From “Supreme Oneness” (‘Taiyi’) to “Principle” (‘Li’): A Comparison of Xing Yunlu and Wang Xichan’s Astronomy System

Introduction

The late Ming and early Qing dynasty of China is a very special and important period of the development of Chinese astronomy. During this period, the study of Chinese traditional astronomy was renewed after the long silence. Many scholars, such as Zhu Zaiyu (1536-1611), Yuan Huang (1533- 1606) and Wei Wenkui (1557-1636) devoted to traditional astronomy research. Meanwhile, Jesuit missionaries came to China to spread Gospel. They also introduced European astronomy under the guidance of “Missionizing through science”. Finally, two European astronomy books were introduced into China. One was Chongzhen lishu (CZLS, Chongzhen-reign Treatises on Calendrical Astronomy) which was compiled during the astronomical reform of Chongzhen reign led by Xu Guangqi (1562-1633). This work, which was re-edited lightly and renamed Xiyang Xinfa Lishu (Treatises on Calendrical Astronomy according to the New Method from the West) by Johann Adam Schall von Bell (1592-1666), became official astronomy in the beginning of Qing dynasty. The other book was Tianbu zhenyuan (True Principles of the Pacing of the Heavens) which was compiled in 1653 by the Polish Jesuit missionary Nikolaus Smogulecki (1611- 1656,) and his Chinese disciple Xue Fengzuo (1600-1680). Mainly because of the immense influence of CZLS, European astronomy finally replaced Chinese traditional astronomy and became the main stream astronomy in Qing dynasty. Many Chinese scholars, such as Wang Xichan (1628-1682), Mei Wending (1633-1721), as well as Xue Fengzuo devoted themselves to it and developed their own system.

On this exciting history, many studies have been done in different aspects and from different perspectives. But in this paper, we will try to explore it in a special approach which few scholars paid attention to. We will first focus on the academic system of astronomers’ works, not about their computational methods or celestial bodies’ model, but the system which was comprised of philosophical categories and their learning. Then we will compare different systems. Our comparison will especially pay attention to the metaphysical part, and try to combine philosophical background to analyze. Specifically, we will focus on two astronomers’ works during this period in this paper. One is Xing Yunlu (c.1549-c.1621), an important astronomer in late Ming dynasty. His work was typically about Chinese traditional astronomy which was represented by Guo Shoujing’s (1231-1316) Shoushi li (Time Granting System of Calendrical Astronomy)1. Another was Wang Xichan, who was influenced by European classic astronomy work CZLS, and developed his own system under the Neo-Confucianism. We will analyze their system respectively and combine the thought background of that period to compare them. We hope we can reveal the features of two systems and the influence of European astronomy from a new perspective.

The Astronomical Aystem under Taiyi (“Supreme Oneness”): Xing Yunlu

Before our discussion about Xing Yunlu’s system, we would like to discuss our method of analyzing. Science isn’t an isolate entirety, but the production of culture. This is extremely obvious before modern society. In pre-modern period, different cultures generate different sciences. We can find their differences in different aspects. For example, contrasting to ancient Chinese astronomy, ancient European astronomy is definitely another system, not only in the way of calculation or presentation, but also their function, methodology and metaphysical foundations.2 Therefore, when we try to analyze pre-modern sciences, we should avoid conceiving of them in certain mode-usually in the way of modern science, but combine their own culture, follow their own way of thinking, such as their philosophical conceptions in their texts or background to understand their own system.

Xing Yunlu, whose courtesy name was Shideng, was born in about 1549 and died between 1621 to 1626. He was the administrative official of Ming Empire and studied astronomy in his free time. As his achievement and enthusiasm to the calendrical reform, he participated twice calendrical reform

1  For the latest study on Xu Guangqi’s Shoushili, see:, Kiyoshi Yabuuti and Shigeru Nakayama, Jujireki: Yakujū to Kenkyū (Kawasaki: Ai Kei Corporation 2006); Nathan Sivin, Granting the Seasons: The Chinese Astronomical Reform of 1280, with a Study of its many Dimensions and a Translation of its Records (New York: Springer, 2009).

2  The relative discussion could be seen in David Pingree, The Logic of Non- Western Science: Mathematical Discoveries in Medieval India, Daedalus, 2003, 132 (4), pp. 45-53.

during Wanli reign-period and became the leader in the second one. Although the reforms were not successful, they could be viewed as the prelude of calendrical reform in the late Ming dynasty. His representative works of astronomy include Gujin lüli kao (GJLLK, Investigation into Harmonics and Calendrical Astronomy from Antiquity to the Present) and Taiyi shu (The Book on “Supreme Oneness”).

According to his discourse, we can divide his work into two parts or steps, viz, Bo (to be erudite ) and Yue (to reduce). The first step Bo meant widely learning calendrical astronomy which Xing considered as Li (principle) and Shu (number). The second step Yue meant getting basic category Taiyi (Supreme Oneness) from Bo and applied it in the calendrical astronomy, so that he could master or understand calendrical astronomy completely. As he said in the preface to Taiyi Shu:

I, as a not smart man, try to study and understand calendrical astronomy. I study widely. So carefully did I collate and correct Li(principle) and Shu (number) during all the times! Now when I try to attain the essence from my wide study, to explore the origin directly, I get what is called Taiyi.3 Then which book did represent the first step? The answer was GJLLK, which was completed no later than the 27th year of Wanli-reign (1599) and first published in 28th year (1600). GJLVK involved 72 volumes, and could be divided into 8 parts. In these 8 parts, Xing mainly reviewed and summarized the calendrical astronomy from early period to the Ming dynasty. For example, from volume 9 to 19, he discussed different kinds of calendrical astronomy recorded in official history books and other literatures. In volume 28 he even introduced the astronomy knowledge in the Taoist and Buddhist canons. Among these calendrical systems, what he paid most attention to were Shoushi li and Datong li (Great Unification System of Calendrical Astronomy), especially Shoushi li. From volume 36 to 59, he studied the contents of Shoushi li and Datong li specifically. In other volumes, he also tried to recover the underlying mathematical principle of Shoushi li’s computational method. Actually, Shoushi li was the best calendar before Ming dynasty in Xing Yunlu’s opinion. He wanted to recover it and find deficiencies, so that he could correct them and achieve his goal of reforming calendar.

Besides calendrical astronomy, Xing Yunlu also expressed some important thoughts about calendrical astronomy in GJLLK. He emphasized calendar should be reformed perpetually. The celestial phenomenon should be observed at any time. He also proposed an interesting physical mechanism which employed Chinese traditional conception

3  Xing Yunlu, Taiyi shu, in additional vol. of Xing Yunlu, Gujin lüli kao, printed by Sun Wei in 1608 at Baoding, p.1a.

Qi (pneuma) to interpret the movements of moon and five planets. He thought their cycle movements were caused by the pull of sun’s Qi. Moreover, Xing Yunlu also employed volume 29 to 35, less than 10 percent of whole book, as his musical harmonic part. Obviously, they were secondary part in GJLLK. The reason may be music harmonics was based on calendrical astronomy in Xing Yunlu’s opinion. In the preface to GJLLK, he said:

However, the musical harmonics comes from calendrical astronomy. Hence, the calendrical astronomy is more important.”4 Just as he said in the preface to Taiyi shu, in GJLLK, Xing Yunlu really studied the Li and Shu, viz. calendrical astronomy widely. However, as he said, GJLLK was just the step of Bo of his academic system. There was also another step Yue which attached his calendrical astronomy work to Taiyi. The book representing Yue was Taiyi shu.

Taiyi shu is a very brief book, just including 19 pages in one volume. We only find one existing version by now which is attached in the end of Sun Wei’s Baoding GJLLK. It can be divided into four parts. The first, from page 1a to 5a, discussed the meaning of Taiyi and a constellation of constants coming from Taiyi. The second, from page 5b to 10a, introduced the computational methods of diameter, the area of Huangzhong pipe, the diameter and circumference of golden ball, the length of a side of golden cube, the length of the sides of right triangle, the geometric data of square or circle field in the circle or square field and so on. In Xing’s opinion, we could understand the computational algorithms of calendrical astronomy through these methods, because they were similar to calendrical methods and easier to comprehend through these examples than the ones of calendrical astronomy. The third part, from page 10a to 18b, was about the application of Taiyi in the calculation of calendrical astronomy. Xing Yunlu gave two examples -the calculation of numbers of the diameter of heaven5 and the length of two sagittal sides of ecliptic and equator- at first. And then he deduced a series of Chinese traditional astronomical data. In this part, Xing Yunlu directly expressed that Taiyi was the basis and key to calendrical astronomy. All the methods of calendrical astronomy were based on Taiyi. All the numbers of calendrical astronomy came from Taiyi. Just as he said: “Taiyi is the law of ten thousand of methods

4  Xing Yunlu, Gujin lüli kao, in vol.787 of Siku quanshu (Taibei: Taiwan shangwu yinshuguan, 1983), p.3. About the contents of GJLLK, see Wang Miao, A Study on Xing Yunlu’s Gujin lüli kao. Journal of Dialectics of Nature, 2005, 27(4): 92-98.

5  It’s not about the real length of the diameter of heaven, but the numbers of degrees of the it. Xing Yunlu thought the length of the circumference of heaven is 365.25.

(of calendrical astronomy).”6 “The ten thousand and irregular numbers of the Qizheng and Siyu of heaven during millions and the thousand years all come from the one, thus (I) call Taiyi.” 7 The last part, from 18b to 19b, was the conclusion, in which Xing Yunlu criticized Shoushi li and spoke highly of Taiyi.

If we probe the meaning of Taiyi, we will find Taiyi isn’t just the origin of calendrical astronomy. It’s the most basic and important essence or the most primary noumenon as well as the creator of the world. In other words, it is typically the universal noumenon in Chinese traditional philosophy which usually includes the double features of cosmology and ontology. For example, Xing Yunlu said:

It’s the one, but why do I say Tai (highest or most basic)? Taiyi is Wuyi (no the one). There is no the one before the Wushi (no beginning), but becomes the one in the beginning of that there is the one. This the one, can’t be named but is named forcedly, can’t be restrained in square and cube (the figure or material), doesn’t attach and dwell (on matters), however not doesn’t attach and dwell. Hence it is called Tai.8 The heaven and the earth as well as ten thousand of things can’t avoid this (Taiyi). The ghosts and the gods, the changes and the forms are all involved in it (Taiyi).9 Being identical with Wuyi, existing before the beginning of world, becoming the one in the beginning of the world and that everything can’t avoid it imply the cosmic ontology feature of Taiyi. Therefore Taiyi is not only the noumenon of natural phenomenon such as celestial bodies’ movements, but also the one of humanity, as the Way or Tao in traditional Chinese philosophy:

Taiyi is the beginning of the Way. Yao and Shun pass it on by Only One. (The Tao of) Yu, Tang, the King of Wen, the King of Wu, Duke Zhou, Confucius and Mencius are all this Tao. 10 From above discussion, it’s also easy for us to guess that Taiyi was similar to Taiji (Supreme Ultimate), the typical category of Chinese philosophy. Actually, we could find evidence in Xing Yunlu’s discussion:

Taiyi moves and generates Liangyi (two elementary

6  Xing Yunlu, Taiyi shu, 16b.

7  Xing Yunlu, Taiyi shu, 18b. Qizheng refers to the moon, the sun and five planets. Siyu is an astronomical term designating the four invisible celestial bodies, Rahu (luohou), Ketu (jidu), Yuebo, and Ziqi.

8  Xing Yunlu, Taiyi shu, 3b.

9  Xing Yunlu, Taiyi shu, 4b.

10  Xing Yunlu, Taiyi shu, 1a.

Forms). Those two forms part and produce Sixiang (Four emblematic Symbols), which evolve and breed Bagua (eight Trigrams). 11 This sentence obviously comes from the Chinese classic treatise Yijing (Book of Changes): “Therefore in (the system of) the Yi there is the Grand Terminus, which produced the two elementary Forms. Those two Forms produced the Four emblematic Symbols, which again produced the eight Trigrams. ”12 In GJLLK Xing Yunlu also expressed that if the calendrical astronomy was rooted in Taiji, we could obtain the everlastingly correct calendar: “The number of Huangzhong is 81. The number of Dayan is 2040. These have been farfetched. However (Wang) Pu presented these numbers immediately, and seems come from Taiji, Yinyang and Wuxing (five elements). If this is true, the calendrical astronomy should everlastingly errorless. Why do (the calculation of Wang Pu’s calendar) more than (the movements of) Heaven? (Wang’s behaviors) just let Yinyang’s imprecise and leave Taiji unjust.”13 This is similar to Taiyi shu, in which Xing Yunlu originated his calendrical astronomy to Taiyi and thought he has gotten the best way.14 Therefore we can say, Taiyi is similar to Taiji. It’s the development of Taiji which Xing Yunlu expressed in GJLLK.

The similarity between Taiji and Taiyi reveals the close relationship between Taiyi shu and Yi-ology. Above we have mentioned Xing Yunlu’s critique of Wang Pu, whose calendrical astronomy was combined with the Yizhuan (The Commentary of Yijing) of Guan Lang. Hence, obviously the Taiji, Yinyang and Wuxing in Xing Yunlu’s discussion are the terms in Yi-ology. In Taiyi shu, Xing Yunlu used Wuxing, Dayan (great evolution), Sancai (three powers), Liangyi (two forms), Liulü (six bamboo pitch pipes among the twelve), Bagua, Jiugong (nine modes of ancient Chinese music) etc. to construct terms, such as Liangyi Bianlü (The two elementary Forms changing rate) and Bagua Bianlü (The eight Trigrams changing rate). This also showed the close relationship between Taiyi shu and Yi-ology. Moreover, Xing Yunlu even expressed the opinion that calendrical astronomy was under Yi-ology: “This Yi-ology, manifests the Way and assists the spiritual. Which thing is not in it? The calendrical astronomy belongs to it doubtlessly. ”15 The interesting question is how did Xing Yunlu let his calendrical astronomy system under Taiyi? As we know,

11  Xing Yunlu, Taiyi shu, 2a.

12  The I Ching, translated by James Legge (New York: Dover Publictions, Inc. second version), p.373.

13  Xing Yunlu. Gujin lüli kao, p.195.

14  Xing Yunlu, Taiyi shu, 18b, 19b.

15  Xing Yunlu. Gujin lüli kao, p.14.

Taiyi was the origin and primary noumenon of the cosmos. It produced the universe and was in everything. Contrasting to Taiji, Taiyi doubtlessly contains the feature of number. Therefore, the process that Taiyi produced the universe was also the evolvement of number, just as Xing Yunlu said:

The Way comes from the One, and goes back to the One. What is the one? It’s ○. The one produces the Two. The Two produces the Three. (The Three) produces three one two five five seven, which is the heaven, manages the circle. (The Three) produces four four six nine nine eight, which is the earth, manages square. (They) all go back to the One.16 The evolution of universe was not only from Taiyi to heaven and earth, but also from the One to Two, Three and the numbers of heaven and earth. Numbers were not just for calculation, but obtain the cosmologic and ontological meaning. They were attached with the Way. Obviously, Xing Yunlu presented a kind of very special numerical cosmology here. It’s reasonable for us to deduce that Xing Yunlu would give other numbers about things between heaven and earth in his next step. Because according to traditional Chinese philosophy things would be produced after the appearance of the heaven and earth. But maybe Xing Yunlu was aware of the difficulty and mass of this way, he instead tried to give a series of constants which came from Taiyi. He divided these constants into three parts: Taiyi Wuxing Sancai Yuanlü (Taiyi Wuxing and Sancai circle rate), Taiyi Laingyi Sixiang Fanglü (Taiyi Liangyi Sixiang square rate) and Taiyi Fangyuan Dongjing Shenghualv (Taiyi circle square movement stillness producing change rate). These three parts represented the circle, square and exchange between circle and square respectively. As the circle meant heaven, square meant earth. The exchange of them obviously meant the exchange of heaven and earth. Actually, these three aspects were the whole view of universe in ancient Chinese. But these constants were not the numbers of heaven, earth and their exchange directly. They were the rates used in the calculation of circle and square as well as of heaven and earth. After giving these rates, Xing Yunlu showed some examples that used these constants to calculate. Although we could find these rates could be used in the calculation of the existence such as field, Huangzhong and golden ball, his main goal was to apply them to his calendrical astronomy so that he could base astronomy on metaphysical categories. This can be proved by the facts that the examples of field, Huangzhong and golden ball were used to explain the calculation of

16  Xing Yunlu, Taiyi shu, 1b. In this fascinating sentence in which we can find the influence from Zhou Dunyi’s (1017-1073) Taiji tushuo (Explanation of the Diagram of the Supreme Ultimate) and Daode jing (Classic of the Way and its Virtue). The one produces the Two, and then the Three. We can find the influence of Daode Jing here. Producing heaven and earth after the Three and regarding the figure ○ as the Way partly come from Zhou Dunyi’s Taiji tushuo.

calendrical astronomy. Besides, he also gave two examples of calendrical astronomy directly. For example, one of them was:

The circumference of heaven is three hundred and sixty- five degrees twenty-five minute and seventy-five second. Question: how long is the diameter of heaven? Answer: diameter is one hundred and seventeen-degree two minute and two second. Method: Place three hundred and sixty-five degrees twenty- five minute and seventy-five second of heaven. Look (divide) Taiyi Sancai Jilü three one two one three two zero three four as one. Get the value of diameter of heaven. Answer the question. 17 As heaven is circle according to Xing Yunlu, this is a very simple mathematical question about the diameter of circle actually. Taiyi Sancai Jilü is also just the approximate value of π. But the application of Taiyi Sancai Jilü was significant for Xing Yunlu. It meant he attached his work to Taiyi, the origin and noumenon of universe. This was an important way that Xing Yunlu connected his work to Taiyi. Besides, Xing Yunlu also thought the observation of astronomy was based on constants of Taiyi:

Taiyi is the law of ten thousand of methods (of calendrical astronomy). Observing heaven through Taiyi’s conference and diameter rate (we) get the conference of heaven. Observing sun through Taiyi’s legs of right triangle rate (we) get the value of tropical year.18 Then he discussed many important astronomical terms which were related to tropical year and mutually related. As the observation of tropical year was relate to Taiyi’s constants, it’s reasonable for us to say that these terms were also related to Taiyi in Xing Yunlu’s mind. Actually, we can also conjecture that the calculation and observation of these terms were also based on them.

Therefore, we can say the way that Xing Yunlu applied Taiyi in the practice of calendrical astronomy was to calculate and observe astronomical problems and terms with constants of Taiyi. These constants were produced by Taiyi in a numerical cosmology way.

To Obtain the Li (Principle): Wang Xichan

Wang Xichan was one of the most important astronomers in the early Qing period, born in Wujiang, Jiangsu province, also known as Zhaomin, with the courtesy name Yin Xu,

17  Xing Yunlu, Taiyi shu, 10b.

18  Xing Yunlu, Taiyi shu, 16b.

art name Xiao An, also known as Tiantong Yisheng, Yu Bu, Caifang Shijun. His main works include two volumes of Xiao An xiansheng shiji (Master Xiao An’s Poetry Collection), three volumes of Xiao An xiansheng wenji (Master Xiao An’s Anthology), and Xiao An xinfa (Xiao An’s New Method), Datong lifa qimeng (The Enlightenment of the Great Unification System of Calendrical Astronomy), Zazhu (Miscellaneous Works, later included in Xiao An yishu (Xiao An’s Legacy of Book)).

Wang Xichan paid close attention to Confucianism all his life. He hoped to carry forward the Neo-Confucianism and trace it back to the Six Classics of primitive Confucianism, so as to grasp the true meaning of Confucianism. He said, “I think that the profound meaning of the Six Classics has already been understood by Cheng Hao (1032-1085), Cheng Yi (1033-1107), Zhu Xi (1130-1200), Hu Anguo (1074-1138) and Cai Yuanding (1135-1198). However, their thoughts are too profound for future generations to really understand, so these Classics are usually packaged and abandoned, and the future generations even put up flags and beat the drums to compete with each other … I hope people can try to understand the classics within the biographical notes and don’t doubt the classics with the content other than the biographical notes.”19 He severely criticized “learning of the mind” (xinxue) which was proposed by Lu Jiuyuan (1139- 1193) and Wang Shouren (1472-1528), “Some scholars of younger age had an severalfold faith in these theories, so that they finally became the meditators.”20 At the same time, he also criticized Buddhism.21 Therefore, generally speaking, Wang Xichan advocated Cheng- Zhu School and opposed Lu- Wang school of mind, hoping to achieve the true meaning of Confucius and Mencius through the Cheng-Zhu school.

As to Wang Xichan’s studies on calendrial astronomy, Xiao An xinfa is his representative work. Wang Xichan opposed the practice of only using Western calendars and abandoning Chinese calendars in CZLS, so he created this almanac combining Chinese and Western methods of calendrical astronomy. He said, “Therefore, I took both Chinese and Western methods of calendrical astronomy into consideration, removed the dross, combined with my own point of view, and wrote a six-volume book on

19  Wang Xichan, Xiao An xiansheng wenji, vol.2, edited by Zhang Haishan in 1821. See also: Zhang Yongtang, Mingmo qingchu lixue yu kexue guanxi zailun (Re-discussion on the Relationship between Neo-Confucianism and Science) (Taipei: Taiwan xuesheng shuju, 1994), pp. 190-191.

20  Wang Xichan, Xiao An xiansheng wenji, vol.2, edited by Zhang Haishan in 1821. See also: Zhang Yongtang, Mingmo qingchu lixue yu kexue guanxi zailun, p. 186.

21  For the Confucianism thought of Wang Xichan, see: Zhang Yongtang, Mingmo qingchu lixue yu kexue guanxi zailun, pp. 185-186.

calendrical astronomy.” 22 This book has six volumes. The first volume discusses the basic mathematical knowledge used in astronomy at that time, which is mainly to find trigonometric functions by cyclotomic method. The second volume is about basic astronomical data. The third volume combines Chinese and Western methods to calculate the phases of the moon in the lunar month and the positions of sun, moon and five planets. The fourth volume discusses the wax and wane of the planets in the moon, the five planets and the apparent diameter of the moon, etc. The fifth volume is about the difference of air and time, and the light and spirit orientation of the moon. The sixth volume is the calculation of solar and lunar eclipses, transit of Venus, etc.23 On the whole, Wang Xichan’s calendrical astronomy is based on the Western calendar and has been innovated and improved, while retaining some characteristics of Chinese traditional calendrical astronomy. 24 Wang Xichan admired the academic thought of Cheng- Zhu school, so when Xu Guangqi introduced Euclid’s Elements, CZLS and other Western mathematical astronomy works in the name of the study of investigating things and pursing the principles, he naturally treated them as the study of investigating things and principles. Therefore, he paid special attention to the discussion of the principles of the calendrical astronomy, emphasizing that we should know why in the study of the calendrical astronomy. “There were two perfect discussions about the calendrical in ancient times: it says in the Great Symbolism of the Yijing, ‘in accordance with the form Ge (revolution), the superior man formulates his astronomical calculations and makes clear the seasons and times’; Mencius once said, ‘If we have investigated the Gu (principle), we may, while yet sitting in our places, go back to the solstice of a thousand years ago.’ The key to the calendrical astronomy is Ge, so there is no calendar that has not changed for hundreds of years; However, if people do not understand the Gu, there is no starting point for changing the calendar.” 25 He also lamented that, in the early Ming dynasty, Li Defang could not surpass Yuan Tong, because the former did not know the principle of the calendrical astronomy, which led to the promulgation and implementation of the rough

22  Wang Xichan, Xiao An yishu, in vol. 78 of Congshu jicheng xubian (Taipei: Xinwenfeng chuban gongsi), 1988, p. 637.

23  For the content of Xiao An xianfa, see: Xi Zezong, Shilun Wang Xichan de tianwen gongzuo (Discussion on the Wang Xichan’s astronomical works), in Wang Xichan yanjiu wenji, edited by Chen Meidong and Shen Rongfa, Shijiazhuang: Hebei kexue jishu chubanshe, 2000, pp. 1-20.

24  See: Jiao Xiaoyuan, Wang Xichan jiqi Xiao An xinfa (Wang Xichan and his Xiao An xinfa), in Wang Xichan yanjiu wenji, pp. 39-46.

25  Wang Xichan, Lice (On calendrical astronomy), in Xiao An xiansheng wenji, vol.2, edited by Zhang Haishan, 1821. See also: Zhang Yongtang, Mingmo qingchu lixue yu kexue guanxi zailun, p.196.

Datong li designed by the latter, “The level of calendrical astronomy of Yuan Tong was not as good as that of Guo Shoujing, and the ministers at that time were not as good as that of the Yuan dynasty, which eventually led to the continuing using of the old method. Although Li Defang tried to change it, he did not understand the Li (principle) of the calendrical astronomy. Thus, he had to stick to the old ways and failed in the end, which is very regrettable.”26 Wang Xichan also refers to the study of calendrical with the study of Li, “In the study of astronomy … must deeply understand the changes of numbers and the profoundness of the Li.” 27 He also called a person who knows the calendrical astronomy as a reasonable person, “The so-called theory of ghosts and gods is just a false statement of astrology, and people who understand the Li of calendrical astronomy will not agree with it.”28 In addition, Wang Xichan sometimes referred to the Li of calendrical astronomy as method and implication. For example, he thought that the reason why the Chinese traditional calendrical astronomy was defeated by the Western calendar during the change of calendar in Chongzhen-reign was that people don’t understand the method and implication, that is, the Li, “The old calendrical astronomy lost to the Western astronomy, not because the calendrical astronomy itself is bad. This is because there is no one who understands the Li of the calendrical astronomy.”29 Wang Xichan emphasized the principle in the study of the calendrical astronomy, but this principle was really not tenderminded. On the contrary, it was closely related to numbers. When he summarized the development of calendrical astronomy in the past dynasties, he believed that calendar researchers were divided into two groups in the Song dynasty, namely the calendrical astronomy of Confucianist and of the calendrical astronomer. But neither of these two is on the right way. Because they either only know the Li or only know the Shu, “To the Song dynasty, the study of calendrical astronomy divided into two groups, namely the Confucian Calendar and the calendrical astronomy of astronomer, the Confucian scholars don’t know the Shu, they only study the calendrical astronomy through quoting the empty Li. The astronomers don’t know the Li, and they only study the calendrical astronomy in a fixed way, which leads to the inability to obtain the truth.”30 Therefore, the calendrical astronomy research requires a deep understanding of Shu and Li, “Since ancient times, there have been more than 70 theories of studying calendrical astronomy, all of which have

26  Wang Xichan, Xiao An yishu (Xiao An’s Legacy of Book), in vol. 78 of Congshu jicheng xubian (Taipei: Xinwenfeng chuban gongsi, 1988), p. 635.

27  Wang Xichan, Xiao An yishu, p. 805.

28  Wang Xichan, Xiao An yishu, p. 636.

29  Wang Xichan, Xiao An yishu, p. 782.

30  Wang Xichan, Xiao An yishu, p. 635.

made some achievements. They all claim to be superior to their predecessors. But it didn’t take long for the calendrical astronomy to be deviated and eventually abandoned. Why is this? The reason is that the person who made the calendrical astronomy did not have a deep understanding of Shu and Li, but simply echoed the laws summarized in the past and accumulated data.” 31 The Shu and Li also became the standard for him to retain and abandon the concepts in the calendrical astronomy, “The people who make calendars say that solar terms should use the new calendar, and lunar terms should use the old calendar. What is the relationship between this and the Shu and Li?” 32 That is to say, in the face of the dispute between Chinese and Western calendars at that time, Wang Xichan believes that the calendar calculation method proposed by the calendar reformers in the Chongzhen-reign has nothing to do with the Shu and Li.

However, what is the relationship between Li and Shu? In short, he believes that Shu and Li are different, but Shu are produced from Li. So, people can understand Li through Shu, “The ultimate thing in the world is Li, but people can only understand it vaguely. If people want to explain the principle precisely, they must use Shu. The Shu is not Li, but Shu is produced from Li. Therefore, Li can be understood through Shu.” 33 The final state achieved by Shu and principle is similar to the state of sudden enlightenment described by Cheng Hao, Cheng Yi and Zhu Xi in the investigating the things and pursing the principles. In the Ceri xiaoji (Notes on Measuring the Sun), he once said, “In the study of astronomy, there is Li first, then Shu, and then method. Therefore, those who want to create method must deeply understand Shu and Li.” 34 The deep understanding of Shu and Li can fully comprehend the logic of astronomy, and can be “integrated”, so that people can reach the state of creating astronomical calculation methods. This is also the state of integration of method, Li and Shu. It is the ultimate state of Wang Xichan’s astronomical research. In addition, Wang Xichan often said: “I think the advantage of the Western astronomy lies in its accuracy of measurement, rather than a deep understanding of the meaning of the methods and implications. It is feasible to pursue the integration according to its Li, but it is not feasible without distinguishing its shortcomings.” 35 These are similar to what Zhu Xi said, “Encountering things in the world, one must base oneself upon the Li of what one has already known and exhaust it further so that one may seek to reach the extreme. After having exerted efforts for a long time, one day one suddenly ‘penetrates thoroughly’, then, of the

31  Wang Xichan, Xiao An yishu, p. 782.

32  Wang Xichan, Xiao An yishu, p. 784.

33  Wang Xichan, Xiao An yishu, p. 783.

34  Wang Xichan, Xiao An yishu, p. 805.

35  Wang Xichan, Xiao An yishu, p. 635.

outside and the inside or the refinement and the coarseness of many things, there will be none that one cannot reach, and of the entire substance and the great function of one’s mind, there will be none that is not bright.” 36 As discussed above, it has been connected with Wang Xichan’s background in the Neo-Confucianism.

The System about the Way and Two Kinds of Metaphysical Foundation: From Xing Yunlu to Wang Xichan

Now we can begin our comparative part about these two scholars’ astronomic system. We will especially concentrate our comparison on the metaphysical foundation parts of their system.

It’s easy for us to figure out that both Xing and Wang connected their systems to the supreme existence of the world. They constructed their system based on this supreme existence and secondary categories relating to it. The supreme existence and secondary categories also penetrated and combined different kinds of learning in their systems. As for Xing’s system, he connected his system to Taiyi, which was supreme existence in his system. The secondary categories in his system were a series of constants. They came from Taiyi and represented heaven, earth and mutual action of heaven and earth. Taiyi and these constants closely combined his calculation and observation. As for Wang, he connected his system to Li, the supreme existence in Neo-Confucianism which was his faith. The secondary ones were Shu, which came from Li. Through Li and Shu in calendrical astronomy, Wang can obtain the human’s supreme goal Li according to Neo-Confucianism.

Constructing their scientific system under the supreme existence revealed an important feature of some Chinese scholars’ astronomy works in imperial China. Astronomy was not just the learning to calculate the celestial bodies’ movements or to guide our daily life, but also the way to pursue the supreme existence or the origin of the cosmos, the way to understand world through the application of the supreme existence and the elements related to supreme existence. We can’t say that all scholars’ astronomy works possessed this feature. But it really had a sort of universality. Besides Xing Yunlu and Wang Xichan, we can also find other scholars who were similar to them. For example, Zhou Shuxue, who was an important astronomer in the middle of Ming dynasty, said:

36  Zhu Xi, Daxue zhangju, in Zhuzi quanshu, vol. 6, Sishu zhangju jizhu (Hefei: Anhui jiaoyu chubanshe), 2002, p. 20. See also: Yung Sik Kim. “Analogical Extension” (‘leitui’) in Zhu Xi’s Methodology of “Investigation of Things” (‘gewu’) and “Extension of Knowledge” (‘zhizhi’). Journal of Song- Yuan Studies, No. 34 (2004), pp. 41-57.

Yi-ology was the Way of heaven, the origin of calendrical astronomy. Understanding the calendrical astronomy means understanding the heaven. Understanding the heaven means understanding the Yi-ology.37 In Zhou Shuxue’s opinion, the study on calendrical astronomy was the way to understand the Yi-ology which contained the supreme category of world.

Actually, constructing systems under Taiyi and Li is also a way to gain the Way as Daoism or Confucianism does. This meant astronomy which was not the mainstream learning in ancient China also shared the same goal with Daoism or Confucianism. In fact, we could find more similarities between them. For example, there were two steps Bo and Yue in Xing’s system. We can also find discussions about them in The Analects of Confucius and its commentaries. If we compare the meaning of these two steps, we will also find that they are similar to Xiaxue (“study down below”) and Shangda (“attain up above”) in Confucianism.38 This means the steps employed in Xing’s system were typically Confucian pattern. Moreover, the discussion of Wang that the supreme state of studying calendrical astronomy is similar to the discussion of Zhu Xi, the representative scholar of Neo-Confucianism. We can also find the influence from Lao Tseu and Zhou Dunyi on Xing’s notion of Taiyi. Obviously, the academic systems of two astronomers were not independent from the mainstream learning in ancient China.

Although Xing Yunlu and Wang Xichan all constructed their systems under the supreme existence and had the similar goal, the categories they employed were very different. They were Taiyi and constants coming from Taiyi in Xing’s system, but Li, Shu in Xue Fengzuo’s system. Actually, we could find Li and Shu in Xing’s work, but they were not the main categories as in Xing’s system. This was different from the one which was the supreme category in Wang’s system. The period of Xing and Wang are not so different. According to modern Chinese scholars’ division, both of them can be classified to the period of the late Ming and early Qing dynasty, which was an important period of academic development. So, how could we understand this phenomenon? Besides, Xing’s Taiyi was closely related to Taiji in Yi-ology. We also mentioned that Zhou Shuxue related calendrical astronomy to the Way of Yi-ology. Actually, many astronomers in the second half

37  He Jigao, The Preface to the Yunyuan xiansheng wenxuan. Yunyuan xiansheng wenxuan (The Anthology of Master Yunyuan), edited and printed by He Jigao in 1592, p.1a.

38  Yung Sik Kim, ‘Confucian Scholars and Specialized Scientific and Technical Knowledge in Traditional China, 1000-1700: A Preliminary Overview’, East Asian Science, Technology and Society: an International Journal, 2010 (4), 207-228 (pp. 209-210, 215).

of Ming dynasty, such as Tang Shunzhi (1507-1560), Yuan Huang and Zhu Zaiyu also attached their astronomical work to Yi-ology in order to connected to the Way.39 However, we can’t find the similar relationship between Wang’s categories and Yi-ology. So why did not Wang construct his system in a way similar to Xing, but in another way? In order to answer these questions and understand these differences, we should discuss the influence of European science and other thought background in late Ming and early Qing China.

Many scholars have pointed out that the compilers of CZLS, especially Xu Guangqi, denied the relationship between calendrical astronomy and Yi-ology. On the one hand, they didn’t accept the connection between two kinds of learning. On the other hand, they discarded the opinion that numbers have mystery and divine ability. This kind of ability was emphasized in Yi-ology, especially Shaoyong’s (1011- 1077) work. Moreover, Zhou Dunyi’s Taiji tu (Diagram of the Supreme Ultimate), Hetu ([Yellow] River Diagram), Luoshu (Inscription of the River Luo) in Yi-ology which related to astronomy closely began being criticized heavily in the early Qing dynasty. Many works, such as Huang Zongxi’s (1610- 1695) Yixue Xiangshu Lun (On the Images and Numbers School of the Book of Changes), Mao Qiling’s (1623-1716) Zhongshi Yi (My Second Elder Brother’s Comment on the Book of Changes), engaged in this critical movement.40 Although the books of this movement were written mainly after Shunzhi reign-period, the emergence of its tendency must be earlier. These factors led scholars to begin giving up the close relationship between astronomy and Yi- ology. Considering the system of Xing, we would find the metaphysical foundation of his system was closely related to Yi-ology. This revealed that giving up the relationship between calendrical astronomy and Yi-ology meant giving up the metaphysical foundation of traditional calendrical astronomy. However, for the scholars who were influenced by Chinese traditional culture such as Xing, it’s important for them to pursue the supreme existence through calendrical astronomy and construct their systems with metaphysical part. Therefore, when European astronomy replaced Chinese traditional astronomy in early Qing China and had wide influences on the scholars, how to construct their systems with metaphysical part became an important problem.

As the believers of God, the compilers of CZLS were impossible to keep the supreme existence as Xing’s Taiyi in astronomy. It’s also impossible for them to prove God or manifest the glory of God in the official complication

39  The way Tang Shunzhi, Yuan Huang and Zhu Zaiyu employed was different. They attached their astronomical works to Hetu and Luoshu, which were important images in Yi-ology.

40  Zhu Bokun, Yizue Zhexue Shi, vol.4 (Beijing: Huaxia chubanshe, 1995), pp.230-292.

of calendrical astronomy. Actually, previous study has revealed that when Xu Guangqi, the main compiler of CZLS, integrated European natural philosophy into Chinese culture as the learning of Gewu qiongli (investigating things and principles), he stripped the metaphysical part of western natural philosophy and only kept the physical part which corresponded to the “below physical form” in Chinese philosophy.41 Nevertheless, analyzing CZLS and relative discourses, we would find although Xu Guangqi discarded the metaphysical part of western natural philosophy, his classification of western learning and the categories in CZLS provided another way to construct astronomical systems with metaphysical part.

In the preface to Jihe yuanben (Euclid’s Elements of Geometry), Xu Guangqi expressed his notion of the classification of western learning through the introduction of Matteo Ricci (1552-1610):

Teacher (Matteo Ricci) has about three kinds of learning: The high one is cultivating moral character and serving the heaven (theology). The low one is Gewu qiongli. The one branch of Wuli (principle of things) is “learning of images and numbers”. Every kind of learning is precise, standardized and undeniable. 42 In this sentence, Xu Guangqi actually distinguished two kinds of learning: the theology and the investigation of things. Among the investigation of things, he emphasized the “learning of images and numbers”, which included mathematics and astronomy. We can also see his similar discussion in the preface to Taixi Shuifa (Hydraulic Methods of the Great West):

(When the Jesuit missionaries) discuss the Way, (they) take practicing their bodies and exhausting their nature, respecting and serving the God as the standard ……And their minor part (of their learning) is the learning of Gewu qiongli. All principles in and out the society as well as principles of ten thousand of affairs and things, could be answered clearly and quickly if (you) ask……Among (the learning) of Gewu qiongli, there is a branch called “learning of images and numbers”. (Among the learning of images and numbers), the important ones are calendrical astronomy and musical harmonics. As for the other things possessing form and body, affairs having degree and number, we are all based on it to deal and handle and deal with. We can handle and deal

41  Shang Zhicong, Mingmo qingchu de gewu qiongli zhi xue (1582-1687) (Chengdu: Sichuang jiaoyu chubanshe, 2003), p.34.

42  Xu Guangqi, The Preface to the print of Jihe yuanben, in Xu Guangqi quanji (Complete Works of Xu Guangqi), vol. 4, edited by Zhu Weizheng and Li Tiangang (Shanghai: Shanghai guji chubanshe, 2011), p.5.

with them marvelously and fantastically.43 From this discourse, we could find although astronomy was an important learning, it was not about the Way. The Way was discussed in the theology. It was about God. The “learning of images and numbers” was an important conception related closely to Yi-ology. But Xu Guangqi used it with new meaning that has no relation to Yi-ology. The most important point was Xu Guangqi regarded astronomy which belonged to the “learning of images and numbers” as the learning of Gewu qiongli. Gewu (investigating of things) and Qiongli (investigating of principles), important categories in Neo-Confucianism. Through Gewu and Qiongli, people could understand or gain the Way. This is typically expressed in Zhu Xi’s Gewu buzhuan (Supplementary Comment on Investigating Things).44 Besides, in CZLS, the compilers emphasized Li, Shu. For example, in Xinli Xiaohuo (Understanding the New Calendrical Astronomy), Schall von Bell said: If it can be based on Li, there is discussion (about it). It can be measured by Shu, there is calculation.45 In Wuwei Lizhi (Astronomical Guide for Five Planets), the compiler said: According to above two observations, (we) know that the numbers (we) set are all right. The reason is that (they) match the (number of) heaven.46 What needs to be point out is that the name of Li and Shu in CZLS is as same as the ones in Xing Yunlu’s work, even as same as the ones in Chinese traditional Yi-ology book. However, their meanings have been changed thoroughly. Influenced by Jesuits and the style of Chinese traditional scholarship in late Ming, Xu Guangqi thought the traditional Li and Shu which were related to Yi-ology were mysterious and void. Therefore, the new Li and Shu should be used in scientific work in China. He said: “The study of arithmetic was abandoned in recent centuries. There are two reasons for the abolition: firstly, the famous Confucians look down on practical learning and take it as dross. Secondly, superstition holds that there are gods in numbers, which can know the ancient and modern times. In the end, there is no manifestation of gods, and none of the practical studies survive.”47 Therefore, when he introduced western geometry

43  Xu Guangqi, Taixi Shuifa Xu, Xuguangqi Quanji. Xu Guangqi, The Preface to the print of Taixi shuifa, in Xu Guangqi quanji, vol. 5, p.290.

44  See: Chan, Wing-tsit (trans. and comp.), A Source Book in Chinese Philosophy (Princeton, NJ: Princeton University Press, 1963), p.89.

45  Xu Guangqi, Chongzhen Lishu, vol.2, edited by Pan Nai (Shanghai: Shanghai guji chubanshe, 2009), p.1772.

46  Xu Guangqi, Chongzhen Lishu, vol.1, p.383.

47  Xu Guangqi, The Preface to the print of Tongwen suanzhi, in Tianxue chuhan, edited by Li Zhizao (Taipei: Taiwan xuesheng shuju,1965), p.1775.

and mathematical astronomy, although he still used the concept of Li and Shu, he had eliminated the characteristics of Yi-ology and replaced it with what he thought was the “reality” in order to become “practical”. From the perspective of Euclid’s Elements which he introduced into China, this kind of “reality” is characterized by geometric axiomatic system, that is, a series of propositions are deduced by logical deduction through basic definitions, axioms and postulates. From the perspective of CZLS, “reality” is based on a certain geometric model of the cosmos and certain observation data, and uses geometry to deduce the results that conform to the astronomical phenomena. This is something that China’s previous study of calendrical astronomy didn’t have. The ancient Chinese calendrical astronomy mainly studies the operation of the sun, the moon and the five stars by means of algebra. Cosmology and calendar calculation are relatively independent, and the sources of calculation methods are not carefully introduced in the calendar books. For this reason, the calculation method of calendar shows strong characteristics of constructivism and gives people a feeling of being groundless. However, European astronomy based on geometric models and derived from geometry is different. As long as the model is determined and the basic data parameters are given, European astronomy can be inferred according to geometric principles. Therefore, the calculation sources of various astronomical data are also rooted in their models and other quantitative factors, so it shows strong “real” characteristics.

Wang Xichan’s astronomy system was based on European astronomy, and his Li and Shu were mainly influenced by CZLS compiled by Xu Guangqi and missionaries, so it basically does not have the characteristics of Yi-ology. He has equated the Li here with the “Li” in the Gewu qiongli, which is based on a definite geometric model of the universe and mathematical calculations, is the principle of mathematical deduction in Geometric cosmos model and premise or basis of this deduction. Through specific mathematical deductive way according to the real geometric model of cosmos, we can get the precise numbers in astronomy, so he said that “the Li gives birth to the Shu”. Because mathematical calculation can test whether the model and calculation principle are correct or not, he said that “numbers can comprehend reason”. In another words, Shu are important supplements to Li, and also a way to study Li. Through the study of Shu, he can obtain Li, and eventually get the thorough understanding and enlightenment which was supreme state in Neo- Confucianism. Obviously, the theology had no attraction for scholars such as Wang Xichan who was the believer of Neo-Confucianism but not Christianity. However, they could discuss the Way through “learning of images and numbers” which belonged to the learning of Gewu qiongli. This Way was not the God, but the Way with Confucian background. Influenced by CZLS and Neo-Confucianism, Wang completed metaphysical foundation of his system in a new way.

Conclusion

Late Ming and Early Qing dynasty was an important period of the development to Chinese ancient astronomy. In this paper, we studied the systems of two important astronomers -Xing Yunlu and Wang Xichan- and compared them in a metaphysical approach. We found Xing’s system was divided into two parts –Bo and Yue. Bo was the step in which he studied astronomical works widely. It’s represented by GJLLK. Yue meant gaining the Taiyi which was the Tao in Xing’s opinion from Bo and constructed his system with Taiyi. It’s completed in Taiyi Shu. The way that Xing constructed his system under Taiyi was very special. He let Taiyi produce some constants in a numerical cosmology way first. And then he applied Taiyi and these constants which came from Taiyi in the calculation, observation and terms of calendrical astronomy. Through this way, he thought he gained the supreme existence of the world.

Wang Xichan was an important astronomer in early Qing. The contents of Wang Xichan’s calendrical astronomy were mainly based on innovated and improved European calendar, meanwhile remained some characteristics of Chinese traditional calendar. These contents were rooted on two basic concepts- Li and Shu. Li was the principle of mathematical deduction in Geometric cosmos model and premise or basis of this deduction. Shu was the result of the deduction, the constants and calculation of astronomy. Shu came from Li, but through Shu, we could understand Li better. Finally, through the understanding of Li in astronomy, we can obtain the supreme sate in Neo-Confucianism- the thorough understanding and enlightenment of astronomy.

Through the comparison of their systems, we find both Xing and Wang tried to pursue the supreme existence, the Way in their works. Both of them constructed their system with the supreme existence and combined the learning in their system with it. This shows astronomical works in ancient China was not only the leaning to observe and calculation the movements of celestial bodies, but also the learning to gain the Way, just as Confucianism and Taoism did. However, we can also find the difference between these two systems. The basic categories of Xing’s system were Taiyi and constants coming from Taiyi which related to Yi- ology. Actually, the relation between Yi-ology and astronomy is a general phenomenon before late Ming China. However, Wang’s were Li and Shu which has no relation to Yi-ology. This change mainly came from the influence of European science, especially CZLS during late Ming and early Qing. CZLS denied the relationship between calendrical astronomy and Yi-ology, which meant giving up the metaphysical foundation of traditional calendrical astronomy. Meanwhile, the fact Xu

Guangqi regarded astronomy as the learning of Gewu qiongli provided another way to connect astronomical work with the Way. Wang developed this way and constructed his system through employing the basic categories and way in CZLS as his metaphysical foundation. This phenomenon told us the influence of CZLS was not only confined to the epistemology, calculation and cosmological model48, but the metaphysical

48  Nathan Sivin. Why the scientific revolution did not take place in China — or did it? in Explorations in the History of Science and Technology in China: A Special Number of the “Collections of Essays on Chinese Literature and History”, edited by Li Guohao (Shanghai: Shanghai Chinese Classics foundation of astronomy. It changed the metaphysical foundation of the traditional astronomy.

Funding

This work was supported by National Social Science Fund of China [grant number 18CZX031] and Specialized Project for the Development of Teaching and Scientific Research of the Teachers of Liberal Arts in Zhejiang University [grant number 105000-541903/061].

Publishing House, 1982), pp. 89-107.