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review of Joseph Mazur's "The Motion Paradox" [Aug. 19th, 2007|05:35 pm]


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.

[User Picture]From: st_rev
2007-08-20 02:37 am (UTC)
I'm not sure anybody actually understands limits. I sure as hell don't, and I have a PhD.
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[User Picture]From: hbergeronx
2007-08-20 03:02 am (UTC)
I guess I don't know what you're trying to say, by that.
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[User Picture]From: st_rev
2007-08-20 03:16 am (UTC)
Not really directly related to your review, I suppose, just brought to mind. Continuity/limits/calculus...I can compute stuff, prove the theorems, I can (pretend to) teach it, but there's a gap between the formalism and the intuition for me where it all crumbles into nonsense. Classical epsilon-delta proofs are shabby, and students never really seem to understand them; alternate formulations (nonstandard analysis and other filter-based schemes) never caught on.

The formalism just covers the gap. Not sure what I'm trying to say, I guess.
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[User Picture]From: hbergeronx
2007-08-20 03:40 am (UTC)
You see, that's what I find more interesting. There's a certain truism to the fact that a lot of the formalism is a fig leaf of modesty, and that we're not really closer to understanding this... we're probably further away, if that's possible.

It might have been in Mary Tiles' book on philosophy of set theory that I reviewed earlier, but I distinctly remember there being something quite gapingly wrong with the epsilon-delta appoach, and I can't for the life of me remember what it was.
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