Zeno’s Paradox: Unraveling the Ancient Mystery Behind the Science of Space and Time

202 Pages·2008·1.13 MB·English

by  Joseph Mazur

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
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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
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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