Kālacakra and the Tibetan Calendar 9780975373491

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I(alacakra and the Tibetan Calendar Kalacakra and the Tibetan Calendar describes the contents of current Tibetan almanacs, from the most basic mathematics to the symbolic and historical information they contain. Essential for understanding the Kalacakra Tantra's first chapter, it traces and describes the origin of the calendrical systems in the Kalacakra Tantra, and it translates and elucidates the key relevant sections from the famous commentary to this Tantra, the Vimalaprabha. The main calendars in use in Tibet today have remained unchanged since the 15th century, when lamas in several different traditions tried to make sense of the calculation systems they had inherited from India, and to adjust them to remove increasingly obvious errors in their results. This book analyzes the main systems that survive today, assessing their accuracy and comparing them with the methods described in the original Tantra.

EDWARD HENNING is a mathematician with

a long career in computer journalism and programming. An experienced translator, he has specialized in Kalacakra literature for over three decades.

Kalacakra and the Tibetan Calendar

TREASURY OF THE BUDDHIST SCIENCES series Editor-in-Chief: Robert A.F. Thurman Jey Tsong Khapa Professor of Indo-Tibetan Buddhist Studies, Columbia University President, American Institute of Buddhist Studies Executive Editor: Thomas F. Yarnall Department of Religion Columbia University

Editorial Board: Ryuichi Abe, Jay Garfield, David Gray, Laura Harrington, Thubten Jinpa, Joseph Loizzo, Gary Tubb, Christian Wedemeyer, Chun-fang Yu The American Institute of Buddhist Studies (AIBS), in affiliation with the Columbia University Center for Buddhist Studies (CBS) and Tibet House US (THUS), has established the Treasury of the Buddhist Sciences series to provide authoritative English translations, studies, and editions of the texts of the Tibetan Tengyur (bstan 'gyur) and its associated literature. The Tibetan Tengyur is a vast collection of over 3,600 classical Indian Buddhist scientific treatises (sastra) written in Sanskrit by over 700 authors from the first millennium CE, now preserved mainly in systematic 7th-12th century Tibetan translation. Its topics span all of India's "outer" arts and sciences, including linguistics, medicine, astronomy, sociopolitical theory, ethics, art, and so on, as well as all of her "inner" arts and sciences such as philosophy, psychology ("mind science"), meditation, and yoga.

Kalacakra and the Tibetan Calendar by

Edward Henning

Treasury of the Buddhist Sciences series Published by The American Institute of Buddhist Studies at Columbia University in New York Co-published with Columbia University's Center for Buddhist Studies and Tibet House US

New York 2007

Treasury of the Buddhist Sciences series A refereed series published by: American Institute of Buddhist Studies Columbia University 80 Claremont Avenue, room 303 New York, NY 10027 http://www.aibs.columbia.edu Co-published with Columbia University's Center for Buddhist Studies and Tibet House US. Distributed by Columbia University Press. Copyright © 2007 by Edward Henning All rights reserved. No portion of this work may be reproduced in any form or by any means, electronic or mechanical, including photography, recording, or by any information storage and retrieval system or technologies now known or later developed, without written permission from the publisher.

Printed in Canada on acid-free paper. ISBN

978-0-9753734-9-l (cloth) Library of Congress Cataloging-in-Publication Data

Henning, Edward, 1949Kalacakra and the Tibetan calendar I by Edward Henning. p. cm. - (Treasury of the Buddhist sciences series) "Co-published with Columbia University's Center for Buddhist Studies and Tibet House US." Includes bibliographical references and index. ISBN 978-0-9753734-9-1 (alk. paper) 1. Calendar, Tibetan. I. Title. CE38.5.H46 2007 529'.309515--dc22 2007060675

Dedicated to the memory of Khenpo Tseundru

Contents ix

Series Editor's Preface Author's Preface and Acknowledgements

xiii

Introduction

1

Chapter I: Five Components of the Calendar

7

Chapter II: The Five Planets

55

Chapter III: Rahu and Eclipses

95

Chapter IV: The Tibetan Almanac

141

Chapter V: The Kalacakra Tantra and Vimalaprabha

211

Chapter VI: Different Calculation Systems

295

Appendix I: The Sixty- Year Cycles

351

Appendix II: Chronology of the Sambhala Kings

365

Glossary

375

Bibliography

381

Index

387

..

Vll

Series Editor's Preface We are extremely pleased to present this fascinating book by Edward Henning, our first monograph associated with the Tibetan Tengyur Translation Initiative underlying this Treasury of the Buddhist Sciences series. It is a labor of love and deep erudition on the part of an exceptional independent Buddhist scholar, physicist, mathematician, and linguist. Herein, with the help of the most insightful Tibetan teachers and a wide range of the central texts of the tradition, he elucidates the principles of Tibetan astronomy. He shows how a Tibetan scientist calculates the yearly calendar, the times of eclipses of sun and moon (extremely precise although calculated within a cosmological model quite different from the modern one), and the positions of the planets. Based on that thorough and clear elucidation, he translates the textual locus classicus of the Tibetan Buddhist method, verses 13 to 52 of the First Chapter of the Kalacakra Tantra, and its commentary the Stainless Light ( Vimalaprabha), showing how the instructions therein function as the foundation of the later works. The Kalacakra Tantra, or "Wheel of Time Technology," as it can be impressionistically translated, is a scientific way of understanding and engaging the universe-including the inner realm of the mind as well as the outer realm of the environment-that enables the scientific explorer to consciously maximize her or his evolutionary progress toward happiness and fulfillment through also assisting others. One of its central insights is that we are completely interwoven with our environment in time and space, and that therefore the more we know about the events around us, the better we are positioned to help ourselves and others avoid suffering and achieve happiness. We need to know what we are as evolutionary beings, where we are in the cosmos, and what time it is in regard to the dangers and opportunities we face. Therefore, the understanding of astronomical events is foundationally important to the quality of our lX

x · Series Editor's Preface lives, and an accurate and thorough calendar is something like a weather report, necessary for us to be prepared for the realities ahead of us. I personally do not pretend to understand the details of this subject well, though in my youth I learned the rudimentary principles of one Tibetan system as I worked with fellow students on the Tibetan calendar for the year 1964 under Tsipay Gen Amdo Lotreu, the State Astronomer of the Tibetan Government in Exile in Dharamsala, India. From whatever of that remains dimly in memory, I know just enough to be able to recognize and admire the excellence of Henning's accomplishment. Not only has he mastered the intricacies of the system and the ability to use it in practice, while understanding in detail the differences between the different systems, but also he has found a key problem with the current practice, based on a modern critical understanding as well as on his teacher's and his own rediscovery in the root sources of the principle needed to resolve this problem-a principle totally in consonance with modern science. Indeed, it is absolutely marvelous that the Kalacakra system, after giving detailed instructions on the calculation of the calendar, recommends one indispensable practice to keep its practice effective-the actual observation of nature. Such attention to precise and careful examination befits the Buddhist scientific emphasis on the importance of experience, and its critical observation. That is, in the present context, no matter how sophisticated any mathematical system may be, based on no matter what theory or worldview, you have to get out at the winter and summer solstices, at least one of them, and observe the exact moment when the sun's shadow at noon changes its motion relative to previous days, signaling the yearly shift from the southern to the northern passage of the sun, or vice versa. Only by fixing this time and adjusting calculations to fit it can subtle corrections be made to the yearly calculations, avoiding the gradual compounding of error over decades and centuries that would otherwise ruin the accuracy of the calendar. One of the first books in our Tengyur series was the English translation of the Second Chapter of the Kalacakra Tantra together with its Stainless Light commentary, beautifully accomplished by Dr. Vesna Wallace. We have the three other later chapters in the pipeline in various stages of completion, and we hope to publish eventually the First Chapter in its entirety. The present book by Edward Henning will serve as a precious key to unlock the all-important astronomical perspective of this

Series Editor's Preface· xi the First Chapter, leading the way and continuing to provide the great benefit of showing the actual use of this remarkable system. My congratulations go to Edward Henning for his careful perseverance and outstanding accomplishment. It is our honor to publish his work. Robert A. F. Thurman American Institute for Buddhist Studies Columbia University Center for Buddhist Studies Tibet House US February 18, 2007 New Year's Day, Fire Pig Year

Author's Preface and Acknowledgements The catalyst that started me on the task of learning Tibetan was an artefact closely related to the Tibetan calendar; this was also an important factor that eventually led to the writing of this book. My background had been in mathematics and physics, with a strong interest in astronomy-all good grounding for working on any calendar, but an oriental language was a major departure. I was given a fascinating present in 1973, that turned out to be a Tibetan srid pa ho-a copper plaque depicting the great golden turtle of Chinese mythology, together with various other astrological signs. These are intended to ward off negative influences of the planets, lunar mansions, and so forth. Around this time I had developed an interest in northern, particularly Tibetan, Buddhism and was somewhat frustrated by having read everything I could find in the English language on the subject. The thought had crossed my mind that if I wanted to study and practise it properly, I would have to turn to original sources-which would not be in English. My curiosity regarding this plaque quickly had me learning Tibetan. Over the next few months I started collecting from various sources Tibetan texts and photocopies of others. I was lucky to have the collection in the British Library close at hand, and soon came across some important astrological and astronomical material, but found it mostly indecipherable. Two years later, whilst on a long visit to India, I spent a very brief amount of time with a Tibetan teacher, the late Khenpo Tseundru. He was renowned as one of the greatest experts in Tibetan astrology, and very easily pointed me in the right direction with my studies, particularly with regard to the accuracy of the calendar. On my return to England, partly thanks to his guidance, I found I was increasingly able to make sense of the basic texts I had acquired, but still I did nothing about writing any of this up. I knew that microcomputers were about to become available and I waited impatiently for this to become a reality. As soon as I was able to buy a PC (in 1984), I set about computerizing a version of the Tibetan lunar calendar. Very often I translated Xlll

xiv· Author's Preface

directly from Tibetan into the C programming language, and then, once I had ascertained that a certain algorithm worked correctly, translated into English. I completed this program and first printed out my computerized version of the lunar calendar during the afternoon of what I discovered later that evening to be the day of the centenary of the adoption of the Greenwich meridian. A good omen indeed for an Englishman, but I still made no plans to write about the calendar. Eventually I realized that in order to examine the calendar properly, it would not be enough simply to look at the calendar as used by Tibetans today, but it would be necessary to go back to the original sources and create a translation and analysis of the basic calculations in the original Indian Kalacakra system, the source of the calculations used by the Tibetans. As time has passed I have come to consider the translation and analysis of the original Indian material the most important and interesting aspect of this project. One could also make a fascinating study of the early Tibetan origins of some aspects of the calendar as well as its Chinese and Mongolian background, but the Kalacakra influence is certainly the most important, and has been my main focus. As will be clear by the end of this work, the Tibetans in part either did not understand or did not accept the intentions of the Kalacakra system for the calendar. This is a great pity, as the Kalacakra system itself seems to me to have a positive reforming spirit to it. The Tibetan calendar, particular in its most common form, from the Phugpa tradition, is now in a sorry state, itself very much in need of just the kind of reform encouraged in the Kalacakra literature. I know that most Tibetans do not accept this point of view, but I also know that some do, and it was, after all, a most distinguished Tibetan Kalacakra expert, Khenpo Tseundru, who directed my studies in such a way that led to this conclusion. As he passed on just a couple of years after our meeting, I have no way of thanking him for his help or of checking if this present work satisfies his intentions, but I am reasonably confident that it does. He confirmed what I had been told about him, that he held a secret key (presumably a method of some kind) that enabled proper accuracy of the calendar, and told me that if I applied a western (scientific) analysis in the

Author's Preface· xv

particular areas that he suggested, I would not need this key. In this he has certainly been proved correct. Apart from Khenpo Tseundru, I would like to single out a couple of other individuals for particular thanks, the first of whom I happened to meet in the same year as the Khenpo, 1976. At that time Gene Smith was running the U.S. Library of Congress' Tibetan Text Publication Project (PIA80) out of New Delhi. During this work he accumulated a most impressive personal library of Tibetan materials, now housed in a continuous state of chaotic expansion in the Tibetan Buddhist Resource Center, New York. Some of the Tibetan texts mentioned in the bibliography at the back of this book were made available to me by Gene, and the present work would be much poorer were it not for his help and support. The other is Gunther Gronbold, of the Bayerische Staatbibliothek, Munich. Gunther was a student of the famous Kalacakra scholar Helmut Hoffmann, and shares my interest in Kalacakra. This interest usefully influenced acquisitions at the library, and on the many occasions that I visited during the last 20 years, there was nearly always a pile of recommended reading awaiting me, as well as the materials I had requested before travelling. My hope is that this book will help in some small way towards a better understanding of both the Tibetan calendar and the Kalacakra system. To that end I am also particularly grateful to Dr. Robert Thurman, Dr. Thomas Yarnall, and the AIBS for accepting this book into their series. I could not ask for a more suitable home for this work, and they have even been willing to accommodate my request to preserve native British spellings throughout the book! In particular, Dr. Yarnall has paid meticulous attention to the editing, design, and layout of this book, which is somewhat complex due to the number of calculations, tables, and graphics that it contains. Any errors that may remain are of course entirely my own. Edward Henning February 2007

Introduction In the west, we take the existence of an almanac, or ephemeris, with its precise planetary positions, as a given. For the Tibetans, and their predecessors in India, the situation was very different. The calendar itself had to be calculated by hand from fundamental formulae, and I have been told that it could take an individual seven months to perform the calculations for a calendar for one year. Tibetan astronomy and astrology·have three main sources: Indian Buddhist and Hindu systems, and Chinese. The Indian systems include what we could call 'positional' astrology. Much of this is familiar to westerners, and includes such concepts as the 12 signs of the zodiac, the 12 houses, and takes into consideration the positions of the planets within these. One interesting addition is the use of the 27 lunar mansions as an additional division of the ecliptic. These are known in the west, but are used very infrequently. The Indian and Chinese systems both use a method that I term 'cyclic' astrology. Here, most of the cycles depend upon the actual positions of the Sun and Moon. The cycles are the years, lunar months, lunar days, and so forth. The definition of these, particularly of the months, is different in Chinese and Indian systems, but sufficiently compatible that the Tibetans have been able to combine them. The work of calculating the Tibetan lunar calendar consists in determining these basic cycles, and onto this structure then dropping the symbolic elements from the Indian and Chinese traditions. The calculations derive the position of the Sun and Moon, and then go on to determine the positions of Rahu (the ascending node of the Moon's orbit) and the five visible planets. No aspect of the calculations has been derived from Chinese sources (although there is certainly some Chinese influence in later almanacs), and the single source for the calculations is the Kalacakra Buddhist system. The main source text for this tradition is the Kalacakra Tantra, which, together with its main commentary, has been one of the main sources for this current work. The commentary is called the Vimalaprabha, and this appears to have been written around the beginning of the 11th century. The text describes two epochs for calculation. The basic one for which planetary 1

2 · Introduction

positions are given is 806 CE, and the one that calculations are described as starting from is 1027. Fortunately, both the Kalacakra Tantra itself and the Vimalaprabha are available in both Sanskrit and Tibetan, and this enables the comparison of technical terms in both languages. This is useful, as much has been written in English about Indian systems of astronomy and astrology, based on Sanskrit sources. The other main commentary that I have used on the Kalacakra Tantra itself has been the "Illumination of the Vajra Sun" (MiKal), an excellent work by Mipham (mi pham rgya mtsho). He died early last century (1912), and is one of the most recent authoritative writers on the Kalacakra. His style is clear and lucid, and is particularly suitable in my opinion for translation into western languages. Also useful in helping understand parts of the original Tantra and the Vimalaprabha has been a work by Pawo Tsuklag (dpa' ho gtsug lag) called the "Treasury of Jewels" (Tlkuntu). This is a commentary to an earlier work by the third Karmapa, Rangjung Dorje (rang byung rdo rje), called the "Compendium of Astronomy" (rtsis kun btus pa), which was the first native Tibetan text on the subject. The date for the epoch given in Pawo Tsuklag's text is 1536, and that in Rangjung Dorje's text, unfortunately not now available, 1326. The other main texts that I have used have been specific works on astronomy and astrology rather than commentaries on the original Kalacakra system. There are now two main calendrical traditions in Tibet, the Phugpa (or Phugluk) and Tsurphu (or Tsurluk), and most of these texts come from one of these traditions. There were others, and perhaps pockets of their practice survive still in Tibet, but these two seem to be the only ones that remain in extensive use. The most important of these that I have used has been one written less than a hundred years ago in the Phugpa tradition. This is the "Essence of the KalkI" (Rigthig, 1927) by Chenrab Norbu (mkhyen rah nor bu). For many Tibetans creating calendars today, this will be the definitive source book. It is this text that I have mainly used as the basis for my discussion of the main calculations in the calendar. Older texts tend to give shorter versions of the calculations, sometimes missing details that were either preserved in an oral tradition, or perhaps devised later. Chenrab Norbu's work is itself based on another text from the Phugpa tradition, written over 200 years earlier, and arguably the most

Introduction · 3

famous Tibetan book on the subject: the "White Beryl" (Baidkar, 1687), attributed to Desi Sangje Gyatso (sde srid sang rgyas rgya mtsho). Regarding this particularly important work, Gene Smith (Smith, p. 243) points out that the actual author was almost certainly Dumbu Dondrup Wangyal (ldum bu don grub dbang rgyal). Another text from the same tradition of which I have made extensive use is the "Illumination of the Day-maker" (Nangrtsa, 1681) and its commentary, the "Golden Chariot" (Nangser), by Minling Lochen DharmasrI (smin glin lo chen dharma_ .frl'). This is a particularly lucid work, and I have used it mainly for the calculation of eclipse predictions. I have also made use of the original work in the Phugpa tradition, the "The Oral Instructions of PuI) 22;45,37,1,192,66869 (229,149209) The next step is an operation that should by now be familiar. After a first calculation, an index and a fractional part are used to calculate a correction, and this will then be applied to the heliocentric longitude of the planet to give the true longitude from the Earth. The first step is to subtract the longitude of the planet from that of the Sun: 22;45,37,1,192,66869 - 9;9,23,5,93,0 = 13;36,13,2,99,66869 Mars Index Total 1 24 2 47 3 70 4 93 5 114 135 6 7 153 8 168 179 9 10 182 171 11 133 12 13 53 0 0

Coefficient 24 23 23 23 21 21 18 15 11 3 11 38 80 53 Table 2-2

Total 0 24 47 70 93 114

135 153 168 179 182 171 133 53

Index 0 13 12 11 10 9 8 7 6 5 4 3 2 1

66 · Chapter II As in similar calculations, if this result is greater than a half-circle (13;30) then a half-circle is subtracted from it, making a note of whether this was done. In this example it is necessary, and gives a result of: 13;36,13,2,99,66869 - 13;30 = 0;6,13,2,99,66869 In this case the mansion and na