How amazing is the Klein bottle? Why do scientists say that human beings can never build it?

How amazing is the Klein bottle? Why do scientists say that human beings can never build it?

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There are many magical substances on the earth. The reason for their appearance has been criticized by the scientific community, which has already gone beyond the scope of human cognition. Have you heard of the Klein bottle? It is quite different from the cup that we usually drink water from. Its overall structure is very peculiar. It has no face and no end. It is not like an object in three-dimensional space at all. Most people interpret it as a bottle with a hole at the bottom. Let the neck of the bottle enter into the bottle orderly and connect with the hole at the bottom. In this way, the Klein bottle appears.

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Many people think that Klein bottle has both sides. This understanding is actually wrong. It is much more complicated than we think. There are many sellers selling Klein bottles on the market. They are not real Klein bottles. It is difficult to make real Klein bottles with human technology, because it is a kind of supernatural material, which is different from spherical surface. If a fly can fly directly from the inside of the bottle to the outside without passing through the surface, that is to say, there is no distinction between inside and outside, that is it It’s amazing. How amazing is the Klein bottle? Why do scientists say that human beings can never build it?

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Mobius belt and Klein bottle

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It is strange that the bottle neck and the bottle body intersect. The points on the bottle neck and the bottle wall occupy the same position in the three-dimensional space. In other words, can a piece of paper have only one surface? This is the fabled Mobius belt. What is Mobius belt? Turn the paper 180 degrees and connect it end to end to get the Mobius belt.

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It is not a three-dimensional world, but a two-dimensional world. But it has only one face in the three-dimensional world. There is a clever coincidence between it and Klein bottle. If Klein bottle is tangent along the symmetry line, two Mobius rings will be obtained. In fact, Klein bottle belongs to the product of four-dimensional space. After it is tangent, it becomes two objects in two-dimensional space.

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Klein’s bottle may have something to do with the universe

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To take a typical example, if you think of ants as creatures in a two-dimensional world and take them all the way along Mobius, you will get a result that Mobius belt has no end, as if it has no edge. This is the same with the three-dimensional world. This leads to a question: is the universe as boundless as Klein’s bottle? Human beings have known about the universe for such a long time. It is boundless and endless. Human beings can only wander in the observable field, and the unobservable zone is unknown. The essence of Klein bottle is the same as the universe.

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So far, human beings have not been able to make a real Klein bottle, which has great limitations. Using the example of Klein bottle, can we think that the universe is more like a high-dimensional Klein bottle, seemingly boundless on the surface, but in fact it is a circular space. The inside of the universe is the outside of the universe, and the edge of the universe is the intersection of Klein bottles. If it’s true, no matter how we escape, we can’t leave the universe. We are bound by the universe. What do you think is the ultimate reason why humans can’t make Klein bottles? You can leave a message for interaction.

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