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Methodological Issues concerning the Astronomy of Qumran

In: Dead Sea Discoveries
Author: Eshbal Ratzon1
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  • 1 The Cohn Institute for the History and Philosophy of Science and Ideas, Tel Aviv Universityeshbal@gmail.com
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In the 21st issue of Dead Sea Discoveries, Dennis Duke and Matthew Goff offered their collaboration as physicist and Dead Sea Scrolls scholar in order to study the lunar theory of the Aramaic Astronomical Book (aab). They use the astronomical model of lunar elongation—the angular distance between the moon and the sun on the observed heavenly sphere—to compute the times of the moon’s visibility and invisibility. They conclude that the times written on the Aramaic fragments are closer to reality than the times written in the Babylonian sources of the aab. This paper concludes that lunar elongation is not the best explanation of the astronomical data of the aab, and Duke and Goff’s computations should be refined according to some astronomical, cosmological, textual, and historical considerations.

Abstract

In the 21st issue of Dead Sea Discoveries, Dennis Duke and Matthew Goff offered their collaboration as physicist and Dead Sea Scrolls scholar in order to study the lunar theory of the Aramaic Astronomical Book (aab). They use the astronomical model of lunar elongation—the angular distance between the moon and the sun on the observed heavenly sphere—to compute the times of the moon’s visibility and invisibility. They conclude that the times written on the Aramaic fragments are closer to reality than the times written in the Babylonian sources of the aab. This paper concludes that lunar elongation is not the best explanation of the astronomical data of the aab, and Duke and Goff’s computations should be refined according to some astronomical, cosmological, textual, and historical considerations.

In the 21st issue of Dead Sea Discoveries, Dennis Duke and Matthew Goff offered their collaboration as physicist and Dead Sea Scrolls scholar in order to study the lunar theory of the Aramaic Astronomical Book (aab). The aab is a very early version of a book that was also preserved in a somewhat different form as the third section of the Ethiopic Book of Enoch (1 Enoch). Duke and Goff’s interdisciplinary approach is necessary in the field of the History of Science in general and in the scholarly examination of the Astronomical Book in particular. In their paper, Duke and Goff attempt to reconstruct the calculations that may have resulted in the numerical values for the times of the moon’s visibility and invisibility during day and night, detailed in a document called the “Synchronistic Calendar,” found in the Qumran fragments of 4Q208 and 4Q209 of the aab. Duke and Goff use the astronomical model of lunar elongation—the angular distance between the moon and the sun on the observed heavenly sphere—to compute the times of the moon’s visibility and invisibility. They conclude that the times written on the Aramaic fragments are closer to reality than the times written in the Babylonian sources of the aab, some of which are known to us from tablet xiv of the astronomical collection the Enuma Anu Enlil (eae).

Duke and Goff explain the discrepancy between the times in the aab and the eae in terms of two computational differences. First, the aab assumes an average month of 29.5 days, whereas the eae assumes idle months of 30 days each; second, while the eae assumes that during the time between sunset and moonset the elongation remains constant, the aab corrects this assumption, taking into account the moon’s constant velocity, and thus a variable elongation.1 Although the first difference is well documented by previous research, their second observation proposes a new approach the subject. However, in order to assess whether Duke and Goff’s approach fits the Qumranic text, several methodological issues must be examined.

Day-Night Ratio

From page 194 onwards, Duke and Goff base their computations on the assumption that “sunset to sunrise is always 1/2 a day.”2 This assumption is astronomically incorrect. The time from sunset to sunrise equals 1/2 a day only on the equinoxes. Aside from those two days, the ratio of daytime hours to nighttime hours changes with the seasons. This phenomenon is schematically described in 1 Enoch 72. There, the whole day is divided into 18 equal parts. At the equinoxes, day and night each have nine equal parts. As summer progresses the number of daytime hours increases by one part each month—at the expense of the same number of nighttime hours—until, at the summer solstice, the day consists of 12 parts, and the night consists of six (a ratio of 2:1). The opposite occurs—the number of nighttime hours increases at the expense of the length of the day—as the winter approaches.

It is true that this treatise of seasonal changes in daytime and nighttime hours exists today only in the Ethiopic version of the book, which varies significantly from the Aramaic version.3 However, it is very likely that this treatise also existed in the Aramaic. It is highly improbable that the origin of this chapter is Ethiopic, as Ethiopia’s proximity to the equator renders such seasonal differences virtually unnoticeable there. Additionally, other Babylonian astronomical texts also identify the 1:2 ratio of daytime hours to nighttime hours in the winter, and the 2:1 ratio in the summer. One such text is table C of eae xiv, which is recognized as one of the sources of the aab.4 Furthermore, there seem to be shared concepts between the aab and 1 Enoch 72, strengthening the argument that the authors of the aab were aware of the variations in length of daytime and nighttime during a year. 1 Enoch 72 describes a set of twelve heavenly gates standing on the eastern and western edges of the earth for the passage of the sun and moon while rising and setting. These gates are also assumed by the aab.5 Taking all the above into account, it is very plausible that the authors of the aab were also familiar with the changes in the ratio of daytime hours to nighttime hours during the cycle of the year. The authors’ assumption that “sunset to sunrise is always 1/2 a day” does not acknowledge the inherent contradictions that this assumption creates between the aab and the Ethiopic version of 1 Enoch, between the aab and the eae, and between the aab and reality. It is this assumption that lies at the foundation of their conclusions, as every inference that Duke and Goff draw in their paper—including the values provided in tables 4–6, which should match those of 4Q208 and 4Q209—derives from the assumption that “sunset to sunrise is always 1/2 a day.”6

Precision

Duke and Goff present their results in a table demonstrating how the outcomes from their calculations “match exactly those read in 4Q208–209.”7 At first glance this is an impressive achievement, and might make us consider the possibility that the calculations at the foundation of the Aramaic scrolls’ analysis of moon visibility did not take into consideration the variations in the length of daytime and nighttime hours. However, the way Duke and Goff present the tables is too optimistic. In order to achieve these results the authors selected an initial value of elongation at the beginning of the month (α) that would make these calculations possible. This value has no textual base in the scrolls; rather, it was only added so that the results would match the numerical values found in them. Thus, Duke and Goff’s reliance on this matching to support their own astronomical and mathematical model would be a circular argument. In addition, the results presented by the authors in the tables are rounded, thus they are presented as if they were the same as those values recorded in the scroll, but are actually only close approximations. For example, the value of ss2mr (sunset to moonrise) in table 4 computed from their calculations for day 2 is not exactly 1, but 17/57, for day 3 the value is not 11/2, but 1708/1140. While the exact values are not far from those that bolster the authors’ argument, providing rounded estimates as opposed to exact values removes evidence that would be helpful in evaluating their theory.

Matching the Data from aab

Duke and Goff claim that the numerical values that they compute match the data in Henryk Drawnel’s edition of the aab. Yet, even if one accepts the random α values and the rounded results, a closer examination of the numbers provides cause for greater concern. Duke and Goff acknowledge that according to their theory a “full moon never occurs on day 15 of any month.”8 However, 4Q209 offers evidence for the existence of such a month. Drawnel has demonstrated that two kinds of months exist in the aab, which follow two patterns: Pattern i fits 29-day hollow months, in which the full moon turns out on the 14th day of the month; Pattern ii fits 30-day full months, in which a full moon presents on the 15th day of the month.9 Drawnel bases his theory mainly on 4Q209. 4Q209 7 ii preserves the numerical values (using the acronyms denoted by Duke and Goff ):10

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Continuing the numbers backwards will give us a full moon on day 15:

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In addition, in section 4 of their paper, Duke and Goff discuss the relation between the eae and the aab. They posit that “it seems statistically odd that of the eight surviving fragments that we have used, at least seven and possibly eight attest a 30 day month.”11 Indeed, while demonstrating the consistency between their results and the data found in the aab, the authors quote all values from the aab to be from the same kind of month (a full month of 30 days).12 However, days 8–9 are taken from 4Q209 7 iii, belonging to Drawnel’s Pattern i (i.e.: 29-day months, with the full moon on the 14th day), while days 24–27 are taken from the previous month preserved in 4Q209 7 ii, belonging to Drawnel’s Pattern ii (i.e.: 30-day months, with the full moon on the 15th day).

Mathematical Complexity

Though in modern terms, Duke and Goff use simple mathematical calculations, their methods are much too complicated for the ancient authors of the aab. The authors employ mathematical variables, a relatively recent mathematical tool, and substitute them for functions, another modern mathematical tool. Even their use of simpler mathematical operations, such as addition, subtraction, multiplication, and division of fractions is more difficult than the mathematical knowledge applied in the Dead Sea Scrolls. Despite the fact that each one of these simpler operations is demonstrated individually in the Dead Sea Scrolls, and even in the aab,13 the combination of all four operations in a single computation is not found in any fragment of the scrolls. The assumption that this mathematical knowledge existed in Second Temple Judea, but is not documented on any surviving scrolls, needs further evidence.

Lunar Elongation

Though the particular mathematics that Duke and Goff employ do not represent the ancient mathematical procedure leading to the numerical values found in the aab, the basic idea that lunar elongation was the astronomical model at the basis of the aab deserves a separate discussion. Lunar elongation is the angular distance between the sun and the moon on the heavenly sphere, and more specifically on the ecliptic circle lying on the heavenly sphere. From a modern astronomical point of view, the times of day and night at which the moon rises and sets are clearly dependent on lunar elongation. However, it is important to assess whether the computations of the aab took this phenomenon into consideration.

Otto Neugebauer understood the Ethiopic version of 1 Enoch 73:5, 8, and 78:10–14 as referring to lunar elongation.14 However, the main focus of Duke and Goff’s paper is the Aramaic Astronomical Book, not its Ethiopic version, so this paper will not address the question of whether Neugebauer’s explanation is correct. In the Aramaic fragments from Qumran the main focus is on the temporal aspects of lunar theory, comparing the times of the rising and setting of the moon with the rising and setting of the sun. All references to the phenomenon of lunar elongation are completely absent from the aab.

As the aab has not been well preserved, the absence of a mention of lunar elongation might be a coincidence; but a more probable explanation is that the absence of this term is related to the entirely different cosmology reflected in the aab fragments. The celestial sphere is a Greek concept,15 not known to the authors of the Book of Enoch,16 and not even used by their contemporary Babylonian astronomers. Admittedly, the Babylonian astronomers of the Persian and Hellenistic times did develop the zodiac, lying on the ecliptic, however, without the assumption of a celestial sphere.17 Lately, several scholars have demonstrated a familiarity of the authors of the aab with the Babylonian zodiac. These scholars do not claim that the aab adopted the zodiac as is, but instead used a projection of its signs on the horizon, calling them “gates.”18 These gates are described as openings in the firmament standing on the edges of a flat earth. As the spatial aspects of the lunar theory are discussed only from the horizontal point of view—and as far as we know, lunar elongation is not at all mentioned in the aab—it is implausible to assume that lunar elongation was the basic concept underlying the entire computations of the lunar theory represented in the aab.

Moreover, the aab’s theory on what happens to setting luminaries also contradicts the theory of lunar elongation. Lunar elongation assumes that the paths of the moon and sun are a circle around the earth; the aab posits that after setting, all luminaries went back eastwards above the firmament through the northern areas of the sky (1 Enoch 72:5; 4Q209 23 6; 4Q210 1 ii 2a 17), thus not moving in a circular movement.19

Conclusion

In conclusion, Duke and Goff’s theory is in need of substantial methodological refinement based on mathematical, astronomical, and textual considerations. Despite the problems with their theory, their work offers an advantage to further research on the aab. Not many published papers attempt to approach the Astronomical Book with serious astronomical and mathematical tools. Duke and Goff try to build an astronomical model to explain the numerical values found in the fragmented scrolls, and want to explain all the data, without the “excuse” of scribal errors. Even if their particular model is probably not the best reconstruction of the original one, we can only hope that other scholars will follow their lead and continue to apply an interdisciplinary approach while studying this complicated text.

1 Dennis Duke and Matthew Goff, “The Astronomy of the Qumran Fragments 4Q208 and 4Q209,” dsd 21 (2014): 176–210.

2 Duke and Goff, “Astronomy,” 194.

3 The Astronomical Book is the third section of 1 Enoch, which like the rest of the booklets, was translated from the Aramaic original through a Greek translation into Gəʿəz during the 4th to the 6th centuries ce. However, the Gəʿəz version of this booklet is significantly different from the fragmentary Aramaic scrolls found in the caves of Qumran. For a summary of the scholarly discussion of the Ethiopic translation of the Book of Enoch see George W. E. Nickelsburg, 1 Enoch: A Commentary on the Book of 1 Enoch, Chapters 1–36; 81–108 (Hermenia; Minneapolis: Fortress Press, 2001), 15–17, and more recently Eshbal Ratzon, “The Conception of the Universe in the First Book of Enoch” (Ph.D. Diss., Tel Aviv University, 2012), 45–48. For a discussion of the Ethiopic version of the Astronomical Book see James VanderKam’s discussion in: George W. E. Nickelsburg & James C. VanderKam, 1 Enoch 2 (Hermenia; Minneapolis: Fortress Press, 2012), 350–6.

4 Farouk N. H. Al-Rawi and A. R. George, “Enuma Anu Enlil xiv and Other Early Astronomical Tables,” AfO 38–39 (1991–1992): 52–69.

5 Each one of the six gates is mentioned in the Aramaic manuscripts: the first gate in 4Q208 1 4 (לתרע]א֯ קדמיא ) and 4Q209 7iii 2 (בתרעא קדמיא); the second in 4Q209 7ii 8 (לתרעא תנינא) and in line 10 (תרעא תנינא); the third in 4Q209 3 7 (לתרעא תליתֹ[יא) and 4Q209 16 2 (ל]תרעא תֹליתיאֹ[); the fourth in 4Q208 24 3 (תרע]א רביעיא); the fifth in 4Q209 7iii 6 (לתרעא חמישיא) and in line 8 (תרעא [ח]מ֯י֯[שיא); and the sixth in 4Q208 33 2 (תרעא] שתיתיא) and 4Q209 26 2 (]בֹתרעא שתיתיא).

6 Duke and Goff, “Astronomy,” 194–201.

7 Duke and Goff, “Astronomy,” 197.

8 Duke and Goff, “Astronomy,” 193.

9 Henryk Drawnel, The Aramaic Astronomical Book (4Q208–4Q211) from Qumran (Oxford: Clarendon, 2011), 421–424, 440–453.

10 Duke and Goff, “Astronomy,” 182. The acronyms mean: ss2mr = sunset to moonrise; mr2sr = moonrise to sunrise; sr2ms = sunrise to moonset; ms2ss = moonset to sunset; dark frac. = dark fraction of the moon.

11 Duke and Goff, “Astronomy,” 204.

12 Duke and Goff, “Astronomy,” 197–200.

13 Thus, the “Synchronistic Calendar” itself describes the growth and reduction of lunar visibility and the change in the phases of the moon through addition and subtraction of halves of sevenths every day; 4Q211, the fourth copy of the aab, develops a stellar theory through a multiplication of different kinds of fractions.

14 Otto Neugebauer, “The ‘Astronomical’ Chapters of the Ethiopic Book of Enoch (72 to 82)” in The Book of Enoch or 1 Enoch (ed. M. Black; Studia in Veteris Testamenti Pseudepigrapha, 7; Leiden: Brill, 1985), 397, 409.

15 This is a well known detail that is mentioned in many publications, for example see: Daryn Lehoux, “Astronomy,” The Oxford Encyclopedia of Ancient Greece and Rome, n.p. [cited 24 August, 2014]. Online: http://www.oxfordreference.com/view/10.1093/acref/9780195170726.001.0001/acref-9780195170726-e-132?rskey=a2AShA&result=132.

16 Ratzon, “The Conception of the Universe”, 256–258.

17 Wayne Horowitz, Mesopotamian Cosmic Geography (Winona Lake, Ind.: Eisenbrauns, 1998), 264–265.

18 Lis Brack-Bernsen and Herman Hunger, “The Babylonian Zodiac: Speculations on its Invention and Significance,” Centaurus 41 (1999): 280–292 compared the aab gates to a hypothesized Babylonian horizontal origin of the zodiac; Jonathan Ben-Dov, Head of All Years: Astronomy and Calendars at Qumran in Their Ancient Context (stdj 78; Leiden – Boston: 2008): 185–189 first suggested that the gates are in fact a projection of the signs of the zodiac on the horizon. Further evidence and development of this argument is found in Eshbal Ratzon, “The Gates for the Sun and Moon in the Astronomical Book of Enoch,” Tarbiz 82,4 (2014): 497–512 [Hebrew]; eadem, “The Gates Cosmology of the Astronomical Book of Enoch,” dsd 22 (2015): 93–111.

19 Ratzon, “The Conception of the Universe”, 177; Drawnel, Aramaic Astronomical Book, 362.

  • 2

    Duke and Goff, “Astronomy,” 194.

  • 6

    Duke and Goff, “Astronomy,” 194–201.

  • 7

    Duke and Goff, “Astronomy,” 197.

  • 8

    Duke and Goff, “Astronomy,” 193.

  • 9

    Henryk Drawnel, The Aramaic Astronomical Book (4Q208–4Q211) from Qumran (Oxford: Clarendon, 2011), 421–424, 440–453.

  • 10

    Duke and Goff, “Astronomy,” 182. The acronyms mean: ss2mr = sunset to moonrise; mr2sr = moonrise to sunrise; sr2ms = sunrise to moonset; ms2ss = moonset to sunset; dark frac. = dark fraction of the moon.

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  • 11

    Duke and Goff, “Astronomy,” 204.

  • 12

    Duke and Goff, “Astronomy,” 197–200.

  • 14

    Otto Neugebauer, “The ‘Astronomical’ Chapters of the Ethiopic Book of Enoch (72 to 82)” in The Book of Enoch or 1 Enoch (ed. M. Black; Studia in Veteris Testamenti Pseudepigrapha, 7; Leiden: Brill, 1985), 397, 409.

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  • 16

    Ratzon, “The Conception of the Universe”, 256–258.

  • 17

    Wayne Horowitz, Mesopotamian Cosmic Geography (Winona Lake, Ind.: Eisenbrauns, 1998), 264–265.

  • 18

    Lis Brack-Bernsen and Herman Hunger, “The Babylonian Zodiac: Speculations on its Invention and Significance,” Centaurus 41 (1999): 280–292 compared the aab gates to a hypothesized Babylonian horizontal origin of the zodiac; Jonathan Ben-Dov, Head of All Years: Astronomy and Calendars at Qumran in Their Ancient Context (stdj 78; Leiden – Boston: 2008): 185–189 first suggested that the gates are in fact a projection of the signs of the zodiac on the horizon. Further evidence and development of this argument is found in Eshbal Ratzon, “The Gates for the Sun and Moon in the Astronomical Book of Enoch,” Tarbiz 82,4 (2014): 497–512 [Hebrew]; eadem, “The Gates Cosmology of the Astronomical Book of Enoch,” dsd 22 (2015): 93–111.

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  • 19

    Ratzon, “The Conception of the Universe”, 177; Drawnel, Aramaic Astronomical Book, 362.

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