Zeno’s Paradox: Unraveling the Ancient Mystery Behind the Science of Space and Time PDF
Preview Zeno’s Paradox: Unraveling the Ancient Mystery Behind the Science of Space and Time
A PLUME BOOK ZENO’S PARADOX is a professor of mathematics at Marlboro College, where he has taught a JOSEPH MAZUR variety of classes in mathematics, including its history and philosophy. He received a Guggenheim Fellowship in 2006 and is the author of Euclid in the Rainforest, which was a finalist for the 2005 PEN/Martha Albrand Award for First Nonfiction. He lives with his wife, Jennifer, in Vermont. “Mazur spins a good yarn…Entertaining and informative.” —Publishers Weekly “Motion simply didn’t make sense to the philosophers of ancient Greece; Zeno and his paradox seemed to show that it was impossible. In [Zeno’s Paradox], Joseph Mazur explains how more than two millennia of grappling—from Aristotle to Newton to Einstein and beyond—have left us with a deeper, yet stranger view of the universe than even Zeno could have imagined. It’s a fascinating tale, and it’s well told.” —Charles Seife, author, Zero: The Biography of a Dangerous Idea and Decoding the Universe: How the New Science of Information Is Explaining Everything in the Cosmos, from Our Brains to Black Holes “[Zeno’s Paradox] is a wonderful book that combines the profound mathematical ideas of ancient Greece with science through the ages. It is an entertaining and informative romp through the mysteries of the universe and their explanation through ancient wisdom. Superb.” —Amir Aczel, author, Fermat’s Last Theorem, The Mystery of the Aleph, and Entanglement “An enchanting—and unsettling—exploration of mathematics, its human soul, and the world we live in. Read this and you will see everything differently.” —William Cullerne Bown, editor, Research Fortnight and Research Europe “Vivid and witty in his evocation of historical period, precise but accessible in his recounting of scientific argument, Mazur has written a mathematical ‘page- turner’ in which we keep hoping to find out how and why motion is possible. And how does it all turn out? Does Achilles ever catch up with the tortoise? Can the arrow in flight really move from one point of space-time to the next, when there is no ‘next’ and space-time itself may be a transcendental can of worms wiggling about 1040 orders of magnitude below us?” —Emily Grosholz, department of philosophy, Pennsylvania State University “In a lively setting of history and anecdote, Joe Mazur, clearly a terrific teacher, sets out the crucial discoveries that progressively solved problems of motion without dissolving its enigmas. He has the art of making revolutions in thought and their mathematical underpinnings accessible without loss of depth. Anyone, from beginning amateur to longtime teacher, can read [Zeno’s Paradox] with pleasure and profit.” —Eva Brann, St. John’s College, Annapolis “Using Zeno’s paradox, Mazur opens the door to a wonderful tour of the important notions in mathematics and physics related to motion, including planetary motion, calculus, the speed of light, relativity, and string theory. A fascinating look at what we often mistakenly take for granted.” —Colin C. Adams, professor of mathematics, Williams College “Joseph Mazur takes us on a fascinating tour with history’s greatest scientists and their quest to understand the very structure of time and space. I would be hard-pressed to find a more readable account of these developments, which range from the ideas of Zeno, Archimedes, Aristotle, Newton, and many others, to the revolutionary insights of Einstein and relativity, quantum mechanics and string theory.” —Ronald Graham, professor of information science, University of California, San Diego ZENO’S PARADOX Unraveling the Ancient Mystery Behind the Science of Space and Time JOSEPH MAZUR Previously published as The Motion Paradox PLUME Published by the Penguin Group Penguin Group (USA) Inc., 375 Hudson Street, New York, New York 10014, U.S.A. • Penguin Group (Canada), 90 Eglinton Avenue East, Suite 700, Toronto, Ontario, Canada M4P 2Y3 (a division of Pearson Penguin Canada Inc.) • Penguin Books Ltd., 80 Strand, London WC2R 0RL, England • Penguin Ireland, 25 St. Stephen’s Green, Dublin 2, Ireland (a division of Penguin Books Ltd.) • Penguin Group (Australia), 250 Camberwell Road, Camberwell, Victoria 3124, Australia (a division of Pearson Australia Group Pty. Ltd.) • Penguin Books India Pvt. Ltd., 11 Community Centre, Panchsheel Park, New Delhi–110 017, India • Penguin Group (NZ), 67 Apollo Drive, Rosedale, North Shore 0632, New Zealand (a division of Pearson New Zealand Ltd.) • Penguin Books (South Africa) (Pty.) Ltd., 24 Sturdee Avenue, Rosebank, Johannesburg 2196, South Africa Penguin Books Ltd., Registered Offices: 80 Strand, London WC2R 0RL, England Published by Plume, a member of Penguin Group (USA) Inc. Previously published under the title The Motion Paradox in a Dutton edition. Copyright © Joseph Mazur, 2007 All rights reserved The Library of Congress has catalogued the Dutton edition as follows: Mazur, Joseph. The motion paradox: the 2,500-year-old puzzle behind all the mysteries of time and space / Joseph Mazur. p. cm. Includes bibliographical references and index. ISBN: 978-1-4406-3963-0 1. Motion. 2. Space and time. I. Title. QC133.M39 2007 530.11—dc22 2007004075 Without limiting the rights under copyright reserved above, no part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior written permission of both the copyright owner and the above publisher of this book. PUBLISHER’S NOTE While the author has made every effort to provide accurate telephone numbers and Internet addresses at the time of publication, neither the publisher nor the author assumes any responsibility for errors, or for changes that occur after publication. Further, publisher does not have any control over and does not assume any responsibility for author or third-party websites or their content. The scanning, uploading, and distribution of this book via the Internet or via any other means without the permission of the publisher is illegal and punishable by law. Please purchase only authorized electronic editions, and do not participate in or encourage electronic piracy of copyrighted materials. Your support of the author’s rights is appreciated. To Jennifer In memory of her mother, my dearly beloved mother-in-law, Anne Joffe— perceptive questioner, astute listener, kindhearted caregiver. Contents Part 1 A Commotion of Absurdities 1. Preamble to the Paradoxes of Motion 2. Zeno’s Visit to Athens 3. The World Through Aristotle’s Eyes Part 2 Zeno Survives the Renaissance 4. Speed Becomes a Quantity 5. Galileo Galilei, the Father of Modern Science 6. Dance of the Planets Part 3 Zeno in the Sands of Time 7. A Step Back for Time 8. Descartes and the Magic of x and y 9. The Arrow’s Trajectory 10. Falling Toward the Enlightenment Part 4 A Commotion of Absurdities, Revisited 11. The Speed of Light 12. The Space-time Revolution 13. Oops, Things Get Grainy Again 14. There’s No Next, but What’s Next? 15. The One Stream Acknowledgments Notes Further Reading Index ZENO’S PARADOX
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