CHINESE MATHEMATICAL ASTROLOGY The ability to predict has always been, and remains, an important aim of science. In traditional China, astronomers devised methods of divination that were not only applied to natural events such as weather forecasting, but also to mundane human affairs. The three most sophisticated devices were shrouded in clouds of secrecy. During the eleventh century and for hundreds of years thereafter, candidates were examined on their knowledge of these devices behind the closed doors of the Chinese Astronomical Bureau. Known by little other than their names, this is the first book in any language that attempts to make an academic study of the three methods, known as the sanshi (three cosmic boards), which turned out to have a profound influence on Chinese society. Ho Peng Yoke has published widely on Chinese alchemy, astronomy, divination and mathematics. He occupied senior academic positions in Singapore, Kuala Lumpur, Australia and Hong Kong before becoming the Director of the Needham Research Institute in 1990. He is an academician of the Australian Academy of Humanities, Academia Sinica and the Inter- national Euro-Asia Academy of Science. NEEDHAM RESEARCH INSTITUTE SERIES Series Editor: Christopher Cullen Joseph Needham’s ‘Science and Civilisation’ series began publication in the 1950s. At first, it was seen as a piece of brilliant but isolated pioneering. However, at the beginning of the twenty-first century, it is clear that Needham’s work has succeeded in creating a vibrant new intellectual field in the West. The books in this series cover topics relating broadly to the practice of science, technology and medicine in East Asia, including China, Japan, Korea and Vietnam. The emphasis is on traditional forms of know- ledge and practice, but without excluding modern studies which connect the topics with their historical and cultural context. CELESTIAL LANCETS A history and rationale of acupuncture and moxa Lu Gwei-Djen and Joseph Needham With a new introduction by Vivienne Lo A CHINESE PHYSICIAN Wang Ji and the Stone Mountain medical case histories Joanna Grant CHINESE MATHEMATICAL ASTROLOGY Reaching out to the stars Ho Peng Yoke CHINESE MATHEMATICAL ASTROLOGY Reaching out to the stars Ho Peng Yoke First published 2003 by RoutledgeCurzon 11 New Fetter Lane, London EC4P 4EE Simultaneously published in the USA and Canada by RoutledgeCurzon 29 West 35th Street, New York, NY 10001 This edition published in the Taylor & Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” RoutledgeCurzon is an imprint of the Taylor & Francis Group © 2003 Ho Peng Yoke All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Every effort has been made to contact copyright holders for their permission to reprint material in this book. The publishers would be grateful to hear from any copyright holder who is not here acknowledged and will undertake to rectify any errors or omissions in future editions of this book. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data A catalog record for this book has been requested ISBN 0-203-63363-6 Master e-book ISBN ISBN 0-203-63734-8 (Adobe eReader Format) ISBN 0–415–29759–1 (Print Edition) This book is dedicated to the memory of Dr Wu Lien-teh, renowned Plague Fighter and Founder of Modern Hospitals in China, Healer and Philanthropist in Southeast Asia and Dato Dr Lee Kong Chian, celebrated Industrialist and Banker in Southeast Asia, Philanthropist and Patron of Learning and Education and their two families in friendship vi CONTENTS List of figures viii Preface xi References to historical Chinese geographical names xvi A brief note on Chinese romanization xxii 1 Introduction 1 2 Fundamental principles 12 3 The Taiyi system in the three cosmic boards: method of the Taiyi deity 36 4 Qimen Dunjia: Strange Gates Escaping Techniques 83 5 Liuren: the art of the six Yang Waters 113 Appendix I: traditional Chinese astrology 139 Appendix II: the Ziping method of fate-calculation 153 Appendix III: table of Chinese dynasties 165 Notes 167 Bibliography 179 Index 193 vii LIST OF FIGURES 2.1 Order of Mutual Production and Conquest of wuxing 15 2.2 The Luoshu Chart 21 2.3 The Hetu Diagram 22 2.4a Yubu steps following the Plough 24 2.4b Yubu steps following the jiugong magic square 25 2.5 Feigong variations in the jiugong magic square 26 2.6 Feigong variations and ‘colour-coded’ (zibai) diagrams 27 2.7 Zibai diagram for 1985 in a Chinese calendar 28 2.8 Zibai diagram for 1976 in a calendar from a Japanese shrine 29 2.9 The yijing Trigrams 34 3.1 Text of the ‘Remarks’ from the Nan Qi shu 37 3.2 Archaeological specimen of Han cosmic board 41 3.3 Basic Taiyi board 45 3.4 The Five yuan Epochs 47 3.5 Taiyi Configuration 276 (= Configuration 60) 50 3.6 Taiyi Configuration 160 (= Configuration 16) 51 3.7 Taiyi Configuration 161 (= Configuration 17) 52 3.8 Taiyi Configuration 181 (= Configuration 37) 53 3.9 Taiyi Configuration 187 (= Configuration 43) 54 3.10 Taiyi Configuration 198 (= Configuration 54) 55 3.11 Taiyi Configuration 222 (= Configuration 6) 56 3.12 Taiyi Configuration 223 (= Configuration 7) 57 3.13 Taiyi Configuration 231 (= Configuration 15) 58 3.14 Taiyi Configuration 234 (= Configuration 18) 59 3.15 Taiyi Configuration 102 (= Configuration 30) 62 3.16 The fangzhen (Square) Battle Formation 66 3.17 Meteorological forecasting with the Taiyi method 72 3.18 Houses in the Qiyao rangzaijue from the Taishd Tripitaka 74 3.19 A fourteenth-century horoscope from the Zhengshi xing’an, an appendix to the Zhang Guo xingzong 75 3.20 A horoscope from Ziwei doushu 76 3.21a Recasting of horoscope in Figure 3.19 by the author using a modern Ziwei doushu method 78 viii LIST OF FIGURES 3.21b Recasting of the same horoscope by a practitioner in Taiwan using another version of the Ziwei doushu method 79 3.22 Transmission of the Ziwei doushu system of astrology 81 4.1 Huangdi yinfujing text from Dunjia yanyi 88 4.2 Initial set-up of the dipan with Trigrams, Luoshu numbers, the Nine Stars and the Eight Gates in fixed positions 97 4.3 Fortnightly periods and Qimen Dunjia Configurations 99 4.4 Dipan with the day-stem added 101 4.5 Qimen Dunjia Configuration complete with earth board and heaven board in place 103 4.6 Modern earth board and heaven board model illustrating Configuration shown in Figure 4.5 104 5.1 Passage on the Liuren from Mengxi bitan 118–119 5.2 Determination of the position for yuesa (from Xieji bianfangshu) 122 5.3 Determination of the position for yuekong (from Xieji bianfangshu) 123 5.4 Determination of the position for Tianyi guiren (from Xieji bianfangshu) 125 5.5 The left palm as earth board in Liuren divination 136 Star Map I.1 Ziweiyuan and the circumpolar constellations 141 Star Map I.2 Taiweiyuan and surrounding constellations 143 Star Map I.3 Tianshiyuan and surrounding constellations 144 Star Map I.4 Region around the Northern Palace 145 Star Map I.5 Region around the Western Palace 146 Star Map I.6 The southern sky in Chinese astronomy 149 II.1 Mutual Production and Conquest of stems and branches 157 II.2 The riyuan and fate-calculation sociogram 158 II.3 Auspicious and ominous combinations of stems with branches 161 II.4 Auspicious and ominous combinations of branches with stems and branches 161 II.5 Auspicious and ominous ‘stars’ from branch combinations 162 ix x PREFACE In the year 1953 I embarked on translating and annotating the astronomical chapters (tianwenzhi ) in the official history of the Jin dynasty (251–420) at the suggestion of Joseph Needham (1900–1995). The aim was twofold. Dr Needham considered that a full translation of the astro- nomical chapters in one of the Chinese official histories was an essential reference for his preparation of the astronomy section in Volume 3 of Science and Civilisation in China and, in exchange, my translation and annotations, having benefited from Needham’s advice, would serve as the first draft of my doctoral dissertation. Our interest then was mainly con- fined to the astronomy content of the text, although by modern standards the predominance of astrological material would suggest a different title more in keeping with modern usage. My research was focused on astro- nomical records in the official dynastic histories as a result of my initial training and employment as a physicist.1 Thus, my interest in the history of science came essentially from the standpoint of science. This was the same standpoint I adopted whenever I collaborated with Needham on three different occasions in his Science and Civilisation in China project.2 In 1964 I accepted an invitation to take up the Chair of Chinese Studies at the University of Malaya. In order to avoid working in splendid isolation away from my own colleagues in the humanities and to show the leadership in research as expected of a departmental head, the main thrust of my research turned towards the relation of Chinese science to literature and poetry, with textual collations and dating of texts, and other areas more remote from those taken up by Needham.