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

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.

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All Customer Reviews
Average Customer Review:
0 of 0 people found the following review helpful:

There is no paradox, 2008-06-04
Aristole was completely right claiming that Zeno had made false assumptions.The false assumption is to suppose that a sum with an infinite number of terms has to produce an infinite number as a result.
The study of geometric series shows that some can converge and others do diverge.An exact criteria exists to determine what is the limit of a converging series.
To discard Zeno's paradox one only needs to be mathematically convinced -which is easy enough,that the sum 1/2 + 1/4 + 1/8 +......1/2^n = 1 , where n goes to infinty.

How can we say that we know nothing of motion when physical constants, for example the magnetic moment of the electron can be calculated (theory) and measured (experimental verification) to be -928.476 377 x 10^-26 Joules /Tesla. The number has 9 significant figures !!

I do recommend the book as an outline of the development and mutual influence of Calculus and Physics.


1 of 1 people found the following review helpful:

Metaphysics of Being, 2007-08-31
The motion paradox is one of the most important books that you could ever read. After 2500 years of scientific development we still can not understand or quantify an indivisible moment in time. Mathematics tells us that a finite set encloses an infinite series and this creates one of the greatest paradoxes ever conceived of by man.

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11 of 11 people found the following review helpful:

Why the Universe is Exceedingly Strange, 2007-08-29
Modern physics often reads like the ravings of a deluded crank, yet much of the paradox and counter-intuitive ramblings seems to be the way the universe works. For example while string theory is mind-bogglingly bizarre, one is drawn to the conclusion that it, or something akin to it, is probably true at some ultra-micro level.

"The Motion Paradox" discusses many of these issues, based on the Greek philosopher Zeno's ideas of 2500 years ago. Now the Achilles and the tortoise paradox has been simply solved with modern algebra, but the other paradoxes, although seemingly silly, are not so easily solved. As Joseph Mazur points out in this book, they are not quite as silly on close examination as one would suppose. Why does an arrow appear to have a smooth motion? Why do some calculations approach a limit, like Achilles approaching the tortoise, yet never seem to reach it? In fact as the matter-energy, motion-rest, time-space, microscopic-macroscopic and other paired concepts about our universe are examined closely, the solid world around us seems to disappear leaving us with a very Hindu or Buddhist sounding concept that all is illusion!

This is a very interesting book from a number of standpoints. I dropped it a star because there are parts that I think could have been more clearly written, but overall the author got most of his points across. The upshot is that we live in a very strange planet in a very strange universe and we may never really grasp exactly how very strange this "reality" really is!


20 of 23 people found the following review helpful:

unsatisfying, 2007-08-19
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.


3 of 3 people found the following review helpful:

Fascinating and thought-provoking!, 2007-07-26
The Motion Paradox is a fascinating mix of science, math, and philosophy that draws the reader deeper and deeper into one of the most interesting puzzles of all time. Mazur's prose is joyfully thought-provoking and is not distracted by unnecessary mathematical equations. I thoroughly enjoyed this book -- Mazur's best to date!

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