China was a distinctively astronomical empire. From the time when the Qin 秦 (221–206 bce) empire first united ‘all under the heaven’ tian xia 天下, astronomy and astronomers were recognised as indispensable to the work of the imperial government and played an important role in state political life. These circumstances endured until the end of the last imperial dynasty, the Qing 清 (1644–1911 ce). During the Qin and Han 汉 dynasty (206 bce-220 ce), the basic content, thought and method of Chinese mathematical astronomy was shaped in the context of intense rivalry, discussions and conflicts between experts. In his new book Heavenly Numbers: Astronomy and Authority in Early Imperial China, which was published in November of 2017, Christopher Cullen tells the stories of Han specialists who studied astronomy, and describes what they thought about astronomy and how they did their work. These stories clearly show how the astronomical expertise that served the empire—what has been called the ‘Han paradigm’—was created.

The book consists of nine chapters. In Chapter 1, the author explains the importance of the calendar in the historical self-image of the Chinese imperial state, and outlines the basic structures of calculation that underpinned it. Chapter 2 looks at the ancient Chinese documents that we today call “calendars”, outlines their structure and content and explains the ways that officials and the population as a whole related to them in their daily lives. In Chapter 3, the author tells the story of the first great reform of the astronomical system, i.e. the Grand Inception Reform that took place in 104 bce. Chapter 4 contains full details of the structure and theoretical underpinning of China's first complete extant system of astronomical calculation, i.e. the Triple Concordance system(San tong li 三統曆), as well as discussing the ways in which this system played its part in supporting Wang Mang's 王莽 new dynasty when it seized power. Chapter 5 discusses Huan Tan's 桓譚 personal concerns and views of astronomy, especially on measures and forms of the heaven, and his arguments about astronomy with his friend and colleague Yang Xiong 揚雄 who thought differently. In Chapters 6 and 7, the author moves from the private to the official: a long series of archived documents enables us to see how experts argued for their point of view, often through the preparation of written documents or public confrontations in the presence of large numbers of colleagues and peers. The list of experts that the author discussed includes Bian Xin 編䜣, Li Fan 李梵, Jia Kui 賈逵, Huo Rong 霍融, Zhang Heng 張衡, Lang Yi 朗顗, Xiang Kai 襄楷, Cai Yong 蔡邕, and so on. In Chapter 8, the author recounts the work of Liu Hong 劉洪 who created the Uranic Manifestation system (Qian xiang li 乾象曆) which was the first system to give a complete account of the main irregularities of lunar motion. This book ends with a brief epilogue in Chapter 9, which surveys the following centuries to detecting persistent remnants of the ancient Chinese astronomical tradition up to the present day.

This is a history of astronomy in a single volume, however, it is different from general chronological works on this subject. It provides clear clues to the development of mathematical astronomy during the Qin and Han dynasties by focusing on the activity of the individual human beings who observed the heavens, recorded what they saw and made calculations to analyze and eventually make predictions about the motions of the celestial bodies. These individual human beings included the emperors, professional astronomers, officials in the government and those who held no official rank but showed themselves capable of expounding about the heavens at an expert level. It is these individuals, their observations, their calculations and their words which provide the narrative thread that runs through this work. By telling the stories of these individual human beings, this book gives clear explanations of the development of technical practice in observation, instrumentation and calculation, and the steady accumulation of data over many years.

This book gives us access to an ancient tradition that appears to be effectively independent of those more familiar to historians writing in western languages. It is a tradition that has commonly been given little attention in the history of astronomy as recounted by such historians. I believe that this book is useful and interesting to historians of science worldwide, and to general historians of China, as well as to those with more specialist interests in the history of astronomy, or the history of science in China. In fact, the author has indeed written as far as possible with the needs of a broad and disparate readership in mind. In order to meet the needs of different readers, he has frequently given the main points of a technical discussion in the main text, while putting the detailed calculations in a box that can be ignored by those not interested in it. This formatting is consistent throughout the book.