The Motion Paradox: The 2,500-Year Old Puzzle Behind All the Mysteries of Time and Space [Hardcover]

Joseph Mazur (Author)

Book Description

Publication Date: April 19, 2007

The epic tale of an ancient, unsolved puzzle and how it relates to all scientific attempts to explain the basic structure of the universe

At the dawn of science the ancient Greek philosopher Zeno formulated his paradox of motion, and amazingly, it is still on the cutting edge of all investigations into the fabric of reality.

Zeno used logic to argue that motion is impossible, and at the heart of his maddening puzzle is the nature of space and time. Is space-time continuous or broken up like a string of beads? Over the past two millennia, many of our greatest minds—including Aristotle, Galileo, Newton, Einstein, Stephen Hawking, and other current theoreticians—have been gripped by the mystery this puzzle represents.

Joseph Mazur, acclaimed author of Euclid in the Rainforest, shows how historic breakthroughs in our understanding of motion shed light on Zeno’s paradox. The orbits of the planets were explained, the laws of motion were revealed, the theory of relativity was discovered—but the basic structure of time and space remained elusive.

In the tradition of Fermat’s Enigma and Zero, The Motion Paradox is a lively history of this apparently simple puzzle whose solution—if indeed it can be solved—will reveal nothing less than the fundamental nature of reality.

Editorial Reviews

From Publishers Weekly

The Greek philosopher Zeno sought to reveal that motion and speed were logical impossibilities; one of his famous four paradoxes argued that a moving object can never reach its destination, because it must first travel half the distance, then half the remaining distance, and so on. In this entertaining, informative diversion, Mazur (Euclid in the Rainforest) spins out the discoveries of the mathematicians and scientists who have grappled with the riddles of time and space over the last two millennia, from Aristotle up to Heisenberg and contemporary string theorists. Yet for all their answers, the fundamental premise that motion is an illusion created by consciousness still remains. Many elements of the story, such as the astronomical breakthroughs of Galileo and Tycho, or the simultaneous development of calculus by Leibniz and Newton, have been discussed in greater detail in other recent books. But Mazur spins a good yarn, and his conversational tone holds readers' attention even as the mathematical formulae pile up in later chapters. (Apr.)
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From Booklist

Zeno's four paradoxes have bamboozled the greatest mathematical minds, for he purported to prove that motion is impossible, a conclusion somewhat at variance with experience. In this history of puzzlement over the paradoxes, mathematician Mazur begins by imagining Zeno stumping the entire ancient-Greek brain trust except for Aristotle, who offered refutations of Zeno. With Aristotle's own notions of motion refuted by Kepler, Galileo, and Newton, Zeno enjoyed a brief renaissance but seemed tamed once more by calculus and its mathematical tool kit. Motion and time again were continuous, not infinitely divisible, which is the underlying assertion that lets Zeno claim that fleet-footed Achilles can never catch up to a tortoise that has a head start. Then, as Mazur relates, Planck's discovery of the quantum, and Einstein's of relativity, restored Zeno's paradoxes to philosophical relevance. Entrained with some requisite algebra, Mazur's account achieves an entrancing verbal clarity in its discussion of the success and limits of mathematically modeling motion, and itself is a fine example of popularizing a famous philosophical mind-bender. Gilbert Taylor
Copyright © American Library Association. All rights reserved

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Product Details

• Reading level: Ages 14 and up
  
• Hardcover: 272 pages
• Publisher: Dutton Adult (April 19, 2007)
• Language: English
• ISBN-10: 0525949925
• ISBN-13: 978-0525949923
• Product Dimensions: 8.5 x 6 x 1.1 inches
• Shipping Weight: 10.6 ounces (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (9 customer reviews)
• Amazon Best Sellers Rank: #1,258,894 in Books (See Top 100 in Books)

More About the Author

His full name is Joseph Conrad Mazur. His mother bought a used copy of Lord Jim in London on her way from Vienna to America, thinking that if she could read it with a dictionary it might improve her English. Like Mazur's mother, Conrad was Polish-born, so she felt that English written by a Pole must be easy to understand.

JOSEPH MAZUR is Professor Emeritus of Mathematics at Marlboro College where he has taught a wide range of classes in all areas of mathematics, its history and philosophy. He holds a Ph.D. in mathematics from M.I.T., and is a Guggenheim Fellow. He is the author of Euclid in the Rainforest: Discovering Universal Truth in Mathematics (Finalist of the 2005 PEN/​Martha Albrand Award and chosen as one of Choice's 2005 Outstanding Academic Titles of the Year) and the editor of the recently republished classic by Tobias Dantzig, Number: The Language of Science. He is the author of The Motion Paradox: The 2,500-Year Old Puzzle Behind All the Mysteries of Time and Space. His latest book is What's Luck Got to do With it?, published by Princeton University Press in 2011.

Customer Reviews

Most Helpful Customer Reviews

44 of 46 people found the following review helpful:

5.0 out of 5 stars Mystifying the Nuts and Bolts, May 2, 2007

By 

drew hempel (Minnesota) - See all my reviews

This review is from: The Motion Paradox: The 2,500-Year Old Puzzle Behind All the Mysteries of Time and Space (Hardcover)

Professor Mazur does an expert job of giving the behind-the-scenes wrangling of conceptual philosophy which gave rise to applied science. What is the difference between time and motion exactly? If that question seems too abstract, this book proves the opposite.

Most college graduates assume that Zeno's paradoxes of motion were solved by calculus with its continuous functions. Mazur puts the calculus at the heart of the book, from Descartes and Cavalieri to Galileo, Newton and last but not least Mazur's favorite: Gabrielle-Emilie de Breteuil.

In fact, upon investigation, one finds many top scientists still studying and learning from the anomalies in infinite measurement. Regarding relativity Mazur states the wonder of absolute motion is that it "conspires with our measuring instruments to prevent any possibility of detection."

As Mazur points out "we don't measure with infinitesmial instruments" and so the perceptual illusion of time continuity remains despite the reliance of science on discrete symbols. With attempts at a unification of quantum mechanics and relativity Zeno's paradoxes reemerge with full-force in the "Calabi-Yau manifold." Mazur writes that the original concept of dimension still holds but now means measuring more by abstract reason than by sight.

Although each scientist featured by Mazur appears to have increasingly solved the paradox of motion in the end I think Zeno will be avenged and science will return to right back where it started. There seems to be a deadlocked struggle between discreteness (particle) and continuity (wave) in science and Mazur argues that indeed Nature "makes jumps" despite seeming continuous. But Mazur admits we are left with "splitting operations that can take place only in the mind."

21 of 24 people found the following review helpful:

3.0 out of 5 stars Excellent but for mathematically oriented reader a little bit frustrating, July 19, 2007

By 

Arzi (L'Isle d'Abeau, France) - See all my reviews
(REAL NAME)   

This review is from: The Motion Paradox: The 2,500-Year Old Puzzle Behind All the Mysteries of Time and Space (Hardcover)

This is an excellent account of the development of the ideas around an intriguing question (zeno's paradox) through two and a half millenia of the history of mathematics and physics. In fact this paradox is ultimately related to the problem of the link between discrete and continuous in the linear number system (real line). If one digs deep enough, one can find also links to famous paradoxes of twentieth century mathematics (for example the banach-tarsky paradox or the paradox of the "pea and the sun"). Unfortunately the author overlooks these issues which have caused virulent debates between best mathematicians of the history (supporters of cantor's ideas against his adversaries). The author follows scupulously the maxim that every mathematical formula divides by two the number of peaple who will read the book, so he forbids himself of introducing any formula. I think in many places, mathematical formulation is much clearer than a long text (it could at least be presented as notes).

25 of 30 people found the following review helpful:

2.0 out of 5 stars unsatisfying, August 19, 2007

By 

Matthew E. Harbowy "the bear that went over t... (San Francisco, CA) - See all my reviews
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This review is from: The Motion Paradox: The 2,500-Year Old Puzzle Behind All the Mysteries of Time and Space (Hardcover)

I had high hopes for this book, but I feel like the author has let me down.

My principal complaint with the book is akin to the complaint about the three statisticians who go hunting- one shoots high, the other shoots low, and the third yells "we got it!" Mazur looks at the world through a mathematicians eyes, and misses the forest for the trees. He is attempting to summarize his thoughts on the physical ramifications for the philosophy and math behind Zeno's paradox, completely ignoring the fact that one can pit Achilles and the tortoise in a race and observe Achilles' win. Were he to attempt to focus on this goal, even if he had to do so ironically by halves, he would have a better chance of leaving solid concepts in the reader's mind. Rather, he fills the reader with a hocus-pocus level of wonder, marveling at the impossibility of motion and it all. One can open their eyes, and, like a child, exclaim, "yet it moves!", and not be mystified at all. Is Mazur trying to make the reader feel inferior?

For example, he spends a certain amount of time at the end of the book marveling at the persistance of vision, wondering if our eyesight averages discrete images into a false perception of continuous motion, what if our vision were that of a strobe camera and the universe were continuous, would our vision be different? This is interesting, and the sense of wonder seems genuine; but there is a physical explanation for the persistance of vision, in that eyesight is a chemical phenomemon and as the chemical reactions become saturated, there is a natural decay required before a new image might render fully. Indeed, he completely ignores wondering about two images (such as the bird and the cage) when flipped at high speed, seem to merge into one bird in a cage. He is restricted into a highly constructed narrative, saying, "follow me along this path", to his conclusion, ignoring that the educated reader is constatly going to say "but... what about..", and be left either lost and frustrated, or dumbly following as if in a boring guided tour. Either way, the reader will not feel better about themselves at the end of the tour.

More troublingly, there are extensive unmentioned mathmatical insights that he completely overlooks, when as a mathematician, he should be at least mentioning them. For example, Hilbert's Grand Hotel paradox seems worth at least a brief mention as belonging in the same class, and yet despite three references to David Hilbert in the index, no hint is given. If Zeno's paradoxes are the root puzzle, as the cover suggests, of "all the mysteries of time and space"- then why does he not spend more time giving concrete examples of how that is? Clearly, Zeno's paradox seems to be at the root of calculus, which is extremely relevant for mathematics, but he fails to convey sufficiently how and what that means for real world problems. That there is and has always been a deep divide between pure applied math, and practically applied science, is glossed over. If he is saying, "math is the root of all science", he does not bravely say so. Many people can do science without math, and as such the physical scientist in me is unimpressed with his tack.

More minor peccadilloes: This book was not carefully edited, and the hardcover edition contains many typos, sometimes distractingly so. It is also useless as a reference book. The style and subject matter does not leave the reader more educated- rather it is written in a mystical style which doesn't clearly open or close its subjects, and smacks of a Whig history of Zeno's paradox. When you separate out his whiggish narration, you quickly begin to realize that this book isn't really saying anything. He leaves you not much more significantly educated than many putative purchasers of this book, and as such, you'd be better off saving the money. If it's not educating, it should be entertaining, but he fails on this as well. It does not have well drawn characters, and except for the first few pages, we get no sense of struggle or personality. In fact, reading the first few pages as an excerpt clearly leaves you feeling like it's going to be a more interesting book- for example, how has Zeno's paradox been a personal struggle for the author? But instead, it falls flat. It is a dry retelling of history, and I feel cheated by having wasted my time reading it.