Astronomy and Calendars — The Other Chinese Mathematics

As an author myself, the first thing that I look at in a book is its Preface. At my age of 75+, I do not want to waste my precious time randomly on a book — whether for reviewing or reading it. This book has no Preface! Out of a total of very tightly bound 472 pages in hardcover, 134 pages include seven appendices, tables of Chinese calendars, a list of primary and secondary sources, a glossary, and an index. For researchers in Chinese Calendrical studies and astronomy, this book is likely to be useful. But, I am not aware of a US college course, where this can be used as a textbook. Sure, it is an author’s labor of love.

This book was first published in French in 2009, and this English version came out in 2016. Strangely, it is not clear whether the translation was done by the author himself. It is said that an author’s clarity of ideas is rarely lost in the translation of a mathematical work. But in this book, I wrestled with the meanings in several passages. The translated English reads Frenglish, analogous to popular Hinglish, a hybrid of Hindi and English languages. Hopefully, in a revised English edition, the translation may be improved.

In the Acknowledgements, supposedly, the author (no name, no date or no place at the end) states that the writing of this book was undertaken because, there was no one-stop book on the Chinese calendars and their role in the history of mathematics in China. It reminded me of how in the European-colonized world, all the books in sciences, mathematics, history, psychology, sociology etc. were written up by their colonizers, or by native scholars who were their sycophants. This continues even after de-colonization. However, the Chinese government has been taking drastic measures to increase Chinese nationalism. At the same time, high quality intellectual works are like a good wine: the time to produce a mature product cannot be cut short. Being a native of India, I must add that Indians are far behind the Chinese in raising their respective national resurgence.

The book has 12 chapters, which are distributed, over three sections: Chinese Astronomical Canons and Calendars, Calculations, and Examples of Calculations. Wading through the first chapter transported me back in time to a year or two before my joining MA (Mathematics) in 1959 at Panjab University (PU), Chandigarh, where Astronomy, as a course of study, was replaced with Modern Algebra in MA Part II. It is worth noting that in the PU syllabus, there was a provision for the study of several subjects including Theory of Relativity, but there were not enough faculty to teach them. Curriculum diversity boils down to the economic health of a nation. In contrast, the US colleges offer buffets of courses and seminars sometimes even with 2 or 3 students.

Mathematics trains the mind in a binary mode — either go for a full grasp of the material at hand, or just bypass it. That is how I felt about the material of the first two Chapters of Section I. Apart from too many texts and terminology in the Chinese language, it took me a while to understand why the time period from 104 BC to 1644 AD was selected.

The reference to Islamic astronomy in Chapter 2 comes before the Hindu astronomy, which of course predates anything Islamic. This practice is very common in western academe — exaggerating Islamic scholarship and underemphasizing the Hindu achievements. The book notes the influence of European astronomers with the arrival of Jesuit missionaries in China in the 16th century. Buddhism, a reformist movement of Hinduism, was introduced into China before the 3rd century BC and the Chinese had widely accepted Buddhism in the next two hundred years. Both China and India are known to have used astronomical and astrological predictions in military expeditions and religious events.

Chapter 3 references the popular Hindu navagraha — nine planets (Page 109). An interesting scenario describes how the astronomical tables were revised with the change of the national capital from Nanjing to Beijing in the 15th century. Chapter 3 has a narrative on ‘various zeros’ both symbolically and conceptually. Kong in Chinese describes Zero and is denoted by a circle, O — a variant of the Indian dot for zero. This chapter also has a bunch of definitions and clarifications of calendrical terms explained in the context of modern times.

Chapter 4, one of two small chapters having just 11 pages, is on the mean solar and lunar elements of all Chinese astronomical canons issued between 104 BC and 1644 AD. Chapter 5 deals with the calculations of moon phases with True Elements — concerning astronomical canons adopted between 619 and 1280. Chapter 6 deals with canons 1281–1364 and 1385–1644. Mathematics involved in these two chapters suggest that the Chinese were quite sophisticated in the broad area of number theory that eventually influenced astronomy in Korea and Japan. In 1732, the Chinese astronomical work was translated into French for the first time. Chapter 7 is devoted to fundamental days of Mo and Mie in Chinese astronomy. At the end, it is shown how these concepts were mentioned in a classic Indian treatise, Arthashastra, written in 300 BC!

The five chapters (8–12) of Section III dealing with specific examples of calculations suggest a lack of the kind of mathematical theory behind them that a typical mathematician looks for. This, perhaps, may stem from the fact that proofs had not captured the minds in China and India. Nevertheless, it should be understood that these examples are landmark astronomical problems and their results are interpreted and compared in Gregorian and Julian calendars, and other predictions like that of eclipses. These chapters are packed with several tables and long calculations on specific years, namely, 450, 451, 877, and 1417.

Finally, there is very little that I could distillate from the book, as far as hard-core modern mathematics was concerned. Congruences are all over, however, culminating in the famous Chinese Remainder Theorem in 1247, when Europe was still living in the “dark ages.” Also, there is not much that I could see sequentially in the name of history of mathematics with Chinese emphasis. The entire material is heavily calculation-based rather than being narratives on specific topics and themes.

Satish C. Bhatnagar is Professor of Mathematics at the University of Nevada, Las Vegas.