What do you think?
Rate this book
The Motion Paradox: The 2,500-Year Old Puzzle Behind All the Mysteries of Time and Space
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.
272 pages, Kindle Edition
First published April 19, 2007
9 people are currently reading
123 people want to read
About the author
Joseph Mazur
12 books20 followersJoseph C. Mazur is Professor Emeritus of Mathematics at Marlboro College in Vermont. He earned his Ph.D. in algebraic geometry from MIT and has held visiting positions at MIT and the University of Warwick. A recipient of Guggenheim, Bellagio, and Bogliasco Fellowships, he has written widely on the history and philosophy of mathematics, with books translated into over a dozen languages.
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 18 of 18 reviews
August 12, 2016
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 mathematical 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 (an example: the pi symbol π is replaced with a not-equals symbol). 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.
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 mathematical 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 (an example: the pi symbol π is replaced with a not-equals symbol). 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.
December 14, 2014
Zeno's paradox is essentially this:
To get from point A to point B, you must first arrive halfway between points A and B. Then you must get to halfway between that point and point B. Then to halfway between that point and point B. And you must do this infinitely many times before you get to point B, so you never arrive at B. Of course in practice you do manage to get to point B, hence the paradox.
There's a bit more to it than that, but that's more or less the idea.
The paradox is solved rather succinctly when you realize that the sum of an infinite series (e.g. 1/2 + 1/4 + 1/8 + 1/16 + ...) can be finite (in this case = 1). Personally, I find this explanation for the paradox to be perfectly adequate, so I don't really get why the author finds the whole thing so fascinating. The author talks about things other than Zeno's paradox in this book, but for the most part it's equally superficial. It's not terrible, but not necessarily worth the time.
To get from point A to point B, you must first arrive halfway between points A and B. Then you must get to halfway between that point and point B. Then to halfway between that point and point B. And you must do this infinitely many times before you get to point B, so you never arrive at B. Of course in practice you do manage to get to point B, hence the paradox.
There's a bit more to it than that, but that's more or less the idea.
The paradox is solved rather succinctly when you realize that the sum of an infinite series (e.g. 1/2 + 1/4 + 1/8 + 1/16 + ...) can be finite (in this case = 1). Personally, I find this explanation for the paradox to be perfectly adequate, so I don't really get why the author finds the whole thing so fascinating. The author talks about things other than Zeno's paradox in this book, but for the most part it's equally superficial. It's not terrible, but not necessarily worth the time.
July 11, 2016
I am by no means (and far from) an expert throughout the topics of mathematics, mechanics, philosophy, and anthropology; however, what I did learn from this book was a sense of unlimited wonder.
Mazur takes a seemingly blunt paradox and explores its various origins, evolutions, and meanings. Although sometimes the perspective was narrowed and strict, Mazur created an awe-inspiring, almost innocent, atmosphere. This made his tone incredibly genuine.
When I thought there was less to the paradox, he would expound even further. Although at times these additions proved unnecessary, Mazur truly sheds light on the unending and ever-growing significance of scientific advancement.
Mazur takes a seemingly blunt paradox and explores its various origins, evolutions, and meanings. Although sometimes the perspective was narrowed and strict, Mazur created an awe-inspiring, almost innocent, atmosphere. This made his tone incredibly genuine.
When I thought there was less to the paradox, he would expound even further. Although at times these additions proved unnecessary, Mazur truly sheds light on the unending and ever-growing significance of scientific advancement.
May 31, 2021
Not many books on the subject, and it lays out the background quite well in the early chapters. In general though, I think the book tries to draw a line between being technical and popular and misses out on both in key respects. At times it goes along too readily with popular interpretations of things such as quantum theory and relativity. At other times it goes into great depth about some historical footnote regarding the development of clocks. As if this particular history says anything about time itself, which I don't think it does. It certainly says very little compared to notions such as entropy, regularity in nature etc. At other times I would like to have seen more about modern examples of paradoxes in mathematics, such as Gabriels horn and the Cantor set, to give support to the continuing relevance of paradoxes, rather than him spending so much time specifically trying to defend Zeno's paradoxes.
I think those paradoxes remain important philosophically, but not so much mathematically. The issue remains as ever how we can formulate a reasonable conception of reality without getting stuck in paradoxes. Zeno's suggestion was we cannot avoid it, and so reality must be an illusion. Most completely sidestep this philosophical debate, and talk about in practice how certain infinite series can be summed for instance, as being some sort of resolution of the problem. That could perhaps be the case if infinite series didn't give rise themselves to a new set of paradoxes. The difference now is that people don't even bother to make their reasoning consistent and feel comfortable just either "shutting up and calculating", or taking the authority of some expert in a field on trust.
He talks a lot about continuity late in the book, but seems to me he skips over the surface of this debate. How about a discussion of recent mathematical paradoxes in relation to this notion? And what about things such as the need in Quantum field theory for renormalisation of infinities. The emergence of singularities and time paradoxes in general relativity equation solutions. Also, what about the hole problem in general relativity. The basic issue of whether space is relational or absolute. These, to me, are the real and alive discussions in this area, philosophically, and I was disappointed to not see much on any of them.
I think those paradoxes remain important philosophically, but not so much mathematically. The issue remains as ever how we can formulate a reasonable conception of reality without getting stuck in paradoxes. Zeno's suggestion was we cannot avoid it, and so reality must be an illusion. Most completely sidestep this philosophical debate, and talk about in practice how certain infinite series can be summed for instance, as being some sort of resolution of the problem. That could perhaps be the case if infinite series didn't give rise themselves to a new set of paradoxes. The difference now is that people don't even bother to make their reasoning consistent and feel comfortable just either "shutting up and calculating", or taking the authority of some expert in a field on trust.
He talks a lot about continuity late in the book, but seems to me he skips over the surface of this debate. How about a discussion of recent mathematical paradoxes in relation to this notion? And what about things such as the need in Quantum field theory for renormalisation of infinities. The emergence of singularities and time paradoxes in general relativity equation solutions. Also, what about the hole problem in general relativity. The basic issue of whether space is relational or absolute. These, to me, are the real and alive discussions in this area, philosophically, and I was disappointed to not see much on any of them.
September 26, 2018
The Motion Paradox by Joseph Mazur is very interesting. It discusses the paradoxes of Zeno of Elea that argue against motion being possible and places them in more modern contexts. This is especially the case with our concepts of motion and time. Take time for instance. It is assumed that there is the shortest duration of time possible, which would make it discrete and not continuous. All of it depends on the size of the measuring device used for the quantity.
Since the book discusses motion and time it talks about the development of mathematical tools necessary to model these phenomena.
There really isn’t much else to discuss. The book was enjoyable and very informative. It talked about a lot of things I was familiar with such as relativity and Zeno of Elea but did so in an innovative manner.
Since the book discusses motion and time it talks about the development of mathematical tools necessary to model these phenomena.
There really isn’t much else to discuss. The book was enjoyable and very informative. It talked about a lot of things I was familiar with such as relativity and Zeno of Elea but did so in an innovative manner.
September 4, 2023
Already knew everything 💪💪💪💪. Everything Zeno has thought, I have as well.
July 28, 2024
A light history of measuring movement, from Zeno to String Theory.
January 14, 2016
This is a terrific and comprehensive book. It appears that some people didn't get the book's many subtleties, which is of course to be expected since the subject of the book are mysteries of reality that are still puzzled over by the best and brightest the world over. Disregard any review here below that presumes to have solid and simple grasp of the deep questions this book addresses. Mazur demonstrates a masterful understanding of the complexities of both the math and the philosophy, and elucidates the inherently difficult aspects in remarkably clear prose.
December 5, 2009
An elegant book about Zeno's paradox and, to use a cliche that's appropriate here, the mysteries of time and space. There are some equations in the text, but they are understandable in context even for the mathematically challenged.
Want to read
August 23, 2010I got a few chapters into it and set it down to finish something else. My mother then borrowed it and didn't give it back until it was due at the library. I'll have to place a hold on it again for a chance to finish it.
January 25, 2011
I think the premise of this book was pretty weak, or wasn't well-developed. The history mentioned in this book was great to read, but I don't think things were pulled together very well - it didn't feel like an urgent problem to me.
July 31, 2009
A moderately interesting book, but not the best I've read of a scientific nature. It didn't seem to live up to its promise all that well - I felt distracted by the end.
December 20, 2014
too bad I just find this book when I have been enrolled in college, as a social science student. :(
April 18, 2012
Useful to see if you can pick out all the weird mistakes
September 8, 2013
Fantastic book. Easy to read and understand even for a layman like myself. I particularly enjoyed the
historical overview.
historical overview.
February 11, 2015
interesting but sometimes difficult to follow the reasoning if you don't get all the math
Read
May 13, 2016I WANT TO BELIEVE
July 20, 2024
Plentiful contexts. Might need a re-read!!
Displaying 1 - 18 of 18 reviews