Student: Four dimensions?German mathematicians have proved that what happens when you go into four dimensions?

2022-06-18 0 By

The world is both what it is and what human imagination has made it to be.As a result, imaginative people can often travel in different Spaces, and their dreams are more fantastical than the average person’s.Einstein’s theories opened up another way of looking at the world, and the mathematical framework for his general theory of relativity came from a brilliant German mathematician.The mathematician proved that 4-dimensional Spaces really existed, that he was Riemann, and it’s no exaggeration to say that Riemann geometry helped Einstein solve many of his problems.Riemann’s full name is Bernhard Riemann, graduated from the University of Gottingen, mathematician and physicist, is also the pioneer of Riemann geometry.He made great contributions to differential geometry and mathematical analysis, and died of tuberculosis in his late 40s.Riemann surface We use in daily life are generally “Euclidean geometry”, compulsory education courses learning type is also based on Euclidean geometry as the standard.Only in college, advanced mathematics will introduce some knowledge about non-Euclidean geometry, and Riemannian geometry is developed on the basis of non-Euclidean geometry.So if you want to understand what Riemannian geometry is all about, you need to get out of the way of thinking that’s inherent in Euclidean geometry, or you’ll always be confused.Riemannian geometry is also known as elliptic geometry. Its founding was marked by the publication of “On the Construction of The Foundation of Geometry” in 1854.It is important to note that there are no parallel lines in Riemannian geometry, so you can see how different it is from Euclidean geometry.And Riemannian geometry says that straight lines can go on indefinitely.In short, the model of Riemannian geometry is more like a “sphere”, but the sphere is modified.When we think of a sphere, we naturally think of the surface of the Earth and the nuclear world in the microscopic world and so on.The study of constant curvature space in Riemannian geometry helps us to understand higher latitude space.He got rid of the constraint that Gauss and other mathematicians limited geometry to the three-dimensional world, but set out from a higher dimension, established a new abstract geometry, and proved that 4-dimensional space is real.After that, Einstein used Riemannian geometry as the mathematical basis and the equivalence principle to demonstrate that when there is a gravitational field, the four-dimensional physical space-time should be “curved Riemannian space”.Einstein had an unusual insight into the importance of mathematics to physics during his ten-year search for general relativity.”Theoretical physicists increasingly have to submit themselves to the dictates of pure mathematical forms,” he says.It can be said that Einstein’s general theory of relativity could not have been developed so quickly without the support of Riemannian geometry.Riemannian geometry has virtually pushed both mathematics and physics forward for several generations and is now the mathematical basis of modern physics research.After those who enter the four-dimensional space learn about the creation of Riemannian geometry and related concepts, we can begin to discuss the most mysterious “four-dimensional space”.Four-dimensional space, or higher-dimensional space, has long seemed to exist only in science fiction movies like Interstellar.So if scientists do discover a way to enter the “four dimensions” in the real world and successfully send people there, what will become of them?First, changes in body shape.This point may be difficult for you to understand, after all, the concrete appearance of four-dimensional space, we can not imagine with three-dimensional cognition.So let’s take two-dimensional as an example. You must have seen two-dimensional cartoons, and people sometimes refer to the characters as “paper men”.So, imagine what it would be like to pull these pieces of paper into three dimensions.Their bodies must surely be re-modeled, pulling these “flat” figures into “three-dimensional” shapes, which can be easily done with tools such as computers.But the point is these pieces of paper are inanimate, so it doesn’t matter if you change the form, just change some data.The person that can enter four dimensional space is living, want to add a scale to carry on transformation to its body form there, surely will experience painful.Second, even if one successfully enters the fourth dimension, one cannot understand the rules of that world.After all, entering it does not mean that what your eyes see and mind think is four-dimensional, in other words, entering a four-dimensional space but your mind is still three-dimensional, you are doomed to be unable to understand that space.In this case, one’s mind can be thrown into confusion.Like ants looking at human towers, they can’t understand what we’re doing.Well, ants don’t keep asking questions or thinking about things they don’t understand, but humans do, and that’s the problem.A person with a mind will also become an “incapable of thinking” in the four-dimensional space.Combined with the change of body form mentioned above, this double blow of mind and body is very fatal.Moreover, if a four-dimensional creature does appear in our three-dimensional world, we will certainly not see it in its entirety, because our perspective is always one dimension less than theirs.In that case, we might see only a “part” of his body, just as ants see only a “cross section” of humans.The reason why “ant” is frequently used as an example is that although ants live in three-dimensional space, they see the world in two-dimensional due to the structure of their eyes.So we are trying to enter and understand the four dimensions of space, where we are supposed to be ants in the eyes of the creatures.Belong to the four dimensional klein bottles in recent years, is very popular on the market “mobius ring”, its design prototype is the famous mathematician gauss ta mobius design “mobius strip”, a symbol of the cycle, are also used to marketing into eternal love, after all, if go on the ring, anyway back to the origin.Mobius rings use two-dimensional “pieces of paper” to represent a three-dimensional world. Is there anything that can represent a four-dimensional world?Indeed, German mathematician Felix Klein created a self-enclosed bottle with no obvious boundaries called the Klein bottle.If you look up this bottle on the Internet, it looks very strange, and from our point of view, it clearly has edges and intersects, and the neck goes through the wall of the bottle.This is normal, after all, we are looking at it in three dimensions, and klein bottles only make sense in four or higher dimensions.So we can never make a real Klein bottle in three dimensions.After all, no matter how hard we try, we still can’t break through the limit of one more “dimension”, which is probably the so-called dimension reduction blow. The inability to understand and the inability to break through will make human beings stop at the higher dimensional space.If the extra dimension is time, whether in science fiction or science fiction movies, people like to define the extra dimension as “time”, and the protagonist will naturally complete the “time travel” in the higher dimension space.After all, in the three-dimensional world of human beings, time is a river that can never flow backwards, but if the extra dimension in the four-dimensional space is time, then we have every chance to cross the time limit in that world and go back to the past.What’s worth mentioning is that if the extra dimension really is time, will humans be plunged into a new kind of mental chaos?You know, in the three-dimensional world, money, power, status even in the advantage, but in the face of time, but everyone is equal.When we enter the fourth dimension, the meaning of time suddenly disappears. After all, we can repeatedly hop between multiple time nodes in various ways.In other words, in the four-dimensional space, birth, aging, illness and death may only be born. People can define their own time and choose the time period of life at this moment.In this case, will the meaning of life become meaningless?In short, four-dimensional space and even higher-dimensional space have long been proven to be real.But even if it does exist, it’s hard for us ordinary people to imagine, because we’ll never be able to escape the shackles of three-dimensional cognition.