Cha Youliang: Qin Jiushao, who is 500 years ahead of Western mathematics

Author: "Bashu History" Editorial Office Koala Look (Chuangsheng Culture) Source: Sichuan Provincial Local History Work Office Release time:2021-09-09 14:45:34 Views:1 【Font:Small】

This article is published in the special issue of "Sichuan Historical Celebrities" in the 5th issue of the History of Bashu in 2020

Check the beams

Qin Jiushao, who is 500 years ahead of Western mathematics

Editorial Board of the History of Bashu Koala look

Mr. Wang Guowei once wrote in the preface to the "Guoxue Series": "The world's learning does not produce science, history, and literature. Therefore, the study of China is of the Western category, and the study of the Western Kingdom is also available in China. ”

Mr. Wang Guowei believes that from the analogy of "Western studies", there is also science in "Chinese studies". The natural sciences of ancient China were once in the leading position in the world, especially ancient mathematics, which had its own unique thinking and logic, and in some respects, Western mathematics was even difficult to reach. For example, during the Southern Song Dynasty, Qin Jiushao's "Great Yan Qiu Yi Technique" created in the "Nine Chapters of the Book of Numbers" was 500 years ahead of the remaining theorem in the West.

"Qin Jiushao's Nine Chapters of the Book of Numbers, completed in 1247, is a classic sinology in mathematics and science." Zha Youliang, a researcher at the Sichuan Academy of Social Sciences, commented. Cha Youliang and Qin Jiushao's research association is quite early. In 1972, when Zha Youliang was working at the Chengdu Institute of Education and Science, when he read the history of the development of mathematics, he came into contact with Qin Jiushao and his book "Nine Chapters of the Book of Numbers". In May 1987, Cha Youliang participated in the "International Conference on the 740th Anniversary of the Completion of Qin Jiushao's Nine Chapters of The Book of Numbers" and the International Conference of Academic Discussion held by Beijing Normal University. The international academic conference 33 years ago was of great significance, not only promoting the further study of Qin Jiushao and his mathematical masterpieces in Chinese academic circles, but also repositioning Qin Jiushao's position in the history of mathematics in the world.

Zha Youliang, a researcher at the Institute of Management of the Sichuan Academy of Social Sciences, participated in the writing of the book "Outstanding Mathematician Qin Jiushao" and deeply studied Qin Jiushao's mathematical thought

Qin Jiushao was born into a family of eunuchs in Puzhou (present-day Anyue County, Sichuan), and his book Nine Chapters of the Book of Numbers represents the peak of mathematics in the Song and Yuan dynasties. In the self-prologue of the Nine Chapters of the Book of Numbers, Qin Jiushao once wrote a self-note: "Jiushao is stupid and does not idle in art. Since he was a child, Qin Jiushao has been deeply interested in the "six arts" (ritual, music, shooting, imperial court, book, and number), but he has not had so much desire to explore the Four Books and Five Classics. He had followed his father to live in the capital, and because of his father's official position and connections, he had the privilege of studying many classics related to mathematics, and also got acquainted with many astronomical calendarists and architects of the imperial court. In an environment where laughter and laughter are all about Confucianism, Qin Jiushao learned a lot of scientific and technological and humanistic and social knowledge, which laid the foundation for his dedication to writing the "Nine Chapters of the Book of Numbers".

The Nine Chapters of the Book of Numbers are "set as questions and answers, to be used for use", and are divided into 9 chapters: Dayan, Tianshi, Tianyu, Survey, Enlistment, Qiangu, Construction, Military, and Shiyi.

Influenced by traditional Chinese mathematics, Qin Jiushao attaches great importance to the practicality of mathematics. In the preface to the Nine Chapters of the Book of Numbers, Qin Jiushao openly and explicitly revealed his own view of mathematics, believing that mathematics "can be used through the affairs of the world and like all things" and has a wide range of applications; at the same time, due to the influence of Taoist doctrine, he also agreed that mathematics "can communicate with the gods and follow life", and put forward the view that "numbers and Taoism are not two books", with unique philosophical implications.

Zha Youliang mentioned that the most dazzling achievements of the Nine Chapters of the Book of Numbers are the "Great Yan Qiu Yi Technique" and the "Positive and Negative Prescription Technique". Qin Jiushao has constructed a complete system of strict argumentation for the "Great Yan Seeking One Technique" and "Positive and Negative Prescription Technique", which is quite valuable. "This is moving towards a 'principle theory,' not simply constructing a 'model theory.'" To a certain extent, this breaks the assertion that traditional Chinese mathematics only focuses on practicality and does not pay attention to theory.

Qin Jiushao is "the master of ancient Chinese mathematics", but in addition to mathematics, Qin Jiushao has also made achievements in other fields. The literary scholar of Qin Jiushao's contemporary, Zhou Mi, once recorded Qin Jiushao in the "Sequel to The Miscellaneous Knowledge of Decoction": "Sex is extremely clever, and the stars, rhythms, arithmetic, and even construction and other things are all exquisitely studied." And "the beauty, the poetry, the game, the horse, the bow and the sword, can not be known."

This was Zhou Mi's praise for Qin Jiushao, but Zhou Mi also denounced Qin Jiushao in his notes, branding him with a notoriety of "fierce heart". In this regard, Zha Youliang explained: "This is simply a great injustice! Because at that time, the capital of the Southern Song Dynasty was divided into two factions: the main battle, the main war, and the main faction. Qin Jiushao was the main war faction, and it was precisely because of the different political stances that there were many situations in which opposing factions threw filthy words at him. ”

In the preface to the Nine Chapters of the Book of Numbers, Qin Jiushao has sentences such as "Staggle in wealth and service, and bow down to the king", "Annexation at the end, thick of non-countries", "uneven enlistment, rather than thinking", which shows his frank and worried mentality. In the first year of the Southern Song Dynasty (1259), Qin Jiushao submitted the Nine Chapters of the Book of Numbers to Emperor Lizong of Song. But at that time, the Southern Song Dynasty was already crumbling, and Song Lizong had no time to take care of this "idle book" that could not resist the enemy's sword. As a result, posterity can only sigh that "mathematical masterpieces are not born at the right time."

The political "obliteration" did not obliterate the brilliance of the Nine Chapters of the Book of Numbers, nor did it hide Qin Jiushao's talent. Cha Youliang once wrote in the article: "In school education in today's world, the comprehensive education of science, technology, engineering, and mathematics (referred to as STEM education) is promoted. We can find the ancient prototype of STEM education in Qin Jiushao's "Nine Chapters of the Book of Numbers". For example, the remarkable feature of the Nine Chapters of the Book of Numbers is that it closely combines mathematics with science, technology, engineering, economics, and the military.

In addition, Zha Youliang also said that Qin Jiushao's achievements are quite abundant, but its popularity and influence are still relatively small, and the popularization of the "Nine Chapters of the Book of Numbers" to the education of middle school students can not only deepen the understanding of middle school students about this mathematical giant, but also promote the comprehensive and balanced development of middle school students. The enlightening significance of the Nine Chapters of the Book of Numbers for modern education deserves more in-depth exploration and development.

Q

When did you start studying Qin Jiushao? You are a physics major, what was the opportunity to study Qin Jiushao at that time?

A

I graduated from the Department of Physics of Southwest Normal University in 1963. Physics majors have high requirements for mathematics, and I have a foundation in mathematical research. The study of Qin Jiushao originated in 1972 when I went to work at the Chengdu Municipal Institute of Education, when there were many people in the physics group and a small number of people in the mathematics group of the institute, so I was transferred from the physics group to the mathematics group to engage in professional research in mathematics. Generally when I study a major, I will first study the history of the development of this profession and important works in the history of development, such as "Nine Chapters of Arithmetic" and "Nine Chapters of Number Books" in the history of mathematics, etc. I will go to see it. The Nine Chapters of the Book of Numbers is Qin Jiushao's work, and through this way, I came into contact with Qin Jiushao. I spent middle school in Chengdu Shishi Middle School, and in high school, I systematically studied literary history, which laid a good literary foundation for my research on the Nine Chapters of the Book of Numbers.

You once said in the article that Qin Jiushao's "Nine Chapters of the Book of Numbers" is one of the classics of Traditional Chinese Studies?

What is "Sinology"? The literature, history, science and technology founded by the outstanding talents of the Chinese nation are all "sinology" in China. From this point of view, Qin Jiushao's book "Nine Chapters of the Book of Numbers" completed in 1247 is a classic "Guoxue" in mathematics and science.

The name "Guoxue" is a concept that only exists in relation to "Western Studies". Since the 15th century, "east learning and west learning" and "west learning east gradually" have been carried out at the same time. Since modern times, the cultures of all countries in the world have exchanged with each other, and there is no longer a "local culture" in the absolute sense. Therefore, the study of Sinology should keep pace with the times.

In various cultures, it is now "you have me" and "I have you". Each country has its own "sinology". In the wave of "globalization", the truly quintessential "sinology" may be transformed into "international studies" and become the common intellectual wealth of all mankind. Qin Jiushao's "Nine Chapters of the Book of Numbers" has been written for more than 770 years, and has been transformed from "Guoxue" to "International Studies".

What do you think Qin Jiushao's mathematical outlook is?

Qin Jiushao's view of mathematics is a mathematical view in a broad sense. The narrow concept of mathematics is to say that mathematics is a tool, but Qin Jiushao, in the preface to the Nine Chapters of the Book of Numbers, pointed out straight to the point that mathematics, as a culture, is closely related to philosophy. It shows that mathematics and philosophy are so closely linked that they are not just a tool. The reason why Qin Jiushao has a broad view of mathematics is that he attaches importance to the "external application" of mathematics as a "tool" and the "inner completeness" of mathematics as a "thinking". For example, Qin Jiushao's "Great Yan Qiu Yi Technique" and "Positive and Negative Prescription Technique" have a wide range of applications, and they all construct a complete system with relatively rigorous argumentation. This is moving towards the "principle theory", not simply the construction of the "model theory", which is a major contribution of Qin Jiushao.

Qin Jiushao was born in the Southern Song Dynasty scholarly family, and there are records that he likes to pursue fame and profit, how do you think of this view?

This is a great injustice. Because at that time, the capital of the Southern Song Dynasty was divided into two factions: the main war and the main peace. Qin Jiushao was the main war faction, and it was precisely because of the different political stances that the opposing main peace factions threw filthy words at him. Our later media is unclear, so as soon as we render it, we demonize Qin Jiushao.

Wen Tianxiang at the end of the Southern Song Dynasty was also the main warrior faction, he was only 30 years later than Qin Jiushao, he had a famous verse: "Whoever lives since ancient times has not died, leave Dan heart to take care of Khan Qing." "You see that the main battle faction is very backbone, how can such a person who is worried about the country and the people have those bad thoughts?" And we look at Qin Jiushao's words in the "Nine Chapters of the Book of Numbers": "I smell financial management, like wisdom governing water." Chengyuan is a dredging stream, and the dimension is deep. Peter Fucha, miserable and troubled. Go to the far side, call for unkindness. I translate this passage as follows: "I have heard that the management of finances should be like the rule of water by the wise." The original source is clear, the order is not chaotic, the symptoms are cured, and the hidden dangers are eliminated. Those stupid and corrupt officials turned a blind eye, the people were miserable, and they were tortured continuously. This is getting farther and farther away from reason, and corrupt officials are not benevolent! Sigh! In this text, there is the embodiment of Qin Jiushao's thoughts, from which it can be seen that Qin Jiushao is a very good and upright person.

Qin Jiushao's "Great Yan Qiu Yi Shu" is 500 years ahead of the West and is known as the "Chinese Residual Theorem", but why was the "Great Yan Qiu Yi Shu" almost lost in the middle of the Ming Dynasty?

It's not actually lost. It was at that time that the Western calendar came, and the Chinese calendar was impacted, but in fact, the Chinese calendar was more scientific. We just can't see the moon on the first day, and the fifteenth moon must be round. And the twenty-four solar terms have nothing to do with the moon, they have to do with the sun. We have been looking for the least common multiple. But later calendars don't use this. However, the way of "seeking one technique of great derivation" is still circulating, and it is solving other problems.

Why is It said that Qin Jiushao is "the master of ancient Chinese mathematics"?

First of all, Qin Jiushao inherited the essence of ancient Chinese mathematics and developed and developed it; second, his mathematical concept and mathematical thinking have made new breakthroughs and creative ideas; third, Qin Jiushao has made great contributions to the development of mathematics in the world. From these three aspects, it can be shown that Qin Jiushao is "the master of ancient Chinese mathematics".

The late American historian of science, Sutton, praised Qin Jiushao, saying that he was "one of the greatest mathematicians of his people, of his time, and indeed of all his time." This sentence is very pertinent.

Qin Jiushao himself was versatile, and his Nine Chapters of the Book of Numbers was not only a high-level mathematical treatise, but also a microcosm of many aspects of Southern Song society. The book asks 81 questions, "set as questions and answers for use." It is divided into: Dayan, Tianshi, Tianyu, Survey, Conscription, Qiangu, Construction, Military Brigade, and Shiyi 9 aspects, which are widely used.

Of course, the most representative in the book, and the most emblematic of Qin Jiushao's value, is the "Great Yan Seeking One Technique". This theory is 500 years ahead of the world and reflects the achievements of ancient Chinese mathematics. I wrote a sentence for Qin Jiushao: Since ancient times, life expectancy is limited, and knowledge innovation has been passed down from generation to generation. He is indeed a well-deserved master of ancient Chinese mathematics.

What is the practical significance of studying Qin Jiushao's Nine Chapters of the Book of Numbers?

In school education in today's world, the comprehensive education of "science, technology, engineering" and mathematics is promoted, referred to as STEM education. Recently, ART has been added to STEM education and upgraded to STEAM education.

The distinctive feature of the Nine Chapters of the Book of Numbers is the close integration of mathematics with science, technology, engineering, economics, military, agriculture, and meteorology. We can find the ancient prototype of STEM education in Qin Jiushao's "Nine Chapters of the Book of Numbers".

What spirit do you think we need to learn and inherit from Qin Jiushao?

On this question, I think the Qin Jiushao culture extracted by the team of teacher Chen Gengsheng of Anyue Middle School can be well answered. Teacher Chen believes that there are two main aspects of Qin Jiushao culture, one is Qin Jiushao thought, and the other is Qin Jiushao spirit. Qin Jiushao's thought includes three aspects: the first is to brainstorm from the vast number of books, that is, Qin Jiushao's harvest "comes from life"; the second is to expand knowledge and advocate science, indicating that Qin Jiushao is very "innovative and exploratory"; the third is the formation of achievements to contribute and share, which can be found in the preface of the "Nine Chapters of the Book of Numbers", that is, after the results are formed, they must be dedicated and shared, with the purpose of "serving the society".

The spirit of Qin Jiushao also includes three sentences: First, it is the "national spirit" of not being humble and unobtrusive, worrying about the country and the people, and in the community and the people, we must advocate the study of this spirit; then there is the "spirit of study" that is bold in innovation and persistent exploration, which should be vigorously promoted among middle school students; and finally, it is also the highest "academic spirit" of not seeking fame and fortune and seeking truth from facts. Because Qin Jiushao's life was suppressed a lot. In an era of heavy literature and light reason, as a natural scientist, he could not seek too much profit, so he must seek truth from facts to reflect his academic spirit.

These ideas and spirits of Qin Jiushao culture are very precious and are worthy of our study and inheritance.

(Published in the special issue of "Sichuan Historical Celebrities" in the 5th issue of "Bashu History" in 2020)