrong.

The Klein bottle is a "Mobius belt" that only exists in four-dimensional states that people imagine. It is impossible to exist in reality, just like you cannot obtain a Mobius belt through plane means, because the most important process of making the Mobius belt is to "flip" it by 180 degrees, and the concept of flip is actually only a concept unique to three-dimensional.

In a one-dimensional state, a point or a line can only be translated left and right. In a two-dimensional state, plane rotation and translation can be achieved, because each additional dimension is added, there is an additional degree of freedom in the direction. The Mobius belt can be regarded as a two-dimensional object, but it needs to be formed through three-digit flips, otherwise it will always be two faces.

The closed balloon was originally a three-dimensional curved surface, like a piece of paper, divided into two different surfaces inside and outside. However, through the "incomplete space hand", Ivan made the surface "four turns" - "four-dimensional angle flip", and the result was that such a balloon that could not be blown up.

Why can't the balloon be blown up? Because there is no distinction between inside and outside, its inner wall and the outer wall have been connected by "four turns", just like the front and back of the Mobius belt are flipped and connected, and the air blown into the inside goes directly to the outside through the "loophole" that cannot be seen in three dimensions...

Ivan looked at the "Klein balloon" in his hand and suddenly had a lot of thoughts in his mind.

First of all, I admire the thinking of the earthlings. Four-dimensional is a dimension that the earthlings cannot reach at all. Before Ivan came into contact with this information, he did not know what the concept of four-dimensionality would be. However, the earthlings summarized the rules that did not belong to their own world through mathematics. The true nature of the Klein balloon is completely corresponding to the topological theory.

The second is the understanding of magic. Although he can't see anything at the moment, he has a premonition that magic should be able to be explained. Before this experiment, Ivan always believed that there were two rules in the world, the rules of civilians, just like gravity, everywhere, and all things are included. There is also the rules of magic, which are beyond the rules of civilians.

Now, he has doubts about this simple theory.

In fact, there have always been doubts from the mage, but because of the lack of necessary basis, many of these ideas are only reflected in some unrealistic fantasies.

"Ivan, is it you?" Zhao Zhenxue's voice outside the door.

Ivan opened the door. After Zhao Zhenxue entered the door, she saw Ivan holding a yellow balloon in a daze, her mouth pursed tightly, and she seemed to be a little nervous and excited.

"Why are you still here?" Zhao Zhenxue asked. It was already past 8 o'clock in the evening, why is he still staying here?

Ivan did not move, but just quickly recorded some of his thoughts with a pen.

Zhao Zhenxue walked to Ivan and took the balloon.

At first glance, it looked like a circle-shaped balloon. Zhao Zhenxue spread the balloon and saw that one of them looked weird, just like a snake's tail drilling into his mouth. No, it drilled into his skin from the side, but when he looked closely, he could not find the broken gap.

I pulled it along the place I went in. It was connected and could be pulled out, but my eyes clearly saw it close to the outside. If there were no loopholes, where did it be pulled out?

Zhao Zhenxue glanced at the book Ivan placed on the table. It was a topology. The page I opened happened to draw a twisted Klein bottle.

Zhao Zhenxue has been watching science fiction since she was a child, and she immediately understood what was in her hands.

Perhaps Ivan is the only one in this world who can do this.

Zhao Zhenxue blew into the air blow hole of the balloon. As expected, as she thought, she couldn't feel any pressure at all.

This is a miracle on earth, the real miracle. The weirdness of this miracle is no less than the resurrection of the dead and aliens come to earth.

If this thing is held in the hands of a physicist, the next day the physicist can go to this place to win the Nobel Prize and then be regarded as Einstein's second.

Zhao Zhenxue took out a lighter from Chen Lei's drawer and placed it next to Yifan.

Chen Lei did not smoke, it was prepared for possible customers and placed in front of Yifan.

"Or hide it or burn it."

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