Trends in the History of Science Chris Rorres Editor Archimedes in the 21st Century Proceedings of a World Conference at the Courant Institute of Mathematical Sciences Trends in the History of Science Trends in the History of Science is a series devoted to the publication of volumes arising from workshops and conferences in all areas of current research in the his- tory of science, primarily with a focus on the history of mathematics, physics, and their applications. Its aim is to make current developments available to the commu- nity as rapidly as possible without compromising quality, and to archive those devel- opments for reference purposes. Proposals for volumes can be submitted using the online book project submission form at our website www.birkhauserscience.com. More information about this series at http://www.springer.com/series/11668 Chris Rorres Editor Archimedes in the 21st Century Proceedings of a World Conference at the Courant Institute of Mathematical Sciences Editor Chris Rorres Drexel University Philadelphia, PA, USA ISSN 2297-2951 ISSN 2297-296X (electronic) Trends in the History of Science ISBN 978-3-319-58058-6 ISBN 978-3-319-58059-3 (eBook) DOI 10.1007/978-3-319-58059-3 Library of Congress Control Number: 2017944105 Mathematics Subject Classification (2010): 00B25, 01A20, 01A61, 01-06. © Springer International Publishing AG 2017 This work is subject to copyright. 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Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This book is published under the trade name Birkhäuser, www.birkhauser-science.com The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland These Proceedings are dedicated to Dennis L. Simms (1926–2010) Archimedes scholar, colleague, and friend— who would have been a valuable contributor to this conference. Preface Archimedes in the 21st Century, a two-day world conference held in Spring 2013 at the Courant Institute of Mathematical Sciences, New York University, took place during what is believed to have been Archimedes’ 2300th birth year. This conference was focused on the enduring and continuing influence of Archimedes in our modern world. Specifically, it celebrated his 23 centuries of influence on mathematics, science, and engineering. Courant Institute Director Gérard Ben Arous opened the conference with this inspiring observation: I’m impressed by the idea that, 23 centuries after his lifetime, we’re still looking at the influence of Archimedes in our modern world. It’s as close a shot at immortality as one can imagine. Eight invited talks presented during the first day of the conference are printed in this volume. The conference speakers were chosen because they are actively involved in fields whose origins trace back to Archimedes. As well, many of the presenters have conducted and published research that extends Archimedes’ work in the twenty-first century. The fields of mathematics, science, and engineering each claim Archimedes as one of their own. For that reason, the conference talks were divided into three cat- egories: Archimedes the Mathematician/Geometer, Archimedes the Scientist, and Archimedes the Engineer. Let me say a few words about what the conference was not. Archimedes in the 21st Century was not a history of science conference, and therefore, no historians of science were invited to present. That was certainly no slight to the importance of the work of historians of science; many other confer- ences have emphasized that aspect of Archimedean scholarship (e.g., [1]). An example surrounding this distinction is the Archimedes Palimpsest, which is mentioned only tangentially in these conference proceedings. This collection of works of Archimedes, hidden beneath the text of a prayer book sometime in the thirteenth century, was unveiled and edited by Heiberg in 1906 [2] and analyzed with modern technology in the last twenty years [3]. Its discovery was of immense ix x Preface value to historians, but its mathematical results had to be rediscovered indepen- dently in the sixteenth and seventeenth centuries by the pioneers of the mathematical Renaissance. Had its contents not been obscured in the thirteenth century, it could have had a significant influence on twenty-first-century mathematics and science. But the window of opportunity for the palimpsest came and went, and so humankind took a different path in the tree of possibilities. Our conference drew an audience of mathematicians, scientists, and engineers who were primarily interested in learning about the latest twenty-first-century appli- cations of Archimedes’ works—along with their historical roots. Individuals already familiar with the history of Archimedes who were interested in learning what his works have led to in the twenty-first century also attended our conference. As conference organizer and editor of these proceedings, I would now like to speak personally about our distinguished speakers: Moshe Kam is the quintessential professional engineer and historian of sci- ence, a university dean of engineering, and a former president of IEEE (Institute of Electrical and Electronics Engineers). Moshe was our opening speaker, and he presented a complete and thoughtful timeline of engineering from ancient times to the twenty-first century, highlighting Archimedes’ contributions to the field. Larrie D. Ferreiro is an authority on military strategies and weaponry, a historian of naval architecture, a university professor of systems engineering, and an author of several books and many articles on these themes. Larrie’s focus on defense in depth was astute and compelling, particularly when he applied Archimedean ideas to twenty-first-century military stratagems [4]. Mamikon Mnatsakanian is the developer of Visual Calculus, an ingenious approach to solving many problems in geometry and integral calculus. He is the coauthor of a recently published geometry work that provides fresh and powerful insights to that field [5]. His richly illustrated conference talk brought Archimedes’ renowned tombstone theorem into the twenty-first century, extending it in numerous directions. Horst Nowacki is a world authority on naval history and the author of Archimedes and Ship Stability [6]. Having extensively consulted with Horst during my own floating-bodies research [7, 8], I commend his encyclopedic knowledge of Archimedean laws as they have been applied to ship design over two millennia. Dirk M. Nuernbergk is a world expert on the Archimedes Screw, particularly for the newest twenty-first-century application of operating Archimedes screws in reverse over rivers and streams in order to generate cheap electricity. This applica- tion is proving to be a boon all across Europe, Canada, and New Zealand. Dirk is at the center of this innovative research, both as a consultant engineer and as the author of numerous engineering journal articles; he has also written a handbook for setting up a hydropower screw [9]. Michael T. Wright is an ancient technology scholar and a mechanician who brought two of his handwrought models to our conference: the much-acclaimed Antikythera Mechanism and his newly created Sphere of Archimedes—which he unveiled in pub- lic for the first time at the conclusion of his talk. Michael’s Sphere is the first model of Preface xi an Archimedes’ sphere that anyone in any century has ever attempted to reconstruct; it is a clear precursor of our modern-day planetarium and a marvel to behold. Mary Jaeger was the only invited non-STEM presenter at our conference. She is the author of the scholarly volume, Archimedes and the Roman Imagination [10], and presented the classicist’s perspective. In her well-researched talk, Mary chroni- cled events and people who have brought Archimedes into our modern world—sur- prisingly (and sometimes amusingly) perpetuating the anecdotes and myths about him. At this conference, I presented the Archimedes the Mathematician segment along with Sylvain Cappell, Silver Professor of Mathematics at the Courant Institute of Mathematical Sciences. You can view videos of all the Archimedes conference talks and learn more about the greatest mathematician and scientist of antiquity on my Archimedes website: https://www.cs.drexel.edu/~crorres/Archimedes/AWC/ This site is the repository of my 50-year fascination with Archimedes. In it I’ve compiled knowledge about his inventions, the numerous fields of science and math- ematics he engendered, discussions of many of his finished works, and my own research that extends and applies Archimedean principles to twenty-first-century problems. I created this website in 1995, and it has been under continual develop- ment and expansion since then. Acknowledgments I wish to thank all our speakers, both Friday and Saturday, for their thoughtful and inspiring presentations. Thanks, particularly, to my Drexel colleague, structural engineer Harry Harris, who transported his remarkable 1/60-scale working model of an Archimedes Claw/Iron Hand to the conference and spoke about it during our Saturday session. I am very grateful to our sponsors who made the conference possible: First, the Courant Institute of Mathematical Sciences for hosting the conference and for pro- viding guidance and support. Among my colleagues at Courant, I warmly thank Sylvain Cappell and Gérard Ben Arous. Similarly, I want to thank the directors of the Institute of Electrical and Electronics Engineers (IEEE) for providing the lead grant for this conference; most especially, I thank Moshe Kam for helping us qualify for the IEEE grant. Many thanks, as well, to Math for America and to MfA President John Ewing for their conference grant and enthusiastic support. Also, a warm thank-you to professional staffers at NYU who helped plan, man- age, and promote the conference, specifically James Devitt of NYU’s Media Relations Department for disseminating communications about the Archimedes conference to the news media and to the greater NYU community, and Elizabeth