It seems that the late Kiyosi Yabuuti's 藪内清 works have not been fully translated into either Chinese nor Western languages. Parts of his major works are available in Chinese, thanks to Du Shiran杜石然. In the West, his work has been discussed in several articles, but most of them are quite sketchy overviews. His analysis of Western influence on Chinese astronomy has been translated by Benno van Dalen. Yabuuti's small popular account entitled Chinese Mathematics was recently translated into French, which has led readers in that country to consider him a historian of Chinese mathematics.

When I visited Joseph Needham for the first time in 1957, Volume 3 of Science and Civilisation in China (Cambridge University Press, 1954- , hereafter abbreviated SCC) was in galley proofs. I noticed a grave hiatus. Needham had overlooked the significance of Chinese calendrical science, saying "although there is a very large literature, still growing almost daily, on the Chinese calendar, its interest is, we suggest, much more archaeological and historical than scientific," and "the whole history of calendar-making is that of successive attempts to reconcile the irreconcilable, and the numberless systems of intercalated months, and the like, are thus of minor scientific interest." (SCC, 3:390).

I told him that calendrical science was central in Chinese exact science, and that Yabuuti was spending his whole life exploring it by thoroughly studying the calendrical chapter of each dynastic history. Needham's response was that it was too late at this galley-proof stage to discuss Yabuuti's work.

Since then, Needham moved on to the later volumes of SCC on other topics, and never returned to astronomy. In the Introduction of my History of Japanese Astronomy: Chinese Background and Western Impact (Harvard University Press, 1969, 3), I put it this way: "Chinese calendar-making has been almost entirely overlooked, as in Needham's volumes, despite the fact that calendar-making held a central position in Chinese exact science." Needham reviewed my book in Science (3 October 1969, 95) favorably. While reading the book, when he came across the sentence quoted above, he penciled a comment in the margin of his copy: "fair enough." Where I went on to say "This neglect is probably because of its technical complexity and the lack of a Western counterpart," he wrote "no" and "but difficult to get hold of YK's [Yabuuti Kiyosi's] work." This indicates he thought he should have covered Yabuuti's work.1 But Needham never had a chance to work on calendrical science himself.

In this essay, to supplement the meager information in Western languages about Yabuuti's work on the history of Chinese mathematical astronomy, I would like to focus on his two major works in that field of what the Chinese called "calendrical science."

The two books are his doctoral dissertation, published during wartime, Zui T? rekih?shi no kenky? 隋唐暦法史之研究 (Researches on the history of calendrical science during the Sui and Tang periods, 1944, hereafter abbreviated as A) as a paradigm of such research and a summary of his work in that field, and Ch?goku no Tenmon Rekiho 中国の天文暦法 (Chinese observational and mathematical astronomy, revised and augmented 1990, hereafter abbreviated as B). In B, Yabuuti divides his work into three parts: (1) computational methods, (2) historical surveys, and (3) interactions with Western astronomy.
Computational Methods
I claim Yabuuti's A is a paradigm for the study of Chinese calendrical science. In spite of the contemporary vulgar usage of "paradigm," I use it in a sense extended from the original sense of Thomas Kuhn to refer to a classical treatise that allows followers to develop a line of normal-science research. Analyzing the Ta Yen 大衍and especially the Hsuan Ming宣明 calendar as an exemplar of eclipse prediction, Yabuuti was the first to show the structure of a computational system using modern mathematical notations, formulae and algorithms.
Yabuuti's strong point was his analytical power based on mastery of modern astronomy and celestial mechanics (he acknowledged the influence of Hirayama Seiji's 平山清次 lectures in 1942.) Predecessors in China such as Li Yen李儼 had done mathematical analyses, but in my view Yabuuti actually was the first to show how the ancients had worked out their astronomical methods and observations. He reconstructed their numerical, empirical approach, which used sophisticated interpolation techniques to fill in between observational values. His Japanese students, including myself, applied the Yabuuti paradigm to various calendars in East Asia. while Chinese scholars like Chen Chiuching陳九金and Chen Meidong陳美東 worked on calendrical science independently of Yabuuti's paradigmn as it was not well known among Chinese scholars until recently when Du Shiran made it available to Chinese colleagues at the end of 1980s in his partial translation of B, part 3, "Tenmon keisanho 天文計算法(Astronomical Computation). Nathan Sivin, who spent several years on and off in Yabuuti's seminar in Kyoto, is among the Western scholars who have used and taught his methods.
In A, Yabuuti started with the basic parameters, first dealing with the motion of the sun and moon and then combining them to show the art of solar and lunar eclipse prediction. He followed exactly the order and style of traditional astronomical treatises. In part 3 of B, he moved beyond the specifics of the Sui and Tang systems by inserting a chapter on coordinate transformation.
Why, then, did he consider the Hsuan Ming system more examplary than the earliest systems of the Han period, which were prototypical, or the Shoushi授時 system of the 13th century that other historians regard as the crowning achievement of the tradition? This was probably because medieval China provided a paradigm for Japanese computational systems. In fact, the Hsuan Ming treatise became the basis of the official Japanese calendar from the 8th to the 17th century.2
Qu Anjing 曲安京 has raised the question of why, despite Yabuuti's great general influence on historians of science in Japan, few Japanese scholars followed his methodology in the study of Chinese mathematical astronomy--fewer, in fact, than Chinese scholars?3 Because the subject is of so technical and esoteric discipline, he had few followers until more specialists in this topic came on the scene.
I investigated the eclipse prediction technique of the Shou Shih calendar in 1959 in my Harvard Ph.D. thesis, based on Yabuuti's paradigm for the Hsuan Ming calendar. He later asked me whether I had found any errors in the calculations in A. I had taken it for granted that the book had already been accepted as paradigmatic for the history of East Asian astronomy. But Yabuuti was aware that, in the fifteen years between his publication in 1944 and my normal-science use of it in 1959, no one had checked his mathematical derivation. After the Cultural Revolution, which had shut down the universities but allowed limited historical training in astronomical observatories, many Chinese scholars began technical inquiries in the history of mathematical astronomy. This enabled them to work on a broad range of previously unexplored primary sources. Because very few such specialists have been trained since 1980 in Japan, Europe, or the United States, most of the advances in the field are now coming from China.
Historical Surveys
The works of Yabuuti's main Japanese predecessors, Shinj? Shinz? 新城新蔵and N?da Chury?能田忠亮, were Orientalist in their aims, interested primarily in the origins of Chinese civilization. Yabuuti was the first Japanese scholar to make a thorough historical survey by critically examining the calendrical chapters of each dynastic history. The topic of A was the computational methods of the Sui and Tang calendars, but in an appendix Yabuuti provided an outline of developments from antiquity through the Tang period. After A was published, he contributed to T?h? Gakuho (Kyoto) 東方学報（京都） a series of articles on the most important astronomical developments in each dynasty. His numerous articles on the history of Chinese calendrical science were epitomized in Part 1 of B in 1969, and revised with augmentation in 1990. He was fortunate enough to be a pioneer, for the calendrical chapters of the official histories had been very sparsely explored by previous scholars of the twentieth century.
In this area too, the growth of scholarship in China has made it possible to surpass the standard of Yabuuti (known in China through Du's translation). His research was mostly limited to the dynastic histories, although he cited other sources available to him. Chinese specialists have drawn on a wide variety of sources in additional to the official printed ones. The large volume of recent Chinese publications in the field have made additional materials, including newly excavated ones, available worldwide.
Interactions with Western Astronomy
Yabuuti wrote about another interest of his, East-West trans-cultural intercourse, in chapters 5 and 6 of A and Part 2 of B.
I once asked Otto Neugebauer about interchange between Babylonia and China. He flatly denied that Babylonia had influenced ancient China, since there were no parallels in their astronomical parameters. Yabuuti worked on Buddhist and Islamic influence on China, but showed that neither influenced the mainstream traditional Chinese astronomical paradigm. Now that both Neugebauer and Yabuuti have passed away, I would like to examine the state of research on each area of influence, and encourage the specialists to establish a network for trans-cultural investigation of mathematical astronomy.
At a nodal point between Western and Eastern traditions was E. S. Kennedy, whom Yabuuti and I visited in Beirut in 1959. At the time, Kennedy was interested in translating Islamic sources of the Chinese-Uighur calendar. We encouraged him to reveal westward Chinese influence. An article of 1964 by Kennedy in Isis showed that the solar equation of center was represented in the fifteenth century with a parabolic function. In the same year, I analyzed a Japanese fragment of the solar table of the Fu-t'ien li, and found the same parabolic expression which originated in west China in the eighth century, thus proving that Chinese astronomy had moved westward.
While the Western tradition used geometry to express planetary movements, Chinese employed a numerical, empirical approach, with sophisticated techniques to interpolate between observational values. The Fu-t'ien li's algebraic function, which was quite novel, entered the mainstream of Chinese mathematical astronomy. The Turkish historian Aydin Sayili was fascinated with those findings. In his last days he tried to prove that Turkish Buddhists in Central Asia originated algebraic astronomy, but could find only circumstantial evidence (Erdem. (1993)).
Today, however, scholars such as Yano Michio矢野道雄and Benno van Dalen, with deep understanding of more than one language and culture, would do well to establish a network and pool their findings. Several others, such as Hashimoto Keizo橋本敬造and Catherine Jami, are also working primarily on the relationship of Chinese astronomy to that of other cultures. Some Chinese of a still younger generation, for instance Han Qi, are following in Yabuuti's footsteps.
Shoushih li Project
Yabuuti and I spent some time during the 1960s, with a Harvard-Yenching Institute research grant, studying the astronomical treatise of 1279, the Shoushi li. At the time he was a Professor of Kyoto University, and I was teaching at Tokyo University. We met halfway between Kyoto and Tokyo every year. At first we wanted to translate the treatise into Japanese with full of introductory comments, and actually completed a draft (Yabuuti translated the basic treatise, li-ching暦経, and I did the evaluation, li-I暦議). We developed doubts about whether it was worth publishing. There was no point in translating the technical terms, but as long as they remained in Chinese characters, they did not communicate the gist of the technical content. At the same time, Nathan Sivin had become interested in doing an English translation to extend his work on Han astronomy. An English version, unlike a Japanese one, would be forced to interpret technical terms, as Joseph Needham had done with many in Science and Civilisation in China. The three of us duly joined forces, and an English draft was completed in 1974.
At that point, it was definitely not ready for the press. Part of the annotation remained to be done. Yamada Keiji eventually showed that the social organization and political motivation of the calendar reform of 1279 were so important that they required full discussion. Certain technical problems also remained to be resolved. For instance, we were not able to comprehend the physical meaning of one column 限度 in the table of planetary motions. Sivin also felt it advisable to do a complete error analysis in order to understand the many peculiarities of the computational procedures. We hope in the next year or two to resolve all of these problems so that the translation can be published.
History of Chinese Science and Technology Project
At a time when mainland Chinese scholarship was still paralyzed by the Cultural Revolution, Joseph Needham and Yabuuti managed the two main centers of the history of Chinese science, at Cambridge, England and Kyoto, Japan. Their styles made a remarkable contrast. While Needham divided his volumes according to the disciplines of modern science, such as astronomy, physics, chemistry, and biology, and pursued each discipline diachronically, Yabuuti arranged his collective project synchronically in four volumes, moving from Han to Sui and Tang, to Sung and Yuan, and then to Ming and Ch'ing. In each, he provided an overview of the age and then articles on various specialties by his collaborators, mostly of the same generation.
Whether to arrange a broad historical survey synchronically or diachronically is a
perennial subject of debate. Since each policy has its strengths and weaknesses, historians often combine the two. Yabuuti's synchronic treatment was rather typical of historical description that aims to exhibit the characteristic features of each age. Needham's diachronic treatment arises from his assumption that there is a single measuring-stick of progress for the history of science, namely current knowledge-an assumption decisively rejected by the last generation of specialists.
The chronological tradition that Yabuuti initiated has influenced his successors to a limited extent. Yoshida Mitsukuni 吉田光邦, Yamada Keiji 山田慶児 and Tanaka Tan田中淡 followed him as leaders of the Seminar in the History of Chinese Science of the Institute for Research in the Humanities (Jimbun Kagaku Kenkyujo Kagakushi Kenkyushitsu人文科学研究所、科学史研究室). Their collective publications have been topical in content, with titles such as Chugoku no Kagaku to Kagakusha中国の科学と科学者(Chinese Science and Scientists,1978), Chugoku Kodai Kagakushi Ron中国古代科学史論(Discussions of the History of Ancient Chinese Science, 1989 and 1998), and Shinhakken Chugoku Kagakushi Shiryo no Kenkyu新発見中国科学史資料の研究(Studies of Newly Discovered Materials for the History of Chinese Science, 1985). Within each volume, the editors have generally followed a chronological arrangement, and the authors have on the whole not been attracted by Needham's positivism.
In Yabuuti's specialty of astronomy, he trained Yano, Hashimoto Keizo, Miyajima Kazuhiko 宮島一彦, Kawahara Hideki川原秀城and myself. In this field for many years, there has been no central figure like Yabuuti. Yano has led in maintaining the tradition by organizing a group to study calendrical astronomy, following Yabuuti's paradigm, but with computers now at hand.
1 This copy of my book is available at the East Asian History of Science Library at the Needham Research Institute, Cambridge, UK.
2 In A Yabuuti consulted a Japanese treatise on the Hsuan Ming calendar (7 volumes published in 1644), with commentary Koshoku Shiki交蝕私記(private account of eclipse theory) by the Japanese astronomer Nakahara Moroto中原師遠in 1115.
3 "Responses to Prof. Yabuuti's work: Chinese studies on ancient mathematical astronomy" Special in Memorial of Prof. Yabuuti Kiyosi (1906-2000), Resume, Special Session of XXI International Congress of History of Science
NAKAYAMA YABUUTI PARADIGM 11 OF 11

Yabuuti Kiyosi in his latest days provided by Prof. Kazuhiko Miyajima