"What happens to people if they enter the four-dimensional space?"
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This is a very interesting question, three-dimensional space is very common in our daily life, such as tables, chairs, clothes, etc. are three-dimensional, and we can also move freely in three-dimensional space, so three-dimensional space is also called three-dimensional space.
So what does a four-dimensional space look like?
We can start from the definition of four-dimensional space, understand the difference between it and three-dimensional space, and discuss what happens to human beings after entering the four-dimensional space.
1. Three-dimensional space and four-dimensional space.
The so-called dimension of space is a concept used to describe the characteristics of space, and in simple terms, it is used to describe the degrees of freedom.
Three-dimensional space is a space with three degrees of freedom, which is what it is characterized by, allowing us to move freely in three directions: width, height, and depth.
The four-dimensional space adds an extra dimension to the three known directions, so that objects in the three-dimensional space can move freely in this additional direction, that is, they have more degrees of freedom.
In addition, there is another important feature of four-dimensional space that cannot be achieved in three-dimensional space, that is, the full development of the cube.
In three-dimensional space, only three directions of the cube can be expanded, but in four-dimensional space, the cube can be expanded in the direction of four-dimensional space, which is unimaginable in three-dimensional space.
So who exactly came up with the concept of four-dimensional space?
It all starts with the German mathematician Riemann.
Riemann was a 19th-century mathematician, he was a student of the German mathematician Riemann, from his birth in 1836 to his death in 1868, he lived only a short 32 years, during which he made a very important contribution to the development of the field of mathematics.
Speaking of his contributions, it is necessary to mention his concept of "Riemannian geometry", which is also a very important direction in the later development of mathematics.
Speaking of "Riemannian geometry", it is important to mention non-Euclidean geometry and Euclidean geometry.
Before Riemann was proposed, Euclidean geometry had been the main direction of mathematicians' research, and it was also the only geometric system considered at that time.
Euclidean geometry is a geometric system represented by Euclid's "Geometric Primitive", which is very perfect, but it also has a big drawback that it can only be used to study two-dimensional and three-dimensional space.
But in the 19th century, Riemann of Russia proposed the concept of non-Euclidean geometry, which opened the door to the study of multidimensional space.
There is a big difference between non-Euclidean geometry and Euclidean geometry, that is, the space of non-Euclidean geometric systems is infinitely extensible and unlimited.
Euclidean geometry, on the other hand, can only study a limited space.
Riemann combined non-Euclidean geometry with Euclidean geometry to create modern geometry.
The proposal of this theory not only caused a great sensation in the field of mathematics, but also had a great impact on the fields of physics, philosophy, and art.
Mathematicians have begun to enter the high-dimensional space beyond human imagination, and Riemann has also made a lot of contributions to the research in this direction, among which the four-dimensional space is a very important one, which is also the pioneer of the second golden age in the field of mathematics.
2. Mathematical models of four-dimensional space.
Since Riemann has made great contributions to the study of four-dimensional space, what does four-dimensional space look like according to his definition of four-dimensional space?
When Riemann studied the four-dimensional space, he described the dimensional space mathematically, and this mathematical model is the "Riemann metric space" that we often hear.
The so-called "Riemannian metric space" is a space with a measure, which is a function used to measure the length and angle between two points, just like the distance function we commonly use in three-dimensional space.
This distance function can be calculated from Euclidean distances in three-dimensional space, and in four-dimensional space, we can calculate it from "Riemannian metrics".
The so-called "Riemannian metric" is a description of the angle and length of two vectors in space, which can map the two vectors into a field of real numbers.
This "Riemannian metric" is also a binary symmetry function, when two vectors are the same, this function is the length of the corresponding vector, when the two vectors are different, this function is the angle of the corresponding vector.
Therefore, the Riemann metric can be used to describe the angles and lengths in the four-dimensional space, so that the lengths and angles of the vectors in the four-dimensional space can be mapped to the real number field, that is, they satisfy the properties of the distance function.
After calculating the distance in the four-dimensional space through the Riemann metric, we can also represent the points in the four-dimensional space as coordinates, so that the four-dimensional space can be described in the form of coordinates, just as we describe the space in the three-dimensional space.
But in the four-dimensional space, to describe a point, we need to use four coordinates, so the point in the four-dimensional space can be represented in the form of (x, y, z, w), where x, y, z, and w correspond to the coordinates in each direction.
In this way, we can describe the four-dimensional space, and by performing vector operations in the four-dimensional space, we can also find the angle and length of the four-dimensional space, so that we can study the geometry in the four-dimensional space.
Research and development of three- and four-dimensional space.
Riemann proposed the concept of four-dimensional space, which not only opened up the way for the study of high-dimensional space, but also provided theoretical support for Einstein's theory of relativity.
Before Einstein proposed the theory of relativity, he had been thinking about the origin and evolution of the universe, but to explain the origin of the universe, it is necessary to describe the shape of the universe through mathematical models, which requires a higher-dimensional space.
It was inspired by Riemann's development of the "Riemannian metric space" that Einstein began to study the general theory of relativity, and he regarded space-time as a subset of the Riemannian metric space, and the form of the universe as a subset of a high-dimensional space.
It was under the description of this space model that Einstein finally formed a theoretical system of relativity, which not only explained the origin of the universe, but also explained the evolution of the universe.
It was the concept of Riemann metric space that provided theoretical support for Einstein's general theory of relativity, thus promoting the development of physics.
Riemann had a very profound influence not only in the fields of mathematics and physics, but also in philosophy, art, and other fields.
4. What happens after entering the four-dimensional space?
What happens to humans in the four-dimensional space?
For this problem, we can discuss it from several angles, first of all, in the field of mathematics, four-dimensional space can not only study the geometry in space, but also solve some problems in mathematics.
In addition to mathematics, four-dimensional space can also be applied to the field of physics, and Einstein used the concept of Riemann metric space to describe the origin and evolution of the universe.
In the field of philosophy, the four-dimensional space can also be applied to human philosophical thinking, and new thinking about the existence and meaning of human beings can be carried out.
In the field of art, the four-dimensional space can also be used for painting, which can draw some patterns in the four-dimensional space, and can also be used to create film and television works.
In addition, there are some writers who have discussed the four-dimensional space, the most famous of which is the American writer Aldes Huxley, whose works contain the content of the four-dimensional space.
Human exploration of the four-dimensional space is not limited to abstract discussions, but can also be explored through some models, although we cannot really enter the four-dimensional space, but can be simulated through some models.
In the four-dimensional space, we can carry out some interesting explorations, such as in the four-dimensional space, there may be scenes of traveling between different three-dimensional spaces, there may also be scenes of changing the shape and position of objects, and there may also be some strange four-dimensional monsters and four-dimensional labyrinths.
V. Conclusion
It is the exploration of the four-dimensional space that produces these interesting exploration scenarios, which inspires people to think new and promote some new creations.
Therefore, there is no end to the exploration of the four-dimensional space by human beings, and there may be more breakthroughs and deeper developments in the future, and we look forward to more discoveries and breakthroughs in the exploration of the dimensional space.