During the long vacation, Zhi Zhu forwarded an article about "* * * a picture to understand from zero dimension to ten dimensional space * * *", which unexpectedly triggered the hottest forwarding. So far, there have been over 500,000 hits and hundreds of comments. The original text of this article was transferred from the official number "Shang Teacher Design School".

However, after reading this estimate, there are still many controversies. Although Qi Zu graduated from Huazhong University of Science and Technology and Fudan University, he is only a liberal arts student. Although he is a sci-fi fan, he knows little about high-energy physics. I found two materials for reference: one is an interesting version and the other is a serious version.

A popular interpretation from 0 dimension to 10 dimension

Dimension 0 is a point without length, width and height.

1 dimension: a line

2 dimensions: length and width

3 dimensions: length, width and height

4-D: By joining the timeline, people in 4-D space can visit any point in the future and the past at will, but they can't change the future and the past.

5-D: You can change the future and the past. Anything people do in 4-D space will immediately affect everything in this timeline, but people in 5-D space can see all the timelines, that is, people in 5-D space can foresee all the butterfly effects. See the Prophet in Men in Black 3. He can see all the timelines, and any current behavior will make him see a timeline disappear. But once a possibility is chosen, other timelines disappear.

In other words (according to the previous law), people in four-dimensional space only see what happens in a certain timeline, and he can't jump from one timeline to another, but people in five-dimensional space can provide people in four-dimensional space with such a possibility, and he can tell people in four-dimensional space with certainty that if you do something now, you can get a certain result in the future.

Obviously, people in four-dimensional space can't do this, because even if people in four-dimensional space go back to the past and change something, because of the butterfly effect, they can't predict what results will be brought by changing this thing, and they can only see it after the change.

In other words, people in 4-dimensional space can only see a section of all timelines seen by people in 5-dimensional space. If people in 5-dimensional space perform miracles for people in 4-dimensional space, that is, in front of people in 4-dimensional space, this timeline will be changed at will by people in 5-dimensional space.

People in five-dimensional space stir coffee cups, and maybe people in four-dimensional space can see his clothes change from blue to gray at some point in the future.

However, a person in 5-dimensional space cannot change causality, that is, he must modify the timeline by influencing a coordinate in 4-dimensional space, in other words, he must modify his fate through causality.

It's like Cooper, the father of StarCraft, signaling his former daughter in the study. This study is a four-dimensional hypercube, as shown in the figure below. In the higher dimensional space, Cooper just entered one side of a quadrilateral.

On the other side is his daughter's room. Through the fifth dimension, these two distant spaces are connected. This concept is the same as a wormhole. Because light travels in the low dimension, that is, the plane in the picture, Cooper can see his daughter's bedroom from left to right, from top to bottom, and from front to back (this is a four-dimensional hypercube! Think about why? )

Cooper in the four-dimensional hypercube can see his daughter from six directions.

This fifth dimension is not only the fourth dimension of space (the high dimension in physics is usually just a higher spatial latitude), but also a higher latitude where three low dimensions and a time latitude can be seen at the same time. In the words of movies, in this five-dimensional space, time becomes a physical spatial latitude, and all time points can be seen at the same time.

So Nolan expanded the four-dimensional hypercube in time. In Cooper's view, the daughter's room was expanded in three directions by time, so the six rooms that can be seen in six directions became countless rooms that expanded in time, as shown in the following figure:

So how did he promote this book? According to the hypothesis of movies (and physics), gravity can travel through high dimensions, while according to Einstein's general theory of relativity, gravity is only the distortion of time and space, which is like a ravine, and the motion of objects only naturally follows their "world line" in this distorted time and space, and the distortion of time and space will change, so the distortion of time and space can be changed through gravity, and then the world line will be changed, so that the motion of objects will change. So every time direction in the movie is the "world line" of an object, just like a string.

When Cooper hit the wall for the first time, these strings fluctuated, that is, the world line began to change and spread in the direction of time flow.

Simply put, Cooper can act on an object by pulling its "world line".

If you watch the movie carefully, you will find that Cooper is actually poking the "world line" of the watch pointer behind him.

6-dimensional (more and more difficult to understand at first): People in 6-dimensional space can not only see all the timelines, but also exchange things in each timeline at will, which means that people in 6-dimensional space can modify their fate at will. Suppose a person in five-dimensional space sees a timeline: if a person walks with his left foot when he goes out one day, he will become a millionaire ten years later. If a person in five-dimensional space wants to trigger this timeline, he must go back and let that person go out with his left foot, but for people in six-dimensional world, it is not that troublesome. People in the six-dimensional world will ask, "You want him to enter the timeline of becoming a millionaire in ten years, don't you?" All right! Then with a flick of a finger, the timeline became "Ten years later, he became a millionaire". " .

Then people in the 5-dimensional space saw that the man with short oil was really left-footed when he went out, and was not influenced by anyone. He just walked out naturally and took his left foot.

In other words, for people in six-dimensional space, the time axis can be switched at will. If a person in the six-dimensional world shows miracles to a person in the five-dimensional world, then in the eyes of people in the five-dimensional world, all the timelines he sees are constantly changing.

(The picture below shows the hypercube)

Speaking of this, we must introduce a methodology of dimension expansion to help the following understanding: the ways of dimension expansion (in fact, the means are different but the final result is the same, all of which are dimension expansion) are:

1, from low dimension to high dimension, only covering all low dimensions can become high dimension, but this "all" means an infinite number, such as countless points combined into a line, that is, 0 dimension becomes 1 dimension, but it is obviously impossible for 0-dimensional creatures.

Three-dimensional to four-dimensional is the same, but it covers all three dimensions. For example, according to physicists, time is actually just the movement of matter. When all matter stops moving, time stops. All the substances mentioned here stop moving, including microscopic particles such as electrons and atoms, and isotope decay also stops.

Time has stood still. On the surface of a black hole, time is still.

2. You only need to regard what you can observe in this dimension as a section and a fragment, and then imagine all the sections. Those who can visit all the plates at will are high-dimensional creatures.

For example, for creatures in three dimensions, what is happening at the moment is a cross section. You can think of things that happened at other times, but you can't see them.

3, access by folding and jumping, needless to say.

4. People who can create another low dimension must be high-dimensional people. For example, a three-dimensional person can create 0-dimension, 1 dimension and 2-dimension at will (of course, it is actually impossible to create it, this is just a metaphor), but you can't ask a person with 1 dimension to draw another line with 1 dimension.

Then, combined with the above methodology, what is the cross section that people see in the five-dimensional space? That's all the timelines, but all he sees is limited possibilities. He may see that if someone goes out at a certain time, there are three possibilities: walking with his left foot, walking with his right foot, and falling out, and then the result in the back timeline is: millionaire, multimillionaire, billionaire. But he can't say, what if this person jumped out when he went out? He can't make such a prediction. People in five-dimensional space can only come to that coordinate and let that person jump out. Then, in front of people in five-dimensional space, this timeline will appear. Of course, next, he can still influence the timeline at will, come to that coordinate again, and let that person's left foot go out of bounds. However, there are infinite possibilities for going out. People in the five-dimensional space can't cover all the possibilities, but they can only try them out one by one, but "all" means that it is impossible to try them out one by one, and the possibilities are infinite.

Next, it's the turn of the 6-dimensional people to show it. 6-dimensional people not only see all the timelines, but also all the possibilities. He can create a timeline. He can tell 5-dimensional people that if you want him to be a billionaire in the future, you just need to let him out. Then five-dimensional people tried it, and sure enough, there was another timeline ahead.

The first six dimensions have covered everything that may happen in this universe. What can people in the seventh dimension do that people in the sixth dimension can't? This is the universe.

The big bang theory (the same guess has not been confirmed, but it is almost confirmed. I don't think it can be completely proved by human wisdom, so it is like this. I think our universe started with an explosion, and there was no time and space before BIGBANG. Time can only be the time and space of this universe, only the space of this universe.

From a microscopic point of view, everything that happens in this universe is actually just the movement of various particles. Timeline and possibility, in the final analysis, are all changes of particles. All the changes originated from the big bang.

Imagine a table tennis match, BIGBANG, which is equivalent to the first kick-off, and all the timelines and possibilities derived from it depend on that kick-off. A person in six-dimensional space can see all the possibilities on the timeline, but can't see the "impossible possibility".

What do you mean by "impossible possibility"? In other words, your tee shot broke a billiard ball at once, so you can't say that no matter what changes and possibilities, the billiard ball will be in the bag. This result was completely ruled out from the beginning.

BIGBANG is such a restriction that determines all the possibilities in the future. Wave function can describe the probability of an event, but it can't describe the negative space, which can't be calculated.

Then people who live in the seventh dimension are such people who can "see the impossible possibility". People in the 7th dimension can see other T's, that is, other BIGBANG, that is, other parallel universes.

Maybe this is not easy to understand. Let's put it another way. As a person in six-dimensional space, any possibility he sees, any time line, is based on several basic physical constants, such as the speed of light, Planck constant, and other constants that human beings have discovered or have not discovered. Physical constants determine the movement of microscopic particles and the operation mode of the macro world. So what happens if we modify a constant? No one knows, maybe according to this constant, the universe may not exist. However, according to the anthropic theory, what is impossible in our eyes may not be really impossible.

So let's imagine that a person in 7-dimensional space and a person in 6-dimensional space will have such a dialogue:

7-dimensional man: If that person goes out at a speed of 800,000 kilometers per second, that person will become the king of the universe in ten years.

Six-dimensional man: I looked at it and exclaimed, "Impossible! The fastest speed that can be achieved in this universe is only 300,000 kilometers per second. "

7-dimensional man: Mysterious smile: "Really? But in another universe, the fastest speed limit is 9 billion kilometers per second. "

This conversation is enough to illustrate the problem. In the eyes of people in six-dimensional space, going out at a speed of 800,000 kilometers per second is the so-called "impossible possibility".

8-D: It's much simpler. People in the 7-dimensional world see other big bangs and other cosmological constants, but people in the 8-dimensional world can see big bangs that may appear but can't. That is, other BIGBANG possibilities (too cunning, too cunning)

Here, dimensions 7 to 8 can be understood by referring to the previous explanations of dimensions 5 to 6. Take table tennis as an example. People with dimension 8 can name all the tees, including spiking, flying and so on.

9-D: People in 8-D saw the possibility of other BIGBANG. What about people in 9-D? Naturally, I saw the possibility of "BIGBANG that is impossible in BIGBANG". Also refer to 6-D's explanation of seven dimensions!

Let's talk more. When an 8-dimensional person covers all the possibilities, it becomes 9-dimensional. Or use ping-pong for example. No matter how you tee off, you still have to hit the ball with a pole, and then some great people hit the ball with JJ. This is obviously a foul!

I think the anthropic principle should be introduced here. The so-called impossible is not impossible, but an existence that human beings cannot understand.

So here we see the limitations of string theory. How can you fool around again?

10 dimension: string theory means the end! Refer to the 7-to 8-dimensional explanation.

... the copyright of the article belongs to Shang teacher design school ...

.. the pictures are all hand-painted by Mr. Shang. ..

Here's the thing. This week, I gave my students a lesson on 3dmax. In order to let students understand the three views, I learned some knowledge of zero-dimensional, one-dimensional, two-dimensional and three-dimensional space. It's not enough to finish writing. It's great to discuss dimensions with a piece of chalk and a blackboard, so ...

Please open your mind and watch me travel from zero-dimensional space to ten dimensional space with a pen and a few pieces of paper!

Disclaimer: The theories in this paper are all based on the knowledge of string theory physics, combined with simple charts and popular truth to explain, not just nonsense, but also have scientific basis.

zero dimension

Let me start with a point. Just like a point in our geometric sense, it has no size and no dimension. It's just an imaginary point, marking a position. It has nothing, and neither space nor time exists. This is zero dimension.

one-dimensional space

Well, after understanding the zero dimension, we will start the one-dimensional space. A little bit already. Draw another point. Connect between two points. Knock, knock. One-dimensional space was born! We created space!

One-dimensional space has only length, but no width and depth.