Focus on the development and innovation of academics

Editor's Note

As one of the representative figures of the Yangzhou School in the Qing Dynasty, Jiao Xuncheng, who was known as "a generation of Confucians", "a scholar of "Yi", read and reasoned, loyal and honest, knowledge and honesty" family style, rigorous study, writing Hongfu, lifelong research involved in the classics, history, almanac, rhyme, exhortation, poetry, opera, medicine and other fields, which had a far-reaching impact on future generations. This issue focuses on Jiao Xun and shows the world of his well-written writings.

Author: Chen Juyuan (Professor, Huixue Research Center, Anhui University)

Jiao Xun (1763-1820) Zi Li Tang, Yi Zi Li Tang, the old man of the late Li Tang, a native of Yangzhou, Jiangsu Province, a famous scribe and Yi scholar at the time of Qianjia in the Qing Dynasty, and an important representative of the Yangzhou School. He is rigorous in his studies, rich in writing, insightful, courageous in pioneering and innovative, and is known as "a generation of Confucians".

Jiao Xun's lifelong academic research, the most diligent, the deepest skill, the greatest achievements, the greatest influence is to open up the "Zhou Yi" of the elephant number paradigm research. He is the author of "Carved Building Yixue" ("Yixue Three Books"), "Yi Shu", "Yi Guangji", etc., jumping out of the barrier of the elephant number paradigm to study "Zhou Yi", inventing the easy to learn laws such as "bypass", "wrong", "time line", etc., thus demonstrating the law of displacement movement between the three hundred and eighty-four masters of the sixty-four gua of "Zhou Yi", revealing the rich yin and yang and change ideas contained in it, expanding the traditional elephant number easy learning, bringing people a variety of reverie and mysterious thoughts, which was called "non-Han, non-Jin Tang, non-Song" by the academic circles at that time , the development of the ancient has not been developed" easy to learn strange. Jiao Xun believes that "bypass" is the mutual substitution of one yin and one yang in the sixty-four gua of Zhou Yi, and the main purpose is to transform or obtain another gua with the mutual exchange of yin and yang in each gua. For example, if the "Qian" Gua Liu Yao is composed of all the Yang, then the gua that is bypassed with the "Qian" gua must be the "Kun" gua, because the "Kun" gua liu yao is composed of all yin, and the "Qian" gua of the liu yao quanyang is opposed to the "Kun" gua of the liu yao quan yin, and the bypass of the two gua of "Qian" and "Kun" can be established. The main connotations of bypass are three: First, bypass gua yao must be yin and yang. Second, the yin-yang transformation of bypassing gua yao must be carried out in order. Third, the purpose of bypass is to make each of them in their place. Jiao Xun also believes that the "phase error" is based on the thirty-two sets of bypass gua in the sixty-four gua of the Zhou Yi, and the conversion between the gua and the gua is carried out. The main connotations of the discrepancy are fourfold: First, all the inferior trigrams that bypass the trigram are replaced with each other to form a discrepancy. Second, where the position of the bypass gua two five yao is changed, and the combination is the wrong of the new gua. 3. Where the position of the first four or three upper gua is changed and combined into a new trigram. Fourth, where the bypass gua first two five followed by the three upper or first four positions are changed and combined into a new gua of the wrong. Jiao Xun also believes that "time travel" is based on the "bypass" and "wrong" guayao position change movement, and examines the sixty-four gua of the Zhou Yi as an inevitable connection, thus amplifying the internal connection between the guayan. For example, Jiao Xun once gathered the "yuan" in the sixty-four gua into twenty-four gua, and used the law of "time to walk" to change the position between the gua, comprehensively expounding the meaning of the word "yuan" in the various gua, "either explicitly or mutually".

In order to further develop the paradigm of zhou yi, Jiao Xun introduced the laws of "multiplication", "tianyuan", "qitong" and "proportion" in traditional Chinese mathematics into the study of Yixue. For example, "multiplication" is a calculation method for finding a six-way power (opening a five-powered square), and the class introduces a new permutation of sixty-four trigrams. In modern mathematical notations, it can be expressed as (a+b)6, and if you expand its equations, you get the result of "a6+6a5b+15a4b2+20a3b3+15a2b4+6ab5+b6". If "a" and "b" are used to represent "A" and "B", and "A" and "B" represent yin and yang, then the permutations and combinations of the "five-square" calculation of the sixty-four gua can take on seven different forms. This undoubtedly provided a new way for Jiao Xun to construct a new mathematical paradigm of the new elephant, reflecting his expansion and transformation of the flexibility theory of "Zhou Yi", which caused a shock in the academic circles at that time, and was praised as "stone breaking the sky" and "elite soldier".

In fact, Jiao Xun's creation of the Easy-to-Learn Law and its relationship with mathematics are all references for Jiao Xun to construct the Symbol System of Zhou Yi. Using numbers to attach to the Gua Yao, according to the mode of mathematical laws to establish the relationship between the "Zhou Yi" Gua Yao and the mutual movement and transformation, this set of symbol systems is the structural form of jiao", which is the carrier of its ideological content. Following the ideological content of the Yi study, Jiao has never been able to jump out of the relevant principles of the social system and ethics and morality derived by the Elephant Number School with gua xiang and numbers. Although Jiao Xun had the desire to rebuild the study of heaven and man, he still referred to the "right life of each person, and the protection of Taihe", pursuing the Confucian "benevolent way" and envisioning the world of "the world is just".

Reinterpreting the Confucian classics is another feature of Jiao Xun's academic pioneering and innovation. Taking Pu Xue as the starting point, he systematically sorted out and made new interpretations of Confucian classics such as the Book of Poetry, the Reappraisal of the Book of Shang, the Admiration of the Book of Rites, the Questioning of the Zuo Chuan, and the Realization of the Analects. For example, he wrote "Shangshu Kong's Biography Supplement", a "Shangshu Supplement", two volumes. The sixty-two examinations listed have two themes discussed: First, although the Shangshu Kong Biography is a pseudo-book, its interpretation is more detailed than the commentaries of Ma Rong, Zheng Xuan, Wang Su and other Han and Wei families, and lists the seven advantages of the pseudo-"Shang Shu Kong Biography", believing that the classic falsification is different from the classical commentary, it is not a field of speculation but should be a mutually corroborating and empirical activity, and this activity, in essence, should be mainly implemented in the specific analysis of the classical original materials, so it is an empirical thinking. Classical research does not take the creation of an authoritative image as its own responsibility, but observes the authoritative image that has been created in the classics and clarifies its inherent precise meaning and value. This elaboration actually includes the unity of the ancient meaning of the classics with the modern interpretation of the commentary. Thus, although it has been proven to be a forgery, it still has historical value in thought. Second, the YaoDian is not dead, and the Da Yu Mo and Gao Tao Mo were originally one, believing that any scripture handed down from ancient times has a relative authenticity from a linguistic point of view. For every modern person, however, it means a fragment that has been interrupted. Because it is a fragmentary fragment, it also provides various conjectures for the reliability of its text.

Jiao Xun also wrote the three volumes of the Analects supplementary, listing seventy-four examinations, covering nineteen chapters of the Analects in addition to the Ji Shi, and making a more exquisite argument and play on Confucius's ideas of "loyalty and forgiveness", "consistency", and "heresy". For example, in the Analects' "For the Government": "Zi Yue: 'Attacking heresies, the evils are already there.' However, there have been many opinions about the interpretation of "heresy" throughout the ages. He Yan considered "the small way to be a heretic", Huang Kan thought it was a "miscellaneous book" that was different from the "Five Classics", Xing Fu of the Song Dynasty proposed that it was the "Book of the Hundred Sons and Hundred Families", and Zhu Xi pointed out that it was yang Mo Buddha.' Because Mencius had criticized Yang and Mo's ideas of "for me" and "love at the same time", Zhu Xi only extended Mencius's views. Jiao Xun believes that "heresy" refers to both ends of things, and no matter which end of the attachment, it can be regarded as heresy. Confucianism is also only one of the two ends, no different from Yang Zhu, Mozi, and Zi, and the key is to connect the two ends, that is, the so-called "way of the saints, through the self, love, and clinging to the middle." In particular, Jiao Xun believes that the ideas of FuXi, King Wen, and Zhou Gong were originally expressed by the Zhou Yi in the form of symbols, so it is difficult for ordinary people to understand, and the Analects make up for this shortcoming, and the Analects are actually the footnotes of the Zhou Yi, which is also a highlight of Jiao Xun's study of the Analects.

Jiao Xun's academic pioneering innovation is also reflected in the intensive study of Chinese and Western arithmetic. He befriended wang lai and Li Rui, who were famous arithmetic scholars at that time, to discuss difficult mathematical problems, and was known as the "three friends of the heavens". After reading Mei Wending's "Outline of the Arc Triangle", "The Ruler in the Ring", and Dai Zhen's "Record of Pythagorean Cutting Circles", he deeply felt that the Meishu was "complicated and disorderly", and Dai Shu was "simple and simple", so he "took the second book to refer to it" and wrote "Interpretation of the Arc", discussing the generation of triangular octagons and the solution of spherical triangles. This book was praised by Qian Daxin as "compared with the positive arc oblique arc subform arrow, the reason is not all inclusive, and the law is not prepared". Later, he wrote two books, "ShiLun" and "Shi Oval", which clarified the similarities and differences of the wheels and the changes in the arc of interpretation, and discussed the geometric principles of the current and secondary wheels in the astronomical theory of the Danish astronomer Tycho Brahe (1546-1601) and the geometric principle of the ellipse in the astronomical theory of the Italian astronomer Giovanni Domenico Cassini (1625-1712). Jiao Xun's most prominent contribution to mathematical research is his "Addition, Subtraction, Multiplication, and Division".

"Addition, Subtraction, Multiplication and Division", was drafted in the fifty-ninth year of Qianlong (1794), and then interrupted at the invitation of Ruan Yuanzhi as "Qilu Tour", which lasted for five years and was completed in the third year of Qing Jiaqing (1798). The purpose of the book is to "add, subtract, multiply and divide as the guideline, and to distinguish it by the nine chapters of the commentary." The book consists of eight volumes, the first and fifth volumes mainly deal with the rules of addition and subtraction of numbers; the second volume mainly deals with the binomial power operation; the third volume mainly discusses the rules of multiplication and division of numbers; the fourth and sixth volumes mainly discuss the nature of fractions and their operation rules; the seventh volume mainly deals with various types of proportional problems; and the eighth volume mainly deals with the rules of addition, subtraction, multiplication, and division. The book lists ninety-three rules of operation, each equivalent to a theorem or formula in modern mathematics. It discusses and summarizes the operation rules and theories of ancient Chinese mathematics, creates a precedent for borrowing A, B, C, D and other Tiangan characters to express the law of operation symbols (equivalent to the Latin letters such as a, b, c, d and so on that we use today), and elaborates on the traditional operation methods, including "addition exchange law", "addition combination law", "multiplication exchange law", "multiplication combination law", "addition to multiplication law", "addition to multiplication distribution law", etc., which was a pioneering research result in the field of mathematical research at that time. At the same time, Jiao Xun also put forward mathematical ideas such as "rational nature", "name after law", "number before form", etc., regarded the natural numbers in mathematics as the principle of nature, and tried to make up for the few theoretical defects of traditional Chinese mathematics from the theory of logic and philosophy, reflecting that the traditional arithmetic of Qianjia was gradually moving towards Confucianism, which was also of great significance in the history of ancient Chinese mathematical thought.

Jiao Xun undoubtedly belonged to the pioneering and innovative scholar in the academic history of the Qing Dynasty, comparable to the academic generalists of his contemporaries, and his knowledge was better than that of Hui Dong; the depth of his thought could be compared with Dai Zhen. The ideas and scholarship he retains are not only the historical echoes of his time, but also a precious cultural heritage worthy of joint examination when we develop socialist culture with Chinese characteristics and build a socialist cultural power today.

Guangming Daily ( 2022-04-02 11th edition)

Source: Guangming Network - Guangming Daily