Joseph Mazur - Zeno’s Paradox: Unraveling the Ancient Mystery Behind the Science of Space and Time
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Three millennia ago, the Greek philosopher Zeno constructed a series of logical paradoxes to prove that motion is impossible. Today, these paradoxes remain on the cutting edge of our investigations into the fabric of space and time. Zeno?s Paradox uses the motion paradox as a jumping-off point for an exploration of the twenty-five-hundred-year quest to uncover the true nature of the universe. From Galileo to Einstein to Stephen Hawking, some of the greatest minds in history have tackled the problem and made spectacular breakthroughs?but through it all, the paradox of motion remains.
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ZENOS PARADOX
JOSEPH MAZUR is a professor of mathematics at Marlboro College, where he has taught a 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 yarnEntertaining and informative.
Publishers Weekly
Motion simply didnt make sense to the philosophers of ancient Greece; Zeno and his paradox seemed to show that it was impossible. In [ Zenos Paradox ], Joseph Mazur explains how more than two millennia of grapplingfrom Aristotle to Newton to Einstein and beyondhave left us with a deeper, yet stranger view of the universe than even Zeno could have imagined. Its a fascinating tale, and its 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
[ Zenos 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, Fermats Last Theorem ,
The Mystery of the Aleph , and Entanglement
An enchantingand unsettlingexploration 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 [ Zenos Paradox ] with pleasure and profit.
Eva Brann, St. Johns College, Annapolis
Using Zenos 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 historys 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
Unraveling the Ancient Mystery
Behind the Science
of Space and Time
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. Stephens 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 Delhi110 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
530.11dc22 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.
PUBLISHERS 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 authors rights is appreciated.
To Jennifer
In memory of her mother,
my dearly beloved mother-in-law,
Anne Joffe
perceptive questioner, astute listener,
kindhearted caregiver.
My father was the first person to tell me about paradoxes of time. He had never heard of Zenos paradoxes, those peculiar arguments on motion that contradict common sense and that have been misunderstood these last two and a half millennia, but was a gentleman philosopher with instinctive wisdom about the world and how it turned. My brother had just received a brand-new Schwinn bicycle with chrome fenders, a speedometer, and battery-operated horn for his birthday. Boy, was that neat. The gentleman philosopher knew just what I was thinking. To soothe my jealousy, he took me aside and told me that I was half my brothers age, but in eight years I would be three-quarters his age and that from then on there would hardly be a difference. Of course, I had no idea what he meant by three-quarters, let alone three-quarters of someones age. When I asked how old would I have to be to catch up completely, he laughed and said that that would never happen, but that the difference would always be getting smaller. Years later, I thought I understood; but, now, rapidly gaining on my brother as I pass sixteen-seventeenths of his age, Im just beginning to. Incidentally, my brothers bicycle was stolen shortly before his next birthday.
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