Ancient Babylonian astronomers calculated Jupiter’s position from the area under a time-velocity graph
Babylonian astronomers tracked Jupiter
Ancient Babylonian astronomers developed many important concepts that are still in use, including the division of the sky into 360 degrees. They could also predict the positions of the planets using arithmetic. Ossendrijver translated several Babylonian cuneiform tablets from 350 to 50 BCE and found that they contain a sophisticated calculation of the position of Jupiter. The method relies on determining the area of a trapezium under a graph. This technique was previously thought to have been invented at least 1400 years later in 14th-century Oxford. This surprising discovery changes our ideas about how Babylonian astronomers worked and may have influenced Western science.
Science, this issue p. 482
Abstract
The idea of computing a body’s displacement as an area in time-velocity space is usually traced back to 14th-century Europe. I show that in four ancient Babylonian cuneiform tablets, Jupiter’s displacement along the ecliptic is computed as the area of a trapezoidal figure obtained by drawing its daily displacement against time. This interpretation is prompted by a newly discovered tablet on which the same computation is presented in an equivalent arithmetical formulation. The tablets date from 350 to 50 BCE. The trapezoid procedures offer the first evidence for the use of geometrical methods in Babylonian mathematical astronomy, which was thus far viewed as operating exclusively with arithmetical concepts.
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Supplementary Material
Summary
Materials and Methods
Figs. S1 to S4
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File (ossendrijver.sm.pdf)
References and Notes
1
O. Neugebauer, Astronomical Cuneiform Texts (Lund Humphries, London, 1955).
2
M. Ossendrijver, Babylonian Mathematical Astronomy: Procedure Texts (Springer, New York, 2012).
3
Britton J. P., Studies in Babylonian lunar theory: Part III. The introduction of the uniform zodiac. Arch. Hist. Exact Sci. 64, 617–663 (2010).
4
J. Høyrup, Lengths, Widths, Surfaces. A Portrait of Old Babylonian Algebra and Its Kin (Springer, New York, 2002).
5
A. A. Vaiman, Shumero-Vavilonskaya matematika III-I tysyacheletiya do n. e. (Izdatel’stvo Vostochnoy Literatury, Moscow, 1961).
6
J. Friberg, Mathematik, sec. 5.4k, Partitioned trapezoids and trapezoid stripes, in Reallexikon der Assyriologie, D. O. Edzard, Ed. (De Gruyter, Berlin, 1990), vol. 7, pp. 561–563.
7
J. Friberg, A Remarkable Collection of Babylonian Mathematical Texts. Manuscripts in the Schøyen Collection: Cuneiform Texts I (Springer, New York, 2007).
8
Materials and methods are available as supplementary materials on Science Online.
9
Huber P. J., Zur täglichen Bewegung des Jupiter nach babylonischen Texten. Z. Assyriol. 52, 265–303 (1957).
10
O. Neugebauer, Mathematische Keilschrifttexte, I–III (Springer, Berlin, 1935–1937).
11
Friberg J., Mathematics at Ur in the Old Babylonian period. Rev. Assyriol. Archeol. Orient. 94, 97–188 (2000).
12
O. Pedersen, Early Physics and Astronomy. A Historical Introduction (Cambridge Univ. Press, Cambridge, 1974).
13
E. D. Sylla, The Oxford calculators, in The Cambridge History of Later Medieval Philosophy, N. Kretzmann, A. Kenny, J. Pinborg, Eds. (Cambridge Univ. Press, Cambridge, 1982), pp. 540–563.
14
Freeth T., Jones A., Steele J. M., Bitsakis Y., Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism. Nature 454, 614–617 (2008).
15
A. Jones, Astronomical Papyri from Oxyrhynchus (American Philosophical Society, Philadelphia, 1999).
16
E. Leichty, Catalogue of the Babylonian Tablets in the British Museum, vol. VI, Tablets from Sippar 1 (1986).
17
M. Dietrich, Die neubabylonischen Konjunktionen, in Lišān mithurti: Festschrift Wolfgang Freiher von Soden zum 19. VI. 1968 gewidmet, Alter Orient und Altes Testament, M. Dietrich, W. Röllig, Eds. (Butzon and Bercker, Kevelaer, Germany, 1969), pp. 1, pp. 65–99.
18
J. Hackl, Der subordinierte Satz in den spätbabylonischen Briefen, Alter Orient Altes und Testament 341 (Ugarit, Münster, Germany, 2007).
19
W. von Soden, Grundriss der akkadischen Grammatik, Analecta Orientalia 33 (Pontifical Pontifical Biblical Institute, Rome, 1995).
20
Ossendrijver M., Evidence for an instrumental meaning of ina libbi. Nouvelles Assyriologiques Brèves et Utilitaries 44, 51 (2010).
21
O. Neugebauer, A. Sachs, Mathematical Cuneiform Texts, Americal Oriental Series 29 (American Oriental Society, New Haven, CT, 1945).
Information & Authors
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Published In
Science
Volume 351 | Issue 6272
29 January 2016
29 January 2016
Copyright
Copyright © 2016, American Association for the Advancement of Science.
Submission history
Received: 4 November 2015
Accepted: 23 December 2015
Published in print: 29 January 2016
Acknowledgments
The Trustees of the British Museum (London) are thanked for permission to photograph, study, and publish the tablets. Work was supported by the Excellence Cluster TOPOI, “The Formation and Transformation of Space and Knowledge in Ancient Cultures” (Deutsche Forschungsgemeinschaft grant EXC 264), Berlin. Photographs, transliterations, and translations of the relevant parts of the tablets are included in the supplementary materials. The tablets are accessible in the Middle Eastern Department of the British Museum under the registration numbers BM 40054 (text A), BM 36801, BM 41043, BM 34757 (text B), BM 34081+34622+34846+42816+45851+46135 (text C), BM 35915 (text D), and BM 82824+99697+99742 (text E). H. Hunger (Vienna) is acknowledged for providing an unpublished photograph of BM 40054.
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