Customer Reviews

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

5 star:		(5)
4 star:		(2)
3 star:		(1)
2 star:		(1)
1 star:		(0)

 

 

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."

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).

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.

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!

This is a book about the birth and history of scientific knowledge as we know it today. I didn't know a lot of the things I read about in this fascinating book. So that was the best part: I learn something new with every page. Everything is put in a historical context, and this gives the topic an unexpected freshness.

Zeno's paradoxes are quite intriguing, especially because a couple of millennia later we still have trouble explaining them. This book is about the four "motion is impossible" paradoxes (The Dichotomy, Achilles, Flying arrow, and Stadium), and how they sparked controversy and ignited discoveries century after century. We learn about motion in the context of the astronomical genius of Galileo Galilei, continuity and calculus, Newton's law of gravity, light Einsteinian relativity, quantum mechanics and finally, string theory. It's almost impossible to believe that so much is covered in a 200 page book.

Dr. Mazur seems to have a winning writing formula, seen before in " Euclid in the Rainforest". Besides the scientific facts, there is always a human element, and bits of trivia about the people that made these amazing discoveries. You could actually imagine the times and places, so vivid, humorous and absorbing are the descriptions of both people and places. Zeno was a "tall and attractive... citizen of Elea", Aristotle wore "conspicuously fanciful clothes", and rings on his fingers. Tycho Brahe had a handlebar mustache, and a `prosthetic copper nose bridge", after losing his real one in a duel. Gottingen is a "great European center of science", situated between "rolling mountains and famous for it lime tree, sausages, beer and influential mathematics".

What is most fascinating about this book is that the concepts are explained with such clarity and focus that you only need to read to fully understand. Here you get a feel of what an artful teacher Joseph Mazur is. You almost wish you took math and physics with him.

I just came across Marcus Chown's review in the New Scientist who said it best (New Scientist,2007, March, p50), "This is one of the most fascinating science books I have ever read . . . Joseph Mazur has succeeded in telling a fresh and untold story with clarity and style." I couldn't have said it better.

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!

The Motion Paradox rewards the reader abundantly. The author manifests a scholar's deep appreciation for the social history of mathematics, a master teacher's grace and wit, a poet's reverence for words and their arrangements.

The dust jacket blurbs are unusually apt, calling the book "wonderful," "entertaining and informative," "a fascinating tale, well told," "vivid and witty," "a wonderful tour of the important notions in mathematics and physics." I found all these judgments convincingly demonstrated over and over as I read the book. I've read with pleasure some books of the authors who wrote the blurbs, but unlike their books, The Motion Paradox is a book I'll probably read again.

In a late chapter Mazur quotes Leopold Kronecker's one-liner: "God created the integers, the rest is the work of man," which made me recall Robert Musil's young Torless's declaration to his math teacher that mathematicians should not have invented imaginary numbers. Mazur is driving at quite another point, but I have no doubt that he was aware of young Torless and will find a way to sympathize with his bewilderment on an appropriate occasion. The book is full of observations that challenge the mind to postpone explorations of such implied byways.
It will not disappoint.

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.

[...].

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.