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Title: Zero: The Biography of a Dangerous Idea by Charles Seife, Matt Zimet ISBN: 0-14-029647-6 Publisher: Penguin USA (Paper) Pub. Date: 05 September, 2000 Format: Paperback Volumes: 1 List Price(USD): $14.00 |
Average Customer Rating: 3.67 (79 reviews)
Rating: 1
Summary: Seems like a different book after chapter 6
Comment: Without doubt, this book has one of the best "Chapter 5's" I've ever read. "Infinite Zeros and Infidel Mathematicians" is everything a reader could want in a book. Up to chapter 5, Seife has traced the history of zero and its appearance in European math systems, starting from its origins in the Middle East to its careening path eastward and westward. Chapters 0 and 1 are a bit plodding but 2-4 are more than adequate. Chapter 5, as well as Chapter 6, is wonderful-- this is where Seife speaks about how zero was essential for the scientific revolution in europe, with calculus, Newton, Leibniz, and Kepler. The discussions on L'Hopital's rule and fluxions are a little confusing, but their minor quibbles here. What makes these two chapters so useful is that Seife talks about all those weird mathematical problems with scary symbols and confusing references that we're all familiar with from math class, and does a really good job. He uses intuitive descriptions to make sense out of otherwise incomprehensible concepts-- a tangent, for example, is explained by pointing out how an object swung on a string, when released, flies in a tangent line to the string's curve, with the same going for a ball released by a pitcher moving an arm in an arc before releasing the baseball. Also useful is the explanation of the two foci of an ellipse, with the description of lines of light sent out from one focus ultimately reflecting and centering upon the next focus. I encountered all these concepts in math class and couldn't understand why they were important or what they meant, and Seife explains the origins of these problems, their importance, and how all those terms and equations came about. He makes the difficult seem intuitive. Even his tangents and side discussions, while occasionally distracting, are usually entertaining and fun in these chapters.
I would've given the book 4 stars if it had stopped at Chapter 6, where Seife seems to be most on top of his material-- math, it's history, and the way it was changed when zero entered the picture. But the whole book is undone by the last three chapters. These are the ones that deal with physics and astrophysics, and the book just seems out of its element here. The last chapter, "Chapter Infinity-- End Time," has both a too-cute (to the point of being lame) title as well as a smorgasbord of confusing statements, weak logic, and unsubstantiated conclusions. The earlier two chapters aren't much better. They touch on a lot of subjects and do begin to explore them somewhat, but explain none of them very well. It's almost as if we're reading a different book by a different author after Chapter 6! Few things are more frustrating in a book than inconsistency like this. I'd get it for the first 6 chapters alone, but this seems to be a good example of the value of quitting while so far ahead in the project.
Rating: 4
Summary: Popular Intro to the Zero
Comment: On the premise that you read a book for its good points, I give this book a four.
I'd assigned it as a possible book report subject to my honors algebra class, so I thought I better read it. ;)
I give it four stars because it is a good intro to much of the history of the zero in the number system. Also, it's accessible to secondary students. The history in the book only suffers from running back and forth through time, through time tunnels of the author's own. Yet I must say the book reminded me of that wonder I feel for math.
[However,] the book splices in a whole lot of history of philosophy. It seemed wrong, but it's not my field.
Where the book takes a surprising turn is in the last third, when suddenly we abandon the number system and take up another field, physics. Mind you, we are no longer talking about math, we are talking about cosmology and very small things. I love physics, too, but I was dismayed, disheartened to see this shift. Here the concept of zero is used as an analogy. The physics has nothing to do with the number line or the coordinate plane.
Then one of my students extended the proof in the Appendix, whereby via division by zero one is able to prove that 1 = 0, and also that Winston Churchill is a carrot. Everyone already knows that Winston Churchill is a carrot. But not via the author's proof. The author makes a mistake right off the bat, and his proof is spurious. The author says, let a=1 and b=1. Then he proceeds to divide by a-b. But one must say, in doing this division, that a and b cannot be equal, so as to avoid dividing by 0, which is not allowed. I pointed this error out to my student, who had already seen the mistake for himself. We are studying rational expressions at the moment, looking for extraneous roots, and one of the first things you must point out is that the denominator may not be zero. This isn't a paradox. This is simply an algebra 1 error. I marvel that some editor didn't catch it.
Rating: 1
Summary: Jumbled mess of ideas
Comment: This is a mildly interesting and entertaining book about history of zero that unfortunately tries to be too cute with its style and to pull in so many unrelated ideas, it loses focus as you turn the pages. When "Zero" stays on topic it's OK. Seife has a pretty good grounding in most of the history, and it was facsinating to read about how the number was used for such simple purpose for Babylonians but became so important for abstract number systems later.
Middle section of the book deals with zero in calculus, useful for any student toughing it out thru intro calc. But Seife gets too drawn in to all the goofy philosophical wanderings you can make about zero, he goes off on way too many tangents that don't make sense. Yes, you can't divide 1 by 0 and the number has a special role in most operations, but how do these properties threaten to bring down the whole framework of math (to paraphrase)? There's all kinds of talk about how zero and infinity are just two sides of the same coin-- why? The author tries to sound like a sage but doesn't make much sense with the claims on these pages.
Whole thing comes apart in the last couple of chapters on physics, cosmology, and applied math which are slim on facts and chock-full of flowery language about how important zero is but where the author really doesn't back his claims. In fact, as the book goes on it seems to make less sense, as though it doesn't quite know what it's supposed to be saying as it moves farther afield from history and calculus. Why are these later chapters even here? They don't add anything and detract from the book's overall value.
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Title: e: The Story of a Number by Eli Maor ISBN: 0691058547 Publisher: Princeton Univ Pr Pub. Date: 04 May, 1998 List Price(USD): $18.95 |
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Title: Alpha and Omega: The Search for the Beginning and End of the Universe by Charles Seife ISBN: 0670031798 Publisher: Viking Press Pub. Date: 10 July, 2003 List Price(USD): $24.95 |
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Title: The Joy of Pi by David Blatner ISBN: 0802775624 Publisher: Walker & Co Pub. Date: September, 1999 List Price(USD): $12.00 |
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Title: The Nothing That Is: A Natural History of Zero by Robert Kaplan, Ellen Kaplan ISBN: 0195142373 Publisher: Oxford Press Pub. Date: January, 2001 List Price(USD): $11.95 |
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Title: To Infinity and Beyond by Eli Maor ISBN: 0691025118 Publisher: Princeton Univ Pr Pub. Date: 09 July, 1991 List Price(USD): $19.95 |
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