More than two thousand years ago, almost all our geometry knowledge came from Euclid's Elements of Geometry. This book is regarded as the foundation work of modern mathematics, and on this basis, human beings have developed astronomical geography knowledge. Later, the famous mathematician Gauss began to question its limitations. Because Euclid thinks that points have no dimensions in space; Lines have one dimension, that is, length; A plane has two dimensions, namely, length and width; Stereo has three dimensions, namely, length, width and height. Besides, nothing, nothing will have four dimensions.

Gauss believes that Euclid's understanding of dimensions is entirely based on human intuitive understanding, which is very limited in the borderless mathematical world. He told his colleagues that Euclid's geometry hypothesis is like an "ant" living on a two-dimensional plane, and only sees the length and width from its world, so it thinks that the world is only "long" and "wide", and there will be no "high" dimension. However, because Gauss is a very conservative person, at that time, the western mathematical circles lashed out at the concept of "high dimension", thinking that it was a "fallacy" that could shake the foundation of scientific rationality more than a scourge. Therefore, Gauss has not published any works on the theory of high-dimensional geometry.

Later, the mathematician Riemann discovered that Euclid geometry was based on a plane. In nature, it is difficult for us to see idealized Euclidean geometry, and mountains and valleys are not perfect geometry. In a flat space, the sum of the interior angles of a triangle is 180, but if the space is uneven but has a certain curvature, then the sum of the interior angles of a triangle is related to its curvature, which is greater than or less than 180. In other words, if our space is curved, then the theory of Euclid geometry is wrong.

Thus, if we still think in one, two or three dimensions, we can only see the geometry of plane and solid, and if we understand the existence of four dimensions, we will enter the world of Riemannian geometry, from which Einstein put forward the famous general theory of relativity.

Without the dimension increase of Euclidean geometry, there would be no general relativity, which is the power of dimension increase. It can let us see a brand-new world completely different from the previous world. In this way, some problems we encounter will be solved.

As Einstein said, "our thinking level of solving problems cannot be the same as our thinking level of creating problems."

Ascending thinking is the kind of thinking that can make us by going up one flight of stairs. Upgraded thinking refers to the thinking mode of rethinking problems and their solutions through the transformation of levels, time, perspectives, boundaries, positions and structures. If we say that essential thinking is a way of thinking to find a fundamental solution by thinking about the root of the problem within the existing structure or system; Then, ascending thinking is a way of thinking that breaks the existing hierarchy, time, boundary, position and structure and solves problems by jumping, updating, expanding and rebuilding.

Several ways of thinking that can greatly change our behavior and life are hierarchical thinking, timeline thinking, perspective thinking, third choice thinking, borderless thinking and shaper thinking.