Zhou Jianming: An Intuitive Training Method for Taiji Diagram Research
Taiji diagram is the totem of China's academic thought, which has been shrouded in a mysterious brilliance. Its mystery is because it has a seemingly incomprehensible infinite hint, but it is different from the real mystery, such as the induction of religious experience and superstitious spells, which comes from its inherent geometric essence. The mystery of Taiji diagram is a kind of rational brilliance, strong contrast, harmonious flow, self-consistent perfection, and a life-like spirituality and freedom. The article "China Thought and Plato's Philosophy" reveals its relationship with topology, and "China's Philosophy-Taiji Geometry" reveals its inner essence. However, if we want to see its theoretical content directly from the Taiji diagram, it is not enough to rely solely on theoretical deduction. Even if you have advanced mathematics professional knowledge, you must have strong geometric intuition ability to do this. Realizing rational thinking as a flowing image is a conscious thinking practice, a fuzzy intuition that the form of mathematics and geometry adapts to the physical content, and an ideological experiment called fuzzy imagination by many scientific masters in mathematical physics, such as phase space, phase space and quantum state. It has this characteristic and plays a huge role in scientific theory. The creative ability of human beings, the so-called inspiration, is actually the embodiment of a certain aspect of this ability, but it can not be obtained by direct learning, but by academic accomplishment and long-term ideological self-training. In fact, the phenomenological intuitive method in philosophical phenomenology theory is very similar to this. This is not a mystery, but a process state of ideological rationality, which is a concrete way to realize epistemology. In a sense, these can be regarded as human rationality. This ability is of great help for learning the most advanced theories of modern mathematics and physics, and it is a purely academic skill in philosophy. For China people, we can deeply understand and enjoy the essence of China culture through this learning method, so the intuitive training of Taiji diagram can be regarded as an exercise of advanced intelligence.
1. First of all, we should establish an ideological framework for the projection of high-dimensional space in low dimensions, starting with the repeated imagination and understanding of three-dimensional (volume) images of two dimensions (surfaces), two dimensions (lines) and one dimension (points). The key here is to realize and imagine the geometric projection process, and vaguely imagine the projection process as a space crossing. After that, those of us in the three-dimensional world can't have any perceptual knowledge of the four-dimensional world, and the high-dimensional geometry can be expressed by the low-dimensional model, so we can imagine the high-dimensional situation through the fuzzy construction process of the projection from high-dimensional to low-dimensional. 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.
2. 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.
3. 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 Chinese and foreign academic circles, is such a kind of fluidity, 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.
4. 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.
5. 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.