Is taiji diagram really a two-dimensional projection of high-dimensional space?

Taiji diagram is the totem of China's academic thought, which has been shrouded in mysterious brilliance. Its mystery lies in its seemingly incomprehensible infinite hints.

First of all, to establish an ideological framework of high-dimensional space projection in low dimension, we can start with repeatedly imagining and understanding images from three-dimensional (volume) to two-dimensional (surface), two-dimensional to one-dimensional (line) and one-dimensional to zero-dimensional (point). The key here is to realize the process of geometric projection, and vaguely imagine the projection process as space crossing. After such ideological training, the imagination of four-dimensional space will also be improved. Those of us in the three-dimensional world can't have any perceptual knowledge of the four-dimensional world, but high-dimensional geometry can be expressed by low-dimensional model, so we can imagine the high-dimensional situation through the fuzzy construction process of high-dimensional projection to low-dimensional projection. In the cultural environment of China, the concepts of Taiji Point and Yin and Yang have a cultural intuition for us in China, which is better than our intuitive understanding of China.

The simplest and most intuitive topological image is a topological sphere with inner and outer surfaces. Topological sphere with internal and external surfaces of yin and yang is different from geometric sphere in the usual sense. A purely geometric sphere is defined by only one surface, and there is no distinction between inner and outer surfaces. Although the topological sphere is also a two-dimensional surface, Yin and Yang are different, so it has an inherent three-dimensional essence, which is also the most intuitive manifestation of China's theory of Yin and Yang. Because there is no geometric expression in China's traditional academic studies, the concept of Yin and He can only be expressed in language through the attribute of examples, which is difficult to be clarified. Through the definition of topological sphere, the theoretical content of yin and yang is fully developed. Of course, even so, the meaning contained in the theory of Yin and Yang is not simple, but more profound.

On this basis, we can further imagine this topological sphere as a topological solid sphere with some fluid content. (The specification of terms cannot be emphasized here. The so-called topological sphere here is a mixed image of geometry and physics. Ether and vitality, which have always been mysterious in academic circles at home and abroad, are such a flowing immanence, but this step can only be preserved as a vague image, which is a key to further understanding Taiji diagram. The most subtle concept of inaction in China's traditional academic thought is the theoretical language expression of this wonderful realm, which is natural but not mysterious for China people who grew up in China cultural environment. The representation of Taiji diagram came out later than China's traditional philosophy, and it is very secret and difficult, because it uses symbolic diagrams to express theoretical content. Taiji diagram is not a simple symbol or geometric figure, but a figure with totem cultural nature and strong theoretical connotation. What it wants to express, its nature and level are too profound.

The four-dimensional geometry expressed in three-dimensional space is a geometric model that needs intelligence very much: the "projection" of four dimensions in three dimensions is a three-dimensional topological sphere (body), which is already the essence of Taiji diagram, but we can't express its geometric rigidity and physical fluidity with a real three-dimensional entity. The liquid metal man in science fiction movies has successfully done this, and the imagination of human beings far exceeds the actual ability. Theoretically speaking, the four-dimensional pure geometric model is a topological sphere whose inside and outside are reduced to three dimensions, that is, the two-dimensional topological sphere in three-dimensional space becomes a four-dimensional space model by expressing its inherent three-dimensionality. Therefore, people can easily open holes in the topological sphere to expose and communicate Yin and Yang, and form topological geometry in three-dimensional space. A relative concept in mathematical physics theory is manifold. There is already a model in topological geometry that three-dimensional space is represented by two dimensions, which is the "projection" of three-dimensional plane in four-dimensional space-Klein bottle (Mobius belt is just a cut Klein bottle). This complex expression relationship is the secret of the incomprehensible mystery of Klein bottle and Mobius belt in a simple form.

Theoretical realm: Taiji diagram is the projection of four-dimensional topological sphere represented by three-dimensional space on Euclidean plane.

The visual training of Taiji diagram is much more difficult than the visual training of simply looking at a three-dimensional diagram. From intuition to intuition, it is completely accomplished by personal self-training. At first, the expression elements of Taiji diagram can be understood as follows: the great circle and S-shaped curve represent the projection of high dimension in low dimension, black and white represent the inversion of space, and the fisheye represents its own crossing. But this is just a hint. If you are only satisfied with this paper explanation, this article will say nothing. It must be remembered that the images in the mind are fluid, the projection must be imagined as crossing in different dimensions, all the elements are always changing in different dimensions, and you must keep the imaginary state of pure images like traveling in time. With this intuitive reason, you can truly understand the highest state of China Thought-change.