Astronomy and Calendars - The Other Chinese Mathematics  [electronic resource] : 104 BC - AD 1644  /
Martzloff, Jean-Claude.author.
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.
CONTENTS;  List of Illustrations; LIST OF ILLUSTRATIONS; ACKNOWLEDGEMENTS; ABBREVIATIONS AND CONVENTIONS; FOREWORD; INITIAL FOREWORD; Part I Chinese Astronomical Canons and Calendars; 1 PRELIMINARY OBSERVATIONS; The State of the Art; Methodological Orientations; Computistics and Predictive Astronomy; The Paradox of the Chinese Calendar; The Calendar and its Calculations; The Difficulty of Access to Astronomical Knowledge; The Surface and Deep Structures; Two Notions of Time; The Double History of the Calendar; Historical Sources (Surface Structure); Historical sources (Deep Structure)
NumbersThe Key Ideas of Astronomical Canons; Political and Cultural Factors: An Example; The Reforms of Astronomical Canons; The Bureau of Astronomy; The Names of Astronomical Canons; 2 GENERAL DESCRIPTION OF THE CHINESE CALENDAR; Limitation and Scope; Fundamental Components; The Day; The Solar Year; The Twenty-Four Solar Breaths; The Seventy-Two Seasonal Indicators; The Five Phases; The Lunar Year; Lunar Months, Ordinary and Intercalary; The Structure of the Lunar Year; The Percentage of Full and Hollow Months; Local Patterns of Full and Hollow Months
The Astronomical Months and the Lunisolar CouplingThe Beginning of the Lunar Year; Dynastic Eras and Concordance Tables; Cycles and Pseudo-Cycles; Definitions; The Denary Cycle; The Duodecimal Cycle; The Inverted Tree; The Sexagenary Cycle; Various Uses of the Sexagenary Cycle; The Nine Color Palaces; The Planetary Week; The Twenty-Eight Mansions; The Jianchu Pseudo-Cycle with Reduplications; The Nayin Cycle with Reduplications; Other Aspects; Festivals and Annual Observances; Irregular Years; Part II Calculations; 3 NUMBERS AND CALCULATION; Modes of Representation of Numbers; Various Zeroes
The Zero-CircleThe History Zero Revisited; Numerical Constants; The Epoch; The Superior Epoch; The Support Year; The Emerging Year; Numbers of Years from the Epoch; Changes of Origin; Support Days; Binomial Representations; Fractional Representations; Mean and True Elements; Definitions; Historical Aspects; Notation and Terminology; Fundamental Elements; The Last Solar Breath of a Lunar Year; The Numbering of New Moons; The Lunisolar Shift; Introduction; The Epact; The intercalary remainder (Runyu); The Monthly Epact and the Intercalary Month; Consequences; Pathological Calendars
4 MEAN ELEMENTSMean Elements in Practice; Metonic constants; Metonic Calculations; Justifications; Non-Metonic Canons; Calculation Variants; 5 TRUE ELEMENTS (618-1280); Introduction; True Solar Breaths; Some Peculiarities Leading to Simplifications; A Technical Term: The ruqi; A General Mode of Calculation of the ruqi; Another Mode of Calculation; The Calculation of the ruqi from Mean Solar Breaths; Another Technical Term: The ruli; The ruli; Tables and Interpolation Techniques; Solar Tables; Lunar Tables; The Solar Correction; Further Remarks On the Solar Correction; The Lunar Correction
Calculations Without Tables
Includes index.
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.
History.
Mathematical physics.
History of Mathematical Sciences.
Mathematical Physics.