translating ancient chinese calendars

Revue de synthèse : tome 131, 6e série, n° 4, 2010, p. 605-612. DOI : 10.1007/s11873-010-0136-x

REVUE CRITIQUE

TRANSLATING ANCIENT CHINESE CALENDARS

Christopher CULLEN *

When Joseph Needham published volume three of his massive Science and Civilisation in China in 1959, there was one striking omission in his historical

treatment of Chinese knowledge of the heavens : that part of the subject relating to mathematical systems intended to predict the motions of the celestial bodies was treated very briefly, and its importance minimised as of « minor scientific interest 1 ». Few modern scholars who have studied the subject seriously in any part of the world would agree. Like Confucius, however, Needham has been fortunate in the number of people who have been eager to point out his mistakes, and this error has been no exception 2.

The days are now past when Needham’s omission made it diffi cult for the non-sinologue reader to gain a basic understanding of the methods used in China over the centuries to calculate the motions of the sun, moon and planets. A large amount of scholarship in western languages has been published in recent decades in both monograph and periodical form, and although no single student is likely to fi nd that any one of these publications meets his or her particular needs entirely, the situation is much better than it once was.

My aim in this review is to give the reader a brief glance at four recent publica-tions in this fi eld that have a certain degree of connection with each other, and which might (for readers with the necessary linguistic ability) be consulted together. I begin with the work of Nathan Sivin Granting the Seasons : the Chinese Astronomical Reform of 1280, and indeed devote most attention to it, since I think it not only leads

* This review takes the form of a discussion of the following publications : YABUUTI (Kiyosi) and NAKAYAMA (Shigeru) 中山茂藪內清, 授時暦 : 訳注と研究 Jujireki : yakuchū to kenkyū (The Shou shi li : Annotated Translation and Studies), Kawasaki City, I & K Corporation アイ・ケイコーポレーション, 2006 ; QU (Anjing) 曲安京, 中国数理天文学 Zhong guo shu li tian wen xue (Chinese Mathematical Astronomy), Beijing, Science Press, 2008 ; SIVIN (Nathan), 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 ; MARTZLOFF (Jean-Claude), Le Calendrier chinois : structure et calculs, 104 av. J.-C.-1644. Indétermination céleste et réforme permanente. La construction chinoise officielle du temps quotidien discret à partir d’un temps mathématique caché, linéaire et continu, Paris, Honoré Champion, 2009. Christopher Cullen, born in 1946, is Director of the Needham Research Institute and Honorary Professor of the History of East Asian Science, Technology and Medicine in the University of Cambridge. His current research mainly concerns the use of numbers for calculation and for the prediction of celestial phenomena in early imperial China. He has recently published « People and Numbers in Early Imperial China », in Eleanor ROBSON and Jackie STEDALL, Oxford Handbook of the History of Mathematics, Oxford, Oxford University Press, 2008. Address : Needham Research Institute, 8, Sylvester Road, Cambridge CB3 9AF, UK ([email protected]).

1. NEEDHAM and LING, 1959, p. 390. 2. Lun yu 7, 30 ; for one example of Needham’s good fortune, see CULLEN, 1980, p. 49.

606 REVUE DE SYNTHÈSE : TOME 131, 6e SÉRIE, N° 4, 2010

naturally to mentions of the other three works, but also comes closest to the kind of treatment that the reader disappointed by Needham’s omission would have liked to have had available much earlier.

SIVIN ON THE SHOU SHI LI

Sivin’s book is an annotated translation, with introductory material, of the Shou shi li 授時曆 « Season-Granting astronomical system » (to use the author’s favoured translation), a Chinese astronomical treatise completed in 1280 CE for the government of the Yuan dynasty (1276-1368) under the leadership of Guo Shoujing 郭守敬 (1231-1316). It represents the last substantial innovation under the ancient Chinese astronomical tradition before western missionaries arrived in China at the end of the 16th century, bringing with them fi rst Ptolemaic and then post-Renaissance western astronomical learning. As such a document, the Shou shi li is clearly important for the history of astronomy, and fully deserves the considerable work that this author has devoted to making it accessible to an English language readership. The book is divided into the following major sections. 1) Introduction and chapters 1-6 (p. 1-247) : these parts of the book give readers ample background on the material that is to be presented in later sections. They discuss the cultural, political and other aspects of the context within which the Shou shi li was created, and then devote a hundred pages to careful explanations of the basic technical aspects of this and preceding astronomical systems. This section is a good place to look for clear and on the whole balanced explanations of what Chinese celestial calculators did, and how they did it. The text then moves back to the Shou shi li itself, and discusses the genesis of the project, the people who worked on it, the institutions they worked in and the instruments that they used, followed by a review of the documentary sources that provide the evidence on which this book is based. 2) Translation and annotations, chapters 7-10 (p. 249-550), appendices A and B (p. 561-595) : this part of his work contains a translation, with explanatory annotations, of the main Chinese sources (taken from the Yuan shi 元史 « History of the Yuan dynasty », presented to the throne in 1370) dealing with the Shou shi li project. First, in chapters 7 and 8, we are given the « Evaluation » (yi 議), a discussion of the basis on which the system is constructed, followed in chapters 9 and 10, by the main body of text (the jing 經 « Canon ») in which the computational methods to be used are carefully set out step by step. In the appendices, we are given accounts of the instruments available, and a biography of Guo Shoujing.

This is a clearly written book, and its renderings of Chinese texts are largely successful in conveying content and fl avour without importing modern assumptions. The treatment of technical astronomical matters is competent, and usually clear – and is performed in purely verbal terms without the use of modern mathematical symbolism. The signifi cance of this choice will become clear later in this review. The author’s discussion of what he calls « the many dimensions » of the astronomical project he studies is competent and thorough. This is as it should be : almost all the relevant material from offi cial fi les was collected by the late 14th century compilers of

607C. CULLEN : TRANSLATING ANCIENT CHINESE CALENDARS

the « Yuan history », and its interpretation is largely non-controversial. Nevertheless, the non-sinologue reader will be justly grateful for having been given access to these texts.

One unfortunate feature of the book no doubt originates in the fact that this project was begun several decades ago – that of the chosen system for romanisation of Chinese. For reasons that are not convincing, the author insists on using the Wade-Giles system, which has not been used to train language students for many years. Pinyin, the offi cial system of the People’s Republic, is now universal except in some long-lived book series (such as the Cambridge History of China) where problems of internal consistency would follow from a change. It is very relevant however that the even longer-lived Science and Civilisation in China series has at last made the change to pinyin. The question is not which system is better at approximating the actual sounds of Chinese, but which system is more likely to make this book useful to readers who know no Chinese but will want to compare this author’s work with that of other scholars now publishing, who will inevitably use pinyin. By sticking with Wade-Giles, this book has for example set its lay readers the problem of identifying the man it calls Kuo Shou-ching with the Guo Shoujing referred to by other writers. No-one else has written at length about Chinese astronomy using Wade-Giles since the last century, and no-one is ever likely to do so again. None of this is a problem for experienced sinologues, but for the sake of others I regret that the publishers did not feel able to require that the author either updated his manuscript in this respect or paid an indigent post-doctoral scholar to do so on his behalf. The job could have been done in a couple of weeks.

The author uses tables and diagrams quite helpfully in explaining the text. One missing feature that could have been helpful would have been a series of worked examples, as for instance given by Toomer for Ptolemy 3. The author concedes that these would have been helpful 4 and since he has undoubtedly worked through such examples himself in the course of his research it is puzzling that none have been given.

YABUUTI AND NAKAYAMA ON THE SHOU SHI LI

As Sivin tells us, he spent several substantial periods of time during the 1970s and 1980s at the Research Institute for Humanistic studies in Kyoto, where (amongst other things) he studied the Shou shi li with the late great Japanese scholar of the history of East Asian science Yabuuti Kiyosi 5 藪内清 (1906-2000) and his former student Nakayama Shigeru 中山茂. The title page of the book gives credit to both of them for « research collaboration ». It is interesting therefore to look at the book on the Shou shi li that was published in Japanese under the names of these two

3. TOOMER, 1998, appendix A. 4. SIVIN, 2009, p. 49. 5. I use here the form of romanisation preferred by this scholar, rather than the more standard

« Yabuuchi Kiyoshi ».


scholars in 2006. The work is divided into four sections. 1) Annotated translation of the Canon of the Shou shi li (p. 2-58) : the annotations here are considerably briefer and less frequent than those in Sivin’s book. A partial explanation of this brevity is of course that it is not an obvious imperative for an author writing in Japanese to discuss problems of translations of Chinese technical terms at length, since Chinese and Japanese share a common repertoire of characters. 2) Translation of the evaluation of the Shou shi li (p. 60-106) : this section is not annotated. 3) Discussion of the main structure of the Shou Shi li and related points (p. 108-154) : the theoretical procedures of the Shou Shi li are analysed in the historical context of the development of Chinese astronomy. 4) Supplementary discussion on points relating to the planets (p. 156-164) : here Nakayama tells us that the fi rst draft of sections 1-3 of the present book was already completed in the 1960s, and states that Sivin, working with them, completed an English translation in the 1970s. But one problem remained, that of the technical term xian du 限度 « limit degrees », used in the theory of the planets, of which the astronomical signifi cance remained unclear. Pending resolution of this diffi culty, the two Japanese researchers held back their work from publication. It was only when a Chinese researcher, Qu Anjing, proposed what Nakayama saw as a satisfactory solution that he decided to publish the book that he and his late teacher had written, together with this supplementary section discussing Qu’s research and its relation to the Shou Shi li.

Clearly therefore, both the books discussed so far have long histories. Had it not been for the xian du problem, we might have had the book by Yabuuti and Nakayama about forty years earlier. In the case of Sivin, that does not appear to be the reason for delay, since when he does refer to Qu’s work 6, he does so only to dismiss it as « valuable but narrowly positivistic », and he does not indicate that the lack of a solution to the xian du problem held him up. Presumably we have to lay the blame on the many distractions that take a leading US scholar away from his desk, and the inherent diffi culty of doing work of this kind. Something one would have liked to have had in Sivin’s book is an indication of how far he agrees or disagrees with the positions taken by his former colleagues in their book, published three years before his own. But despite his expressions of appreciation for their collaboration, he passes over the work of the Japanese scholars in silence.

At the time this review was fi rst drafted, the story of the xian du problem had reached the stage set out above. But in the summer of 2010 Nakayama published some penetrating refl ections provoked by this issue, refl ections which go to the heart of some of the main questions touched on in the present review : Shigeru Nakayama, « Incommensurability between Western Geometrical and Chinese Numericoalgebraic Astronomy. Takebe Katahiro’s interpretation of Planetary Limit Degrees 7 ». In the fi rst place, Nakayama confesses that, after all, « what [he] was satisfi ed with [i.e., Qu’s explanation of xian du, characterized by Nakayama as being

6. SIVIN, 2009, p. 521 and biography, p. 627. 7. NAKAYAMA, 2009 (this publication is dated as 2009 but was published in 2010).


“based on a purely geometric model of Western homocentric cosmology”] was not a true understanding of what Limit Degrees really meant », and states that « the real signifi cance of [Qu’s] work » was that it « showed that when we compare a modern Western geometrical approach with a Chinese numerico-algebraic one, they may be fundamentally incommensurable ». On reconsideration, he prefers an explanation of xian du fi rst advanced by the Japanese shogunal astronomer Takebe Katahiro 建部賢弘 (1664-1739) : « […] the Yuan method uses a very simple numerico-algebraic scheme combining the solar and planetary equations of centre [i.e., their deviations from mean motion], nothing else. » The reader who wants full technical details will fi nd them clearly set out in Nakayama’s paper. But for a review such as the present essay, much more signifi cant is Nakayama’s consequent questioning of a major methodological premise of the school of historians of Chinese astronomy founded by Yabuuti, a school whose work Nakayama has worked for years to make better known outside Japan : « Positivist historians of mathematics defi ne their task as translating ancient mathematical astronomy into the terminology of modern science. They assume that if it is translatable, it has scientifi c value. Yabuuti and I took that approach […] our method turned out to be too Whiggish to be reliable. » Like Nakayama, the present reviewer has a deep admiration for the many insights into pre-modern East Asian astronomy that Yabuuti’s modern technical astronomical training gave him. Few researchers in this fi eld have seen things more clearly, or expounded their fi ndings more lucidly. And, as Nakayama says, it would be « foolish to renounce the advantages of hindsight » in trying to comprehend « the thought processes of an astronomer in China seven hundred years ago ». History is, as Nakayama says, « a conversation between past and present ». But scholars who seek to understand the past sometimes need to listen to what it has to say more humbly than they sometimes have done, and the problem of the xian du seems to be a case in point.

QU ANJING AND HIS WORK

A reader who wishes to know more about Qu’s contribution will naturally turn to his book, which is based on a great deal of research by many Chinese scholars who have worked on the history of astronomy, mostly since the middle of the last century, as well as by Qu himself 8. It is to some extent a companion volume to another book by Qu 中国历法与数学 Zhong guo li fa yu shu xue (Chinese Astronomical Systems and Mathematics) 9. In this latest work, Qu sets out to write a systematic textbook discussing the technical procedures by which Chinese sky-watchers made calculations to predict the motions of celestial bodies. The work is divided into fi ve sections. 1) Generalities (p. 1-80) : the main features of Chinese astronomical systems are set out, and a historical sketch of the development of successive systems is given. 2) The divisions of time (p. 81-132) : discusses the divisions of the solar

8. QU, 2008. 9. QU, 2005.


and lunar cycles, together with cycles of a hemerological nature related to them. 3) Solar motion (p. 133-232) : discusses different analyses of all aspects of solar motion in successive astronomical systems. 4) Gnomons and clepsydra (p. 233-307) : discusses all aspects of time measurement, and the use of the gnomon in relation to the determination of seasons, including the variation of shadows with geographical location. 5) Lunar motion (p. 308-389). 6) Solar and lunar eclipse prediction (p. 390-531). 7) Planetary motion (p. 532-628). This includes discussion of the xian du concept in the context of a substantial chronological and theoretical survey.

A great virtue of this book is that it says something informative on almost every technical aspect of quantitative pre-modern Chinese thought about the heavens in all periods up to the beginning of contacts with early modern western astronomy. Its perspective is fi rmly positivistic, and oriented towards an account of the progress and improvement of the specialist skills of those who concerned themselves with the matters it treats. Unlike Sivin, Qu takes the position that the most natural thing to do with a pre-modern statement of a calculation procedure is to translate it into modern symbolic algebra. Most other Chinese historians of astronomy (and indeed of mathematics) who have written in recent decades have also followed this approach, which is essentially that criticised by Nakayama in his 2010 paper as « Whiggish ». While Nakayama’s criticism is certainly valid, Qu’s book is still an excellent example of how much can be achieved by a determined and technically well informed Whiggism, even if the very successes of such an approach may sometimes seem to point to the need to transcend it.

MARTZLOFF ON THE THEORETICAL STRUCTURES OF CHINESE CELESTIAL PREDICTION

A cultural historian of the history of science might see the three works already discussed as in some way representative of the approaches to this subject characteristic of the Anglophone cultural milieu (what some French writers call the « Anglo-Saxon » world), Japanese culture and the culture of the People’s Republic of China. While that might be something of a caricature, it would not be entirely without truth. In Jean-Claude Martzloff’s book, Le Calendrier chinois : structure et calculs, 104 av. J.-C.-1644, we may perhaps see a « fourth way » exemplifi ed. Martzloff’s approach results in the following structure for the main part of his book. 1) The Chinese calendar (p. 23-106) : beginning from a distinction between « surface » and « deep » structures – the fi rst found in published almanacs (where Martzloff’s attention to actual documents is exemplary amongst the works reviewed here), the second in the calculation procedures of astronomical systems – this section reviews the main elements of Chinese calendrical structures, such as the divisions of the seasons, the cycles of the sun and moon and other hemerological structures. It also reviews the broad historical and institutional background from which successive systems emerged. 2) Calculation (p. 107-240) : here the reader fi nds a discussion of the core modes of calculation on which Chinese astronomical systems were based. The discussion is highly general in form, and attempts as far as possible


to characterise what the author believes to be common to all such systems, while pointing to the increasing complexity resulting from (for instance) the attempt to predict true rather than mean values. 3) Examples of calculations (p. 241-334) : here are given examples of the application of the techniques discussed in the previous section, as found in four systems from different periods, and also for the calculation of the so-called « mo 沒 and mie 滅 » days. Finally a number of appendices take up various special topics, such as the author’s favoured translation of the Chinese term li 曆, which refers to the systems of astronomical calculation discussed in this and the other works reviewed here.

What, if anything, emerges from a comparison of the four works outlined in this review ? In the limited space remaining, I should like to focus on the general theme of translation as it emerges from a comparison of at least the books of Sivin, Qu and Martzloff. In the case of Qu, the translation is not a linguistic one in the normal sense – a premodern technical term, even an ancient one, can be used in modern Chinese with no obvious sense of linguistic discontinuity 10. It is, rather, that he approaches his material in a way shared by many modern mathematicians, in which it is assumed that any pre-modern verbal statement of the relations between quantities can unproblematically be translated into its « equivalent » in modern symbolic algebra. Thus if an ancient Greek writer writes a sentence in his own language equivalent to « the square on the hypotenuse of a right triangle is equal to the sum of the squares on the opposite and adjacent sides », the researcher says something like « here [name] writes the equation h2 = a2 + b2 ». The problems consequent on this kind of procedure were pointed out long ago in Sabetai Unguru, « On the Need to Rewrite the History of Greek Mathematics 11 » : one obvious point is that it exports the notion of « algebraic equation », with all that it involves by way of manipulative possibilities to a period when no such concept existed. Sivin explicitly shuns this, and translates verbal expressions into verbal expressions throughout. Thus to take one example, Sivin renders the instructions for how to fi nd the noon position of the sun on the ecliptic (« The Yellow Way » huang dao 黃道) as follows « Set up the daily corrected solar motion [for the given day], halve it, and add to the position of the sun on the Yellow Way at the preceding midnight to yield the Position of the Sun on the Yellow Way at Noon in tu and parts 12 », rather than writing an equation of some such form as Pnoon = Pmidnight + M/2. Martzloff, on the other hand, follows Qu in using modern algebra throughout, but the idea of translation is less present : his work actually contains relatively little translated text as such. The explicit aim of his book is rather that of abstraction, and of deliberate distancing from the complications and particularities of the original documents, or as he puts it « il nous a paru plus urgent de commencer par chercher à mettre en évidence la structure générale des calculs du calendrier chinois que d’entrer de plain-pied dans la forêt quasi-tropicale de ses

10. It should not be assumed that the effect of this linguistic fact has always been to make it easier for a modern Chinese author to develop insights into the distinctive features of an ancient text.

11. UNGURU, 1975. 12. SIVIN, 2009, p. 448.


manifestations linguistiques concrètes 13. » Is it unfair to characterise this approach as demanding that we move as quickly as possible away from the actual historical evidence about the varied ways in which Chinese people over nearly two millenia actually did calculations about the heavens, and instead try to glimpse some kind of « ideal-type » or non-historical invariant behind it all ? If so, such an approach does not seem to me to be the pursuit of history in the normal sense, but rather some kind of philosophical programme. Whatever it is, such a distancing from the concrete certainly demands a degree of trust in the author’s powers of insight that may be greater than most readers would want to concede to anybody.

This then, is a very varied collection of books that consider the same basic theme using a wide range of styles and methods. All of them are sincere efforts to open the way to a diffi cult subject that demands unusual combinations of skills, and deserve respect and gratitude for these authors from the interested reader. As ever the chal-lenge for any critic has to be to use what they offer to create something better…

LIST OF REFERENCES

CULLEN (Christopher), 1980, « Joseph Needham on Chinese Astronomy », Past & Present, n° 87, p. 39-53.

MARTZLOFF (Jean-Claude), 2009, Le Calendrier chinois : structure et calculs, 104 av. J.-C.-1644. Indétermination céleste et réforme permanente. La construction chinoise officielle du temps quotidien discret à partir d’un temps mathématique caché, linéaire et continu, Paris, Honoré Champion.

NAKAYAMA (Shigeru), 2009, « Incommensurability between Western Geometrical and Chinese Numericoalgebraic Astronomy. Takebe Katahiro’s interpretation of Planetary Limit Degrees », East Asian Science, Technology and Medicine, n° 30, p. 93-102.

NEEDHAM (Joseph) and LING (Wang), 1959, Science and Civilisation in China, vol. 3 : Mathematics and the Sciences of the Heavens and the Earth, Cambridge, Cambridge University Press.

QU (Anjing) 曲安京, 2005, 中国历法与数学 Zhong guo li fa yu shu xue (Chinese Astronomical Systems and Mathematics), Beijing, Science Press.

QU (Anjing) 曲安京, 2008, 中国数理天文学 Zhong guo shu li tian wen xue (Chinese Mathematical Astronomy), Beijing, Science Press.

SIVIN (Nathan), 2009, 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.

TOOMER (G. J.), 1998, Ptolemy’s Almagest, Princeton, Princeton University Press.UNGURU (Sabetai), 1975, « On the Need to Rewrite the History of Greek Mathematics », Archive

for History of Exact Sciences, n° 15, p. 67-114.YABUUTI (Kiyosi) and NAKAYAMA (Shigeru) 中山茂藪內清, 2006, 授時暦 : 訳注と研究

Jujireki : yakuchū to kenkyū (The Shou shi li : Annotated Translation and Studies), Kawasaki City, I & K Corporation アイ・ケイコーポレーション.

13. MARTZLOFF, 2009, p. 19.

translating ancient chinese calendars

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