The Circulation of Astronomical Knowledge in the Ancient World (Time, Astronomy, and Calendars, 6)

Astronomical and astrological knowledge circulated in many ways in the ancient world: in the form of written texts and through oral communication, and by the conscious assimilation of sought-after knowledge and the unconscious absorption of ideas to which scholars were exposed. The circulation of knowledge happened both between cultures, for example the transmission of astronomical texts, theories or parameters from one culture to another, and within cultures, both spatially, for example, between scholars in different cities, between “elite” and “popular” astronomical traditions, and between different genres of scholarship, and temporally, for example later interpretations of and reaction to earlier works. I use the term “circulation” deliberately here to emphasize that the transmission of knowledge is not a unidirectional process: astronomical knowledge from one group is not imposed upon another group; rather the process is one of negotiation between the two parties. Furthermore, the act of receiving knowledge almost always involves a process of adaptation of that knowledge to make it relevant to and compatible with the existing scholarly practices of the recipients.1 As discussed by Rochberg, pioneering work on the transmission of astronomical knowledge between cultures was undertaken by members of Brown University’s Department of History of Mathematics during the second half of the twentieth and the first few years of the twenty-first centuries. Through the work of Otto Neugebauer, Gerald Toomer, David Pingree, and others it has become evident how much astronomical knowledge was transmitted between Mesopotamia, Greece, India, the medieval Islamic World, and medieval and Renaissance Europe. As recognized by Neugebauer, a particularly good marker of transmission are precise numerical parameters used within mathematical astronomy.2 The transmission of broader astronomical or astrological concepts and methods can also be traced between cultures, but the evidence for transmission is not always so clear cut and we must be wary of assuming transmission where there are merely similarities in the tradition.3 When dealing with celestial omens, for example, how similar must omens be to allow us to conclude that they have been transmitted from one culture to another? In order to answer this methodological question it is necessary to consider things such as wider historical evidence for contact between the two cultures and possible routes of transmission, the number of “similar” cases (a few similar omens may simply be coincidence, a large number, especially if they share other features such as order within a text, making transmission more likely), and whether the similarities are unique to the cultures in question or whether similar material exists from cultures where it is clear that there can have been no contact. The papers by Rutz, looking at the transmission of Mesopotamian astral knowledge to other parts of the near east in the late second millennium bc, Misiewicz, considering the transmission of Mesopotamian lunar omens through the Greek tradition into late antiquity, Montelle, examining the transmission of Babylonian schemes for the rising times of the ecliptic to the Greek world, and Duke, looking at the transmission of Greek astronomy to India, all address these questions. Once knowledge is transmitted into a culture it then becomes adapted and naturalized to its new cultural setting. Thus process has been studied in detail by Sabra and others for cases of transmission between Mesopotamia, the Greco-Roman World, India, the Islamic world and Europe.4 A less known case is the transmission of western astrology from India to China during the Tang dynasty and its subsequent “Sinicization”. The paper by Song provides a detailed census and analysis of Chinese names and use of the twelve signs of the zodiac and their assimilation within traditional Chinese forms of divination. Niu provides a translation and study of a tenth century Chinese horoscope found at Dunhuang which blends elements of western and Chinese astrology. The circulation of astronomical knowledge within cultures sometimes shares some of the same characteristics of adaptation and naturalization as cross-cultural transmission. Geographically, texts may be rewritten to fit the norms of local traditions, and a variety of factors including the desire of scholars to retain power over astronomical activity through secrecy and restricting access to material may result in only certain aspects of the astronomical tradition circulating widely. Introduction 1 1 The Brown School of the History of Science: Historiography and the Astral Sciences 5 Francesca Rochberg 2 Astral Knowledge in an International Age: Transmission of the Cuneiform Tradition, ca. 1500–1000b.c. 18 Matthew T. Rutz 3 Traditions of Mesopotamian Celestial-Divinatory Schemes and the 4th Tablet of Šumma Sin ina Tāmartišu 55 Zackary Wainer 4 The Circulation of Astronomical Knowledge between Babylon and Uruk 83 John M. Steele 5 The Micro-Zodiac in Babylon and Uruk: Seleucid Zodiacal Astrology 119 M. Willis Monroe 6 Virtual Moons over Babylonia: The Calendar Text System, Its Micro-Zodiac of 13, and the Making of Medical Zodiology 139 John Z. Wee 7 On the Concomitancy of the Seemingly Incommensurable, or Why Egyptian Astral Tradition Needs to be Analyzed within Its Cultural Context 230 Joachim Friedrich Quack 8 Some Astrologers and Their Handbooks in Demotic Egyptian 245 Andreas Winkler vi contents 9 The Anaphoricus of Hypsicles of Alexandria 287 Clemency Montelle 10 Interpolated Observations and Historical Observational Records in Ptolemy’s Astronomy 316 Alexander Jones 11 Mesopotamian Lunar Omens in Justinian’s Constantinople 350 Zoë Misiewicz 12 A Parallel Universe: The Transmission of Astronomical Terminology in Early Chinese Almanacs 396 Ethan Harkness 13 Mercury and the Case for Plural Planetary Traditions in Early Imperial China 416 Daniel Patrick Morgan 14 Calendrical Systems in Early Imperial China: Reform, Evaluation and Tradition 451 Yuzhen Guan 15 The Twelve Signs of the Zodiac during the Tang and Song Dynasties: A Set of Signs Which Lost Their Meanings within Chinese Horoscopic Astrology 478 Shenmi Song 16 On the Dunhuang Manuscript p.4071: A Case Study on the Sinicization of Western Horoscope in Late 10th Century China 527 Weixing Niu 17 Were Planetary Models of Ancient India Strongly Influenced by Greek Astronomy? 559 Dennis Duke Index of Modern Authors 577 Index of Subjects 579 Index of Sources 582 List of Figures and Tables Figures 3.1 k 8088 obverse 74 3.2 k 8088 reverse 75 5.1 Layout of typical micro-zodiac tablets from Uruk (vat 7847+) and Babylon (bm 34572) 135 6.1 Dodekatemoria and Calendar Text Schemes 144 6.2 The Micro-zodiac as Compression of the Zodiac 158 6.3 The ‘Micro-zodiac of 13’ 165 6.4 Calendar Text Dates and Micro-Zodiacal Signs 166 6.5 The Sun’s ‘Micro-Zodiac of 13’ in Tablet brm iv, 19 173 6.6 The Calendar Text System 174 6.7 Prescriptions and Combinations of Micro-zodiacal and Zodiacal Signs 186 6.8 Photo of Reverse Side of Tablet bm 56605 215 6.9 Diagram of Astrological Table on Tablet bm 56605, Reverse 216 6.10 Reinterpreting the Cuneiform in Astrological Table (bm 56605, Reverse) Row 2 217 9.1 Circular diagram depicting the rising times in each zodiacal sign (redrawn from the diagram in Vat. Gr. 204 f. 135v) 296 10.1 A conjectural scheme for Ptolemy’s reception of historical planetary observations 325 10.2 A simple epicyclic model for an inferior planet, shown approximately to scale for Venus 331 10.3 Ptolemy’s equant model for Venus 332 10.4 Locations of Mercury on the dates of surviving Babylonian Normal Star observations 340 10.5 Locations of mean Sun on the dates of surviving Babylonian Normal Star observations of Mercury 341 10.6 Locations of Mercury relative to Normal Star on dates of surviving Babylonian observations 342 10.7 Locations of Venus relative to Normal Star on dates of surviving Babylonian observations 343 10.8 Greatest elongations of Mercury from mean Sun computed by modern theory for 270–258bc 346 13.1 Rise times and visibility phenomena for Mercury (203 b.c.) 424 13.2 Wuxing zhan planetary hemerology (year 1 of 60) 425 13.3 The twenty-eight lodges ‘ancient du widths’ 426 viii list of figures and tables 13.4 Li model prediction of position and visibility for a.d. 5–6 430 16.1 A natal chart from qyrzj of the 9th century 542 16.2 A natal chart from the Zoku Gunsho Ruiju 544 16.3 A tentative reconstruction of the p.4071 natal chart 545 17.1 The Almagest equant plus epicycle for an outer planet. The Earth is at o, the equant point is at e, the center of the deferent is at d (the midpoint of oe), the center of the epicycle is on the deferent at c, and the planet is at p. Calculation of the lengths 1 r , 2 r , and 2 D in terms of e, r, and the anglesa andg , and application of the law of sines to the triangles oec and ocp, yield the equations q and p. 561 17.2 The concentric equant model. The Earth and the center of the deferent are at o, and the equant point is at e. The planet is at p. 563 17.3 The epicycle model. The Earth and the center of the deferent are at o, and the equant point is at e. The planet is at p. 563 17.4 The difference between the longitudes of Jupiter predicted by modern theory and those predicted by the equant model (open circles), the eccentre plus epicycle model (solid circles), and the Indian (sunrise) model (solid line), using the same (Almagest) parameters for all three ancient models. The equant and Indian models are very nearly coincident in the figure, while the eccentre model differs significantly from both. 567 17.5 As in Fig. 17.4 except for Mars. Note that for Mars the Indian model now differs noticeably from the equant, but is an even poorer match to the eccentre. 568 17.6 The concentric equant has the Earth at o, the planet at s on a deferent of radius r, and the equant at e. The equivalent simple eccentric has an eccentric deferent also of radius r but centered at d, and the planet is now at t. Since es and dt are parallel both models have the same mean centrum (angles fdt and des), and since ost is a straight line, the s and t have the same position as seen from the Earth and so both models have the same true centrum (angles eos and dot). 572 17.7 The eccentric has a deferent circle of radius r centered at d with the Earth at o and the Sun orMoon at c. Assuming R =1 , the distance 2 2 r = (esina ) + (1+ e cosa ) . By conventiong =a + q , so in the configuration shown q < 0 . Then the law of sines gives sin q sin sin e R a g r - = = . 573 list of figures and tables ix Tables 2.1 Section topics of the thematic lexical text ur5-ra = ḫubullu (Ura) with their corresponding major divisions in the early second millennium (Old Babylonian version from Nippur), later second millennium (Middle Babylonian version), and first millennium (Standard version) b.c. 23 3.1 Celestial divinatory schemes in sit 4 and parallels 59 3.2 Schemes c and c′ 61 3.3 Month–land schemes 63 4.1 A rough comparison of the numbers of different genres of astronomical texts at Babylon and Uruk 86 4.2 ‘Observational’ texts from Uruk 93 4.3 Almanacs and Normal Star Almanacs from Uruk 101 4.4 Overlapping data on the Normal Star Almanacs mlc 1860 from Babylon and Rm 731+ from Babylon 103 4.5 Number and attested date ranges for tablets containing lunar and planetary synodic and auxiliary tables at Babylon and Uruk. Date marked with a * indicate that the tablet is broken at the beginning/end and so the date range of the original table extended earlier/later. 107 4.6 A comparison of the preserved Horoscopes from Babylon and Uruk 111 5.1 The Micro-Zodiac Scheme 124 5.2 Catalogue of micro-zodiac tablets 127 8.1 Left CtYBR 1132 verso; Right: P.Carlsb. 420 262 8.2 Left P.Cair. ii 31220 and P.Tebt.Tait 22; Right P.Carlsb. 420 276 11.1 Apodoses associated with lunar eclipse or dimness 363 11.2 Cuneiform and Greek watch schemata 368 11.3 Agricultural Apodoses 376 11.4 Military Apodoses 378 11.5 Other Apodoses 379 13.1 Triple Concordance motion-degree model for Mercury (c. a.d. 5) 429 13.2 Four-season schemes for Mercury in tian-wen omen literature 432 13.3 Mercury four-season omen series 435 13.4 Mercury model & series permutations 436 14.1 The positions of the sun at winter solstices according to observation of lunar eclipses 468 14.2 Winter solstices according to measurement of the shadow cast by a gnomon 471 15.1 Names of the Twelve Signs of the Zodiac 481 15.2 Sequences of the Twelve Signs of the Zodiac 482 x list of figures and tables 15.3 Correspondence between the Twelve Signs and Twenty-eight Lunar Mansions 488 15.4 Correspondence between the Twelve Signs and the Seven Luminaries 492 15.5 Correspondence between the Twelve Signs, the Seven Luminaries and Five Phases in Qiyao rangzai jue 492 15.6 The “Seven Luminaries” Property of the Lunar Mansions in Horoscope Astrology 496 15.7 Correspondence between the Twenty-eight Lunar Mansions and Five Planets-Five Phases in Chinese Astrology 502 15.8 Correspondence between the Twelve Signs, Twelve Ci and the Twelve Earthly Branches 516 15.9 Different “Five Phases” properties of the Twelve Earthly Branches 518 15.10 Correspondence between the Twelve Signs and the Twelve Districts of China 520 16.1 Constellation-Planet-Animal dating system 534 16.2 A comparison of the Trine Lords between A Complete Collection of Genethlialogy and Ptolemy’s Tetrabiblos i.18 535 16.3 Positions and Field Allocations of the eleven luminaries in p.4071 537 16.4 The planetary positions in p.4071 compared with the results of calculation by qyrzj (t.1308) and the modern ephemeris de404 538 16.5 Main compositions in a natal chart from qyrzj of the 9th century 543 16.6 Compositions in an actual natal chart on 14 January 1113 from Zoku Gunsho Ruiju 544 16.7 The frequency of a certain configurations of planet and house mentioned in p.4071 553 Introduction -- The Brown School Of The History Of Science : Historiography And The Astral Sciences / Francesca Rochberg -- Astral Knowledge In An International Age : Transmission Of The Cuneiform Tradition, Ca. 1500-1000 B.c. / Matthew T. Rutz -- Traditions Of Mesopotamian Celestial-divinatory Schemes And The 4th Tablet Of Šumma Sin Ina Tāmartišu / Zackary Wainer -- The Circulation Of Astronomical Knowledge Between Babylon And Uruk / John M. Steele -- The Micro-zodiac In Babylon And Uruk : Seleucid Zodiacal Astrology / M. Willis Monroe -- Virtual Moons Over Babylonia : The Calendar Text System, Its Micro-zodiac Of 13, And The Making Of Medical Zodiology / John Z. Wee -- On The Concomitancy Of The Seemingly Incommensurable, Or Why Egyptian Astral Tradition Needs To Be Analyzed Within Its Cultural Context / Joachim Friedrich Quack -- Some Astrologers And Their Handbooks In Demotic Egyptian / Andreas Winkler -- The Anaphoricus Of Hypsicles Of Alexandria / Clemency Montelle -- Interpolated Observations And Historical Observational Records In Ptolemy's Astronomy / Alexander Jones -- Mesopotamian Lunar Omens In Justinian's Constantinople / Zoe Misiewicz -- A Parallel Universe : The Transmission Of Astronomical Terminology In Early Chinese Almanacs / Ethan Harkness -- Mercury And The Case For Plural Planetary Traditions In Early Imperial China / Daniel Patrick Morgan -- Calendrical Systems In Early Imperial China : Reform, Evaluation And Tradition / Yuzhen Guan -- The Twelve Signs Of The Zodiac During The Tang And Song Dynasties : A Set Of Signs Which Lost Their Meanings Within Chinese Horoscopic Astrology / Shenmi Song -- On The Dunhuang Manuscript P.4071 : A Case Study On The Sinicization Of Western Horoscope In Late 10th Century China / Weixing Niu -- Were Planetary Models Of Ancient India Strongly Influenced By Greek Astronomy? / Dennis Duke. Edited By John M. Steele. Includes Bibliographical References And Index. Astronomical and astrological knowledge circulated in many ways in the ancient world: in the form of written texts and through oral communication; by the conscious assimilation of sought-after knowledge and the unconscious absorption of ideas to which scholars were exposed. The Circulation of Astronomical Knowledge in the Ancient World explores the ways in which astronomical knowledge circulated between different communities of scholars over time and space, and what was done with that knowledge when it was received. Examples are discussed from Mesopotamia, Egypt, the Greco-Roman world, India, and China.