Does anyone have any English information about introducing Tai Chi?

Jianming Zhou: An Intuitive Training Method for the Study of Taijitu

Taijitu, the totem of Chinese academic thought, has always been shrouded in a mysterious light. It is mysterious because it has a kind of infinite suggestion that seems to be comprehensible and unintelligible, but this is not the same as a true mystery such as the induction of a religious experience, or the incantation of a superstition, etc., which is derived from its intrinsic geometrical essentiality. a kind of rational light, strong contrast, flowing harmony, self-referential perfection, with a life-like spirituality, self-contained, infinite, free, associative, and infinitely transcendent, which contains the true secrets of thought. The article "Chinese Thought and Plato's Philosophy" reveals its relation to topology, and the article "Chinese Philosophy - Tai Chi Geometry" reveals its intrinsic nature, but it is not possible to see it directly from the Tai Chi diagram. But to see the content of Tai Chi directly from its diagrams is not possible by theoretical deduction alone, and even if you have expertise in higher mathematics, you must have strong geometric intuition in order to do so. Let the rational thought realize as a kind of flowing imagery, this is a kind of physical thought practice, is the form of mathematics, geometry and physical content compatible mixed with the fuzzy intuition, it is called by many scientific masters the so-called fuzzy imagination thought experiment, for example, mathematical physics in the phase space, the field, the quantum state, and so on have this kind of quality, which has a great role in scientific theories of the human ability to create, The human creative ability, the so-called inspiration is also the embodiment of some aspects of this ability, but this basically can not be obtained through direct learning methods, but to rely on academic training and long-term thought self-training and formation, in fact, philosophical phenomenological theory of phenomenological intuition method has a great deal of similarity with this, this is not a mystery, but is the formation of the process of thought and rationality of the process of state, is the epistemology of the realization of the concrete way. The concrete ways of realization, in a sense, these can be seen as signs of the kind of progress that the rational mind of mankind is facing in modern times after the slow development and accumulation of recent millennia. This ability is extremely helpful for learning the most cutting-edge theories of modern mathematics and physics, and is a purely academic merit in philosophy. For Chinese people, the essence of Chinese culture can be more y understood and enjoyed through such a method of cultivation, and therefore it is entirely possible to treat the intuitive training of taijitu as a kind of exercise in advanced intellectual ability.

1. First of all, it is necessary to establish a frame of mind for the projection of high dimensional space in low dimensions, which can be started from the repeated imagination and understanding of the image of three-dimensional (body) to two-dimensional (surface), two-dimensional to one-dimensional (line), and one-dimensional to zero-dimensional (point), and the key here is the process of geometrical projection of the realization of the imagination, and vaguely imagining the process of projection as a traversal of the space, and after such a training of mind, the ability to imagine four-dimensional space will also be trained. After this kind of training, the ability to imagine four-dimensional space is basically available. We in the three-dimensional world cannot have any perceptual knowledge of the four-dimensional world, but high-dimensional geometries can be expressed through low-dimensional models, so we can vaguely imagine high-dimensional scenarios through the construction of high-dimensional projections of low-dimensional processes. Being in the Chinese cultural environment, concepts such as tai-polar points and yin-yang surfaces have a cultural intuition for us Chinese, which is superior to the Chinese intuitive understanding.

2. The easiest topological image to visualize is the topological sphere with inside and outside, the topological sphere with yin and yang inside and outside faces is different from the geometric sphere in the usual sense, the purely geometric sense of the sphere is only the surface of the one-sided definition, there is no inside and outside, while the topological sphere, although it is also a two-dimensional surface, but yin and yang have a different, and therefore has an intrinsic three-dimensional essence, which is the Chinese doctrine of yin and yang, the doctrinal performance of the Chinese people to get the most out of the Chinese intuitive understanding. This is where the Chinese doctrine of yin and yang is most intuitively manifested. Due to the traditional Chinese academics do not have geometric expression, the concept of yin and yang has been only language through the example of attribute expression, it is difficult to clarify, through the definition of the topological sphere, yin and yang of the scientific and rational content of the full unfolding, of course, although, yin and yang doctrine of the mystery is not shallow, but more profound.

3. On this basis, the topological sphere can be further imagined as a topological solid sphere with a certain fluid content, (here it is not possible to speak of the standardization of terminology,) the so-called topological sphere is a mixed image of geometry and physics, the Chinese and foreign academics have always been with a mysterious Ether, the Yuanqi is precisely such a flow of intrinsic nature, but this step can not be visualized and can only be conserved as a vague imaginative. But this step can not be visualized but can only be kept as vague imagery, which is a key to further understanding of the Taiji diagram. The most exquisite concepts of Wu Wei and Zhong Yi in traditional Chinese academic thought are the linguistic expressions of this wonderful state, which is natural and not mysterious to the Chinese people who have grown up in the Chinese cultural environment. The representation of taijitu came out later than the traditional Chinese philosophical thought, and it is very secretive and difficult, because it has to express the doctrinal content by the symbolical nature of the illustration, taijitu that is, it is not a pure symbol, nor is it a geometrical figure, but it is an illustration, which is of the nature of the culture of totem, and it has a powerful doctrinal connotation, and it has to express the things which are too deep in the nature and the level.

4. The four-dimensional geometry expressed in three-dimensional space is a very intellectually demanding geometric model: the "projection" of four dimensions in three dimensions is the three-dimensional topological sphere (body), which is already the essence of the taijitu, but we can't take the three-dimensional entity as a reality that expresses its geometrical rigidity and at the same time is physically fluid. The liquid metal man in the sci-fi movie managed to do this, and the human imagination far exceeds the practical ability. In theory, the four-dimensional pure geometric model is reduced to three-dimensional topological sphere with inside and outside, that is, three-dimensional space in the two-dimensional topological sphere through the expression of their own intrinsic three-dimensional and become a four-dimensional model of space, so that people can easily in the topological sphere on the opening of holes to make the yin and yang sides of each other exposed to connect to become a three-dimensional space in the topological geometry, mathematical theory of physics there is a relative concept is the manifold. In topological geometry, there is already a model of three-dimensional space expressed in two-dimensional form, which is the "projection" of the three-dimensional plane in four-dimensional space in three-dimensional space - Klein's bottle (the M?bius strip is just a dissected Klein's bottle), and this complex expression of relations between the This complex relationship of expression is the secret of the incomprehensible mystery of the Klein bottle and the M?bius strip in their simple form.

5. Theoretical realm: the taijitu is the projection on the Euclidean plane of the four-dimensional topological sphere expressed in three-dimensional space.

The intuitive training of the Tai Chi diagram is much more difficult than the simple visual training to see the three-dimensional diagram, from intuition into intuition is completely dependent on the individual self-training is completed, the most preliminary, the expression of the elements of the Tai Chi diagram can be broken down in the following way to understand: the great circle and the S-shaped curve represents the projection of the high-dimensional in the low-dimensional, black and white represents the flip space, the fisheye represents the crossing of its own. But this is only a hint; if one were content with this paper interpretation, this paper would have said nothing. It must be remembered: the imagery in thought is fluid, the projection must be imagined as a traversal in different dimensions of space, all the elements are always changing with each other in different dimensions, you must maintain that so-called travel in time as pure imagery of the imagery of the state, and with this kind of intuitive rationality, you can really understand the highest realm of the Chinese thought --- change and change. -The most important thing is that you have to keep the pure imagery of traveling through time in a state of imagination.