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Down to the Hour: Short Time in the Ancient Mediterranean and Near East Time, Astronomy, and Calendars Texts and Studies Editors Charles Burnett Sacha Stern Editorial Board Dáibhí Ó Cróinín Benno van Dalen Gad Freudenthal Tony Grafton Leofranc Holford Strevens Bernard R. Goldstein Alexander Jones Daryn Lehoux Jörg Rüpke Julio Samsó Shlomo Sela John Steele VOLUME 8 The titles published in this series are listed at brill.com/tac Down to the Hour: Short Time in the Ancient Mediterranean and Near East Edited by Kassandra J. Miller Sarah L. Symons LEIDEN | BOSTON Cover illustration: Original artwork by Kenneth Jackson depicting (top to bottom) Babylonian astronomical tablets, Sol Invictus, a water clock, an ancient Egyptian lunar deity, star clocks, and Ahura Mazda, all within a sundial’s grid. © Kenneth Jackson. Library of Congress Cataloging-in-Publication Data Names: Miller, Kassandra J., editor. | Symons, Sarah L., editor. Title: Down to the hour : short time in the ancient Mediterranean and Near East / edited by Kassandra J. Miller, Sarah L. Symons. Description: Leiden ; Boston : Brill, [2020] | Series: Time, astronomy, and calendars 2211-632X ; volume 8 | Short time: measuring time at the sub-day level (e.g., hours, minutes). | Includes bibliographical references. Identifiers: LCCN 2019039734 (print) | LCCN 2019039735 (ebook) | ISBN 9789004373471 (hardback) | ISBN 9789004416291 (ebook) Subjects: LCSH: Time measurements—History. | Statistical astronomy. | Clocks and watches--History. Classification: LCC QB213 .D77 2020 (print) | LCC QB213 (ebook) | DDC 529/.70938—dc23 LC record available at https://lccn.loc.gov/2019039734 LC ebook record available at https://lccn.loc.gov/2019039735 Typeface for the Latin, Greek, and Cyrillic scripts: “Brill”. See and download: brill.com/brill-typeface. ISSN 2211-632X ISBN 978-90-04-37347-1 (hardback) ISBN 978-90-04-41629-1 (e-book) Copyright 2020 by Koninklijke Brill NV, Leiden, The Netherlands. Koninklijke Brill NV incorporates the imprints Brill, Brill Hes & De Graaf, Brill Nijhoff, Brill Rodopi, Brill Sense, Hotei Publishing, mentis Verlag, Verlag Ferdinand Schöningh and Wilhelm Fink Verlag. All rights reserved. No part of this publication may be reproduced, translated, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission from the publisher. Authorization to photocopy items for internal or personal use is granted by Koninklijke Brill NV provided that the appropriate fees are paid directly to The Copyright Clearance Center, 222 Rosewood Drive, Suite 910, Danvers, MA 01923, USA. Fees are subject to change. This book is printed on acid-free paper and produced in a sustainable manner. Contents Acknowledgments vii List of Illustrations Viii Notes on Editors and Contributors x Introduction  1 1 Sun and Stars: Astronomical Timekeeping in Ancient Egypt 14 Sarah L. Symons 2 The Ancient Egyptian Water Clock between Religious Significance and Scientific Functionality 52 Alexandra von Lieven and Anette Schomberg 3 Short Time in Mesopotamia 90 John Steele 4 Greco-Roman Sundials: Precision and Displacement 125 Alexander Jones 5 Cosmology and Ideal Society: the Division of the Day into Hours in Plato’s Laws 158 Barbara M. Sattler 6 Diurnal Selves in Ancient Rome 184 James Ker 7 Time, Punctuality, and Chronotopes: Concepts and Attitudes Concerning Short Time in Ancient Rome 214 Anja Wolkenhauer 8 Short Time in Greco-Roman Astrology 239 Stephan Heilen 9 Hourly Timekeeping and the Problem of Irregular Fevers 271 Kassandra Jackson Miller Index 293 Acknowledgments The idea for this volume first germinated in 2015 when Kassandra Jackson Miller (then at the University of Chicago) and the late Robert Germany (Haverford) decided to organize a panel on “Representations of Time in the Hellenistic and Roman Worlds” at the 2016 annual meeting of the Society for Classical Studies. This panel, which also featured papers by Alexander Jones and Barbara Sattler, was so stimulating that the four speakers felt a follow-up conference was need- ed, which would allow them to dig more deeply into the material and involve more voices in the conversation. Thus, in February 2017, they reconvened at the University of Chicago for a conference, organized by Miller, called “Down to the Hour: Perspectives on Short Time in the Ancient Mediterranean.” The chapters of the present volume represent revised versions of papers delivered at this conference, as well as pieces specially commissioned from other experts. We are grateful to the many individuals and institutions without whom this project might never have come to fruition. The Society for Classical Studies and the Franke Institute for the Humanities at the University of Chicago provided us with important venues in which our ideas could be developed. New York University’s Institute for the Study of the Ancient World, as well as University of Chicago’s Oriental Institute, Fishbein Center for the History of Science and Medicine, Center for the Study of Ancient Religion, Stevanovich Institute for the Formation of Knowledge, and the departments of Classics and of Near Eastern Languages & Literature contributed funding to the conference at the University of Chicago and thereby helped us to bring participants to the United States from Canada, Germany, and the United Kingdom. Many thanks are owed to Prof. Christopher Faraone (University of Chicago), who helped to facilitate the conference and advised the editors of this volume at critical junctures along the way, and to Giulia Moriconi, Assistant Editor of Classical Studies for Brill, who has guided us through the publication process. We would also like to thank the Israel Institute for Advanced Study, which hosted several of our contributors as part of its working group on “The Day Unit in Antiquity and the Middle Ages,” led by Profs. Sacha Stern and Jonathan Ben-Dov. The editors wish to express their gratitude to the contributors to this vol- ume, to the other colleagues who attended or participated in the activities out of which this volume grew, and to our families who supported us throughout the editorial process. Our final thanks must be reserved for Robert Germany, who did not live to see this volume completed. His sudden death in 2017 saddened the authorial team deeply. His future contributions to the field must surely have enriched it, and we dedicate this volume to his memory. Illustrations Tables 1.1 Twelve characteristics of timekeeping methods, divided into three groups, that can be used to compare methodologies. 15 1.2 Concave sundials from ancient Egyptian cultural areas, including their identi- fiers in two databases. 23 4.1 Analyses of eleven roofed spherical sundials. 150 7.1 History of time measurement in Rome according to Pliny, Naturalis Historia 7, 212–215. 219 8.1 The “Egyptian terms” of the planets. 250 8.2 Greek horoscopes containing claims to accuracy. 256 8.3 Astronomical longitudes in P. Lond. 130. 259 9.1 The pattern of paroxysms experienced by the patient within the first five days of his illness, and Galen’s attribution of them to particular tertians. 278 9.2 The paroxysms of what Galen identifies as Tertian 1. 279 Figures Sources for figures are in italics. If no source is given, the figure was constructed by the chapter author. 1.1 Arrangement of six attested hieroglyph shapes. (Hieroglyphs redrawn from Dau- mas 1995.) 18 1.2 Neugebauer and Parker’s geometric scheme for locating the “decanal belt.” (Based on figures from Neugebauer and Parker 1960.) 31 1.3 The problem of mixed-magnitude decans. 33 2.1 Different views of the outside decoration of the oldest preserved water clock from Karnak, bearing the names of Amenhotep III. (Neugebauer and Parker 1969, pl. 2 by kind permission of Brown University.) 59 2.2 Ceiling in the Ramesseum, showing the template of a water clock, with the Classical Sky Picture above and the king (Ramesses II) offering to the deities of the months below. (After Neugebauer and Parker 1969, pl. 5 by kind permission of Brown University.) 60–61 2.3 Interior of the Karnak clock with hour scales. (Desroches-Noblecourt 1976, 141) 64 2.4 Hour scales of the Karnak clock. 75 2.5 3-D-model of the clock in the Museo Barracco in Rome. 78 Illustrations ix 4.1 Seasonal hour-boundary points of a horizontal sundial for latitude 41°, com- puted for all solar declinations corresponding to the Sun’s entry into a zodiacal sign. 134 4.2 The hour-boundary points of Figure 4.1 superimposed on the grid of a horizon- tal sundial from Pompeii, Museo Archeologico Nazionale, Naples, inv. 2476. 134 4.3 The hour-boundary points of Figure 4.1 superimposed on the grid of a horizon- tal sundial from Pompeii, Soprintendenza Speciale per i Beni Archeologici di Napoli e Pompei inv. 49725. 134 4.4 The grid of the east-facing sundial on the Tower of the Winds, Athens. 136 4.5 Grid for a roofed spherical sundial for latitude 48°, projected into the equatorial plane. 136 4.6 The central Mediterranean, with Rome, Catania, and the fictitious Para- Catania. (Source for map: http://d-maps.com/m/mediterranean/meditmin/medit- min03.svg.) 139 4.7 Grid of a horizontal sundial computed for the latitude of Catania (fine black lines) superimposed on a grid computed for Rome’s latitude (thick gray lines). 142 4.8 Orthographic image of the BSDP digital model of the dial surface of Pompeii Granario inv. 52789. 146 4.9 Digital model of the dial surface with planar slices removed. 146 4.10 Orthogonal image of the sliced model in a plane parallel to the slices, with con- centric reference circles in black. 146 4.11 Orthogonal image of the sundial surface bisected along the meridian plane. 148 4.12 The orthogonal image from Figure 4.11 with lines traced for Tests 2 and 3. 148 4.13 Orthogonal image of the dial surface in the equatorial plane. 149 4.14 The dial surface as in Figure 4.12, with ideal grid for latitude 41° superimposed. 149 8.1 a) CIL IX.5808 (© Famiglia Leopardi Recanati). b) Graphic reconstruction (Mommsen 1883, 556). 245 Notes on Editors and Contributors Editor and contributing author Kassandra Jackson Miller is a Visiting Assistant Professor of Classics at Bard College, New York. Her research is in the areas of ancient religion, magic, and medicine, with a focus on timekeeping. Editor and contributing author Sarah L. Symons is an Associate Professor in the School of Interdisciplinary Science, McMaster University, Canada. Her re- search in history of astronomy concentrates on interpreting astronomical texts and instruments from ancient Egypt and investigating how the night sky was perceived, explained, and depicted. Alexandra von Lieven is an Extracurricular Professor at Westfälische Wilhelms-Universität Münster. Her research interests focus on ancient Egyptian religion, science, and cultural history, particularly on Religious Astronomy. Anette Schomberg is part of a research group in the Topoi Excellence Cluster at the Humboldt- Universität, Berlin, investigating the unequal armed balance in antiquity. She is also developing a database of ancient water clocks. John Steele is Professor of the History of the Exact Sciences in Antiquity and Chair of the Department of Egyptology and Assyriology at Brown University, Rhode Island. His research focuses on the history of Babylonian astronomy and astrology and its reception in other cultures. Alexander Jones is the Director of the Institute for the Study of the Ancient World (New York University). He studies the history and transmission of the mathemati- cal sciences, especially astronomy, in antiquity, with particular focus on the Greco-Roman world. Barbara M. Sattler is a Senior Lecturer in Philosophy at the University of St Andrews, UK. The main area of her research is metaphysics and natural philosophy in the ancient Greek world, especially with the Presocratics, Plato, and Aristotle.

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