on April 4, 2004
The title of this book is "Zero: the Biography of a Dangerous Idea." Certainly, what Charles Seife wrote does not disappoint: it IS a biography of zero. It starts from its conception in early history, and progresses to outline its development in history through the branches of mathematics, physics, art, and even philosophy. A previous reader was disappointed that the book took time to focus on physics and philosophy, but keep in mind that zero is not limited only to the mathematical realm. Indeed, it is pervasive in society, and it has affected the way we view the world. So to talk about zero yet disregard its important contributions to fields other than mathematics would be a travesty.
Seife's book is a very engaging and enlightening read. Seife looks at how zero has become: the foundation for calculus (taking limits to zero), a revolutionary idea in art (3d drawings have a point of infinity to give depth perception...and infinity and zero are just different sides of the same coin), an important concept of the numberline, and many other places. Indeed, I have read this book many times, sometimes for a quick browse and sometimes for an indepth read, and it has always been a pleasure to read.
Moreover, Seife is very knowledgeable in what he writes, and he brings a sense of humor as well--if you have ever read his article about the debate on cold fusion in 'Science' or 'Scientific American' (it was one or the other, its been a while since that article was published in the early 90s I believe) you'll see his sense of humor in his concluding paragraph (cold fusion or confusion anyone?).
And in response to another review earlier, the reader said that in the appendix there was a proof where a=1 and b=1, and from the equation a^2 - b^2 = a^2 - ab it can be found that 1=0 by factoring the difference of squares and dividing by (a-b). The reader commented that this is dividing by 0, that such an operation violates a fundamental law of algebra (cannot divide by zero), and that an editor should have caught it.
The point is that Seife is showing WHY you cannot divide by 0, that the result is 1=0 and that logic and mathematics would be invalid. He is showing why zero may be a 'dangerous idea'!
In conclusion, this book is superb in its writing and content. It lives up to what it was meant to do, to show the development of zero through history. It is clear, concise, and witty. You will not be disappointed.
on November 15, 2003
This book was recommended to us as "ancillary reading" in Maths because it supposedly 1. would improve our understanding of how zero entered modern number systems and allowed for the foundations of calculus, and 2. help us to understand how the approaching-the-limit procedures basic to calculus are actually used in some applicable examples. It has done neither. The book jumps around far too much in its treatment of the history part. It would have better served its subject by more coherently examining how and why zero was initially left out and the practical reasons that it was let back into mathematics. The author seems to believe that there was some kind of philosophical conspiracy against the poor number among the Greeks, but the omission of zero from early number systems seems to result more from the fact that early civilisations did not find it useful in their daily affairs, except insofar as the Babylonians used it as a place-holder. Its acceptance later had more to do with its utility to merchants than to a philosophical "awakening" as the author seems to believe, and he should have given more attention to this commercial aspect.
The second part of the book, which considers the uses of zero in practical mathematics and technical fields, suffers from the same flaw that hampers the first part. The author is far too enamoured of zero as a sort of semi-philosophical keystone and he fails to explain why zero's inclusion has been truly useful. He becomes self-indulgent in the extent to which he admires the number and gets drawn so astray in the admiration of his subject that a dispassionate reader is left wondering what his point is. The latter pages are an especial let-down because the author briefly talks about some interesting subjects in physics and astronomy without addressing them in proper depth or making sense out of them. Disappointing overall.
on January 30, 2004
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.
on June 24, 2004
Entertaining book for students of philosophy, historians, and math neophytes, but Seife's simple-minded application of the principle of the conservation of energy to the quantum electrodynamic sea of spacetimemassenergy, i.e. the "zero point field," among other things, reveals him to be among the least imaginitive of physicists. His dismissive proposition that "nothing can come from nothing," overlooks the very simple fact that the QED sea of energy is hardly "nothing," otherwise there would be no such thing as Brownian motion or the Casimir Effect, not to mention the space, time, mass, and energy of our universe. Hal Puthoff claims that a cupful of this so called "vacuum energy" could boil away the oceans of our planet. (The most intriguing concept of "zero" is that promulageted by today's heretics such as Tom Bearden.) Presumably, however, Seife's math and philosophical history of zero is accurate. Before reading this book, this reader had known very little of it, and it was this part that he found quite enjoyable.
on June 16, 2004
Despite the abstract nature of it's subject matter, this book is a surprisingly breezy and informative read about the history of zero and it's value in the mathematics (and scientific) revolutions of the 1600s and still today. It's part history, part math primer, and part practical guide, with the later chapters focussing on how the zero is used in physics and astronomy.
Seiff has an engaging style and he doesn't talk down or talk above the reader. Although Seiff obviously is an expert in difficult math, he doesn't overwhelm you with equations or get too abstract. Even sections on trig and calculus are written in everyday language that you can easily follow. The book does begin to trail off at Chapter 7-8, from here much of the book seems like filler. I preferred "The Nothing That Is" (also about the zero number) a little because I was more interested in the history and that book covers it more, but Seiff still does a fine job here with history of zero, and his book is probably more useful for students trying to know how to use the zero and it's concepts for their math classes, especially figuring out the limit and other calculations.
on April 2, 2004
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.
on February 14, 2004
I had a frustrating experience reading this book because of the way the author gets the history of Aristotle's teachings and thought in Europe so thoroughly mixed up.
Most of this book is about the history of the number zero and how it wound up in European number systems, which originally lacked it. The writer shows how zero gradually appeared in numeral systems in Asia and the Middle East, then began to crop up in European numbers when Mediterranean merchants in the Middle Ages found it to be useful. He shows how the important advancements of science and calculus in Europe in the 1600's depended on it so much. All true and fair enough.
But it's galling how the book works in the impact of Greek philosophy, which it lays out quite wrong. A theme repeated throughout the book is that medieval Europe was stuck in its anti-intellectual Dark Ages, blocked from the Scientific Revolution, and refusing to accept the zero in mathematics because its intellectual foundation was grounded too much in the thought of Aristotle. This is just plain wrong!
Medieval Europe was stuck in its unproductive doldrums precisely because it had forgotten about and virtually ignored the teachings of Aristotle. Aristotle was the one who had emphasized empirical observation and classification of facts-- the idea that would be at the basis of the scientific method. It was the thought of Plato and some of his colleagues, not Aristotle, that had been dominating Europe in the Middle Ages.
When Aristotle was finally re-introduced into Europe in the late Middle Ages from Middle Eastern scholars-- that's what sparked the changes in ideas that allowed the Renaissance and Age of Reason to take hold in the first place.
And Aristotle was not in any way the whole basis for Europe's lack of a zero in its numbers. There's a lot of citing of Aristotle's "Nature abhors a vacuum" comment here, but this had little to do with Europe consciously rejecting the zero, because there was no conscious rejection to begin with.
The Europeans were just using the Roman numeral system, which had no zero, because that was the custom of the day and people were used to it. Most number systems worldwide didn't have a zero because the various cultures figured they didn't need it-- there was no European "math legislature" that rejected a proposal to add a zero, it's just that nobody thought to add it in.
When the Mediterranean merchants began using the Arabic numerals with the zero, they just found it to be more useful than the Roman numerals, and for that practical reason people switched over. Simple as that.
Maybe Aristotle's "Nature abhors a vacuum" comment is right, since physicists seem to finding all kinds of wild particles and constituents filling up what's been called the vacuum. (The later part of this book explores these areas a little, and doesn't do a good job of it-- it's out of date and disorganized.) I don't know, I'm not an expert in this, but there's probably no easy explanation and the book's tendency to paint Aristotle as a misleading scholar becomes downright irritating.
Maybe I'm just being a picky classics student here, but it's frustrating to read the history of Aristotle in Europe be told so incorrectly. Aristotle's ideas if anything were the most essential ingredient for Europe's ability to wake up out of the Middle Ages and experience an intellectual flowering.
on February 5, 2004
I learned a lot reading this book, the best parts were the sections on the golden ratio and perspective. The golden ratio explanation on pp. 28-34 was awesome. The author shows how Phythagoras and the students in his school found a geometric ratio in all kinds of patterns in nature, from musical tones to the shape of a nautilus shell. He later even shows how Fibonacci, who was an Italian mathematician, found the golden ratio again in a number sequence which he first came up with when he posed a problem about increases in a rabbit population of all things! I was so amazed to read something like this, about a simple numerical ratio that would crop up over and over again in nature in so many different ways.
The book also gets into perspective on p. 85-87, which made paintings in the Renaissance look 3-D and so more accurate than medieval paintings, which looked flat and 2-D. It was so neat to discover how perspective depends on the vanishing point, which depends on an approximation to zero a lot like in calculus. So the painters in the Renaissance did such good work because they were able to use a new concept in math! Some of the book didnâ€™t seem well-written and was disorganized, especially later on. The quotes early in the chapters often didnâ€™t make much sense, and some of the figures shouldâ€™ve had legendsâ€"they were sometimes tough to follow and make sense out of. But I still learned a lot from this book.
on January 15, 2004
"Zero" is a potentially interesting book about a long-rejected mathematical concept that winds up reading like a bumpy subway ride. Seife's telling of the number's history is adequate, but the book begins to fizzle out about halfway through. There's a nice interlude on the way zero quickly changed mathematical theory and practice in the 1600s, with useful examples of how it's used to obtain a derivative. But when the book starts getting into the way that zero impacts not only modern mathematics but physics, it totally loses its audience. Seife almost sounds like someone wanting to be an oracle later in the book, and it gets to be irritating-- there are a lot of grandiose statements and specious bits of "wisdom" about zero and how it's changed the landscape of modern thought, with very little to back it up.
Modern physical theories use limit functions an awful lot which involve extrapolations to zero, but they also use pi, the natural log, all kinds of physical constants with weird values-- in short, there are a lot of "special numbers" with interesting applications, but Seife loses touch with reality in the extent that he portrays zero as a sort of scholar's gold. The practical result is that the book falls apart into a rambling clutter of disjointed, unorganized statements and references, and the last couple chapters are almost a labor to sit and read.
on January 3, 2004
Actually, 4 stars for the first half of the book, and 2 stars for the second half.
The 1st half of the book was an excellent review of the history of numbers since the days of Babylon, through Egypt, Persia, Greece, India, Arabia, Rome etc. Very well researched and very well presented.
Then after the Middle Ages something starts to go wrong. Seife seems to start throwing in anything he could think of that might remotely involve zero. Since 1 divide by 0 equals infinity, we started getting digressions about infinity. Some strange metaphysical musings started appearing, such as after describing the work of an Indian Mathematician, the chapter closed with "God was found in infinity - and in zero" -- huh?
Siefe was (overly) diligent in explaining the square root of -1 before introducing the concept of 'i'. However, he was less diligent (as in not at all) in introducing 'e' and 'pi', but that didn't stop him from simply stating one of Euler's discoveries that "e raised to the power (i times pi) = -1". However for Siefe this wasn't good enough, because there's no zero - so he rephrased it as "e raised to the power (i times pi) + 1 = 0". And he didn't share the proof, but simply stated the equation in vacuo, so to speak.
Similarly he then moved on to describe the Casimir effect (about the mutual attraction between 2 parallel plates in a vacuum). But this is a physical effect, not related to the history of the zero - but if a vacuum is a synonym for zero, then anything about vacuums is in scope. So we also move on to the speed of light, and works by Einstein & Maxwell, without a zero in sight?
Finally in one of the appendices Siefe presents one of the more famous paradoxes which appears to prove that 1=0; but then he spoils it by extending the number theory to show that Winston Churchill was actually a Carrot (as in the vegetable)? A silly move which added nothing to the value of the exercise.