Dimension, this word must have been heard of by everyone. So, what exactly is a dimension?
In fact, dimensions are the number of parameters in mathematics. In the field of physics, it refers to the number of independent space-time coordinates. Philosophically speaking, it refers to the way people observe, think, or describe things.
Here's a quick description:
Mathematical dimension: The number of parameters required to describe a mathematical object under certain premises, the complete statement should be "the object x is based on the premise a is n-dimensional".
We can simply understand that the point is 0 dimension, the line is 1 dimension, the plane is 2 dimension, and the body is 3 dimension. However, this understanding is incomplete, and its full description should be: point based on point is 0 dimension, point based line is 1 dimension, point based on plane is 2 dimension, point based on body is 3 dimension.
Let's explain further: describing a point on a point is the point itself and does not require parameters; describing a point on a straight line requires 1 parameter; describing a point on a plane requires 2 parameters; describing a point on a body requires 3 parameters. These parameters are what we often call coordinate values.
But if the object we describe changes, then we will come to different conclusions, such as: the line is 4-dimensional based on the plane, the line is 6-dimensional based on the body, and the plane-based body is 9-dimensional. Further understood: two points can determine a straight line, so describing a line requires 2 ×2 parameters on the plane, and 2×3 parameters on the body; three points that are not collinear can determine a plane, so it takes 3×3 parameters to describe a plane on the body.
Physical dimensions: There are link pathways and fractional dimensions. For example, two parallel lines can be thought of as two relatively independent dimensions, and to get from one line to another requires establishing a new straight line connecting the two, which is the dimension. Dimension 0 is a point with no length; dimension 1 is a line (string), only length. A 2-dimensional is a plane that is formed by length and width (or curve) a polygon that can hold n lines or be composed of n lines. 3 dimensions are 2 dimensions plus height to form a stereoscopic.
(Note: 0 dimension is a point, in fact, it is not rigorous, if it is a point, even if it is small, it must have a length and width.) So, 0 dimension is not a point, 0 dimension is actually negligible, 0 dimension is nothing)
Fractions are, in the 19th century, mathematicians discovered fractals, thus creating a new dimension - "fractional dimension". People realize that dimensions don't just have integers, but also can be fractions, or even irrational numbers. The famous British physicist Stephen Hawking has such an explanation: like a hair, we look at a one-dimensional line from a distance, but under a magnifying glass, but it is three-dimensional; then for space-time, if we have a high enough magnification, we should also be able to reveal other possible 4-dimensional, 5-dimensional space, up to 11-dimensional space.
Philosophical field: We observe, think or describe problems from several points of view, which is called a few dimensions. For example, people who have lost consciousness and have no obvious thinking activities are called "zero dimension"; the mind is simple, a road goes to black, and its way of thinking is called "one dimension"; good at "one divided into two", observing and thinking about problems from both positive and negative aspects, and its way of thinking is called "two dimensions"; accustomed to "one divided into three", the way of thinking that can investigate and analyze from three main aspects is called "three-dimensional".
These are simply descriptions and understandings. Let's talk about the multidimensionality often referred to in physics.
Physicists divide the dimensions into eleven. One dimension is line, two dimension is polygon, three dimension is static space, and four dimension is dynamic space.
The parameters that we must change in physics to describe a changing event. This parameter is called a dimension. Simply put: 0 dimension is a point, there is no length, width, or height. A dimension is a line made up of countless points, only in length, not in width or height. Two-dimensional is a surface composed of countless lines, with length, width and height. Three-dimensional is a body composed of countless faces, with length, width and height. Dimensions can also be understood as directions.
Four-dimensional: Most refer to the concept of "four-dimensional space-time" mentioned in "General Relativity" and "Special Relativity". Our universe is made up of time and space. The relationship between space-time is that a timeline is added to the structure of space to the length, width and height of ordinary three-dimensional space, but this timeline is an axis of imaginary values. According to the theory of relativity, the three-dimensional space we face in our lives plus time constitutes four-dimensional space-time.
Five-dimensional: There are an infinite number of trends at any point on a four-dimensional timeline. In this way, an infinite number of timelines are separated from a point in the fourth dimension, forming the fifth dimension.
Six-dimensional: Two timelines in five-dimensional space, just as two-dimensional space cannot be reached directly. In six-dimensional space, just as two-dimensional space is bent, five-dimensional space can also be bent, resulting in a six-dimensional space, in which it can directly reach any point on the five-dimensional timeline.
Seven-dimensional: Seven-dimensional space includes all the dimensions of space from the beginning of the Big Bang to the end of the universe, all the possibilities on all the dimensions of time, and the feasibility of reaching directly at any two points. Five-dimensional space is a point that produces an infinite number of development trends, and seven dimensions is an infinite timeline of all points, that is, infinite points.
Eight-dimensional: Eight-dimensional space includes an infinite number of universes arising from the Big Bang, which have different laws of physics and different gravitational constants.
Nine-dimensional: Nine-dimensional space is the curvature of eight-dimensional space, in eight-dimensional space, it is not possible to reach different points in each universe directly, while in nine-dimensional space, it can be directly reached between two points in eight-dimensional space.
Ten Dimensions: According to superstring theory, the smallest particle is not a solid matter, but a matter formed by superstrings of different vibrational frequencies, and different frequencies produce different external manifestations. In the ten-dimensional space, there is no matter anymore, only strings with different vibrational frequencies. Anything is possible in ten dimensions.
Eleven-dimensional: Eleven-dimensional space is composed of ten-dimensional space plus memory and perception, Einstein believed that memory is extensible and elastic, and perception exists outside of time, space, and memory. After the ten-dimensional space of superstring theory, the supermembrane theory of eleven-dimensional space was introduced. In short, eleven-dimensional space is made up of time, space, memory, and perception.
Of course, five- to eleven-dimensional spaces are only theoretical possibilities. For us humans, other dimensions are difficult to perceive.