However, there are no outstanding characters in this drama, and 9 episodes have been abandoned.
Klein bottle under popular science. . .
The Klein bottle is a famous "bottle" named after the discoverer mathematician Felix Klein (Felix Klein) in 1882. It is a closed (that is, no edges) surface like a spherical surface. , But it has only one side. In the field of mathematics, Klein bottle refers to a non-directional plane, such as a two-dimensional plane, there is no distinction between "inside" and "outside".
The Klein bottle does look like a bottle, but it has no bottom, its neck is stretched, and then it seems to pass through the bottle wall, and finally the bottle neck and the bottom circle are connected together. If the bottleneck does not pass through the bottle wall but connects to the bottom ring from the other side, we will get a tire tread.
We usually say that a ball has two sides-the outer surface and the inner surface. If an ant crawls on the outer surface of a ball, if it does not bite a hole on the spherical surface, it cannot climb onto the inner surface. The same is true for the tire surface. , There are internal and external surfaces. But the Klein bottle is different. An ant crawling "outside the Klein bottle" can easily climb into the "Klein bottle" through the bottleneck. In fact, the Klein bottle has no distinction between inside and outside. !
Mathematically, we call the Klein bottle a non-orientable two-dimensional compact flow pattern, while the spherical surface or tire surface is a two-dimensional compact flow pattern that can be orientated.
If we look at the picture of the Klein bottle, one thing seems confusing: the bottleneck of the Klein bottle intersects with the body. In other words, certain points on the bottleneck and certain points on the bottle wall occupy The same position in three-dimensional space. But this is not the case. The fact is: the Klein bottle is a surface that can be truly expressed in a four-dimensional space. If we must express it in the three-dimensional space of our lives, we have to click it and express it as if we are ourselves. It's the same as intersecting with yourself.
The fact is: the bottleneck of the Klein bottle passes through the fourth-dimensional space and then connects to the bottom circle of the bottle, not through the wall of the bottle. What is going on here? We use the kink as an analogy. If we think of it as a curve on a plane, then it seems to intersect with itself, and at first glance it seems to be broken into three sections. But in fact, this figure is actually a curve in three-dimensional space. It does not intersect itself, and is a continuous curve. Naturally, a curve on the plane cannot do this, but if there is a fourth dimension, it can pass through the third dimension to avoid intersecting itself. It's just because when we want to draw it on a two-dimensional plane, we have to draw it at one point and draw it as if it intersects or breaks. The same goes for the Klein bottle, which is actually a curved surface in a four-dimensional space. In our three-dimensional space, even the most brilliant craftsman has to make it into the appearance of intersecting itself in order to form a bottle that seems to have no distinction between inside and outside; it is like the most brilliant painter who draws kinks on paper. At that time, I had to paint them as if they intersect themselves.
The Klein bottle exists in the four-dimensional space, and it can bypass the intersection with itself through the fourth dimension. In the string theory that is still being established in quantum mechanics, the world is considered to be 11-dimensional, which is far more complicated than we think, except that most of the dimensions are curled in a very small space, and only the three-dimensional space is spread out. In the four-dimensional space, one dimension is a line, two-dimensional is a surface, three-dimensional is a static space, and four-dimensional is a dynamic space (because of time).
If the principle of the dome leans toward the four dimensions, it can extend a lot of topics: multiverse, wormholes, and distortion of time and space. . . . It's a pity that this play tends to deconstruct the human nature in the collapsed society. . .
It is much simpler to lean towards the three-dimensionality. Just explain the material, power source and purpose of the dome. . .
There is another interesting topic: if you cut the Klein bottle along its symmetry line, you will get two Mobius rings!
The Mobius ring was discovered by German mathematicians Mobius (1790～1868) and John Listing in 1858: a piece of paper was twisted 180°, and the two ends were glued together to make paper. The band has magical properties. Ordinary paper tape has two sides (namely double-sided curved surfaces), one obverse and one reverse. The two sides can be painted in different colors; and such paper tape has only one face (namely, single Side surface), a bug can crawl across the entire surface without crossing its edge, that is, it has only one surface. This paper tape is called "Mobius tape".
If the screenwriter of the dome wants to create more suspense, he can use the Mobius ring in the symmetry of the Klein bottle to create weirdness. . .
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