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Modern Star Map. Publisher: Astronomy Charted Worcester (Mass.).
SCIENCE AWAKENING II
SCIENCE AWAKENING
II THE BIRTH OF ASTRONOMY
by
Bartel L. van der Waerden
with contributions by
Peter Huber
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
© 1974 Springer Science+Business Media Dordrecht Origina11y published by Noordhoff International Publishing in 1974
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical,photocopying,
recording or otherwise without the prior permission of the copyright owner.
ISBN 978-90-481-8247-3 ISBN 978-94-017-2952-9 (eBook) DOI 10.1007/978-94-017-2952-9
Library of Congress Catalog Card Number A54-7774
TABLE OF CONTENTS
Preface
lNTRODUCTION.
civilization . . The role of astronomy in the history of
1-7
The purpose of astronomy The divinity of the stars .
ASTRONOMICAL INTRODUCTJON • . .
The stellar sphere, poles and equator The zodiac ........... . The moon ........... . The phases of the fixed stars and planets . The planets. . . . . . . . . . . . . . Historical and astronomical reckoning of years
CHAPTER 1. Astronomy in ancient Egypt
1 2 3 3 4 5 6 6 7
8-45
HISTORICAL PERIODS . . . . . . . . . . . . . 8 THE RISING OF SIRJUS AND THE EGYPTIAN CALENDAR 8
Sirius as berald of the new year . . . . . 8 The Egyptian year. . . . . . . . . . . 9 Was there a scientific astronomy in the Egyptian Old Kingdom? 10 The Sothis period . . . . . . . . . . . . . . . . . . 10 The phases of stars in Hesiodos• poem . . . . . . . . 11 The significance of the phases of the stars for agriculture . 13
THE EGYPTIAN DECANS . . . . . . . . . . . 13 The diagonal calendars . . . . . . 14. The position of the decans in the sky 17 The rising of the decans in the night . 19 The headings of the columns . . . . 26 Later development of the decan theory 26 Historical consequences . . . . . . 28 Other astronomical tomb-inscriptions 28 The decans in astrology 29
THE LATE EGYPTIAN PERIOD 32 Astrology . . . . . . 32
VIII T ABLE OF CONTENTS
Astronomy ..... Calculation of periods . Eudoxos' Egyptian journey . Geometry ....... . The significance of geometry for astronomy. New trends in religion . . . . . . . . . .
CHAPTER 2. Old-Babylonian astronomy ....
HAMMURABI AND HIS DYNASTY . . . . .
The beginning of astrology . . The series 'Enuma Anu Enlil' .
THE VENUS TABLETS OF AMMIZADUGA . .
The phases of Venus. . . . . The 'Year of the golden throne' . The time intervals . . . . . Errors in the text . . . . . . . The chronological problern . . . Schematic calculation of the phases of Venus . The identity of the morning and evening star Astral religion . . . . . . Astral religion and astrology . . . . . . .
CHAPTER 3. The Assyrian period ....... .
TIME TABLE ..... .
General survey THE EARLIER TEXTS . . .
Hilprecht's text HS 229 'The three stars each' . The stars of Elam, Akkad and Amurru The numbers on Pinches' astrolabe Which stars were meant? .
THE SERIES mul APIN . . . . . . .
The star catalogue The three paths in the sky The 36 morning risings . Further sections of the text mu 1APIN Ziqpu stars . . . . . . . . . . . . The constellations in the path of the moon . The four astronomical seasons Gnomon Tables. . . . . . . . . . . . .
37
37 39 41 42 43
46-59
46 48 49 50 51 52 52 52 53 55 56 57 59
60-92
60 61 62 62 64 67 69 69 70 71 74 74 77 77 79 80 84
T ABLE OF CONTENTS
DURATION OF THE NIGHT AND VISIBILITY OF THE MOON .
SUMMARY
The British museum ivory prism . . Popular and astronomical time units The reports of the astrologers
CHAPTER 4. The neo-Babylonian and Persian period .
General review . . . . . . Chronology . . . . . . . Chaldaean kings of Babyion Persian kings . . . . . . . The characteristics of the astronomy of this period
OBSERVATIONAL TEXTS ....... .
Observations and predictions . Astronomical diades The earliest preserved diary. . The 'Lunar six' . . . . . . . The course of the moon in the zodiac Collections of ancient eclipse and planetary observations . The text Strassmaier Kambyses 400 The text CBS 11 901.
CALCULATION OF PERIODS . . .
The 'Saros' . . . . . Intercalation periods. The relation year: month. Planetary periods Goal-year texts . Long periods . . The 'great year' .
PREDICTION OF ECLIPSES
The premature eclipse Thompson 271 Eclipse that failed . . . . . . . . The solareclipsein October, -424 Methods of prediction . The eclipse of Thales . . .
THE ZODIAC ....•......
The boundaries of the signs Mathematical astronomy . .
IX
84 86 88 89
91
93-126
93 94 94 94 95
95 95 96 96 98 98 99
100 101
102 102 103 104 107 108 110 112
115 116 117 117 117 120
122 125 126
X T ABLE OF CONTENTS
CHAPTER 5. Cosmic religion, astrology and astronomy .
SUMMARY OF THIS CHAPTER . . . . . . . . . • . .
Connections between religion and astrology
TRADITION AND NEW RELIGIOUS CURRENTS .
The polytheism of earlier times New religious currents ..
THE RELIGION OF ZARATHUSTRA • •
The Gathas of the Avesta The ethics of Zarathustra The judgement by fire at the end of time .
THE SKY -GOD . • • • . . • • . . . . •
Ahura Mazda as the highest god . Syncretism and monotheism . . . Monotheistic tendencies in Greece The cosmos as living being . . . .
IMMORTALITY AND TRANSMIGRATION OF SOULS
The immortality of the soul in the A vesta Greek ideas about the soul . . . . Heaven as the Horne of Souls. . .
THE CULT OF MITHRAS AND SOLAR THEOLOGY .
Mithras as Sun-god . . . . . The spread of the Mithras cult The three worlds of Julianusr . The sun as highest god.
ZERVANISM AND ASTRAL FATALISM
The time-god Zervan . The myth of the twins . The male-female god . Chronos Apeiros . . . The god with the lion-head . The theogony of ÜRPHEUS .
The dating of Zervanism . .
STAGES IN THE DEVELOPMENT OF COSMIC RELIGION AND ASTROLOGY
The development of cosmic religion Three stages of astrology . . . . . . . . Sirius and the harvest . . . . . . . . . The dating of primitive zodiacal astrology Horoscopy ........... . Horoscopes for conception and birth. . .
127-204
127 128
128 129 129
133 133 134 135
137 138 139 140 141
142 142 144 146 150 150 155 156 160 161 162 163 165 168 168 169 170 172 175 176 178 180 181 182
T ABLE OF CONTENTS
THE DEVELOPMENT OF ASTRONOMY IN THE SIXTH CENTURY
Summary of previous results . . . . . . . Relations between astrology and astronomy . Observational texts from the 6th Century. . . The art of soothsaying at the court of the Chaldaean kings .
DIVINE NAMES OF PLANETS . . . . . . . . .
Greek and Latin names of planets . Babylonian names of planets Persian names of planets . The sun . The moon Mars . Jupiter Venus . Mercury and Sirius Saturn ..... . Two systems of gods
THE INSCRIPTIONS OF THE ACHAEMENIDS
Decrees and inscriptions of Cyrus . Kambyses and Darius . . . Inscriptions of Xerxes . . . Inscriptions of Artaxerxes II Darius and the Magi . . .
CHAPTER 6. Theory of the moon . . . . . . . . .
The systems A and B . . SYSTEM A .•.........
Meaning of the columns . Calculation of Column c[J
Calculation of Column B Calculation of Column C Calculation of Column E Column P: Magnitudes of eclipses Calculation of Column F. Calculation of Column G Calculation of Column J . Table for G ..... . Calculation of Columns K, L and M Column cfJ and the Saros . . . . . The basic assumptions of System A .
XI
183 183 183 184 185 186 186 187 188 189 189 189 191 192 193 194 196 197 197 199 201 201 202
205-249
208 210 210 211 212 214 216 221 221 222 223 224 225 226 229
XII T ABLE OF CONTENTS
An approximation procedure . . . The role of observation . . . . . The latitudinal motion of the moon The scientific character of System A .
SYSTEM B .•....•.•.•..
The 'Crescent Table' ACT 122 . . The meaning of Columns A-D . . Column IJI: Magnitudes of eclipses Column F: Lunar velocity . . . . Column G: Uncorrected duration of the month. Columns H and J: Cmrection to the duration of the month Columns K, L and M . The remaining Columns ..... . Auxiliary tables . . . . . . . . . .
THE DAILY MOTION OF THE SUN AND THE MOON .
The sun's motion . . . . . . . . . The moon's motion . . . . . . . .
THE DATE OF INVENTION OF BABYLONIAN LUNAR THEORIES
The date of System A . Meton and Euktemon . . . . . . . . The date of system B . . . . . . . . A high point of Babylonian astronomy.
CHAPTER 7. Babylonian planetary theory
JUPITER
SATURN
MARS •
General survey
System A .. The sidereal period of Jupiter. The calculation of the time intervals . From cardinal point to cardinal point System A' System B ............ . System B' ........... . An arithmetical series of the third order
System A System B.
Calculation of the Synodic Path Steps ........... .
230 231 233 233 236 236 237 238 239 240 240 241 242 244 244 244 244 245 245 246 247 248
250-283
250 253 253 254 256 257 258 259 260 261 262 262 263 264 264 265
VENUS .
T ABLE OF CONTENTS
The sidereal period . . . The sun-distance principle The elongations . . . . . Summary ...... . Deviations between cardinal tables The retrograde motion . System B.
System A0
Systems A2 and A1
MERCURY .....
System A2 ••
System A 1 •.
Daily motion . THE TIME OF INVENTION OF BABYLONIAN PLANETARY THEORIES
CHAPTER 8. The spread of Babylonian astronomy
EARLY GREEK EVIDENCE ......... .
The eclipse of Thales . . . . . . Gnomon and division of the hours Nurobersand heaven according to the Pythagoreans The zodiac .............. . The names of the signs. . . . . . . . . . Sidereal and tropical divisions of the zodiac Observations and period& . . . . The rising and setting of the moon Rising times of zodiacal signs . . .
THE EVIDENCE FROM GEMINOS . . . . . . .
The calculation of the moon's velocity . THE CHALDAEANS AND THEIR ASTROLOGY ...
Evidence referring to the Chaldaeans. SANSKRIT TEXTS . . . . . . . .
The Paiichasiddhänt1ka 1. Paitamaha-Siddhänta 2. Vasistha-Siddhänta . A. General Information B. Motion of the moon C. Motion of the planets D. On the origin of the Vasishtha-Siddhänta Great periods . . . . . . . . . . . . .
XIII
266 266 268 271 271 273 273 275 275 276 279 279 280 280 281
284-324
284 284 285 285 287 287 288 290 291 292 294 294 295 297 299 299 300 301 301 301 302 305 306
XIV T ABLE OF CONTENTS
EGYPTIAN PLANETARY TABLES •.••
The tables ....... . The division of the ecliptic . How were the tables calculated?. The motion of Venus in text S . Comparison with Varaha Mihara The motion of Mars in text S . . Comparison of text P with Babylonian texts An Egyptian Mercury Table
SUMMARY
ABBREVIATIONS •••
CUNEIFORM TEXTS • •
NAMES AND SUBJECTS
PLATES
308 308 309 309 311 314 316 323 324 324 327 328 331 347
PREFACE
Whoever wants to understand the genesis of modern Science has to follow three lines
of development, all starting in antiquity, which were brought together in the work of
ISAAC NEWTON, namely
1. Ancient Mathematics => DESCARTES 2. Ancient Astronomy => COPERNICUS 3. Ancient Mechanics => GALILEO
: ~~~~ I=> NEWTON => HUYGENS
In Science Awakening I (Dutch edition 1950, first Eng1ish edition 1954, second 1961, first German edition 1956, second 1965) I have followed the first 1ine, giving an outline
of the development of Mathematics in Egypt, Babylonia, and Greece. Volume II, dealing with Egyptian and Baby1onian Astronomy first appeared in German
under the title 'Die Anfänge der Astronomie' (Noordhoff, Groningen 1965 and Birkhäu
ser, Basel 1968). The volume was written in collaboration with PETER HUBER (Swiss
Federal School of Technology, Zürich). HUBER has written considerable parts of Chapters 3 and 4, in particular all transcriptions of cuneiform texts in these chapters. I also
had much help from ERNST WEIDNER (Graz), MARTIN VERMASEREN (Amsterdam),
JOSEF JANSEN (Leiden) and MANU LEUMANN (Zürich). The present English edition of Volume II is not just a translation: it is a completely
revised text. Its history is roughly as follows. First, the German text was translated by MICHAEL HELL; next, the English version was revised and brought up to date by the
author. Tedious calculations were suppressed, new parts were added, recent publications
were used to simplify and to modernize the presentation. The more di:fficult chapters were put at the end of the book in order to make it easier for the reader. KLAUS BAER
(Oriental Institute, Chicago) helped me to improve Chapter 1, which deals with Egyptian
astronomy. Finally, the wording of the textwas thoroughly revised by WILLYS BANDLER (University of Essex, Colchester). ERWIN NEUENSCHWANDER and PETER WIRTH helped
me to correct the proofs and to compose the Index. To all these my hearty thanks!
The most important changes were made in Chapter 5, which deals with Astrology and Cosmic Religion. The last part of this chapter, on the identification of planets with gods
in ancient Persia, and on the attitude of CYRUS and DARIUS towards Astrology and
Zervanism are completely new. The publisher generously fulfilled all my wishes concerning printing and illustrations.
Many thanks to Mr. MOLENKAMP and Mrs. STEPHANIE VENEMA-NOORDHOFF!
Zürich, December 1972 B. L. VAN DER WAERDEN