From the Banks of the Euphrates: Studies in Honor of Alice Louise Slotsky

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List of Contributors Lis Brack-Bernsen John P. Britton Leo Depuydt Benjamin R. Foster Karen Polinger Foster Jens Høyrup Hermann Hunger Toke Lindegaard Knudsen Jessica Lévai Sarah C. Melville Duncan J. Melville Marie Passanante Elizabeth E. Payne Kim Plofker Erica Reiner Eleanor Robson Francesca Rochberg Micah Ross John M. Steele Ronald Wallenfels Christopher Walker Clemency Williams

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From the Banks of the Euphrates Studies in Honor of

Alice Louise Slotsky

Edited by Micah Ross

Winona Lake, Indiana Eisenbrauns 2008

00-FrontMatter-SlotskyFs Page iv Saturday, December 1, 2007 3:07 PM

ç Copyright 2008 by Eisenbrauns. All rights reserved. Printed in the United States of America. www.eisenbrauns.com

Library of Congress Cataloging-in-Publication Data From the banks of the Euphrates : studies in honor of Alice Louise Slotsky / edited by Micah Ross. p. cm. Includes bibliographical references. ISBN-13: 978-1-57506-144-3 (hardback : alk. paper) 1. Middle East—Civilization—To 622. 2. Middle East—Antiquities. I. Ross, Micah. DS57.F76 2008 939u.4—dc22 2007044883 The paper used in this publication meets the minimum requirements of the American National Standard for Information Sciences—Permanence of Paper for Printed Library Materials, ANSI Z39.48-1984. †‘

Qu’est-ce qu’un fleuve sans sa source? Qu’est-ce qu’un peuple sans son passé? Victor Hugo, Les Pyrénées

Contents 1

KUR – When the Old Moon Can Be Seen a Day Later Lis Brack-Bernsen, Hermann Hunger and Christopher Walker

1

2

Remarks on Strassmaier Cambyses 400 John P. Britton

7

3

Ancient Chronology’s Alpha and Egyptian Chronology’s Debt to Babylon Leo Depuydt

35

4

Assyriology and English Literature Benjamin R. Foster

51

5

The Eyes of Nefertiti Karen Polinger Foster

83

6

Les Lais: or, What Ever Became of Mesopotamian Mathematics? Jens Høyrup

99

7

House Omens in Mesopotamia and India Toke Lindegaard Knudsen

121

8

Anat for Nephthys: A Possible Substitution in the Documents of the Ramesside Period Jessica Lévai

135

9

Observations on the Diffusion of Military Technology: Siege Warfare in the Near East and Greece Sarah C. Melville and Duncan J. Melville

145

10 Two Ivory Carvings from Hierakonpolis Marie Passanante

169

11 The “Rough Draft” of a Neo-Babylonian Accounting Document Elizabeth E. Payne

181

viii

Contents

12 Mesopotamian Sexagesimal Numbers in Indian Arithmetic Kim Plofker

193

13 In Praise of the Just Erica Reiner

207

14 The Long Career of a Favorite Figure: The apsamikku in Neo-Babylonian Mathematics Eleanor Robson

211

15 A Short History of the Waters of the Firmament Francesca Rochberg

227

16 All’s DUR That Ends Twr Micah Ross

245

17 A Commentary Text to En¯ uma Anu Enlil 14 John M. Steele and Lis Brack-Bernsen

257

18 A New Stone Inscription of Nebuchadnezzar II Ronald Wallenfels

267

19 Some Details on the Transmission of Astral Omens Clemency Williams

295

List of Tables 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12

Format of Reporting Lunar Six Text [Obverse] Adjusted Calculations Textual Values − Calculated Values B. Planetary Synodic Phenomena (Jupiter) B. Planetary Synodic Phenomena (Venus) B. Planetary Synodic Phenomena (Saturn) B. Planetary Synodic Phenomena (Mars) B. Planetary Synodic Phenomena (Mercury) Plausible Compilation of Strm. Camb. 400 C. Planetary Passages D. Lunar Eclipses

11 11 12 14 21 22 23 24 25 26 27 28

3.1

Entries 20 through 35 of King-List

42

16.1 Composition of Medˆınet Habˆ u Horoscopes

246

ˇ during an 17.1 Duration of Lunar Visibility in US Equinoctial Month according to EAE 14 Tables A and B

259

19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 19.9 19.10 19.11 19.12 19.13 19.14 19.15

298 300 301 302 304 305 307 308 310 310 311 311 311 312 312

Correlation of Planets and Colors Correlation of Colors and Lunar Quadrants Correlation of Directions and Locations Translations of Akkadian Terms Names of Nocturnal Watches Correlation of Nocturnal Watches and Adannu Hour Distributions for Solar Eclipses Hour Distributions for Lunar Eclipses System I: Correlation of Months and Locations System II: Correlation of Months and Locations System II: Correlation of Hours and Locations System II: Correlation of Divisions and Locations System I: Correlation of Months and Locations System II: Correlation of Months and Locations System II: Correlation of Hours and Locations

List of Figures 2.1 Comparison of NAN from Strm. Camb. 400 with Modern Calculations 2.2 Comparison of ME+GE6 from Strm. Camb. 400 with Modern Calculations 2.3 Comparison of ME+GE6 from Strm. Camb. 400 with Modern Calculations 2.4 Comparison of KUR from Strm. Camb. 400 with Modern Calculations

15

¨ 5.1 Right eye of Nefertiti, courtesy Agyptisches Museum und Papyrussammlung, Berlin. ¨ 5.2 Left eye of Nefertiti, courtesy Agyptisches Museum und Papyrussammlung, Berlin.

86

9.1 Cross-section of the Ramp

162

10.1 Ivory One, reproduced from Adams, Ancient Hierakonpolis, pl. 39, fig. 327 with permission of the publisher. 10.2 Ivory Two, from Quibell, Ancient Hierakonpolis, vol. 1, pl. XVI, figs. 1 and 2.

170

11.1 Upper Edge and Obverse of YBC 9030 (undated) 11.2 Lower Edge and Reverse of YBC 9030 (undated)

182 184

12.1 The Shadow-Triangle of a 12-digit Gnomon

201

14.1 The Old Babylonian apsamikkum 14.2 BM 47431

212 213

17.1 BM 45900 Obv. (Copyright the Trustees of the British Museum) 17.2 BM 45900 Rev. (Copyright the Trustees of the British Museum) 17.3 BM 99745 (Copyright the Trustees of the British Museum)

260 260 260

15 15 16

87

172

265

Preface Alice Louise Slotsky began her studies in Economics at Bryn Mawr College and continued graduate study in Economics at New York University. Although many economic practices originated in Mesopotamia, Alice Slotsky did not extend her academic interests into the ancient world until nearly twenty years after her initial studies. Professor Slotsky completed her studies at Yale, laying important groundwork in the study of Babylonian economics with The Bourse of Babylon: An Analysis of the Market Quotations in the Astronomical Diaries of Babylonia. Because economic and astronomic data were recorded on the same tablets, Slotsky became known to the historians of astronomy; and because both economic and astronomic historians rely on numeric analyses little appreciated in the field of ancient history, she quickly won the respect and friendship of the historians of the exact sciences. Although Near Eastern languages and the history of the exact sciences are known for being obscure and deliberately arcane to general audiences, Alice Slotsky has paradoxically established her legacy by exposing these topics to a wider audience. As a visiting professor at Brown University, Slotsky has taught more students than any previous Assyriologist and successfully brought this discipline to a wider audience than previously imagined possible. On 5 January, 2005, I circulated a letter among graduate students who had worked with Slotsky, surveying the interest in a festschrift and asking for assistance. At the time, I wrote that letter I did not envision a grand work such as the Pingree festschrift. After all, festschrifts are generally written by past students, with occasional assistance from friends and colleagues. Slotsky’s late arrival in academics precluded her having once taught current luminaries. Indeed, none of her students had, at that time, completed their initial studies. Nonetheless, I hoped to put something together. Because none of Alice Slotsky’s past students were at that time Assyriologists in the strictest sense, I proposed that the offerings present the elements of Akkadian wisdom which had been carried from the banks of the Euphrates into the surrounding cultures. Since that initial letter, the project grew considerably through the support of her friends and colleagues. Happily, current luminaries contributed their works to this volume, and in all cases the presentations contain more than a few pages. Well-wishers from her time studying at Yale University include Benjamin R. Foster, Karen Polinger Foster, Sarah C. Melville, Duncan J. Melville, and her collaborator Ronald Wallenfels. Historians of mathematics and astronomy also paid honor to

xii

Preface

this scholar, with Lis Brack-Bernsen, John P. Britton, Jens Høyrup, Hermann Hunger, Kim Plofker, Eleanor Robson, John M. Steele, and Christopher Walker making contributions. Closely related to these scholars are the Assyriologists with interests in the astral sciences, Erica Reiner and Francesca Rochberg. Slotsky’s friends from her days at Brown University also contributed. Among these, Leo Depuydt, an Egyptologist, and her students Toke Lindegaard Knudsen, Jessica Lévai, Marie Passanante, Elizabeth E. Payne and Clemency Williams honor her with their contributions. The production of this volume could not have been accomplished without the help of many whose names are not attached to particular articles. Dean of Faculty at Brown University Rajiv Vohra ensured the funding of the volume. When the late Professor David Pingree first learned of the plan, he was overjoyed and provided assistance which guaranteed the eventual completion of the volume. His initial wishes were furthered by his wife, Isabella Pingree, who assisted the project even amid her own sorrows. Fortunately, the late Gordon Slotsky had full knowledge of the volume and played a role in the planning of the announcement of the volume. M. Katherine Rance provided initial assistance with editing. Professor Stephan Heilen helped with several difficult decisions with prudence, discretion, and wisdom. Dorian Gieseler Greenbaum made good on a previously extended favor in service of this project. Dean Serenevy gave technical direction at several crucial moments. John Pariseault provided moral guidance, and special thanks are due to Tessa Campanelli. The photographs of the right and left eye of Nefertiti on pages 86 and ¨ 87 are reproduced by courtesy of the Agyptisches Museum und Papyrussammlung, Berlin. The image of Ivory One on page 170 is reproduced with the permission of Oxbow Books. The photographs of BM 45900 on page 256 and BM 99745 on page 261 are reproduced by permission of the Trustees of the British Museum. The photographs of the Sackler Nebuchadnezzar stone (82.2.8) are reproduced by permission of The Arthur M. Sackler Foundation and Simon Feldman, and the text appears courtesy of the Arthur M. Sackler Collections.

Micah Ross Paris

KUR – When the Old Moon Can Be Seen a Day Later Lis Brack-Bernsen,1 Hermann Hunger and Christopher Walker University of Regensburg, University of Vienna, and British Museum

Preface It is our great pleasure to contribute this little paper to honor Alice Slotsky. We have chosen to write about the cuneiform tablet BM 37110. It is our greeting to a dear friend who is excited about all kinds of cuneiform writing. Indeed, Alice is the happy center of communication between scholars of the field. Introduction As Sachs was working on all types of astronomical cuneiform texts in the British Museum, he classified them as mathematical astronomical texts (now called ACT) and as non-mathematical astronomical types: Diaries, Almanacs, Normal Star Almanacs and Goal-Year Texts.2 All fragments of tablets from the intermediate period which belonged neither to one of these categories nor to ACT material and which were difficult to understand were put away in a box. Our text BM 37110 was in that box until Christopher Walker drew our attention to the text, since it seemed to be connected to the so-called “Goal-Year Method” for the prediction of lunar phases. Indeed, BM 37110 is the first cuneiform tablet found so far, which is concerned with the Goal-Year method for the calculation of kur, one of the six special time intervals, which, around new moon and full moon, were observed regularly by Babylonian astronomers. The Lunar Six At the end of the (synodic) Babylonian month, the event of kur took place and could be measured: kur=time from last visible moonrise before conjunction to sunrise. 1. Research supported by Deutsche Forschungsgemeinschaft. 2. Abraham Sachs, “A Classification of the Babylonian Astronomical Tablets of the Seleucid Period,” Journal of Cuneiform Studies 2, no. 4 (1948): 271–290.

1

2

Lis Brack-Bernsen, Hermann Hunger and Christopher Walker

The time interval nan was observed on the evening when the new crescent was visible for the first time after conjunction, indicating the first day of the month. Thus, nan = sunset to the first visible setting of the new moon.3 At sunrise and sunset in the days around opposition, i.e., in the middle of the Babylonian month, the following Lunar Four time intervals were regularly measured: ˇ ´ = moonset to sunrise of the last moonset before sunrise. su na = sunrise to moonset of the first moonset after sunrise. me = moonrise to sunset of the last moonrise before sunset. ge6 = sunset to moonrise of the first moonrise after sunset. me and ge6 were measured on two consecutive evenings, and their sum, me+ge6 , tells how much time (with respect to sunset) the rising of the moon had been delayed from one evening to the next. Therefore we call me+ge6 the daily retardation of the rising moon. In spite of the fact that these time intervals—from a modern theoretical point of view—are very complicated quantities, the Babylonians succeeded in predicting them. They utilized the knowledge that a Saros, or 223 synodic months, was about 31 of a day longer than an integer number (6585) of days. And, they must have noticed that me+ge6 , the daily retardation of the rising moon, repeats after one Saros. The Goal-Year Method for Predicting Lunar Six A special type of astronomical cuneiform tablets, the Goal-Year Texts, presents raw materials for the prediction of planetary and lunar phenomena for a given year, called the “goal year.”4 A systematic analysis of the lunar data collected on Goal-Year tablets resulted in a proposal about how such data could have been used for predicting the Lunar Six time intervals, and the procedure text TU 11 indeed confirmed the proposal.5 The Goal-Year Method predicts all elements of the Lunar Six for a given month by means of two sets of Lunar Sixes, the first observed 3. In the texts with which we are working, this interval is called na, but it always occurs with an indication that it is the na of the first day or the na at the beginning of the month. We put this identification into the name, calling it na(of the new crescent), or nan . We have established this convention in order to be as precise as the Babylonian texts. There the term na is also used for a time interval in the middle of the month, but it is always identified by calling it the na of day 14 or the na opposite the sun. 4. Sachs, “Classification,” 282 n. 2. 5. Lis Brack-Bernsen, “Goal-Year Tablets: Lunar Data and Predictions,” in Ancient Astronomy and Celestial Divination, ed. Noel Swerdlow (Cambridge, Massachusetts: MIT Press, 1999), 149–77 and Lis Brack-Bernsen and Hermann Hunger, “TU 11: A Collection of Rules for the Prediction of Lunar Phases and of Month Lengths,” SCIAMVS 3 (2002): 3–90.

KUR – When the Old Moon Can Be Seen a Day Later

3

one Saros (or, 223 synodic months) earlier than the month in question, and the other measured one Saros and six months (that is, 229 synodic months) prior to the given month. At this point we shall simply indicate the procedure and refer to earlier publications for further details.6 The cuneiform texts give the procedure in words to the effect: in order to find me in the new year, go eighteen years (that is, one Saros) back, take one third of the sum me+ge6 and add it to me from the old year. We prefer to give the procedures in the form of equations. The one for finding me is given in equation (1.4) below: ´ + na)old−6months , (nan )new = (nan )old − 1/3 (ˇ su

(1.1)

ˇ ´ new = ˇ ´ old + 1/3 (ˇ ´ + na)old , su su su

(1.2)

´ + na)old , nanew = naold − 1/3 (ˇ su

(1.3)

menew = meold + 1/3 (me + ge6 )old ,

(1.4)

(ge6 )new = meold − 1/3 (me + ge6 )old .

(1.5)

Note that the new and old months are exactly 223 synodic months, i.e., one Saros apart. For finding the new nan , the value of nan from the ´ +na lunation one Saros earlier was used in connection with the sum ˇ su measured one Saros and six months earlier. TU 11 has traces of these five formulæ, but nothing on kur. However, corresponding to equation (1.1), the reconstructed formula for calculating kur must be kurnew = kurold + 1/3 (me + ge6 )old−6months .

(1.6)

Here one must read (me+ge6 )old−6months as the sum me+ge6 measured eighteen years plus six months earlier than the new month in question. Until now this reconstruction has not been supported by textual evidence. Luckily, BM 37110 seems to be concerned with finding kur by means of the Goal-Year Method, so now we have the textual confirmation for the procedure postulated in equation (1.6). The Textual Proof Of BM 37110 only one side is preserved—the beginning and the end are lost as well as the beginning and end of each line. Still, what is left clearly refers to the Goal-Year method. It mentions eighteen years, a new year, an old year, the last visibility (i.e., kur) and tells us to go six 6. For a more thorough explanation, astronomical comments and textual evidence, see Brack-Bernsen, “Goal-Year Tablets.” See also Brack-Bernsen and Hunger, “TU 11.”

4


months back (from month I to month VII). Therefore we surmise that lines 3’ to 5’ of BM 37110 are concerned with rules for finding kur: 3’

4’ 5’

3’

4’

5’

` -ka ta bar ˇs´ [gaba-ri 18 ana du a 18] 6 itu ta bar gur-ma [20 me u] ge6 ˇs´ a du6 [. . . ] [. . . ˇs´ a bar ˇs´ a ] 18 x tab-ma ki-i 23 danna i tab lu ka [. . . ] ´ .a ˇs´ [. . . me u g]e6 bal-t.u ˇs´ a du6 ta ud.na a bar zi-ma [. . . ] [In order for you to calculate the equivalent for 18 (years): from month I of the 18(th year preceding)] you return 6 months from month I, and [one-third of] me+ge6 of month VII [. . . ]. [. . . of month I of] the 18(th year preceding) you add, and if . . . two-thirds of a beru [. . . ]. [. . . ] you subtract the complete me+ge of month VII from kur of month I [. . . ].

Now, lines 3’, 4’, and 5’ are so similar to and parallel to TU 11, section 16, that we can identify the procedure and add the missing text. Section 16 gives the rule for finding nan and for correcting the result if the calculated nan happens to become smaller than 10 uˇs, so that the moon will not be visible. In this case, nan will be visible on the ´ +na, which next day, and its value will become larger by the whole ˇ su is the daily retardation of the setting moon. The remnants on BM 37110 can be identified as the Goal-Year procedure for finding kur and for the correction necessary if the calculated kur happens to be larger than 32 danna (that is, 20 uˇs ). In such a case, the old moon would probably be visible one day later than first assumed. Consequently, its calculated value shall be reduced by (me+ge6 )old−6month , which is the daily retardation of the rising moon. The procedure for finding nan , together with the corrected rule for the case when the new nan happens to become too small, is given in equation (1.1) and (1.7). Section 16 of TU 11 gives the Goal-Year procedure for lunations two Saroi apart, which is equivalent to equation (1.1) used twice. The text BM 37110 mentions 18. Clearly, it is concerned with lunations one Saros apart. Therefore, below we give the formula and correction for finding nan after one Saros. ´ + na)old−6months . (nan )new = (nan )old − 1/3 (ˇ su

(1.1)

´ +na: If nan < 10 uˇs, a correction may be made by adding the whole ˇ su ´ + na)old−6months . (nan )newC = (nan )old + 2/3 (ˇ su

(1.7)

KUR – When the Old Moon Can Be Seen a Day Later

5

Similarly, the formula for the corrected kur can be derived from equation (1.6): kurnew = kurold + 1/3 (me + ge6 )old−6months .

(1.6)

If kurnew > 20 uˇs, a correction may be made by subtracting the whole me+ge6 : kurnewC = kurold − 2/3 (me + ge6 )old−6months .

(1.8)

We are convinced that BM 37110 is concerned with these rules. As evidence, we reproduce below TU 11, obv. 36 and 37. In these lines, the rule for finding nan from its value established two Saroi earlier is given together with corrections for the case of nan becoming too small. ` -ka ta bar ˇs´ gaba-ri 36 ana du a 36 6 itu bar gur-ma 40 ´ u na ˇs´ ˇs´ aˇ su a du6 giˇ s-ma ta na ˇs´ a ud-1 ˇ ´ u na bal-t.u-ut 37 ˇs´ a bar ˇs´ a 36 zi-ma be-ma al-la 10 us lal ˇ su ana ugu dah . . . ˘ Lines 36 and 37 of TU 11 are quite similar to lines 3’ through 5’ of BM 37110, which we see as the rule for finding kur from its value established for the lunation one Saros earlier together with corrections to be applied in case the old moon could be seen one day later. It is obvious that the two sections are parallel. Both texts give advice for times when one element of the Lunar Six, NAN or KUR, eventually could (and hence should) be measured a day later than according to the standard procedure. There is, however, an asymmetry with the observable nan and kur. If the new nan becomes so small that it is questionable whether or not the new crescent will be visible on the expected evening, then, in a clear sky, it will always be observable the next evening. Likewise, kur—as found by equation (1.6)— can become so large that the old moon might still be visible the next morning, but one cannot be sure. A large kur does not guarantee that the old moon really will be visible one day longer than expected. It should be tested. The text says if kur becomes larger than 20 uˇs, subtract me+ge. But, me+ge varies between roughly 6 uˇs and about 18 uˇs, so that kurnewC = kurnew − (me+ge6 ) might become too small (smaller than 8 to 10 uˇs ) for the old moon to be visible. The text should give a limit for the new and corrected kur.7 36

7. We thank John Britton for fruitful discussions. He proposed that the text might have had rules for checking the size of the new kur and through that for controlling the visibility of the kurnewC .

6


References Brack-Bernsen, Lis. “Goal-Year Tablets: Lunar Data and Predictions.” In Ancient Astronomy and Celestial Divination, edited by Noel Swerdlow, 149–77. Cambridge, Massachusetts: MIT Press, 1999. Brack-Bernsen, Lis and Hermann Hunger. “TU 11 : A Collection of Rules for the Prediction of Lunar Phases and of Month Lengths.” SCIAMVS 3 (2002): 3–90. Sachs, Abraham. “A Classification of the Babylonian Astronomical Tablets of the Seleucid Period.” Journal of Cuneiform Studies 2, no. 4 (1948): 271–90.

Remarks on Strassmaier Cambyses 400 John P. Britton Wilson, Wyoming

BM 33066 (78–11–7, 4), better known as Strm. Camb. 400, is a unique proto-almanac, which contains Lunar Six1 for the year 7 Cambyses (−522/1) on one side and planetary and lunar eclipse data on the other. The text is well preserved and distinctive in several respects: it is two centuries earlier than any other complete set of a year’s worth of Lunar Six; it is the sole unbroken cuneiform record of an eclipse described in Ptolemy’s Almagest; and it is the only astronomical text known to me which records events in a year which exceeds the known reign of the king in question. The text consists of four sections: Obverse: Reverse:

A. Lunar Six for months I–XII2 (!) of 7 Cambyses; B. Planetary synodic phenomena for complete synodic cycles beginning in 7 Cambyses with Ω (disappearance [in the west for inner planets] in the order: Jupiter, Venus, Saturn, Mars, Mercury); C. Miscellaneous conjunctions of Moon and planets with planets in 7 Cambyses, up to month X day 5 and; D. Lunar eclipses in 7 Cambyses, months IV and X.

1. Lunar Six comprise the dates and intervals of lunar visibility between sunrise (SR) or sunset (SS) and moonrise (MR) or moonset (MS) near new and full moon. Specifically, nan is the date and time interval from sunset to moonset (MS−SS) of the first visible lunar crescent; me (SS−MR) and ge6 (MR−SS) are the dates and ´ (SR−MS) and na intervals between SS and MR on either side of the full moon; ˇ su (MS−SR) are dates and intervals between SR and MS on either side of the full moon; and kur (SR−MR) is the date and interval from moonrise to sunrise, when the moon is last visible. The two pairs of visibility phenomena around full moon, the first being ´ and na, are frequently designated as the me and ge6 and the other consisting of ˇ su Lunar Four. The dates of me and ge6 assume that these sunset events occur on the night which begins with the sunset in question, although technically the interval from MR to SS (me) takes place toward the end of the prior day. It will be convenient ´ are properly to express the Lunar Four as MR−SS or MS−SR, so that me and ˇ su negative quantities.

7

8

John P. Britton

Some unusual features include older terminology, such as d sag.me.gar for Jupiter and d .sal-bat-a-nu (but d an once) for Mars; also 9 written mostly in the three wedge cursive form, but twice in the older nine wedge form, once following a cursive 9 in the same line (i.e., rev. 11). The Lunar Six are recorded with a precision of 31 or 12 a degree, in contrast to later texts which typically reflect a precision of 16 of a degree. The Lunar ´ Four specify the “night” of me and ge6 but give simply the date of ˇ su and na, again in contrast to later practice, which evidently regarded this ´ u na nu tuk.” In clarification as unnecessary.2 Zero is denoted as “ˇ su general, the terminology and orthography seems unsettled, with older and unusual practices being present but not predominating. Since its original publication by Strassmaier, the text has been the subject of published discussion by Epping, Oppert, Kugler, Brack-Bernsen, and most recently by Hunger and Pingree3 who include details of earlier discussions. Sachs lists it as LBAT 1477 but did not publish the piece.4 A modern edition and translation has recently been published by Hunger.5 Except where noted the comments, which follow, are based on Hunger’s transliteration. At least two issues have eluded consensus in these discussions. One is the date of the text’s compilation; the other is the likely source(s) 2. Note the similar format in undated BM 55554. See Hermann Hunger, ed. Lunar and Planetary Texts, vol. 5 of Astronomical Diaries and Related ¨ Texts from Babylonia, Denkschriften Osterreichische Akademie der Wissenschaften ¨ Philosophisch-Historische Klasse, vol. 299 (Vienna: Verlag der Osterreichischen Akademie der Wissenschaften, 2001), no. 49, 201. 3. Johann Strassmaier, Inschriften von Cambyses, vol. 9 of Babylonische Texte (Leipzig: Eduard Pfeiffer, 1890), no. 400, 231–32. Josef Epping, “Sachliche Erkl¨ arung des Tablets No. 400 der Cambyses-Inschriften,” Zeitschrift f¨ ur Assyriologie 5 (1890): 281–88. Jules Oppert, “Une texte babylonien astronomique et sa traduction grecque d’apres Claude Ptol´ em´ ee,” Zeitschrift f¨ ur Assyriologie 6 (1891): 103–23. Franz Kugler, Sternkunde und Sterndienst in Babel I: Babylonische Planetenkunde (Munster in Westfallen: Aschendorff, 1907), 61–75. Lis BrackBernsen, Zur Entstehung der babylonischen Mondtheorie: Beobachtung und theoretische Berechnung von Mondphasien, Boethius, vol. 40 (Stuttgart: Franz Steiner Verlag, 1997), 99–103. Lis Brack-Bernsen, “Ancient and Modern Utilization of the Lunar Data Recorded on the Babylonian Goal-Year Tablets,” in Actes de la Ve`me Conf´ erence Annuelle de la SEAC, eds. Mariusz Zi´ olkowski, Arnold Lebeuf, and Arkadiusz Soltysiak, SWIATOWIT Supplement Series H: Anthropology, vol. 2 (Warsaw: Warsaw University Institute of Archaeology, 1999), 13–39. Lis Brack-Bernsen, review of Astral Sciences in Mesopotamia, by Hermann Hunger and David Pingree, Archiv f¨ ur Orientforschung 48 (2001): 244–47. Hermann Hunger and David Pingree, Astral Sciences in Mesopotamia, Handbuch der Orientalistik, Erste Abteilung: Nahe und der Mittlere Osten, vol. 44 (Leiden: Brill, 1999), 174–75, 197. 4. Theophilus Pinches and Johann Strassmaier, Late Babylonian Astronomical and Related Texts, ed. Abraham Sachs. Brown University Studies, vol. 18 (Providence: Brown University Press, 1955), xxxiv. 5. Hunger, Lunar and Planetary Texts, no. 55, 164–72.

Remarks on Strassmaier Cambyses 400

9

of its contents. The first stems from several peculiarities in the text— namely, its complete set of Lunar Six, at least some of which must have been computed; several references to an intercalary XII2 in year 7, which actually occurred in year 8; and a reference to a year 9 of Cambyses, who died in year 8, making the year in question year 1 of Darius I. The second issue arises from disparities between recorded and actual phenomena, most famously involving the lunar eclipse on July 16, −522, details of which conflict with Ptolemy’s report and reality. These anomalies led Hunger and Pingree to conclude that the tablet was “executed in the late fifth or early fourth century b.c.” and “based in part on Diaries or other observational texts for −522/1 to −520/19 and in part on computations.”6 This conclusion rests largely on the authors’ disbelief that the techniques permitting the competent computation of Lunar Six existed in the sixth century b.c. Subsequently, Brack-Bernsen7 showed that clever, but computationally simple, Goal Year procedures existed for the computation of Lunar Six and would have required only similar data from eighteen years earlier. One object of this paper is therefore to reexamine this issue in light of BrackBernsen’s discovery. I conclude that Hunger and Pingree’s skepticism on this point is unwarranted and that the Lunar Six data in the text were probably a combination of contemporary observations and competent calculations based on data eighteen and possibly fifty-four years earlier. A consequence of this conclusion is that reasonably complete Lunar Six data must have existed from at least −540 on and perhaps as early as −576. The planetary data are uneven and generally of poor quality, but here again—at least for synodic phenomena—it appears that some data have been drawn from reports composed earlier at intervals which correspond to various Goal Years. Among these, Venus represents the longest interval, extending back fifty-six years. Similarly, the discrepancy between the reported and actual magnitude of the lunar eclipse in month IV, which the text records as almost total but actually was very nearly half as Ptolemy reports, suggests that the reported magnitude was taken from an (accurate) observation fifty-four years earlier. Thus, the planetary and lunar eclipse sections seem to combine contemporary observations with data derived from reports at Goal Year intervals earlier. 6. Hunger and Pingree, Astral Sciences in Mesopotamia, 175. 7. Lis Brack-Bernsen, “Goal-Year Tablets: Lunar Data and Predictions,” in Ancient Astronomy and Celestial Divination, ed. Noel Swerdlow, 149–77 (Cambridge, Massachusetts: MIT Press, 1999) and Lis Brack-Bernsen and Hermann Hunger, “TU 11: A Collection of Rules for the Prediction of Lunar Phases and of Month Lengths,” SCIAMVS 3 (2002): 3–90.

10

John P. Britton

In short, from such considerations and the several archaic conventions reflected in the text, it seems likely that the text was written during the span of its contents, perhaps towards the end of year 7 and that it drew extensively on Goal Year methods and earlier records for some of the data it reports. That the text should place a XII2 month in year 7 remains an anomaly8 under any dating, but an incompetent one if the text were written after year 7 and one seemingly at odds with the consistent quality of the Lunar Six. Similarly the reference to a year 9 Cambyses, would be incompetent if the text were written after Darius’s reign was established, but a simple extrapolation if written during the reign of Cambyses. Obverse: A. Lunar Six The entire obverse is devoted to Lunar Six which are presented in three columns of four months with the last month squeezed in across the bottom of columns two and three. Month I begins with 1 2 3 4 5 6 7 8

Year 7 Cambyses Month I, 1 dir, the Moon appeared in 1 beru (30uˇs), na[n] night 13 dir, in 9[uˇs] , me ´ 13, 2;30[uˇs] , ˇ su night 14 dir, in 8;20[uˇs] me 14, 7;40[uˇs] , na 27 dir, in 16[uˇs] .

Inserted in lines 2, 4, 6, and 8 after the first mention of each date is “dir,” which is not repeated in the subsequent months. Hunger notes that this is not the usual position for a weather comment, which typically follows the designation of the specific phenomenon.9 In this context dir must have thus had a different meaning from “clouds.” I suspect that here it has the meaning of “extra” or “additional,” implying that a day was added to the computed date of the beginning of the month and consequently to subsequent dates.

8. An intercalary 7 Cambyses would have caused successive intercalations separated by two years. Such intercalations occurred during the reigns of Nebuchadnezzar and his successors but had not occurred for thirty years. BM 75383 and BM 75521, among others, attest a XII2 in year 8 as expected. Perhaps significantly, all of the earlier years at Goal Year intervals, seemingly drawn upon in compiling the text, had XII2 months. 9. Hunger, Lunar and Planetary Texts, 170.


11

For subsequent months the data is similar but reported in abbreviated format: Table 2.1: Format of Reporting Lunar Six Month, Beginning date (30 or 1) nan First Lunar Four Date, Duration, type Next Lunar Four Date, Duration, type Next Lunar Four Date, Duration, type Last Lunar Four Date, Duration, type kur date, Duration [but no designation of type]

II 30 23[uˇs] na[n] ´ 13, 8;20[uˇs] ˇ su Night 14, 1[uˇs] me 14, 1;40[uˇs] na Night 15, 14;30[uˇs] ge6 27 21[uˇs] [kur]

Dates for me and ge6 , as noted, are designated by “night n,” so that ´ the potential ambiguity of an event bounded by sunset is avoided. ˇ su and na, being sunrise events, require no similar clarification.

Table 2.2: Text [Obverse] Mo I II III IV V VI VII VIII IX X XI XII XII2 (!)

d(nan ) nan 1 30.0 30 23.0 30 18.5 1 27.0 30 10+[x] 1 15.7 1 16.7 30 12.7

n(me) me 13 −9.0 14 −1.0 14 −9.5 14 −4.0 15 −2.3 15 −1.3 14 −7.5 15 −1.0

1 30 1

14 13 13 13

22.0 15.5 19.0

ge6 8.3 14.5 5.0 8.5 8.5 8.7 3.0 14.0

10.3 −17.3 1.7 −5.3 10.0 −[1]1.5 3.0

´) ˇ ´ d(ˇ su su 13 −2.5 13 −8.3 14 −4.0 13 −11.0 14 −3.5 13 −11.0 13 −6.5 13 −15.0

na 7.7 1.7 8.5 4.0 11.0 4.0 12.0 5.0

d(kur) 27 27 27 27 27 28 26 26

kur 16.0 21.0 24.0 15.0 22.5 15.0 22.0 26.0

13 13 12 13

5.0 7.0 0.0 5.7

27 27 27 27

24.0 17.0 12.0 21.0

−4.7 −10.5 −5.3

Table 2.2 shows the substantive contents of the text rearranged in tabular form by month. All data is missing for month IX and some for month X; otherwise, it is remarkably complete. The first column after the month gives the date of first visibility, expressed as either day 1, following a “regular” 30-day month, or as day 30 of the previous, 29day, “hollow” month. Next is nan , the interval (MS−SS) in time degrees (uˇ s) from sunset to moonset. The next three columns give successively: the date of the “night” beginning with sunset when the moon last rose

12

John P. Britton

before sunset, n(me), followed by the interval MR−SS that day (−me), and then the corresponding interval for the following day ge6 .10 These are followed by three similar columns for sunrise events giving: the date ´ ); the interval MR−SR on which the moon last set before sunrise, d(ˇ su ´ ); and the corresponding interval the following day (na). that day (−ˇ su Finally the last two columns give the date when the moon was last visible before sunrise and the interval between SR−MR (kur) on that day. In month VI the date of kur, read as 28, is pitted on the tablet and could be 27. Month XII also includes the anomalous and unexplained numbers “25 23” immediately before d(kur) = 27. Of the sixty-eight legible visibility intervals, thirty-seven are reported with a precision of whole time-degrees; fourteen with a precision of half a degree; and seventeen with a precision of one third of a degree. Interestingly, eight of the eleven preserved na and all but one of the kur are recorded as integers, while fractional data are more evenly distributed among other phenomena. It seems plausible that actual measurements were mainly recorded with a precision of whole and, less frequently, half degrees, while fractional data with endings of one-third or two-thirds of a degree resulted from calculations. If so, then more than 25% of the Lunar Six — a reasonable proportion — would have been calculated, but relatively few of the calculated intervals were na and even fewer were kur.

Table 2.3: Adjusted Calculations GN 5915 5916 5917 5918 5919 5920 5921 5922 5923 5924 5925 5926 5927

d(nan ) nan 1 29.3 30 25.9 30 20.5 1 24.1 30 13.1 1 12.7 1 15.4 30 12.1 1 21.2 30 16.1 1 21.3 30 11.9 1 18.8

n(me) me 13 −5.7 14 1.1 14 −6.8 14 −3.3 15 −2.4 15 −1.6 14 −7.0 15 −1.1 14 −5.0 14 −10.6 13 −16.8 14 −5.3 13 −11.3

ge6 8.7 15.1 5.9 6.5 5.3 6.3 2.2 12.6 11.8 7.8 1.3 11.2 4.6

´) d(ˇ su 13 13 14 13 14 13 13 13 13 13 13 13 13

ˇ ´ su −2.4 −7.5 −2.4 −9.2 −3.1 −11.8 −5.3 −13.8 −4.0 −10.9 −4.2 −9.4 −5.0

na 5.9 2.3 10.5 4.9 11.5 3.0 10.9 3.6 12.8 3.3 5.8 −0.6 3.9

d(kur) 27 27 27 27 27 27 26 26 26 27 27 28 27

kur 15.5 21.6 28.7 17.6 22.6 12.5 20.4 29.3 23.6 18.3 15.1 13.1 18.7

10. The text also gives the dates of ge6 and na, but since these are always one ´ , they have been omitted to simplify these tables. day later than those for me and ˇ su


13

Table 2.3 shows the same data calculated by means of Huber’s visibility programs.11 Meaningful results can be obtained only if care is taken to compare corresponding visibility intervals rather than simply visibilities for the dates reported. Comparison of corresponding intervals results in two types of potential adjustments. One involves dates for the beginnings of months which differ because of marginal visibility conditions. Such an adjustment affects all subsequent dates in that month. The other, also involving marginal visibilities, places the date of me or ˇ ´ a day earlier or later than computed. su The first adjustment occurs in months I and IV when initial calculations made the lunar crescent marginally visible by Huber’s criteria one day earlier than day 30 given in the text. The initial day of months I and IV had nan s of 11.8uˇs and 12.2uˇs, respectively. However, the differences, dh, from the critical Moon-Sun altitude difference necessary for visibility by Huber’s criteria are only +0.1 ◦ and +0.2 ◦ in the two cases, so the later dates and corresponding nan s in the text are entirely plausible. These adjustments require reductions of one day in the dates of the other phenomena in the months and change the calculated beginning dates of the following months from “1” to “30.” The second adjustment occurs in months II and XII. In month II, me (+1.0uˇs) should actually be ge6 and its date lowered by a day, but the text reflects a small me (−1.0uˇs) instead. Similarly in month XII, ´ , the date of which should therefore na (−0.6uˇs) should actually be ˇ su be a day higher, but here the text records na as zero, explicitly noting the marginal visibility condition. Data affected by these adjustments are shown in bold. Table 2.4 shows the resulting errors (Text−Calculated Value) followed by a few summary statistics. These are remarkably free of gross errors. Apart from the previously discussed marginal visibilities at the beginnings of months I and IV and the possible error in the reading of the date of kur in month VI, there are only three date errors, all in month XII, when the dates of both Lunar Four and kur are all a day earlier than the computed dates—a difference consistent with the recorded visibility intervals. The results reflect recorded intervals that are systematically larger on average by roughly 34 of a degree than the calculated intervals. Except for one kur, maximal errors are less than 4uˇs. Standard deviations are roughly ±1uˇs for the Lunar Four; ±1.5uˇs for nan ; and roughly ±2uˇs for kur, all about as good as one might expect, if not better. Fractional uˇ s intervals with a precision of 31 account for roughly 13 of nan , me, and 11. CRESDAT and BABSIX, reflecting updated expressions for ∆T.

14

John P. Britton

Table 2.4: Textual Values − Calculated Values Mo 1 2 3 4 5 6 7 8 9 10 11 12 13 Avg. Max. Min. SD n 3

int.

d(nan ) nan 0 0.7 0 −2.9 0 −2.0 0 2.9 0 0 3.0 0 1.3 0 0.6

n(me) me 0 −3.3 0 −2.1 0 −2.7 0 −0.8 0 0.1 0 0.3 0 −0.5 0 0.1

´) ge6 d(ˇ su −0.4 0 −0.6 0 −0.9 0 2.0 0 3.2 0 2.4 0 0.8 0 1.4 0

0 0 0

0 0 −1 0

2.5 0 0.4 0 −1.2 −1 −1.6 0 0.7 3.2 0 −1.6 −1 1.4 33% 42%

0 0

0.7 3.6 0.2 0.8 3.6 −2.9 1.5 30% 50%

0 −1

−0.5 0.0 −0.2 −0.9 0.3 −3.3 1.0 36% 40%

ˇ ´ su −0.1 −0.8 −1.6 −1.8 −0.4 0.8 −1.2 −1.2

−0.5 −1.1 −0.3 −0.7 0.8 −1.8 0.6 27% 40%

na 1.8 −0.6 −2.0 −0.9 −0.5 1.0 1.1 1.4

d(kur) 0 0 0 0 0 1 0 0

1.7 1.2 0.6 1.8 0.5 1.8 −2.0 1.0 25% 67%

0 0 −1 0 1 −1

kur 0.5 −0.6 −4.7 −2.6 −0.1 2.5 1.6 −3.3

1.9 −1.1 2.3 −0.3 2.5 −4.7 1.9 0% 92%

´ and na, and none of the kur. Conversely, integer ge6 , but only 41 of ˇ su ´ , but 32 of intervals account for 12 of nan , roughly 40% of me, ge6 and ˇ su na and nearly all (92%) of kur. Seemingly, a different procedure was involved in securing the data reported for kur and perhaps a somewhat different method was used for na, as well. All in all, the comparison reflects a remarkably careful and competent compilation. Figures 2.1–2.4 further illustrate the remarkable quality of the text’s visibility intervals. Similar charts of the Lunar Four and their components can be found in Brack-Bernsen12 However, here we see that the quality of the Lunar Four data extends also to the more volatile and observationally challenging nan and kur data as well.

12. Brack-Bernsen, Babylonischen Mondtheorie, 100–103. Brack-Bernsen, “Lunar Data Recorded on the Babylonian Goal-Year Tablets,” 18.


Figure 2.1: Comparison of Calculations

NAN

15

from Strm. Camb. 400 with Modern

Figure 2.2: Comparison of ME+GE6 from Strm. Camb. 400 with Modern Calculations

Figure 2.3: Comparison of ME+GE6 from Strm. Camb. 400 with Modern Calculations

16

John P. Britton

Figure 2.4: Comparison of Calculations

KUR

from Strm. Camb. 400 with Modern

The computation of these predictions is explained by a set of Goal Year procedures, discovered and described with increasing detail and textual support by Brack-Bernsen. A key element in these procedures ´ +na represented a day’s was recognition that the sum of me+ge6 or ˇ su change in the corresponding visibility phenomenon. This recognition leads to the conclusion that the change of these phenomena over 223 months, or roughly 6,585 31 days, should be 13 of such sums. A second and more remarkable component was recognition that visibility phenomena at sunset should reflect the same changes as those at sunrise six months earlier (and vice-versa). This correlation implied that changes in nan and kur could be calculated at two-hundred and twenty-three month intervals from appropriate Lunar Four six months earlier. The specific rules, discovered or inferred by Brack-Bernsen, are as follows: ( ´ + na)i−229 if (nan )i ≥ 10uˇs su (nan )i−223 − 31 (ˇ (2.1) (nan )i = ´ + na)i−229 if (nan )i < 10uˇs (nan )i−223 + 23 (ˇ su mei = mei−223 + 13 (me + ge6 )i−223 (ge6 )i = (ge6 )i−223 − ˇ í = su

1 3 (me

+ ge6 )i−223

ˇ ´ i−223 − 31 (ˇ ´ + na)i−223 su su ´ + na)i−223 nai−223 + 13 (ˇ su

nai = ( kuri−223 − 23 (me + ge6 )i−229 kuri = kuri−223 + 13 (me + ge6 )i−229

if kuri ≥ 10uˇs if kuri < 10uˇs

(2.2) (2.3) (2.4) (2.5) (2.6)

Although cleverly conceived, these are very simple to apply and require only visibility data 223 and 229 months earlier to compute any


17

of the Lunar Six. The rules also show that fractional endings of thirds of a degree are likely whenever visibilities are calculated. Thus, the values found in the text (plus a few more) are probably the result of calculations, rather than observations. Getting the days of the Lunar Six right turns out to be trickier than calculating the visibility intervals, and the procedures actually used are still unclear. Brack-Bernsen and Hunger13 describe two potential techniques for determining the dates of nan . One uses only successive current values for nan , while the other draws upon data 223 months earlier and employs equation (2.1) to obtain the current nan . Combining elements of both, I find that the following single rule yields as good of an agreement (3.4% differences) with calculations from modern data as seems obtainable; it also yields dates which, adjusted for marginal visibilities in months I and IV, agree with the text. This rule, which I call “R+,” can be expressed as follows: ´ +na)i−229 < 10uˇs, If d(nan )i−223 = 1 and (nan )i−233 − 31 (ˇ su or if (nan )i > (nan )1−i , then d(nan )i = 1; otherwise, d(nan )i = 30.

(2.7)

In words, the rule is more cumbersome: If the month 224 months (18 years and one month) prior to the given month (i.e., month i − 224) is full and an addition is required in computing the nan of the month, ´ + na)i−229 < 10, or if the nan of the month su (i.e., (nan )i−233 − 31 (ˇ is greater than nan of the preceding month, the month preceding the month is full (d(nan )i = 1); otherwise it is hollow (d(nan )i = 30). This is not quite the same as the rule expressed in TU 11,14 which seems at least partly garbled with “full” and “hollow” perhaps reversed, but it combines the same elements, namely a criterion dependent on whether an “addition” is required in computing nan from that 223 months earlier and a comparison of successive nan . Whatever the procedure employed, it is clear that the compiler of Strm. Camb. 400 possessed powerful techniques for computing with reasonable accuracy both the dates and visibility intervals of the new lunar crescent. The procedure for determining the dates of the Lunar Four is even more obscure and warrants further investigation. However, the following rule, allowing for marginal visibilities, yields the dates in the text with 13. Brack-Bernsen and Hunger, “TU 11,” 41, 53. 14. Ibid., 14.

18

John P. Britton

one significant exception.

If

i X

d(nan )i =

0

i X

d(nan )i−669 , d(me, ˇ su, kur)i = d(me, ˇ su, kur)i−669 ;

0

(2.8) otherwise, if d(nan )i−669 = 1, then d(me, ˇ su, kur)i = d(me, ˇ su, kur)i−669 + 1, (2.9) and if d(nan )i−669 = 30, then, d(me, ˇ su, kur)i = d(me, ˇ su, kur)i−669 − 1. (2.10) In other words, if every initial date of the months through month i are the same for the year in question and three Saroi earlier, the dates of the Lunar Four and kur are also the same; otherwise, if the beginning date of the month three Saroi earlier is 1 or 30, the dates of the Lunar Four and kur are respectively one day later or earlier than their counterparts three Saroi earlier. This formula clearly needs further investigation and testing. Nevertheless, it yields precisely the dates found in the text (assuming 27 for d(kur) in month VI), except for month XII, when the text’s dates for both pairs of Lunar Four and kur are all the same day as three Saroi earlier and one day earlier than required by their associated visibility intervals. The simplest explanation for all three errors is a failure to apply the required correction described in equation (2.9). Apart from this error all the text’s dates, allowing for marginal visibilities, agree with the procedure described and are consistent with their associated visibility intervals. In short, we find in the Lunar Six described on the obverse of Strm. Camb. 400 a set of dates and visibility intervals compiled with evident competence and notable accuracy from contemporary observations and calculations based on observations extending at least 223, and possibly 669, months earlier than the contents of the text. One unavoidable conclusion is that comparable Lunar Six data must have existed at least as early as −540, if not by −576. [Added in proof: Peter Huber’s and John Steele’s recent and still-to-be published discovery that BM 55554 contains complete Lunar Six data for 12 years beginning in 14 Nebuchadnezzar (−590) and that BM 38414 contains partial Lunar Six data for −642 places the availability of complete Lunar Six data from −576 beyond doubt.]


19

Reverse: B. Planetary Synodic Phenomena The first section at the top of the reverse gives for each planet the date, place, and type of successive synodic phenomena beginning with the planet’s disappearance, Ω (in the west for inner planets), in 7 Cambyses. The phenomena are shown in Tables 2.5 to 2.9 in the order in which they appear, first as computed, then as reported in the text. Also shown are computations for earlier dates which may explain some of the disparities encountered. These are followed by potential “GY Dates” derived from the earlier dates by adding increments, here denoted “dD.” Calculated months followed by an asterisk (*) have been reduced by 1 to agree with the text’s assumption of a month XII2 in 7 Cambyses. Several of the intervals comprising these earlier dates are known from later Goal Year texts, notably seventy-one years for Jupiter, forty-seven years for Mars, and fifty-nine years for Saturn. For inner planets, however, better comparisons are returned from intervals of fifty-six years for Venus and six years for Mercury. For Venus, synodic dates after fifty-six years should fall twenty-eight days earlier or effectively two days later in the month, compared with four days earlier in the month after eight years. The thirty-two year interval for Mars and six year interval for Mercury, equivalent to nineteen synodic periods are also attested in BM 45728, possibly written in 28 Nebuchadnezzar (−576) but in any event probably in the first half of the sixth century.15 The phenomena described are familiar “Greek Letter” phenomena, but they differ from planet to planet and also vary from the complete set of standard phenomena encountered in later texts. Generally full cycles from disappearance (Ωi ) to disappearance (Ωi+n ) are recorded, although for Venus the subsequent Ω is omitted, perhaps because on the same day as that Ω, Venus reappeared in the east (Γ). For Mercury, whose data are squeezed on the edge, there seems to be room for all three complete cycles which occurred in 7 Cambyses because in the first cycle Mercury was invisible in the east so that Γ and Σ were omitted. Only for Jupiter are both stations recorded; for Mars only Φ is recorded, while for Saturn and both inner planets, no station is recorded. For none of the outer planets is opposition (Θ) recorded. Generally, the phenomena recorded here reflect familiar astronomical events, but at this time the standardization of these phenomena had not yet been completed. For each planet except Mercury (whose reported synodic phenomena all fall within 7 Cambyses), the statement “ˇ se dir” (month XII2 ) separates descriptions of synodic phenomena in 7 Cambyses from those in 15. John Britton, “Treatments of Annual Phenomena in Cuneiform Sources,” in Under One Sky, eds. John M. Steele and Annette Imhausen, Alter Orient und Altes Testament, vol. 297 (M¨ unster: Ugarit Verlag, 2002), 59–61.

20

John P. Britton

subsequent years. Presumably, this practice indicated that the months cited in 8 Cambyses assume an intercalary XII2 in year 7. Thus this section appears entirely consistent with the Lunar Six on the obverse in making 7 Cambyses intercalary, contrary to expected and attested practice. This and other discrepancies between text and calculation are highlighted in bold in tables 2.5 through 2.9 as are the instances when drawing upon earlier phenomena gives good or at least better agreement. The most conspicuous and consistent discrepancy, already noted, is the repeated insertion of a seemingly unwarranted (and otherwise unnecessary) XII2 between data for years 7 and 8. However, it is noteworthy and perhaps significant that in every case the alternative year, n-years earlier, was in fact intercalary with a XII2 month. Another conspicuous error, noted by others, is that the date “year 9” (month II day 9) is given for Mars’ second disappearance. Cambyses died in either month I or IV of year 8, but the subsequent reign of Darius I was not securely established until month VIII of the following year, after being contested by Bardia, Nebuchadnezzar III, Darius I himself, and Nebuchadnezzar IV. Thus at the date cited the succession would have been unsettled. On the other hand, it would also have been a logical dating at any time prior to Cambyses’ death. Following the dates in Table 2.5 through Table 2.9 are comments on the quality of agreement between text and calculation. In general, I’ve considered as plausible and thus “ok,” reported dates that are several days earlier than calculated disappearances or later than calculated reappearances but dates more than a few days later or earlier than the calculated Ω and Γ are unlikely to have been observed. For Jupiter, the dates of the visibility phenomena are all “ok,” in contrast to those for stations which are respectively half a month too early and nearly a month too late (but “ok” for the day, if this last is simply an error in the month name). For Venus, the text’s dates are “ok,” except for Σ. In this case, Venus seems unlikely to have remained visible 5 days later than calculated. Considering dates 56 years earlier does not help, but in dates eight years earlier (not shown), Σ should have occurred on XII 5 in a reasonable agreement (without adjustment) with the text. For Saturn, only Ω1 is a plausible date, but dates 59 years earlier for Γ and Ω2 are respectively “fair” and “good.” For Mars, the dates in year 7 for Ω1 and Γ are plausible, while both later dates are clearly wrong—Φ by nearly a month (another poor station date) and Ω2 by a month and a half. The last might be explained as mistakenly derived from either the immediately preceding synodic cycle in which Ω1 occurred on II 9 (as in the text) or from observations 32 (II 4) or 47 (II 6) years earlier. Clearly,

Ψ Ω

29 7

25 21 23

−592 −592

11 11 11 11 12 12

5 6 10 122 1 6

II II II II II II

Ω Γ Φ

−593 −593 −592

Nebu. Nebu. Nebu. Nebu. Nebu. Nebu.

GY Date

29 7

25 21 24

D

71 years earlier (dD(71y) = 0d)

Ψ Ω

−521 −521

7 7 7 7 8 8

5 6 10 na 1* 6*

Cambyses Cambyses Cambyses Cambyses Cambyses Cambyses

M

Ω Γ Φ

RY

−522 −522 −521

Reign

Calc.

Phen.

Jupiter

JY

5 6 10 122 1 6

5 6 10 122 2 6

Text

M

29 7

25 21 23

25 4

22 22 7

D

ok ok ? yes ?? ok

ok ok ? no ?? ok

dD

ok?

185 203

172 178 195

180 198

167 173 190

Calc.

sid λ ◦

area of Virgo behind Libra

in front of Virgo behind Virgo in front of Libra

area of Virgo behind Libra

in front of Virgo behind Virgo in front of Libra

Place

γ vir α vir α lib β lib

γ vir α vir α vir β lib

NS

166 179 200 205

166 179 200 205

λ◦

ok ok

ok fair ok

ok no

ok ?? ok

δλ ◦

ok?


Table 2.5: B. Planetary Synodic Phenomena (Jupiter)

21

Ξ Ω*

Nebu. II Nebu. II

27 27

12 10

8 22 26

−577 −576

26 26 26

4 4 12 122 2 11

Nebu. II Nebu. II Nebu. II

Ω Γ Σ

−578 −578 −577

17

GY Date

9

56 years earlier (dD(56y) = -28d)

Cyrus

2

Ξ

−529

16 28 5

3 3 12

8 8 8

Ω Γ Σ

−530 −530 −529

Cyrus Cyrus Cyrus

GY Date

14 13

12 25 2

D

8 years earlier (dD(56y) = -4d)

Ξ [ Ω*]

−521 −520

7 7 7 7 8 8

3 3 12 na 1* 10*

Cambyses Cambyses Cambyses Cambyses Cambyses Cambyses

M

Ω Γ Σ

RY

−522 −522 −521

Reign

Calc.

Phen.

Venus

JY

3 3 11 122 1

3 3 12 122 1

3 3 12 122 1 na

Text

M

14

10 24 28

12 24 1 no 13

13 na

10 27 7

D

ok ?? no yes ok

ok

ok ok ??

ok ok ?? no ok na!

dD

ok?

72 330

111 102 343

58

96 88 332

57 313

94 86 330

Calc.

sid λ ◦

area of Chariot

begin (SAG) Leo area of Cancer area of Pisces

area of Chariot


area of Chariot


Place

β tau

leo γ cnc ω psc

β tau

leo γ cnc ω psc

leo γ cnc ω psc β lib β tau

NS

58

116 103 338

58

116 103 338

116 103 338 205 58

λ◦

no

ok ok ok

ok

no no poor

ok na!

no no poor

δλ ◦

ok?

22 John P. Britton

Table 2.6: B. Planetary Synodic Phenomena (Venus)

Ω

Nebu. II

24

1

8 11

−580

23 23

6 7 122 6

Nebu. II Nebu. II

Ω Γ

−581 −581

25

GY Date

8

2 4

D


Cambyses

Ω

−521

7 7

6 7 na 5*

Cambyses Cambyses

M

Ω Γ

RY

−522 −522

Reign

Calc.

Phen.

Saturn

JY

6 7 122 6

6 7 122 5

Text

M

1

8 11

29

3 13

D

no fair yes ok

ok ?? no no

dD

ok?

188

177 180

189

178 181

Calc.

sid λ ◦

area of Virgo behind Virgo

area of Virgo behind Virgo

Place

α vir

α vir

NS

179

179

λ◦

ok ok

ok ok

δλ ◦

ok?


Table 2.7: B. Planetary Synodic Phenomena (Saturn)

23

Φ Ω

−553 −552

Φ Ω

−568 −567

Nebu. II Nebu. II

Nebu. II

36 37

35

6 na 4* 3

Γ 15 22

4

2

−569

35

3

Nebu. II

Ω

−569

6 27

7

GY Date

2 3

1


Nabonidus Nabonidus

Nabonidus

6 122 4 3

Γ

−554

4

3

1

Ω

−554

Nabonidus

GY Date

14 27

8

7

D

32 years earlier (dD(32y) = +5d)

7 8 9(!)

Cambyses Cambyses Cambyses

Φ Ω

6 na na 4* 3

−521 −520

7

Cambyses

Γ

−522

7

3

Cambyses

M

Ω

RY

−522

Reign

Calc.

Phen.

Mars

JY

6 122 4 3

3

6 122 4 4

3

6 122 122 5 2

2

Text

M

12 22

4

2

10 2

12

9

12 9

13

28

D

ok yes no no

no

ok yes no no

no

ok no no no no

fair

dD

ok?

8 131

160

102

341 120

147

89

357 127

154

96

Calc.

sid λ ◦

behind Regulus

in front of Gemini in foot of Leo 122

behind Regulus

in front of Gemini in foot of Leo 122

na! behind Regulus

in front of Gemini in foot of Leo

Place

α leo

β vir

β gem

α leo

β vir

β gem

α leo

β lib

β vir

β gem

NS

125

152

89

125

152

89

125

205

152

89

λ◦

ok

ok yes

no

no

ok yes

ok

na! ok

ok

no

δλ ◦

ok?

24 John P. Britton

Table 2.8: B. Planetary Synodic Phenomena (Mars)

JY Phen. Reign RY Mercury −522 [Ω] Cambyses 7 −522 [Ξ] Cambyses 7 −522 [Ω] Cambyses 7 −522 Γ Cambyses 7 −522 Σ Cambyses 7 −522 Ξ Cambyses 7 −522 [Ω] Cambyses 7 −522 [Γ] Cambyses 7 −522 [Σ] Cambyses 7 −521 Ξ Cambyses 7 −521 [Ω] Cambyses 7 6 years earlier (dD(6y) = +17d) −528 Ω Cyrus 9 −528 Ξ Cambyses 1 −528 Ω Cambyses 1 −528 Γ Cambyses 1 −528 Σ Cambyses 1 −528 Ξ Cambyses 1 −528 Ω Cambyses 1 −528 Γ Cambyses 1 −527 Σ Cambyses 1 −527 Ξ Cambyses 1 −527 Ω Cambyses 1

M D Calc. 1 1 3 17 5 1 5 23 6 17 8 9 8 25 9 9 10 24 11 24 12 22 GY Date 12 12 3 1 4 14 5 8 5 30 7 23 8 8 8 23 10 8 11 9 12 4 ] ] ] ] ] ] ] ] ] ] 19

21

12

D

M Text [ [ [ [ [ [ [ [ [ [ 12

ok

ok

ok? dD

18 94 145 131 158 239 251 236 282 336 360

sid λ ◦ Calc. 29 103 155 140 169 248 260 246 291 346 10

152

2

band of fishes

2

foot of Leo

152

λ◦

[] [] [] [] [] band of fishes

NS

[] [] [] [] foot of Leo

Place

ok?

ok

ok

no

no

δλ ◦

Remarks on Strassmaier Cambyses 400 25

Table 2.9: B. Planetary Synodic Phenomena (Mercury)

26

John P. Britton

however, both month and day as stated are impossible. Lastly, the sole preserved date for Mercury is fine. In sum, of the fourteen dates of visibility phenomena, ten are plausible observations, while the rest might have been derived from earlier observations. In contrast, all three of the dates for stations are surprisingly inaccurate. In the case of places reported for synodic phenomena, a total of sixteen are preserved, half of which are poor or implausible—a conspicuously larger fraction than that found for dates. Of these positions, the two places for Jupiter are “ok” or better seventy-one years earlier; the three locations for Venus are “ok” fifty-six years earlier; the single place for Mars is “ok” thirty-two years earlier; and both positions for Mercury are “ok” six years earlier. Since in several of these cases the dates appear “ok” as reported but not “ok” earlier, it looks as though the reports from Goal Year intervals earlier were used to fill in the gaps in positions recorded in the more recent observational records. If we assume that reasonable agreements between text and calculation are likely to reflect actual observations, while substantial errors are likely to reflect calculations of the text’s compiler, then the following range of plausible dates for the text’s compilation emerge from this section.

Table 2.10: Plausible Compilation of Strm. Camb. 400 Planet Jupiter Venus Saturn Mars

After Year 7, Month VI Year 8, Month I Year 7, Month VI Year 7, Month VI

Before Year 8, Month VI* Year 8, Month V* Year 8, Month IV*

Except for the Σ of Venus in the Year 8 of Cambyses, Month I which could have been derived from an observation eight years earlier, there is considerable consistency suggesting that the text was compiled after Year 7 of Cambyses, Month VI and before Year 8 of Cambyses, Month IV. An additional bit of potential evidence is the appearance of the older form of “9” in the dates of Ω2 for Saturn in Year 8 of Cambyses, Month V, Day 29 and of Ω2 for Mars in Year 9(!) of Cambyses, Month II, Day 9, in contrast to elsewhere in the text (including Year 9 of Cambyses) where 9 regularly occurs in the cursive form. C: Planetary Passages The next section of the reverse contains reports of eight close approaches of the Moon to a planet or a planet to another planet. The


27

report cites dates in Year 7, followed by a description composed of the mention of the two bodies, a distance, a relative direction of the first to the second, and in two instances a time. Hunger read the first date as du6 (Month VII),16 but Hunger and Pingree had understood that it should have been read ˇ su (Month IV),17 a sign easily mistaken for du6 and securely confirmed by calculation. As noted by Hunger and Pingree, the reports appear nearly in chronological order, the exceptions being Month VII, days 12 and 11, which Hunger and Pingree suggest may have been overlooked at first writing or taken from another source of observations.

Table 2.11: C: Planetary Passages Y 7

M D 418 1

7

6

24

7

7

23

7

7

29

7

7

12

7

7

11

7

8

2

7

10

5

16. 17. 18. 19. 20. 21.

Text Moon 3 cubits behind Mercury Venus 1+x cubits above Mars at dawn Jupiter 3 cubits above Moon at dawn Venus, north side, 2 fingers to Jupiter Saturn 1 cubit in front of Jupiter Mars 2 fingers near Jupiter Saturn passed 8 fingers above Venus Mercury 1/2 cubit behind Venus

Calc Moon 9.7 ◦ behind Mercury at Moonset Venus 2.6 ◦ above Moon at dawn19 d 24, Jupiter 5.5 ◦ above Moon, 6.7 ◦ behind20 d 28, Venus 0.5 ◦ above, 0.4 ◦ ahead of Jupiter Mars 0.9 ◦ in front of Jupiter, 0.17 ◦ below, eve21 d 14 8 P.M., conj., distance Mars − Jupiter = 0.19 ◦ d 3 11 P.M., conj., Saturn 0.5 ◦ above Venus

Mercury 2.4 ◦ behind Venus, 0.4 ◦ below, dawn

Hunger, Lunar and Planetary Texts, 170. Hunger and Pingree, Astral Sciences in Mesopotamia, 175. Reading ˇ su for du6 . Venus 24 ◦ ahead, 1 ◦ below Mars 25th , Jupiter 6.1 ◦ above Moon, 6.6 ◦ ahead Saturn 5.2 ◦ behind, 1.1 ◦ above Jupiter, eve

28

John P. Britton

Table 2.11 shows the substance of the section together with calculated comparisons and notes bearing on major disparities. Presumably each report reflects an observation, since it is hard to imagine a source. However, generally the quality is pretty poor with virtually every report having some problem, whether as regards the day, the distance, or— in two cases—one of the bodies in question. However, if one accepts the proposed substitutions—Moon for Mars in #2 and Mars for Saturn in # 5—the disparities are not severe enough to call into question the validity of the entire section. As a result we can confidently conclude that the text must have been composed after the last reported passage, which narrows the range of its likely composition to the interval Year 7 of Cambyses, Month X, Day 6 – Year 8 of Cambyses, Month IV. Lunar Eclipses The last section of the reverse describes two lunar eclipses which occurred in Year 7 of Cambyses: Year 7, Month IV, night of the 14th , 1 2/3 double hours after sunset, the Moon made a total eclipse; a little remained; the north wind blew. Month X, night of the 14th , 2 1/2 double hours remaining to sunrise, the Moon made a total eclipse; during it the south and north winds blew. Table 2.12 summarizes the data as presented in the text and as calculated. Both times are reasonably correct (and averaged together almost exactly so), the stated intervals being roughly both 14 beru or 7uˇs too long, well within the range of errors typical of Babylonian eclipse timings, and making the reported beginnings of the two eclipses roughly half an hour later and earlier, respectively, than the times indicated by modern calculations.

Table 2.12: D: Lunar Eclipses Y 7

M 4

D 14

7

10

14

Text 1 2/3 beru > Sunset; nearly total lunar eclipse 2 1/2 beru < Sunset; total lunar eclipse

Calc beg. 1.43 beru > Sunset; mag 6.522 ; short Saros beg. 2.27 beru < Sunset; mag 22.2; long Saros

22. 54 years earlier, Year 28 of Nebuchadnezzar, Month XII2 , beg. 3.4 beru > Sunset; mag 11.9


29

However, the magnitude reported for the first eclipse—“a little remaining to totality”—is grossly wrong, since the eclipse was partial with an actual magnitude of only slightly more than six digits. A possible explanation is that the magnitude was taken from an accurate record of the eclipse which occurred three Saroi earlier in Year 28 of Nebuchadnezzar (−576), a year with an intercalary XII2 month. The magnitude of this eclipse—11.9 digits—agrees precisely with the description “a little remaining to totality” reported in the text. It is not impossible that the entire report of the first eclipse was derived from the earlier report, with the time of beginning adjusted to reflect a minimal Saros length of 100uˇs over whole days. However, from the accuracy of Ptolemy’s reported magnitude (below) I think it likely that the eclipse was in fact observed and that the time reported reflected a contemporary observation with the magnitude either filled in from or mistakenly confused with that of the earlier report. About the first eclipse, Ptolemy (Almagest 5.14 ) states that at “one hour before midnight in Babylon, the Moon was eclipsed from the north half of its diameter.” Here, he assumes that the indicated time refers to mid-eclipse. In fact, mid-eclipse occurred half an hour later, so Ptolemy’s time differs from the text’s by roughly half an hour, with both being wrong by half an hour in opposite directions. Ptolemy, however, accurately reports the magnitude, suggesting that the eclipse was actually observed (i.e., not obscured by weather) and that the compiler of this text may have had access to a different and less complete report of it than Ptolemy. Finally, there is nothing about the eclipse report for Month X, day 14, which suggests that it was other than observed. Both time and magnitude are correct, whereas the eclipse three Saroi earlier began 3 31 beru before sunrise. Summary and Conclusions The Lunar Six, comprising the obverse of the text, are compiled with conspicuous competence and considerable accuracy. From the fractional endings ( 13 , 23 ) it can be deduced that more than a third, but probably less than half, of the Lunar Four plus nan are likely to be computed. kur lack fractional endings of n3 uˇs and exhibit a different pattern of errors; thus kur seem to have an origin different from the others. For the rest, intervals are overstated on average by 0.7uˇs with an average scatter (std) of ±1.1uˇs. nan exhibit slightly greater scatter (±1.5uˇs) than the Lunar Four. kur, in contrast, are understated on average by −0.3uˇs with a standard deviation of ±1.9uˇs. No distinguishable difference is evident between the rest and the presumably computed errors of values with n3

30

John P. Britton

fractional endings. All in all, the Lunar Six reflect the existence of a powerful, consistent method of computation, drawing upon an evidently well-ordered and complete set of comparable data from −540. Furthermore, computed dates of the Lunar Four may have required similar data three Saroi earlier, which would push the origin and routine collection of Lunar Six data back to the first quarter of the sixth century. The planetary and lunar phenomena on the reverse are reported neither as accurately nor as consistently as are the Lunar Six. Nevertheless, many of the discrepancies encountered appear to reflect the insertion of data from plausible observations some Goal Year interval earlier. Two of these intervals (seventy-one years for Jupiter and fifty-nine years for Saturn) are the same as those found in later Goal Year texts. The others (fifty-six years for Venus, thirty-two years for Mars, and six years for Mercury) are reasonable and attested elsewhere but seem to reflect an earlier stage in the understanding of planetary behavior than that of the later Goal Year texts. Perhaps significantly, none of such earlier dates precedes the sixth century. Such earlier records appear to have been used, at least sometimes, to complete partial contemporary records, the best example being the lunar eclipse report for 7 Cambyses IV, which combines a relatively accurate time of beginning with a magnitude from 54 years earlier.

Date Issues There remain questions: when was the tablet compiled, and from what original data? Also, why is there an incorrect month XII2 in year 7, and how should we understand the incorrect reference to a year 9 Cambyses? The original data, it seems clear, were either from contemporary or earlier observations, none of which preceded the sixth century, but all of which were from years with XII2 months.23 Why this precedent should have motivated the assumption of a XII2 month in year 7 is unclear, but that this was entirely coincidental seems unlikely. The reference to 9 Cambyses, as noted, makes sense if and only if the text were written before Darius I was securely established. Otherwise we should have to credit the author with a gross chronological error, very much at odds with the competence demonstrated in the Lunar Six section. This firm limit, effectively 1 Darius, month VIII, can probably be pushed back to before 8 Cambyses, month V (4* in Table 2.5 through Table 2.10) on the evidence of gross errors in the dates of planetary visibilities. 23. Brack-Bernsen, review of Astral Sciences, 246, notes the XII2 a Saros earlier in 15 Nabonidus (−540), and suggests that this might explain the XII2 in this text, observing that “similar irregularities are seen in some of the Goal Year tablets.”


31

In the other direction, the reports of planetary passages cannot have been written before 7 Cambyses, X 5, while the second lunar eclipse appears to have been observed ten days later. From such evidence the text appears likely to have been compiled some time after 7 Cambyses X 15 and before 8 Cambyses V. If it were compiled in 8 Cambyses, it is difficult to imagine the author being unaware that 7 Cambyses was a normal (12 month) year. Rather, it seems likely that the text was compiled in the last months of 7 Cambyses, when the possibility of a decreed XII2 was not yet foregone. In any event, the text was all but certainly contemporary with its contents. Against such a contemporary date, Hunger and Pingree note that (a) 150 years separate this data from the next complete set of Lunar Six for −372; (b) no plausible method for computing Lunar Six was (at least widely) known at the time; and (c) certain terminology in the text is more characteristic of the later period. The first consideration, as the authors themselves note, is hardly determinative, in view of the paucity of textual material from the fifth and fourth centuries. The second consideration has been effectively removed by Brack-Bernsen’s discovery and illumination of Goal Year methods for computing Lunar Six, which would have been well within the competence of knowledgeable sixthcentury scribes, a discovery still imperfectly understood when Hunger and Pingree were finishing their book. Finally the last argument rests principally on the text’s use of e for ‘above’ as an abbreviation of elat and of d an for Mars alongside of .salbatanu.24 However, both forms appear regularly in the Diary for −567, which also consistently uses the cursive form “9,” in contrast to the text’s occasional use of the older nine-wedge form. Thus, there appears to be no compelling reason to reject a contemporary date for the text. The significance of this conclusion is that, as a contemporary document (as opposed to a mish-mash of contemporary and later elements), the text provides a welcome glimpse into astronomical practices in the late sixth century, for which other sources are sorely lacking. In particular we see that by this date, Goal Year methods for computing Lunar Six and especially for determining when individual months would begin were well established and supported by a systematically organized and available body of historical data extending back to at least −540 and perhaps to the first half of the century. In contrast planetary records and procedures seem to have been less advanced. Goal Year intervals were evidently known for each, but with some differences from those later incorporated in Goal Year texts. Thus we find no evidence of the 24. Hunger, Lunar and Planetary Texts, 173.

32

John P. Britton

83 year period for Jupiter or the 47 year period for Mars, while for Mercury a six year interval, previously encountered in BM 45728 from early in the sixth century, still seems to have been employed. Observations of the planets and their recordings also seem to have been more haphazard than those for the Lunar Six, as evidenced especially by the errors encountered in the reports of planetary conjunctions. All in all, the treatment of planetary phenomena appears considerably less advanced than will eventually be reflected in Goal Year texts and Almanacs. References Brack-Bernsen, Lis. Zur Entstehung der babylonischen Mondtheorie: Beobachtung und theoretische Berechnung von Mondphasien. Boethius, vol. 40. Stuttgart: Franz Steiner Verlag, 1997. ———. “Goal-Year Tablets: Lunar Data and Predictions.” In Ancient Astronomy and Celestial Divination, ed. Noel Swerdlow, 149–77. Cambridge, MA: MIT Press, 1999. ———. “Ancient and Modern Utilization of the Lunar Data Recorded on the Babylonian Goal-Year Tablets.” In Actes de la Ve`me Conférence Annuelle de la SEAC, edited by Mariusz Ziólkowski, Arnold Lebeuf, and Arkadiusz Soltysiak, 13–39. SWIATOWIT Supplement Series H: Anthropology, vol. 2. Warsaw: Warsaw University Institute of Archaeology, 1999. ———. Review of Astral Sciences in Mesopotamia, by Hermann Hunger and David Pingree, Archiv f¨ ur Orientforschung 48 (2001):244–47. Brack-Bernsen, Lis and Hermann Hunger. “TU 11: A Collection of Rules for the Prediction of Lunar Phases and of Month Lengths.” SCIAMVS 3 (2002): 3–90. Britton, John. “Treatments of Annual Phenomena in Cuneiform Sources.” In Under One Sky, edited by John M. Steele and Annette Imhausen, 21–78. Alter Orient und Altes Testament, vol. 297. M¨ unster: Ugarit Verlag, 2002. Epping, Josef. “Sachliche Erkl¨ arung des Tablets No. 400 der CambysesInschriften.” Zeitschrift f¨ ur Assyriologie 5 (1890): 281–88. Hunger, Hermann, ed. Lunar and Planetary Texts. Vol. 5 of Astronomical Diaries and Related Texts from Babylonia. Denkschriften ¨ Osterreichische Akademie der Wissenschaften Philosophisch¨ Historische Klasse, vol. 299. Vienna: Verlag der Osterreichischen Akademie der Wissenschaften, 2001. Hunger, Hermann and David Pingree. Astral Sciences in Mesopotamia. Handbuch der Orientalistik, Erste Abteilung: Nahe und der Mittlere Osten, vol. 44. Leiden: Brill, 1999.


33

Kugler, Franz. Sternkunde und Sterndienst in Babel I: Babylonische Planetenkunde. Munster in Westfallen: Aschendorff, 1907. Oppert, Jules. “Une texte babylonien astronomique et sa traduction grecque d’apres Claude Ptolémée.” Zeitschrift f¨ ur Assyriologie 6 (1891): 281–88. Pinches, Theophilus and Johann Strassmaier. Late Babylonian Astronomica and Related Texts. Edited by Abraham Sachs. Brown University Studies, vol. 18. Providence: Brown University Press, 1955. Strassmaier, Johann. Inschriften von Cambyses. Vol. 9 of Babylonische Texte. Leipzig: Eduard Pfeiffer, 1890.

Ancient Chronology’s Alpha and Egyptian Chronology’s Debt to Babylon Leo Depuydt Brown University

One often reads that ancient Egyptian chronology serves as the backbone for the rest of ancient Near Eastern chronology in the years b.c. That premise is true to an extent. But it is too little realized—and hardly ever expressed—that the foundation of Egyptian chronology lies outside Egypt—in Babylon. The theme recommended for this festive volume by its editor to participants is the effect of Babylonian culture outside Babylonia. While the present contribution does concern a kind of influence, the influence concerns the loss and survival of ancient sources and the effect of these on the analysis of ancient history by modern scholars. The modalities of this loss and survival have inevitably made Egyptian chronology and, in fact, all of ancient Near Eastern chronology dependent on Babylonian astronomy for its deepest foundation, its Alpha. The present contribution presents a search for Egyptian and all of ancient chronology’s Alpha. In addition, it will be useful to present the stark outlines of the reigning Model of ancient chronology that is responsible for the dates in textbooks. The discipline of ancient studies would be stronger if more people understood how this Model works and why most scholars are convinced of its reliability. This paper contains only a few bibliographical references. Such an omission would normally be taboo in a scholarly publication. However, having written on all kinds of details regarding ancient chronology, I feel that the need has grown ever more urgent in recent years for contributions that highlight the basic structure of ancient chronology—not only its Alpha but also the skeletal outlines of the Model that is based on the Alpha. For example, most Egyptologists know that Ramses II flourished in the thirteenth century b.c. Yet, when asked point blank how we know this fact, hardly anyone has a ready answer. There seems to be a lack of awareness about the foundations of the field. Peripheral detail, including extensive bibliographical references, can serve only to distract from fundamental issues 35

36

Leo Depuydt

in a contribution subject to limitations of space. Obviously, other writings on chronology constitute a necessary complement to an account of the present type. Furthermore, a shortened adaptation of this text addressed to a wider audience has appeared in the July/August 2005 issue of the magazine Archaeology Odyssey. All in all, by its mere topic, the present article would seem to be a suitable tribute by an Egyptologist to an Assyriologist whose main interests include the Babylonian Astronomical Diaries. I hope that the article’s worth rises to the same standard of suitability. Alice Slotsky’s history and my own as students of antiquity first overlapped when we were both graduate students at Yale University and when, as a senior lector of Coptic and Syriac, I attended Alice’s comprehensive oral exams, which dealt in large part with Babylonian Astronomical Diaries. Our paths have crossed again at Brown University, where we both teach. Meanwhile, I have developed an interest in chronology that includes the Diaries. I greatly value my personal and professional acquaintance with Alice and wish her many more productive years in teaching and research. Ancient history books are full of dates. Rarely does anyone stop to wonder about them. Can the dates be trusted? Is there any chance we live with a false conception of when specific events occurred in antiquity? History books do not explain how the dates contained in them are determined. Chronology is the field devoted to the study of dates. Many treatises on ancient chronology are in existence, most not without merit. They address multiple facets regarding the time of ancient events. Among those facets are general topics such as eras, calendars, lunar cycles, regnal year counting, co-regencies, and specific topics such as the date of a certain historical event or the order in which certain kings reigned. What is generally lacking in these histories is the probing of chronology. Chronology is a conceptual structure gradually and incrementally built up from the first principles that serve as its foundations. If the foundations crumble, the whole building comes down. In a different metaphor, history is like a body, and chronology is like its skeleton. The foundation of chronology is the backbone. It is not immediately obvious from looking at a body that everything is held together by the spine. For many years now, the modern view of the ancient world has settled on a set of dates that seem to have attained general consensus. Many if not most dates will of course remain approximate. One reads that the Great Pyramid of Giza was built around 2500 b.c. and not, say, around 3000 b.c. or 2000 b.c. Few would contest this assertion. But how do we know it? The question is not answered in the history books.

Ancient Chronology’s Alpha

37

There exists at this time no self-contained account of the foundations of ancient chronology. In regard to ancient dates, only rarely is something applied by so many understood by so few. Is there any way by which ancient history could have been hijacked years ago by a band of conspiring chronology whizzes setting into motion the endless repetition of wrong dates for past events? In 45 b.c. Julius Cæsar instituted the Julian calendar we still use today. It was slightly modified by Pope Gregory XIII in 1582 and is now known as the Julian-Gregorian calendar. This calendar offers a kind of continuity from 45 b.c. to the present time that makes chronology of little concern to the historian of such topics as Charlemagne or the Renaissance. Chronology does not mean the same thing to b.c. historians as it does to a.d. historians. Chronology demands a much higher degree of attention and energy from b.c. historians. The present essay concerns the foundations of chronology for the era b.c. The special focus is on ancient Egypt. The chronology of the era b.c. is a structure. This structure is articulated into a number of clearly definable steps. The steps come in a fixed order, each step following from the previous one. Naturally, there ought to be a first step. That first step is the true origin, the Alpha, of ancient chronology. For the cause of ancient chronology specifically and in the interest of scientific rigor in general, few things matter more than the identification of the Alpha and the calibration of its exactitude. The structure of chronology for the era b.c. may be called the Model. The term “model” conveniently evokes certain connotations. First, models are put together by the insightful efforts of inspired human beings. They are constructions of some kind. Second, models can be tinkered with. They can be changed. They can be improved. Third, models inspire repeated imitation. The Model of ancient chronology is responsible for the fact that all the history books agree roughly when Ramses II reigned. Ancient historians rely on a handful of scholars interested in chronology to watch over and maintain the Model. Even so, the Model is hardly ever contemplated by anyone in its full scope. Yet, it seems firmly in place. It is a kind of hidden command center that steers and controls the dating of ancient events in all the books. How can something so influential lie so deep below the surface? And what is its ultimate origin, the Alpha? Most importantly, one may ask: “Is the Model true?” In answer to this question, a crucial and absolute limitation is valid. The Model is inductive. It is an explanation derived from the observation of a large number of facts. Like the laws of nature, which are all inductive, the Model is therefore only probable. Increased observation may produce

38

Leo Depuydt

increased probability and even near certainty. But it can never wholly divest itself of probability. Absolute certainty is too much to hope for under any circumstance. Only the deductive derivations of mathematics and logic are absolutely certain. Even then, deductive derivations are not based in fact. History and chronology exhibit two handicaps in comparison with other inductive fields of study such as biology and geology. The first handicap is non-repetitiveness. Simply put, we cannot take Egyptian history or chronology to a laboratory and duplicate it in order to verify that our current understanding is correct. The second handicap is indirectness. Often in history or chronology, as opposed to biology or geology, the facts cannot be observed directly. Rather, one needs to rely on reports by ancients of what happened. But can we take their word for it? Might certain factors have made their accounts less than trustworthy? These handicaps set apart the historical method from the strictly scientific method. The historical method is a kind of diminished scientific method. The sources are paramount. Historians of antiquity are in a way source technicians. What differentiates professional students of antiquity from amateurs is their ability to evaluate primary sources. The key questions in ancient history always include: What little do the sorry tatters of surviving evidence tell us with certainty, and much more often, what do they definitively not tell us? Modern historians face an embarrass of sources and must be selective. By contrast, most evidence for the ancient world has been lost. Every tiny little scrap counts. Absolute certainty is too much to hope for with regard to the Model, as it is for all of history and chronology. Having looked at the evidence from many angles for some time now, I personally do not see how the existing Model could ever change in any substantial way. But that is just one opinion. In the absence of absolute certainty, inductive explanations derive strength from consensus. Consensus is the unforced agreement between observers at once independent and disinterested. At first, there seems to be cause for alarm. There is definitely no one hundred percent consensus about the Model. Alternative chronologies do exist. These chronologies lead a life in the margins of the field. Rarely do they receive attention in mainstream literature. Nor have they made as much as a dent in the received chronology of the handbooks. Yet, competing chronologies have wide followings. It almost seems as if there are more of them than there are of us. By their mere existence, alternative chronologies seem to deprive the dominant chronology of any claim to consensus. But is consensus really the accord of everyone involved? There are other ways of quantifying consensus. One might think, for example, of an agreement between two people as one unit of consensus.


39

Alternative chronologies all agree to disagree with the accepted chronology. But as far as I know, no positive proposal for a more detailed alternative chronology has ever had more than one proponent. The quantity of consensus for all of these alternative chronologies is therefore zero. And zero is still infinitely smaller than one, as dividing by zero shows. The following question applies to ancient chronology as to any field: Are staid academic circles sometimes shielding themselves unjustifiably from innovation by instinctive reflexes of self-preservation? From the outside, the ivory tower may at times seem a little impenetrable. As an insider, I do not believe that the most common-sense solution for a problem can ever be prevented from rising to the surface. Short term resistance seems natural. Also, as Max Planck once wrote, not without a hint of cynicism, the opponents of a theory are rarely won over; they just die. Recent developments in Egyptian chronology itself support the notion that academic consensus can change and change fast if need be. Until the 1930s and 1940s, the three pyramids of Giza were still often dated to the fourth millennium b.c. or even earlier. In the early twentieth century, luminaries such as Flinders Petrie and Gaston Maspero never suspected the possibility of a much later date. Some of the senior scholars in the field may recall these early dates as textbook fare. Meanwhile, in the 1920s and 1930s, Egyptologists such as Alexander Scharff relied on their well-developed sense of the size of the archaeological evidence in suspecting that Egyptian history, the time period from which we have written sources, spanned two Sothic cycles of about 1460 years, not three Sothic cycles. The Sothic cycle is defined below. The subtraction of one full cycle of about 1460 years brought down the beginning of Egyptian history from around 4200 b.c. to the early third millennium b.c. Then, just as Scharff’s view seemed to be gaining strength on its own, two types of evidence surfaced in the 1930s and 1940s that changed the landscape of Egyptian chronology of the third and second millennium b.c. almost overnight. They are, first, Assyrian year-lists for the first millennium b.c. and the late second millennium b.c. and, second, radiocarbon dating. In the Assyrian year-lists, each year is named after an official called the limu whose main function was eponymous, that is, to lend his name to the year. The year-lists are not king-lists, even if kings sometimes functioned as the limu for the year. Alan Millard has collected and edited all the tablets containing the year lists.1 1. Alan Millard, The Eponyms of the Assyrian Empire, 910–612 B.C. (Helsinki: Neo-Assyrian Text Corpus Project, 1994).

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To this day, these two types of evidence remain veritable pillars of the Model. They are the last lines of defense when all else fails. The only way to discount them is to assume error or even deliberate falsification. I have therefore not been surprised to see accusations of fraudulent behavior being leveled against radiocarbon dating experts. The focus is on the reigning Model for ancient chronology, that is, more or less for chronology of the era b.c. There is no denying that this Model is the generator—some might say it is the culprit—of the accepted chronology of all the history books. There exists no concise description of the Model in its totality. This absence does not promote and hardly even permits a broad-based evaluation of ancient chronology. It leaves ancient historians defenseless. It limits the potential for a wider consensus. Whether the Model is true or not is irrelevant here. The aim is transparency, not persuasion. The structure of the Model is what it is, and there is no denying that. The search is for the Alpha, or origin, of the Model. In identifying the Alpha, the observation that must precede all other observations already introduces a critical complication. The origin of ancient chronology is in the course of shifting. This fluctuation seems like a bad start and cannot inspire confidence. How can a structure be solid if its foundations are shifting under it? The answer is the accidental ways in which the evidence from antiquity has come to light. It is the incomplete nature of archaeological evidence which is responsible for the complication. The vicissitudes of survival of the evidence have necessitated a shift in the foundations of ancient chronology. I have described this shift in more detail in another article.2 According to Goethe, the history of a science is the science itself. The Model and the aforementioned on-going shift in its foundation cannot be fully understood without a grasp of how the Model originated and developed. The chronology of the era b.c. begins soon after the era b.c. itself. To be singled out is the Latin translation and expansion by the early Christian scholar Jerome (ca. a.d. 340–420) of the Greek Chronicle by Eusebios of Cæsarea in Palestine (ca. a.d. 260–340). Counting years as “b.c.” and “a.d.” did not yet exist in Eusebios’s and Jerome’s time. Instead, to count years, they used techniques such as identifying years as first, second, third or fourth in Olympiads, that is, periods of four years of which the first began in 776 b.c. Olympiads derive from the 2. Leo Depuydt, “The Shifting Foundation of Ancient Chronology,” in Modern Trends in European Egyptology: Papers from a Session Held at the European Association for Archaeologists Ninth Annual Meeting in St. Petersburg 2003, ed. AmandaAlice Maravelia, British Archaeological Reports International Series, vol. 1448 (Oxford: Archaeopress, 2005), 52–63.


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Greek tradition of holding athletic games every four years at the site of Olympia, that is, the Olympic games. Jerome’s Chronicle became the basic textbook of ancient history and chronology in the West for a thousand years and more. But its chronology for the era b.c. is not very accurate. One reason is the break with the past that accompanied the decline or extinction of the hieroglyphic and cuneiform writing traditions in the first and second centuries a.d., not long before the Chronicle was composed. Another reason is the desire to subordinate all chronology to biblical chronology, which is not very precise to begin with. For more than a millennium, chronology for the era b.c. hardly progressed. Then, in the sixteenth century, the modern study of ancient chronology began. The pioneer was Joseph Scaliger (a.d. 1540–1609), the French scholar and Protestant refugee who spent the latter part of his productive career at the University of Leiden in Holland. The decline and fall of Constantinople in the fifteenth century precipitated the flow of Greek manuscripts to the Latin West. These manuscripts introduced much unknown classical Greek and Hellenistic learning into Western Europe. Scaliger was a child of the Renaissance. He was also the first to gather and organize vast amounts of data on ancient chronology in his epochal De Emendatione Temporum (‘On the Emendation of Times’) of 1583. Scaliger was occasionally prone to fantasy, but his status as a pioneer in the field of chronology is secure. Soon after Scaliger’s death, a chronological tool emerged in a Greek manuscript that for more than three hundred years remained the Alpha of chronology for dates b.c. Scaliger had known only an erroneous version. The earliest representations in print of the correct version are those in John Bainbridge’s edition of the Sphæra of Proclus and in the fourth edition of Seth Calvisius’s Opus chronologicum. Both appeared in 1620. The three oldest copies are found in Byzantine uncial manuscripts of the eighth to tenth centuries a.d. kept at Leiden, Rome (Vatican City), and Florence. The manuscripts are Vaticanus græcus 1291, Leidensis BPG 78, and Laurentianus 28–26. The text in question is a king-list. The list begins in 747 b.c., on 26 February. The first king is the Babylonian Nabonassar. In some late versions, the list is extended to Turkish rulers of Constantinople in the fifteenth century a.d. Obviously, on 26 February 747 b.c., there was neither a 26 February nor a 747 b.c. Our modern time-reckoning has been extended backward for years before the Christian era, according to a convention which was first applied in the seventeenth century. The notion of counting years after the birth of Jesus as a.d., that is, Anno Domini, “in the year of the Lord,” was in large part the invention of

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Dionysius Exiguus (Dennis the Little), a monk who lived in Rome in the sixth century a.d. The practice of dating the years before a.d. as b.c., that is “before Christ,” dates to the seventeenth century a.d. The counting of years as b.c. is first used systematically in the works of the French Jesuit Dionysius Petavius (Dennis Petau) (1583–1652), the other great pioneer of chronology along with Scaliger. The present concern is with the list’s portion for the years b.c., down to 30 August 30 b.c. That portion encompasses forty-three rulers dated to the first millennium b.c. Ruler forty-four is the Roman ruler Octavian, later emperor Augustus, who annexed Egypt in 30 b.c. The early rulers of the portion for the years b.c. are Assyrian, Babylonian, and Persian kings of Babylon. The later rulers are kings and one queen of Egypt. These Egyptian rulers are of Macedonian descent. They came to power after Alexander’s conquest of Egypt in 332 b.c. They are called the Ptolemaic dynasty because all are named Ptolemy, except the last and most famous ruler of all, Cleopatra. The following slightly modernized version of an excerpt of the king-list contains sixteen rulers, entries 20 through 35 (see table 3.1). For being the single most important

Table 3.1: Entries 20 through 35 of King-List Ruler Years of Reign Accumulated Years Nabonidus 17 209 Cyrus 9 218 Cambyses 8 226 Darius I 36 262 Xerxes I 21 283 Artaxerxes I 41 324 Darius II 19 343 Artaxerxes II 46 389 Artaxerxes III 21 410 Arses 2 412 Darius III 4 416 Alexander the Great 8 424 Philip Arrhidæus 7 431 Alexander IV 12 443 Ptolemy I Soter 20 463 Ptolemy II Philadelphus 38 501 chronological document of antiquity, this list does not seem all that impressive at first sight. Each of the forty-three lines pertaining to the


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period 747–30 b.c. contains just three items, a royal name and two numbers for a total of 129 items (43 × 3). The number to the left is the length of the reign rounded off to a full number of Egyptian civil years of 365 days (no leap years!), or twelve months of thirty days plus five added (“epagomenal”) days (12 × 30 + 5 = 365). There is no room here to explain the technical principles by which the reigns are rounded off. Obviously, kings normally don’t begin or end their reign on New Year’s Day. For example, according to the king-list, Cambyses reigned eight years or 2920 days (8 × 365). The number to the right is the cumulative count of years, from 26 February 747 b.c. This cumulative count is also called the Era of Nabonassar, after the list’s first king. The king-list appears in the works of antiquity’s greatest astronomer, the Alexandrian Claudius Ptolemy (no known relation to the kings of that name), who lived in the second century a.d. and taught at the ancient university of Alexandria, some of whose buildings have recently been unearthed by Polish excavators. The list is therefore called Ptolemy’s Canon. The Canon was made for astronomers, not historians. But historians have surely benefitted from the Canon for dating purposes. Present space constraints do not permit a more detailed description of the precise role of the Canon in Greek astronomy. Such an understanding is ultimately desirable for an in-depth understanding of ancient chronology. May it suffice to make four observations. First, the Canon’s year of 12 × 30 + 5 = 365 days is wonderfully simple. This simplicity comes in handy when astronomers need to count the exact number of days between two astronomical events that are hundreds of years apart. Second, astronomers used the Egyptian year and the Era of Nabonassar down to early modern times. Copernicus and Kepler, for example, did. Third, the Egyptian year wanders very slowly in relation to the seasons, at a rate of about one day in four years, because there are no leap years. In 747 b.c., the Egyptian New Year’s Day fell on 26 February. By 525 b.c., the Egyptian New Year’s Day had moved backward in the artificially retrocalculated Julian calendar to 2 January. By 30 b.c., New Year’s Day was back to 31 August. Thus, the Egyptian New Year’s Day ran backward through all the seasons in about 1460 years. Fourth, the shift from rulers of Babylon to rulers of Egypt in the Canon’s portion for the era b.c. is owed to the fact that, while the Canon is a product of Alexandria, a city founded in the late fourth century b.c., Babylonian astronomical observations dating before the city’s founding were used by Greek astronomers such as Ptolemy. In the early seventeenth century a.d., Ptolemy’s Canon became the Alpha of chronology for the era b.c., at least for the period it covers. The period preceding it is of course also affected: on a time-line, what

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comes earlier owes its overall place in time to what comes later. But at the time, the chronology of the third millennium b.c. and the second millennium b.c. was theoretical. Egyptian hieroglyphic and Mesopotamian cuneiform would be deciphered only two centuries later, in the nineteenth century. There was barely any history for that earlier period. There was therefore no need for a chronology. The function of Ptolemy’s Canon as the Alpha means that some general understanding of the nature of Greek astronomy, especially of Ptolemy’s work, is beneficial to an understanding of chronology. The chronology’s Alpha is embedded in Greek astronomy. Obviously, this is not the place to summarize Greek astronomy. All that can be done is to apprize and alert the reader to the relevance of Greek astronomy to ancient chronology. Is the Canon true? If ancient chronology rests on the Alpha as the first step, then on what does the Alpha rest? The Era of Nabonassar, one of the two rows of numbers in the Canon, obviously must be true: astronomical events dated by Ptolemy according to the Era can unfailingly be matched to the time when modern computations say they happened. But then, the Era need not be more than a simple count of numbers. Even if Nabonassar never existed, the naked year-count may be considered true. Nonetheless, the following questions remain: Did all the kings listed in the Canon really exist, and did they reign exactly when the Canon says they did? It is assumed that one is cognizant of how the Canon converts the real lengths of the reigns into an integer number of 365-day years. A description of this procedure would take up too much space here. It is a plain fact that the Canon’s veracity has never been proven systematically. For more than three centuries, the Canon served as a kind of fundamental axiom of ancient chronology. No mainstream historians have ever seen reason to doubt its veracity. Then, in the twentieth century, new evidence came to light that holds the key to proving the Canon. This evidence will demote the Canon from the Alpha of ancient chronology to its Beta. Possibly, the Canon will retain its primary role with regard to certain details. Its replacement as the Alpha is much more unshakable as a foundation. The shift began about a century ago. But it has been slow to develop. Its completion is fully expected in the twenty-first century. What happened about a hundred years ago that put the shift into motion? To what circumstance do we owe this new, dawning Alpha? Around the mid-nineteenth century, the cuneiform script was deciphered. A couple of decades later, cuneiform texts of astronomical purport surfaced. The decipherment of Babylonian astronomy began at


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the end of the nineteenth century. The key texts came to the British Museum between 1876 and 1882, presumably mostly from excavations at Babylon. Johann Nepomuk Strassmaier transcribed many of these astronomical texts, and Julius Epping began the decipherment of the texts’ astronomical system. A milestone is Franz Xaver Kugler’s book on lunar motion according to the Babylonians, his Babylonische Mondrechnung, published in the year 1900. Over the decades, understanding of Babylonian astronomy and mathematics gradually advanced. Otto Neugebauer of Brown University played an important role in this development with studies such as Astronomical Cuneiform Texts (1955) and History of Ancient Mathematical Astronomy (1975). The empirical data on which theoretical Babylonian astronomy is based is contained in the so-called Babylonian Astronomical Diaries. These Astronomical Diaries constitute the empirical basis of the longest sustained research project in the history of mankind. For about 800 years, or about 10,000 lunar months, from some time in the eighth century b.c. to some time in the first century a.d., Babylonian priestscholars recorded celestial events day by day and meticulously maintained these records over the centuries. The long time-span of the data allowed them to discern patterns in the movement of the heavens. It is in these Astronomical Diaries and related texts that the proof of Ptolemy’s Canon is to be found. The Astronomical Diaries have now become easily accessible owing to Abraham Sachs and Hermann Hunger and their Astronomical Diaries and Related Texts from Babylonia. The first three volumes of this work, containing most of the diaries, appeared in 1988, 1989, and 1996. About a century ago, when Babylonian astronomy began to be deciphered, another type of chronological evidence also happened to come to light. It consists of Aramaic papyri from Egypt dating to the fifth century b.c. All the texts are now easily accessible in the new comprehensive edition by Bezalel Porten and Ada Yardeni. Their Textbook of Aramaic Documents from Ancient Egypt, volumes 1 to 3, appeared in 1986, 1989, and 1993. Many of the papyri were found on Elephantine, an island in the Nile in the deep south of Egypt. These papyri contain double dates, that is, a single day dated independently in both the Babylonian lunar calendar and the Egyptian non-lunar calendar. It appears that the two independent dates of the double dates as a rule match. This agreement marvelously confirms that our understanding of both calendars is correct. Astronomical events reported in the Babylonian Astronomical Diaries are dated by the reigns of some kings found in Ptolemy’s Canon. Some of these events are the positions at one moment in time of two or

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more of the following: the sun, the moon, the planets, and the stars. Many such combinations of positions of celestial bodies in the sky occur only once in all of human history. There are ways of dating these unique clusters of positions in the sky. First, by the date given in the Astronomical Diaries. And second, by modern astronomical theory, counting back from the present time. It is an undeniable fact that the dates of the Astronomical Diaries and the dates obtained by modern computation match. Positions of the sun, moon, planets, and stars in relation to one another at particular points in time often exhibit the uniqueness of human fingerprints. When hundreds of these fingerprints match with modern computations, all doubt about the veracity of the data in the Astronomical Diaries is simply suspended and potential exceptions become meaningless, being easily attributed to textual error or some such factor. Furthermore, the dates of the Astronomical Diaries can be matched with the dates of the Canon. That correspondence in turn proves the Canon’s veracity. For example, Ptolemy’s great work, the Almagest, uses the chronological system of the Canon. In Almagest 5.14, a lunar eclipse is dated by the Egyptian civil calendar to Month 7 Day 17 of Year 7 of the Persian king Cambyses, who ruled Egypt. In the astronomical cuneiform tablet known as Strassmaier Cambyses 400 after the editor and the number of the tablet in his edition, a lunar eclipse is dated by the Babylonian civil calendar to Month 4 Day 14 of Year 7 of Cambyses. The two dates each independently produce the eclipse of 16 July 523 b.c. Both texts mention that the eclipse began about an hour before midnight. The result is one of many matches that cement confidence in the dating of the Canon. Such proof of the Canon’s veracity based on the Babylonian evidence has been presented in only piecemeal form so far. Full, systematic proof of the Canon is a task that still lies ahead. There is no reason to suspect at this point that the Canon is in any way erroneous. As the Alpha of ancient chronology, the Canon has been more of an axiom. The main argument in favor of its veracity was the coherence and non-contradiction with all else that we know about antiquity. By contrast, as the new Alpha, the dated astronomical observations of the Babylonian Astronomical Diaries meet a much higher standard of proof and therefore provide a much more solid foundation for chronology of the era b.c. I hope that it will be clear to the reader that some knowledge of Greek astronomy and Babylonian astronomy is indispensable for a profound understanding of ancient chronology. All that can be done here is to raise a certain awareness of this fact. But Babylonian astronomy and Ptolemy’s Canon are only two components of ancient chronology. They


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are limited in scope. The structure of the Model is much more elaborate. However, these two sources do make up the foundation. They therefore deserve disproportionate attention. Chronology is flourishing nowadays as a field of study. But the time seems right for subjecting the foundations to special scrutiny. What follows are some additional articulations of the Model, with special focus on ancient Egypt. These articulations cannot be detailed here as much as would be desirable. It is a happy confluence of circumstances for the chronologist that Cambyses conquered Egypt around 525 b.c. and that Persian kings ruled both Egypt and Babylon for more than a century. As a result, Persian kings are dated by Egyptian sources, Ptolemy’s Canon, and Babylonian astronomical texts all at the same time. This intertwining and overlapping allows Egyptian chronology to be fixed back to 525 b.c. Before 525 b.c., texts from the burial chambers of the sacred Apis bulls in Memphis allow fixing Egyptian chronology back to 664 b.c. Apis bulls born under one king and dying under the next king are of special interest to the chronologist. The texts list date of birth, date of death, and life-span of Apis bulls. By manipulating this information, one can string together the reigns of Egyptian pharaohs with certitude back to 664 b.c. The year 664 b.c. may well mark the most important division in all of world chronology. It is the beginning of day-exact chronology, which means that, if we have an ancient date for an event, then it is possible to establish to the exact day how long ago counting from today the event happened. For several centuries, in fact, day-exact chronology is a monopoly of the chronology of Egypt among all the nations of the earth. For example, Psammetichus II is known to have died on Month 1 Day 23 of Year 7 of his reign. That day is 9 February 589 b.c. in the fictional extension of our calendar back into the past. The time of day at which the death presumably occurred on 9 February 589 b.c. is removed from the same time of day, whatever it was, on 1 January a.d. 2003 by exactly 946,311 days. Before 664 b.c., only approximate dates are possible. Assyrian yearlists and radiocarbon dating inspire confidence in the Model. But the dates resulting from these two sources are only approximate. The Assyrian year-lists are useful to Egyptian chronology back to about 1500 b.c. because Anatolian and Mesopotamian kings corresponded with Egyptian pharaohs. These connections make it possible to know which Assyrian kings are contemporaneous with which Egyptian pharaohs. These matches are called synchronies. For dating the third and second millennium b.c., the current Model of ancient Egyptian chronology relies on so-called Sothic dating, which is itself refined by Sothic-lunar dating. Sothic-lunar dating is of such

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complexity that there is no room here to describe it adequately. The margin of error of dates obtained from Sothic dating is roughly ten to twenty years for the second half of the second millennium b.c., roughly forty to fifty years for the first half of the second millennium b.c., and about one to two centuries for the third millennium b.c. Sothic dating is easily the single most characteristic concept of Egyptian chronology. Sothic means “pertaining to the rising of Sirius.” “Sothic” is an adjective derived from Sothis. Sothis is the Greek form of the Egyptian Spdt, the Egyptian name of the star Sirius. Every year, the star Sirius is invisible for two months or so. As the earth revolves around the sun, Sirius is at a certain point behind the sun for an observer on earth. The blinding light of the sun makes Sirius invisible. But as the earth continues its journey around the sun, Sirius is no longer behind the sun. The effect is that one early morning in July, just before sunrise, Sirius becomes visible again for the first time. The first visibility of Sirius is called the rising of Sirius. The Egyptian term is prt Spdt, ‘coming forth of Sirius.’ A Sothic date is a date of the rising of Sirius in the Egyptian 365-day civil calendar. Sothis was an important goddess, often associated with Isis. Ancient Egyptians took note of the rising, or return, of the star, presumably happy that Sothis had not left them for good. They dated the rising by their civil calendar. A date of the rising of Sirius according to the Egyptian civil calendar is a Sothic date. Not many Sothic dates have been preserved. Two stand out. The first is Month 8 Day 16 of Year 7. The batch of documents in which the first Sothic date appears was found in the mortuary complex of Sesostris II, the immediate predecessor of Sesostris III. The documents therefore do not date to the reign of Sesostris II himself. The handwriting of the document containing the date in question resembles that of other documents explicitly dated to Sesostris III. There is general agreement that this Sothic date falls in the nineteenth century b.c., the 1800s. The second Sothic date is Month 11 Day 9 of Year 9 New Kingdom Pharaoh Amenhotep I. It is found in the calendar concordance inscribed on the verso of the Ebers papyrus. The name of the New Kingdom Pharaoh Amenhotep I is explicitly mentioned in the date of the Ebers calendar. There is general agreement that this Sothic date falls in the later sixteenth century b.c., the low 1500s. Sothic dating, then, is dating Egyptian history in relation to our time by manipulating Sothic dates. Sothic dates can be used as anchors for Egyptian chronology. This procedure rests on four principles. The first principle is the regular shift forward of the day of the rising in the civil calendar. The rising occurs about every 365 41 days. But the Egyptian year is only 365 days long.


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The rising therefore shifts forward to the next calendar day after about four years. It is assumed that the regularity of this shift was never disrupted by changes to the calendar. The Sothic cycle is the time that it takes for the rising of Sirius to return to the Egyptian New Year’s Day. This astronomical event happens after 1460 years. The second principle is that if the rising shifts forward by one day about every four years, then every set of about four years in Egyptian history has its own Egyptian date for the rising. The third principle states that if we know the Egyptian date of a rising, we can assign that rising to a certain set of four years in Egyptian history. Finally, the fourth principle holds that, if the rising shifts forward regularly by one day in four years, then all we need to know is when it fell at one point in Egyptian history in order to roll the wheel backward and forward and know when it fell at other times in Egyptian history. From a report by the Roman author Censorinus, we know that the rising fell on the Egyptian New Year’s Day in a.d. 139. In order to span the distances between Sothic dates by filling them in with reigns, a principal tool is the king-list by Manetho, who wrote in Greek in the third century b.c. The German classicist August Böckh once stated, “I have never encountered a more confusing topic than this Manetho.” Everyone accepts that Manetho states both much that is true and much that is false. But disregarding him is not an option. It is he who gave us the thirty dynasties into which Egyptian history before his time is now generally subdivided in modern scholarship. In addition, king-lists dating to the late second millennium b.c. have survived in hieroglyphic sources. They hold similar, essential information for building bridges from one Sothic date to another. Ptolemy’s Canon, Babylonian astronomy, Assyrian year-lists, radiocarbon dating, texts commemorating the death of an Apis bull, and Sothic dates—these are just some of the sources that need to be studied in depth in order for us to gain an adequate grasp of the current Model of ancient chronology. Ancient history can only benefit from an increase in the number of initiates into this Model. The Model is, after all, responsible for all the dates regarding antiquity in all the history books.

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References Calvisius, Seth. Opus chronologicum. Fourth edition. Frankfurt: Anthonius Hummius, 1620. Depuydt, Leo. “How to Date a Pharaoh.” Archaeology Odyssey 8, no. 4 (2005): 27–33. ———. “The Shifting Foundation of Ancient Chronology.” In Modern Trends in European Egyptology: Papers from a Session Held at the European Association forArchaeologists Ninth Annual Meeting in St. Petersburg 2003, edited by Amanda-Alice Maravelia, 52–63. British Archaeological Reports International Series, vol. 1448. Oxford: Archaeopress, 2005. Kugler, Franz. Babylonische Mondrechnung. Zwei Systeme der Chald¨ aer u ¨ber den Lauf des Mondes und der Sonne. Freiburg im Breisgau: Herder, 1900. Millard, Alan. The Eponyms of the Assyrian Empire, 910–612 B.C. Helsinki: Neo-Assyrian Text Corpus Project, 1994. Neugebauer, Otto. Astronomical Cuneiform Texts: Babylonian Ephemerides of the Seleucid Period for the Motion of the Sun, the Moon, and the Planets. 3 vols. London: Lund Humphries for the Institute for Advanced Study, 1955. ———. History of Ancient Mathematical Astronomy. 3 vols. New York: Springer, 1975. Porten, Bezalel and Ada Yardeni. Textbook of Aramaic Documents from Ancient Egypt. 4 vols. Jerusalem: Hebrew University, Department of the History of the Jewish People; distributed by Eisenbrauns, 1986–99. Proclus. Sphæra. Edited by John Bainbridge. London: Guilielmus Jones, 1620. Sachs, Abraham and Hermann Hunger. Astronomical Diaries and Related Texts from Babylonia. vols. 1–3 and 5. Denkschriften der ¨ Osterreichischen Akademie der Wissenschaften Philosophisch¨ Historische Klasse, vols. 195, 210, 246, 299. Vienna: Osterreichische Akademie der Wissenschaften Verlag, 1988–2001. Scaliger, Joseph. De Emendatione Temporum. Paris: Mamertius Patissonius, 1583.

Assyriology and English Literature Benjamin R. Foster Yale University

Since the decipherment of cuneiform, Assyriologists have laid broad claims to the importance of their discipline.1 One way to assess the validity of their claims is to survey the impact of Assyriology on general culture, for example, on literature, music, the visual or decorative arts. Egyptomania is a well-known phenomenon, and English literature is rife with books and tales featuring mummies, pyramids, and Cleopatra, to name just a few.2 Mesopotamia, however, in comparison to Egypt, remains in the shadow of a recondite academic specialty, so direct traces of it in literature are scattered far and thin. This inquiry properly would consider Assyriology in the broader context of oriental and archaeological influences on European and American arts and letters, especially during the nineteenth century, identifying both scholarly and imaginative sources of influence. This is not possible here. Indeed, the enormous agenda of orientalizing influences on European culture has now surpassed the reach of a single researcher, especially where the influences of the Islamic world are concerned.3 It 1. Jean Bott´ ero, “In Defense of a Useless Science,” in Mesopotamia, Writing, Reasoning and the Gods, translated by Zainab Bahrani and Marc Van De Mieroop (Chicago: University of Chicago Press, 1993), 15–25. Bott´ ero was struck by the fact that Assyriologists, unlike many scientists, have left the universe and its inhabitants in peace, imposing on no one. The universe and its inhabitants now do Assyriology the same courtesy. 2. Jean-Marcel Humbert, Egyptomania: Egypt in Western Art 1730-1930 (Ottawa: National Gallery of Canada, 1994). I do not know of a study of ancient Egypt in English literature. H. Rider Haggard, for example, contributed complementary novels, set in ancient and modern times, Cleopatra and She. Zulu life for him merited a novel, but not Babylonian. 3. See Arthur Christy, ed., The Asian Legacy and American Life (New York: The John Day Company, 1945); Martha Conant, The Oriental Tale in England in the Eighteenth Century (New York: The Columbia University Press, 1908); Marie de Meester, Oriental Influences in the English Literature of the Nineteenth Century, Anglistische Forschungen, vol. 46 (Heidelberg: Carl Winter, 1915); Fuad Sha’ban, Islam and Arabs in Early American Thought: The Roots of Orientalism in America

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would also consider in detail the critical and intrepretive writing on some of the authors mentioned later, but for the present I am content to blaze a trail rather than lay out a broad inquiry. It is a particular pleasure to dedicate this essay on Assyriological echoes in English literature to Alice Slotsky, who has taught Akkadian to more students than has any other Assyriologist who ever lived. Three main subjects may be examined for their influence on English literature: first, the professional subject matter of Assyriology, that is, the ancient civilizations of Mesopotamia; second, Assyriologists themselves; and third, ancient Mesopotamia as a setting for imaginative literature. Babylon as Literary Topos Until the mid-nineteenth century, the source of Babylonian presence in English literature was the Bible and to a lesser extent Classical sources.4 Allusions fall into three categories: Babylon as a symbol for many languages, as a symbol of doomed greatness, and as the ultimate in immorality. From the Bible and Classical writers, Babylon and its various adjectival forms entered English to a greater extent than any other toponym in Western Asia or Egypt, outside of Jerusalem. Three important passages within the Biblical text are the basis for most of the Mesopotamian allusions, the first being the story of the tower of Babel in Genesis 11. Thence comes, ultimately, the English word “Babel,” meaning a confusion or medley of sounds, especially human voices, thanks in part to Josephus, who wrote that Babel meant ‘confusion’ among the Jews because of the confusion of languages there.5 Although the English word “Babel” is known, according to dictionaries, as early as the middle of the sixteenth century, Johnathan Swift pioneered its use in belles-lettres about 1733 when he referred in a pamphlet to a “Babel (Durham, North Carolina: Acorn Press, 1991). A witty and enjoyable essay on this subject will be found in Norman Daniel, Islam, Europe and Empire (Edinburgh: University of Edinburgh Press, 1966), 48–61. 4. For a richly documented study of Babylon in Classical and medieval sources, as well as in modern German literature, see Volkert Haas, “Die literarische Rezeption Babylons von der Antike bis zur Gegenwart,” in Babylon: Focus mesopotamischer Geschichte, Wiege fr¨ uher Gelehrsamkeit, Mythos in der Moderne: 2. Internationales Colloquium der Deutschen Orient-Gesellschaft 24.–26. M¨ arz 1998 in Berlin, ed. Johannes Renger (Saarbr¨ ucken: Saarbr¨ ucker Druckerei und Verlag, 1999), 523–52. For the Bible, see Reinhard Kratz, “Babylon im Alten Testament,” in Babylon: Focus mesopotamischer Geschichte, 477–90. For the Greek authors, there is a survey by Robert Drews, The Greek Accounts of Eastern History (Washington, District of Columbia: Center for Hellenic Studies, 1973), but the grand nineteenth-century histories, such as Duncker’s (see p. 70, n. 75 below), marshal the sources in wonderful detail, better than any modern treatise. 5. Josephus Antiquities 1.4.3

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of sectaries joined against the church.”6 The fortuitous resemblance between Babel and the good English word “babble” only reinforced this usage, so one has the impression that Babel could be viewed as a literary form for babble. Genesis 11 can therefore scarcely be said to add to the luster of Assyriology. We owe to Samuel Butler (1612–1680), in his satire of a metaphysical sectarian, a memorable turn of phrase, “Babylonish dialect.” 91 92 93 94 95 96 97 98

But, when he pleas’d to shew’t, his speech In loftiness of sound was rich; A Babylonish dialect, Which learned pedants much affect; It was a party colour’d dress Of patch’d and piebald languages: ’Twas English cut on Greek and Latin, Like fustian heretofore on satin.7

This phrase was frequently quoted thereafter by the learned, such as Dr. Johnson, in his case referring to Milton.8 A gloss on Butler’s line by Zachary Grey, LL.D., reads “A confusion of languages, such as some of our modern virtuosi used to express themselves in.”9 Butler liked the figure: 98 99 100 101

It had an odd promiscuous tone, As if h’ had talk’d three parts in one; Which made some think, when he did gabble, Th’ had heard three Labourers of Babel. 10

The “three parts” here refer to singing parts in music; the learned Mr. Grey further refers to people who could converse in two languages at once,11 to Rabelais’ monster Hearsay with seven tongues, and to a wealth of other sources, so it is clear that to Butler and his admirers, Babel meant many languages. 6. The Oxford English Dictionary cites the pamphlet “Reasons Humbly offered to the Parliament of Ireland For Repealing the Sacramental Test, etc. in favour of the Catholics, Otherwise called Roman Catholics, and by their Ill-Willers Papists.” 7. Samuel Butler, Hudibras, in Three Parts, Written in the Time of the Late Wars (1663–64; reprint, with large annotations and a preface by Zachary Grey, LL.D., London: T. Bensley, 1799), part 1, canto 1, lines 91–98. 8. Samuel Johnson, “Life of Milton,” in The Lives of the Most Eminent English Poets with Critical Observations on their Works, vol. 1 (London: C. Bathurst, et al., 1781). 9. In Butler, Hudibras, vol. 1, 13. 10. Butler, Hudibras, part 1, canto 1, lines 98–101. 11. Diodorus Siculus Bibliotheca Historia 3.13.

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Benjamin R. Foster Milton’s image of Mesopotamia was not very positive:

41 42 43 44

The Plain, wherein a black bituminous gurge Boiles out from under ground, the mouth of Hell; Of Brick, and of that stuff they cast to build A Citie and Tow’r, whose top may reach to Heav’n.12

Milton, like others of his time, saw the profusion of languages as a divine miracle, not as something inherently evil, though he did not approve of its sound. Following Josephus, he understood that Babel meant “confusion” in Hebrew: 52 53 54 55 56 57 58 59 60 61 62

. . . and in derision sets Upon thir Tongues a various Spirit to rase Quite out thir Native Language, and instead To sow a jangling noise of words unknown: Forthwith a hideous gabble rises loud Among the Builders; each to other calls Not understood, till hoarse, and all in rage, As mockt they storm; great laughter was in Heav’n And looking down, to see the hubbub strange And hear the din; thus was the building left Ridiculous, and the work Confusion nam’d.13

The essayist William Hazlitt (1778–1830) gives a different perspective on Babylonish: “a jargon of their own, a Babylonish dialect, crude, unconcocted, harsh, discordant, to which it is impossible for anyone else to attach either meaning or respect.”14 This would probably not be true of discourse larded with Latin. Although I can find no proof, I wonder if “Babylonish” in this usage actually refers to Aramaic. Both Hebrew and Aramaic were referred to by Christian authors in the Middle Ages and Renaissance for their alleged harsh sounds, thanks to Jerome, when he referred to the “harsh and guttural words” of Hebrew and the “puffing and hissing sounds” of Aramaic.15 12. John Milton, Paradise Lost, book 12, lines 41–44. 13. Ibid., book 12, lines 52–62. 14. William Hazlitt, “On Paradox and Common-Place,” Table Talk 1 (1821). 15. Frederick Wright, ed. and trans., Select Letters of St. Jerome, Loeb Classical Library, vol. 262 (Cambridge, Massachusetts: Harvard University Press, 1963), 419. This may have given rise to the legend recounted in the fifteenth century that Jerome had filed down his teeth to pronounce the language correctly; see Eugene Rice, Saint Jerome in the Renaissance (Baltimore: Johns Hopkins University Press, 1985), 205. For Jerome and Aramaic, see Dennis Brown, Vir Trilinguis: A Study in the Biblical Exegesis of Saint Jerome (Kampen: Kok Pharos Publishing House, 1992), 83.


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In another oblique reference to Babylon as a place for obscure language, Charlotte Brontë, thinking of Daniel, broods over what she felt she could not say: Speak of it! You might almost as well stand up in a European market-place and propound dark sayings in that language and mood wherein Nebuchadnezzar, the imperial hypochondriac, communed with his baffled Chaldeans. . . 16 Brontë had of course read both the Bible and Butler. The bitterness in this passage pervades the whole book, making it disagreeable reading; what impresses here is the imaginative expansion of the Babylonian cliché, we might call it, into an image that has a certain appeal. Did she by any chance think that Nebuchadnezzar spoke Aramaic? Perhaps, after all, she was correct. Daniel’s portrait of Nebuchadnezzar, which underlies this passage, made that king’s name proverbial in English. It bears little resemblance to the image of that king as rehabilitated in Assyriological scholarship, which makes him an axial figure. Le grec Thalès ouvre l’ère du rationnel, Nabuchodnosor clôt celle du raisonnable. Mais Nabuchodnosor resta toujours le maˆıtre de son projet. Cette pleine conscience définit les limites de ses réussites comme elle rend raison de son incomparable renommé.17 The Assyrians fare little better than the Babylonians in older English literature. Falstaff calls Pistol a “base Assyrian knight,”18 though precisely what he means by this, in the rather confused dialogue that is taking place, is unclear to an Assyriologist; Falstaff may think that the Assyrians lived in Africa. The Assyrians come across as a symbol of militancy in a speech by Henry V, who says: “[a]nd make them skirr away, as swift as stones / Enforced from the old Assyrian slings,”19 an interesting allusion, since the tribe of Benjamin was more famous in Shakespeare’s time for their sling work than were the Assyrians.20 Alas, the outlook for the prestige of Assyriology is even bleaker when we turn to a third major source of biblical Babylonian influence, St. John the Divine.21 There we read of a “great whore who sitteth upon many 16. chap. 17. 18. 19. 20. 21.

Charlotte Bront¨ e, Villette, vol. 2 (London: Smith, Elder, and Company, 1853), 24. Daniel Arnaud, Nabuchodnosor II roi de Babylone (Paris: Fayard, 2004), 365. 2 Henry IV, 5.3.105. Henry V 4.7.63. Judg 20:16. Rev 17:1–6.

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waters, with whom the kings of the earth have committed fornication, and the inhabitants of the earth have been made drunk with the wine of her fornication.” To allay any doubts as to the lady’s identity, she has her name written on her forehead: “Babylon the great, the mother of harlots and abominations of the earth.” Swift and his English Protestant contemporaries would have read this passage as an allegory for Rome, and Rome is duly entered in the appropriate glossaries and concordances to the passage already in the King James Bible published in 1611. Indeed, they had the best of authorities for this reading in the embittered Jerome, who, leaving Rome forever in the wake of scandal, wrote that Rome had become to him Babylon, the great harlot turned out in purple and scarlet.22 To a Protestant Englishman of the seventeenth and eighteenth centuries, “Babylonian” could have meant “Romish” or “papist” or “popish,” as was said in those days, not as a compliment. Ironically, Babylonian was used as well by adherents of the Church of Rome, but it referred of course to the papacy at Avignon, whose residence there was referred to as the “Babylonian Exile.” This usage is still current, for example, in a 1987 collection of documents about the Avignon papacy, edited by Robert Coogan, called Babylon on the Rhˆ one—a juxtaposition an Assyriologist finds jarring. “Babylonian” in the sense of “popish” seems to have gone the way of “popish” itself. Shakespeare, at least, got a jest out of the passage, in a dialogue between a tavern keeper and a boy, concerning Falstaff: Boy: A’ said once, the devil would have him about women. Hostess: A’ did in some sort, indeed, handle women; but then he was rheumatic, and talked of the whore of Babylon.23 W. Somerset Maugham joins the bard in making a quip on St. John in his novel The Narrow Corner (1932): “If two grown men can’t drink one bottle of port between them I despair of the human race. Babylon is fallen, is fallen.” Did Maugham recall John’s vision well enough to remember that the infamous whore held a golden cup in her hand? The portrayal of Babylon as a mighty city has excellent Classical antecedants, including Herodotus, Strabo, Quintus Curtius, Xenophon, and Josephus, and, more vaguely, the Roman heroic poet Lucan, whose Pharsalia 6 is here quoted: 54 55

. . . Let ancient tales To the gods work adscribe the Trojan walls;

22. Epistle 45. 23. Henry V, 2.4.39–40.

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Let flying Parthians still admire alone The brittle earth, built walls of Babylon, As far as Tigris, and Orontes run, As the Assyrian Kings dominion Stretch’d in the East, a sudden work of war Encloses here. Lost those great labours are.24

Assyriologists, when discussing literature, are wont to quote multiple treatments of the same passage, so here is a second rendering of these lines. This rendering is of interest as it appears to be contaminated by Genesis. 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123

Now let us heare those fables old, That of the Troians walles were told, Ascribed to the God-heads cares, Although but fram’d of brittle wares: And those great wonders that doe flye Of Babylonian walles so hye, That seem’d to front and threat the skye, Made by the Parthian turne againe, That flying doth his sight maintaine. But looke what spacious fields and lands, Or swift Orontes doth embrace, From which the king of Easterne race Did at first with suddaine might, Small kingdoms share unto their right, Even so much ground . . . Are compast with fierce Tygris bands. 25

This may seem prosy to modern tastes, so here is a modern rendering distributed on the internet: 59 60 61 62 63

. . . let the fragile bricks Which compass in great Babylon, amaze The fleeting Parthian. Here larger space Than those great cities which Orontes swift

24. Thomas May, trans., Lucans Pharsalia, or, The civil-wars of Rome, between Pompey the Great, and Julius Cæsar, the whole ten books Englished by Thomas May, Esquire, fourth edition (London: William Beaty, 1650), 129. 25. Arthur Gorges, ed., Lucans Pharsalia: containing the ciuill warres betweene Cæsar and Pompey. Written in Latine heroicall verse by M. Annæus Lucanus. Translated into English verse by Sir Arthur Gorges Knight. Whereunto is annexed the life of the authour, collected out of divers authors (London: [Nicholas Okes], 1614), 214.

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Benjamin R. Foster And Tigris’ stream enclose, Or that which boasts In Eastern climes, the lordly palaces, Fit for Assyria’s kings . . . . 26

Thackeray, for his part, turns the image of Babylon as a great cosmopolitan city on its head, stooping to a word play, when he calls Baden (“the prettiest town of all the places where Pleasure has set up her tents”) “that Babel.”27 Although Sir Toby never gets beyond the incipit of his song, “There dwelt a man in Babylon, lady, lady!”28 one may guess that the rest of it had to do with whoredom. We find then an inauspicious beginning for Assyriology in English literature. Assyria is grim and violent; Babylon is great (but ruined) and the abode of harlotry, vanity, and doom, source of the unproductive confusion of incomprehensible languages. Let us pursue the last point briefly. Whereas now English speakers (misunderstanding Shakespeare29 ) refer to incomprehensible tongues as “Greek to me” and the French say “c’est de l’Hebreu pour moi,” in nineteenth-century literature, when Greek was a commonplace accomplishment of the educated, the expression would have been placed in the mouths of only the ignorant. Thackeray gives it to an unlettered soldier who has the good fortune to serve in arms with Richard Steele.30 More exotic languages than Greek were needed, therefore, to make the point, as Brontë tried to do with Chaldean. In a survey of such expressions, the linguist Ullendorf claims that Swedes say for this “Mesopotam,” which I cannot verify, and he claims that in more Assyriological Denmark one says “Elamite,”31 but this idiom is rejected by a native speaker who tells me that multilingual Danes prefer to invoke the languages of Lapland or Malabar, in extreme cases Volap¨ uk, but not Elamite.

26. The Pharsalia of Lucan, trans. Edward Ridley (London: Longmans, Green, and Co., 1896), electronic edition edited, proofed, and prepared by Douglas Killings, May 1996. Available at http://omacl.org/Pharsalia/. 27. William Thackeray [A. Pendennis, Esq. pseud.], The Newcomes: Memoirs of a Most Respectable Family vol. 1, no. 9 (London: Bradbury and Evans, June 1854), chap. 27, 264. 28. Twelfth Night, 2.3.38 29. Julius Caesar, 1.2.287 30. William Thackeray, History of Henry Esmond, Esq. : a colonel in the service of Her Majesty Queen Anne written by himself (London: Smith, Elder and Company, 1852), chap. 6, 130. 31. Edward Ullendorff, “ ‘C’est de l’Hebreu pour moi!’,” Journal of Semitic Studies 13, no. 1 (1968): 125–35.


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The English novelist George Meredith refurbishes Brontë’s Chaldean incomprehensibility in a sporting dialogue:“ ‘You read me?’ ‘Egyptian, but decipherable.’ ”32 Surely the most tortured reference to “Babylonish” and its congeners occurs in Melville’s 1851 novel Moby-Dick, which refers to “the awful Chaldee of the sperm whale’s brow,”33 an image that I leave to a biologist rather than a philologist to sort out. This must mark the outer limit to which the old metaphor can be forced. The passage of time does not mean disappearance of the usage of Babylon to refer to the obscure. One instance at least introduces the Babylonians themselves, but negatively; here the author refers to the airy babble of some French dinner-goers: Yet they might have been discussing the psychology of the ancient Babylonians, so completely unclouded by any prejudice was their desire to reach the truth.34 Bennett disappoints Assyriologists with a novel entitled The Grand Babylon Hotel (1902), as it has nothing to do with the great city motif. In fact, he specifically informs his readers that Babylon is a French surname, not the city; he must have known that the surname was better known in England as Babelon, haply the author of a book well known in its time, Manual of Oriental Antiquities.35 The anti-Catholic bias implied by Babylon, however, faded away in English letters by the early nineteenth century, leaving current only the usage of Babylon to stand for a great city, especially London. The Oxford English Dictionary cites for this usage Byron, not a man to be horrified by harlotry, alluding to London as “mighty Babylon,” but St. Bernard was well ahead of Byron, denouncing Paris for all its Babylonian proclivities. Byron is the source of a famous allusion to Assur and cohorts (whence would he have summoned their colors?): 1 2

The Assyrian came down like the wolf on the fold, And his cohorts were gleaming in purple and gold;

32. George Meredith, The Amazing Marriage (New York: C. Scribner’s Sons, 1895), chap. 39. 33. Herman Melville, Moby-Dick; or, The Whale (New York: Harper and Brothers, 1851), chap. 79. 34. Arnold Bennett, The Lion’s Share (London: Cassell, 1916), 159. 35. Ernest Babelon, Manual of Oriental antiquities, including the architecture, sculpture, and industrial arts of Chaldæa, Assyria, Persia, Syria, Judæa, Phœnicia, and Carthage (London: H. Grevel and Co., 1906).

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And the sheen of their spears was like stars on the sea, When the blue wave rolls nightly on deep Galilee.36

This passage is so well known that even that consummate ignoramus, Bertie Wooster, had some vague memory of it, though of course not an accurate one: “Who was it who came down like a wolf on the fold?” “The Assyrian, sir.” “That’s right. Well, that is what I have been through since I saw you last.”37 To keep Assyria and Babylon in fair balance, Byron also penned a denunciation of Belshazzar: 1 2 3 4

Belshazzar! From the banquet turn, Nor in thy sensuous fulness fall; Behold! while yet before thee burn, The graven words, thy glowing wall.38

Byron, who deserved an honorary degree in Assyriology had there been such a discipline in his time, also wrote a tragedy, Sardanapalus, dedicated to that pioneering orientalist Goethe, with historical notes, the whole based on Diodorus. Byron’s Sardanapalus, rather than being the type of the effete oriental monarch, hoped to avoid imposing further pain and suffering on the human race by pursuing a life of pleasure, an interesting twist on the old story. The philologist will be struck by Byron’s idiomatic rendering of an alleged Assyrian inscription: 296 297 298 299

. . . “Sardanapalus, The king, and son of Anacyndaraxes, In one day built Anchialus and Tarsus. Eat, drink, and love; the rest’s not worth a fillip.”

39

Assyrian inscriptions being noted for their variants, one may note that a different, less flip, rendering of the same text appears in his Don Juan, Canto 2.207: “Eat, drink, and love, what can the rest avail us?” To return to that fertile satirist Samuel Butler, he was intrigued by the story retailed in Ammianus Marcellinus 1, that “Semiramis teneros mares castravit omnium prima.” Attributing to her the invention of castration, Butler wrote: 36. The Destruction of Sennacherib (1815). 37. P. G. Wodehouse, Joy in the Morning. (Garden City, NY: Doubleday and Company, 1946), chap. 11, 88. 38. To Belshazzar (1814). 39. Sardanapalus (1821).

Assyriology and English Literature 713 714 715 716 717 718

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This first a woman did invent, In envy of man’s ornament, Semiramis of Babylon, Who first of all cut men o’ th’ stone, To mar their beards, and laid foundation Of sow-geldering operation. 40

The learned editor Mr. Grey allows himself a wisecrack on this passage:“Which is something strange in a lady of her constitution, who is said to have received horses into her embraces, (as another queen did a bull) but that perhaps may be the reason why she after thought Men not worth the while.”41 Byron, who saw Sardanapalus as a kindred spirit, perhaps thinking of this passage, rehabilitated Semiramis, in good Assyriological fashion, with a conjectural text emendation: 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487

Babel was Nimrod’s hunting-box, and then A town of gardens, walls, and wealth amazing, Where Nabuchadonosor, king of men, Reign’d, till one summer’s day he took to grazing, And Daniel tamed the lions in their den, The people’s awe and admiration raising; ‘Twas famous, too, for Thisbe and for Pyramus, And the calumniated queen Semiramis. That injured Queen by chroniclers so coarse Has been accused (I doubt not by conspiracy) Of an improper friendship for her horse (Love, like religion, sometimes runs to heresy): This monstrous tale had probably its source (For such exaggerations here and there I see) In writing ‘Courser’ by mistake for ‘Courier:’ I wish the case could come before a jury here.42

Space scarcely permits further pursuit of Semiramis on the European scene. In medieval and Renaissance poetry, Semiramis was either supremely lustful or a dutiful Amazon who rushed into battle without stopping to fix her hair.43 40. Butler, Hudibras, part 2, canto 1, lines 713–18. 41. In Butler, Hudibras, vol. 1, 341. 42. George Byron, Don Juan (1821), canto 5. 43. Giovanni Pettinato, Semiramis: Herrin u ¨ber Assur und Babylon: Biographie (Zurich: Artemis, 1988); Irene Samuel, “Semiramis in the Middle Ages: The History of a Legend,” Medievalia et Humanistica 2 (1944), 32–44; Adrian Armstrong, “Semiramis in Grand Rh´ etoriqueur Writing,” in Centres of Learning, Learning and

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Yet by the early twentieth century, Babylon as a great city has passed into a cliché: how else can we explain F. Scott Fitzgerald’s Babylon Revisited (1931)? There is no limit to American arrogance, for in that novel Babylon has been translated from London to the New World. We meet the Knickerbocker Babylon frequently, such as in a tale entitled Babylon on Hudson (1932), one of but two novels produced by Charles Recht (1907–1976) over his long career. What exactly were the glories of Babylon that allusions to its greatness commemorate, assuming they were more than the fornication and abominations of St. John’s vision? Byron, with his profound Classical education, was thinking, like Lucan, of a large and splendid urban complex. F. Frankfort Moore, in his romantic novel The White Causeway (1905), evidently held some confused notion that it was the waters of Babylon that made it special, visualizing perhaps a sort of Venice: The waters of Babylon were undoubtedly impressive, but they only caused the exiles wandering on the banks to have more vivid remembrances of Zion. The mountains of Switzerland and the blue charm of the Mediterranean had never been able to take the place in her own memory that was occupied by the soft green landscape [of England] which smiled upon her the smile of an old servitor every time that she returned from abroad.44 Mr. Golding, in a ghastly piece entitled “Bare-Knuckle Lover,” was thinking of Babylon as a place of great antiquity, site of proverbial hanging gardens, but peopled with the fancy ladies of Herodotus and Baruch 6:42–43: “It was old in the hanging gardens of Babylon, when some lady of Nebuchadnezzar’s court smiled at the stalwart guardsman by the gate.”45 I read this as gritty realism rather than as a World War II era revival of the harlot image of the city, in those tumultuous times lacking moral import. One must conclude that Babylonia and Assyria, prior to the advent of Assyriology, entered the public consciousness with decidedly negative connotations and that these negative, especially biblical, overtones linger until the present as literary topoi, even in the writing of authors so worldly as W. Somerset Maugham. Although in literature, Babylon Location in Pre-Modern Europe and the Near East, eds. Jan Drijvers and Alasdair MacDonald (Leiden: E. J. Brill, 1995), 159–71. 44. F. Frankfort Moore, The White Causeway (London: Hutchinson, 1905), chap. 12. 45. Louis Golding, “Bare-Knuckle Lover,” in The Evening Standard Book of Best Short Stories (London: Search Publications, 1933), 152.


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gradually passed from being a biblical symbol of whoredom to a Classical metonym for “great metropolis,” even that was not always with positive connotations. Mesopotamian Discoveries When actual Mesopotamian relics reached public consciousness, it was the Assyrian bulls rather than the ruins of Babylon that inspired the strongest reaction. Dante Gabriel Rosetti was moved to ask: 23 24 25 26 27 28 29 30

What song did the brown maidens sing, From purple mouths alternating, When that was woven languidly? What vows, what rites, what prayers preferr’d, What songs has the strange image heard? In what blind vigil stood interr’d For ages, till an English word Broke silence first at Nineveh. 46

To Alfred Tennyson, the bulls looked pompous and oriental: 3 4 5 6 7

What if that dandy-despot, he, That jewell’d mass of millinery, That oil’d and curl’d Assyrian Bull Smelling of musk and of insolence, Her brother, from whom I keep aloof . . . .

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A. Conan Doyle saw the bulls as manly and virile; his professor (no philologist) “had the face and beard I associate with the Assyrian Bull.”48 The bull even spoke for himself, a Mesopotamian Ozymandias, in Charles Dickens’s Household Words (8 February 1851).49 I felt myself the guardian of the nation’s history, the emblem of its power, and the thought stamped itself on my features in a smile which has endured up to now, proud and at once solemn . . . . Now I stand in a strange land . . . in a city prouder, greater, more glorious than my native realm; but boast not ye vainglorious creatures of an hour. I have outlived many mighty kingdoms. . . . 46. Dante Rosetti, The Burden of Nineveh (1850). 47. Alfred Tennyson, Maud, a monodrama (1855) part 1, 6, stanza 6. 48. A. Conan Doyle, The Lost World (London: Hodder and Stoughton, [1912]). 49. I owe this reference to Henrietta Mc Call and Johnathan Tubb, I am the Bull of Nineveh: Victorian Design in the Assyrian Style (London: British Museum Press, 2003), 1.

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It is difficult today to realize the impact of Layard’s books about his excavations at Nineveh on nineteenth-century English and American writing. The American novelist Herman Melville, for example, was fascinated with Nineveh and Assyrians, references to which abound in his work, and the aged Wordsworth pronounced Nineveh and Its Remains the only interesting modern book he had read.50 Thackeray (see p. 65, n. 59 below) alludes to Layard by name. In the realm of decorative arts, the Assyrian bull appeared in British ceramics in 1851.51 One of Joseph Conrad’s characters uses stationery with a device of an Assyrian bull at the head.52 Edith Wharton permitted herself a reference to Assyrian art, perhaps not thinking of a bull, but a feminized Assurnasirpal: She still permitted herself the frivolity of waving her pale hair and its tight little ridges, stiff as the tresses of an Assyrian statue, were flattened under a dotted veil which ended at the tip of her cold-reddened nose.53 Moving beyond bulls, we find only a few references to inscriptions, such as Byron’s commemoration of Claudius Rich and his Babylonian bricks, a favorite among Assyriologists, in a rather lame passage: 62 63 64 65 66 67

Because they can’t find out the very spot Of that same Babel, or because they won’t (Though Claudius Rich, Esquire, some bricks has got And written lately two memoirs upon’t) Believe the Jews, those unbelievers, who Must be believed, though they believe not you. . . .54

I wonder, in my ignorance of its precise meaning, if the last couplet refers to Benjamin of Tudela, not the usual reading for an English milord. I suspect that he cribbed the information from Rich, who mentions Benjamin of Tudela as “who first revived the remembrance of the ruins.”55 50. Melville’s Assyriological allusions have been collected and analyzed by Dorothee Finkelstein, Melville’s Orienda (New Haven: Yale University Press, 1961), 144–51; extensive material has been assembled also by Steven Holloway, “Nineveh Sails for the New World: Assyria Envisioned in Nineteenth-Century America,” Iraq 66 (2004): 243–56. 51. Mc Call and Tubb, I am the Bull of Nineveh, 1, n. 6. 52. Joseph Conrad, The Arrow of Gold (London: T.F. Unwin, Ltd., 1919), chap. 3, 52. 53. Edith Wharton, “The Bunner Sisters,” in Xingu and Other Stories (New York: Charles Scribner’s Sons, 1916), 313. 54. Byron, Don Juan (1818), canto 5. 55. Claudius Rich, Memoir on the Ruins of Babylon (London: Longman, 1816), 48.


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Byron’s sense of doubt in these lines may be drawn from Rich’s Second Memoir on Babylon,56 which argues at length against a certain misguided major who had different views about the location of the place, so to Byron the question may have seemed doubtful as to what and where the ruins were. In any case, Rich is in good poetic company, for the same ample poem pillories Wordsworth’s verse in Babylonish terms: 7 8

And he who understands it would be able To add a story to the Tower of Babel.57

Gilbert and Sullivan, in the Major-General’s Song, refer to a “washing bill in Babylonic cuneiform,” updating and trivializing for the Victorian stage Butler, Hazlitt, and Brontë, but at least separating Babylonian from Aramaic.58 Thackeray, in his novel The Newcomes, also makes a direct reference to cuneiform, interesting for its early date of October 1854: When I quitted the hotel, a brown brougham, with a pair of beautiful horses, the harness and panels emblazoned with the neatest little ducal coronets you ever saw, and a cypher under each crown as easy to read as the arrow-headed inscriptions on one of Mr. Layard’s Assyrian chariots, was in waiting, and I presumed that Madame la Princesse was about to take an airing.59 Ruins are not a subject to inspire original thoughts; even for this millennial topos Assyrian and Babylonian ruins are rarely cited. An exception, however, is provided by Edith Wharton’s novel Glimpses of the Moon, where study of Mesopotamian archaeology is pronounced a dismal occupation for a young woman: “. . . she got so bitten with Oriental archaeology that she took a course last year at Bryn Mawr. She means to go to Baghdad next spring, and back by the Persian plateau and Turkestan . . . ” “Poor Coral! How dreary—”60 56. Claudius Rich, Second Memoir on Babylon (London: Longman, 1818). 57. Byron, Don Juan (1818), dedication. 58. William Gilbert and Arthur Sullivan, “Major-General’s Song,” The Pirates of Penzance (1879). 59. Thackeray, The Newcomes, vol. 2, no. 13 (October 1854), chapter 2, 17. 60. Edith Wharton, Glimpses of the Moon (New York; London: D. Appleton and Company, 1922), chap. 6, 59

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The proposed expedition becomes in that novel a sad symbol of a determined but second-rate mind’s aspirations. The housebroken archaeologist brought along by the family in its travels does not often get his chance to talk at lunch, though he adumbrates such subjects as Saracenic versus Sassanian influences on Byzantine art. Coral eventually marries an impoverished European nobleman instead of going to Mesopotamia, wistfully turning away from the only man for whom she might have felt real love. Two more specific Mesopotamian cultural references in English literature run to the bizarre. R. Austin Freeman, an English writer of detective fiction (1869–1943), refers in “The Red Thumb Mark” to a “rump steak fit for Shamash.”61 Freeman had a weakness for Assyria, it seems, for, under the pseudonym Clifford Ashdown, he published a story called “The Assyrian Rejuvenator.” The allusion, however, is simply to a fraud perpetrated by one of the characters in the story, so there is no question of an Assyrian coming to life, like the Egyptian museum guard in Doyle’s “Ring of Thoth,” not to mention other surviving ancient Egyptians in Gothic tales. Assyriologists in English Literature We begin with the acknowledgment that overly educated people, the sort to appreciate the possibilities of Assyriology, do not fare well in English novels. Heroines prefer sportsmen and good shots and riders, men of noble birth and long purses, good looks, gracious manners, a certain amount of wit and love of epigrams but not of learning. The only Assyriologist to meet many of these English novelistic criteria, Sir Henry Rawlinson, was active only at the beginning of the discipline and did not inspire any literature, so far as I am aware. A choice of devastating portraits of scholars in English literature will make this point. Hugh Broughton, perhaps England’s leading Hebraist of the early seventeenth century, was satirized, according to the Dictionary of National Biography, in Ben Jonson’s Volpone (acted 1605, printed 1607) and The Alchemist (1610), but these works spare no one, nor is philological scholarship an issue beyond the fact that Volpone, like gold, has the gift of many tongues. In his own time, Broughton was noted for his obnoxious personality, so we may ascribe Jonson’s attention to the man rather than to the profession of scholarship. Elizabeth Gaskell, in her gentler domestic comedy, Cranford (1851), sketches a pompous, pedantic, English clergyman who insists on pronouncing his daughter’s biblical name in Hebrew fashion. Among his widow’s papers is found one forlorn item, “Hebrew verses sent me by 61. Austin Freeman, “The Red Thumb Mark” (1907).


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my honoured husband. I thowt to have had a letter about killing the pig, but must wait.”62 This draws on a persistent theme in English literature, the sterility of Hebrew study, for which a seventeenth- and a nineteenth-century quotation will suffice. 57 58 59 60

For Hebrew roots, although they’re found To flourish most in barren ground, He had such plenty, as suffic’d To make some think him circumcis’d.63

The second is drawn from Robert Louis Stevenson, “An Apology for Idlers”: Might not the student afford some Hebrew roots, and the business man some of his half-crowns, for a share of the idler’s knowledge of life at large, and Art of Living?64 A particularly biting portrait of a scholar is that of Casaubon in George Eliot’s Middlemarch (1871–1872, set in the period 1829–1832). The novelist’s choice of name is no doubt owed to the great French Protestant Classicist, Isaac Casaubon (1559–1614), who, ironically, wasted years of his life on a futile inquiry for James I. The vexed question of who, if anyone, was the living model for Casaubon is discussed by G. Haight.65 Eliot’s Casaubon is an arid pamphleteer in the eighteenthcentury mode, of whose work Will Ladislaw has this to say, “. . . it is a pity that it should be thrown away, as so much English scholarship is, for want of knowing what is being done in the rest of the world. If Mr. Casaubon read German he would save himself a great deal of trouble . . . the Germans have taken the lead in historical inquiries, and they laugh at results which are got by groping about in the woods with a pocket compass while they have made good roads.”66 The worst criticism of Casaubon is yet to come, however: “He is not an Orientalist, you know. He does not profess to have more than second-hand knowledge there . . . Do you not 62. Elizabeth Gaskell, Cranford, in Household Words, vol. 4, no. 103 (1852): 590. 63. Butler, Hudibras, part 1, canto 1, lines 57–60. 64. Robert Louis Stevenson, “An Apology for Idlers,” in The Travels and Essays of Robert Louis Stevenson, Virginibus Puerisque, Memories and Portraits (New York: Charles Scribner’s Sons, 1900), 72. 65. Gordon Haight, George Eliot: A Biography (New York: Oxford University Press, 1968), 448–50 and appendix 1. 66. George Eliot, Middlemarch, chap. 21.

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Benjamin R. Foster see that it is no use now to be crawling a little way after men of the last century — living in an lumber-room and furbishing up broken-legged theories about Chus and Mizraim?”67

Poor Dorothy, who knows there is some truth to this, can only rejoin: “How can you bear to speak so lightly . . . If it were as you say, what could be sadder than so much ardent labor in vain . . . ?” Was Dorothy unconsciously echoing Jeremiah 51:58, where it is predicted that the Babylonians “shall labor in vain?” Casaubon of Middlemarch was writing a book like Fraser’s Golden Bough, in which Babylon probably had a place, but it was never finished. Dorothy marries a better man, who is no Orientalist either; however, George Eliot reminds us that Will’s was a cheap shot, as very little achievement is required to pity another man’s shortcomings. Even worse, Oliver Goldsmith (1728-1774) let his na¨ıve Vicar of Wakefield be swindled out of a horse by a rascal quoting Berossus and Manetho: “Manetho also, who lived about the time of NebuchadonAsser—Asser being a Syriac word usually applied as a surname to the kings of the country, as Teglat Phael-Asser, Nabon-Asser—he, I say, formed a conjecture equally absurd.”68 We thus rejoice in meeting a decent and tender-hearted philologist, Thurston Benson, in Elizabeth Gaskell’s Ruth (1853), Chapter XI, who goes so far as to pawn his copy of Jacopo Facciolati’s Lexicon Septem Linguarum (1835, assuming he had the latest edition) to help the spurned and fallen heroine stranded at a country inn.69 How many Assyriologists today would pawn their prized dictionary to help a damsel in distress? A novel by Rex Warner, The Professor (1938), imagines what would happen if a Classicist had become “chancellor” of England during the grim years before World War II. One is relieved that this literary mantle did not fall on Sidney Smith or Cyril Gadd. If scholars as a group did not fare well, Assyriologists hardly appear at all in English literature. If one may claim him for the brotherhood, A. H. Layard is sometimes thought to have been the model for the trav67. Ibid., chap. 22. 68. Oliver Goldsmith, The Vicar of Wakefield (Dublin: W. and W. Smith et al., 1766), chap. 14. 69. Elizabeth Gaskell, Ruth (London: Chapman and Hall, 1853), 222-250.


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eller Murthwaite in Wilkie Collins’s The Moonstone (1868).70 Layard was a celebrity whom Collins had met, but other candidates have been offered, so the honor is not uncontested. Sinclair Lewis refers in passing to a “kindly and ruminating old Professor Deakins, the Assyriologist,” whom Dodsworth meets, along with other interesting types, on his first ocean voyage.71 Kindliness not being a quality readily associated with Assyriologists, one wonders who prompted this recollection in Lewis’s mind. Sayce, both a kindly and an inveterate traveler, comes to mind, but not for a transatlantic voyage; perhaps Langdon or Lyon might be suitable candidates. By far the most memorable Assyriologist in English literature is Dr. Ledsmar in Harold Frederic’s novel The Damnation of Theron Ware (1896). Decent, sincere young Theron Ware is brought to perdition by a handsome young woman of pagan Classical inclinations, a Roman Catholic priest, and an Assyriologist, as unholy a trinity as could be found anywhere in American conservative Protestant demonology. The not-very-kindly Ledsmar is author of a book on snake worship (to me heavy-handed Edenic symbolism on the part of Frederic), the English edition of which sold poorly in comparison to the German one, as might be expected, since it was proverbial among American Orientalists that Germans would believe anything. This person is introduced with the American hyperbole of the time, “there is perhaps not another man in the country who knows Assyriology so thoroughly as our friend here, Dr. Ledsmar.”72 Ledsmar, unlike most Assyriologists, is only a year or two behind in his reading. He possesses a fine library: “Delitzsch is very interesting; but Baudissin’s Studien zur Semitischen Religionsgeschichte would come closer to what you need. There are several other important Germans, — Schrader, Bunsen, Duncker, Hommel, and so on.”73 Theron Ware, not unlike many American graduate students of later generations, has to explain, “Unluckily I — I don’t read German readily.” Very much in the spirit of Will Ladislaw, the remorseless Ledsmar goes on, 70. I thank Joyce Connolly, Department of Classics, New York University, for this suggestion. 71. Sinclair Lewis, Dodsworth (New York: Harcourt, Brace and Company, 1929), chap. 6, 44. 72. Harold Frederic, The Damnation of Theron Ware; or, Illumination (New York: Stone and Kimball, 1896), 105. 73. Ibid., 106.

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Benjamin R. Foster “That’s a pity, . . . because they do the best work,—not only in the field, but in most others. And they do so much that the mass defies translation. Well, the best thing outside of German of course is Sayce. I daresay you know him, though.” The Rev. Mr. Ware shook his head mournfully. “I don’t seem to know any one,” he murmured. The others exchanged glances. . . .74

This heavy reading list may not be so familiar to today’s Assyriologist as it was to Ledsmar. Max Duncker wrote a massive universal ancient history, a triumph of Classical learning.75 An English translation, History of Antiquity, appeared in 1877, the existence of which Ledsmar perhaps concealed from Ware out of pedantry (like Ledsmar’s book, Duncker’s was clearly more popular in the German-speaking world than in England or the United States). Carl Bunsen (1791–1860) was different fare. Several of his works appeared in English, such as Christianity and Mankind,76 and Outlines of the Philosophy of Universal History, Applied to the Language and Religion.77 He was, however, probably best known to American readers like Ledsmar from the five volumes of chatty notes and essays by the linguist Max M¨ uller, entitled Chips from a German Workshop.78 Ware finally borrows books by Sayce, Budge, Lenormant, and Renan but does not get much further in his reading than Renan’s Recollections of My Youth, perhaps because of Renan’s infamous confession of his loss of faith. Delitzsch to an American readership would have implied the height of modern German scholarly atheism, even though his famous lectures had not yet appeared in Theron’s time. The Assyriologist will find much of interest in this novel and will wonder where the novelist got his Assyriology. The priest, Father Forbes, who is given to purring chuckles and twinkles in his eye, informs the horrified Ware (Chapter 7) that the English name Marmaduke is derived from Marduk: “Take the modern name Marmaduke, for example. It strikes one as peculiarly modern, up-to-date, doesn’t it? Well, it is the oldest name on earth, — thousands of years older than Adam. It is the ancient Chaldaean Meridug, or Merodach. 74. Ibid., 106. 75. Geschichte des Alterthums, with editions in 1852, 1855, 1860, 1875, and 1879. 76. Carl Bunsen, Christianity and Mankind (London: Longman, 1854). 77. Carl Bunsen, Outlines of the Philosophy of Universal History, Applied to the Language and Religion (London: Longman, 1854). 78. Max M¨ uller, Chips from a German Workshop (New York, C. Scribner’s Sons, 1869–1877).


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He was the young god who interceded continually between the angry, omnipotent Ea, his father, and the humble and unhappy Damkina, or Earth, who was his mother. This is interesting from another point of view, because this Merodach or Marmaduke is, so far as we can see now, the original prototype of our ‘divine intermediary’ idea. I daresay, though, that if we could go back still other scores of centuries, we should find the whole receding series of types of this Christmyth of ours.”79 Ware understandably feels that he was “among sinister enemies, at the mercy of criminals,” “the sweat standing on his brow, and his jaw dropped in a scared and bewildered stare.” I have not looked for the source of Father Forbes’ remarks. While one might immediately suggest some of Sayce’s numerous publications and public lectures or perhaps articles by William Hayes Ward (1835– 1916), who wrote frequently, after 1867, on Assyriological topics in the New York Independent, replete with translations from Akkadian, these two men were both Christian gentlemen, unlike Father Forbes, so one hesitates to ascribe such blasphemy to them. Sayce, for example, prefaced his lecture series, The Religions of Ancient Egypt and Babylonia,80 by declaring an “impassable gulf” between those extinct and barbaric faiths and Christianity. Marmaduke not being a common American name, however, one looks to England for the source of this curious idea, even if it is here propounded by an Irishman. Forbes’s ghastly heresy would not have been out of place or even remarkable in the German Assyriology of the time. Hugo Radau, a firstrate epigrapher of the next generation, produced a monograph called Bel, the Christ of Ancient Times.81 This has a lot about Marduk rising from the dead (no mention of Marmaduke), and some association the scabrous priest would have enjoyed, such as “Easter and Ishtar are the same word. It has come into the English language from the Germans, who worshipped the goddess Ostara. . . .”82 Marduk’s major achievement each spring, besides coming alive, was, according to Radau, who perhaps spent too much time in Chicago, driving away the cold wintry weather.83 Honorable mention must be made of Agatha Christie’s Murder in Mesopotamia, which includes not only an Assyriologist but some As79. Frederic, The Damnation of Theron Ware, 110–11. 80. Archibald Sayce, The Religions of Ancient Egypt and Bablyonia (Edinburgh: T. & T. Clark, 1903). 81. Hugo Radau, Bel, the Christ of Ancient Times (Chicago: Open Court, 1908). 82. Radau, Bel, 49, n. 2. 83. Ibid., 54.

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syriology, drawn from a historical omen on the Sargonic kings. But this was an inside job. Assyriology and the Artistic Imagination Cuneiformists today bask in the lights of stage productions of Gilgamesh too numerous to number, not to mention retellings of the epic for children and seekers after erotic fantasy. They never tire of mentioning that Rilke said he liked the epic; indeed, one leading Assyriologist wrote an article on that rather slender subject.84 Predictable portions of the epic have been set to music, such as an elaborate oratorio by the expatriate Czech composer Martin˚ u (1954), based on Campbell Thompson’s 1928 translation.85 It was written when Martin˚ u, in exile from his homeland, was hoping to escape “the Babylon which is New York” (I owe this reference to an essay in the 1974 Supraphon recording). Martin˚ u, in his gilded youth, wrote a ballet, Istar (1924), in which the goddess seeks out Tammuz from jealous Irkalla and wins him back with her love. There is even a musical setting of portions of the Babylonian Creation Epic by a Manchurian composer, Vladimir Ussachevsky, but few Assyriologists have been privileged to hear this work performed.86 Belshazzar also stars in an opera by G.F. Handel and Semiramis in one by Rossini, but these, of course, owe nothing to Assyriology. For belles-lettres, however, the harvest is meager, but not without interest. A technically rich nineteenth-century novel set in Babylonia comes from the pen of a best-selling author of her time, Elizabeth Stuart Phelps (1844–1911). This is called The Master of the Magicians and appeared in 1890. The Assyriologist will peruse it with something like fascination for the forgotten professional lore of his discipline that it purveys. Who recalls today what Ledsmar surely knew, that Egibi was once considered a Jewish firm, Egibi being Babylonian for Jacob? What enterprising mathematician calculated the number of bricks in the wall Imgur-Bel: “eighteen thousand seven hundred and sixty five millions, or twice the amount of masonry used in building the great Chinese wall”? There are even translations of Babylonian literature ornamenting the puny plot. The eminence grise behind the production of this piece was Ms. Phelps’s husband and co-author, Herbert D. Ward, son of William Hayes Ward. Young Ward must have soaked up a fair amount of 84. William Moran, “Rilke and the Gilgamesh Epic,” Journal of Cuneiform Studies 32 (1980): 208–10. 85. Bohuslav Martin˚ u, The Epic of Gilgamesh, 1954. 86. Jack Sasson, “Musical Settings for Cuneiform Literature: A Discography,” in Gilgamesh: A Reader, ed. John Maier (Wauconda, Illinois: Bolchazy-Carducci Publishers, 1997), 169–74. Sasson draws attention as well to another treatment of the Istar-Tammuz story by the French composer d’Indy.


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Assyriology in his parental home, as William published regularly about Mesopotamia and had led the Wolfe expedition that identified Nippur as the most promising site for an American excavation. A later novelistic entry on the the Babylonian scene is Margaret Horton Potter’s Istar of Babylon, A Phantasy (1902).87 An American who died young (1881–1911), she produced various novels, set in the United States for the most part, dealing with urban life, the evils of wealth and loveless marriages, and the like. This novel seems to be her sole venture into Mesopotamia. The Assyriologist twitches to make it Ishtar, as he wants to with the Martin˚ u ballet, but Mrs. Potter, like Martin˚ u, overlooked a diacritic somewhere in her reading (an odd omission for a Czech). The novel begins with some elevating quotations from Plato, preparing us for the main plot: a Greek youth, feeling a strange yearning to meet Istar of Babylon, forsakes the parental roof in Sicily to set out for the Orient. He receives his éducation sentimentale from a Phoenician priestess, in keeping with the traditional belief that Phoenicians had no morals, and finds his way to Babylon, where he is caught up in a whole series of adventures culminating in the death of Nabonidus, the murder of Belshazzar, and the conquest of Cyrus, called Kurush for authentic local color. In this work too the Egibi are Jews of fabulous wealth. I doubt if any other historical novel in English can claim chapter titles as tantalizing as “Sippar” and “The Regiment of Guti,” but rivals may lurk among the remnants of Victorian imagination that must have escaped my attention. In Istar of Babylon, the goddess herself is a character; her speech can run to the mystical: “Sweeter than all the rest are hard, higher than sin is low, more joyful than death is sad, love reigns over men. Love is the central fire of God, as we are but its outer rays. Love walks through all the earth, passing to and fro among men, making them to forswear sin, to forget suffering, to overcome death.”88 Suitably for its lofty subject, the prose of this work is sometimes overheated: “But now—now —for two years past, all Babylonia, from Agˆ adé to the gulf, had been in a state of feverish religiosity, for the reason that there was a goddess in Babylon: a 87. Margaret Potter, Istar of Babylon, A Phantasy (New York: Harper and Brothers, 1902). 88. Ibid., 135.

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Benjamin R. Foster goddess—a living, baffling, radiant presence, whose origin none knew. . . .”’89

Istar, who has harbored a tender passion for Belshazzar, reveals her plague-stricken face to Cyrus at the end. She tells Cyrus that “There is no god but God” and “Him, in their hearts, all men must worship,” then drops her veil to reveal her “frightful complexion” and “swollen, red, matterated, nearly closed” eyes. “She was hideous now—hideous beyond belief.” In the emotional colloquy that follows, Istar rather tactlessly predicts the coming of Alexander: “One more conqueror she shall know: a youth of iron from a land of gold. . . After him the East grows black. The rose shall wither unseen upon her tree.”’90 This prediction leads us to suspect that Istar was not professing Islam in her previous remarks, as could well be supposed. In any case, Cyrus tells his son Bardiya, in the same hushed tone as the centurion at the crucifixion, “She is a woman sent of God.” Suffice it to say that Istar, having suffered, is transfigured and carried up to heaven with her soul mate, Belshazzar. At the risk of being cloyed by the Neo-Babylonian period, one may make honorable mention of a distinctive combination of learning and fantasy that appeared in English in 1931, G.R. Tabouis’s Nebuchadnezzar. Ms. Tabouis had already produced a private life of Tutankhamun that had been crowned by the French Academy, but the new subject posed, even for her, a mighty challenge: “To cope with it required all the qual´ ifications of this Parisienne, a pupil of the Ecole du Louvre, who sat at the feet of men like Dussaud and Contenau and had been nurtured in the bosom of politics and history.” This fourfold qualification stood her in good stead, as her mélange of a novel and a historical work, teeming with learned commentary and translations from original sources, Gallic eroticism, and archaeological discourse, is on quite a different level from the preceding. A section having to do with prostitution, for example, is richer with footnotes (here omitted) than such episodes usually are and is carried on in authenticated racy Babylonian love-talk, drawn from Gilgamesh: “In the lower quarters, the harlots, ‘the daughters of sweetness,’ with their girdles of string around their waists,72 sat 89. Ibid., 177. 90. Ibid., 480.


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on their doorsteps, burning olive-stones to their gods on braziers,73 and watched for young noblemen returning from the Bride Fair. From their necks hung Aban-la-erie, the Stone of Non-conception, the harlot’s stone,74 on their scarcely veiled bosoms. “One of them pointed to a blushing youth, and said to her neighbours, ‘See him! Behold his face! He shines with nobility, he is mighty, all his body breathes delight!’ Flattered, the youth went up to them, stammering, ‘They are filled with delight. They are full of joy.’75 ”91 More recent novelistic works about Mesopotamia have fortunately branched out to other periods and subjects, as one has the feeling that the Neo-Babylonian Empire has been adequately fictionalized. Nicholas Guild’s The Assyrian (1987), for example, stars Tiglath Ashur and Esarhaddon, who “share their women, their secrets, and their dreams.” Their “enchanting cousin,” Esharhamat, becomes the wife of one and the lover of the other, and so forth. Needless to say, Esarhaddon wins out in the race to be king, but Tiglath Ashur finds other consolations. According to one blurb, reviewers deemed it “stunning,” “not stuffy,” “not a novel to be swilled down in gulps,” and with good “period detail,” so the Assyriologist will keep mum before such a claque. Would “stuffy” characterize a work of more authoritative Assyriological content? The student of Neo-Assyrian epistolography can console himself by reading a letter of Esarhaddon otherwise not attested: “I am constantly pestered with warnings that I must rebuild Babylon before the patience of heaven is exhausted. . . .”92 In mirror image of the Sicilian Greek hero of Istar, who ultimately settles happily in Babylon, the Assyrian hero of this tale settles happily somewhere in the Greek-speaking world. Jenny G. Fyson, thanks to Woolley’s work at Ur, contributed a novel called The Three Brothers of Ur (1964), starring the likes of Shamashazir, Serag, and Haran, set in the Old Babylonian period. These people speak normally, unlike the Neo-Babylonians (“Don’t be silly!”), and the Sumerians among them are “round, kindly, and laughing.” The “accurate historical detail” includes a key role for the sacred Teraphim. Should we thank the Assyriologist E.A. Speiser for this, who thought he had found Teraphim at Nuzi? 91. Genvi` eve Tabouis, Nebuchadnezzar, with a preface by Gabriel Hanotaux of the French Academy (London: George Routledge and Sons, Ltd., 1931), 252. 92. Nicholas Guild, The Assyrian (New York: Atheneum, 1987), 332.

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Robert Silverberg’s Gilgamesh the King (1984) is another entry in the “blockbuster” category, imaginative and clever, with plenty of randy Sumerian love dialogue but no footnotes, as the author had not sat at the feet of Contenau. A French translation of it, Gilgamesh, roi d’Ourouk (1990) has returned the favor of Tabouis to Paris: “Vous n’ignorez pas le rituel des amants devins, le jeu des lèvres et des mamelons, des fesses et des mains, des bouches et des sexes. Sa peau était brˆ ulante comme la glace des montagnes du Nord, ses mamelons dans mes mains plus durs que l’albˆ atre. . . .”93 The contemporary American writer Rhoda Lerman evokes Melville, whose Assyriological interests were noted above, in the punning title of her memoir Call Me Ishtar (1973). The goddess obligingly enough begins by providing a detailed curriculum vitæ, giving her age as e=mc2 , her social activities as sacred prostitution, and her temporary address as Syracuse, New York. The narrative is in a rather different style from Ms. Potter’s: “Ishtar lay in her king-size bed, lilies of semen-crusted Kleenex scattered on the olive turf floor beneath her as she languidly twisted the globe of her Spitz Junior Planetarium, weaving summer heavens into winter heavens, night by night on the darkened plaster of the ceiling. She plunged Ursa Major over a green fly flattened last summer.”94 The goddess’s language is rather less chaste than that in Ms. Potter’s version: “I, who am unsparing of the fang. I who am both cunning and lingual.” Assyriology is the quintessential boring subject in Angus March’s satirical novel on the British academic scene, Anglo-Saxon Attitudes (1956), in which a pathetic old geezer on a TV show spouts: “Mesopotamia, the birthplace of civilization, has revealed its mighty temples, its rich carvings and its strange writing cut in stone known to scholars as cuneiform . . . .”95 93. Robert Silverberg, Gilgamesh, roi d’Ourouk (Paris: L’Atalante), 125. 94. Rhoda Lerman, Call Me Ishtar (New York: Holt, Reinhart, and Winston, 1973), 143. 95. Part 2, chapter 2.


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His embarrassed daughter, watching him, exclaims, “Oh my God! . . . I can’t bear it! . . . I knew something awful would happen. . . .” The bad habits of Assyriologists have come home to roost in a farrago by Armand Schwerner, The Tablets (1968). This is dressed up in the grimoires of Assyriology, including square brackets, dots, and missing fragments, and may be inspired by the old fantasy that ancient Oriental literatures were as obsessed with sex as modern literatures can be. It is dismally fleshy, for line after flaccid line, and left this reader wishing that its particular tablets had been more thoroughly broken before publication. It lacks the spice of Lerman’s ready wit and endless puns. To say that ancient Mesopotamian still needs a first-rate Muse in English literature would be a sad understatement. References Armstrong, Adrian. “Semiramis in Grand Rhétoriqueur Writing.” In Centres of Learning, Learning and Location in Pre-Modern Europe and the Near East, edited by Jan Drijvers and Alasdair MacDonald, 159–71. Leiden: E. J. Brill, 1995. Arnaud, Daniel. Nabuchodnosor II roi de Babylone. Paris: Fayard, 2004. Babelon, Ernest. Manual of Oriental antiquities, including the architecture, sculpture, and industrial arts of Chaldæa, Assyria, Persia, Syria, Judæa, Phœnicia, and Carthage. London: H. Grevel and Co., 1906. Bennett, Arnold. The Grand Babylon Hotel. New York: New Amsterdam Book Company, 1902. ———. The Lion’s Share. London: Cassell, 1916. Bottéro, Jean. “In Defense of a Useless Science.” In Mesopotamia, Writing, Reasoning and the Gods, translated by Zainab Bahrani and Marc Van De Mieroop, 15–25. Chicago: University of Chicago Press, 1993. Brontë, Charlotte. Villette. 3 vols. London: Smith, Elder, and Co., 1853. Brown, Dennis. Vir Trilinguis: A Study in the Biblical Exegesis of Saint Jerome. Kampen: Kok Pharos Publishing House, 1992. Bunsen, Carl. Christianity and Mankind. London: Longman, 1854. ———. Outlines of the Philosophy of Universal History, Applied to the Language and Religion. London: Longman, 1854. Butler, Samuel. Hudibras, in Three Parts, Written in the Time of the Late Wars. 1663–64. Reprint, with large annotations and a preface by Zachary Grey, LL.D., London: T. Bensley, 1799.

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Byron, George. To Belshazzar. 1814. ———. The Destruction of Sennacherib. 1815. ———. Sardanapalus. 1821. ———. Don Juan. 1821. Christie, Agatha. Murder in Mesopotamia. New York: Dodd, Mead and Company, 1936. Christy, Arthur, ed. The Asian Legacy and American Life. New York : The John Day Company, 1945. Collins, Wilkie. The Moonstone. A Novel. New York : Harper and Brothers, 1868. Conant, Martha. The Oriental Tale in England in the Eighteenth Century. New York: The Columbia University Press, 1908. Conrad, Joseph. The Arrow of Gold. London: T.F. Unwin, Ltd., 1919. Coogan, Robert. Babylon on the Rhˆ one: A Translation of Letters by Dante, Petrarch, and Catherine of Siena on the Avignon Papacy. Madrid: José Porr´ ua Turanza, 1987. d’Indy, Paul. Istar. 1896. Daniel, Norman. Islam, Europe and Empire. Edinburgh: University of Edinburgh Press, 1966. de Meester, Marie. Oriental Influences in the English Literature of the Nineteenth Century. Anglistische Forschungen, vol. 46. Heidelberg: Carl Winter, 1915. Doyle, A. Conan. The Lost World. London: Hodder and Stoughton, 1912. ———, “The Ring of Thoth.” 1890. Drews, Robert. The Greek Accounts of Eastern History. Washington, District of Columbia: Center for Hellenic Studies, 1973. Eliot, George. Middlemarch. Harper’s Weekly, 16 December, 1871–15 February, 1873. Finkelstein, Dorothee. Melville’s Orienda. New Haven: Yale University Press, 1961. Fitzgerald, F. Scott. Babylon Revisited. The Saturday Evening Post, 21 February, 1931. Fraser, James. Golden Bough. 1890. Frederic, Harold. The Damnation of Theron Ware; or, Illumination. New York: Stone and Kimball, 1896. Freeman, Austin. “The Red Thumb Mark.” 1907. ———. [Clifford Ashdown pseud.] “The Assyrian Rejuvenator.” 1902. Fyson, Jenny. The Three Brothers of Ur. London: Oxford University Press, 1964.


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Gaskell, Elizabeth. Cranford. Household Words, December 1851–May 1853. ———, Ruth. London: Chapman and Hall, 1853. Gilbert, William and Arthur Sullivan. “Major-General’s Song,” The Pirates of Penzance. 1879. Golding, Louis. “Bare-Knuckle Lover.” In The Evening Standard Book of Best Short Stories. London: Search Publications, 1933. Goldsmith, Oliver. The Vicar of Wakefield. Dublin: W. and W. Smith et al., 1766. Gorges, Arthur, ed. Lucans Pharsalia: Containing the Ciuill Warres betweene Cæsar and Pompey. Written in Latine heroicall verse by M. Annæus Lucanus. Translated into English verse by Sir Arthur Gorges Knight. Whereunto is annexed the life of the authour, collected out of divers authors. London: [Nicholas Okes], 1614. Guild, Nicholas. The Assyrian. New York: Atheneum, 1987. Haas, Volkert. “Die literarische Rezeption Babylons von der Antike bis zur Gegenwart.” In Babylon: Focus mesopotamischer Geschichte, Wiege fr¨ uher Gelehrsamkeit, Mythos in der Moderne: 2. Internationales Colloquium der Deutschen Orient-Gesellschaft 24.–26. M¨ arz 1998 in Berlin, edited by Johannes Renger, 523–52. Saarbr¨ ucken: Saarbr¨ ucker Druckerei und Verlag, 1999. Haight, Gordon. George Eliot: A Biography. New York: Oxford University Press, 1968. Handel, George. Belshazzar. 1744. Hazlitt, William. “On Paradox and Common-Place.” Table Talk 1 (1821). Holloway, Steven. “Nineveh Sails for the New World: Assyria Envisioned in Nineteenth-Century America.” Iraq 66 (2004): 243– 56. Humbert, Jean-Marcel. Egyptomania: Egypt in Western Art 1730-1930. Ottawa: National Gallery of Canada, 1994. Johnson, Samuel. “Life of Milton.” In The Lives of the Most Eminent English Poets with Critical Observations on their Works. Vol. 1. London: C. Bathurst, et al., 1781. Jonson, Ben. “Volpone.” 1605. ———. “Alchemist.” 1610.

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Kratz, Reinhard. “Babylon im Alten Testament.” In Babylon: Focus mesopotamischer Geschichte, Wiege fr¨ uher Gelehrsamkeit, Mythos in der Moderne: 2. Internationales Colloquium der Deutschen Orient-Gesellschaft 24.–26. M¨ arz 1998 in Berlin, edited by Johannes Renger, 477–90. Saarbr¨ ucken: Saarbr¨ ucker Druckerei und Verlag, 1999. Layard, Austen. Nineveh and Its Remains. 2 vols. London: John Murray, 1849. Lerman, Rhoda. Call Me Ishtar. New York: Doubleday and Co., 1973. Lewis, Sinclair. Dodsworth. New York: Harcourt, Brace and Company, 1929. Martin˚ u, Bohuslav. Istar. 1924. ———. The Epic of Gilgamesh. 1954. March, Angus. Anglo-Saxon Attitudes. New York: Viking Press, 1956. Maugham, W. Somerset. The Narrow Corner. 1932. May, Thomas, trans. Lucans Pharsalia, or, The civil-wars of Rome, between Pompey the Great, and Julius Cæsar, the Whole Ten Books Englished by Thomas May, Esquire, fourth edition. London: William Beaty, 1650. Mc Call, Henrietta and Johnathan Tubb. I am the Bull of Nineveh: Victorian Design in the Assyrian Style. London: British Museum Press, 2003. Meredith, George. The Amazing Marriage. New York: C. Scribner’s Sons, 1895. Melville, Herman. Moby-Dick; or, The Whale. (New York: Harper and Brothers, 1851). Milton, John. Paradise Lost. 1667. Moran, William. “Rilke and the Gilgamesh Epic.” Journal of Cuneiform Studies 32 (1980): 208–210. Moore, F. Frankfort. The White Causeway. London: Hutchinson, 1905. M¨ uller, Max. Chips from a German Workshop. 5 vols. New York, C. Scribner’s Sons, 1869–1877. Pettinato, Giovanni. Semiramis: Herrin u ¨ber Assur und Babylon: Biographie. Zurich: Artemis, 1988. Phelps, Elizabeth. The Master of the Magicians. Boston; New York: Houghton, Mifflin and Company, 1890. Potter, Margaret. Istar of Babylon, A Phantasy. New York: Harper and Brothers, 1902. Radau, Hugo. Bel, the Christ of Ancient Times. Chicago: Open Court, 1908. Recht, Charles. Babylon on Hudson. New York: Harper, 1932. Renan, Ernest. Recollections of My Youth. London: Chapman, 1883.


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Rice, Eugene. Saint Jerome in the Renaissance. Baltimore: Johns Hopkins University Press, 1985. Rich, Claudius. Memoir on the Ruins of Babylon. London: Longman, 1816. ———. Second Memoir on Babylon. London: Longman, 1818. Ridley, Edward, trans. “The Pharsalia of Lucan.” London: Longman, Green, and Co., 1896. Rosetti, Dante. The Burden of Nineveh. 1850. Rossini, Gioacchino. Semiramide. 1823. Samuel, Irene. “Semiramis in the Middle Ages: The History of a Legend.” Medievalia et Humanistica 2 (1944): 32–44. Sasson, Jack. “Musical Settings for Cuneiform Literature: A Discography.” In Gilgamesh: A Reader, edited by John Maier, 169– 74. Wauconda, Illinois: Bolchazy-Carducci Publishers, 1997. Sayce, Archibald. The Religions of Ancient Egypt and Bablyonia. Edinburgh: T. & T. Clark, 1903. Schwerner, Armand. The Tablets. Orono, Maine: National Poetry Foundation, 1999. Sha’ban, Fuad. Islam and Arabs in Early American Thought: The Roots of Orientalism in America. Durham, North Carolina: Acorn Press, 1991. Shakespeare, William. 2 Henry IV. ———. Henry V. ———. Julius Caesar. ———. Twelfth Night. Silverberg, Robert. Gilgamesh, roi d’Ourouk. Paris: L’Atalante,1990. Stevenson, Robert Louis. “An Apology for Idlers.” In The Travels and Essays of Robert Louis Stevenson, Virginibus Puerisque, Memories and Portraits. New York: Charles Scribner’s Sons, 1900. Swift, Johnathan. “Reasons Humbly offered to the Parliament of Ireland for Repealing the Sacramental Test, etc. in favour of the Catholics, Otherwise called Roman Catholics, and by their IllWillers Papists.” 1733. Tabouis, Geneviève. Nebuchadnezzar. With a preface by Gabriel Hanotaux of the French Academy. London: George Routledge and Sons, Ltd., 1931. Tennyson, Alfred. Maud, A Monodrama. 1855. Thackeray, William [A. Pendennis, Esq. pseud.]. The Newcomes : Memoirs of a Most Respectable Family. London: Bradbury and Evans, 1853–55.

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———. History of Henry Esmond, Esq. : A Colonel in the Service of Her Majesty Queen Anne Written by Himself. London: Smith, Elder and Company, 1852. Ullendorff, Edward. “ ‘C’est de l’Hebreu pour moi!’.” Journal of Semitic Studies 13, no. 1 (1968): 125-135. Ussachevsky, Vladimir. Creation Prologue. 1961. ———. Conflict. 1971. ———. Creation Epilogue. 1971. Warner, Rex. The Professor. London: Boriswood, 1938. Wharton, Edith. “The Bunner Sisters.” In Xingu and Other Stories. New York: Charles Scribner’s Sons, 1916. ———. Glimpses of the Moon. New York; London: D. Appleton and Company, 1922. Wodehouse, P. G. Joy in the Morning. Garden City, New York: Doubleday and Company, 1946. Wright, Frederick, ed. and trans. Select Letters of St. Jerome. Loeb Classical Library, vol. 262. Cambridge, Massachusetts: Harvard University Press, 1963.

The Eyes of Nefertiti Karen Polinger Foster∗ Yale University

Introduction On 6 December 1912, German archaeologists excavating the compound of the sculptor Thutmose at Amarna (Akhetaten) discovered one of the most famous pieces of Egyptian art, as well as a modern icon of ancient beauty—the bust of Nefertiti.1 Thutmose, “Chief Crafts∗ Early versions of this paper were given in 1991 at the College Art Association panel session on “Unfinished Works of Art,” organized by Charles K. Steiner; in 1996 in New York and Cairo, under the auspices of the American Research Council in Egypt lecture series; and in 1996 at Connecticut College. I am grateful to Florence Friedman, William K. Simpson, John Baines, and Roswitha Schulz for many helpful comments and other assistance. It has been a special pleasure to contribute a revised version to this volume honoring Alice Slotsky, the kind of student every teacher dreams of having, who went from sitting diffidently in the back row of my classes to standing deservedly at the forefront of pedagogy and scholarship. 1. The bust bears museum number Berlin 213000; height 48 cm, width at base 19.5 cm. For an account of the discovery and subsequent history of the bust, with full references, see Rolf Krauss, “1913–1988: 75 Jahre Buste der Nofrete-Ete/NeferetIti in Berlin,” Jahrbuch Preussischer Kulturbesitz 24 (1987): 87–124 and Jahrbuch Preussischer Kulturbesitz 28 (1991): 123–57. According to some, after World War I Germany considered returning the piece: Pierre Crabit` es, “The Bust of Queen Nefertiti,” The Catholic World 139 (1934): 207–12. Today it is among the marquee works sought by Egypt. For two current views on the matter, see the articles by Kurt Siehr and Stephen Urice in Imperialism, Art, and Restitution, ed. John Merryman (Cambridge, forthcoming). The most thorough art historical treatment of the bust remains Rudolf Anthes, The Head of Queen Nofretete (Berlin: Mann, 1961). The Amarna bibliography is vast. To Geoffrey Martin’s compilation of over 2000 items in A Bibliography of the Amarna Period and Its Aftermath (London: Kegan Paul International, 1991), add now especially Dorothea Arnold, The Royal Women of Amarna: Images of Beauty from Ancient Egypt (New York: Metropolitan Museum of Art, 1996) and Rita Freed et al., eds., Pharaohs of the Sun: Akhenaten, Nefertiti, Tutankhamen (Boston: Museum of Fine Arts, 1999), both of them exhibition catalogues with lengthy bibliographies. For many, Nefertiti transcends scholarship and time. Nikos Katzanzakis, for instance, thought that the poet Rachel Mintz was the reincarnation of Nefertiti, as reported in Elie Wiesel, Memoirs: All Rivers Run to the Sea (New York: Knopf, 1995), 201–2. To cite another example, for a 1930s

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man, Sculptor, and Favorite of the King” in the latter years of Akhenaten’s seventeen-year reign, seems to have run an increasingly busy establishment, enlarging the original studio plan on several occasions to accommodate workspace and sleeping quarters for additional craftsmen.2 Nearly all of the projects he undertook were royal commissions; he perhaps had some private clients too.3 When Thutmose’s studio was abandoned in the early post-Amarna period, chisels, palettes, and other tools were left in the workrooms, even a set of house keys in a jar.4 Dozens of artworks were collected, evidently no longer wanted as the royal and non-royal individuals depicted were either dead or had ceased to be important in the new era. Over fifty sculptures and inlays, the bust among them, were placed in a small, pantry-like room, 2.5×5.7 m, just off a columned hall, its second door to a courtyard with a central well having been blocked.5 Many of the objects seem to have served as models or essays, with black lines and hatch marks indicating areas to be colored, inlaid, or contoured, as guidance for future efforts.6 The painted limestone bust costume ball the Santa Fe activist Elizabeth White transformed herself into a compelling Nefertiti, albeit with Pueblo and Orientalist elements: Gregor Stark and E. Catherine Rayne, El Delirio: The Santa Fe World of Elizabeth White (Santa Fe: School of American Research Press, 1998). 2. On the studio of Thutmose, see Arnold, The Royal Women of Amarna, 41– 83. The sculptor’s names and titles are known from an ivory fragment found in the house, which has been newly reconstructed as a horse blinder, not a lid as previously thought: Rolf Krauss, “Der Bildhauser Thutmose in Amarna,” Jahrbuch Preussischer Kulturbesitz 20 (1983): 119–32. 3. Arnold, The Royal Women of Amarna, 41–42. 4. The stages and chronology of the exodus from Amarna are still not entirely clear. On the removal of building materials, see Piers Crocker, “Status Symbols in the Architecture of el-Amarna,” Journal of Egyptian Archaeology 71 (1985): 52–65; Ian Shaw, “Balustrades, Stairs, and Altars in the Cult of the Aten at el-Amarna,” Journal of Egyptian Archaeology 80 (1994): 122. Recent stratified finds of certain inscribed objects suggest that during the reign of Tutankhamun “parts of the city were seen to have a very definite future” (Barry Kemp, “El-Amarna,” Report of the Egypt Exploration Society, 1986–1987, 7). 5. Arnold, The Royal Women of Amarna, 36 and 43, where she speculates that Thutmose and his assistants took their most valuable tools and still-useful models with them. As she observes, the context and room alterations probably carried out at the time of storage would seem to argue against these sculptures having been simply forgotten. 6. Among numerous studies of Egyptian sculptors’ methods, see Whitney Davis, The Canonical Tradition in Ancient Egypt (Cambridge: Cambridge University Press, 1989), 41–46, 94–115; Gay Robins, Proportion and Style in Ancient Egyptian Art (Austin: University of Texas Press, 1994); Eric Young, “Sculptors’ Models or Votives? In Defense of a Scholarly Tradition,” Bulletin of the Metropolitan Museum of Art 22 (1964): 246–56. C. C. Edgar, Sculptors’ Studies and Unfinished Works (Cairo: Institut fran¸cais d’arch´ eologie orientale, 1906) catalogues Late instructional examples.

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of Nefertiti stands in sharp contrast to the rest. Here the work appears fully conceived, complete with blue crown, golden-yellow headband tied with red ribbons at the nape, and polychrome double wreath collar representing an elaborate arrangement of beads, flower petals, leaves, and mandrake fruits.7 Only the left eye, lacking its inlay, has any didactic features, tiny traces of black on the white ground (see figure 5.2). Why should the bust have had an inlay at all? Was the choice of the right eye and its inlay type significant, and if so, how? Did Thutmose make or respond to a series of deliberate conceptual and aesthetic decisions, stemming from fundamental tenets of the Amarna iconographic, theological, and political program? When in the career of Nefertiti was it made? What light might the eyes shed on Nefertiti’s extraordinary roles in the Amarna world? Nefertiti as Queen, Co-Regent, and King Despite many proposals, the parentage of Nefertiti remains unknown. She married the future Akhenaten before he became pharaoh in about 1353 b.c. During his early regnal years, her titular changes reflect her progressive elevation in status, among them the adoption of a second name, Neferneferuaten, and the doubling of her queenly cartouche. Three years before Akhenaten’s death in 1336 b.c., she vanishes from the documentary record, an event hitherto ascribed to her death or to her fall from grace. Recent scholarship suggests that something quite different happened: Nefertiti became co-regent, taking the kingly titulary of Ankhkheperure-Neferneferuaten. When Akhenaten died, an enigmatic figure called Ankhkheperure-Smenkhkare became pharaoh, ruling for no more than two or three years before Tutankhaten (later Tutankhamun) was crowned. This shadowy, short-ruled king, according to an increasing number of Egyptologists, was none other than Nefertiti.8 Tomb KV 55 in the Valley of the Kings may hold her damaged mortal remains,

7. For analysis of the pigments, see Hans-Georg Wiedemann and Gerhard Bayer, “The Bust of Nefertiti,” Analytical Chemistry 54 (1982): 619A–628A. On plant-form and other collar designs at Amarna, see Andrew Boyce, “Collar and Necklace Designs at Amarna: A Preliminary Study of Faience Pendants,” in Amarna Reports 6, ed. Barry Kemp. Occasional Publications, vol. 10 (London: Egypt Exploration Society, 1995), 336–71. 8. In a series of articles written in the early 1970s, John Harris opened the matter of Nefertiti’s wider political roles. Julia Samson and Sayed Tawfik, among others, pursued the issue further, with studies on her titulary and other epigraphic and artifactual evidence. For full citation of the literature and cogent assessment of the arguments, see Arnold, The Royal Women of Amarna and Nicholas Reeves, “The Royal Family,” in Pharaohs of the Sun: Akhenaten, Nefertiti, Tutankhamen, eds. Freed et al., 87–95.

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¨ Figure 5.1: Right eye of Nefertiti, courtesy Agyptisches Museum und Papyrussammlung, Berlin. the “Younger Woman,” whose face bears a striking resemblance to the celebrated bust.9 Whatever the precise outlines of her career may have been, no other Egyptian queen is shown so frequently and in such unprecedented contexts. She makes offerings directly to the Aten, often centered under its rays. She receives prayers, awards honors, and smites enemies. She appears with Akhenaten and the Aten in a triad patterned after that of the divine Tefnut, Shu, and Atum. She identifies herself further with Tefnut through regularly wearing a version of the goddess’s tall blue headdress, as she does in the bust. Even the way Neferneferuaten is written is remarkable, for the Aten element is exceptionally reversed so that the seated-queen determinative faces it, in an “eye-catching relation to the god.”10 9. Joann Fletcher, The Search for Nefertiti: The True Story of a Remarkable Discovery (New York: William Morrow, 2004), with extensive bibliography; see the first and third sets of color plates, including the newly taken digital X-ray images. 10. John Wilson, “Akh-en-Aton and Nefer-titi,” Journal of Near Eastern Studies 32 (1973): 238. On reversals, see Henry Fischer, The Orientation of Hieroglyphs I: Reversals (New York: Metropolitan Museum of Art, 1977), especially 92–93 on the Nefertiti ones. A rare gold scarab of Nefertiti, recently found at the Ulu Burun underwater site, bears a partial reversal. For a detailed discussion, see James Weinstein, “The Gold Scarab of Nefertiti from Ulu Burun: Its Implications for Egyptian


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¨ Figure 5.2: Left eye of Nefertiti, courtesy Agyptisches Museum und Papyrussammlung, Berlin. Indeed, in the solar theology of Amarna, eyes, vision, and light assumed preeminent positions.11 The texts tell us that when “all eyes” (human beings) beheld the solar rays, the manifestation of the physical presence of the god, his beauty entered the heart and released love. As depicted repeatedly in reliefs, however, the aniconic Aten extended his rays only to Nefertiti and Akhenaten, forming a closed triad that would have balanced perfectly with Nefertiti as co-regent. Eyes Right and Left The rather disconcerting aspect of the bust’s empty left eye has tended to draw notice away from the treatment of the inlaid right eye (see figure 5.1). The earliest Egyptian eye inlays are predynastic white shells and ring beads. In the dynastic age, Lucas has identified five major classes of eye inlays, ranging from simple irises of conical glass plugs History and Egyptian-Aegean Relations,” American Journal of Archaeology 93, no. 1 (1989): 17–29. 11. Among numerous studies of Amarna religion in the context of Egyptian solar theology, see Jan Assmann, Egyptian Solar Religion in the New Kingdom: Re, Amun and the Crisis of Polytheism, trans. Anthony Alcock, Studies in Egyptology (London; New York: Kegan Paul International, 1995); Erik Hornung, Conceptions of God in Ancient Egypt: The One and the Many, trans. John Baines (Ithaca: Cornell University Press, 1982).

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to multimedia simulacra of all the ocular parts, eyelashes and eyelids included.12 It is unfortunate that so many eyes have been lost to time and ancient thieves, or we would have a much better idea of how Nefertiti’s right eye fits into the inlay corpus. As matters stand, Lucas classed it with Group IV eyes, rock crystal insets with reverse-painted iris, pupil, and caruncle. The extant examples come mainly from the Fourth Dynasty; later ones are found in the tomb of Tutankhamun. In Nefertiti’s case, the eye is an apparently singular variant of the type. The crystal was not painted white, but instead, the white limestone showed through in a particularly naturalistic fashion. Behind the crystal, two lightly incised arcs enclose an applied dark disc of pigment bound with beeswax, a minute portion of which is now missing. As for the ocular orbit and cranial setting, relatively little attention was paid to them until the mid-Eighteenth Dynasty. During the reigns of Amenhotep III and Akhenaten, there was “unparalleled innovation, creative license, and unique diversity in the representation of the human eye.”13 Upper eyelids were thickened, hooded, or lined to suggest aging; lower rim bands were omitted or chiseled off so the eye would fit more anatomically into its orbit; the eyeball profile was shaped to conform more closely to its sculptural context. These developments in rendering the human eye were part of numerous concurrent experiments. In the Amarna faience and glass industries, for example, there were new color juxtapositions, as well as novel threedimensional illusionistic effects achieved using a variety of sophisticated methods. This, as Vandiver says, was “tour de force craftsmanship. . . the limits of what is possible with faience as a material, given a mastery of the techniques.”14 The bust of Nefertiti has its share of innovations. Recent CAT scan investigations have confirmed that a very thin layer of gypsum stucco coats the face, neck, and ears, while thicker layers cover the back of the crown and shoulders.15 As gypsum stucco weighs far less than limestone, 12. Alfred Lucas, Ancient Egyptian Materials and Industries (London: E. Arnold, 1962), 98–127. 13. Bernard von Bothmer, “Eyes and Iconography in the Splendid Century: King Amenhotep III and His Aftermath,” in The Art of Amenhotep III: Art Historical Analysis, ed. Lawrence Berman (Cleveland: Cleveland Museum of Art, 1990), 90. 14. Pamela Vandiver, “Appendix A: The Manufacture of Faience,” in Ancient Egyptian Faience: An Analytical Survey of Egyptian Faience from Predynastic to Roman Times, eds. Alexander Kaczamarczyk and Robert Hedges (Warminster: Aris and Phillips, 1983), A–113. See also Andrew Shortland, Vitreous Materials at Amarna: The Production of Glass and Faience in 18th Dynasty Egypt (Oxford: Archaeopress, 2000). 15. Dietrich Wildung, “Einblicke: Zerst¨ orunsfreie Untersuchungen an alt¨ agyptis-


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the tall crown could rest more lightly upon the neck and shoulders than a solid stone one, eliminating the usual need for a supporting rear pillar. The use of stucco also permitted the sculptor to color the piece more readily, to perfect the symmetry and proportions more easily, and to complete the work more rapidly. Eyes, Discs, Mirrors, and the Aten In Egyptian religious thought, “the eye provides one of the richest, most enduring and pervasive of Egyptian motifs. It relates sometimes to the creator, to Ra, sometimes to Horus, but always to the power to see, illuminate and act.”16 According to certain Heliopolitan and Osirian/Horus mythological traditions, the right eye was deemed the solar one, and the left eye the lunar. One of the most commonly found images in Egyptian iconography is the wedjat, the human eye with falcon markings in reference to the eye myths of Horus, which is usually rendered as the right eye, especially in protective amulets and ring bezels.17 Other texts identify both eyes with the solar bark, the right being the nighttime bark and the left the daytime one. In the Eighteenth Dynasty, particularly during the reign of Amenhotep III, the solar eye was often associated with the goddesses Hathor and Sekhmet, who served as avengers of Ra in several important myths. At Amarna, as we have noted, eye imagery was omnipresent, from the figurative language of the Atenist solar hymns to the blue- and yellow-bodied glass vessels decorated with eyelike discs.18 chen Objekten,” Jahrbuch Preussischer Kulturbesitz 29 (1993): 147–48; first observed by Anthes, The Head of Queen Nofretete. 16. Stephen Quirke, Ancient Egyptian Religion (London: British Museum Press, 1992), 26. 17. Among many treatments, Eberhard Otto, Egyptian Art and the Cults of Osiris and Amon, trans. Kate Bosse Griffiths (London: Thames and Hudson, 1968); G¨ unter Rudnitzky, Die Aussage u ¨ber “Das Auge des Horus”: eine alt¨ agyptische Art geinstiger Ausserung nach dem Zeugnis des Alten Reiches, Analecta Aegyptiaca, vol. 5 (Copenhagen: Einar Munksgaard, 1956); James Allen, Genesis in Egypt: The Philosophy of Ancient Egyptian Creation Accounts, Yale Egyptological Studies, vol. 2 (New Haven: Yale Egyptological Seminar, 1988). On the exclusively right eye wedjat ring bezels from Amarna, see Andrew Boyce, “Report on the 1987 Excavations, House P46.33: The Finds,” in Amarna Reports 6, ed. Barry Kemp. Occasional Publications, vol. 10 (London: Egypt Exploration Society, 1995), 72, with note made of Kemp’s suggestion that this reflects writing directional preference from right to left, so the hieroglyphic eye would face right. 18. I. E. S. Edwards, Treasures of Tutankhamun: Catalogue (New York: Metropolitan Museum of Art, 1976), 134; Fran¸coise de Cenival, Le mythe de l’œil du soleil: translitt´ eration et traduction avec commentaire philologique (Sommerhausen: G. Zauzich Verlag, 1988); Karol Mysliwiec, Eighteenth Dynasty Before the Amarna Period (Leiden: E.J. Brill, 1985); Jan Assmann, “State and Religion in the New Kingdom,” in Religion and Philosophy in Ancient Egypt, ed. William Simpson, Yale

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Is it by happenstance that Thutmose chose to inlay the right eye of Nefertiti? The solar significance of that eye would hardly have been lost on any Amarna viewer, much less on Nefertiti herself. One is tempted to find further meaning in the inlay components. Could Thutmose have reverse-painted the waxen disc behind Nefertiti’s eye to evoke the aniconic Aten? Beginning in the fourth year of Akhenaten’s reign, the Aten became a solitary disc with rays terminating in human hands cupped in eyelike shapes, a god described as silent, abstract, a featureless form that “no craftsman knows.” The concept of the Aten continued to evolve, from encapsulated sunlight within the disc to a cosmic underlying light that “comes into the world through the disc.”19 Might Thutmose have intended the waxen disc in the right eye as an eloquent signifier of the relationship between Nefertiti and the Aten, which “penetrates into the inmost heart through the eye”?20 We recall that rather than painting the crystal white, as was customary with this class of inlay, Thutmose chose to have the limestone show through. Was this conceived as a more direct route to the heart? We shall return to this point below. As for the left eye, what was Thutmose seeking to demonstrate?21 Egyptological Studies, vol. 3 (New Haven: Yale Egyptological Seminar, 1989) 55–88; Jan Assmann, Egyptian Solar Religion, 22, 145–46, 181. For Amarna “eye vessels,” see Freed et al., eds., Pharaohs of the Sun, 266. 19. James Allen, “The Natural Philosophy of Akhenaten,” in Religion and Philosophy, ed. Simpson, 92–94. See also Donald Redford, “The Sun-disc in Akhenaten’s Program: Its Worship and Antecedants,” Journal of the American Research Center in Egypt 13 (1976): 47–61 and Journal of the American Research Center in Egypt 17 (1980): 21–38. 20. Assmann, “State and Religion,” 79. 21. Some have interpreted the left eye as an indication that Nefertiti was partially blind, either physically or symbolically. See, for instance, Nial Charlton, “The Berlin Head of Nefertiti,” Journal of Egyptian Archaeology 62 (1976): 184; Phillip Vandenberg, Nofretete: Eine arch¨ aologische Biographie (Bindlach: Gondrom Verlag, 1987), 46–47, where he suggests that Thutmose left the eye empty in revenge for being Nefertiti’s jilted lover. This would ignore the black guidelines in the eye, as well as the absence of any of the usual iconography for sightlessness. On ancient Egyptian blindness, blindfolding and related matters, see Hellmut Brunner, “Blindheit,” ¨ Lexikon der Agyptologie, vol. 1 (Wiesbaden: Harrassowitz, 1975), cols. 828–33; Jan Assmann, “Oracular Desire in a Time of Darkness: Urban Festivals and Divine Visibility in Ancient Egypt,” in Ocular Desire/Sehnsucht des Auges, eds. Aharon Agus and Jan Assmann, Yearbook for Religious Anthropology (Berlin: Berlin Akademie Verlag, 1994), 25–6; V´ eronique Dasen, Dwarfs in Ancient Egypt and Greece (Oxford: ´ Clarendon Press, 1993); Lise Manniche, “Symbolic Blindness,” Chronique d’Egypte 53 (1978): 12–21. Today, most images of the bust in general publications show a right profile view, avoiding the left eye issue entirely. A recent advertisement for a hand-colored reproduction includes a cautionary note: “Original has only one eye. Designate if you wish second eye painted” (The New Yorker, 20–27 February 1995: 263).


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Prior to and during the Amarna period, the new sculptural approaches to rendering the ocular setting, discussed above, may have been motivated in part by the increasingly complex roles eyes were expected to play in religious thought. The more naturalistic the orbit and surrounding structure, the better the eye conveyed its position as the essential transmitting medium between solar rays and human heart. By leaving the painted guidelines in Nefertiti’s left eye, Thutmose could show exactly how to achieve an outstanding ocular integration. The subtle contouring of the white limestone inlay foundation was a crucial element in the visual and conceptual effectiveness of the crystal and disc. This may lead us to yet another layer of meaning, for the crystal, backed by the waxen disc, appears mirrorlike. As early as the Old King, dom, the word ıtn (aten) was used as a common noun for mirrors, discs, and other circular items, including the disc of the sun; we find Aten in the sense of divinity from the Middle Kingdom on.22 Good evidence for the symbolic function of mirrors comes from Middle Kingdom funerary contexts, where they were painted on coffins, put under the heads of mummies, or placed on the east side of coffins, as though they were rising suns, apparently to aid the deceased in his or her revitalization and regaining of vision. The late Middle Kingdom mirrors inscribed with eyes and labeled “one who sees the face” or “one who sees Ra” suggest that mirrors were capable of vision, as well as reflection.23 Mirrors from the Amarna period typically comprise round or pearshaped metal discs polished to a high shine and set into a papyriform or Hathoric handle. The tomb of Tutankhamun contained a unique ankhshaped mirror case, whose mirror, perhaps of silver, was no doubt taken by ancient robbers. Generally, cases protected only the disc, but there the entire mirror was enclosed in a wooden box covered with sheet gold inlaid with colored glass and semi-precious stones and lined with sheet silver. Even more unusual is its shape, which seems to play on the fact that the hieroglyphic sign for life was the same as ankh, an alternative word for mirror.24 Word plays and rebuses are common in Egyptian texts and thought as a “calculated entwining of the material world with the world of the gods.”25 Amenhotep III’s prenomen, Nebmaatre, for example, occurs as a hieroglyphic pun on documents and seal impressions throughout 22. Sayed Tawfik, “Aton Studies,” Mitteilungen des Deutschen Arch¨ aologischen Instituts, Abteilung Kairo 29 (1973): 77–86; Donald Redford, Akhenaten the Heretic King (Princeton: Princeton University Press, 1984), 170. 23. Christine Lilyquist, Ancient Egyptian Mirrors from the Earliest Times through the Middle Kingdom (Munich: Deutscher Kunstverlag, 1979), 70–71, 97–99. 24. Edwards, Treasures of Tutankhamun, 140–41. 25. Quirke, Ancient Egyptian Religion, 154.

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Egypt.26 To cite another instance, when the divine offspring of Shu and Tefnut (with whom Akhenaten and Nefertiti identified, as we have seen) , ran from their creator-god, he wept tears (rmıt) that became human beings (rmt).27 ¯ Whether Tutankhamun’s mirror case was made during his lifetime or for his tomb furnishings, it nevertheless affords very relevant support for the existence of visual/artifactual puns in the Amarna period. Might not the eye of Nefertiti form just such a play involving a disc, a mirror, and the Aten? Conclusions Many have suggested that the bust of Nefertiti served as the definitive model for her depiction in composite statues from about year 8 of Akhenaten on. Her ruddy skin, for instance, would likely have been rendered in red quartzite or perhaps in yellow jasper, to judge from extant sculptures of the royal women of Amarna. While red was often negatively associated with the disruption of order, the color was also positively used, notably for the sun disc (interchangeably with yellow), for the dots in the corner of the wedjat eye, and for garments worn by Sekhmet and Hathor in magical texts.28 How might the eyes have been inlaid? Unfortunately, no Amarna eyes survive, only the hollowed settings. The use of such materials as red quartzite meant that at least one aspect of Thutmose’s model’s eye would have needed to be modified, since white could no longer show through the translucent crystal, glass, or alabaster. Properly contoured and integrated, however, the eyes would still have smoothly conveyed light to the heart. One wonders about the iris and the pupil. Were they a mirrorlike obsidian? Or might a waxen disc have been gilded? This perhaps surprising idea is inspired by the recent discovery that the eye of a bird-catching cat in the well-known Eighteenth Dynasty wall painting, often said to be from the tomb of Nebamun, is gilded over a resinous adhesive layer. According to Miller and Parkinson, this gleaming yellow feline eye may allude to Hathor as the personified solar eye, “evoking the eroticism of eternal potency, rebirth, and triumph over hostile forces.”29 26. Freed et al., eds., Pharaohs of the Sun, 43. 27. Assmann, Egyptian Solar Religion, 168. 28. Geraldine Pinch, “Red Things: The Symbolism of Colour in Magic,” in Colour and Painting in Ancient Egypt, ed. Vivian Davies (London: British Museum Press, 2001), 184. See also Arielle Kozloff, “Nefertiti, Beloved of the Living Disc,” The Bulletin of the Cleveland Museum of Art 64 (1977): 298, n. 19, for the suggestion that the ruddy skin of some Amarna women symbolizes their contact with solar rays. 29. Eric Miller and Richard Parkinson, “Reflections on a Gilded Eye in ‘Fowling in the Marshes’ (British Museum, EA 37977),” in Colour and Painting, ed. Vivian


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While much of the foregoing discussion has focused on Nefertiti and Amarna, the sculptor Thutmose has been present too. We recognize in the works left in his studio a high level of achievement, consummate craftsmanship, and sophisticated understanding of his royal commissions, all of which earned him honors as “Favorite of the King.” Yet we also feel that Thutmose comes quite close to our modern concept of an artist. As Valbelle puts it, many of his pieces seem to “express the personality of Thutmose rather than the personalities of the individuals represented,” and many of his decisions seem to result from his having given “free reign to his artistic sensibilities.”30 Through the eyes of Nefertiti, we may indeed glimpse the artist.

Addendum While this article was in press, Colleen Manassa kindly drew my attention to Marc Gabolde’s detailed study D’Akhenaton ` a Toutˆ ankhamon (Paris: Boccard, 1998), in which he proposes the following provocative, end-of-Amarna sequence: after Nefertiti died, her eldest daughter Merytaten took her place and her regnal titulary, entering into a mariage blanc (p. 286) with her father Akhenaten; upon his death, it was she who wrote the well-known letters to the Hittite king, seeking to marry his son, whom Gabolde identifies with Smenkhare, whose murder en route to Egypt opened the way for Tutankhaten, only son and youngest child of Akhenaten and Nefertiti, to reign.

Davies (London: British Museum Press, 2001), 51. 30. Dominique Valbelle, “Craftsmen,” in The Egyptians, ed. Sergio Donadoni (Chicago: University of Chicago Press, 1997), 58.

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Karen Polinger Foster References

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Les Lais: or, What Ever Became of Mesopotamian Mathematics? Jens Høyrup Roskilde University

The Obvious To the question whether Mesopotamian mathematics left anything to later mathematical cultures, an obvious answer is “Yes, at least rudiments of the sexagesimal place value system”—namely the minutes and seconds of our time-keeping and our division of the degree. To GrecoRoman antiquity and to the Islamic and Christian Middle Ages, it left more than rudiments, namely the systematic use of sexagesimal place value fractions—a striking way to change the original floating-point system into a fixed point system, since the integer part of numbers were not written sexagesimally. Together with the notation came the idea of place-value and thus ultimately our own use of decimal fractions. Al-Uql¯ıdis¯ı’s proposal to use decimal fractions1 as well as Jordandus de Nemore’s generalization to any base (called by him “consimilar fractions”2 ) were derived from the sexagesimal fractions with which they were familiar. The sexagesimal fractions were mainly used in astronomy and were indeed also a legacy of Babylonian mathematical astronomy. One may ask whether this part of Babylonian science left more of its mathematics.3 As a matter of fact it did, some of the methods were taken over by 1. The Arithmetic of Al-Uql¯ıdis¯ı. The Story of Hindu-Arabic Arithmetic as told in Kit¯ ab al-Fus.u ¯l f¯ı al-H ab al-Hind¯ı by Ab¯ u al-H ah¯ım al. is¯ . asan Ah.mad ibn Ibr¯ Uql¯ıdis¯ı written in Damascus in the Year 341 ( a.d. 952/53), trans. and ed. by Ahmad Saidan (Dordrecht: Reidel, 1978), 481–82. 2. Gustaf Enestr¨ om, “Das Bruchrechnen des Nemorarius,” Bibliotheca Mathematica: Zeitschrift f¨ ur Geschichte der Mathematik, 3d ser., 14 (1913): 41–54. 3. That it left astronomical and astrological knowledge (or “astrological persuasions,” if one prefers) is a familiar matter but not my topic; nor is the legacy of astronomical knowledge in India. See David Pingree, “History of Mathematical Astronomy in India,” in The Dictionary of Scientific Biography, vol. 15 (New York: Scribner, 1978), 536–54.

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Greek astronomy4 as well as Hellenistic astrology;5 but this transmission did not spread to other environments, not even to the “philosophical” astrology of Ptolemy (although aspects of Mesopotamian astrology did), and its very existence has indeed been only recently discovered. Contested Conventional Wisdom Shortly after the identification of apparently algebraic cuneiform texts of Old Babylonian as well as Seleucid date, Otto Neugebauer suggested that even this level of Babylonian mathematics had influenced Greek and hence later mathematics. In his argument entered the assumption, current at the time, that Greek mathematics had undergone a “foundation crisis” at the discovery of incommensurability,6 similar to that Grundlagenkrise which had recently made itself felt in German mathematics. He noticed that the Old Babylonian procedures (which he took to be purely numerical) were structurally similar to the proofs of the so-called “geometric algebra” of Elements II and concluded: Die Antwort auf . . . die Frage nach der geschichtlichen Ursache der Grundaufgabe der gesamten geometrischen Algebra,7 kann man heute vollst¨ andig geben: sie liegt einerseits in der aus der Entwicklung der irrationalen Größen folgenden Forderung der Griechen, der Mathematik ihre Allgemein¨ g¨ ultigkeit zu sichern durch Ubergang vom Bereich der rationalen Zahlen zum Bereich der allgemeinen Größenverhältnisse, andererseits in der daraus resultierenden Notwendigkeit, auch die Ergebnisse de vorgriechischen “algebraischen” Algebra zu u ¨bersetzen. Hat man das Problem in dieser Weise formuliert, so ist alles Weitere vollst¨ andig trivial und liefert den glatten Anschluß der babylonischen Algebra an die Formulierungen bei Euklid.8 4. Alexander Jones, “Evidence for Babylonian Arithmetical Schemes in Greek Astronomy,” in Die Rolle der Astronomie in den Kulturen Mesopotamiens. Beitr¨ age zum 3. Grazer Morgenl¨ andischen Symposion (23.–27. September 1991), ed. Hannes Galter (Graz: GrazKult, 1993), 77–94. 5. Otto Neugebauer, “A Babylonian Lunar Ephemeris from Roman Egypt,” in A Scientific Humanist: Studies in Memory of Abraham Sachs, eds. Erle Leichty, Maria Ellis and Pamela Gerardi, Occasional Publications of the Samuel Noah Kramer Fund, vol. 9 (Philadelphia: The University Museum, 1988), 301–4. 6. Helmut Hasse and Heinrich Scholz, “Die Grundlagenkrise der griechischen Mathematik,” Kant-Studien, Philosophische Zeitschrift 33 (1928): 4–34. 7. Namely, the application of an area with deficiency or excess, Elements II.5–6; this gives rise to the characteristic use of semi-sum and semi-difference of the sides of a rectangle—in other words, their average or deviation. 8. Otto Neugebauer, “Zur geometrischen Algebra (Studien zur Geschichte der

What Ever Became of Mesopotamian Mathematics?

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This translation thesis was accepted widely, even by scholars who knew too little about Babylonian and Greek mathematics to be able to evaluate it; putting it sharply, we may say that for most, it became a piece of conventional wisdom. Not for Neugebauer, of course, who knew what he was speaking about (and knew much more than he put into writing9 ); in 1963, he added that the Babylonian heritage had become “common mathematical knowledge all over the ancient Near East”10 and that a (historically rather implausible) direct translation of cuneiform tablets hence need not be involved. Neugebauer’s thesis was submitted only to attack for more than three decades after it was presented, and actually at the level of conventional wisdom. The main contesters were Arp´ ad Szabó11 and Sabetai Un12 guru, both much more familiar with the Greek than with the Babylonian material. Neither had noticed what Neugebauer stated in 1963, and both made much of the incompatibility between the arithmetical and the geometrical approach (Unguru also of the supposed incompatibility between the solution of a problem and the justification of the methods used to solve it).13 At least Unguru’s attack aroused a certain echo, being published in English and in a major journal, being held in an unusually aggressive tone and receiving equally vicious replies from André Weil14 antiken Algebra II),” in Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik. Abteilung B: Studien, vol. 3 (Berlin: Springer, 1936), 250. 9. See Jens Høyrup, Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin, Studies and Sources in the History of Mathematics and Physical Sciences (New York: Springer, 2002), 274 and passim. Indeed, as Neugebauer stated explicitly concerning his monumental Mathematische Keilschrift-Texte, it did not belong “zu den Aufgaben, die ich mir in dieser Edition gestellt habe, die Konsequenzen zu entwickeln, die sich nun aus diesem Textmaterial ziehen lassen.” See Otto Neugebauer, Mathematische Keilschrift-Texte, vol. 1, Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik. Abteilung A: Quellen, vol. 3 (Berlin: Springer, 1937), 79. Being first of all a historian of astronomy, he never took time to draw these consequences in writing, even though he published another volume of texts together with Abraham Sachs, namely, Mathematical Cuneiform Texts, American Oriental Series, vol. 29 (New Haven: American Oriental Society; American Schools of Oriental Research, 1945). 10. Otto Neugebauer, “Survival of Babylonian Methods in the Exact Sciences of Antiquity and Middle Ages,” Proceedings of the American Philosophical Society 107 (1963): 530. 11. Arp´ ad Szab´ o, Anf¨ ange der griechischen Mathematik (Munich and Vienna: R. Oldenbourg, 1969). 12. Sabetai Unguru, “On the Need to Rewrite the History of Greek Mathematics,” Archive for History of Exact Sciences 15 (1975): 199–210. 13. For some reason, none of them took notice of the suspicious similarity between part of Diophantos’s indubitably numerical Arithmetica (I:27–28, 30) and the critical theorems of Elements II. 14. Andr´ e Weil, “Who Betrayed Euclid?” Archive for History of Exact Sciences 19 (1978): 91–93.

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and Hans Freudenthal15 (and a gentle response from van der Waerden16 ) On the whole, however, the general belief in a translation of Babylonian numerical mathematics into Greek geometrical “algebra” survived. The survival was facilitated by an ignorance of certain fundamental differences between Old Babylonian and Seleucid procedures (at the moment no intermediate “algebraic” texts were known); the Euclidean “application of areas” is indeed related to Old Babylonian but not to Seleucid prodecures. Neugebauer Vindicated—With A Twist From 1982 onward, I succeeded gradually in convincing that part of the scholarly world which was interested in the matter that the numerical interpretation of the Babylonian “algebraic” texts was mistaken: the majority of their problems really deal with those measurable geometric entities of which they speak, and this geometry of measurable lines and areas constitutes the basic representation by means of which other problems (about mutually reciprocal number pairs, about commercial rates, etc.) are solved—just as numbers constitute the basic representation for our solution of problems about measurable entities of any ontological kind.17 The method, moreover, was analytic, that is, it treated the representatives of the unknown quantities as known quantities would have been treated (exactly as we do with our x and y), and it was reasoned to the same extent (and in much the same sense) as our solution of equations. Babylonian algebra was thus, to a far larger extent than evident in the reading of the texts as numerical algorithms, a real algebra. By being geometric, it was also even more similar to the geometry of Elements I than Neugebauer had supposed. However, the same analysis revealed much more. First of all, it highlighted the differences between Old Babylonian and Seleucid texts and showed that part of what was just said about the general character of “Babylonian algebra” and its similarity with Elements II is true only of its Old Babylonian phase. The few Late Babylonian “algebraic” texts (the Seleucid specimens already published by Neugebauer, and the Late

15. Hans Freudenthal, “What is Algebra and What has It been in History?” Archive for History of Exact Sciences 16 (1977): 189–200. 16. Bartel van der Waerden, “Defense of a ‘Shocking’ Point of View,” Archive for History of Exact Sciences 15 (1976): 199–210. 17. I shall not dwell on the arguments for this—they are set forth in depth and detail in Høyrup, Lengths, Widths, Surfaces, together with arguments for what else follows in this section of the article. The first suggestion of my thesis was presented (in Danish) at the 1982 meeting of the Danish National Committee for the History and Philosophy of Science.


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Babylonian but pre-Seleucid text W 23291 analyzed by Friberg18 ) differ from the Old Babylonian ones in several respects. First, only the simplest “elements” of the old discipline—problems about rectangles with no arbitrary coefficients—turn up in the late phase; they do not serve in representation and thus do not constitute an algebra in any proper sense. Moreover, while W 23291 still uses the technique of average and deviation, the Seleucid method builds on sum and difference;19 the Seleucid texts also contain new problem types involving the diagonal of rectangles (for instance, to find the sides from the area and the sum of the sides and the diagonal.) Some of the Sumerograms found in the Late Babylonian texts turn out to be new translations from Akkadian (or perhaps Aramaic); this higher level of mathematics thus cannot have been transmitted directly within the environment of scholar-scribes from Old to Late Babylonian times. On the other hand, the Seleucid reappearance of problems in which the sum of reciprocal numbers is given (a familiar Old Babylonian type) shows that at least one transmission channel was familiar with the sexagesimal system—but since precisely these problems still make use of the average-and-deviation procedure, this channel is likely not to be the only one. As in the case of omen science, we may even imagine that part of the transmission has passed through Elamite, Hittite, or other peripheral areas.

18. J¨ oran Friberg, “ ‘Seeds and Reeds Continued.’ Another Metro-Mathematical Topic Text from Late Babylonian Uruk” Baghdader Mitteilungen 28 (1997): 251–365, pl. 45–46. 19. If no diagrams are to be used, the difference between the two approaches is most easily explained in symbolic algebra. We may consider a rectangle @A (x, y) whose area A is known together with the difference d between the sides—hence, arithmetically x · y = A; x − y = d. (6.1) The Old Babylonian and Euclidean construction corresponds to the calculations r x−y 2 x+y d x+y 2 ( ) =( ) + xy; = ( )2 + A; 2 2 2 2 x+y x−y x+y x−y + ; y= − . 2 2 2 2 The Seleucid procedure may be expressed as p (x + y)2 = (x − y)2 + 4xy; x + y = d2 + 4A; x=

x=

1 [(x + y) + (x − y)]; 2

y = (x + y) − x.

(6.2)

(6.3)

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Close scrutiny of the Old Babylonian mathematical terminology20 is also informative about transmission channels. First, it reveals a split between the former Ur III core area and those peripheral areas that had been subjected to Ur III between only c. 1975 b.c. and 1925 b.c. (Susa, and the north-central area with Sippar and Eˇsnunna). In particular, only such texts as were produced in the periphery announce results by the phrase “you see”—mostly in Akkadian, tammar, but at times with a Sumerian igi (often in non-standard orthography);21 even Sargonic schools “see” results—but they use p´ ad. Even here, the transmission thus cannot have been carried by the scribes trained in Sumerian. Investigation at large of the Old Babylonian terminology shows that exactly the metalanguage—that lexicon which is needed, not for prescribing the operations that are to be performed but in order to formulate problems and to structure the description of the procedure—is almost fully devoid of Sumerographic writings in the early Old Babylonian texts (later, Sumerograms and pseudo-Sumerograms turn up). The whole Ur III school appears to have trained only in that level of mathematics which served directly in its accounting22 and to have avoided the use of problems.23 All this flows together as evidence that even between Sargonic and Old Babylonian times, the cluster of geometric problems that was to unfold as Old Babylonian algebra was carried by a non-scribal, Akkadianspeaking environment—no doubt an environment of surveyors. Ulti20. See Jens Høyrup, “The Finer Structure of the Old Babylonian Mathematical Corpus. Elements of Classification, with Some Results,” in Assyriologica et Semitica: Festscrift f¨ ur Joachim Oelsner anl¨ aßlich seines 65. Geburtstages am 18. Februar 1997, eds. Joachim Marzahn and Hans Neumann, Altes Orient und Altes Testament, vol. 252 (M¨ unster: Ugarit, 2000), 117–77, or (with added information about early Old Babylonian Ur and Nippur) Høyrup, Lengths, Widths, Surfaces, 317–61. I use the opportunity to correct a mistake in the latter publication (354): the tablets CBS 43, CBS 154+921 and CBS 165 are not from Nippur and were not claimed by Eleanor Robson to be so; indeed, as she tells me (personal communication, 28 February 2002), they were bought at the antiquity market before the Nippur excavation started. 21. Oblique references to the idiom of “seeing” and a few slips in copies show that the phrase was known in the core area but deliberately avoided. ˇ 22. Evidently this fits well with king Sulgi’s unexpected modesty when he speaks in “Hymn B” about his knowledge of mathematics: addition, subtraction, counting ˇ and accounting. See Giorgio Castellino, Two Sulgi Hymns (BC) Studi Semitici, vol. 42 (Rome: Istituto di studi del Vicino Oriente, 1972), 32. (Castellino’s translation ˇ misunderstands the text at this point.) Evidently, Sulgi’s ghostwriter knew of no other mathematics. 23. This question is treated in depth in Jens Høyrup, “How to Educate a Kapo, or, Reflections on the Absence of a Culture of Mathematical Problems in Ur III,” in Under One Sky: Astronomy and Mathematics in the Ancient Near East, eds. John M. Steele and Annette Imhausen, Alter Orient und Altes Testament, vol. 297 (M¨ unster: Ugarit, 2002), 121–45.


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mately, of course, the methods of practical surveying go back to the “learned” administrators of the proto-literate phase.24 Whether the ˇ “surveyor” mentioned in house-sale contracts from Suruppak was a specialized scribe or a non-scribal practitioner we do not know.25 The appearance of rectangle and square problems (not yet of the second degree but only asking to find one rectangle side from the area and the other side and a square side from the area) in the Old Akkadian school could be due precisely to their presence in an Akkadian-speaking environment, but this conclusion is certainly not mandatory. However, the ´ d as an Old Babylonian igi cannot be reappearance of the Sargonic pa explained without a transmission in non-Sumerian language (undoubtedly, in Akkadian). It is also next to certain that the “quadratic completion” (the trick which is needed to solve the second-degree problems) was invented in this Akkadian-speaking environment somewhere between the end of the Sargonic epoch (in whose schools it left no trace) and early Old Babylonian times. And indeed, a didactical text from Susa which explains it refers to it as “the Akkadian [method].”26 One of the characteristics of oral culture is its eristic orientation; its riddles are not meant as entertainment but as challenges.27 This use of riddles also holds for pre-Modern non-scribal mathematical professions, whether accountants or surveyors. In many cases where their knowledge was adopted by literate environments and thus brought into writing, the problems that are taken over are introduced by phrases like “If you 24. Indeed, the redefinition of what had once been “natural” (irrigation, ploughing, or seed) measures—see Marvin Powell, “Sumerian Area Measures and the Alleged Decimal Substratum,” Zeitschrift f¨ ur Assyriologie und Vorderasiatische Arch¨ aologie 62 (1972): 165–221—as units defined in terms of the length unit nindan is attested in Uruk IV—see Peter Damerow and Robert Englund, “Die Zahlzeichensysteme der Archaischen Texte aus Uruk,” in Zeichenliste der Archaischen Texte aus Uruk, vol. 2, eds. Martin Green and Hans Nissen, Archaische Texte aus Uruk, vol. 2 (Berlin: Mann, 1987), 117–66—and not likely to antedate writing. Without this redefined metrology, areas of rectangles and right triangles could not be determined from their sides. 25. Joachim Krecher, “Neue sumerische Rechtsurkunden des 3. Jahrtausends,” Zeitschrift f¨ ur Assyriologie und Vorderasiatische Arch¨ aologie 63 (1973): 145–271. He is spoken of as the um.mi, “master,” who applied the measuring rope; that um.mi was borrowed into Akkadian as ummˆ anum—an expert artisan rather than a scholar— supports the non-scribal interpretation but does not prove it. 26. TMS IV; see Jens Høyrup, Lengths, Widths, Surfaces, 90–94. 27. The classical discussion of this is Walter Ong, The Presence of the Word: Some Prolegomena for Cultural and Religious History (New Haven: Yale University Press, 1967), but see also Pietro Pucci, Enigma, Segreto, Oracolo (Rome: Istituti Editoriali e Poligrafici, 1997). For the application to mathematical practitioners, see Jens Høyrup, “Sub-Scientific Mathematics: Observations on a Pre-Modern Phenomenon,” History of Science 28 (1990): 63–86.

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are an accomplished calculator, tell me . . . ”; that is, in their original contexts these problems were riddles for professionals, and only those belonging to the profession knew to answer them correctly. Being for professionals, they had to be concerned with such things as fell under the responsibility of the profession. A knight might show his valor not only in real war but also in the fictive aestheticized war of the tournament; a surveyor had to show his by being able to solve difficult problems about the measures of fields—perhaps fairy-tale problems never encountered in real life (like knowing the sum of the four sides and the area of a square field but not its side), in any case problems whose solutions asked for virtuosity beyond trite routine. For such purposes, riddles like these were perfect: 1. On a single square with side s and area (s) (with 4 s standing for “the four sides,” and Greek letters for given numbers): (s) = α

(6.4)

s + (s) = α

(6.5)

4s

+ (s) = α

(6.6)

(s) − s = α

(6.7)

s − (s) = α

(6.8)

2. On two concentric squares with sides s1 and s2 , areas As1 + As2 : (s1 ) + (s2 ) = α, s1 ± s2 = β

(6.9)

(s1 ) − (s2 ) = α, s1 ± s2 = β

(6.10)

3. On a circle with circumference c, diameter d, and area A: c+d+A=α

(6.11)

4. On a rectangle with sides l and w, diagonal d and area A: @A (l, w) = α, l = β or w = γ

(6.12)

@A (l, w) = α, l ± w = β

(6.13)

@A (l, w) + (l ± w) = α, l ∓ w = β

(6.14)

@A (l, w) = α, d = β

(6.15)

@A (l, w) = l + w

(6.16)


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With a small proviso for (6.8), all of these (and probably no others except perhaps the square problem d − s = 4 with the mock solution s = 10) appear to have circulated among the lay surveyors when the Old Babylonian scribe school borrowed from them and developed its fabulous algebraic discipline. As we notice, there are no arbitrary coefficients, and no representation—everything really deals with square and rectangular fields. In the Late Babylonian but pre-Seleucid text W 23891, we encounter (6.4),(6.12), and (6.13). Together with new rectangle riddles involving the diagonal, (6.13) is found in a Seleucid text with the new method.28 (6.5), (6.7), (6.9), (6.10), and (6.13) all turn up (not as problems but as justifications of the way they were solved in pre-Seleucid times) in Elements II; (6.9), (6.10), and (6.13) (as number problems) in Diophantos’s Arithmetica I. A Demotic papyrus29 contains (6.15) with the Seleucid solution, together with a sequence of problems about a pole leaned against a wall, some in a simple variant involving only the Pythagorean theorem and known already from an Old Babylonian text and others in a sophisticated variant known from the Seleucid text BM 34568. Another Demotic papyrus30 contains a couple of summations of series “from 1 to 10,” obviously related to two other summations found in the Seleucid text AO 6484. The Seleucid as well as the Demotic texts are thus certainly evidence of “common mathematical knowledge all over the Near East,” but whether the innovations were made in Syria, in Egypt, or in Mesopotamia (or even farther east—the summation formulæ have unmistakable through later Indian kin) we cannot know. In any case, (6.6), (6.11), and (6.15) (the latter in “Seleucid-Demotic” shape) turn up in pseudo-Heronian and Latin agrimensorial material. Al-Khw¯ arizm¯ı used (6.5), (6.6), and (6.8) in the ninth century a.d. for his geometric proofs of the solution to mixed quadratic equations; since (6.6) is less adequate than (6.5) for the formula he wants to justify, it must have been more familiar either to him or to his public. Almost everything (except [6.9] and [6.10], but together with the Seleucid rectangle-diagonal problems) is found also in Arabic treatises about men28. We should remember that we have essentially one relevant Late Babylonian, pre-Seleucid text and one Seleucid text (BM 34568). When not copied by scholarscribes, the mathematical texts from this period were probably written on wax tablets (most likely in Aramaic); one of the scholarly copies indeed states that it was copied from a wax original. 29. P. Cairo J.E. 89127–30, 89137–43 from the third century b.c. See Richard Parker, Demotic Mathematical Papyri, Brown Egyptological Studies, vol. 7 (Providence: Brown University Press, 1972). 30. P. British Museum 10520 also published in Parker, Demotic Mathematical Papyri.

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suration (including Savasorda’s treatise, which presents Arabic knowlege in Hebrew), and (6.6), (6.13), and (6.14) turn up in Italian abbaco sources in a way that cannot be derived from known Latin translations from the Arabic.31 In the main, Neugebauer was thus fully right; but what went into Greek “geometrical algebra” was not the sophisticated scribal algebra of the Old Babylonian era but the anonymous riddle tradition of Mesopotamian origin. By the later first millennium, this tradition became common knowledge in the whole area where Assyrian and Persian armies and army surveyors—and probably more important—Assyrian and Persian administrators had passed. The problems also reached India. Embedded in the geometrical section of Mah¯ av¯ıra’s ninth century Gan.ita-s¯ ara-sangraha ˙ are problems of indubitably Old Babylonian origin—for instance (6.11)—together with formulæ to find inner heights in an arbitrary triangle which almost certainly arose in the Near Eastern surveyors’ environment in Late Babylonian and pre-Seleucid times32 and exercises similar to the characteristic Demotic-Seleucid rectangle problems; strikingly, these borrowings are located in different chapters in accordance with their age, as if the import had come in three separate waves.33 Mah¯ av¯ıra was a member of the Jaina community. Nothing similar is found in non-Jaina writings with which I am familiar. The direct influence of Mesopotamian astronomical methods in India thus has no counterpart within mathematics in general (apart from what was said above concerning the summation of series, where a link is certain but the direction of influence undetermined).

31. Leonardo Fibonacci also has a number of the problems, but he copied mainly from Gherardo da Cremona’s translation of Ab¯ u Bakr’s Liber mensurationum. 32. Even this method (reshaped and generalized in Elements II.12–2.13 so as to hold even for outer heights in obtuse-angled triangles) returns in pseudo-Heronian and Medieval Arabic treatises. See Jens Høyrup, “Hero, Ps.-Hero, and Near Eastern Practical Geometry: An Investigation of Metrica, Geometrica, and Other Treatises,” in Antike Naturwissenschaft und ihre Rezeption, eds. Klaus D¨ oring, Bernhard Herzhoff and Georg W¨ ohrle, vol. 7 (Trier: Wissenschaftlicher Verlag Trier, 1997), 67–93. It is impossible to know whether it was of strictly Mesopotamian origin. 33. Details and documentation can be found in Jens Høyrup, “Mah¯ av¯ıra’s Geometrical Problems: Traces of Unknown Links between Jaina and Mediterranean Mathematics in the Classical Ages,” in History of Mathematical Sciences, eds. Ivor Grattan-Guinness and Bhuri Yadav (New Delhi: Hindustan Book Agency, 2004), 83–95.


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Simpler Matters and Phraseology If both an Old Babylonian tablet (BM 13901 #23) and Ab¯ u Bakr’s Liber mensurationum 34 state that “I have aggregated the four sides and the area” (namely of a square, in both cases mentioned previously); if in both cases the appearance of the sides before the area is unexpected, given the habits of the times; and if the resulting side is 10 in both cases, then the existence of a shared tradition is not subject to reasonable doubt. On the other hand, the fact that two mathematical cultures share the “surveyor’s formula” for the area of an approximately rectangular quadrangle (average length times average width) proves nothing as to their being connected—even though the formula is only approximate, the idea is simply too close at hand once rectangular areas are determined as the product of length and width. Similarly, taking the perimeter of a circle to be thrice the diameter is an adequate approximation for many purposes, and its being shared has no certain implications. Even though much from the basic level of Mesopotamian practical mathematics reappears in pseudo-Heronian writings from the Hellenistic age, it is therefore not prima facie obvious that such simple matters were borrowed. However, even simple mathematics goes together with language, and at times indubitable traces of borrowing survive the translation involved; several instances of shared phrases point to the existence of shared mathematical traditions with a Mesopotamian core and reach beyond the surveyors’ culture. One such phrase has to do exactly with the perimeter of the circle (and thus remains within the field of practical geometry). It is known but not much noticed that the Old Babylonian operation by which the perimeter is determined from the diameter is to ‘triple’ it (ˇsalaˇsum, ´ 3 tab.ba, e.g., BM 85194 obv. 1.47) or to ‘repeat in three steps’ (a.ra ibid. obv. 2.44, 2.50); it is never a multiplication by three, expressed by the verb naˇsu ˆm/´ıl, the operation invariably used when reciprocals, igi.gub-factors35 or any other operation of proportionality are involved, nor certainly the constructions of a rectangular area (sˆ utak¯ ulum, with a wealth of synonyms and logograms), used also when twelve times the circular area is found as the square on the perimeter. This peculiarity returns not only in the pseudo-Heronian treatises but also when Hero refers to the habits of practitioners. Invariably, the

34. H. L. L. Busard, “L’alg` ebra au moyen ˆ age: Le Liber mensurationum d’Abˆ u Bekr,” Journal des Savants, 1968 (April–June 1968): 87. 35. Including of course the multiplication of the circular perimeter by the factor 0; 20 which produces the diameter.

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expressions τρισσάκις and τριπλάσιον are used, even when neighboring multiplications are ἐπὶ followed by a noun. A fifteenth-century German source shows us that this is no linguistic quirk but a reflection of a practice, which is obviously the reason that it has survived the translation. In Mathes Roriczer’s Geometria deutsch 36 we find the following prescription: If anyone wishes to make a circular line straight, so that the straight line and the circular are the same length, then make three circles next to one another, and divide the first circle into seven equal parts, one of which is marked out in continuation of the three circles. The addition of a seventh is obviously a post-Archimedean innovation37 and irrelevant in the present context; but the whole explanation shows that the length of the perimeter followed from a construction and that it was measured without calculation. This procedure must already have been used in Old Babylonian times and be the reason that the mathematical texts speak as they do.38 Two other phrases are common in pseudo-Heronian and in certain medieval Arabic writings point back to interaction between lay and scribal mathematics in the Old Babylonian age. One occurs, among numerous other places, in the pseudo-Heronian versions of (6.6) and 36. Lon Shelby, ed., Gothic Design Techniques: The Fifteenth Century Design Booklets of Mathes Roriczer and Hanns Schmuttermayer (Carbondale: Southern Illinois University Press, 1977), 121. 37. Already Hero distinguishes between those who took the perimeter to encompass the triple of the diameter and those according to whom the perimeter is the triple diameter and in addition one seventh of the diameter (Metrica 1.30–31); Hero himself multiplies by twenty-two and divides by seven (Metrica 1.26). 38. A somewhat similar case may be constituted by the medieval conservation of the distinctions between the two different additive operations was.a ¯bum and kam¯ arum and between the subtractions ‘by removal’ (nasahum) and ‘by comparison’ ˘ (el¯ı. . . wat¯ arum), for instance in Ab¯ u Bakr’s Liber mensurationum. From Gherardo’s translation of Ab¯ u Bakr’s text itself it is not obvious that the geometric procedures were still in use, but Johannes de Muris’ treatment of problem (6.14) shows that he knew them. See Johannes de Muris, De arte mensurandi: A Geometrical Handbook of the Fourteenth Century, ed. H. L. L. Busard, Boethius, vol. 41 (Stuttgart: Franz Steiner, 1998). Supporting himself on a diagram and taking advantage of the fact that l − w = 2, he reduces the problem to (6.6) (which he does not treat, which shows that he must be copying). See Jens Høyrup, review of De arte mensurandi: A Geometrical Handbook of the Fourteenth Century, edited by H. L. L. Busard, Zentralblatt f¨ ur Mathematik und ihre Grenzgebiete Zbl 0913.01011. Within this geometric representation, the distinctions are meaningful, and it would be almost impossible to lose them; if everything had been thought of in numerical terms, they probably would have been blurred.


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(6.11)39 and in Leonardo Fibonacci’s version of (6.6),40 all of which require that the four sides and the square area—respectively the circular perimeter, diameter, and area—be “separated.” It is also found (as berˆ um) in the Old Babylonian text (AO 8862 IV.21),41 an algebraic problem about the sum of men, days, and the bricks they produce (the number of these being proportional to the number of man-days); in BM 10822 §1, where three types of bricks are to be singled out;42 and in a slightly different function in TMS VII A, 4, a didactical text about how to treat an indeterminate first degree equation (thus far removed from the surveyors’ tradition).43 Although all are “algebraic,” they are either close to scribal computation or meant to point in their formulation toward that area, and we must therefore presume that the idea of separating a sum into constituents (the inverse operation of the symmetric operation kam¯ arum / ul.gar / ˜ gar.˜ gar) comes from here rather than from lay surveyors. The case of kayyam¯ anum/καθολικῶς/ἀεί/semper is similar. In pseudoHeronian and medieval writings, these terms are used to indicate that a particular numerical step in a procedure is made independently of the numerical parameters involved—for instance, in (6.6), that a halving of 4 is independent of the value of α. It occurs in two mathematical texts from Susa: TMS XIV and TMS XII. Its use in TMS XIV is unclear, but in any case the problem deals with a grain pile.44 TMS XII is an “algebraic” but quartic problem,45 thus certainly beyond the horizon of the surveyors, and here the term appears to serve as in the later sources. Other kinds of evidence confirm that Mesopotamian Bronze Age mathematics participated in what was at least later to develop into a transcultural network (if not community) of mathematical practitioners; for instance, the first known appearance of the problem of contin39. Hero of Alexandria, Heronis Definitiones cum variis collectionibus. Heronis quae feruntur Geometrica, ed. and trans. J. L. Heiberg, Heronis Alexandrini Opera quae supersunt omnia, vol. 4 (Leipzig: Teubner, 1912), 418, 444. 40. Leonardo Fibonacci, Practica geometriae et Opusculi, vol. 2 of Scritti di Leonardo Pisano matematico del secolo decimoterzo, ed. Baldassarre Boncompagni (Rome: Tipografica delle Scienze Matematiche e Fisiche, 1862), 59. 41. Neugebauer, Mathematische Keilschrift-Texte, 1935, 1.112. 42. J¨ oran Friberg, “Bricks and Mud in Metro-Mathematical Cuneiform Texts,” in Changing views on Ancient Near Eastern Mathematics, eds. Jens Høyrup and Peter Damerow, Berliner Beitr¨ age zum Vorderen Orient, vol. 19 (Berlin: Dietrich Reimer, 2001), 90. 43. Høyrup, Lengths, Widths, Surfaces, 182. 44. Eleanor Robson, Mesopotamian Mathematics 2100–1600 b.c.: Technical Constants in Bureaucracy and Education, Oxford Editions of Cuneiform Texts, vol. 14 (Oxford: Clarendon Press, 1999), 119–22. 45. Kazuo Muroi, “Reexamination of the Susa Mathematical Text No. 12: A System of Quartic Equations,” SCIAMVS 2 (2001): 3–8.

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ued doublings is in a text from Old Babylonian Mari.46 The details of the formulation and the fact that the doublings are thirty in number show beyond doubt that this occurrence is related to those of Greek Antiquity and the Middle Ages47 —but not that the problem originated in Mesopotamia. In later times, the network was probably carried by trade connections, but it only happens to become visible in places where it collided with literate mathematical cultures leaving surviving sources. A similar transcultural practitioner’s network, if it existed in the beginning of the second millenium, had no chances to become visible to us except through its contacts with Mesopotamian and Egyptian scribes. We know, however, that Mesopotamia was involved in trade with quite remote regions already in the Bronze Age and therefore cannot exclude that the network was transcultural already in the eighteenth century b.c. Once the existence of this network is established, a number of other terminological similarities between Babylonian and later mathematical texts can be supposed with increased certainty to be the results of loantranslations—thus, the Greek notion that a rectangle is “contained” by two sides (περιέχω corresponding to ˇsutak¯ ulum) and the reference to a square figure “being” its side and “having” an area as δύναμις, corresponding to mithartum;48 and the rampant use of “positing,” (ja‘ala, ˘ ponere, porre) in medieval texts corresponding to Old Babylonian ˇsak¯ anum / ˜ gar. The Least Obvious: Metamathematics Numbers, formulæ, procedures, terminology—all of these may be said to belong to mathematics proper. The way mathematics was thought about and the way it influenced thinking about other matters may (with a slight broadening of the normal use of the term) be spoken of as “metamathematics.” Did Mesopotamian metamathematics leave traces in later times? It is certainly easy to find parallels, and I shall discuss two of them. But the existence of parallels implies neither inspiration nor continuity. One parallel is inherent in the very notion of “mathematics.” In discussions about so-called “ethnomathematics,” the point has been made that “mathematics” considered as a closed and coherent field is our concept. However, if we consider Old Babylonian problem texts containing several problems, we find that these may restrict themselves to a particular “theme” (a rectangular excavation, “algebraic” problems 46. Denis Soubeyran, “Textes math´ ematiques de Mari,” Revue d’Assyriologie 78 (1984): 30. 47. Høyrup, “Sub-Scientific Mathematics,” 74. 48. Jens Høyrup, “D´ ynamis, the Babylonians, and Theaetetus 147c7–147d7,” Historia Mathematica 17 (1990), 201–22.


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about squares, problems about subdivisions of squares); they may also be “anthologies” and mix mathematical problems of different kinds; but they never mix mathematics with non-mathematical topics (not even with numerology); what we collect under the heading of “Old Babylonian mathematics” was thus also a closed entity in the view of its own times.49 It appears, however, that this cognitive autonomy of mathematics did not survive the transformations of scribal culture following upon the Kassite conquest (and the disappearance of scribal mathematics from the archaeological horizon for more than a millenium). Indeed, W 23273, a metrological table of Late Babylonian but pre-Seleucid date, starts by listing the sacred numbers of the gods.50 Late Babylonian cuneiform mathematics, as we know, was written by scribes identifying themselves as exorcists, scribes of En¯ uma Anu Enlil, etc. This professional identity did not prevent the astronomer-astrologer-scribes of the Seleucid period from keeping their astronomical tables apart from what we might term the “occult” aspect of their activity; but non-astronomical mathematics was probably so peripheral for them that it did not present itself as something worth keeping distinct. In any case, there is no evidence that the ancient Greek notion of mathematics as an autonomous field51 was inherited from the Old Babylonian scribes via the later scribal tradition. It certainly cannot be fully excluded that non-scribal mathematical practice played a role here, as in the transmission of mathematics itself—but as long as no single piece of evidence speaks in favor of such a hypothesis, it remains gratuitous, not least because of the attitude of Greek “theoreticians” to practitioners. In all probability, Greek “mathematics,” to the extent it was at all thought about as one thing, was a Greek reinvention.

49. This conclusion is not affected by the fact that students’ training pads from the more elementary level of school regularly contain a Sumerian proverb on the obverse and a numerical calculation on the reverse; such texts just mean that the student had to train in both things on the same day, as confirmed by the edifying poem known as “Schooldays.” See Samuel Kramer, “Schooldays: A Sumerian Composition Relating to the Education of a Scribe,” Journal of American Oriental Studies 69 (1949): 201, 205, and correction on 214. 50. See J¨ oran Friberg, “On the Structure of Cuneiform Metrological Table Texts from the First Millenium” in Die Rolle der Astronomie in den Kulturen Mesopotamiens. Beitr¨ age zum 3. Grazer Morgenl¨ andischen Symposion (23.–27. September 1991), ed. Hannes Galter (Graz: GrazKult, 1993), 383–405. 51. Indeed a notion belonging only to a small minority of literate Greeks if we consider the long run of antiquity. Neo-Pythagoreans were far more numerous than “mathematicians,” and even though a Nichomachos was still able to keep arithmetic distinct from numerology, those who read him were mostly not.

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The other parallel has to do with the legitimation of state power and the way the tasks of the state were understood.52 It is well-known that the emergence of the Mesopotamian state is intimately linked to the invention of writing in the later fourth millennium and that the purpose of the invention of writing was bookkeeping, that is, the application of mathematics.53 Already the accounts of the proto-literate period are organized in a way which feels familiar, with single contributions and totals. This “Cartesian product” was also transferred to the way the social structure was conceptualized in the “List of Professions.” The introduction of this extensive accounting appears to be linked to the stepwise transformations of an original redistributive economic structure at village level to the bureaucratic structure of Uruk IV—rations of grain, etc., were distributed to workers in fixed rations which it was the task of the accounting to control, and land was distributed to high officials in mathematically determined ratios. Although the documents of the time do not speak directly about such things, the state structure was apparently legitimized as securing “just measure.” In Ur III, the ˇ only aspect of Sulgi’s status as supremely just which cannot be reduced to a repetition of inherited commonplaces appears to be the metrological reform; even in Old Babylonian times, part of the pride of the scribes resided in their being (for most of them evidently only by proxy) the counsellors of kings who, on their part, were supposed to ensure affluence and justice, the latter at least in part identified with “just measure.” Much of this sounds fairly familiar. The modern state is legitimate only if its taxation is in agreement with rules, and since centuries the state guarantees trade and wealth by providing (supposedly) stable currency and by taking care of a common metrology (most famous in the latter respect is the French Revolutionary introduction of the metric system, but this was not the beginning). All of these, however, are functional requirements; and as in the case of the conceptualization of “mathematics,” there may be a break in Mesopotamian culture in this respect with the Kassite takeover. The metrological innovations of the later second millennium were certainly not devoid of mathematical rationality, but the use of (normalized) seed measures indicates that mathematical regularity was no longer ideologically hegemonic; moreover, the prestigious scholar-scribes who advised 52. The following reflections are extremely sketchy; some substance is provided in Jens Høyrup, In Measure, Number, and Weight: Studies in Mathematics and Culture (Albany: State University of New York Press, 1994), 45–87, 296–306. 53. See, inter alia, Hans Nissen, Peter Damerow, and Robert Englund, Archaic Bookkeeping: Writing and Techniques of Economic Administration in the Ancient Near East (Chicago: University of Chicago Press, 1993).


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the Neo-Assyrian kings were concerned with omina and apotropaic ritual, not with justice, mathematical or otherwise. At this point of history, there was no longer anything to transmit. And indeed, when Solon made metrological innovation part of his reform, he did so in a way which would have made any mathematically competent Mesopotamian scribe since Uruk IV laugh with contempt: “sixty-three minas [against formerly, sixty] going to the talent; and the odd three minas were distributed among the staters and other values.”54 This apparent absence of a “meta-mathematical legacy”—which would be confirmed if we looked at other aspects of mathematics—should be no surprise. After all, attitudes, knowledge, and practices at this level are much more intimately bound up with culture as a whole than, say, a numerical approximation for the ratio between a circular diameter and the perimeter. Even our belief to have inherited the metamathematics of the Hellenistic mathematicians is largely an illusion,55 which we are able to uphold only by reading (that is, misreading) our own understanding for instance of what constitutes a proof into the Greek texts. There certainly is a legacy from Mesopotamian mathematics in the modern world, as there was one in classical antiquity; but there was no collective transmission of an organized whole understood as such. The most adequate metaphor is that of rich wreckage—similar to what Robinson Crusoe brought ashore from his ship. It did not allow him to reconstruct the European civilization from which it came, but it was essential, providing tools for his construction of a somewhat civilized one-man world. In other respects, Mesopotamian culture was certainly much more accessible as an integrated whole in the times of Solon, Alexander, and Cicero; the reason that its mathematics was not was that Mesopotamian mathematics had been shipwrecked already when the Mycenaeans conquered the Minoans, a thousand years earlier.

54. Aristotle, The Complete Works of Aristotle: The Revised Oxford Translation, ed. and trans. Jonathan Barnes, Bollingen Series, vol. 71: 2 (Princeton: Princeton University Press, 1984), 2346. 55. Reviel Netz, “Deuteronomic Texts: Late Antiquity and the History of Mathematics,” Revue d’Histoire des Math´ ematiques 4 (1998): 261–88 and Reviel Netz, The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History, Ideas in Context, vol. 51 (Cambridge: Cambridge University Press, 1999) offer full documentation.

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References al-Uql¯ıdis¯ı, Ah.mad. The Arithmetic of Al-Uql¯ıdis¯ı. The Story of HinduArabic Arithmetic as told in Kit¯ ab al-Fus.u ¯l f¯ı al-H . is¯ab al-Hind¯ı by Ab¯ u al-H asan Ah mad ibn Ibr¯ a h¯ ım al-Uql¯ ıdis¯ ı written in Damas. . cus in the Year 341 ( a.d. 952/53). Translated and edited by Ahmad Saidan. Dordrecht: Reidel, 1978. Aristotle. The Complete Works of Aristotle: The Revised Oxford Translation. Edited by Jonathan Barnes. Bollingen Series, vol. 71: 2. Princeton: Princeton University Press, 1984. Busard, H. L. L. “L’algèbra au moyen ˆ age: Le Liber mensurationum d’Abˆ u Bekr.” Journal des Savants, 1968 (April–June 1968): 65– 125. ˇ Castellino, Giorgio. Two Sulgi Hymns (BC). Studi Semitici, vol. 42. Rome: Istituto di studi del Vicino Oriente, 1972. Damerow, Peter and Robert Englund. “Die Zahlzeichensysteme der Archaischen Texte aus Uruk.” In Zeichenliste der Archaischen Texte aus Uruk, edited by Martin Green and Hans Nissen, vol. 2, 117–66. Archaische Texte aus Uruk, vol. 2. Berlin: Mann, 1987. de Muris, Johannes. De arte mensurandi: A Geometrical Handbook of the Fourteenth Century. Edited by H. L. L. Busard. Boethius, vol. 41. Stuttgart: Franz Steiner, 1998. Enestr¨ om, Gustaf. “Das Bruchrechnen des Nemorarius.” Bibliotheca Mathematica: Zeitschrift f¨ ur Geschichte der Mathematik, 3d ser., 14 (1913–14): 41–54. Fibonacci, Leonardo. Practica geometriae et Opusculi. Vol. 2 of Scritti di Leonardo Pisano matematico del secolo decimoterzo. Edited by Baldassarre Boncompagni. Rome: Tipografica delle Scienze Matematiche e Fisiche, 1862. Freudenthal, Hans. “What is Algebra and What has It been in History?” Archive for History of Exact Sciences 16 (1977): 189–200. Friberg, J¨ oran. “On the Structure of Cuneiform Metrological Table Texts from the First Millenium.” In Die Rolle der Astronomie in den Kulturen Mesopotamiens. Beitr¨ age zum 3. Grazer Morgenl¨ andischen Symposion (23.–27. September 1991), edited by Hannes Galter, 383–405. Graz: GrazKult, 1993. ———. “ ‘Seeds and Reeds Continued.’ Another Metro-Mathematical Topic Text from Late Babylonian Uruk.” Baghdader Mitteilungen 28 (1997): 251–365, pl. 45–46.


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———. “Bricks and Mud in Metro-Mathematical Cuneiform Texts.” In Changing views on Ancient Near Eastern Mathematics, edited by Jens Høyrup and Peter Damerow, 136–40. Berliner Beiträge zum Vorderen Orient, vol. 19. Berlin: Dietrich Reimer, 2001. Hasse, Helmut and Heinrich Scholz. “Die Grundlagenkrise der griechischen Mathematik.” Kant-Studien, Philosophische Zeitschrift 33 (1928): 4–34. Hero of Alexandria. Heronis Definitiones cum variis collectionibus. Heronis quae feruntur Geometrica. Translated and edited by J. L. Heiberg. Heronis Alexandrini Opera quae supersunt omnia, vol. 4. Leipzig: Teubner, 1912. Høyrup, Jens. “Sub-Scientific Mathematics: Observations on a PreModern Phenomenon,” History of Science 28 (1990): 63–86. ———. In Measure, Number, and Weight: Studies in Mathematics and Culture. Albany: State University of New York Press, 1994. ———. “Hero, Ps.-Hero, and Near Eastern Practical Geometry: An Investigation of Metrica, Geometrica, and Other Treatises. In Antike Naturwissenschaft und ihre Rezeption, edited by Klaus D¨ oring, Bernhard Herzhoff and Georg Wöhrle, vol. 7, 67–93. Trier: Wissenschaftlicher Verlag Trier, 1997. ———. Review of De arte mensurandi: A Geometrical Handbook of the Fourteenth Century, edited by H. L. L. Busard. In Zentralblatt f¨ ur Mathematik und ihre Grenzgebiete. Zbl 0913.01011. Available at http://www.emis.de/ZMATH/. ———. “The Finer Structure of the Old Babylonian Mathematical Corpus. Elements of Classification, with Some Results.” In Assyriologica et Semitica: Festscrift f¨ ur Joachim Oelsner anl¨ aßlich seines 65. Geburtstages am 18. Februar 1997, edited by Joachim Marzahn and Hans Neumann, 117–77. Altes Orient und Altes Testament, vol. 252. M¨ unster: Ugarit, 2000. ———. Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin. Studies and Sources in the History of Mathematics and Physical Sciences. New York: Springer, 2002. ———. “How to Educate a Kapo, or, Reflections on the Absence of a Culture of Mathematical Problems in Ur III.” In Under One Sky: Astronomy and Mathematics in the Ancient Near East, edited by John M. Steele and Annette Imhausen, 121–45. Alter Orient und Altes Testament, vol. 297. M¨ unster: Ugarit, 2002.

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———. “Mah¯ av¯ıra’s Geometrical Problems: Traces of Unknown Links between Jaina and Mediterranean Mathematics in the Classical Ages.” In History of Mathematical Sciences, edited by Ivor Grattan-Guinness and Bhuri Yadav, 83–95. New Delhi: Hindustan Book Agency, 2004. Jones, Alexander. “Evidence for Babylonian Arithmetical Schemes in Greek Astronomy.” In Die Rolle der Astronomie in den Kulturen Mesopotamiens. Beitr¨ age zum 3. Grazer Morgenl¨ andischen Symposion (23. –27. September 1991), edited by Hannes Galter, 77– 94. Graz: GrazKult, 1993. Kramer, Samuel. “Schooldays: A Sumerian Composition Relating to the Education of a Scribe.” Journal of American Oriental Studies 69 (1949): 199–215. Krecher, Joachim. “Neue sumerische Rechtsurkunden des 3. Jahrtausends.” Zeitschrift f¨ ur Assyriologie und Vorderasiatische Arch¨ aologie 63 (1973): 145–271. Muroi, Kazuo. “Reexamination of the Susa Mathematical Text No. 12: A System of Quartic Equations.” SCIAMVS 2 (2001): 3–8. Netz, Reviel. “Deuteronomic Texts: Late Antiquity and the History of Mathematics.” Revue d’Histoire des Mathématiques 4 (1998): 261–288. ———. The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. Ideas in Context, vol. 51. Cambridge: Cambridge University Press, 1999. Neugebauer, Otto. “Zur geometrischen Algebra (Studien zur Geschichte der antiken Algebra II).” In Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik. Abteilung B: Studien, vol. 3, 245–59 (Berlin: Springer, 1936). ———. Mathematische Keilschrift-Texte. 3 vols. Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik. Abteilung A: Quellen, vol. 3. Berlin: Springer, 1935–37. ———. “Survival of Babylonian Methods in the Exact Sciences of Antiquity and Middle Ages.” Proceedings of the American Philosophical Society 107 (1963): 528–35. ———. “A Babylonian Lunar Ephemeris from Roman Egypt.” In A Scientific Humanist:Studies in Memory of Abraham Sachs, edited by Erle Leichty, Maria Ellis and Pamela Gerardi, 301–4. Occasional Publications of the Samuel Noah Kramer Fund, vol. 9. Philadelphia: The University Museum, 1988. ——— and Abraham Sachs. Mathematical Cuneiform Texts. American Oriental Series, vol. 29. New Haven: American Oriental Society and the American Schools of Oriental Research, 1945.


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Nissen, Hans, Peter Damerow, and Robert Englund. Archaic Bookkeeping: Writing and Techniques of Economic Administration in the Ancient Near East. Chicago: University of Chicago Press, 1993. Ong, Walter. The Presence of the Word: Some Prolegomena for Cultural and Religious History. New Haven: Yale University Press, 1967. Parker, Richard. Demotic Mathematical Papyri. Brown Egyptological Studies, vol. 7. Providence: Brown University Press, 1972. Pingree, David. “History of Mathematical Astronomy in India.” In The Dictionary of Scientific Biography, vol. 15, 536–54. New York: Scribner, 1978. Pucci, Pietro. Enigma, Segreto, Oracolo. Rome: Istituti Editoriali e Poligrafici, 1997. Powell, Marvin. “Sumerian Area Measures and the Alleged Decimal Substratum.” Zeitschrift f¨ ur Assyriologie undv Vorderasiatische Arch¨ aologie 62 (1972): 165–221. Robson, Eleanor. Mesopotamian Mathematics 2100–1600 b.c.: Technical Constants in Bureaucracy and Education. Oxford Editions of Cuneiform Texts, vol. 14. Oxford: Clarendon Press, 1999. Shelby, Lon, ed. Gothic Design Techniques: The Fifteenth Century Design Booklets of Mathes Roriczer and Hanns Schmuttermayer. Carbondale: Southern Illinois University Press, 1977. Soubeyran,Denis. “Textes mathématiques de Mari.”Revue d’Assyriologie 78 (1984): 19–48. Szab´ o, Arp´ ad. Anf¨ ange der griechischen Mathematik. Munich and Vienna: R. Oldenbourg, 1969. Unguru, Sabetai. “On the Need to Rewrite the History of Greek Mathematics.” Archive for History of Exact Sciences 15 (1975): 67– 114. van der Waerden, Bartel. “Defense of a ‘Shocking’ Point of View.” Archive for History of Exact Sciences 15 (1976): 199–210. Weil, André. “Who Betrayed Euclid?” Archive for History of Exact Sciences 19 (1978): 91–93.

House Omens in Mesopotamia and India Toke Lindegaard Knudsen Brown University

Omens in the Indian Tradition The idea that omens enable one to know and possibly counteract future events dates back to the earliest Indian texts, in which an ominous bird, the ´sakuna, is mentioned.1 Later texts provide a systematic approach to omens, which are classified into various categories, including astral omens, omens based on the behavior of animals, and so on. In the Indian tradition, the Sanskrit word jyotih.´s¯ astra (literally, the science (´s¯ astra) of the movements of the heavenly bodies (jyotis) denotes a broad category, which includes mathematics, astronomy, astrology, and various types of divination. Traditionally, jyotih.´s¯ astra has three divisions: sam hit¯ a ‘omens,’ gan ita ‘mathematics and astronomy,’ and . . hor¯ a ‘astrology.’2 The oldest surviving sam a text is the Gargasam a , attributed . hit¯ . hit¯ by tradition to the sage Garga. According to Pingree, the Gargasam a . hit¯ was most likely composed in northern India in about 100 a.d., but the tradition stretches much further back in time, as is evidenced by refera has not ences to earlier authorities.3 Unfortunately, the Gargasam . hit¯ yet been edited and is available only in manuscript form. The most important of the Indian sam a texts is the Br.hatsam a . hit¯ . hit¯ of Var¯ ahamihira. Var¯ ahamihira, who flourished in the sixth century a.d., was a descendant of Zoroastrian immigrants from Iran to India and resided in the area near Ujjayin¯ı (modern Ujjain in Madhya Pradesh). 1. David Pingree, Jyotih.´s¯ astra: Astral and Mathematical Literature. A History of Indian Literature, vol. 6, pt. 4 (Wiesbaden: Otto Harrassowitz, 1981), 67. 2. Ibid., 1. 3. David Pingree, “Mesopotamian Omens in Sanskrit,” in La circulation des biens, des personnes et des id´ ees dans le Proche-Orient ancien, eds. Dominique ´ Charpin and Francis Joann` es (Paris: Editions Recherche sur les Civilisations, 1992), 375. For a description of the contents of the Gargasam a , see Pingree, Jyotih.´s¯ astra, . hit¯ 69–70 and David Pingree, Census of the Exact Sciences in Sanskrit, series A, vol. 2 (Philadelphia: American Philosophical Society, 1970), 116–17.

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He was a prolific writer, and his works cover all aspects of traditional Indian astrology and astronomy.4 A very valuable commentary on the Br.hatsam a was completed by . hit¯ Bhat.t.otpala in 967 a.d.5 Not all of the material in the Br.hatsam a . hit¯ lists omens. There is also a great deal of prescriptive material. A whole chapter, for example, deals with the preparation of perfumes without attaching any ominous significance to such substances.6 In addition to the Br.hatsam a , Var¯ ahamihira authored two other . hit¯ sam a works: the Sam¯ asasam a , which is an abridgment of the Br.hat. hit¯ . hit¯ sam a , and the Vat.akan.ik¯ a . Both of these works are now lost, although . hit¯ quotations from them are preserved in other works.7 Among the important later sam a works is the Bhadrab¯ ahusam a, . hit¯ . hit¯ composed in the period between Var¯ ahamihira and Bhat.t.otpala.8 Mesopotamia and India According to the theory of omens presented by Var¯ahamihira in the Br.hatsam a , the misconduct of men causes an accumulation of sin . hit¯ (p¯ apa), from which arises misfortune. The gods, dissatisfied by the misconduct, create portents which indicate the impending misfortune. In order to prevent the evil influence of the portents, the king should perform a ´s¯ anti in his dominion.9 4. For more information about Var¯ ahamihira, see David Pingree, “Var¯ ahamihira,” in Dictionary of Scientific Biography, vol. 13 (New York: Charles Scribner’s Sons, 1976), 581–83 and David Pingree, Census of the Exact Sciences in Sanskrit, series A, vol. 5 (Philadelphia: American Philosophical Society, 1994), 563–64. For a description of the contents of the Br.hatsam a, . hit¯ see Pingree, Jyotih.´s¯ astra, 72–74 and David Pingree, Exact Sciences in Sanskrit, series A, vol. 5, 564–65. All references to the Br.hatsam a in the following refer . hit¯ to The Br.hatsam a by Var¯ ahamihir¯ ac¯ arya with the commentary of Bhat..totpala, . hit¯ ed. Avadha Vih¯ ar¯ı Trip¯ at.h¯ı, Sarasvat¯ı Bhavan Grantham¯ al¯ a, vol. 97, pts. I and II (Varanasi: Varanaseya Sanskrit Vishvavidyalaya, 1968), which includes the commentary of Bhat.t.otpala. The Br.hatsam a has been translated into English . hit¯ several times. Among the English translations are that of Kern (published serially in the Journal of the Royal Asiatic Society, 1870–1875), considered by Pingree to the best English translation (see Pingree “Var¯ ahamihira,” 582) and that of M. Ramakrishna Bhat (Delhi: Motilal Banarsidass, 1981). There is also a Japanese translation by Michio Yano and Mizue Sugita (Tokyo: Heibon-sha, 1995). 5. Pingree, Jyotih.´s¯ astra, 74. 6. Chapter 76, entitled gandhayukti. 7. Pingree, “Var¯ ahamihira,” 582. 8. Census of the Exact Sciences in Sanskrit, series A, vol. 4 (Philadelphia: American Philosophical Society, 1981), 285 and Pingree, Jyotih.´s¯ astra, 77. 9. apac¯ aren an ¯m upasargah. p¯ apasa˜ ncay¯ ad bhavati / sam ucayanti . a nar¯ .a . s¯ divy¯ antariks.abhaum¯ as ta utp¯ at¯ ah. / manuj¯ an¯ am apac¯ ar¯ ad aparakt¯ ah. devat¯ ah. sr.janty et¯ an / tatpratigh¯ at¯ aya nr.pah. ´s¯ antim as..tre prayu˜ nj¯ıta / (Br.hatsam a 45.2–3). In . r¯ . hit¯ his commentary on Br.hatsam a 52.3, Bhat.t.otpala cites a number of verses, which . hit¯ he attributes to Garga, in which the same ideas are presented.

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In this context, the word ´s¯ anti refers to an expiatory ritual.10 It is analogous to the Mesopotamian namburbˆ u .11 As noted by Pingree, although Akkadian texts such as the Diviner’s Manual 12 do not state that the evils predicted by the portents are a punishment for the sins of men, this idea is presented in a letter from 669 b.c. sent by the scholar Balas¯ı to the Assyrian king Esarhaddon.13 In any case, both in Mesopotamia and in India it was believed that the gods send portents, the evil influence of which could be averted through various apotropaic rituals,14 and thus the role of omens in the two cultures were very similar. According to Pingree, who has investigated astral omens in Mesopotamia and India,15 there is a connection between the Indian divinatory tradition and that of Mesopotamia. More specifically, “[t]he ultimate sources for much of the material [in the Indian sam a s]. . . were . hit¯ Mesopotamian.”16 Pingree proposed the hypothesis that Mesopotamian omen-literature was transmitted to India during the Achaemenid occupation of northwestern India and the Indus Valley.17 10. In his commentary on Br.hatsam a 45.3, Bhat.t.otpala glosses ´s¯ anti as utp¯ ata. hit¯ prat¯ık¯ ara, i.e., a counteraction of portents. 11. For the Akkadian word namburbˆ u , see Erica Reiner, Astral Magic in Babylonia (Philadelphia: American Philosophical Society, 1995), 81–82. 12. Leo Oppenheim, “A Babylonian Diviner’s Manual,” Journal of Near Eastern Studies 33, no. 2 (1974): 197–220. See also Clemency Williams, “Signs from the Sky, Signs from the Earth: The Diviner’s Manual Revisited,” in Under One Sky, eds. John M. Steele and Annette Imhausen, Alter Orient und Altes Testament, vol. 297 (M¨ unster: Ugarit Verlag, 2002), 473–85. 13. Pingree, “Mesopotamian Omens in Sanskrit,” 376. ´.a ip-ˇsur d e ´.a ˇsa ri-i-bu 14. The Mesopotamian scholar Balas¯ı writes: e-pu-uˇs d e ´ r.bi e-ta-pa-´ i-pu-ˇsu-u-ni ˇsu-tu-ma nam.bu aˇs, ‘ “Ea has done, Ea has undone.” He who caused the earthquake has also created the apotropaic ritual against it.’ See Simo Parpola, Letters from Assyrian and Babylonian Scholars, State Archives of Assyria, vol. 10 (Helsinki: Helsinki University Press, 1993), 41. 15. See David Pingree, “Babylonian Planetary Theory in Sanskrit Omen Texts,” in From Ancient Omens to Statistical Mechanics: Essays on the Exact Sciences Presented to Asger Aaboe, eds. J. Lennart Berggren and Bernard Goldstein (Copenhagen: University Library, 1987), 91–99; David Pingree, “Venus Omens in India and Babylon,” in Language, Literature, and History: Philological and Historical Studies Presented to Erica Reiner, ed. Francesca Rochberg-Halton (New Haven: American Oriental Society, 1987), 293–315; David Pingree, “mul.apin and Vedic Astronomy,” in dumu-e2 -dub-ba-a: Studies in Honor of ˚ Ake W. Sj¨ oberg, eds. Hermann Behrens, Darlene Loding and Martha Roth, 439–45 (Philadelphia: Occasional Publications of the Noah Kramer Fund, 1989); Pingree, “Mesopotamian Omens in Sanskrit,” and David Pingree, “Legacies in Astronomy and Celestial Omens,” in The Legacy of Mesopotamia, eds. Stephanie Dalley and Andr´ es Reyes (New York: Oxford University Press, 1998), 125–37. 16. Pingree, “Mesopotamian Omens in Sanskrit,” 375. 17. In “mul.apin and Vedic Astronomy,” Pingree argued that the Indians had knowledge of Mesopotamian material by the late Vedic period.

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In addition to the evidence from the comparisons of Mesopotamian and Indian astral omens, as well as the influence of Babylonian mathematical astronomy on early Indian astronomy,18 Pingree calls attention to a Buddhist collection, the D¯ıghanik¯ aya, a text dating from the period of Achaemenid influence.19 A text in this collection, the Brahmaj¯ alasutta, describes the Buddha telling his followers about immoral activities, including various types of divination, which certain groups engage in. Pingree calls attention to the fact that the types of divination and the order in which they are mentioned by the Buddha corresponds largely to the way the material is arranged in the Mesopotamian omen ˇ ¯ 20 series Summa Alu. ˇ The similarities are indeed striking. Besides astral omens, the Summa ¯ and the Br.hatsam Alu hit¯ a contain identical categories of omens, includ. ing omens based on the behavior of various animals (dogs, for example) and omens pertaining to houses. House Omens As noted above, much work has already been devoted to the astral omens of Mesopotamia and India and the relationship between them. When it comes to other types of omens, however, little has been done. We will therefore focus on another category of omens here, namely omens pertaining to houses. The house not only provides us with shelter from the elements, it also shelters our imagination and creative faculties. In the words of Bachelard, “[t]he house is one of the greatest powers of integration for the thoughts, memories and dreams of mankind.”21 It is “our corner of the world. As has often been said, it is our first universe, a real cosmos in every sense of the word.”22 Or, in the words of Gibran’s prophet: “Your house is your larger body.”23 Furthermore, the house represents an interesting threshold, “situated at the juncture of separate domains (nature and culture, individual and society, public and private, inside and outside, leaving and returning).”24 Considering the importance of the house, it is no wonder that, if omens were conceived of in the first place, it was thought that omens can 18. See David Pingree, “The Mesopotamian Origin of Early Indian Mathematical Astronomy,” Journal for the History of Astronomy 4 (1973): 1–12. 19. Pingree, “Mesopotamian Omens in Sanskrit,” 376. ˇ ¯ 20. Ibid., 377–78. For the Summa Alu, see below. 21. Gaston Bachelard, The Poetics of Space (Boston: Beacon Press, 1994), 6. 22. Ibid., 4. 23. Kahlil Gibran, The Prophet (New York: Alfred A. Knopf, 2000), 34. 24. Ann Guinan, “Social Constructs and Private Designs: The House Omens of ˇ Summa Alu,” Houses and Households in Ancient Mesopotamia, ed. Klaas Veenhof (Istanbul: Nederlands Historisch-archaeologisch Instituut te Istanbul, 1996), 62.


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be derived from houses. If the greater cosmos presents us with omens, the smaller cosmos, the house, surely does as well. The house is “a natural venue for the observation of omens.”25 “Because [a house] is located at the point where the individual intersects with the social whole, there is a natural connection between the private house and divination.”26 ˇ ¯ The Summa Alu, tablets 3–7, 9–10, 12–15, and 19–21 of which deal with house omens,27 will be our source for the Mesopotamian material. For the Indian material, since the Gargasam a is not easily available, . hit¯ the Br.hatsam a will be used. The house omens of the Br.hatsam a . hit¯ . hit¯ are found in chapter 52 of the work. árd¯ The S¯ ulakarn.¯ avad¯ ana, a Buddhist work from the first century, also contains a section on houses.28 According to Pingree, however, the chapter dealing with houses was, like a number of other chapters, added at a later date.29 In any case, the material dealing with houses is of a prescriptive, rather than of a divinatory, nature. For this reason, it is not considered in this analysis. V¯ astu´s¯ astra In the Indian tradition, the branch of knowledge that deals with houses is called v¯ astu´s¯ astra, the science (´s¯ astra) of houses (v¯ astu).30 Chapter 52 of the Br.hatsam a is entitled v¯ astuvidy¯ a , which means the . hit¯ same. The material on houses in the Br.hatsam a , as is the case for all . hit¯ of v¯ astu´s¯ astra, is not exclusively divinatory. A significant portion of the chapter on houses is prescriptive or definitional. The prescriptive material provides guidelines as to how houses should be constructed, etc., information which may be useful for circumventing problems in the future but which is not divinatory. The definitional material gives, for example, a certain name to a house with certain characteristics31 or names to pillars of various types.32 There are also tests to determine the quality of a given plot of land 25. Ibid., 62. 26. Ibid., 61. ˇ ¯ in the following refer to Sally Freedman, If 27. All references to the Summa Alu ˇ ˇ a City Is Set on a Height: The Akkadian Omen Series Summa Alu ina M¯ elˆ e Sakin, vol. 1: Tablets 1–21 (Philadelphia: Samuel Noah Kramer Fund, 1998). árd¯ 28. Sujitkumar Mukhopadhyaya, ed., The S¯ ulakarn ¯vad¯ ana. (Santiniketan: .a Vi´svabharati, 1954). The section on houses is entitled dv¯ aralaks.an . a, ‘characteristics of doors.’ For a description of this work, see Pingree, Jyotih.´s¯ astra, 69–70. 29. Pingree, Jyotih.´s¯ astra, 69. 30. A comparison between v¯ astu´sa ¯stra and the Chinese system of feng-shui is often made. 31. See, for example, Br.hatsam a 52.31. . hit¯ 32. Br.hatsam a 52.28. . hit¯

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and the social class for which it is suitable. For example, the way the ground slopes and the color of the soil give an indication of the caste suited to build a house on it.33 According to an ancient myth,34 a being once obscured the earth and the sky with its body. The gods threw it down with its face downwards. This being is the v¯ astupurus.a or v¯ astunara, i.e., the house-god. Its body forms the ground-plan of a house, each of its limbs presided over by the deity who seized that limb when it was thrown down. Accordingly, the ground-plan of a house is divided into sections, each presided over by a certain deity. According to one scheme, the square ground-plan of the house is partitioned into 81 sections by drawing ten lines in the east-west direction and ten lines in the north-south direction.35 Another scheme partitions the ground-plan into 64 sections by drawing nine lines in the east-west direction and nine lines in the north-south direction.36 This identification of sections of the house with limbs of the v¯ astupurus.a and particular deities allows a diviner to interpret certain events as signs that a particular section of the house suffers an affliction. For example, if, during a ritual oblation in the sacred fire, there is an inauspicious omen or the fire behaves in an anomalous way, the part of the house which suffers an affliction is the section occupied by the deity to whom the oblation was offered when the inauspicious event occurred.37 If the master of the house scratches a limb during a ritual offering, the section of the house which represents the corresponding limb of the v¯ astupurus.a suffers from an affliction.38 Certain points in the house are designated as vulnerable points.39 If such a point is affected by, say, something impure,40 the master of the house will experience trouble in the limb of his body corresponding to the limb of the v¯ astupurus.a to which the particular vulnerable point belongs.41 33. See Br.hatsam a 52.89–95 for these and other similar tests. . hit¯ 34. Briefly summarized in Br.hatsam a 52.2–3. . hit¯ 35. Br.hatsam a 52.42. For the assignment of deities to the various sections, see . hit¯ Br.hatsam a 52.43–54. . hit¯ 36. Br.hatsam a 52.55. . hit¯ 37. Br.hatsam a 52.59. Bhat.t.otpala explains the inauspicious omens as sneezing, . hit¯ spitting, crying, harsh language, breaking of wind, hearing inauspicious speech, and so on, and the anomalous behavior of the fire includes sparks, crackling, bad smell, and so on. Here, ´salya is translated as ‘affliction.’ Literally, ´salya means a sharp object causing pain such as a thorn but by extension may mean a fault or defect. 38. Br.hatsam a 52.59. . hit¯ 39. Var¯ ahamihira uses the word marman in Br.hatsam a 52.57. . hit¯ 40. Remnants of food (ucchis..ta) is mentioned in this regard in Br.hatsam a 52.64. . hit¯ 41. Br.hatsam a 52.58. . hit¯


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None of these constituents of v¯ astu´s¯ astra seems to have an antecedent in Mesopotamia. Therefore, it seems reasonable to conjecture that the Indians had their own indigenous tradition concerning houses, their construction, omens pertaining to them, and so on. It is not clear whether this tradition predates the transmission of Mesopotamian material or these elements of the Indian tradition arose during or after the adaptation of Mesopotamian material to the Indian cultural context. House Omens in Mesopotamia and India The house omens in Mesopotamia and India show both differences and similarities. That this is the case should not come as a surprise. Mesopotamia and India are two different cultural landscapes. What can be derived as an omen from the material culture in one of them may not present itself or even make sense in the other. The social implications of the Mesopotamian house omens have been investigated by Guinan,42 according to whom divination works in two ways. “On the one hand, it can resolve individual deviations by referring them to a larger cultural context and, as such, divination is a vehicle of social control. On the other hand, it can legitimize a private, innovative, or even potentially subversive course of action.”43 In the context of house omens, these social implications can be seen in omens which predict ill consequences if a house transgresses certain social boundaries.44 Similar omens are found in the Br.hatsam a , in which the negative . hit¯ consequences of the door of a house being near a road or the image of ˇ ¯ a god are laid out.45 These omens, like the ones in the Summa Alu, deal with a house and its proximity to other houses and objects of the community and can thus be said to contain an element of upholding a social status quo. In the Br.hatsam a , this trend is brought out not . hit¯ only via omens, but also more directly, when the text of the Br.hatsam a explicitly states the proper dimensions of a house belonging to . hit¯ a member of a certain social group.46 No specific details regarding the consequences of not adhering to the prescribed dimensions are given. It is merely stated that a house which is smaller or larger than its prescribed measure brings inauspiciousness to all people.47

42. Guinan, “Social Constructs and Private Designs.” 43. Ibid., 61. ˇ ¯ 5.22–24, 5.91–92. See also Guinan, “Social Constructs and Private 44. Summa Alu Designs,” 63–64. 45. Br.hatsam a 52.75–76. . hit¯ 46. Br.hatsam a 52.4–15. . hit¯ 47. h¯ın¯ adhikam an¯ ad a´subhakaram astu sarves.a ¯m (Br.hatsam a 52.15). . svam¯ . v¯ . hit¯

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ˇ ¯ is a series of omens concerning the smell within a In the Summa Alu house.48 As pointed out by Guinan, some of the substances mentioned are those mixed into the mortar used for consecrated buildings.49 The Br.hatsam a contains only one omen concerning the smell in a house, . hit¯ according to which a son will be killed if there is a bad smell in the house.50 The smell which indicates the death (not killing) of a son in ˇ ¯ is that of wine.51 the Summa Alu ˇ ¯ contains a great number of omens dealing with the The Summa Alu appearance of fungus in and around houses.52 These are not paralleled in the Indian material. House Omens Involving Bones ˇ ¯ In the Summa Alu there are a number of omens dealing with objects found in the ground during the digging of the foundation of a house.53 As Guinan has pointed out, such objects, which include silver and gold, are connected with ritual foundation deposits of temples and palaces.54 In the Indian material, too, there are omens dealing with objects underneath a house. When the architect enters a half-finished or completed house,55 he is to look for signs, including where the master of the house is standing and which part of his body he is touching. If at that time a bird shrieks harshly from a certain direction,56 it is to be known that there is a bone corresponding to the one touched by the master of the house at that spot.57 If at the time of observing portents, an elephant, a horse, a dog, or some other animal makes a sound, it is to be known that there is a bone of that animal corresponding to the one touched by the master of the house at that spot.58 If at the time of stretching out a cord, a donkey brays, or a dog or a jackal crosses the string, it is again to be understood that there is a bone on the spot.59 ˇ ¯ 6.98–122. 48. Summa Alu 49. Guinan, “Social Constructs and Private Designs,” 67. 50. sutavadha´s ca durgandhe (Br.hatsam a 52.113). . hit¯ ˇ ¯ 6.104. 51. Summa Alu 52. Tablets 12–13. 53. Tablets 3–4. 54. Guinan, “Social Constructs and Private Designs,” 66. See also Richard Ellis, Foundation Deposits in Ancient Mesopotamia (New Haven: Yale University Press, 1968), 27. 55. ardhanicitam a (Br.hatsam a 52.103). . kr.tam . v¯ . hit¯ 56. According to the position of the sun in the sky, the eight quarters are given different designations. The bird has to be located in a specific one of these. This is explained in detail by Bhat.t.otpala in his commentary on Br.hatsam a 52.103–104. . hit¯ 57. Br.hatsam a 52.103–104. . hit¯ 58. Br.hatsam a 52.105. . hit¯ 59. Br.hatsam a 52.106. The next verse, Br.hatsam a 52.107, concerns the . hit¯ . hit¯ existence of a treasure in the ground.


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One may ask what the significance of bones is in this context and why a bone underneath a house is ominous. Bone is almost always an inauspicious object in the Br.hatsam a , but beyond a generally ominous . hit¯ meaning, the answer to the question is not clear. The commentator, Bhat.t.otpala, does not comment on this issue. It is tempting to seek a Mesopotamian origin for these omens,60 especially considering certain Mesopotamian ideas and practices. In the Mesopotamian tradition, when the flesh of a deceased person perishes, two entities remain: bones (es.emtu) and ghost (et.emmu). After proper burial, memorial rites (kispu) are performed to ensure the preservation of the memory of the deceased. However, if there was no proper burial or if the bones were disturbed, the ghost of the deceased would haunt the living.61 With this burial tradition in mind, it is easy to imagine that the existence of a bone (which could be from a disturbed grave or from a deceased person whose memorial rites have been discontinued) underneath one’s house would be viewed as inauspicious. The household would be in danger from the ghost associated with the bones.62 Furthermore, there was in Mesopotamia a tradition of burials under the floors of houses,63 although, as pointed out by Cooper, “these are never plentiful enough to account for the number of deaths that should occur in a given household during the period for which the house was occupied,” and, therefore, “it is assumed that cemetery burial was common as well.”64 One can imagine that it would be viewed as undesirable to have bones unrelated to one’s family members underneath one’s house, a place where deceased members of the household were to be buried. There is, however, no evidence to support a Mesopotamian origin of these Indian omens. While ghosts in houses is a major concern in the Mesopotamian context, bone does not seem to have an ominous import, and the Indian omens are not paralleled in cuneiform texts. It is also to be noted that the Indian omens differ in their form from the Mesopotamian ones. In the Indian context, the existence of bone under60. I am indebted to Andrew Cohen, Ann Guinan and Erica Reiner for helpful comments in this regard. 61. Jerrold Cooper, “The Fate of Mankind: Death and Afterlife in Ancient Mesopotamia,” in Death and Afterlife: Perspectives of World Religions, ed. Hiroshi Obayashi (Westport, Connecticut: Greenwood Press, 1992), 27. 62. A line spoken by Gibran’s prophet comes to mind: “You shall not dwell in tombs made by the dead for the living.” See Gibran, The Prophet, 37. 63. For a discussion of this practice and the rituals surrounding it, see Akio Tsukimoto, Untersuchungen zur Totenpflege ( kispum) im alten Mesopotamien, Alter Orient und Altes Testament, vol. 216 (Kevelaer: Butzon and Bercker; Neukirchen-Vluyn: Neukirchener, 1985). 64. Cooper, “The Fate of Mankind,” 23.

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neath the house is indicated by sounds or actions of animals, whereas in the Mesopotamian context, the objects are found while digging the foundation of a house (they are instantly visible), and the Br.hatsam a . hit¯ mentions animal bone rather than human bone. The omens involving ˇ ¯ 65 also does not yield anything that could tombs found in the Summa Alu support a link either. The Indian omens discussed in this paragraph does not seem to belong to material borrowed from Mesopotamia, but rather represent an indigenous tradition. Indian Elaboration on Mesopotamian Material Pingree, in his investigation of omens in Mesopotamia and India, concluded that the Indian tradition elaborated upon and expanded the material transmitted to them from Mesopotamia,66 a process forming part of the Indian adaptation of the Mesopotamian material. Pingree notes, though, that the cuneiform tablets and Sanskrit texts that he has examined concerning omens do not indicate the details of a process of elaboration of Mesopotamian material in India. Instead he suggests the hypothesis that the Indian material derives from recensions of the ˇ ¯ and other texts of which there is no direct knowledge from Summa Alu cuneiform sources.67 Such difficulties characterize the study of cultural transmission and illustrate the necessity to draw on as large a body of evidence as possible when investigating cultural borrowings. In the context of house omens, while it is possible that some of the Indian omens are elaborations of Mesopotamian ones, alternative explanations can be given as well. An example of Indian elaboration on Mesopotamian house omens is given by Pingree.68 It concerns the door of a house and the direction it ˇ ¯ faces. According to the Summa Alu, it is good if a door faces north or south, but bad if it faces east or west.69 These omens are compared to similar omens in the Br.hatsam a .70 There, however, each direction has . hit¯ eight subdivisions according to a scheme, described above, of dividing the ground-plan of the house into sections each presided over by a certain deity. In other words, the Br.hatsam a gives thirty-two omens dealing . hit¯ with the position of the door of the house. 65. Tablet 16. 66. Pingree, “Mesopotamian Omens in Sanskrit.” 67. Ibid., 379. 68. Ibid., 377. ˇ ¯ 5.71–74. Although the apodoses are different (the apodosis per69. Summa Alu taining to the east is missing), the same is the case in an omen tablet investigated by Sally Moren, “A Lost ‘Omen’ Tablet,” Journal of Cuneiform Studies 29, no. 2 (1977): 65–72, lines 24–27). 70. Br.hatsam a 52.69–73. . hit¯


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While an elaboration of Mesopotamian material is a possible origin of the Indian omens, it is also possible that their origin is indigenous. Working with the idea that omens can be derived from houses in the first place, it can be argued that the position of the door suggests itself as naturally ominous. The greater number of positions of the door in the Indian tradition also suggest themselves naturally, as the Indians have schemes for division of the ground-plan of the house explained above.71 Conclusion While it has been demonstrated (especially with regard to astral omens) that the Indians adapted Mesopotamian material to their own cultural context, the house omens taken by themselves do not seem to furnish conclusive evidence of cross-cultural transmission. In order to establish a transmission, a greater body of evidence is needed, including that of the astral omens and the references to divination in Buddhist texts mentioned previously. The work done on this greater body of evidence, notably by Pingree, indicates that a transmission took place, but to understand fully how Mesopotamian material was incorporated into the Indian tradition—how the received knowledge was adapted to the new cultural context and how it was simplified or elaborated upon— it is necessary to engage in a more comprehensive study. This study should focus on a wide range of types of omens, as well as incorporate more of the surviving texts. All of the various types of omens, from the astral ones to house omens to omens derived from the behavior of dogs and other animals, need to be considered. The Gargasam a . hit¯ needs to be edited and studied, and other Indian texts, which have been published, need to be studied in greater detail and compared to the Mesopotamian material. In the words of Pingree: “I am confident that the comparison of the two traditions will reveal much not only about how their systems of divination worked, but also about how their societies functioned, and how influential on many aspects of Indian culture the Babylonians ultimately were.”72

71. Pingree also mentions the Mandæan Book of the Zodiac, which has another expanded scheme, but concludes that this was transmitted to the Mandaeans from India via Sasanian intermediaries. 72. Pingree “Mesopotamian Omens in Sanskrit,” 379.

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———. “Babylonian Planetary Theory in Sanskrit Omen Texts.” In From Ancient Omens to Statistical Mechanics: Essays on the Exact Sciences Presented to Asger Aaboe, edited by J. Lennart Berggren and Bernard Goldstein, 91–99. Copenhagen: University Library, 1987. ———. “Venus Omens in India and Babylon.” In Language, Literature, and History: Philological and Historical Studies Presented to Erica Reiner, edited by Francesca Rochberg-Halton, 293–315. New Haven: American Oriental Society, 1987. ———. “mul.apin and Vedic Astronomy.” In dumu-e2 -dub-ba-a: Studies in Honor of ˚ Ake W. Sj¨ oberg, edited by Hermann Behrens, Darlene Loding and Martha Roth, 439–45. Philadelphia: Occasional Publications of the Noah Kramer Fund, 1989. ———. “Mesopotamian Omens in Sanskrit.” In La circulation des biens, des personnes et des idées dans le Proche-Orient ancien, edited by Dominique Charpin and Francis Joannès, 375–79. Paris: ´ Editions Recherche sur les Civilisations, 1992. ———. “Legacies in Astronomy and Celestial Omens.” In The Legacy of Mesopotamia, edited by Stephanie Dalley and Andrés Reyes, 125–37. New York: Oxford University Press, 1998. Ramakrishna Bhat, Mena, Varahamihira’s Brihat Samhita with English Translation, Exhaustive Notes, and Literary Comments. 2 vols. Delhi: Motilal Banarsidass, 1981. Reiner, Erica. Astral Magic in Babylonia. Philadelphia: American Philosophical Society, 1995. Trip¯ at.h¯ı, Avadha Vih¯ ar¯ı, ed. The Br.hatsam a by Var¯ ahamihir¯ ac¯ arya . hit¯ with the commentary of Bhat..totpala, Sarasvat¯ı Bhavan Grantham¯ al¯ a, vol. 97, pts. I and II. Varanasi: Varanaseya Sanskrit Vishvavidyalaya, 1968. Tsukimoto, Akio. Untersuchungen zur Totenpflege ( kispum) im alten Mesopotamien. Alter Orient und Altes Testament, vol. 216. Kevelaer: Butzon and Bercker; Neukirchen-Vluyn: Neukirchener, 1985. Williams, Clemency. “Signs from the Sky, Signs from the Earth: The Diviner’s Manual Revisited.” In Under One Sky: Astronomy and Mathematics in the Ancient Near East, edited by John M. Steele and Annette Imhausen, 473–85. M¨ unster: Ugarit-Verlag, 2002. Yano, Michio and Mizue Sugita. Varahamihira’s Brhatsamhita. Version 4. Tokyo: Heibon-sha, 1995.

Anat for Nephthys: A Possible Substitution in the Documents of the Ramesside Period Jessica Lévai Brown University

I had the joy of studying Akkadian with Alice Slotsky for two semesters. That any of it stuck is a testament to her teaching. Since then she has been a great friend and help during the rough time that was my qualifying exams and selection of a dissertation topic. I hope she enjoys this piece, which may be six degrees separated from her field but was inspired by a comment she once made to me: Goddesses are good! During the New Kingdom, Egypt saw the height of her expansion into lands to the West. As their influence in these lands grew, gods and goddesses from conquered territories found their way into the Egyptian pantheon in various roles. Two goddesses, Anat and Astarte, assumed the role of consorts to the god Seth, whom the Egyptians identified with Baal. Both are mentioned in this capacity in the Egyptian tale, “The Contendings of Horus and Seth.” Anat, by herself, is associated with Seth in magical texts—the Magical Papyrus Harris, Magical Papyrus Leiden I, and the Papyrus Chester Beatty VII, in which Anat may be portrayed as a helper of the Egyptian goddess Isis. In traditional Egyptian myth, the consort of Seth and helper/sister of Isis is the goddess Nephthys. While Nephthys does not disappear from the scene completely during this period, appearing in magical spells, she is replaced by Anat in some written sources. The two appear together in the same text only once, in a spell in the Magical Papyrus Harris. The Egyptian religion was syncretic, and it was not unusual for gods to be identified with one another, but Anat and Nephthys were never combined or otherwise identified. Instead, Anat displaced Nephthys, taking over her roles. This substitution may have reflected a desire to give Seth, a favored god of the Ramesside kings, a dynamic consort better fitting his personality.

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In “The Contendings of Horus and Seth,” we find the most explicit Egyptian telling of the aftermath of the death of Osiris, written on papyrus from the reign of Ramesses V.1 In the story, Osiris’s brother Seth and son Horus fight for over eighty years over his throne. Osiris’s sister and wife Isis is a major player in the tale, by turns wailing and wily, clearly favoring her murdered brother and his son but conflicted over her brother Seth. The goddesses Neith and Hathor also put in appearances. But where is the usual companion of Isis, her sister Nephthys? The traditional role of this goddess in the tale is to assist her sister in finding Osiris’s body and mourning his death. To a lesser extent, she helps rear Isis’s son, Horus. Nephthys is also the spouse of Seth, though more often she is depicted with her sister than with her nominal husband. “The Contendings of Horus and Seth” should be the place for her character, yet she doesn’t show.2 I believe the reason for her nonappearance has to do with the two Semitic goddesses mentioned at the beginning of the tale, Anat and Astarte, who by this time had become members of the Egyptian pantheon. Early in the story, the Ennead asks the goddess Neith, mother of the gods and creator of the universe,3 to judge between Horus and Seth. She replies, in a letter: And let the Universal Lord, the Bull who resides in Heliopolis, be told, ‘Enrich Seth in his possessions. Give him Anat and Astarte, your two daughters, and install Horus in the position of his father, Osiris.’4 Herman te Velde, in his book Seth, God of Confusion, argues that this passage does not mean that the two goddesses should be read as Seth’s wives. “[T]he gods do not entertain this proposal. Apparently, it is not actually possible to get out of the difficulties by arranging a marriage for 1. Edward Wente, Jr., “The Contendings of Horus and Seth,” in The Literature of Ancient Egypt: An Anthology of Stories, Instructions, Stelae, Autobiographies and Poetry, ed. William Simpson, 3rd ed. (New Haven: Yale University Press, 2003), 91–103. 2. Technically, of course, Nephthys is included in the Ennead of Heliopolis, the family of gods consisting of Atum, Shu and Tefnet, Nut and Geb, Isis, Osiris, Seth and Nephthys. The word Ennead, psd.t in the Egyptian, means “nine gods,” but ¯ the applications of this term can be loose indeed. See Lana Troy, “The Ennead: The Collective as Goddess. A Commentary on Textual Personification,” in Religion of the Ancient Egyptians: Cognitive Structures and Popular Expressions. Proceedings of Conferences in Uppsala and Bergen, ed. Gertie Englund Acta Universitatis Upsaliensis, Boreas, vol. 20 (Stockholm: Almqvist & Wiksell International, 1987), 59–69. 3. Barbara Lesko, The Great Goddesses of Egypt (Norman, Oklahoma: University of Oklahoma Press, 1999), 57. 4. Wente, “The Contendings of Horus and Seth,” 94.

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Seth.”5 I believe it is less clear. The Ennead clearly agrees with Neith, while the Universal Lord, who has backed Seth, gets angry, and vents his anger on Horus, calling him too young for the office. Seth himself is not satisfied with losing the throne, but no one says anything about Anat or Astarte for the rest of the story, and no conclusion can be drawn from it about their relationship. Sadly, much of the other evidence for a marriage or sexual relationship between Anat and Seth is just as ambiguous. They appear together in a few contexts. An oft-cited but tricky passage in BM EA 10042, also known at the Harris Magical Papyrus, reads The opening of the womb of Anat and Astarte was closed, • the two 9 great goddesses, • when they were pregnant, but could not give birth. • They were closed by Horus, • they were founded (?) by Seth, • 6 The word “founded” is confusing in this context. It may be an error for the word “opened,” which has been interpreted differently by scholars, who seem to agree that Horus closing their wombs refers to pregnancy. But “opening” by Seth may refer either to intercourse (and thus pregnancy by Seth) or abortion.7 If it does refer to intercourse, then we have evidence that Seth did have sex with the goddesses. Anat, separate from Astarte, is associated with Seth in a few more texts. One is a spell to conjure demons, from the Magical Papyrus Leiden I, which reads, “See, from the breasts of Anat I have suckled the big cow (‘mry.t) of Seth.”8 Being called the cow of Seth hardly seems flattering to the modern reader. However, it calls to mind the images from the tombs of the goddess Hathor, in the guise of a cow suckling the king. If the author intended to invoke this iconography, it would seem to describe Anat as Seth’s mother. Seth’s official mother is the sky goddess Nut, though the syncretistic Egyptians would have had no difficulty assigning the same role to Anat as well. There is an epithet, “Bull of his Mother,” which is applied to the gods Min or Horus, and refers to the god using his own mother to engender his rebirth.9 If this 5. Herman te Velde, Seth, God of Confusion: A Study of his Role in Egyptian ¨ Mythology and Religion, Probleme der Agyptologie, vol. 6 (Leiden: Brill, 1967), 30. 6. Christian Leitz, Magical and Medical Papyri of the New Kingdom, Hieratic Papyri in the British Museum, vol. 7 (London: British Museum Press, 1999), 35. 7. Leitz, Magical and Medical Papyri, 35, n. 26. 8. Joris Borghouts, Ancient Egyptian Magical Texts, Nisaba 9 (Leiden: Brill, 1978), 20, n. 24. 9. Geraldine Pinch, Handbook of Egyptian Mythology (Santa Barbara: ABCCLIO, 2002), 124; 165.

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concept were applied to Seth, Anat could very well be his wife and his mother, cow partner to a bull. I have not found any instances of “Bull of his Mother” applied to Seth, though Seth does take the form of a bull in some stories.10 This detail of Anat as cow has been compared to an Ugaritic myth, in which the god Baal (clearly identified by the Egyptians with Seth) mates with a cow.11 This cow may be Anat, some other goddess in cow form, or just a cow.12 An Ugaritic prayer may refer to Anat as “Cow,” but this is debated.13 The “marriage” of Baal to his sister Anat has been used to support the claim that a sexual relationship existed between Seth and Anat. However, a relationship between Seth and Anat has also been used by scholars to support the theory of a relationship between Baal and Anat. Thus, there is the risk of circular logic here. Anat’s connection to Seth is as ambiguous as hers with Baal, and it is impossible to use either to prove the other. So the question of Anat and Seth, did-they-or-didn’t-they, remains open. But it is important at this point to keep in mind that Seth may never have had sex with Nephthys, his traditional consort, and their marriage may be one of convenience or appearances only. They did not have any children, and one of the few explicit references to their marriage comes from a lamentation of Isis on a statue base: “My elder brother [Seth] is an enemy, obstinate in his malice towards me. My younger (sister) is in his house.”14 This dates to the Ptolemaic period. A story related in P. Chester Beatty VII may offer further evidence of Anat as the wife of Seth. This story takes the form of a histriola, or “mythical precedent”15 to a spell against poision. Histriolæ are a common feature of Egyptian spells, calling upon an example from myth, the event of which parallel the hoped-for result of the spell. This histriola is sometimes called “The Tale of Seth and Anat.” This title is a bit misleading and is actually based on an interpolation of the text which ascribes to Anat a larger role in the tale than she actually has. In the tale, Seth has sex with a goddess he spies bathing in the sea. This dalliance causes him to be ill, and Anat must beg the sun god, Pre, 10. Pinch, Handbook of Egyptian Mythology, 124. 11. Neal Walls, The Goddess Anat in Ugaritic Myth (Atlanta: Scholar’s Press, 1992), 122–23. 12. Johannes van Dijk, “Anat, Seth and the Seed of Pre,” in Scripta Signa Vocis: Studies about Scripts, Scriptures, Scribes and Languages in the Near East, presented to J. H. Hospers by his pupils colleagues and friends, eds. Herman Vantisphout, et al. (Groningen: Egbert Forsten, 1986), 31–52. 13. Walls,The Goddess Anat in Ugaritic Myth, 123. 14. Adolph Klasens, A Magical Statue Base (Socle Behague) in the Museum of Antiquities at Leiden (Leiden, E. J. Brill, 1952), 54. 15. van Dijk, “Anat, Seth and the Seed of Pre,” 32.

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for Seth’s relief. He refuses to help, preferring to let Seth suffer for his transgression of having sex with the goddess intended for Pre. In the end, Isis appears and returns to Pre what belongs to him, curing Seth. A lacuna at the beginning of the papyrus unfortunately obscures the name of the goddess with whom Seth copulates, so many scholars fill in the blank with Anat’s name, citing the above mentioned Ugaritic tale of Baal and Anat copulating. They then proceed to discuss the implications of the story as evidence of everything from Seth and Anat’s sexual relationship to Seth’s homosexual proclivities, since Anat is dressed in items of men’s clothing.16 But in his article, van Dijk compares various versions of this story from ostraca and discoveres that the goddess with whom Seth copulates is a personification of the semen of Pre, necessary for Pre’s rebirth.17 Given this new reading, Anat appears in the middle of the story to ask Pre, her father, for assistance. There is no evidence that she is anything more to Seth than a helpful family member, perhaps a sibling, though close familial relation would not rule out the possibility that she is his wife. Van Dijk’s article takes their marriage as read.18 While the question of Anat’s relationship with Seth may be ambiguous, as is her relationship with Baal in Ugaritic myth, another function of the goddess which makes her similar to Nephthys is her role as mourner of the murdered Baal. Neal Walls explains: Anat’s mourning for Baal is an important element of her character and narrative function in Ugaritic myth. With the aid of Shapsh, Anat searches for Baal’s corpse, vigorously mourns him, and provides elaborate sacrificial offerings at his burial. The maiden goddess then avenges her brother’s death by exterminating Mot.19 The similarities to the Egyptian Osiris myth are striking. Like Osiris, Baal is killed by a rival and later returns from the dead. Like Nephthys, Anat aids in the funerary rites for a slain god, her brother. (It may be important to remember, however, that the Egyptians identified Seth with Baal, not Osiris, and thus the mythic similarities do not quite match up.) Did the Egyptian myth about Anat exploit this similarity? Van Dijk’s article ends with an interesting comparison of the Anat and Seth myth in the Papyrus Chester Beatty VII to the myth of Osiris, in which Anat’s role is compared to that of Nephthys. 16. te Velde, Seth, God of Confusion: A Study of his Role in Egyptian Mythology and Religion, 56; 113. 17. van Dijk, “Anat, Seth and the Seed of Pre,” 38. 18. Ibid., 41. 19. Walls, The Goddess Anat in Ugaritic Myth, 67.

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Jessica Lévai [Osiris myth:] Isis, assisted by Nephthys, recovers the pieces, . . . and, becoming his wife and mother, gives birth to Osiris’ (sic) reincarnation as Horus. [Anat myth:] Isis, assisted by Anat, recovers the seed and, becoming his wife and mother, enables Re to be born in the morning.20

This interpretation is not directly supported by the text but rather comes from a lengthy argument van Dijk makes on the previous pages, identifying Osiris’s seed with Hathor and the three goddesses of the story (the seed, Anat, and Isis) with each other.21 Calling Anat the helper of Isis in this instance is perhaps a bit of a stretch. But let us compare van Dijk’s interpretation to other spells against poison. Isis’s appearance at the end of the historiola in P. Chester Beatty VII resembles other poison spells, where Isis heals her son Horus, who has been bitten by a snake or scorpion. There are a great many such spells in which Horus has been bitten and his mother Isis saves him, assisted by other gods. In the examples from BM EA 9997, she calls upon her parents Geb and Nut and grandfather Atum.22 In another she is assisted by the scorpion goddess Selket,23 and by Nephthys in another.24 Isis and Nephthys figure together in other spells for burns and headaches.25 Anat assisting Isis in a spell against poison does not necessarily mean she replaces Nephthys. She could be filling the position of Selket or Hathor. But with Seth playing so prominent a part in the story, one looks for Nephthys and finds Anat instead. Anat has taken over for Nephthys in this spell. Walls points out that, for all the similarities of Anat in the story of Baal to Nephthys in the story of Osiris, the Egyptians kept the goddesses separate and did not identify the one with the other.26 It is interesting that the goddess are so distinct that they seldom appear in the same place at the same time, rather like Clark Kent and Superman. The only text I have found in which both Anat and Nephthys appear is a spell for the protection of a field and herds, written on the verso of the Harris Magical Papyrus. Nephthys is mentioned right after Isis, as is traditional, while Anat appears with other gods from her own country, Reshef and Hauron. 20. 21. 22. 23. 24. 25. 26.

van Dijk, “Anat, Seth and the Seed of Pre,” 43. Ibid., 42. Leitz, Magical and Medical Papyri of the New Kingdom, 9. Ibid., 16. Ibid., 19. Borghouts, Ancient Egyptian Magical Texts, 24–25; 26–27; 31; 43–44. Walls, The Goddess Anat in Ugaritic Myth, 73.

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Horus cries aloud on the field, • for his 2 herd said ‘stay!’ • Cause there summons to be made for me to Isis, my good mother • and Nephthys, my sister. • ... the sky is opened 7 over you [a jackal] • Hauron ignores your protests. • Your foreleg is severed by Herishef, • You are overpowered by Anat. • 27 Leitz argues, “From the mention of the three Canaanite dieties Reshef (thus originally rather than Herishef), Anat and Hauron, it seems plausible to suggest a foreign origin for this text, particularly in view of Section Z.” 28 Section Z is written in hieratic script, but not in the Egyptian language; it is a Canaanite spell. If these two spells are indeed foreign in origin, then whoever wrote the text may not have had the same background as the Egyptians who wrote the above-cited texts in which Anat replaces Nephthys, and this new trend may have escaped his or her notice. It makes sense that the Ramessides would choose new wives for Seth, a god they held in high esteem. That this dynasty sought to honor Seth is evident from the names of a few of its kings: Sety, Sethnakht. The Hyksos brought in their foreign gods, and the Ramessides, who claimed descent from the Hyksos, would have wanted to incorporate their gods into the Egyptian pantheon. The specific designation of Anat and Astarte as wives of Seth may reflect the habit of Egyptian kings since the Eighteenth Dynasty of taking foreign wives as diplomatic measures.29 These wives also brought with them their own gods from their own countries and may thus have influenced court religion. Seth was also viewed during the New Kingdom as a god of foreigners and foreign lands. It would make sense that he had foreign wives. Finally, the decision to find new wives for Seth may have come down to a clash of personalities. The Ramessides may have agreed with te Velde, Nephthys is also a rather colourless figure in the Egyptian world of gods . . . she is not like Isis the model of conjugal fi27. Leitz, Magical and Medical Papyri, 47–48. 28. Ibid., 47. 29. te Velde, Seth, God of Confusion: A Study of his Role in Egyptian Mythology and Religion, 113.

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Within the Osiris myth, Nephthys is seldom portrayed as a dynamic, active goddess. There are no myths in which she is found operating on her own or even given any prominence. There do not seem to have been any temples or cults dedicated to her alone.31 Her job is mourning and assisting Isis in various ways, and she did not exist outside of these functions. Anat, on the other hand, is occasionally violent. She is a warrior and a huntress, besides being a bit of a tomboy. While both she and Nephthys mourned their brothers, Anat took vengeance on his killer, Mot. The Ramessides weren’t the first to substitute a more forceful goddess for Nephthys. In the Pyramid Texts, which date to the Old Kingdom, Nephthys is sometimes replaced with Neith.32 Neith herself shares characteristics with Anat, being a goddess of war (later identified by the Greeks with Athena). To the Ramessides, Anat must have seemed a better match for Seth. As we have seen above, their marriage does not seem to have been any more romantic than his marriage to Nephthys. Anat assumed the roles of Nephthys in a few texts of the Ramesside Dynasty, providing a more dynamic consort to Seth than did Nephthys. Her introduction reflects the preferences of the kings of that dynasty, whose extensive contacts with the rest of the Near East resulted in the adoption of many gods into the Egyptian mythology. Anat and Nephthys seem to exist separately and they are never identified with each other yet fill the same function. This separation seems unusual for the syncretistic Egyptians, and perhaps more research can explain this dynamic.

30. Herman te Velde, “Relations and Conflicts between Egyptian Gods, Particularly in the Divine Ennead of Heliopolis” in Struggles of Gods: Papers of the Gronigen Work Group for the Study of the History of Religions, ed. Hans Kippenberg (New York: Mouton Publishers, 1984), 253. 31. Lesko, The Great Goddesses of Egypt, 271. 32. te Velde, “Relations and Conflicts,” 242.

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References Klasens, Adolph. A Magical Statue Base (Socle Behague) in the Museum of Antiquities at Leiden. Leiden, E. J. Brill, 1952. Leitz, Christian. Magical and Medical Papyri of the New Kingdom. Hieratic Papyri in the British Museum, vol. 7. London: British Museum Press, 1999. Lesko, Barbara. The Great Goddesses of Egypt. Norman, Oklahoma: University of Oklahoma Press, 1999. Pinch, Geraldine. Handbook of Egyptian Mythology. Santa Barbara: ABC-CLIO, 2002. te Velde, Herman. Seth, God of Confusion: A Study of his Role in ¨ Egyptian Mythology and Religion. Probleme der Agyptologie, vol. 6. Leiden: Brill, 1967. ———. “Relations and Conflicts between Egyptian Gods, Particularly in the Divine Ennead of Heliopolis.” In Struggles of Gods: Papers of the Gronigen Work Group for the Study of the History of Religions, edited by Hans Kippenberg, 239–58. New York: Mouton Publishers, 1984. Troy, Lana. “The Ennead: The Collective as Goddess. A Commentary on Textual Personification.” In Religion of the Ancient Egyptians: Cognitive Structures and Popular Expressions. Proceedings of Conferences in Uppsala and Bergen, edited by Gertie Englund, 59–69. Acta Universitatis Upsaliensis, Boreas 20. Stockholm: Almqvist and Wiksell International, 1987. van Dijk, Johannes. “Anat, Seth and the Seed of Pre.” In Scripta Signa Vocis: Studies about Scripts, Scriptures, Scribes and Languages in the Near East, presented to J. H. Hospers by his pupils, colleagues, and friends, edited by Herman Vantisphout, et al., 31–52. Groningen: Egbert Forsten, 1986. Walls, Neal. The Goddess Anat in Ugaritic Myth. Atlanta: Scholar’s Press, 1992. Wente, Edward, Jr. “The Contendings of Horus and Seth.” In The Literature of Ancient Egypt: An Anthology of Stories, Instructions, Stelæ, Autobiographies and Poetry, edited by William Simpson, 91–103. 3rd ed. New Haven: Yale University Press, 2003.

Observations on The Diffusion of Military Technology: Siege Warfare in the Near East and Greece Sarah C. Melville1 and Duncan J. Melville Clarkson University and Saint Lawrence University

Introduction With great pleasure we dedicate this paper to Alice Slotsky, with whom we spent many diligent and occasionally uproarious hours at graduate school besieging the (seemingly) impenetrable citadel of Assyriological knowledge. In a volume concerned specifically with the transmission of ideas, it seems particularly fitting to examine aspects of military diffusion, warfare being one of the constants of human history. Here we combine textual, archaeological, and artistic sources to consider the transmission of the tactics and technology of siege warfare in the Near East and Greece, with particular emphasis on siege ramps since they are widely represented in all three of our source categories. We approach the issue of diffusion from multiple perspectives, considering both intercultural diffusion across geographical and temporal boundaries and intracultural diffusion between sections of society. In Old Babylonian Mesopotamia, we see an appropriation of practical knowledge into the scribal milieu and its subordination to scholastic ends, rather than utilization by scribes to support military practitioners. Turning to the question of the transmission of siege methods from the Near East to Greece, we apply some of the tenets of military diffusion theory as defined by Goldman and Eliason.2 A careful analysis of Greek accounts indicates a lag between awareness of Near Eastern siege methods and their adoption in native Greek warfare and suggests the agency for transmission of the information as well as the social and cultural barriers to its adoption. 1. Research for this paper was supported in part by a grant from the American Philosophical Society. 2. The Diffusion of Military Technology and Ideas, eds. Emily Goldman and Leslie Eliason (Stanford: Stanford University Press, 2003).

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References to sieges in ancient texts date back to the third millennium b.c. and indicate that the taking of walled cities was commonplace, though no early text describes siege methods in detail. By the beginning of the second millennium b.c. advances in military technology such as the composite bow, battering ram, and siege tower inspired counter-developments in defensive fortifications: the fosse, rampart, and glacis.3 In order to get siege machinery over these obstacles to the city walls, attackers built earthen ramps. Just as we cannot pinpoint the time or place of any of the improvements in weaponry or fortifications, we cannot determine the origin of the siege ramp; it was a natural response to fortification and undoubtedly widely used. Our earliest textual references to siege ramps come from the Old Babylonian period. For example, ARM 1 4:5 relates how Iˇsme-Dagan took the town Nilimar, “when the earth(en ramp) reached the top of the city (wall),” while another tablet details the Eshnunnans’ unsuccessful attempt to take Razama by means of a ramp: And they (the Eshnunnans) piled up earth (eperu) which advanced toward the city. (When) the front of the earth(en ramp) reached the base of the wall of the exterior ramparts, the inhabitants reinforced the wall on the right and left.4 Although these references reveal little about the construction or composition of siege ramps beyond the fact that they were begun at the point farthest from the wall and gradually built inward, they do seem to indicate that ramp building was neither especially difficult nor remarkable. The one type of Old Babylonian textual source that does seem to include extensive details about the construction of siege ramps is mathematical problems. Here we have moved from the directly practical and political sources to those of the scholarly realm, and great care must be taken in interpreting the problems outside of their contexts. Only a few problems involving siege ramps made their way into Old Babylonian mathematics, but they did so in a way that implies the concept was neither new nor unusual, and so they can be used as indirect evidence that such construction was reasonably widespread, sufficiently so to be part of the cultural hinterland of trainee scribes. 3. Aaron Burke, “The Architecture of Defense: Fortified Settlements of the Levant During the Middle Bronze Age” (Ph.D. diss., University of Chicago, 2004). Available at http://oilib.uchicago.edu/dissertations/burkeaa.pdf. 4. ARM 14:104, after Dominique Charpin, “Donn´ ees Nouvelles sur la Po´ liorc´ etique a ` l’Epoque Pal´ eo-Babylonienne,” Mari, annales de recherches interdisciplinaires 7 (1993): 193–203.

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As is well-known, the Old Babylonian mathematical corpus includes many problems on themes taken from practical matters. Among them, there are numerous excavation, irrigation, and construction problems with a variety of approaches to realism.5 In particular, two texts contain problems concerning the construction of siege ramps: BM 85194 and BM 85210. The two tablets are part of a group of seven from Sippar, all written by the same person, one Iˇskur-mansum.6 BM 85194 contains thirty-five problems, typically in small, related groups on a wide variety of topics; BM 85210 is broken and only portions of thirteen problems remain, but the colophon indicates there were originally twenty. Because of the variety of topics, with in most cases groups of two to four problems on a particular theme placed together, it is generally believed that these tablets were copied from a collection of texts that developed each theme in greater detail. The two ramp problems on BM 85194 are the twentyfifth and twenty-sixth in sequence, while the two on BM 85210 are the sixth and seventh of the extant problems. The four problems share the same basic parameters, and it is clear they were drawn from the same source. Indeed, Neugebauer treated all four problems together in his commentary,7 rather than repeating himself when commenting on the second tablet. Høyrup has recently published an up-to-date reading of the two problems from BM 85194.8 What is interesting to us in terms of social transmission is how the practical problem of building a siege ramp was transformed when it was pressed into the service of scribal mathematics. The four problems form a typical group in that the initial conditions are the same 5. For example, the set YBC 4657, YBC 4663, and YBC 4662 cover thirty-one problems on excavation; YBC 4666 and YBC 7164 between them have forty-one problems on canal construction; YBC 4186 involves a cubical cistern 60 m. on a side irrigating a field to a depth of one ˇsu-si, a situation Otto Neugebauer dryly characterized as “strongly idealized,” in Mathematical Cuneiform Texts, American Oriental Series, vol. 29 (New Haven: American Oriental Society; American Schools of Oriental Research, 1945), 91; BM 96957 + VAT 6598 has a sequence on building a brick wall, and VAT 8523 contains six problems on constructing a dam. 6. The tablets are BM 85194, BM 85196, BM 85200 + VAT 6599, BM 85210, ´ 93, BM 96957 + VAT 6598, and VAT 6597. Robson’s BM 96954 + BM 102366 + SE edition of BM 96957 + VAT 6598 provided the clue to their grouping, “The colophon names the copyist of this text — and thereby all the other Sippar texts written in the same hand.” See Eleanor Robson, Mesopotamian Mathematics, 2100–1600 b.c.: Technical Constants in Bureaucracy and Education, Oxford Editions of Cuneiform Texts, vol. 14 (Oxford: Clarendon Press, 1999), 190. 7. Otto Neugebauer, Mathematische Keilschrifttexte, Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik. Abteilungen A: Quellen, vol. 1 (Berlin: Springer, 1935), 182–85. 8. Jens Høyrup, Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin (New York: Springer, 2002) 217–22.

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for each problem with the variety determined by which parameters are given in each problem and which are sought. What clearly caught the eye of the original deviser of these problems was the complications that arise from assuming that the ramp is only partially built and the number of parameters that result from this assumption. The parameters are the constructed length, the height of the partially-completed ramp, the height of the wall of the besieged city, the width of the ramp, the distance left to be built, and the volume of the completed ramp. For each problem, some of these are assumed known, and others must be computed. The difficulty of each problem depends on what is assumed and what must be computed. That is, the structure of each problem is driven by mathematical concerns, not practical ones. For example, here is the simplest of the problems, BM 85194 Problem 26: With earthworks (of volume) 1,30,0 I shall seize a city hostile to Marduk. From the base of the earthwork, I went a length of 32 up to my front. The height of the earthwork is 36. What length must I stamp in order to seize the city? What is the length from the front of the hurhurum 9 ? You, take the ˘ ˘ Multiply 0;1,52,30 by reciprocal of 32 and you see 0;1,52,30. the height, 36, and you see 1;7,30. Take the reciprocal of 6, the width of the earthwork and you see 0;10. Multiply 1,30,0 by 0;10 and you see 15,0. Double 15,0 and you see 30,0. Multiply 1;7,30 by 30,0 and you see 33,45. What is the square root of 33,45? The root is 45. 45 is the height of the wall. How much does 45, the height of the wall, exceed 36, the height of the earthwork? It exceeds it by 9. Take the reciprocal of 1;7,30 and you see 0;53,20. Multiply 0;53,20 by 9 and you see 8. 8, the length in front of you, you stamp. The problem assumes the length and height of the ramp so far constructed are known and seeks to find the distance left to go to reach the wall. This problem presents an apparently reasonable physical set-up, except that the crucial piece of information given in order to solve the problem is the final volume of the completed ramp. In fact, the final volume is assumed known in all of the problems and never derived from other parameters. It would be an unusual engineer who knew exactly how much earth a ramp was going to require but did not know how far from the city wall it had reached. Instead, the problem as given uses an elegant application of similar triangles and quadratic mathematics 9. See The Assyrian Dictionary, s.v. “hurhurum.” This word doesn’t appear ˘ anywhere else, and its meaning is therefore˘unknown, although in context it must refer to the ramp or part of the ramp.


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to find first the height of the wall, then the distance from the ramp to the wall (a more detailed treatment is given in a mathematical excursus below). The other problems involve equally unlikely situations, making it clear that the purpose was not to train scribes in the practical mathematics of quantity surveying, but to give them practice in solving problems about triangles, viz., what Høyrup calls “sham practical geometry.” Noticeably, none of the problems compute how long it would take to build the ramp, perhaps because this is mathematically trivial, given the volume of the completed ramp.10 Other aspects of the problems also show the primacy of the pedagogical over the practical. The ramp itself is simplified to a triangular wedge. That is, the ground is smooth and flat; the wall of the city “hostile to Marduk” is nicely vertical; and the ramp is the same width for all of its length, which, as we see below, is highly unlikely in practice.11 The numbers involved are all conspicuously simple and not necessarily `ˇ realistic. The height of the city wall is given as 45 ku s (about 22.5 12 m.), which is perhaps excessive, but the ramp starts at a distance of 40 nindan (c. 240 m.) from the wall, far farther than any real ramp would. Also, the design is that the height of the completed ramp should equal exactly that of the city wall. Perhaps the most telling fact is the use made of volume. As noted, the final volume of the completed ramp is always presumed known, but its function in the problems is simply to be divided by the width, thereby producing the area of the triangular side of the ramp. With triangles the scribes are back in familiar territory. Excavated First Millennium Examples of Siege Ramps As we have seen, the Old Babylonian mathematical siege ramp problems could not have been designed to prepare scribes to perform field calculations while on campaign; they quite clearly have nothing to do with the real conditions under which siege works were constructed. Even so, we must ask whether mathematical expertise was used to calculate the construction values applied to making ramps. As widespread as 10. Since the volume is given, the student need merely multiply that volume by the standard work-norm for earthworks of 0;10 volume-sar per man-day, to see that 9,0,0 or 32,400 man-days would be required. See Eleanor Robson, Mesopotamian Mathematics, 78–80 and 93–97. 11. The first problem of BM 85194 involves a smaller ramp of trapezoidal crosssection that becomes wider as it gets higher, towards the city gate. 12. For obvious reasons, no ancient near eastern city wall has been preserved to its original height. However, archaeological evidence suggests that walls were usually between 10 and 15 m. high. In his account of the Siege of Armanum, Naram-Sin describes the inner citadel walls as being 20 m. high. For a review of the pertinent evidence, see Burke, The Architecture of Defense, 115–19.

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siege methods were in ancient Near East, only three examples of siege ramps have been extensively excavated (at Lachish, Smyrna, and Palæpaphos on Cyprus), and they belong to a period of a little over two hundred years (c. 701 – 498 b.c.).13 Nevertheless, evidence from these cities may shed light on how siege ramps were built and what kind of technical skills (if any) were necessary to build them. In 701 b.c. the Assyrian king, Sennacherib, led a campaign against Hezekiah and the cities of Judah. Sennacherib’s account of the campaign describes the methods he used to retake the rebellious cities: 46 heavily fortified cities and small cities of their environs, which were countless, with siege ramps, and with siege engines drawn close, combat infantry, mines, breaches and scaling ladders, I surrounded (and) conquered.14 The siege and capture of one of these cities, Lachish, was depicted in detail on a series of bas-reliefs in Sennacherib’s palace at Nineveh. The Lachish reliefs, which are now in the British Museum, show the siege, including the earthworks constructed for the use of battering rams.15 In an unusual but fortunate correlation between art and artifact, the excavators of Lachish discovered the remains of the siege ramp and have made a thorough study of it.16 The ramp was fan-shaped, but its lower part no longer exists, and as a result, its actual size and shape cannot be securely determined. The ramp itself was composed chiefly of soil and small boulders that had been collected from the surrounding countryside. The stones on the surface of the mound were stuck together with a thick layer of mortar, thus providing siege engines a smooth, hard surface on which to operate.17 In response to the Assyrian siege mound, 13. Excavators of Dura-Europus also found remains of a Sassanid siege ramp, but since the date is so late (third century a.d.), we will leave it out of consideration. Since siege methods remained constant during this period, we feel that the time gap between the Old Babylonian and first millennium evidence does not affect our conclusions. 14. Daniel Luckenbill, The Annals of Sennacherib, Oriental Institute Publications, vol. 2 (Chicago: University of Chicago Press, 1924): 32–33. 15. Richard Barnett, Erika Bleibtreu, and Geoffrey Turner, Sculptures from the Southwest Palace of Sennacherib at Nineveh (London: British Museum Press, 1998), pl. 322–24. 16. Israel Eph‘al, “The Assyrian Siege Ramp at Lachish: Military and Lexical Aspects. Tel Aviv 11 (1984): 60–70 and David Ussishkin, “The Assyrian Attack on Lachish: The Archaeological Evidence from the Southwest Corner of the Site. Tel Aviv 17 (1990): 53–86. 17. Based upon initial reports by David Ussishkin, in “Excavations at Tel Lachish 1978–1983: Second Preliminary Report. Tel Aviv 10 (1983): 97–175, Eph‘al attempted to estimate the size of the work force in “The Assyrian Siege Ramp,” 63. However, the uncertainties surrounding the construction (e.g., weight and size of the


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the defenders of Lachish built a large counter ramp out of demolished houses and debris collected throughout the city.18 Both the Assyrian siege tactics and the counter-tactics employed by the besieged citizens of Lachish were standard military practice, demonstrating no innovation and no need of specialized personnel. The power vacuum in northern Syria and Anatolia created when the Assyrian Empire collapsed in 612 b.c. allowed the state of Lydia to pursue an aggressive policy of expansion against the neighboring Greek cities of Ionia. In c. 600 b.c., the Lydian king, Alyattes, besieged and took the city of Smyrna by means of a siege ramp. Only part of this ramp has been excavated, but archaeologists have uncovered much valuable information about how it was constructed. According to the excavators, Cook and Nichols, the ramp consisted of loose debris: stones; chunks of mud brick torn down from nearby houses; burnt wood including branches, small poles and large beams; earth; and a large quantity of broken pottery.19 Nicholls writes, “[t]he whole of this fill simply seemed to consist of masses of debris lying in the meaningless positions in which they had come to rest after having been tipped in from the north.” 20 It is clear from this description that the Lydians used whatever was at hand to build the mound and did so using no precise construction method or mathematical calculation other than the simple notion of “build it.” The subsequent destruction of the city attests to the success of Lydian siege methods. A little over fifty years after the sack of Smyrna, both Lydia and the Ionian cities were part of the Persian Empire. When the Ionian cities revolted against Persia in 499 b.c., Cyprus joined them, and when the Persians responded, the Cypriot cities were the first to come under attack. According to Herodotus, the Persians retook Cyprus quickly, and of the load, method of transportation, distance traveled, etc.) are too great to allow any confidence in such figures, and later excavations considerably revised the estimate of the size of the ramp in any case. In comparison with the mathematical ramp of BM 85194, we note that Ussishkin’s later reconstruction has a length of approximately 50–60 m., a width at the base of the ramp of 70–75 m., and a width at the top of some 25 m. The estimated range for the volume of material was 6500–9500 m3 in Ussishkin, “The Assyrian Attack on Lachish,” 64. Converting into the standard Old Babylonian “scientific” system gives the Lachish ramp a length of around 10 nindan, with a width at the top of approximately 4 nindan, and a width at the base of some 12 nindan; the volume would be about 6,0–9,0 volume-sar. 18. Ussishkin, “The Assyrian Attack on Lachish,” 79. 19. John Cook, “Old Smyrna, 1948–1951,” Annual of the British School at Athens 53–54 (1958): 1–34 and Richard Nicholls, “Old Smyrna: the Iron Age Fortifications and Associated Remains on the City Perimeter,” Annual of the British School at Athens 53–54 (1958): 35–137. 20. Richard Nicholls, “Old Smyrna,” 89.

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besieged cities only one (Soloi) held out for as long as five months.21 Palæpaphos (modern Kouklia), located on the southwest coast of the island, was one of the cities to fall to the Persians. The remains of a Persian siege ramp have been extensively excavated, first by the British Kouklia Expedition between 1950 and 1955 and subsequently by the German-Swiss team from 1966 to 1973. The ramp yielded a large number of arrowheads and spear points, soil, burnt bones, carbonized wood, and a treasure trove of architectural, sculptural and epigraphical pieces looted from a nearby temple by the Persians as fill.22 Although the precise dimensions have not been recorded, the shape of the ramp—a rather amorphous fan-shaped mound—together with the hodge-podge method of construction—again the besiegers clearly just used what was at hand—indicate that experience and “rule of thumb” sufficed, and precise mathematical calculations were unnecessary to build a siege ramp. It is also worth noting that the besieged responded to the ramp by building a counter-ramp and by tunneling under the siege mound in order to undermine it. The charred material found in the mound marks the conflagration caused by the tunnelers, who were able to cause part of the mound to collapse.23 Thus we may conclude that by the fifth century b.c. the people of Cyprus were well aware of siege techniques and how to respond to them, a point to which we will return later. Military Analysis and Conclusions Concerning Intracultural Diffusion Of the three siege mounds discussed above, the Assyrian ramp at Lachish was clearly the most carefully constructed, the other two having been built quite haphazardly. The quality of the Assyrian ramp attests to the high level of organization in the Assyrian army, and while its administration may have included the employ of scribes for general logistical calculations, their use in the construction of siege ramps is unlikely.24 In fact, siege ramps depicted on the Assyrian palace reliefs show 21. Herodotus 5.115.1–2. 22. To be precise, the excavated portion of the ramp contained “448 arrowheads and javelin points, 422 stone missiles, 16 male statues, 21 sphinxes and lions, 158 votive stelæ, 59 votive columns and 11 fragmentary incense altars.” See Kyriakos Nicolaou, “Archaeological News from Cyprus,” American Journal of Archaeology 77 (1973): 56. 23. Franz Maier and Vassos Karageorghis, Paphos: History and Archaeology (Nicosia: The A. G. Leventis Foundation, 1984), 202. 24. There is no doubt that scribes traveled on campaigns. The king (or his generals if the king wasn’t present) had to correspond with others in order to stay apprised of events elsewhere. Several reliefs depict scribes making tallies of booty and enemy dead in the aftermath of battle or siege. See, for example, Barnett, Bleibtrau and Turner, Sculptures, pl. 213, 244 and 253.


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that, like the Lydian and Persian ramps, the materials from which they were built varied quite widely according to terrain and availability.25 The creation of siege works, whether they were well built or arbitrarily piled up, was not the domain of the intellectual, but a standard military task. The Akkadian terminology used to describe them supports this assertion. In Akkadian the activity of building siege ramps is invariably described with some form of the phrases epiri ˇsapaku (piling up earth) or arammu ˇsukbussu (to make a ramp by stamping down earth).26 Assyrian scribes sometimes noted the hard work that went into building such mounds. For example, in his “Letter to the god Assur,” Esarhaddon acknowledged the privation suffered by his soldiers whom he made “pack down under great hardship a ramp of piled up earth, wood and stones (arammu ina ˇsipik epri isse u abne marsiˇs paˇskiˇs [uˇsakbis]).27 Even allowing for scribal convention and narrative embellishment in the texts, it is clear that building siege ramps involved hard physical labor, a great deal of time and loads of perseverance, rather than high tech engineering. From a military standpoint, mathematical calculations would have been of little use in any case. Scribes did not need to calculate the workforce, because for an army on campaign the question would always have been, “how many men can we spare to build a siege ramp?” rather than “how many men do we need to build a siege ramp?”28 And the answer would always have depended entirely upon military circumstances: the total size of the army; the size of the city and the disposition of its fortifications; the number of troops needed for other tactics such as mining, sapping, and blockade if they were applied; the behavior of the besieged troops, who might make sorties against the besiegers; the availability of 25. See, for example, in room XII of Sennacherib’s palace at Nineveh slabs 13–15, which depict the siege of a triple walled city. The siege works include a ramp made of brick and wood, stone and bundled branches. See Barnett, Bleibtrau and Turner, Sculptures, pl. 151–53. John Russell, Sennacherib’s Palace without Rival at Nineveh (Chicago: University of Chicago Press, 1991), 161–63 concludes that these reliefs depict events from Sennacherib’s third campaign against Judah, the same campaign as the siege of Lachish. 26. For detailed discussion of these terms, see Eph‘al, “The Assyrian Siege Ramp,” 64. 27. Riekele Borger, Die Inschriften Asarhaddons K¨ onigs von Assyrien, Archiv f¨ ur Orientforschung, vol. 9 (Graz: Im Selbstverlage des Herausgebers, 1956), 104, i37. 28. Both Eph‘al and Ussishkin have suggested that besieging armies may have used local conscripted labor or prisoners to build siege ramps, but the sources, if they mention the workforce at all, invariably refer to soldiers. See Eph‘al, “The Assyrian Siege Ramp,” 63; Ussishkin, “The Assyrian Attack on Lachish, 79; and Israel Eph‘al, Siege and its Ancient Near Eastern Manifestations (Jerusalem: Magnes Press, 1996), n. 152. The authors would like to thank Oded Tammuz for his generous help translating parts of Eph‘al’s book, which is in Hebrew.

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food and other resources; and the wider military and political situation. Any commander worth his salt could have overseen the construction of a siege ramp without recourse to mathematics. What was essential in building a siege ramp was someone to make sure no bottle necks occurred as workers (of varying numbers) carried materials (of varying types) distances (of varying length) and dumped their loads where they were told to. The type of calculations represented in the Old Babylonian mathematics problems would have been of no use whatsoever to a besieging army and, in fact, have no real value outside the rarefied world of scribal mathematics. Unfortunately, it is all too easy to take mathematical texts at face value and assume a diffusion of knowledge across social and intellectual boundaries that did not actually occur.29 In his book on siege warfare, Bentley Kern asserts that “the engineers who supervised the construction of these ramps applied sophisticated mathematical calculations to the task, as an Old Babylonian mathematical text reveals,”30 and again, “[e]vidence from the Old Babylonian math problems indicates that it should not have taken nearly so long to complete the ramp [at Platæa]. The Babylonians could throw one up in five days.”31 Postgate makes a similar error, noting that our problem, which he translates in full, offers a method for “army commanders to calculate the time needed to construct a siege ramp of a given height.”32 This calculation is precisely what BM 85194, Problem 26 does not do. Without actually referring to the Old Babylonian mathematical problems, Eph‘al alternatively suggests the possibility that mathematics could have been used to “compute the amount of raw materials and work that had to be assigned for the building of ramps,” although there is no evidence that the computation of the amount of raw materials was in fact ever done.33 The temporal gap between second millennium texts and first millennium sources notwithstanding, the evidence indicates that trans29. Although Benjamin Foster correctly points out that in Mesopotamia, “[p]resumption of superior knowledge in proportion to social status implied a theory that useful knowledge was transmitted vertically, from above to below,” he also notes that knowledge of military tactics (among other things) had no written tradition and therefore “had no resonance or prestige in surviving Mesopotamian scholarship, despite their importance in everyday life.” See Benjamin Foster, “Transmission of Knowledge,” in A Companion to the Ancient Near East, ed. Daniel Snell (London: Blackwell, 2005), 246, 249–250. 30. Bentley Kern, Ancient Siege Warfare (Bloomington: Indiana University Press, 1999), 18. 31. Kern, Ancient Siege Warfare, 92–93. 32. Nicholas Postgate, Early Mesopotamia: Society and Economy at the Dawn of History (London: Routledge, 1992), 230. 33. Eph‘al, Siege, 30.


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mission of knowledge and skills in siege warfare between military practitioners and mathematically-inclined scribes was unidirectional and nonpractical.34 Siege Warfare in Greece We now turn to the question of how siege tactics were transmitted across cultural boundaries and under what circumstances they were adopted. As mentioned above, there is ample evidence of the development of siege warfare in the Near East from its most simple form in the third millennium to its most advanced manifestation in the first millennium. Standard siege tactics include escalade, mining, sapping, assault by ramp with siege towers, ruse and blockade. All of these techniques were well established in all regions of the Near East by at least the middle of the second millennium.35 The Babylonians, Assyrians, Hittites,36 and the various peoples of Syria and the Levant37 were all thoroughly conversant with siege tactics. On the other hand, it is a well-known fact that the Greeks came late to the art of siege warfare. The main reasons for Greece’s tardy entry are generally agreed upon but worth reviewing here. In Archaic and Classical Greece, war was primarily carried out by hoplites, the landed male citizenry of the different city-states. Battle evolved from fluid Homeric-style skirmishes to full-fledged phalanx confrontations, the likes of which were unknown in the Near East.38 Limited 34. In a recent article investigating the relationship between elite thinkers and technical practitioners in classical Greece, Tracey Rihll and John Tucker use the example of the Athenian silver mines at Laurium to argue (among other things) that, “practical knowledge does not depend on theoretical knowledge, but that practical knowledge may influence the formulation of theoretical knowledge.” See Tracey Rihll and John Tucker, “Practice Makes Perfect: Knowledge of Materials in Classical Athens,” in Science and Mathematics in Ancient Greek Culture, eds. Christopher Tuplin and Tracey Rihll (London: Oxford University Press, 2002), 305. In general, we believe that the same may be said of Mesopotamian scribes with regard to practical military knowledge. 35. For a full treatment of siege warfare in the ancient Near East, see Eph‘al, Siege. 36. For an example of a Hittite siege including references to ramps, battering rams and towers, see Richard Beal, The Organization of the Hittite Military. vol. 1 (Ph.D. dissertation, University of Chicago, 1986), 684 and Gary Beckman, “The Siege of Urˇsu Text (CTH 7) and Old Hittite Historiography,” Journal of Cuneiform Studies 47 (1995): 23–34. 37. For a thorough treatment of fortifications and warfare in the Middle Bronze Levant, see Burke, Architecture of Defense. See also Yadin’s classic but now somewhat out-of-date treatment of warfare in the ancient Near East: Yigael Yadin, The Art of Warfare in Biblical Lands in the Light of Archaeological Study (New York: Mc Graw-Hill, 1963). 38. The chronological development of the classic hoplite phalanx is still contested.

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warfare was an expression of the individualistic Greek city-state culture; it acted as a means to maintain and promote the social order in each city but did not exceed the city-state’s economic means or human resources. The fierce independence of Greek cities and their refusal to unite under a single government meant that each had a limited population from which to draw its soldiers and limited funds to finance campaigns. Because the expense in manpower and material was too high, campaigns of any great duration were extremely rare before the Peloponnesian War.39 The economic barriers to extended campaigning found expression in hoplite ideology, which shunned siege warfare as unmanly and contrary to the hoplite code of behavior. Plato, writing in the fourth century b.c., by which time siege warfare had become fairly commonplace, nevertheless, complains of the cowardliness of defensive fortifications: A wall is, in the first place, far from conducive to the health of town life and, what is more, commonly breeds a certain softness of soul in the townsmen: it invites inhabitants to seek shelter within it and leave the enemy unrepulsed, tempts them to neglect effecting their deliverance by unrelaxing nightly and daily watching, and to fancy they will find a way to real safety by locking themselves in and going to sleep behind ramparts and bars as though they had been born to shirk toil, and did not know that true ease must come from it.40

For the orthodox view that it was already in use by 650 b.c., see Victor Hanson, The Western Way of War: Infantry Battle in Classical Greece (New York: Knopf, 1989) and bibliography contained therein. For recent arguments that the hoplite phalanx did not reach its fully developed form until after the Persian wars, see Hans van Wees, “The Development of the Hoplite Phalanx: Iconography and Reality in the 7th Century,” in War and Violence in Ancient Greece, ed. Hans van Wees (London: Duckworth and the Classical Press of Wales, 2000), 125–66; Hans van Wees, Greek Warfare: Myths and Realities (London: Duckworth, 2004), 166–83; and Peter Krentz, “Fighting by the Rules: The Invention of the Hoplite Agon,” Hesperia 71 (2002): 23–39. 39. Van Wees estimates the total Athenian annual tax revenue at around one million drachmas a year and notes that the Athenian siege of Samos in 440 b.c. cost more than seven million drachmas, while the prolonged siege of Potidæa cost twelve million. Athens could pay for these sieges only because she had first the revenue from the silver mines at Laurium, then the Delian League, and finally an empire. See van Wees, Greek Warfare, 235–36. See also Hanson, The Western Way of War, 110. Siege warfare tends also to be costly in terms of manpower, especially if a direct assault is attempted. 40. Plato, Leges, 6.778, translated by Alfred Taylor, in Plato: The Collected Dialogues, eds. Edith Hamilton and Huntington Cairns, Bollingen, vol. 71 (Princeton: Princeton University Press, 1961), 1355.


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Ideally, Greek wars were fought for personal glory and the honor or defense of one’s polis, rather than the acquisition of territory. Greece’s victory over Persia in the early fifth century b.c. marked not only the triumph of hoplite warfare but also the first flickers of profound change as Athens, recognizing the potential of naval power, built a fleet of ships that was largely manned by the poor and metics, rather than fully-enfranchised Athenian citizens. As Athens began to fulfill its imperial ambitions and other city-states responded by making alliances and attempting to spread their own hegemonic influence, the victory imperative overcame some of the tenets of hoplite warfare, including the general proscription against sieges. Early Greek efforts at siege warfare seem to have been restricted to rather clumsy and incomplete blockades, direct assault, or the use of stratagems.41 Conversely, during the Peloponnesian War at the siege of Platæa in 429 b.c., the Greeks harnessed the full potential of siege craft, apparently for the first time. In his account of the early years of the war, Thucydides gives a detailed description of the siege of Platæa, including both the besiegers’ tactics and the besieged Platæans’ counter-measures.42 In the following, we review events as told by Thucydides in order to get a clear idea of exactly what transpired.43 The first thing that Spartans did was to enclose Platæa with a wooden palisade made from the trees out of the local orchards. Then they proceeded to build a siege mound in the following manner: . . . they threw up a mound (τό χώμα) against the city, hoping that the largeness of the force employed would insure the speedy reduction of the place. They accordingly cut down timber from Cithæron, and built it up on either side, laying it like latticework to serve as a wall to keep the mound from spreading abroad, and carried to it wood and stones and earth and whatever other material might help to complete it. They continued to work at the mound for seventy days and 41. E.g., the inept Athenian attempt to take Paros in 489 b.c. was described by Herodotus 6.132–136, and the Athenian blockade of Sestos in 431 b.c. was outlined by Herodotus 9.114–118 and Thucydides 1.89. See also Kern, Ancient Siege Warfare, 92–93. 42. Thucydides’ account of the siege of Platæa is not only the most detailed siege narrative from the period, but it is also far more thorough than any other account that has survived from the ancient Near East. 43. It is not within the scope of this paper to question the factual veracity of Thucydides’ account, nor would it be pertinent to our argument. For an assessment of credibility of Thucydides’ work, see Victor Hanson, Introduction to The Landmark Thucydides, trans. and ed. Robert Strassler (New York: Free Press, 1996), xx–xxiii.

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Sarah C. Melville and Duncan J. Melville nights without intermission, being divided into relief parties to allow some to be employed in carrying while others took sleep and refreshment; the Spartan officer attached to each contingent keeping the men to the work.44

Like the Near Eastern siege ramps we have examined, the Spartan ramp was constructed of whatever material could be conveniently gathered from the surrounding area. The ramp supposedly took seventy days of round-the-clock labor to build, which seems excessive until we read of the Platæan counter-measures. First, they successfully raised the height of their wall, and then they “thought of another expedient: they pulled out part of the wall upon which the mound abutted and carried the earth into the city,” thus undoing the Peloponnesians’ work as fast as it was being done.45 The Spartans’ lack of experience may account for their slow response to the Platæan tactics. Thucydides’ narrative continues: Platæans changed their mode of operation, and digging a mine from the city calculated their way under the mound, and began to carry off its material as before. This went on for a long while without the enemy outside finding it out, so that for all they threw on top of their mound made no progress in proportion, being carried away from beneath and constantly settling down in the vacuum.46 A common defensive response to a siege ramp was to tunnel under in order to undermine it. The same tactic was employed by the defenders of Palæpaphos, albeit with even more ingenuity, for the Palæpaphians did not just remove the fabric of the ramp (which would have been fairly easy to detect) but set fire to it from within and so caused a section of the ramp to collapse.47 The Spartan failure to notice that material was being constantly removed from their mound confirms their inexperience with siege warfare. After failing to breach the wall with battering rams and a futile attempt to set fire to the Platæan defenses, the Spartans simply had to sit and wait until the Platæans were eventually starved into surrender. All of the siege and counter-siege techniques employed at Platæa (ramp building, counter-ramp and wall building, mining, fire, battering rams, attempts to break the rams, and blockade) had already been 44. 134. 45. 46. 47.

Thucydides 2.75, translated by Robert Strassler in The Landmark Thucydides, Thucydides 2.75, translated by Strassler in The Landmark Thucydides, 135. Thucydides 2.76, translated by Strassler in The Landmark Thucydides, 135. Maier and Karageorghis, Paphos, 202.


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in wide use in the Near East for well over a thousand years. Thucydides’ narrative suggests that the Greeks knew siege tactics but were woefully inexperienced in their execution. We have reviewed the social and economic reasons why the Greeks lagged behind their Near Eastern neighbors in siege capabilities, and we should add that Greek fortifications were also comparatively rudimentary during this period.48 Yet according to our sources, the Greeks fully applied a wide variety of siege tactics as soon as the economic and manpower resources were sufficient. The implication is that the Greeks were well aware of the range of siege tactics before they were able to put them into practice. Therefore, we must ask when and from whom did the Greeks learn siege warfare? Questions of diffusion are notoriously difficult to answer. Scholars, if they address the issue of Greek siege warfare at all, tend simply to note the contrast between early Greek techniques and the sophisticated tactics of Near Eastern armies,49 comment (with some surprise) on the Spartans’ advanced methods at Platæa,50 assume that the Greeks were influenced by the Persians51 or more vaguely from the East via Carthage and Greek Sicily,52 or suggest that they invented their own siege techniques.53 Surely it is possible to say more. Near Eastern military influence on Greece can be traced to the beginning of the Archaic period and probably earlier. According to Sekunda, the appearance of the Assyrian-style archer/shield bearer pair in Greek vase-painting and literature during the eighth century attests to the “intrusion of Near Eastern military practices into Greek warfare” at this time.54 Some Archaic Greek helmet and armor types were borrowed from Assyrian models55 and there is good, albeit scanty evidence that Greek Mercenaries fought in Near Eastern armies (including those of Assyria, Babylonia, Egypt, Judah, and Tyre) during the seventh century b.c.56 Both mercenary soldiers and merchants helped transfer foreign 48. Michael Sage, Warfare in Ancient Greece : A Sourcebook, (New York: Routledge, 1996), 108 and van Wees, Greek Warfare, 139. 49. van Wees, Greek Warfare, 139. 50. John Lazenby, The Peloponnesian War: A Military Study (New York: Routledge, 2004), 42. 51. Peter Connolly, Greece and Rome at War (Englewood Cliffs, New Jersey: Prentice-Hall, 1981), 277. 52. Sage, Warfare in Ancient Greece, 136. 53. Kern, Ancient Siege Warfare, 103. 54. Nick Sekunda, “The Persians,” in Warfare in the Ancient World, ed. John Hackett (New York: Facts on File, 1989), 82. 55. Tim Everson, Warfare in Ancient Greece: Arms and Armor from the Heroes of Homer to Alexander the Great. (Phoenix Mill: Sutton Publishing, 2004), 73, 75–78, 108–11. 56. Wolf-Dietrich Niemeier, “Archaic Greeks in the Orient: Textual and Archaeo-

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military ideas and technologies from the Near East to Greece.57 In terms of siege warfare, we must remember that Greek cities often came under attack from Near Eastern armies: Greek cities in Asia Minor were besieged, first by Lydians, and then by Persians; cities on Cyprus and the mainland were besieged and taken by the Persians. Herodotus’ descriptions of these conflicts presuppose his audience’s familiarity with siege techniques. For example in The Histories 6.18.1, Herodotus writes, “they used every device (παντοίας μήχανας), such as undermining the walls until the city fell into their hands, acropolis and all, in the sixth year after Aristagoras’ revolt.”58 Evidently, Herodotus assumed that his readers would know what “every device” of a siege entailed. We can adduce that given the extent of the Greek presence in Asia Minor and the Levant from the eighth century b.c. onward, the Greeks must have been aware of Near Eastern siege methods even if, for the social and economic reasons mentioned above, they chose not to employ them. In military terms, it would certainly have been in the best interest of the Greeks to familiarize themselves with the fighting techniques of Near Eastern armies. It has always been common practice for militaries to “monitor closely other militaries, both those in their immediate vicinity as well as the leading militaries of the day, performing ‘net assessments.’ Adversaries have both reasons to use foreign lessons—to gain advantage in conflicts—and opportunity to do so, since most wars are events that can be observed.”59 There is every likelihood that the same situation applied in the Greek world. The Greek evidence demonstrates that first applications of new technology cannot be used to determine the point of introduction into a society. In this case we have a clear example of Bennett’s thesis that “knowledge of a foreign program, utilization of that knowledge, and adoption of logical Evidence,” Bulletin of the American Schools of Oriental Research 322 (2001): 11–32 and Matthew Trundle, Greek Mercenaries: From the Late Archaic Period to Alexander (New York: Routledge, 2004), 5. 57. See Thomas Braun, “The Greeks in the Near East,” in The Expansion of the Greek World, Eighth to Sixth Centuries b.c., vol. 3, pt. 3 of The Cambridge Ancient History, eds. John Boardman and Nicholas Hammond, 3rd ed. (Cambridge: Cambridge University Press, 1982), 1–31 and Niemeier, “Greeks in the Orient,” 11–32, for the considerable bibliography of works concerning Greek–Near Eastern connections. 58. Translation after Robin Waterfield, The Histories (New York: Oxford University Press, 1998), 358. We diverge from Waterfield’s translation with regard to παντοίας μήχανας, which he translates as “all kinds of stratagems.” We feel that “every device” better renders the mechanical and technical sense of the phrase in the context of siege tactics. 59. Emily Goldman and Andrew Ross, “Conclusion: The Diffusion of Military Technology and Ideas—Theory and Practice,” in The Diffusion of Military Technology and Ideas, eds. Emily Goldman and Leslie Eliason (Stanford: Stanford University Press, 2003), 372.


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the same program” are distinct and often occur over an extended period of time.60 Only if we are aware of this distinction and consider the adoption of new technologies in the widest possible historical context can we identify those shifts in local conditions that make the implementation of new skills and knowledge both attractive and feasible. Looked at this way, the development of Greek siege warfare becomes much clearer: although the Greek had knowledge of siege tactics by (at least) the end of the eighth century b.c., they could not fully utilize that knowledge until they had the economic resources and attendant ideology necessary to permit them to adopt foreign siege methods. Conclusion Warfare pervades all cultures. Its conduct and regulation have always been of great concern to societies. On the one hand, social control of warfare acts as a conservative force; on the other hand, the survival value of comparative advantage in military tactics and technology favors early adopters. For these reasons, analysis of adoption of military applications acts as an important test-case for diffusion theories. Here, we primarily focused on two types of connections: between scribes and soldiers in Mesopotamia and between the Near East and Greece. In the first case, while the Old Babylonian mathematical siege ramp problems of BM 85194 and BM 85210 certainly reflect the prevalence of siege warfare in second millennium Mesopotamia, the fact that some scribes studied problems involving ramps is not evidence that they subsequently used the skills learned in the classroom in the field. The internal structure of the problems militates against this conclusion, as do the archaeological evidence and basic military considerations. We cannot assume that advanced mathematical knowledge was used in the construction of actual siege ramps. In the second case, late adoption of siege warfare by the Greeks was due not to lack of knowledge of Near Eastern practice, but to social and cultural barriers that made this expensive form of warfare unnecessary and impractical. When it was needed at Platæa, it is clear that a comprehensive knowledge of siege tactics was available on both sides, although the actual execution of the siege indicates a lack of previous experience. The ubiquity of siege warfare in the Near East, Anatolia, and the Levant, coupled with the pervasive Greek presence in those areas, not only make it unlikely that there was ever a single point for the transmission of information to the Greeks but also make it certain that 60. Colin Bennett, “How States Utilize Foreign Evidence,” Journal of Public Policy 11 (1991): 32–33.

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the Greek militaries were aware of siege techniques long before they were applied. We have mentioned only barriers to diffusion in the ancient world. Modern disciplinary boundaries also create barriers to diffusion of scholarly knowledge. Classicists and Assyriologists tend to work in isolation from each other, as do historians of mathematics, social and political historians and archaeologists. In some small way, we hope this contribution will help to overcome such barriers and follow the inspirational lead of Alice Slotsky whose pioneering introduction of statistical analysis of economic data in astronomical cuneiform documents has initiated a surge of interest by economic historians in what had been to them a hitherto neglected and inaccessible area. Mathematical Excursus: BM 85194, Problem 26 The situation is as depicted in figure 9.1. A partially-completed ramp begins a distance l away from the wall of the city “hostile to Marduk.” The ramp has a length x and a height y. The distance d left to go is sought. In Problem 26, the given data are the ramp length x = 32, the height y = 36, the volume of the completed ramp V = 1, 30, 0 and the width of the ramp w = 6. The units are not explicitly stated, but the `ˇ length and width are in nindan and the height in ku s. The volume is in volume-ˇ sar, a unit using nindan for horizontal measurements and `ˇ ku s for vertical ones.

Figure 9.1: Cross-section of the Ramp

Let A = Vw represent the (cross-sectional) area of the completed ramp, and α ¯ denote the reciprocal of any variable α. The steps of the solution are as follows:

The Diffusion of Military Technology Step

Procedure

Step 1

Reciprocal of 32 = 0; 1, 52, 30 0; 1, 52, 30 × 36 = 1; 7, 30

Step 2

Step 3 Step 4 Step 5

Reciprocal of 6 = 0; 10 1, 30, 0 × 0; 10 = 15, 0 15, 0 × 2 = 30, 0

Step 6

1; 7, 30 × 30, 0 = 33, 45

Step 7

Square Root of 33, 45 = 45 45 exceeds 36 by 9.

Step 8

Step 9

Step 10

Reciprocal of 1; 7, 30 = 0; 53, 20 0; 53, 20 × 9 = 8

Algebraic Result x ¯ x ¯·y

w ¯ A=V ·w ¯ 2A = lh ¯ lh · lh = h2

√

h2 = h

h−y =v — — ¯ = (¯ xy) = (dv)

163 Description Inverse of length. Compute slope. Note ¯ x ¯y = ¯ lh = dv Inverse of width. Compute area, note A = 12 lh Determine rectangle. Scale by slope to produce square of height. Solve for height of wall. Determine remaining height to go. Inverse of slope.

d¯ v d¯ vv = d

Find required length.

The crucial step is the computation of the slope and the realization of the fact that the three triangles determined by x and y, l and h, and d and v are all similar and so have the same slope. Thus, once the slope has been computed, it can be used for finding the sides of any of the three triangles. The slope is computed with reference to the ramp, used to determine the height of the wall, and then used again to find the distance left to go. This exercise is a rather nice problem in similar triangles. Note also that the problem takes a roundabout route to its solution— the distance left to go is determined only once all other variables are known. The problem could have been made much more direct by computing the inverse of the slope in the beginning by multiplying the length by the inverse of the height. This procedure would then allow one to calculate the square of the length rather than the square of the height, so finding the length l and so the difference d = l − x without ever needing to determine the height of the wall.

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The volume and the width are used to compute only the area. Since `ˇ the volume is in volume-sar = nindan2 × ku s and the width is in `ˇ nindan, the resulting area is in the units of nindan × ku s for which no term is known. This fact is presumably why the height is never translated into nindan and the units are effectively ignored—the use of the slope keeps the dimensions correct. Høyrup discusses scaling, units, and geometrical procedures for this problem.61 Note that figure 9.1 is `ˇ exaggerated in height. The actual height of the wall is 45 ku s, or 3.75 nindan, so the ramp is more than ten times as long as it is high, and so has a correspondingly gentle slope. Høyrup includes the figure in true proportions.62

61. Høyrup, Lengths, Widths, Surfaces, 218–20. 62. Ibid., 217.


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References Barnett, Richard, Erika Bleibtreu, and Geoffrey Turner. Sculptures from the Southwest Palace of Sennacherib at Nineveh. London: British Museum Press, 1998. Beal, Richard. The Organization of the Hittite Military. Vol. 1. Ph.D. dissertation, University of Chicago, 1986. Beckman, Gary. “The Siege of Urˇsu Text (CTH 7) and Old Hittite Historiography.” Journal of Cuneiform Studies 47 (1995): 23–34. Bennett, Colin. “How States Utilize Foreign Evidence.” Journal of Public Policy 11 (1991): 31–54. Borger, Riekele. Die Inschriften Asarhaddons K¨ onigs von Assyrien. Archiv f¨ ur Orientforschung, vol. 9. Graz: Im Selbstverlage des Herausgebers, 1956. Braun, Thomas. “The Greeks in the Near East,” in The Expansion of the Greek World, Eighth to Sixth Centuries b.c. Vol. 3, pt. 3 of The Cambridge Ancient History, edited by John Boardman and Nicholas Hammond, 1–31. 3rd ed. Cambridge: Cambridge University Press, 1982. Burke, Aaron. “The Architecture of Defense: Fortified Settlements of the Levant During the Middle Bronze Age.” Ph.D. diss., University of Chicago, 2004. Available at http://oilib.uchicago.edu/dissertations/burkeaa.pdf. ´ Charpin, Dominique. “Données Nouvelles sur la Poliorcétique à l’Epoque Paléo-Babylonienne.” Mari, annales de recherches interdisciplinaires 7 (1993): 193–203. Connolly, Peter. Greece and Rome at War. Englewood Cliffs, New Jersey: Prentice-Hall, 1981. Cook, John. “Old Smyrna, 1948–1951.” Annual of the British School at Athens 53–54 (1958): 1–34. Eph‘al, Israel. “The Assyrian Siege Ramp at Lachish: Military and Lexical Aspects. Tel Aviv 11 (1984): 60–70. ———. Siege and its Ancient Near Eastern Manifestations. Jerusalem: Magnes Press, 1996. Everson, Tim. Warfare in Ancient Greece: Arms and Armor from the Heroes of Homer to Alexander the Great. Phoenix Mill: Sutton Publishing, 2004. Foster, Benjamin. “Transmission of Knowledge.” In A Companion to the Ancient Near East,edited by Daniel Snell. London: Blackwell, 2005. Goldman, Emily, and Leslie Eliason, eds. The Diffusion of Military Technology and Ideas. Stanford: Stanford University Press, 2003.

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——— and Andrew Ross. “Conclusion: The Diffusion of Military Technology and Ideas —Theory and Practice.” In The Diffusion of Military Technology and Ideas, edited by Emily Goldman and Leslie Eliason. Stanford: Stanford University Press, 2003. Hanson, Victor. The Western Way of War: Infantry Battle in Classical Greece. New York: Knopf, 1989. Høyrup, Jens. Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin. New York: Springer, 2002. Kern, Bentley. Ancient Siege Warfare. Bloomington: Indiana University Press, 1999. Krentz, Peter. “Fighting by the Rules: The Invention of the Hoplite Agon.” Hesperia 71 (2002): 23–39. Lazenby, John. The Peloponnesian War: A Military Study. New York: Routledge, 2004. Luckenbill, Daniel. The Annals of Sennacherib. Oriental Institute Publications, vol. 2. Chicago: University of Chicago Press, 1924. Maier, Franz, and Vassos Karageorghis. Paphos: History and Archaeology. Nicosia: The A. G. Leventis Foundation, 1984. Neugebauer, Otto. Mathematische Keilschrift-Texte, I-III. Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik. Abteilungen A: Quellen 1–3. 3 vols. Berlin: Springer, 1935–37. ——— and Abraham Sachs. Mathematical Cuneiform Texts. American Oriental Series, vol. 29. New Haven: American Oriental Society and the American Schools of Oriental Research, 1945. Nicholls, Richard. “Old Smyrna: the Iron Age Fortifications and Associated Remains on the City Perimeter.” Annual of the British School at Athens 53–54 (1958): 35–137. Nicolaou, Kyriakos. “Archaeological News from Cyprus.” American Journal of Archaeology 77 (1973): 51–60. Niemeier, Wolf-Dietrich. “Archaic Greeks in the Orient: Textual and Archaeological Evidence.” Bulletin of the American Schools of Oriental Research 322 (2001): 11–32. Postgate, Nicholas. Early Mesopotamia: Society and Economy at the Dawn of History. London: Routledge, 1992. Rihll, Tracey and John Tucker. “Practice Makes Perfect: Knowledge of Materials in Classical Athens.” In Science and Mathematics in Ancient Greek Culture, edited by Christopher Tuplin and Tracey Rihll, 274–305. London: Oxford University Press, 2002. Robson, Eleanor. Mesopotamian Mathematics, 2100–1600 b.c.: Technical Constants in Bureaucracy and Education. Oxford Editions of Cuneiform Texts, vol. 14. Oxford: Clarendon Press, 1999).


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Russell, John. Sennacherib’s Palace without Rival at Nineveh. Chicago: University of Chicago Press, 1991. Sage, Michael. Warfare in Ancient Greece : A Sourcebook. New York: Routledge, 1996. Sekunda, Nick. “The Persians.” In Warfare in the Ancient World, edited by John Hackett, 82–103. New York: Facts on File, 1989. Strassler, Robert, trans. and ed. The Landmark Thucydides. New York: Free Press, 1996. Taylor, Alfred, trans. Plato: The Collected Dialogues, edited by Edith Hamilton and Huntington Cairns. Bollingen, vol. 71. Princeton: Princeton University Press, 1961. Trundle, Matthew. Greek Mercenaries: From the Late Archaic Period to Alexander. New York: Routledge, 2004. Ussishkin, David. “Excavations at Tel Lachish 1978–1983: Second Preliminary Report. Tel Aviv 10 (1983): 97–175. ———. “The Assyrian Attack on Lachish: The Archaeological Evidence from the Southwest Corner of the Site. Tel Aviv 17 (1990): 53–86. van Wees, Hans. “The Development of the Hoplite Phalanx: Iconography and Reality in the 7th Century.” In War and Violence in Ancient Greece, edited by Hans van Wees, 125–66. London: Duckworth and the Classical Press of Wales, 2000. ———. Greek Warfare: Myths and Realities. London: Duckworth, 2004. Waterfield, Robin, trans. Herodotus: the Histories. New York : Oxford University Press, 1998. Yadin, Yigael. The Art of Warfare in Biblical Lands in the Light of Archaeological Study. New York: Mc Graw-Hill, 1963.

Two Ivory Carvings from Hierakonpolis Marie Passanante Brown University

Perhaps the most intriguing artifacts from Hierakonpolis are the Predynastic and Early Dynastic ivory reliefs featuring ranks of various animals. Unfortunately, it is impossible to fix a definitive date for these objects, as all of them were found in the Main Deposit and none are inscribed. The significance of these objects is unknown, but it is possible that the depicted scenes represent ceremonial offerings or the hunt or both. A likely interpretation is that these scenes depict the chaos over which the king must become victorious if he is to preserve mz‘t.1 Chaos was portrayed on the ivories by prominently featuring wild animals— both dangerous and not—in relief. These animals could be arranged in orderly rows or in random, “chaotic” compositions. In addition, the craftsmen occasionally augmented familiar Egyptian scenes with appropriate designs from other cultures. The assimilation of many of the foreign cultural elements was not permanent and largely disappeared during the Early Dynastic period. The purpose of this paper is to present a possible identification for the animals on two of the Hierakonpolis ivories and to study the Mesopotamian motifs utilized by the creators of these pieces.2 The Ivories Animal identifications have been made with the help of both Egyptological and zoological references.3 The animals are described in order 1. Jarom´ır M´ alek, Egyptian Art (London: Phaidon, 1999), 61. 2. For an excellent and thorough discussion on the topic of Mesopotamian influence on early Egyptian art, see Harry Smith, “The Making of Egypt: A Review of the Influences of Susa and Sumer on Upper Egypt and Lower Nubia in the Fourth Millennium b.c.,” in The Followers of Horus: Studies Dedicated to Michael Allen Hoffman 1944–1990, eds. Ren´ ee Friedman and Barbara Adams, Oxbow Monograph, vol. 20; Publication of the Egyptian Studies Association, vol. 2 (Oxford: Oxbow Books, 1992): 235–46. 3. Leslie Brown, Emil Urban, and Kenneth Newman, The Birds of Africa, vol. 1 (New York: Academic Press, 1982); Richard Estes, The Behavior Guide to African

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starting from the direction in which the animals are facing (i.e., in a line of animals facing to the right, the first one is the one on the far right).

Figure 10.1: Ivory One, reproduced from Adams, Ancient Hierakonpolis, pl. 39, fig. 327 with permission of the publisher.

Ivory One Ivory One (see figure 10.1) retains the shape of the hippopotamus tusk from which it was carved.4 There are three registers running lengthwise on the outer surface of the tusk. Both ends are broken. The top register contains four animals; of the first (from the right) only the hindquarters remain. Adams suggests that this is possibly an ibex. It could be an ibex, but it could also be one of a number of other species of ungulate; to narrow even a guess down to a single species is hasty, since the defining characteristics of the ungulate in early Egyptian art are seen in the foreparts of the animal. The following three animals are however quite clear; they are dogs, with curled tails, small pointed ears, and collars. The middle register contains four animals. As in the first register, only the tail of the first animal can be seen. It is long and curled (as Mammals: Including Hoofed Mammals, Carnivores, Primates (Berkeley: University of California Press, 1991); Patrick Houlihan, The Birds of Ancient Egypt, The Natural History of Egypt, vol. 1 (Warminster, England: Aris and Phillips, 1986); Dale Osborn, The Mammals of Ancient Egypt, The Natural History of Egypt, vol. 4 (Warminster, England: Aris and Phillips, 1998). 4. Barbara Adams, Ancient Hierakonpolis (Warminster, England: Aris and Phillips, 1974), 61–62.

Two Ivory Carvings from Hierakonpolis

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opposed to the short curly tails of the dogs), and again Adams suggests a hyena. At this time, it would be wise to clear up a misconception on the part of Adams. All members of the family Hyænidæ have straight, bushy, short-to-medium length tails. The ancient Egyptian craftsmen were diligent in accurately depicting the hyena,5 Thus this animal is most likely a felid. The second animal is clearly an imaginary griffon also depicted on the reverse of the Hierakonpolis Palette.6 The next animal has a long curved tail and is therefore a felid. It also appears to have the full mane of an adult male lion. The last animal, its hindquarters broken off, has short ears or horns projecting from the base of the skull and so is identified as a hare. However, Osborn states that the Egyptians exaggerated the long ears of the animal,7 whereas the ears of this creature are small, barely extending past the shoulder. The animal could also be a donkey or a goat, but it is hard to ascertain without the hindquarters (the tail of a hare would be much shorter). At this point, the hare seems to be the best identification. The bottom register is broken at the bottom. It contains four animals. The first is similar to two of the dogs on the top register and for that reason must also be identified as a dog. The second animal is an ungulate with short horns extending no farther than the shoulder. It could be an addax (whose horns were depicted as both twisted and straight) or an oryx. The next animal has ears resembling the hare in the middle register and may also be a hare. The fourth animal might also be an hare, but it is damaged.

Ivory Two Ivory Two, a wand, was also made from hippopotamus ivory.8 Two large fragments of the wand survive. Fragment 1 has a projection at the end, probably for attachment to a handle. Fragment 2 is twice as long and is broken at both ends. The two fragments cannot be joined directly to one another, but their widths are similar, as are the style and arrangement of the figures. Also, the lower edges of both fragments have serrations of similar measure. The arrangements of the figures on each side of the wand are different. Side A shows the figures facing left in 5. Osborn, Mammals, 97–104. 6. M´ alek, Egyptian Art, 66–67, including fig. 33. 7. Osborn, Mammals, 43. 8. Adams, Ancient Hierakonpolis, 60; James Quibell, Plates of Discoveries in 1898, vol. 1 of Hierakonpolis, Publications of the Egyptian Research Account, vol. 4 (London: B. Quaritch, 1900), 7, pl. 16; James Quibell and Frederick Green, Plates of discoveries in 1898–99, vol. 2 of Hierakonpolis, Publications of the Egyptian Research Account, vol. 5 (London: B. Quaritch, 1902), 43, pl. 32.5, 32.6.

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Figure 10.2: Ivory Two, from Quibell, Ancient Hierakonpolis, vol 1, pl. XVI, figs. 1 and 2. an orderly line, with all but one standing on the ground line. Side B is more chaotic, with figures facing both right and left, and only eleven of the twenty-one extant figures are standing on the main ground line; one figure has its own ground line above another figure, while the remaining figures stand seemingly on air or on the figures below them. Despite this unruly arrangement, there is very little actual interaction between the figures, save for the “master of the animals” motif shown twice on fragment 2. Fragment 1, Side A Only two animals are visible. Adams suggests an ibex or antelope and a bird. The drawing by Quibell shows them more clearly; one assumes the surface of the ivory has eroded over the years. The ungulate has long, curved horns, similar to those of other figures on fragment 2, although the surfaces of the horns of the ungulates on fragment 2 are undulating, while those of the ungulate on fragment 1 are smooth.9 The ibices shown on the Abu Zaidan knife handle all have beards characteristic of the males.10 The muzzle of the animal on fragment 1 is missing, so it is 9. These smooth horns could be a symptom of the erosion on the fragment or a quirk of the drawing in pl. 16. 10. Charles Churcher, “Zoological Study of the Ivory Knife Handle from Abu Zaidan,” in Predynastic and Archaic Egypt in the Brooklyn Museum Wilbour Monographs 9, ed. Winifred Needler (Brooklyn: The Brooklyn Museum, 1984), 161.


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impossible to tell if the ibex was the intended animal. The bird greatly resembles the secretary bird, with its short, thick neck and projecting nape feathers. Fragment 1, Side B Five birds are visible on this side. One is similar to the secretary bird shown on side A. The distinguishing feature of the second bird is a great crest of feathers on its crown. It is most likely a hoopoe. The third bird resembles the archaic form of the Horus falcon.11 Only the hindquarters of the fourth bird are shown, making an identification very difficult. The fifth bird is shown much larger than the others and appears to have two outstretched or, as Adams describes them, “vestigial” wings. Adams’ description inspires an identification of an ostrich, which certainly would have been present in ancient Egypt. However, here the neck is too short and thick, and the feet are shown with hind toes, which the ostrich does not have. The beak is missing, which adds to the dilemma. There are two animals with paw-like feet, large muzzles, round ears, and long curving tails (one is broken off). These are clearly felines, and the spots suggest leopards (Panthera pardus) or cheetahs (Acinonyn jubatus). There is also an ungulate minus the horns. It has no beard and probably is an oryx. Fragment 2, Side A There are nine animals in this scene. Of the first only the tail remains. It is short and flared and probably belongs to either a falcon or an animal also depicted on side B and discussed in the next paragraph. The second animal is another secretary bird. Next is likely an oryx with scimitar-shaped horns. The head of the fourth animal is gone, but there are no horns, and there is the slightest hint of a round ear. The ear and the curved tail suggest a lionness (the male lion shown on side B has a clearly indicated mane). The next animal is a jackal, probably the golden jackal (Canis aureus). Above the jackal is a bird with its head turned, possibly another falcon. The seventh animal, a bird, has a wisp of feathers emanating from its crown. It is possibly a little egret (Ergetta garzetta) or a grey heron (Ardea cinerea), although the neck is short and thick as opposed to the sinuous neck of the egret or heron. The last two animals are probably oryxes. 11. B´ eatrix Midant-Reynes, The Prehistory of Egypt: From the First Egyptians to the First Pharaohs, trans. Ian Shaw (Malden, Mass.: Blackwell Publishers, 2000), 233, fig. 15.

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Fragment 2, Side B First is one of the “master of the animals” motifs, similar to the figures on the Gebel el-Arak knife handle and in the lower left hand corner of Tomb 100 at Hierakonpolis.12 Only part of the human and the second animal survive. The animal is an amalgamation which can be called a “serpopard;” it has the body of a leopard and the neck and head of a serpent. Above are the hind parts of a bird, possibly a duck. Next comes another ungulate. No horns of any kind survive, but the sharp angle of the hindquarters indicate a bovid. Above and to the right is a quadruped with a square muzzle, a short, flared tail, and cross-hatching on its body. It also has what appears to be a small tuft of spines on its rump and maybe also a small tuft on the nape of its neck. The tail and spines, if those are what they are, suggest that this animal is a porcupine, but the porcupine has a crest of spines down the entire length of its back, a prominent tuft on its nape, and a much smaller head than this animal has. The way the limbs are carved, as if they were an afterthought to the body, and the cross-hatching add to the mystery (none of the other animals on the wand are decorated in this manner). One possible conclusion is that this is an imaginary animal, perhaps part lion and part fish (the “spines” could be taken as fins, the cross-hatching as scales). This conclusion is not so wild, considering the presence of serpopards on this object. Below it is another oryx. Above and to the right is an animal on its own ground line. It has paw-like feet, spots, a curved tail, narrow muzzle, a very large eye, and no visible ears. It is most likely a felid, maybe a leopard. Below it is a lion with a mane indicated with heavy lines. Next is a large bird with a serpentine neck, possibly an egret or a heron. The bird stands on one of the two imaginary creatures in the second of the “master of the animals” motifs. This animal has a sloping back, which could indicate that the animal is part giraffe, or else it was carved to fit in the space remaining. The latter explanation is likely the correct one; like the first mastered animal, this one has a curved tail and spotted body and therefore is probably part leopard. The head is missing, or else this animal, too, is part snake. The second animal in the grouping, however, clearly has the head of a felid. Only the head of the last animal survives. The shape of the muzzle and cheek suggests that this animal is an ass (Equus asinus africanus).

12. M´ alek, Egyptian Art, 52–53, fig. 25; William Smith, The Art and Architecture of Ancient Egypt, rev. 3rd ed. (New Haven: Yale University Press, 1998), 11.


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The Motifs Griffon The griffon on Ivory One has the body of a feline and the head and wings of a bird. As stated above, the griffon is also seen on the Hierakonpolis Palette. The griffon appears on the Gebel Tarif ivory knife handle as well.13 The griffons on the three pieces are modeled in three different styles. The wings of the griffon on Ivory One are clearly separate while on the palette the wings were carved as one continuous component; the wings on the knife handle are curved upwards at the tips. The Gebel Tarif griffon boasts such details as a feathered upper torso and forelegs terminating in talons; the other two griffons are more feline in nature. The griffon is a fairly common motif in Mesopotamian art. Its form is rather plastic here, and creative and interesting variations can be observed. As in Egyptian art, the griffon may or may not have front legs terminating in talons.14 One example from Susa exhibits a griffon with two goats for wings;15 another has two lions!16

Lionfish One of the most interesting figures on Ivory Two is the apparent hybrid of a fish and lion. There is no comparable example from the rest of Egyptian art, nor is there a similar creature found in Mesopotamian art. It is possible that the Egyptians created their own idea of an extraordinary animal based on examples they had seen from other cultures.

Serpopard Simply put, the so-called “serpopard” is a feline with a serpentine neck. Interestingly, the serpopards on Ivory Two seem to have more than one form. Two of the figures have both the heads and necks of snakes, as opposed to having the heads of felids. There is no indication that the feline heads have eroded away; on the contrary, the artisan seems to have deliberately carved the snake-like heads on the figures. The second type of serpopard is of the type shown on the Hierakonpolis, Louvre, and 13. Midant-Reynes, The Prehistory of Egypt, 239, fig. 17. ´ 14. Pierre Amiet, La Glyptique M´ esopotamienne Archa¨ıque (Paris: Editions du Centre National de la Recherche Scientifique, 1961), 249, pl. 16, fig. 274; 265, pl. 25, fig. 417, respectively. 15. Ibid., 241, pl. 14, fig. 236. 16. Ibid., 243, pl. 14 bis, fig. K.

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Narmer palettes;17 it has the body and head of a felid but a serpentine neck. The serpopard can be seen on several seals from the Predynastic and Jemdet Nasr Periods at Uruk and also at Susa. It is always depicted as a feline with a serpentine neck and never has the head of a snake. It always occurs in pairs, with the necks of the two animals entwined.18 When more than one pair of serpopards are shown, the tails of adjacent animals are entwined.19 One example shows the tails crossed, but not entwined.20

“Master of the Animals” In Egyptian art, the “master of the animals” motif consists of a human hero clutching an animal in either hand. The first instance of such a motif is in Tomb 100 at Hierakonpolis, dated to Naqada II.21 In Tomb 100, as on the Gebel el-Arak knife handle, the hero subdues two lions. On Ivory Two, however, the animals are serpopards. This particular motif is particularly widespread in Mesopotamia. A detailed examination of the hero among the animals is impossible here, but there are a few points which must be mentioned. First of all, the hero is not always human. A certain proto-Elamite seal depicts two instances in the motif.22 One of the heroes is a bull, while the other is a lion; the bull is pictured subduing two lions, while the lion is victor over two bulls. When the hero is a human, he often clutches two lions,23 but it is also common to see the hero triumph over a pair of snakes or deer.24 It would be an exaggeration to say that the possibilities are endless, but it is clear that the overall message of the motif—a contest between a hero and his enemies—is more important than the form of the actors. Discussion It is important to keep in mind that while the Egyptian craftsmen may have borrowed certain designs from the cultures of Susa, Sumer, and others, the themes of the compositions remained Egyptian through and through. 17. Midant-Reynes, The Prehistory of Egypt, 241, fig. 18; 242, fig. 19; and 245, fig. 22 respectively. 18. Amiet La Glyptique, 233, pl. 11, fig. 195. 19. Ibid., 233, pl. 11, fig 198. 20. Ibid., 271, pl. 26, fig. 424. 21. Smith, “The Making of Egypt,” 237. 22. Amiet La Glyptique, 295, pl. 38, fig. 585. 23. Ibid., 223, pl. 6, fig. 119A. 24. Ibid., 225, pl. 7, fig. 151; 299, pl. 39, fig. 601, respectively.


177

The serpopard is a perfect example. In Mesopotamian compositions, this fantastical creature was always depicted in pairs and in symmetrical, ordered compositions. It was not normally used as part of the “master of the animals” motif or in the context scenes in general. The Egyptian serpopard, on the other hand, appears primarily in compositions where it is a symbol of the chaos that reigned beyond Egypt’s borders. As described above, this creature could be seen as a symbol of chaos in the clutches of a hero, most likely the ruler. On the reverse of the Hierakonpolis Palette, a lone serpopard is seen attacking an oryx. The composition is a jumble of wild animals, including a giraffe and an ibex, with lions preying on gazelles and a leopard attacking a sheep. Also seen in this scramble for life and death is a griffon and a creature—either a human (a priest?) wearing a tail and a mask or a man with the head and tail of a donkey—playing the flute. The obverse of the palette does show a fairly symmetrical pair of serpopards, but instead of bringing order to the pandemonium, the two creatures are shown as predators consuming a felled gazelle. The two serpopards on the obverse of the Narmer Palette are portrayed in a style much closer to the original motif; the creatures are carved in perfect symmetry, their necks entwined. However, each animal is held at bay by a rope tied around its neck. The meaning of this composition is quite clear. The serpopard symbolizes the chaos which must be controlled by the Egyptian king. But why do these fantastical creatures represent the opposite of mz‘t, the Egyptian ideal? The answer most likely is that these animals—the griffon, the serpopard, the lionfish—were seen as monsters. They were unnatural beasts, unseen within the borders of Egypt. The fact that they were unobserved in Egypt does not mean that they did not exist, but rather that they existed “out there.” The Egyptians saw these creatures as things, enemies even, which must be controlled. While the notion of depicting bizarre animals in art disappeared quite early in Egyptian history, there is one that remained prominent for millennia. This creature is the Seth animal.25 It has a long, curved snout, rectangular ears, and a stiff, arrow-like tail. The god Seth was the antithesis of Horus, of whom the king was the incarnation on earth. Seth was chaos, the god of the desert, and as such, in the later New Kingdom and after, was closely associated with the traditional (human) enemies of Egypt, to the extent of being synonymous with evil. It is clear that in the Early Dynastic period Seth was seen as a rival to Horus, but it is unlikely that he was regarded as truly malevolent at this point in time. Rather, as god of the desert, Seth was considered by the early Egyptians 25. Richard Wilkinson, The Complete Gods and Goddesses of Ancient Egypt (London: Thames and Hudson, 2003), 197–99.

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to be merely a personification of chaos, not “good” like Horus, but not exceptionally “evil” either. It is no accident that Seth, the god of desert and chaos, came to be represented by an unnatural creature. Can the creation of the Seth animal be considered an example of foreign influence? It is impossible to say for sure, but it is dangerous to assume that because the Egyptians did not normally incorporate extraordinary animals in their art, because they borrowed these creatures—among other designs—from Mesopotamia, and because these motifs were largely excised from the canon of Egyptian art, the Egyptians had neither the imagination nor the inclination to create and utilize such motifs without outside influence. One thing is certain—in the relatively few examples of Egyptian art for which foreign motifs have been adopted—the intention remains distinctly Egyptian. References Adams, Barbara. Ancient Hierakonpolis. Warminster, England: Aris and Phillips, 1974. ´ Amiet, Pierre. La Glyptique Mésopotamienne Archa¨ıque. Paris: Editions du Centre National de la Recherche Scientifique, 1961. Brown, Leslie, Emil Urban, and Kenneth Newman. The Birds of Africa. Vol. 1. New York: Academic Press, 1982. Churcher, Charles. “Zoological Study of the Ivory Knife Handle from Abu Zaidan.” In Predynastic and Archaic Egypt in the Brooklyn Museum, edited by Winifred Needler, 152–68. Wilbour Monographs, vol. 9. Brooklyn: The Brooklyn Museum, 1984. Estes, Richard. The Behavior Guide to African Mammals: Including Hoofed Mammals, Carnivores, Primates. Berkeley: University of California Press, 1991. Houlihan, Patrick. The Birds of Ancient Egypt. The Natural History Of Egypt, vol. 1. Warminster, England: Aris and Phillips, 1986. M´ alek, Jarom´ır. Egyptian Art. London: Phaidon, 1999. Midant-Reynes, Béatrix. The Prehistory of Egypt: From the First Egyptians to the First Pharaohs, translated by Ian Shaw. Malden, Massachusetts: Blackwell Publishers, 2000. Osborn, Dale. The Mammals of Ancient Egypt. The Natural History of Egypt, vol. 4. Warminster, England: Aris and Phillips, 1998. Quibell, James. Plates of Discoveries in 1898. Vol. 1 of Hierakonpolis. Publications of the Egyptian Research Account, vol. 4. London: B. Quaritch, 1900. ——— and Frederick Green. Plates of Discoveries in 1898–99. Vol. 2 of Hierakonpolis. Publications of the Egyptian Research Account, vol. 5. London: B. Quaritch, 1902.


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Smith, Harry. “The Making of Egypt: A Review of the Influences of Susa and Sumer on Upper Egypt and Lower Nubia in the Fourth Millennium b.c.” In The Followers of Horus: Studies Dedicated to Michael Allen Hoffman 1944–1990, edited by Renée Friedman and Barbara Adams, 235–46. Oxbow Monograph, vol. 20. Publications of the Egyptian Studies Association, vol. 2. Oxford: Oxbow Books, 1992. Smith, William. The Art and Architecture of Ancient Egypt, rev. 3rd ed. New Haven: Yale University Press, 1998. Wilkinson, Richard. The Complete Gods and Goddesses of Ancient Egypt. London: Thames and Hudson, 2003.

The “Rough Draft” of a Neo-Babylonian Accounting Document Elizabeth E. Payne Yale University

Among the hundreds of texts from the Eanna archive recording the work of craftsmen,1 YBC 9030 stands out as unusual.2 It is offered to Alice Slotsky on this occasion since its contents deal with two of her favorite subjects: accounting and fashion. The text was written within a grid neatly incised on the surface of the tablet. On the obverse, the grid contains three columns, on the reverse four. The contents of the tablet are made up of two parts: text and numerals. The former was carefully written and exhibits several abbreviations; while the latter can be characterized by its large, almost haphazard, style and frequent erasures.3

1. The Eanna archive, consisting of roughly 8,000 cuneiform tablets, comes from the goddess Ishtar’s Eanna temple in the southern Mesopotamian city of Uruk. While tablets coming from this archive are from the late eighth century b.c. through the early fifth century b.c., the majority of the archive dates to the years between 626–520 b.c. Texts concerning the work of craftsmen, especially metal and textile workers, account for approximately twenty percent of the archive and a thorough analysis of this material is the topic of the author’s dissertation. Many issues raised in this discussion will be addressed more fully in this larger work. 2. While this tablet is unusual, it is not unique; another unpublished text in the Yale holdings (NCBT 701) is written in the same style. In that instance, the text records personal names and units of capacity. I would like to thank the curators of the Yale Babylonian Collection, Benjamin R. Foster and Ulla Kasten, for permission to publish this text; for permission to cite unpublished tablets in their collections, these individuals again receive my thanks, as do the Special Collections, Princeton Theological Seminary Libraries. Finally, I would like to thank Michael Jursa for making several helpful suggestions after reading a draft of this article. 3. At the end of this article is appended a brief explanation of the styles used in providing patronymics and giving dates. Abbreviations used can also be found there.

181

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Elizabeth E. Payne

Figure 11.1: Upper Edge and Obverse of YBC 9030 (undated)

A Neo-Babylonian Accounting Document

183

Transliteration4 I

u.e

nun.me

1 obv.

I

II

ge6 ?

III

IV

V

2

pbabbarq-´ u (eras.) 10 (eras.) 1 (tal.) (eras.) 50 5 (eras.) (eras.) 40 (eras.) t´ ug n´ıg.´ıb.l´ ame galme 4.me 35 (eras.)

p

s´ıg

s´ıg

hé.me.da giˇshab ˘ ˘ 1 (tal.) 5/6 ma pxxq

3

t´ ug

lu-bar q ˇsa ´ pd gaˇsanq ˇsa ´ unugki

p43q

ki.min turme

hé.me.da ˇsa ´ in-za˘ hu-re-e-t´ u ˘ 47 (eras.) 36 (eras.)

t´ ug

t´ ug

VI

gu-hal-s.a-a-pt´ uq ˘

lo.e.

ˇsa ´ s´ıg hé ˇsa ´ pinq-za ˘ 21 (eras.) 18

t´ ug

m´ aˇsme turme

81

ptúg lu-bar ˇsa ´ dgaˇsan

2

m´ aˇs gal

p8q

pgu-hal-s.a-a-t´ uq ˘ ˇsa ´ giˇshab ˘ 8 40 lu-bar ˇsa ´ d igi.du

t´ ug

34

t´ ug

1 ptúg lu-bar ˇsa ´? d?

ˇsa ´ sagq

mi-ih-s.u ˇsa ´ ˘ za.g`ın.kur.ra 17 40 (eras.)

s´ıg

me? .me? q

4

2

n´ıg.´ıb.l´ ame ˇsa ´ dah ˘ plaq-ma-a-t´ u

s´ıg

hé.me.da giˇshab ˘ ˘ ˇsa ´ ta-phapq-ˇsu ´ ˘

6

3 (tal.) 20 t´ ug

mi-ih-s.u ˇsa ´ haˇs˘ ˘ hu-re-peq-t´ u ˘ 26

50

4. The following abbreviations have been used in the transliteration: (tal.) = (talent(s)), (eras.) = (erasure).

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Figure 11.2: Lower Edge and Reverse of YBC 9030 (undated)


185

Transliteration lo. e. con’t.

I

1 rev. VII

babbar-´ u 6 (tal.; eras.) (eras.) 6 36 20 t´ ug

s´ıg

VIII

51 (eras.)

IX

X

2 t´ ug

n´ıg.´ıb.l´ a tur

.sil-la-a

4

lu-bar ˇsa ´ d gaˇsan ˇsa ´ unugki 4

m´ aˇs gal 22 (eras.)

t´ ug

hé.me.da ˇsa ´ ˘ in-za 24

t´ ug

mi-ih-s.u ˘ ˇsa ´ giˇsh ab ˘ 30 (eras.) 20 20

gu-hal-s.a-a-t´ u ˘ giˇs ˇsa ´ hab ˘

m´ aˇs turme

s´ıg

22 (eras.)

ptúg mi-ih-s.u ˘ za? .g`ın? q p8q 40? (eras.) (eras.) 3

1? túg lu-bar [ˇsa ´ ] d gaˇsan ˇsa ´ sag

gu-hal-s.a-a-t´ u ˘ ˇsa ´ pin-zaq 10 (eras.) 38 20

ptúg lu-bar ˇsa ´

t´ ug

me

p16q[(+x)]

n´ıg.´ıb.l´ ame gal 2.me 16 (eras.)

4 30 hé.me.pdaq ˘ ? giˇs [ˇsa ´ hab? ] ˘ 1 (tal.) [(+x)]

p2q [(+x)]

d

igi.duq 1

XI

1/3 5 g´ın pt.uq-man-nu ˇsa ´ ina túg lu-bar me ˇsa ´ d me.me

XII

3 t´ ug

s´ıg

hé.me.da ˇsa ´ ha-at-hu-re-pe-t´ uq ˘ ˘ ˘ 10 3 30

186

Elizabeth E. Payne Translation

I

II III

IV

V

VI

VII

VIII

“(Account of) Apkallu: 1 2 11 (talents) 55 8 lub¯ aru-garments (mina) 40 (shekels) of the Lady of Uruk white (woven cloth) 435 large sashes 81 ditto small (hus.annu) ˘ dark (textiles): 1 47 (mina) 36 (talent) 5/6 mina x (shekels) red wool shekels? red wool dyed with dyed with hu ¯ratu inzahur¯etu ˘ ˘ 8 (mina) 40 4 lub¯ aru-garments (shekels) cording of B¯eltu-ˇsa-R¯eˇs (guhals.u) dyed with ˘ hu ¯ratu ˘ 2 lub¯ aru-garments 6 sashes of of d IGI.DU Ahlamay¯ıtu ˘ 21 (mina) 18 (shekels) cording (made) of red wool dyed with inzahur¯ atu ˘ 1 6 (talents) «6?! » 36 (mina) 20 (shekels) white (woven cloth) 51 small sashes

3 43 large .sibtugarments 34 small .sibtugarments 17 (mina) 40 (shekels) woven cloth (made) of purple wool 2? lub¯ aru-garments of Gula?

3 (talents) 20 (mina) red wool dyed with hu ¯ratu ˘ for felt 26 (mina) 50 (shekels) woven cloth (made) of apple-colored wool

(Account of) S.ill¯ aya: 2 3 4 lub¯ aru22 large garments of .sibtuthe Lady of garments Uruk

24 (mina) 22 (shekels) red wool dyed with inzahur¯etu ˘

30 (talents) 20 (mina) 20 (shekels) woven cloth dyed with hu ¯ratu ˘

4 216 large sashes

4 (mina) 30 (shekels) cording dyed with hu ¯ratu ˘

A Neo-Babylonian Accounting Document IX

X

XI

8 (mina) 43? 2? (+) lub¯ aru(shekels) garments of woven cloth B¯eltu-ˇsa-R¯eˇs of purple wool? 10 (talents) 1 lub¯ aru38 (mina) 20 garment of d (shekels) IGI.DU cording dyed with inzahur¯etu ˘ 25 shekels .tummanulinen, which is from the the clothing of Gula.”

16 (+) small .sibtugarments

187

1 (talent) (+) red wool [dyed with hu ¯ratu ? ] ˘

10 (talents) 3 (mina) 30 (shekels) red wool dyed with hathu ¯ru ˘ ˘

XII Commentary5

Of the garments mentioned here, the lub¯ aru- and .sibtu-garments remain difficult to translate. They appear frequently among the wardrobes of the gods and goddesses of Eanna and were generally made of woven, white wool and could be accented with sashes, headdresses, and other apparel, often of brightly colored fabrics. Neither garment was decorated with the golden sequins discussed by Oppenheim.6 Brief comment should also be made concerning the terminology for colors and dyes used in this text.7 In addition to the undyed, or white, wool (pes.u ˆ, babbar-´ u ), red wool (tabbaru, s´ıg hé.me.da) of various types appears, and in each instance, the dye used ˘for attaining that color is specified. The dyes mentioned are hu ¯ratu (giˇshab)—‘(dyer’s) madder’ ob˘ ˘ tained from the root of the Rubia tinctorum plant;8 inzahur¯etu (syll.)— a dye obtained from the “insects living on the kermes˘ oak,” (Coccus ilicis);9 and hathu ¯ru (syll.)—a dye used to create a red color, identifica˘ ˘ 10 tion unknown. Traditionally, a link between this dye and the haˇshu ¯ru ˘ ˘ ‘apple-colored’ wool has been suggested.11 The use of this dye to make a 5. Excerpted lines of this text are quoted in Paul-Alain Beaulieu, The Pantheon of Uruk during the Neo-Babylonian Period, Cuneiform Monographs, vol. 23 (Leiden: Brill, 2003), 21, 155, 220, 277 284, and 309. 6. A. Leo Oppenheim, “The Golden Garments of the Gods,” JNES 8 (1949): 172–93. 7. The most thorough discussion of colors in Mesopotamia continues to be B. ¨ Landsberger, “Uber Farben im Sumerisch-Akkadischen,” JCS 21 (1967): 139–73. 8. M. Stol, “Leder(industrie),” in RlA 6 (1980–1983): 527–43, esp. 534–35; W. H. van Soldt, “Fabrics and Dyes at Ugarit,” UF 22 (1990): 321–57, esp. 347. 9. van Soldt, “Fabrics and Dyes,” 346. 10. See also UCP 9/2, 85, no. 12, lines 4–5 where hathu ¯ru-dye is used to make ˘ ˘ tabarru-wool (4 . . . 1 ma.na s´ıg ta-bar-ri 5ˇs´ a ha ! (=haˇs)-at-h u-re-e-ti). ˘ ˘ hathur¯ 11. See, for example, CAD, s.v. hathu ¯ru ˘and AHw, s.v. etu. ˘ ˘ ˘ ˘

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red wool, however, indicates that either no link existed, or, more likely, that the haˇshu ¯ru-wool was of a reddish hue rather than the yellow-green ˘ ˘ generally suggested.12 The presence of these two terms, juxtaposed as they are, in these two accounts that are otherwise nearly identical argues strongly in favor of a connection between the terms and a revised understanding of the term “apple-colored.” Green textiles, when they appear in the archive, are described as has.artu ‘(yellow)-green’,13 so haˇshu ¯ru ˘ role. Finally, purple wool ˘(takiltu, ˘ need not be called upon to fill that s´ıg za.g`ın.kur.ra) is mentioned; the specific substance used to make the purple wool found in the texts of the Eanna archive cannot be stated with certainty at this time. The two most likely possibilities are either the dye obtained from mollusks of either the Purpura or Murex genus14 or the dye obtained from the leaves of the woad plant (Isatis tinctoria).15 III.1:

The correct interpretation of the mi-sign is uncertain. Neither a phonetic value of /mi / nor a numeric value of ‘14 (talents)’ is expected in this context. Reading the sign as ge6 ‘dark’, in contrast to the white cloth mentioned earlier in the text seems the most likely solution.

IV.3:

This reading is suggested by Beaulieu, Pantheon, 277.

V.1; X.2:

For a discussion of the god d igi.du, see Ibid., 282.

V.3:

For the meaning of taphapˇsu ‘felt’, see J.N. Postgate, “Assyrian Felt,” in Donum˘ Natalicum Studi in onore di Claudio Saporetti in occasione del suo 60o compleanno, eds. P. Negri-Scafa and P. Gentili. (Rome: Borgia Editore, 2000), 213–17.

VII.1:

The interpretation of the numbers in this case is not entirely clear.

12. See, for example, CAD, s.v. haˇshu ¯ru; H. Waetzoldt, “Kleidung,” in RlA 6 ˘ ˘ “Uber ¨ (1980–83): 18–31, esp. 20; Landsberger, Farben,” 172. 13. This term is rare in the Eanna corpus but is attested in UCP 9/2, 103, no. 41, line 1, (1 ma.na s´ıg ha-s.a-´ aˇs-ti). ˘ ¨ 14. van Soldt, “Fabrics and Dyes,” 345–46; Landsberger, “Uber Farben,” 162–63; Stuart Robinson, A History of Dyed Textiles: Dyes, Fibres, Painted Bark, Batik, Starch-resist, Discharge, Tie-dye, Further Sources for Research (Cambridge, Massachusetts: M.I.T. Press, 1969), 24. 15. Robinson, History of Dyed Textiles, 26–27.

A Neo-Babylonian Accounting Document IX.1–2:

189

The restoration of the broken text in these two cases is based on the presence of purple woven cloth in the account of Apkallu and its absence in the account of S.ill¯aya, and the presence of an indisputable initial vertical wedge at the beginning of case IV.1. While the nuance of this wedge is uncertain, its presence here is at least possible. The abbreviated spelling is in keeping with other spellings found elsewhere in the text.

Discussion The text records, on either side, the account of a weaver, providing details concerning the amount of wool issued to each of the two men (that is, the weight of the raw materials) and the number of garments received from them (that is, the total finished products). The context for these transactions can be found within what Oppenheim called “the care and feeding of the gods;”16 the cult statues of the Eanna temple were elaborately attired; and this tablet, like so many others, documents the bureaucratic oversight employed by the temple in maintaining them. Neither of the individuals mentioned in this text is included among the weavers in K¨ ummel’s prosopography of the archive,17 but both were certainly active as such. Apkallu / Nadn¯ aya // Iˇsparu appears in few administrative documents, and only once with the title iˇsparu, ‘weaver’,18 but he certainly had at least a brief career during the years Nbn 8–10 (548–546 b.c.).19 Two additional texts, however, suggest that his career began as early as Nbk 26 (579 b.c.).20 If this is the case he had a lengthy, but not unprecedented, career of thirty-three years.21 S.ill¯aya / 16. A. Leo Oppenheim, “The Care and Feeding of the Gods,” in Ancient Mesopotamia: Portrait of a Dead Civilization, rev. ed. by Erica Reiner (Chicago and London: University of Chicago Press, 1977), 183–98. 17. Hans Martin K¨ ummel, Familie, Beruf und Amt im sp¨ atbabylonischen Uruk: prosopographische Untersuchungen zu Berufsgruppen des 6. Jahrhunderts v. Chr. in Uruk (Berlin: Gebr. Mann Verlag, 1979). A revised prosopography and study of the management of the various craft industries will comprise part of the author’s dissertation. 18. PTS 2100 (Nbn 8 I 10). 19. PTS 3424 (Nbn 8 I 7) and NBC 4934 (Nbn 10 VII? 6+), respectively. 20. These texts are OECT 10, 315 (Nbk 26 – –) in which Apkallu received silver for dye and NCBT 758 (Nbk 42 XIIb 3) in which Apkallu transported purple wool from Babylon to Eanna. 21. For a brief overview of life expectancies and active years of service, see Michael Jursa, Neo-Babylonian Legal and Administrative Documents: Typology, Contents and Archive, Guides to the Mesopotamian Textual Record, vol. 1 (M¨ unster: UgaritVerlag, 2005), 56. For a more detailed study, see Erlend Gehlken, “Childhood and Youth, Work and Old Age in Babylonia – A Statistical Analysis,” in Approaching the Babylonian Economy: Proceedings of the START Project Symposium Held in Vienna, 1–3 July, 2004, eds. Heather D. Baker and Michael Jursa. Ver¨ offentlichun-

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N¯ adinu // Iˇsparu appears in numerous administrative texts and had a career spanning almost twenty years (Nbk 42 - Nbn 10; 563–546 b.c.).22 While not partners, these men had a working relationship, for in the few texts where Apkallu appears as a weaver, he usually appears together with S.ill¯ aya. There was also a familial relationship between them as both men were members of the Iˇsparu family. The precise nature of this relationship is, however, unclear. K¨ ummel reconstructed the family tree in part, and Apkallu appears therein.23 S.ill¯ aya, however, is more difficult to place within the family. His father, N¯adinu, was probably also a weaver, but two possibilities exist within the Iˇsparu family. N¯adinu / Nadn¯ aya appears as a weaver in one text dated to Nbk 30 (575 b.c.).24 If this is S.ill¯ aya’s father, then Apkallu would be S.ill¯aya’s uncle. Alternatively, S.ill¯ aya’s father could have been the weaver N¯adinu / Nergal-n¯as.ir who appears several times between Nbk 21 – Nbk 26 (584–579 b.c.).25 The relationship of these individuals within the larger family structure cannot be determined at this time, and if this is S.ill¯aya’s filiation, then his relationship to Apkallu remains unknown. Since the sums involved are significant, this record must represent a substantial length of time, with Apkallu’s account being roughly twice the size of S.ill¯ aya’s account. Given the degree of similarity between the garment types listed in both accounts, it seems likely that the text represents a tally of those garments produced for a specific purpose, such as their work quota or obligation toward a specific ceremony, over a set period of time. The tablet was written in the following sequence: first the grid was incised, then the text was written, and finally, the numerals were added during which many corrections were made. At least this final step was likely done “on site,” either in the workshop of each man or at the site where accounting documents were stored. The text as it survives today was certainly not a “finished product;” its contents would have been transferred to either a wax board or another clay tablet to which would have been added the information we lack here (transaction verbs and date, most importantly). This text was the “rough draft” on which the numbers were tallied, and it offers some insight into one technique used in creating the written record that survives to us today.

gen zur Wirtschaftsgeschichte Babyloniens im 1. Jahrtausend v. Chr., vol. 2, AOAT 330 (M¨ unster: Ugarit-Verlag, 2005), 89–120. 22. NCBT 758 (Nbk 42 XIIb 3) and NBC 4934 (Nbn 10, VII? 6+), respectively. 23. K¨ ummel, Familie, Beruf und Amt, 131. 24. BIN 1, 146 (Nbk 30* VIII 17*). 25. YOS 17, 112 (Nbk 21 V 29) and YBC 9368 (Nbk 26 I 13), respectively.


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*** All texts cited from collections at Yale have been collated and improved readings are marked with an asterisk (*). Dates are given in the following format: king’s name, year (“0a” indicates an accession year), month (Roman numeral, “b” indicates an intercalary month), and day (for example, Nbk 14 IV 23). Patronymics are given as follows: PN1 / PN2 // PN3 means “PN1 , son of PN2 , of the PN3 family.” Abbreviations used are as follows: AHw – Akkadisches Handw¨ orterbuch, vols. 1–3, (Wiesbaden: Harrassowitz, 1965-1981); AOAT – Alter Orient und Altes Testament; BIN 1 – Clarence Elwood Keiser, Letters and Contracts from Erech Written in the Neo-Babylonian Period, Babylonian Inscriptions in the Collection of James Buchanan Nies, vol. 1 (New Haven and London: Yale University Press, 1917); CAD – The Assyrian Dictionary of the Oriental Institute of the University of Chicago, (Chicago: Oriental Institure 1956-present); JCS – Journal of Cuneiform Studies; JNES – Journal of Near Eastern Studies; NBC – Texts from the Nies Babylonian Collection (Yale); Nbk – Nebuchadnezzar II (604–562 b.c.); Nbn – Nabonidus (555–539 b.c.); NCBT – Texts from the Newell Collection of Babylonian Tablets (Yale); OECT 10 – Gilbert J. P. McEwan, Late Babylonian Texts in the Ashmolean Museum, Oxford Editions of Cuneiform Texts, vol. 10 (Oxford: Clarendon Press, 1984); PTS – Texts from the Princeton Theological Seminary; RlA – Reallexicon der Assyriologie; UCP 9 – Henry Frederick Lutz, Neo-Babylonian Administrative Documents from Erech, Parts I and II, University of California Publications in Semitic Philology, vol. 9, no. 1 (Berkeley: University of California Press, 1927); UF – Ugarit-Forschungen; YBC – Texts from the Yale Babylonian Collection; YOS 17 – David B. Weisberg, Texts from the Time of Nebuchadnezzar. Yale Oriental Series – Babylonian Texts, vol. 17 (New Haven and London: Yale University Press, 1980). References Beaulieu, Paul-Alain. The Pantheon of Uruk during the Neo-Babylonian Period. Cuneiform Monographs, vol. 23. Leiden: Brill, 2003. Gehlken, Erlend. “Childhood and Youth, Work and Old Age in Babylonia – A Statistical Analysis.” In Approaching the Babylonian Economy: Proceedings of the START Project Symposium Held in Vienna, 1–3 July, 2004, 89–120. Edited by Heather D. Baker and Michael Jursa. Ver¨ offentlichungen zur Wirtschaftsgeschichte Babyloniens im 1. Jahrtausend v. Chr.,vol. 2,AOAT 330. M¨ unster: Ugarit-Verlag, 2005.

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Jursa, Michael. Neo-Babylonian Legal and Administrative Documents: Typology, Contents and Archive. Guides to the Mesopotamian Textual Record, vol. 1. M¨ unster: Ugarit-Verlag, 2005. Keiser, Clarence Elwood. Letters and Contracts from Erech Written in the Neo-Babylonian Period. Babylonian Inscriptions in the Collection of James B. Nies, vol. 1. New Haven and London: Yale University Press, 1917. K¨ ummel, Hans Martin. Familie, Beruf und Amt im sp¨ atbabylonischen Uruk: prosopographische Untersuchungen zu Berufsgruppen des 6. Jahrhunderts v. Chr. in Uruk. Abhandlungen der Deutschen Orient-Gesellschaft, vol. 20. Berlin: Gebr. Mann Verlag, 1979. ¨ Landsberger, B. “Uber Farben im Sumerisch-Akkadischen.” JCS 21 (1967): 139–173. Lutz, Henry Frederick. Neo-Babylonian Administrative Documents from Erech, Parts I and II. University of California Publications in Semitic Philology, vol. 9, no. 1. Berkeley: University of California Press, 1927. McEwan, Gilbert J. P. Late Babylonian Texts in the Ashmolean Museum. Oxford Editions of Cuneiform Texts, vol. 10. Oxford: Clarendon Press, 1984. Oppenheim, Leo. “The Golden Garments of the Gods.” JNES 8 (1949): 172–193. ———. “The Care and Feeding of the Gods.” In Ancient Mesopotamia: Portrait of a Dead Civilization, 183–98. Revised edition by Erica Reiner. Chicago: University of Chicago Press, 1977. Postgate, J. N. “Assyrian Felt.” In Donum Natalicum Studi in onore di Claudio Saporetti in occasione del suo 60o compleanno, 213–17. Edited by P. Negri-Scafa and P. Gentili. Rome: Borgia Editore, 2000. Robinson, Stuart. A History of Dyed Textiles: Dyes, Fibres, Painted Bark, Batik, Starch-resist, Discharge, Tie-dye, Further Sources for Research. Cambridge, Massachusetts: M.I.T. Press, 1969. Stol, M. “Leder(industrie).” In RlA 6. 1980–1983: 527–43. van Soldt, W. H. “Fabrics and Dyes at Ugarit.” UF 22 (1990): 321–57. Weisberg, David B. Texts from the Time of Nebuchadnezzar. Yale Oriental Series – Babylonian Texts, vol. 17. New Haven and London: Yale University Press, 1980.

Mesopotamian Sexagesimal Numbers in Indian Arithmetic Kim Plofker Union College

Introduction: Early Number Use in India The ancient Mesopotamian standardized place-value number system with a sexagesimal base was transmitted, via astronomical and protoastrological techniques, to many later mathematical traditions. However, its penetration into all of them seems to have remained only partial. Nowhere but in cuneiform texts were numbers uniformly represented in base-60 place-value. Instead, certain sexagesimal units such as degrees and hours were taken over and combined in various ways with existing non-sexagesimal methods for representing and computing with integers and fractions. The present paper attempts to describe how this process of adaptation took place in the mathematics of India. The surviving corpus of ancient Indian texts cannot compete, at least in quantity, with the enviable wealth of primary source materials available to Assyriologists. Since writing was apparently not used in India until the late first millennium b.c.,1 any sources dating from before that period depended solely on oral transmission for their survival. The oldest such compositions known are the sacred verses in Early Vedic, an archaic form of Sanskrit descended from Proto-Indo-Iranian, compiled in the hymn collection R . gveda. These verses contain no definite chronological data, and consequently the date of their composition has been the subject of much controversy. Based on what can be pieced together from linguistic and archaeological evidence, most Indologists now accept 1. This statement ignores the possible use of writing in the urbanized Indus civilization of the third millennium in the northwestern part of the subcontinent. The extant fragments of this culture’s sign system have never been satisfactorily identified with any representation of language, and it is not certain what linguistic or ethnic relationship its people had with the (apparently) later Indo-Aryan speakers in India.

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(although not without caveats) that this date probably falls within the period 1900–1200 b.c.2 Unsurprisingly, these orally preserved early hymns to the deities of the Vedic pantheon contain very little mathematical material. But they do include several references to number words that attest to a firmly established decimal number system for integers, showing an apparently complete pattern of decades and powers of ten up to the thousands. Cognate number words in most other Indo-European languages indicate that a partial form of this decimal system dates back as far as Proto-Indo-European times,3 and it may have been fully regularized in Indo-Aryan by the second millennium. Typical phrases expressing numerals include “thousands, hundreds, tens,” “eighty, ninety, or a hundred horses,” “ninety and nine cities,” “you destroyed sixty thousand.” (R . gveda 2.1, 2.18, 2.19 and 6.26, respectively.) By about the end of the second millennium, this decimal system had been expanded to an extent unique among ancient civilizations, with regular powers of ten up to at least a trillion. Evidence of this expansion is preserved in some of the “hymns to the numbers” in the Middle Vedic compilation called the Yajurveda. Here numbers themselves, in regular patterns, are addressed in a sacrificial invocation: “Hail to one, hail to two, hail to three. . . hail to eighteen, hail to nineteen, hail to twenty-nine, hail to thirty-nine. . . hail to ninety-nine, hail to a hundred.”4 “Hail to a hundred, hail to a thousand, hail to ayuta [ten thousand], hail to niyuta [hundred thousand]. . . hail to anta (1011 ), hail to par¯ ardha (1012 ).”5 The fully regularized system of decimal number words was applied to fractional numbers by employing ordinal numeral forms, to judge from the evidence of the earliest known mathematically-oriented San´ skrit works, the Sulbas¯ utras or “Rules of the cord.” Composed starting sometime before the middle of the first millennium b.c., these are handbooks of ritual geometry that describe stake-and-cord procedures for constructing sacrificial altars out of baked bricks. The short mnemonic ´ sentences or s¯ utras of even the oldest Sulbas¯ utra exhibit regular verbal representation of arbitrary fractional parts: “Increase the measure by [its] third [part], and [increase] that [one-third] by [its] fourth [part] 2. Michael Witzel, “Substrate Languages in Old Indo-Aryan (Rgvedic, Middle and Late Vedic),” Electronic Journal of Vedic Studies 5, no. 1 (1999): 3. Available at http://users.primushost.com/˜india/ejvs/ejvs0501/ejvs0501article.pdf. 3. See Carol Justus, “Numeracy and the German Upper Decades,” Journal of Indo-European Studies 24 (1996): section 4.0. Available at http://www.utexas.edu/cola/depts/lrc/numerals/cfj-jies/cfj1-section1.html. 4. Yajurveda 7.2.11. 5. Yajurveda 7.2.20.

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decreased by its own thirty-fourth [part].”6 √ There were √ even technical terms for particular square-roots, such as 2 and 3, imagined as hypotenuses of particular right triangles.7 Early Traces of Mesopotamian Influence? Curiously, another Sanskrit text of the early first millennium, although it too uses only decimal numbers, describes a ritual procedure ´ oddly reminiscent of cuneiform sexagesimal arithmetic. This is the Satapathabr¯ ahman.a or “Br¯ ahman.a of a hundred paths,” an exegetical text explaining the symbolism of sacrificial rituals. It recounts the actions of the creator god Praj¯ apati, symbolizing the year as an altar composed of 720 bricks representing the days and nights: Praj¯ apati, the year, has created all existing things. . . Having created all existing things, he felt like one emptied out, and was afraid of death. He bethought himself, “How can I get these beings back into my body?”. . . He divided his body into two; there were three hundred and sixty bricks in the one, and as many in the other; he did not succeed. He made himself three bodies. . . He made himself six bodies of a hundred and twenty bricks each; he did not succeed. He did not divide sevenfold. He made himself eight bodies of ninety bricks each. . . He did not divide elevenfold. . . He did not divide either thirteenfold or fourteenfold. . . He did not divide seventeenfold. He made himself eighteen bodies of forty bricks each; he did not succeed. He did not divide nineteenfold. He made himself twenty bodies of thirty-six bricks each; he did not succeed. He did not divide either twentyonefold, or twenty-twofold, or twenty-threefold. He made himself twenty-four bodies of thirty bricks each. There he stopped. . ..8 Although presented here to explain the cosmic significance of standard divisions of the year, this narrative is mathematically rather similar to cuneiform tables of sexagesimal reciprocals of “regular” numbers— that is, numbers whose only prime factors are 2, 3 and 5. Non-regular 6. Baudh¯ ayana´sulbas¯ utra 2.12. See Samarendra Nath Sen and Amulya Kumar ´ Bag, The Sulbas¯ utras (New Delhi: Indian National Science Academy, 1983), 19. 7. Ibid., 18. ´ 8. Satapathabr¯ ahman . a 10.4.2. See Julius Eggeling, Satapatha-Brahmana According to the Text of the Madhyandina School, vol. 4, Sacred Books of the East, vol. 43 (Oxford: Oxford University Press, 1897), 349–51. I have substituted ‘divide’ as the translation of vi-bh¯ u where Eggeling uses ‘develop.’

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divisors are omitted from the list since they “do not divide.”9 The quantity 720 bricks itself is the standard measure of Old Babylonian metrology known as the “brick-sar.”10 However, these similarities are not conclusive evidence of influence from Mesopotamian mathematics upon ´ the Satapathabr¯ ahman.a. Nor, apparently, are they reinforced by any comparable similarities with base-60 reciprocals or other peculiarities of cuneiform mathematics elsewhere in ancient Sanskrit texts. (In fact, no Babylonian-style arithmetic tables of values for simple operations such as multiplication, division or square-roots are known anywhere in the Sanskrit mathematical corpus, although tables of trigonometric functions appear in later periods.) It has been plausibly suggested11 (although not universally accept12 ed ) that some early astronomical references in Sanskrit indicate Mesopotamian influence via contacts with the Achaemenid empire at the end of the Vedic period in the middle of the first millennium, and perhaps even earlier. The resemblances between Mesopotamian and Indian astronomy involve concepts such as the 360-day ideal year, a quasisexagesimal time unit (360 uˇ s and 30 muh¯ urtas per nychthemeron in Mesopotamia and in India respectively), the use of the gnomon and water-clock for time measurement, and periodic arithmetic schemes for calendar regulation. The 360-day year and the muh¯ urta are known from late Vedic texts, while the water-clock and the calendric techniques are first found in the Jyotis.aved¯ anga ˙ or “Astronomical limb of the Vedas,” a short work on calendrics and timekeeping whose older parts were probably composed around the fifth century.13 But they are not accompa9. Jens Høyrup, Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin, Studies and Sources in the History of Mathematics and Physical Sciences (New York: Springer, 2002), 27–30. 10. Eleanor Robson, Mesopotamian Mathematics, 2100–1600 b.c.: Technical Constants in Bureaucracy and Education, Oxford Editions of Cuneiform Texts, vol. 14 (Oxford: Clarendon Press, 1999), 59. 11. E.g., David Pingree, “mul.apin and Vedic Astronomy,” in dubu-e2 -dub-ba-a: Studies in Honor of ˚ Ake W. Sj¨ oberg, eds. Herman Behrens, Darlene Loding and Martha Roth (Philadelphia: University Museum,1989), 439–45 and David Pingree, “The Mesopotamian Origin of Early Indian Mathematical Astronomy,” Journal for the History of Astronomy 4, (1973): 1–12. 12. E.g., Harry Falk, “Measuring Time in Mesopotamia and Ancient India,” Zeitschrift der Deutschen Morgenl¨ andischen Gesellschaft 150 (1) (2000): 107–32; Yukio Ohashi, “The Legends of Vasis.t.ha–A Note on the Ved¯ anga ˙ Astronomy,” in History of Oriental Astronomy, ed. Razaullah Ansari (Dordrecht: Kluwer, 2002), 75–82; David Brown and Harry Falk, The Interactions of Ancient Astral Science, Vergleichende Studien zu Antike und Orient, vol. 3 (Bremen: Hempen, forthcoming). 13. Pingree, “Mesopotamian Origin,” passim. Astrochronological arguments have been used to argue for a date of the Jyotis.aved¯ anga ˙ as early as the late second millennium, but this remains speculative due to our ignorance of the details of its


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nied by any unambiguously sexagesimal representations or subdivisions of units, unless we choose to classify as such the division of the Vedic time-unit muh¯ urta into two n¯ ad.ik¯ as.14 Nor, in fact, are metrological subdivisions apparently standardized around any other computationally “nice” number instead of sixty: the Jyotis.aved¯ anga ˙ does not blink at making a day equal to 603 kal¯ as or a yearly cycle equal to 27 (or 28) naks.atras.15 A collection of planetary omens in a Sanskrit text composed probably in the first or second century a.d. is also a likely candidate for influence from the classic Babylonian astronomical systems, since like them it treats the so-called “Greek-letter phenomena” of the planets (a particular set of their positions with respect to the sun).16 It is roughly contemporary with the first solidly dated text in Sanskrit mathematical astronomy, the Pait¯ amahasiddh¯ anta of the Pa˜ ncasiddh¯ antik¯ a, which is preserved only in an epitome within a sixth-century a.d. text but bears an epoch date corresponding to 11 January 80 a.d.17 In both of these works as in the Jyotis.aved¯ anga ˙ the quantitative arithmetic models stick to units such as days and naks.atras verbally expressed in the ordinary decimal numbers, rather than adopting sexagesimal representations. Paradoxically, although Mesopotamian mathematical astronomy seems likely to have shared several concepts and techniques with its early Indian counterpart, it apparently did so without transmitting any of the unique features of Mesopotamian mathematics. The First Sexagesimal Numbers in Sanskrit The unambiguous use of sexagesimal place-value in India is not explicitly recorded until a century or so later, when it appears in transastronomical system. 14. Jyotis.aved¯ anga ˙ R akara Dvived¯ı, Br¯ ahmasphut.asiddh¯ anta, . k.16–17. See Sudh¯ The Pandit n.s. 23–24 (1901–02), 64. 15. Jyotis.aved¯ anga ˙ R akara Dvived¯ı, Br¯ ahmasphut.a. k.14–16. See again Sudh¯ siddh¯ anta, The Pandit n.s. 23–24 (1901–02), 64. 16. David Pingree, “Babylonian Planetary Theory in Sanskrit Omen Texts”, in From Ancient Omens to Statistical Mechanics: Essays on the Exact Sciences Presented to Asger Aaboe, eds. J. Lennart Berggren and Bernard Goldstein (Copenhagen: Munksgaard, 1987), 91–99 and David Pingree, “Venus Omens in India and Babylon,” in Language, Literature, and History: Philological and Historical Studies Presented to Erica Reiner, ed. Francesca Rochberg-Halton (New Haven CT: American Oriental Society, 1987), 293–315. 17. George Thibaut and Sudh¯ akara Dvived¯ı, The Pa˜ nchasiddh¯ antik¯ a of Var¯ aha Mihira, 2nd ed., Chowkhamba Sanskrit Studies, vol. 68 (Varanasi: Chowkhamba Sanskrit Series, 1968); Otto Neugebauer and David Pingree, The Pa˜ ncasiddh¯ antik¯ a of Var¯ ahamihira, 2 vols. (Copenhagen: Danish Royal Academy, 1970–1); David Pingree, “History of Mathematical Astronomy in India,” in The Dictionary of Scientific Biography, vol. 15 (New York: Scribner, 1978), 536–54.

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lations and adaptations of Greek texts. The earliest known instance is the Yavanaj¯ ataka or Greek Horoscopy of an Indo-Greek leader named Sphujidhvaja. The Yavanaj¯ ataka, composed in a.d. 269/270, is a versification of a prose Sanskrit translation (made in 149/150) of a Greek astrological work. The numbers in the text are as usual stated verbally and somewhat elaborately, to conform to the requirements of the verse meter, but their significance is clear, as the following examples show: A civil month is thirty days; a solar one is additionally tenplus-three muh¯ urtas and four kal¯ as and fifty-six third parts and two fourth quantities.18 Here a muh¯ urta is still a thirtieth of a day, but a kal¯ a is now not 1/603 of a day, but rather 1/60 of a muh¯ urta. So the difference between the lengths of a civil and a solar month, as stated in the verse, is a number of muh¯ urtas specified to the third sexagesimal place, namely 13; 4, 56, 2. The past years of the era multiplied by the sum of eleven and eleven parts. . . Those n¯ ad.ik¯ as are each sixty lipt¯ as; sixty n¯ ad.ik¯ as are a day. . .19 “The sum of eleven and eleven parts” means 11; 11. The n¯ ad.ik¯ as of the Jyotis.aved¯ anga ˙ have been sexagesimally subdivided into lipt¯ as, a transliteration of Greek lepton. Note that except for the time-units, there is no standard technical term for sexagesimal fractional powers; the generic term “parts” can also refer to other types of fractions. Like the Greeks, the Indians seem to have avoided pure sexagesimal place-value notation, preferring to use instead “mixed” numbers with integer quantities in the more familiar decimal system, as we still do with our Babylonian-derived base-60 angle measurements. These angle measurements also appear in the Yavanaj¯ ataka and in other Greek-derived astronomical texts contemporary with it, which are now known only from the above-mentioned later compilation Pa˜ ncasiddh¯ antik¯ a.20 E.g.: 18. Yavanaj¯ ataka 79.11. This and the subsequent quotations from the Yavanaj¯ ataka are taken from David Pingree, The Yavanaj¯ ataka of Sphujidhvaja, 2 vols. (Cambridge MA: Harvard University Press, 1978). Alternative translations have been suggested for the values of some of the numbers, but their sexagesimal format is undisputed. See the reference in Harry Falk, “The Yuga of Sphujiddhvaja and the Era of the Kusanas,” Silk Road Art and Archaeology 7 [2001]: 123. 19. Yavanaj¯ ataka 79.19 and 79.28. 20. Pingree, “History of Mathematical Astronomy in India,” 538–50.


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A naks.atra is eight hundred lipt¯ as. The tithi is [measured] by twelve degrees [of longitudinal separation] of the sun from the moon.21 This lipt¯ a is a sixtieth of a degree, or arcminute, instead of a sixtieth of a n¯ ad.ik¯ a. Eight hundred arcminutes or 13; 20 degrees is 1/27 of the annual ecliptic circle. Furthermore, we can deduce from another verse of the Yavanaj¯ ataka that Indian astronomers in this period were already using decimal placevalue notation. This mathematical development is frequently assigned to a later time (sixth to eighth century a.d.) on the basis of numerals found in inscriptions, but it was indisputably known by the time of the Yavanaj¯ ataka. For there was evidently already in place the so-called “concrete number” system, allowing a particular number to be expressed in verse by the name of any person or object routinely associated with that number in religious scripture or in everyday life, such as “eye” to mean two or “tooth” to mean thirty-two. This is proven by the occurrence of just such concrete numbers at the end of the Yavanaj¯ ataka: There was a wise king named Sphujidhvaja who made this [work] with four thousand Indravajra [verses in the “Indravajra” meter], appearing in the year Vis.n.u/hook-sign/moon.22 ´ This refers to year 191 of the Saka era or a.d. 269/270, and the chronogram uses the concrete numbers “Vis.n.u” (one), “hook-sign” (nine, from the shape of its figure), “moon” (one). Such a notational system necessarily imples the assumption of decimal place-value rather than any additive or multiplicative numeral system. Otherwise, since the concrete numbers in the sequence are undifferentiated by any words indicating powers or multiples of ten, the numerical value of the total would remain ambiguous. Unfortunately, due to the paucity of earlier technical texts, we have few clues as to exactly how or when decimal place-value representation first emerged in India. It may well be that this notation, along with its inclusion of a tenth decimal digit to represent zero, was reinforced by these encounters with Indo-Greek astronomical texts containing Greek forms of sexagesimal place-value numbers.23 In any case, it seems most likely that sexagesimal place-value itself, in the limited 21. Pa˜ ncasiddh¯ antik¯ a 3.16 (Pauli´sasiddh¯ anta). See Thibaut and Dvived¯ı, The Pa˜ nchasiddh¯ antik¯ a, 8. 22. Yavanaj¯ ataka 79.62. 23. See the discussion of this hypothesis: David Pingree, “Zero and the Symbol for Zero in Early Sexagesimal and Decimal Place-Value Systems,” in The Concept únya, eds. Amulya Kumar Bag and Sreeramula Rajeswara Sarma (New Delhi: of S¯ IGNCA/INSA, 2003), 137–41.

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form of specific sexagesimal units for astronomical and timekeeping calculations, was adopted in India indirectly from Greek texts rather than from earlier Mesopotamian ones. Indian Techniques for Sexagesimal Arithmetic The new Indian sexagesimal numbers seem to have been assimilated as completely as possible into existing decimal mathematics. However, beginning around the middle of the first millennium a.d., medieval Sanskrit texts preserve a few arithmetic techniques evidently designed to facilitate calculating with combinations of integers and sexagesimal fractions. These include the square-root formulas recorded in an early seventh-century text, the Br¯ ahmasphut.asiddh¯ anta of Brahmagupta (a.d. 628), in the section on shadow-computations: The integer multiplied by its own fractional sixtieth-parts and divided by thirty is the square of the fraction, to be added to the square of the integer.24 That is, for a sexagesimal number made up of a units and b sixtieths, which we will express as a; b or a + b/60, Brahmagupta’s rule gives (a; b)2 = (a + b/60)2 ≈

ab + a2 . 30

Comparing the result that we would expect from the usual binomial expansion, 2 b b 2 a + 2a · + , 60 60 we see that Brahmagupta has simply discarded the last term in the product. Since this final term will always be small, Brahmagupta’s approximation will always be within ±1 of the exact result. Another, more opaque rule in the same text explains how to approximate the square root of the sum or difference of the squares of two numbers, one an integer and the other with a sexagesimal fractional part: Two squares of a given smaller quantity are [separately] increased or decreased by two squares of the fractional [part] of the second [quantity and] divided by twice the second quantity, [which is] increased or decreased in the second place by that with which the quotient is equal. The halved divisor increased or decreased by the result, or the second [number] 24. Br¯ ahmasphut.asiddh¯ anta 12.62. See Dvived¯ı, Br¯ ahmasphut.asiddh¯ anta, 211–12.


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increased or decreased by the result, is the square-root of the sum or of the difference of the squares.25

Figure 12.1: The Shadow-Triangle of a 12-digit Gnomon “The square root of the sum or difference of two squares” instantly suggests the solution of right triangles. The rule was evidently devised for timekeeping calculations with shadows cast by vertical gnomons, as illustrated in figure 12.1. The standard gnomon-length in Indian astronomy contains an integer number (usually 12, a value attested in the first known Sanskrit reference to the gnomon in the late first millennium 26 b.c.) of the units called “digits” (Sanskrit angulas). ˙ However, the shadow s and the corresponding hypotenuse h are expressed in terms of digits and sexagesimal parts of digits. (The angula ˙ is an ancient ´ Indian unit of length but not originally a sexagesimal one: in Sulbas¯ utra metrology it is divided instead into some number (e.g., 14, 34, or 6) of barleycorns or other grains.27 Its base-60 subdivision, the vyangula, ˙ was probably introduced along with the other sexagesimal units discussed above.) Therefore, if we know the integer length g of the gnomon and the length a; b of either the shadow or hypotenuse, Brahmagupta’s rule tells us how to find the length of the other leg of the triangle. (The geometry of the situation explains why the integer gnomon-length is called the “smaller quantity” in the rule: when a square-root of the difference of two squares is being computed, that is, when s is to be found from h and g, the gnomon g always will be the smaller of the two given quantities.) The structure of the rule can be explained as follows for the case of the sum, i.e., the computation of h from g and s = a; b. 25. Br¯ ahmasphut.asiddh¯ anta 12.64–65. See Dvived¯ı, Br¯ ahmasphut.asiddh¯ anta, 213. 26. Pingree, “Mesopotamian Origin,” 5. ´ 27. Sen and Bag, Sulbas¯ utras, 17, 60.

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Consider that h=

p

g 2 + (a; b)2 ≈

p

g 2 + a2 + ab/30,

by the previous rule which called ab/30 the “square of the fractional part.” We want to find some quantity, say, x, that can be added on to a such that h is given by a + x (at least up to the accuracy of the above approximation). This implies that p g 2 + a2 + ab/30 = a+x or g 2 +a2 +ab/30 = (a+x)2 = a2 +2ax+x2 , which will be true if

g 2 + ab/30 . 2a + x The equation cannot be solved directly for x in terms of x itself, so an iterative procedure that will produce such an x by repeated application must be used. And in fact, though not so described, Brahmagupta’s rule is just the first two steps of exactly such an iteration. He first computes an initial “result,” say, x0 , from the “square of the smaller quantity increased by the square of the fractional part and divided by twice the second quantity”: g 2 + ab/30 x0 = . 2a + 0 Then the same computation is to be done once more (“in the second place”), but this time with “twice the second quantity” 2a increased by the “result” x0 : g 2 + ab/30 x1 = 2a + x0 And so the “second quantity” a plus that new result will be, approximately, the desired square-root h: x=

h ≈ a + x1 . It has been noted that rules closely related to Brahmagupta’s second formula appear in the possibly contemporary Sanskrit source called the Bakhsh¯ al¯ı Manuscript and in later sources28 and that a more general form of it has been found (or at least inferred) in ancient mathematical traditions from Mesopotamia to China.29 28. Takao Hayashi, The Bakhsh¯ al¯ı Manuscript (Groningen: Egbert Forster, 1995), 100–103. 29. J. Lennart Berggren, “Ancient and Medieval Approximations to Irrational Numbers,” in From China to Paris: 2000 Years Transmission of Mathematical Ideas, eds. Yvonne Dold-Samplonius et al., Boethius, vol. 46 (Stuttgart: Steiner Verlag, 2002), 33–35.


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Thus Indian mathematical science had by this time, shortly after the middle of the first millennium a.d., fully assimilated those parts of the sexagesimal place-value system that it adopted. But as far as we can tell from the texts, that adoption was long delayed. Indian astronomers may have worked for as much as half a millennium with Mesopotamian concepts and tools, without absorbing their units and numbers also.30 Ultimately, the full integration of Indian decimal and Mesopotamian sexagesimal numeration seems to have been impelled in a roundabout way by the lure of Hellenistic astrology.

30. It has recently been argued (see Falk, “Measuring Time.”) that the hypothesis of any significant pre-Hellenistic Mesopotamian influence on Indian science should be discarded or reversed. But this approach is less satisfactory in accounting for the resemblances between the two traditions.

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References Berggren, J. Lennart. “Ancient and Medieval Approximations to Irrational Numbers.” In From China to Paris: 2000 Years Transmission of Mathematical Ideas, edited by Yvonne Dold-Samplonius et al., 31–44. Stuttgart: Steiner Verlag, 2002. Brown, David, and Harry Falk. The Interactions of Ancient Astral Science. Vergleichende Studien zu Antike und Orient, vol. 3. Bremen: Hempen, forthcoming. Dvived¯ı, Sudh¯ akara. Br¯ ahmasphut.asiddh¯ anta. The Pandit n.s. 23–24 (1901–1902). Eggeling, Julius. Satapatha - Brahmana According to the Text of the Madhyandina School. Vol. 4. Sacred Books of the East, vol. 43. Oxford: Oxford University Press, 1897. Falk, Harry. “Measuring Time in Mesopotamia and Ancient India.” Zeitschrift der Deutschen Morgenl¨ andischen Gesellschaft 150 (1) (2000), 107–132. ———. “The Yuga of Sphujiddhvaja and the Era of the Kusanas.’ Silk Road Art and Archaeology 7 (2001): 121–36. Hayashi, Takao. The Bakhsh¯ al¯ı Manuscript. Groningen: Egbert Forster, 1995. Høyrup, Jens. Lengths, Widths, Surfaces: a Portrait of Old Babylonian Algebra and Its Kin. Studies and Sources in the History of Mathematics and Physical Sciences. New York: Springer, 2002. Justus, Carol. “Numeracy and the German Upper Decades.” Journal of Indo-European Studies 24 (1996): 45–80. Available at http:// www.utexas.edu/cola/depts/lrc/numerals/cfj-jies/cfj1-section1. html. Neugebauer, Otto, and David Pingree. The Pa˜ ncasiddh¯ antik¯ a of Var¯ ahamihira, 2 vols. Copenhagen: Danish Royal Academy, 1970–1971. Ohashi, Yukio. “The Legends of Vasis.t.ha – A Note on the Ved¯anga ˙ Astronomy.” In History of Oriental Astronomy, edited by Razaullah Ansari, 75–82. Dordrecht: Kluwer, 2002. Pingree, David. “The Mesopotamian Origin of Early Indian Mathematical Astronomy.” Journal for the History of Astronomy 4 (1973): 1–12. ———. “History of Mathematical Astronomy in India.” In Dictionary of Scientific Biography, vol. 15, 533–633. New York: Scribner’s, 1978. ———. The Yavanaj¯ ataka of Sphujidhvaja. 2 vols. Cambridge, Massachusetts: Harvard University Press, 1978.


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———. “Babylonian Planetary Theory in Sanskrit Omen Texts.” In From Ancient Omens to Statistical Mechanics: Essays on the Exact Sciences Presented to Asger Aaboe, edited by J. Lennart Berggren and Bernard Goldstein, 91–99. Copenhagen: Munksgaard, 1987. ———. “Venus Omens in India and Babylon.” In Language, Literature, and History: Philological and Historical Studies Presented to Erica Reiner, edited by Francesca Rochberg-Halton, 293–315. New Haven, Connecticut: American Oriental Society, 1987. ———. “mul.apin and Vedic Astronomy.” In dubu-e2 -dub-ba-a: Studies in Honor of ˚ Ake W. Sj¨ oberg, edited by Hermann Behrens et al., 439–45. Philadelphia: University Museum, 1989. ———. “Zero and the Symbol for Zero in Early Sexagesimal and Deciúnya, edited by mal Place-Value Systems.” In The Concept of S¯ Amulya Kumar Bag and Sreeramula Rajeswara Sarma, 137–41. New Delhi: IGNCA/INSA, 2003. Robson, Eleanor. Mesopotamian Mathematics, 2100–1600 b.c.: Technical Constants in Bureaucracy and Education. Oxford Editions of Cuneiform Texts, vol. 14. Oxford: Clarendon Press, 1999. ´ Sen, Samarenda Nath, and Amulya Kumar Bag. The Sulbas¯ utras. New Delhi: Indian National Science Academy, 1983. Thibaut, George, and Sudh¯ akara Dvived¯ı. The Pa˜ nchasiddh¯ antik¯ a of Var¯ aha Mihira. Second edition. Chowkhamba Sanskrit Studies, vol. 68. Varanasi: Chowkhamba Sanskrit Series, 1968. Witzel, Michael. “Substrate Languages in Old Indo-Aryan (Rgvedic, Middle and Late Vedic).” Electronic Journal of Vedic Studies 5, no. 1 (1999): 1–67. Available at http://www1.shore.net/˜india/ ejvs/ejvs0501/ejvs0501article.pdf.

In Praise of the Just Erica Reiner University of Chicago

A strange text published over thirty years ago under the title “A Piece of Esoteric Babylonian Learning” has remained without parallel and without adequate interpretation over the years.1 The tablet, BM 34110 + 35163, copied in the third year of Nabonidus, from a red baked original,2 has not given up all of its secrets, but I believe I can contribute somewhat to its understanding. The outward appearance of the tablet is unusual and at first glance misleading. On the obverse, horizontal rulings divide it into units of two lines; two vertical rulings separate each distich by a “middle column” that contains a single word only. The beginning of the reverse is broken, and the first two preserved sections seem to continue the pattern observed on the obverse—that is, a narrow “middle column” interrupts each line, but only traces of one sign, or rather of a drawing, remain visible in this “middle column” of the second section. The first line on the reverse, only partially preserved, is the last line of a section and is followed by a ruling; the second half of the line may be read as [ˇsa] iz-[zi-qa-´ aˇs-ˇsu ´ ] im [dingir] an x [x x]. The “middle column” of the next section of five lines is, as just described, blank but for traces of a drawing near lines 2–3 of this section. These five lines are followed by a single line that stretches across the width of the tablet, possibly as a catch line, and by the colophon. On the obverse, each two-line section is interrupted in the middle by one word that sits on the line which is that section’s first; each of these words is a name, either the name of a Kassite king or of, presumably, a scholar.3 It is this peculiar feature of a “middle column” that has obscured, in my opinion, the interpretation of the seven distichs preserved on the ob1. Wilfred Lambert, “A Piece of Esoteric Babylonian Learning,” Revue d’Assyriologie 68 (1974): 149–56. 2. See The Assyrian Dictionary, s.v. s¯ amu, a.11’. 3. Lambert, “A Piece of Esoteric Babylonian Learning,” 155.

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verse. In his edition, Lambert opined that “the text in the sub-columns to the left and right of each name seems to be mutually unrelated.”4 In fact, the text, though it is interrupted by the “middle column” that contains a name, can be shown to make excellent sense if read across, skipping the name in the middle. While several couplets have been cited and translated in various volumes of The Assyrian Dictionary, the entire text of the obverse has not yet been presented as a whole. It is a pleasure to offer these Babylonian words of wisdom to Alice Slotsky.

Transliteration of Obverse

§1

[ . . . . ] x kit-ti lu-´ u ˇsa ba-s.i ul u ´-sah -h a ˇsa-a-r [u] ˘ ˘ za-q´ı-q´ı u [ . . . ] x la kit-ti lu-´ u ˇsa erˆı urudu i-na ´-tab-bat d 3 [ . . . ] x ki-nim lu-´ u ˇsa lipˆı (`ı.udu) bil.gi ul tum pap5 4 [ ] dlu-´ u e ˇsa sê (na4 .kala.ga) i-na ra-a-di u ´-tab-bat 5 [ . . . ] x a i-t.eb-bu rag-gu ´ .gur8 ) la til-lat b¯ 6 [ ] tam-tim i-na magurri (giˇ s.ma a’iri ´ .ˇ (lu su.ha) ib-bir ki-nu 7 [. . . . .˘ . .] x lu-´ u pe-tu-´ u bu-tuq-tu ul [ubbal (?)6 ] 8 [ . . . ]-´ u lu-´ u ku-ub-bu-ru ˇsu-ru-uˇs x [ . . . ] 9 [ . . . lu] qut-tu-rat i-nam-mir ki [n¯ unˇsu] (k[i.ne-ˇsu]) 10 [ . . . lu i ]ˇs-tap-pu uk-tap-pa-ru [ . . . ] 11 [ . . . ] .sar iz-za-az [ 12 [ . . . d ]a-at i-ma-aq-qut [ . . . ] 13 [ . . . k ]i (?)-nim ul i-nu-uˇs-ˇs´ a i-na m[i-h e-e(?)] ˘aˇsu(?)] 14 [ . . . la kit]-ti qal-liˇs in-na-as-sa-h [a iˇsd¯ ˘ obverse broken. 1

2

§2 §3

§4 §5 §6 §7 Rest of

4. Ibid., 155. 5. I am unable to suggest a convincing reading or emendation for the last two signs; we expect a word such as uˇsharmat. (from naharmut.u) ‘melt’ (the tallow), or ˘ or the like. ˘ a form of the verb ak¯ alu ‘to consume,’ 6. The trace after ul looks more like a vertical than any sign compatible with a reading ubbal.

In Praise of the Just

§1

1 2

§2

3 4

§3

5 6

§4

7 8

§5

9 10

§6

11 12

§7

13

14

209

Translation of Obverse A true [. . . ], be it of sand, the wind cannot disturb it; an untrue [. . . ], be it of copper, will be thrown over by a breeze.7 [. . . of] a true [. . . ], be it of tallow, fire will not melt (it) [. . . of an untrue . . . ], be it of diorite, will be destroyed in a downpour.8 [In . . . ] the evil man will sink [in the . . . ] of the sea in a boat of no use (even) to a fisherman the just man will cross (safely)9 [. . . ] be it open, a breach will not [. . . ], [. . . ] be it thick, [will be torn out (?) by] the root [The . . . ] be it smoky, his hearth will be bright, [. . . ] be it glowing(?) will be cut off [. . . ]10 [. . . ] will stand [. . . ] [. . . ] will fall [. . . ] [The . . . ] of(?) the loyal(?) [. . . ] will not sway in [a storm] [. . . of the dis]loyal (person), [his roots (?)] will be torn out easily.11

The key terms in this text are k¯ınu and kittu which can be translated variously as ‘just,’ ‘true,’ ‘genuine,’ and the like. They are opposed to [la] k¯ınu and la kitti, that is, ‘unjust,’ ‘untrue,’ ‘false,’ ‘disloyal,’ and the like, and once to raggu, of like meaning. These keywords appear in each stanza, unless the pertinent part of the line is not preserved, as in stanzas 4, 5, and 6; to choose the appropriate English translation is difficult wherever the referent of the attribute—presumably a person—is not preserved and cannot be ascertained. Thus, my translations just/unjust, true/untrue, loyal/disloyal are often only guesses and would surely have to be modified if a more complete text were found. As to the reverse of the tablet, I am unable to offer an interpretation that goes beyond the one given by Lambert;12 it does seem that the material on the reverse is of a different nature than that on the obverse 7. The Assyrian Dictionary, s.v. seh u ˆ, 2.a.3’. ˘ poetic license and is not meant to identify 8. My translation “diorite” is used by the ˇsu-stone; the line is translated in The Assyrian Dictionary, s.v. sˆ u, A.a.3’ and s.v. r¯ adu, a.3’. 9. The Assyrian Dictionary, s.v. tillatu, 2.a and s.v. .tebˆ u, 1.b. 10. The Assyrian Dictionary, s.v. qatturu and s.v. ˇsapˆ u, A.1.a.2’. 11. The couplet was quoted in The Assyrian Dictionary, s.v. nˆ aˇsu, 3 and (with slight variation) s.v. qalliˇs. 12. Lambert, “A Piece of Esoteric Babylonian Learning,” 151–53.

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and no longer deals with contrasts. Neither can I explain the presence of the names that appear between the two halves of the first line of the eight distichs on the obverse. This text has not yet given up all of its secrets. I regret that I am not able to dispel any more of its obscurities. References Lambert, Wilfred. “A Piece of Esoteric Babylonian Learning.” Revue d’Assyriologie 68 (1974): 149–56.

The Long Career of a Favorite Figure: The apsamikku in Neo-Babylonian Mathematics Eleanor Robson University of Cambridge

Introduction ` .m´ı, or concave square, is a The apsamikkum, (gana2 ) geˇ stug2 .za well-known geometrical figure in Old Babylonian (OB) mathematics (see figure 14.1).1 It features in eleven entries from five coefficient lists of technical constants; two, possibly four, illustrated statements of problems; and in two problems with worked solutions.2 From this evidence it has been deduced that the apsamikkum was composed of four identical quarter-arcs, as if four identical circles were placed tangent to each other. Its main components are the external arc (sag, p¯ utum) of length 1; the diagonal (dal, tallum), running corner-to-corner, of length 1;20; and the short transversal (pirkum), running across the narrowest part of the figure, of length 0;33 20. Its area is 0;26 40, or 94 , of the arc squared.3 The exact etymology of the Akkadian word remains contentious, though the most plausible remains Goetze’s suggested derivation from ` .m´ı, ‘window of the lyre,’ clearly related to the SumeroSumerian ab za ` .m´ı, literally ‘ear of the lyre,’ both presumably refergram geˇ stug2 .za ring to a sound hole.4 As Anne Kilmer has pointed out, the figure is also highly reminiscent of the shape of the bovid’s noses on lyres from ´ b, the Early Dynastic Royal Cemetery of Ur, suggesting an etymology a ´ b.za ` .m´ı is ‘cow,’ rather than ab, ‘window.’5 However, the logogram a 1. Figure 14.1 is reproduced from Eleanor Robson, Mesopotamian Mathematics, 2100–1600 b.c.: Technical Constants in Bureaucracy and Education, Oxford Editions of Cuneiform Texts, vol. 14 (Oxford: Clarendon Press, 1999), 53, fig. 3.13. 2. See the Appendix for translations and publication details of all these occurrences. 3. Robson, Mesopotamian Mathematics, 17–21. 4. Albrecht Goetze, “A Mathematical Compendium from Tell Harmal,” Sumer 7 (1951): 139. 5. Anne Kilmer, “Sumerian and Akkadian Names for Designs and Geometrical

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Eleanor Robson

Figure 14.1: The Old Babylonian apsamikkum attested only in first-millennium liver omens,6 which implies a rather late folk etymology. Nevertheless the suggestion remains an attractive one. There are also Neo-Assyrian descriptions of the constellations Ursa Major and Cancer as ´ ap-s` a-ma-ak-ku,7 but without accompanying illustrations it is impossible to know how these were visualized. Shapes,” in Investigating Artistic Environments in the Ancient Near East, ed. Ann Gunter (New York: Smithsonian Institution, 1990), 88–89. 6. From Aˇsˇsurbanipal’s library at Nineveh: be ina egir n´ıg.tab g´ır ˇs´ a 2 30 uzu ´ b.za ` .m´ı-ma ra-is., ‘If there is a piece of flesh flattened like an apsamikku in the gim a rear of the Dyeing Vat to the left of the Path. . . .’ P¯ an t¯ akalti Tablet 2, lines 75, 76, 83 and 84, Aˇsˇsurbanipal colophon type 1, published in Ulla Koch-Westenholz, Babylonian Liver Omens: The Chapters Manz¯ azu, Pad¯ anu, and P¯ an t¯ akalti of the Babylonian Extispicy Series, Mainly from Aˇsˇsurbanipal’s Library, CNI Publications, vol. 25 (Copenhagen: The Carsten Niebuhr Institute of Near Eastern Studies), 308– 09. For the handcopy, see Reginald Campbell Thompson, Cuneiform Texts from Babylonian Tablets, etc. in the British Museum, vol. 20 (London: Longmans, et ´ b.za ` .m´ı, ‘If in the Throne Base there al., 1904), pl. 33. be ina ˇ sub aˇ s.ta uzu gim a is a piece of flesh like an apsamikku. . . .’ P¯ an t¯ akalti Tablet 9, line 49, published in Koch-Westenholz, Babylonian Liver Omens, 364; handcopy on pl. XXII (Sm 373). ´ b.za ` .m´ı-ma ra-is., ‘If the Wellbeing is flattened From Seleucid Uruk: be silim gim a like an apsamikku, . . . .’ P¯ an t¯ akalti Tablet 6, line 86, published in Koch-Westenholz, Babylonian Liver Omens, 352. For the handcopy, see Franç ois Thureau-Dangin, Tablettes d’Uruk a ` l’usage des prˆ etres du temple d’Anu au temps des S´ eleucides, Textes Cun´ eiformes de Louvre, vol. 6 (Paris: Librarie Orientaliste Paul Geunther, ` .nigin gim a ´ b.za ` .m´ı, ‘If the coils are like an apsamikku, 1922), pl. IX, ln. 35’. be ˇ sa ˇ . . . .’ Summa t¯ır¯ anu Tablet 3, line 27 in Albert Clay, Babylonian Records in the Library of J. Pierpont Morgan, vol. 4 (New Haven: Yale University Press, 1923), 32. Both tablets were written in year 99 of the Seleucid Era for Nidinti-Anu, son of Anu-b¯ elˇsunu, descendant of Ekur-z¯ akir, a ¯ˇsipu of Anu and Antu. 7. mul al.lul a ´p-ps` a q-[ma]-pak q-[ku], ‘Cancer is an apsamikku;’ mul mar.g´ıd.da a ´p-s` a-ma-ak-ku, ‘Ursa Major is an apsamikku’: VAT 9428 13, r4 from Assur, translated by Ernst Weidner, “Eine Beschreibung des Sternhimmels aus Assur,” Archiv f¨ ur Orientforschung 4 (1927): 73–85.

The Long Career of a Favorite Figure

213

Concave squares are also ubiquitous in Mesopotamian visual culture, from Halaf pottery of the sixth millennium b.c. to images of ˇ 77, an Neo-Assyrian textile designs.8 One is also identifiable in TSS Old Babylonian school tablet from Kisurra (itself perhaps a mathematical exercise).9 It is not surprising, then, to discover an apsamikku(m) in Neo-Babylonian (NB) guise on a mathematical tablet in the British Museum, on a tablet explicitly “written for the scribe [. . . ] to see.” I present a discussion of that tablet here in honor of Alice Slotsky’s work on Neo- and Late Babylonian scientific materials in the British Museum, and trust that she and her scholarship will remain as elegant, popular and productive as the apsamikku(m) for many years to come.10 BM 47431, a Neo-Babylonian Mathematical Exercise

(a) Obverse

(b) Reverse

Figure 14.2: BM 47431

8. Kilmer, “Sumerian and Akkadian Names.” 9. Marvin Powell, “The Antecedents of Old Babylonian Place Notation and the Early History of Babylonian Mathematics,” Historia Mathematica 3 (1976): 431, fig. 2. Manfred Krebernik, “Neues zu den Fara-Texten,” Nouvelles assyriologiques br` eves et utilitaires (2006): 15. 10. As always, I am very grateful to Christopher Walker for his identification and cataloging of the mathematical tablets in the British Museum, which brought this tablet to light. I also warmly thank Duncan Melville, who generously shared a preprint of his article, “The Area and the Side I Added: Some Old Babylonian Geometry,” Revue d’Histoire des Math´ ematiques 11 (2005), as well as Eckhart Frahm, KarlHeinz Kessler, Erica Reiner, Caroline Waerzeggers, and especially Michael Jursa, for invaluable advice on first-millennium orthography and lexicography. BM 47431 is published here with the kind permission of the Trustees of the British Museum.

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Eleanor Robson

Transliteration 1 2

3

4

5

6

7 8

ń ˇ ´ˇ 2 ba se.pnumun u sq.[sa].du ´ ` ˇ 1 ban 3 sıla se.[numun] 4-ta kip-pat ` se.pnumunq 4 sag.du 1 21 s`ıla ˇ pa-tar `> 7 12 ninda ˇ se.numun p4q sag.

From the Banks of the Euphrates: Studies in Honor of Alice Louise Slotsky

The End of Alice

The End of Alice

The Awakening of Alice

The Madness of Alice

The Madness of Alice

The Banks of the Nile

The Euphrates Cipher

In the Name of Honor

In the Name of Honor

In the Name of Honor

In the Name of Honor

In the Name of Honor

In The Name Of Honor

In the Name of Honor

In the Name of Honor

In the Name of Honor

In the Name of Honor

in the Name Of Honor

In the Name of Honor

In the Name of Honor

In the Name of Honor

Alice in Jamesland: The Story of Alice Howe Gibbens James

The Nature of the Word: Studies in Honor of Paul Kiparsky (Current Studies in Linguistics)

The Evolution of Central Banks

The Ghost From The Grand Banks

The Liberation of Alice Love

The Liberation of Alice Love

The Liberation of Alice Love

The Stories of Alice Adams

The Liberation of Alice Love

From the Banks of the Euphrates: Studies in Honor of Alice Louise Slotsky

The End of Alice

The End of Alice

The Awakening of Alice

The Madness of Alice

The Madness of Alice

The Banks of the Nile

The Euphrates Cipher

In the Name of Honor

In the Name of Honor

In the Name of Honor

In the Name of Honor

In the Name of Honor

In The Name Of Honor

In the Name of Honor

In the Name of Honor

In the Name of Honor

In the Name of Honor

in the Name Of Honor

In the Name of Honor

In the Name of Honor

In the Name of Honor

Alice in Jamesland: The Story of Alice Howe Gibbens James

The Nature of the Word: Studies in Honor of Paul Kiparsky (Current Studies in Linguistics)

The Evolution of Central Banks

The Ghost From The Grand Banks

The Liberation of Alice Love

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The Liberation of Alice Love

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