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In his last essay just weeks before his death at the age of 91, David S. Nivison says, "Breaking into a formal system - such as a chronology - must be like breaking into a code. If you are successful, success will show right off." Since the late 1970's Nivison has focused his scholarship on breaking the code of Three Dynasties (Xia, Shang, Zhou) chronology by establishing an innovative methodology based on mourning periods, astronomical phenomenon, and numerical manipulations derived from them. Nivison is most readily known in the field for revising (and then revising again) the date of the Zhou conquest of Shang, and for his theory that Western Zhou kings employed two calendars (His so-called "Two yuan" theory), the second being set in effect upon the death of the new king's predecessor and counted from the completion of post-mourning rites for him (i.e., a "second 'first' year"). Nivison's enabling discovery that the Bamboo Annals (BA) had a historical basis was initially designed to make Wang Guowei's analysis of lunar phase terms (the so-called "Four quarter" theory that separated each month into four quarters) work for Western Zhou bronze inscriptions. In order to do so he had to assume that some inscriptions used a second yuan counted from completion of mourning. The king's death was the most important event late in a reign, so this implied that a king's reign-of-record was normally counted from the second yuan, omitting initial mourning years. It follows that when the unexpressed mourning years are forgotten (or edited out) but the dates of the beginning and end of the dynasty are still known, the remaining reigns-of-record cluster toward the beginning and end, and a reign in the middle is enlarged. Problems, ideas, and solutions like the one described above are found throughout this new collection of important works on chronology, astronomy, and historiography.

Regional studies --- History --- Australasian & Pacific history --- Astronomy, Chinese. --- China --- Chinese astronomy --- Chinese History, Early Chronology, Excavated Texts, Astronomy.

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Presented from the viewpoint of the history of mathematics, this book explores both epistemological aspects of Chinese traditional mathematical astronomy and lunisolar calendrical calculations. The following issues are addressed: (1) connections with non-Chinese cultural areas; (2) the possibility or impossibility of using mathematics to predict astronomical phenomena, a question that was constantly raised by the Chinese from antiquity through medieval times; (3) the modes of representation of numbers, and in particular the zero, found in the context of Chinese calendrical calculations; and (4) a detailed analysis of lunisolar calendrical calculations. Fully worked-out examples and comparisons between the results of calculations and the content of Chinese historical calendars from various periods are provided. Traditional Chinese calendrical and mathematical astronomy consists of permanently reformed mathematical procedures designed to predict, but not explain, phenomena pertaining to astronomy and related areas. Yet, despite appearances, models of the mathematical techniques hidden behind this voluminous corpus reveal that they depend on a limited number of clear-cut mathematical structures. Although only a small fraction of these techniques have been fully studied, what is known surprisingly broadens our knowledge of the history of Chinese mathematics. Sinologists interested in the history of Chinese science, and anyone interested in the history of Chinese mathematics, the Chinese calendar, and the history of Chinese mathematical astronomy from its origin (104 BC) to its European reform (AD 1644) will find this book very useful. The present English language edition is a fully revised and updated version of the French original. Even though this is a research monograph in sinology, no particular sinological background is required, although a basic understanding of ‘concrete mathematics’ is needed. From the reviews of the French edition: This is a demanding, rigorous book to read … worth the concentrated study it requires. The rewards are not only in the details but in the general overview that …[it] provides. Joseph Dauben, EASTM, 2011 ...first Work in a Western language to turn to for anyone interested in the details of Chinese calendrical computations. Benno Van Dalen, ISIS, 2011 Martzloff’s careful scholarship and his overall look at the calendar beyond astronomical calculations, …, make this book a most valuable contributions to a field of increasing interest. U. D’Ambrosio, Mathematical Reviews, 2013.

Mathematics. --- Astronomy, Chinese. --- Calendar, Chinese. --- Mathematics --- Math --- Chinese calendar --- Chinese astronomy --- Science --- History of Mathematical Sciences. --- Mathematical Physics. --- History. --- Mathematical physics. --- Annals --- Auxiliary sciences of history --- Physical mathematics --- Physics