The Foundations of Celestial Reckoning

Three Ancient Chinese Astronomical Systems

Christopher Cullen

• Publisher: Routledge
• Year: 2016
• ISBN:
  9781317327196
• Edition: 1
• Topic: History
• Subtopic: Ancient History
• Index: History

The Foundations of Celestial Reckoning gives the reader direct access to the foundational documents of the tradition of calculation created by astronomers of the early Chinese empire between the late second century BCE and the third century CE. The paradigm they established was to shape East Asian thought and practice in the field of mathematical astronomy for centuries to come. It was in many ways radically different from better known traditions of astronomy in other parts of the ancient world.

This book includes full English translations of the first three systems of mathematical astronomy adopted for use by imperial astronomical officials, together with introductory material explaining the origin and nature of each system, and a general introduction to the work as a whole. The translations, which are accompanied by the original Chinese text, give a consistent rendering of all technical terms, and include detailed explanatory notes. The text in which the second of the three systems is found also includes a unique collection of documents compiled around 178 CE by two experts in the field, one of whom was the author of the third system translated in this book. Using material transcribed from government archives of the two preceding centuries, these scholars carefully document and review controversies and large-scale official debates on astronomical matters up to their own time. Nothing equivalent in detail and clarity has survived from any other ancient culture. The availability of the totality of this material in English opens new perspectives to all historians of pre-modern astronomy.

1
General introduction

This book contains translations of a number of Chinese documents relating to astronomy, dating from around the beginning of the Common Era. They include three complete astronomical systems of the type known as li 曆, and two other documents in which contemporary developments in techniques of astronomical calculation are described and debated.

Ancient material of this kind has until now remained largely unavailable to Western historians of astronomy – except for the very small number who happen to be able to read classical Chinese. Yet if it had not been for the accident of the language barrier, I believe that this material might long have played a major role in any account of the development of astronomy in the ancient world. There are two main reasons why I believe that to be the case.

In the first place, the documents presented here in translation come from a culture that gave astronomy and astronomers a level of importance in government structures unsurpassed elsewhere, both in antiquity and in later times up to the last few centuries. All the documents studied here were either compiled under official patronage of some kind, or were drawn from material in government archives. They therefore exemplify and indeed owe their preservation over the last two millennia to the unique importance of astronomical activity and historical record-keeping for the Chinese imperial state from the third century BCE to its fall in 1911.

Second, a striking feature of these documents is that they come from a time when a number of basic innovations in astronomy were taking place. In comparison, in the ancient Mediterranean world we have very detailed documentation of the highly developed techniques of calculation used in the Greek-speaking world in the second century of the Common Era, thanks to the survival of the work of Ptolemy of Alexandria.¹ But if we look for some indication of how (for instance) the ecliptic was first adopted by Ptolemy’s predecessors as the primary reference frame for the motions of the sun, moon and planets, little direct evidence survives.² By contrast, the Chinese material translated here gives us a first-hand record of the efforts made by one expert to convince his colleagues that the ecliptic must be adopted not only as the preferred frame for calculations of solar, lunar and planetary motions, but also for constructing observational instruments. This innovation is also clearly reflected in changes in the ways that the three systems I have translated deal with celestial motions. To take another example from several, the documents in this book show clearly how the moon’s varying speed was first observed, analysed and made predictable. Taken together, they show us how the East Asian tradition of doing astronomical calculations – what has been called the ‘Han paradigm’³ – was created and consolidated.

I hope that historians of astronomy more familiar with what happened at the other end of the Eurasian continent will find that a reading of this material helps them to see more familiar texts in a fresh light, and introduces them to a new field.

The explanatory material that accompanies the ancient material presented in this book is mainly intended to help the reader understand the technical features of the texts translated, and for that purpose I go into all the detail necessary. Each document is prefaced by a special introduction in which its origins and particular features are described, and the translations are accompanied by explanatory comments, with a number of worked examples. Apart from that, I sketch the historical and cultural context needed to convey a basic idea of what purposes these documents served, who produced them, and how they were evaluated. This book is not, therefore, an attempt to write a social, intellectual and political history of the numerical and quantitative aspects of Chinese astronomy in the period with which it deals, although it does provide access to some of the most important source material for writing a book of that kind. I expect that any reader of this work will see the need for such a history; in another book completed more or less in parallel with this one I have attempted to fill that need.⁴ That book and the present one will, I hope, be regarded as complementary.

1.1 The World of Early Imperial China

The material discussed in this book comes from the period of about four centuries around the start of the Common Era, when unified imperial rule was first established over a large part of the East Asian land mass. More precisely, this was the time of the empires of Qin 秦 (221–206 BCE) and Han 漢 (206 BCE–220 CE). From 9 to 23 CE the Han imperial clan of Liu 劉 was displaced from the throne by a powerful courtier, Wang Mang 王莽, who reigned as first and only emperor of his Xin 新 dynasty until the Han were restored to power in the wake of widespread rebellion. Since the capital of the Han was originally at Chang’an 長安 (modern Xi’an 西安) in the west, and was transferred eastwards to Luoyang 洛陽 after the time of Wang Mang, the Han dynasty is usually divided by historians into the Western Han and Eastern Han. The expressions ‘Former Han’ and ‘Later Han’ are also used.⁵

The Qin, followed by the Han, established an entirely new form of government, under which the country was administered by a non-hereditary corps of salaried officials, each of whom was ultimately responsible to the emperor. These officials were selected on the basis of their competence in the skills needed for their work, which demanded as a minimum a good standard of literacy and a level of numeracy sufficient to enable them to report on the expenditure under their control.⁶ This pattern of rule was followed for most of the next two millennia, up to the final dissolution of the imperial system with the fall of the Qing 清 dynasty in 1911.

Nothing like this form of government had existed for the five centuries before the Qin, during which the territory that was to form the empire had been divided into a number of effectively independent states, closely related in culture and language, always in competition for dominance or protection, and sometimes in a state of open warfare with each other. This period of disunion is conventionally divided into the Spring and Autumn Chun qiu 春秋 period (c.771 BCE to early fifth century BCE), named after a book of annals from the state of Lu 魯 (in modern Shandong 山東),⁷ and the Warring States Zhan guo 戰國 period, from the end of the Spring and Autumn to the time when Qin conquered all other states to establish its empire.

Historians of the imperial age preserved traditions of earlier periods of unified rule before the disunion of the Spring and Autumn and Warring States. The earliest of these was said to have been the Xia 夏 dynasty, conventionally dated from the end of the third millennium BCE to the first half of the second. The subsequent Shang 商 (or Yin 殷) dynasty was said to have been overthrown by the Zhou 周 near the end of the second millennium BCE, and the Zhou kings maintained their power until they were forced to flee their capital in 771 BCE.⁸ There has never been doubt about the historicity of the Zhou, but many Western historians discount the idea that anything like a ‘Xia dynasty’ ever existed and maintained central control of a large territory. As for the Shang, the latter part of the dynasty is well attested by finds from the 1920s onwards of inscribed animal bones used for divination, deposited in caches at the site of the last Shang capital at Anyang 安陽, and giving names of Shang kings close to those recorded by historians of the imperial age. But none of these ancient kingdoms had a form of government resembling that of the Qin and Han.

The kings of Zhou, of whom we know the most, were supported by groups of closely interrelated aristocratic clans, to whom the governance of the royal territories was entrusted in a way that bears some resemblance to the feudal system as pictured by historians of medieval Europe. These were the clans that, after the fall of Western Zhou power, set themselves up as the de facto rulers of the competing states of the Spring and Autumn and Warring States periods. In many cases these rulers eventually abandoned their Zhou feudal rank titles such as gong 公 ‘duke’ or bo 伯 ‘count’ in favour of the title wang 王 ‘king’, which was by strict propriety reserved for the king of Zhou himself, their theoretical sovereign. It was the king of Qin who eventually managed to overthrow his rivals in other states and establish imperial rule over the whole of what was often called Tian xia 天下 ‘[All that is] under Heaven’. To symbolise the radical political change brought about by his victory, he adopted the ancient title di 帝, commonly translated as ‘emperor’ when applied to human rulers, but which also carries strong suggestions of divine status. As we shall see, the rulers of Han continued this practice.

The keeping of detailed and carefully dated records of important activities has been an essential part of the work of officials in many cultures. In the huge East Asian empires that concern us, this record-keeping took on a correspondingly large importance. The creation and preservation of official records relates to the material translated in this book in two separate ways. In the first place, no such records could be produced without a universally accepted system of calendrical dating, centrally promulgated and used throughout the empire, and without such a system no coordinated advance pla...

Table of contents

• Cover
• Title
• Copyright
• Contents
• List of figures
• List of tables
• 1 General introduction
• 2 The Triple Concordance system
• 3 The Han Quarter Remainder system
• 4 The Uranic Manifestation system
• 5 Han discussions of astronomical systems and their development: Two texts
• Bibliography
• Index