Customer Reviews

Zero: The Biography of a Dangerous Idea

5 star:		(73)
4 star:		(45)
3 star:		(22)
2 star:		(9)
1 star:		(15)

 

 

I've recently read both Charles Seife's "Zero:The Biography of a Dangerous Idea" and Robert Kaplan's "The Nothing That Is: A Natural History of Zero." They are at the same time very similar and very different. They each follow an almost identical line, presenting the evolution of zero chronologically, and they each make almost identical stops along the way. The difference is in how they treat the steps in zero's evolution which is conditioned by their differing metaphysical views. An illuminating example is how they each treat Aristotle's role in zero's history.

Charles Seife, from the beginning, reifies zero: the author accepts the misconception that zero is some sort of actually existing mystical force resting at the center of black holes. He doesn't step back to take a look at the concept as concept. Nor does he appear to keep in mind that mathematics is the science of measurement, or that time is not a force or dimension, but merely a measurement of motion. This distorts his perspective, from which he attempts to refute Aristotle's refutation of the existence of the void: for Seife, zero exists and is a force in and of itself. In Seife's hands, zero certainly is a dangerous idea!

Robert Kaplan, on the other hand, delves deeper. His work is informed by an obvious love for history and classic literature, and while this results in many obscure literary asides, one feels that this book takes part in the Great Conversation. As a result he steps back and takes a critical look at the true meaning and usefulness of the concept as a concept. Is zero a number? Is it noun, adjective, or verb? Does it actually exist outside of conceptual consciousness or is it exclusively a tool of the mind?

Both authors follow zero's role in the development of algebra and the calculus. As a math "infant", this reader, having read Seife's book first, found that the explanations of these two developments by Kaplan cleared away the haze, which Seife's book was unable to do. I found both books to be illuminating. Seife's book contains much valuable historical information. He did his homework. If one were to read only this book on the subject, one would have learned a great deal about the history of mathematics. But if I were to have to choose one to recommend, it would be Kaplan's book. It is more informed, more seasoned, more honestly inductive in its approach.

This book is about the history of zero, from ancient times to modern concepts. It's quite interesting and encompasses a lot of mathematics and philosophy as well as a bit of physics.

Although the book reads well, is nicely documented, and extensively researched, the author has a style that I found aggravating; his frequent use of poetic hyperbole. This limits the book's value for someone unfamiliar with basic concepts in mathematics and physics.

I'm not sure why Seife choose this style. There seems to be a movement (hopefully short lived) among science writers to dress up science and mathematics in poetic, flowery language. Whatever the reason, science has good reason to use strict meanings for words and a disciplined approach to scientific concepts. When authors poetically use words in technically incorrect ways they can make the prose pretty, but they often create confusion.

For example, Saif says "Zero and infinity are eternally locked in a struggle to engulf all the numbers. Like a Manichaean nightmare, the two sit on opposite poles of the number sphere, sucking numbers in like tiny black holes." [p. 145]

From a mathematical point of view this is pure gibberish. If one's intent is to educate others about mathematics, such poetic hyperbole is not only useless, but counter productive as well. For folks who don't already know a bit about mathematics, Seife's book is as likely to confuse as to educate. For those who already understand the concepts, the poetry might be pleasing, but from an educational point of view the hyperbole found throughout this book is a definite stumbling block.

Another problem I had with this book is the way Seife misstates some key aspects in modern science. For example, on page 171 he asserts the classical definition of a vacuum: "The vacuum, by definition, has nothing in it - no particles, no light, nothing." He then describes the quantum mechanical view of the vacuum, and the zero-point energy. Part of this explanation includes a nice description of the Casimir effect [p. 172], which is a measurement of the literal existence of the "virtual" particles predicted by Quantum Mechanics. What these experiments show is that these "virtual" particles actually exist, and can be detected by the force they exert on closely spaced metal plates. This is actually a beautiful example of how science changed our concept of the vacuum. Classically, we thought of the vacuum as having "nothing in it," but Quantum Mechanics tells us that the classical vacuum cannot exist. But even after his nice explanation of the Casimir effect, Seife goes and spoils it with this absurd statement:

"Casimir realized that he had felt the force of nothing." [p. 172] "This is the force of the vacuum, a force produced by nothing at all. This is the Casimir effect."

It's as if someone asserted that the space around us has "nothing in it," and then rejoices when the wind touches his face, and runs off spouting "I've felt the force of nothing." What the Casimir effect teaches us is that what we thought was "nothing at all" really is something, and that calling them "virtual" particles is just as silly as early mathematicians who called the square root of negative numbers "imaginary."

There are other mistakes as well. For example, on page 178 he says: "The speed of light is the ultimate speed limit; you cannot reach it, much less exceed it. Nature has defended itself from an unruly zero."

But this simply isn't true. Even a casual reader knows that the statement "you cannot reach it" is wrong. After all, photons travel at the speed of light all the time. Furthermore, scientists have known for years that, given the right materials, both the phase velocity and the group velocity of light can exceed the speed of light in a vacuum [Optics and Photonics News, June 2002]. All this is consistent within the framework of relativity, but Seife's hyperbole is likely to mislead the novice. Indeed, recent experiments showing these phenomena have resulted in all sorts of pundits on the Internet claiming that relativity had been falsified.

By getting all wound up with poetic hyperbole about nature "[defending] itself from an unruly zero" the author has, I fear, unwittingly contributed to the confusion of non-scientists about the science of relativity.

I don't mean to give the impression that this is a bad book. I actually found most of it readable and pleasant. I enjoyed the historical aspects and appreciated how the author illustrates the influence of philosophy, and especially religion, in either advancing or retarding cultural acceptance of the concept of zero. I thought he did a particularly nice job of explaining the development of the calculus, and how the concept of zero played its part. As usual, the primary distractions were related to his use of poetic hyperbole, as well as careless analogies. For example, on page 126 he writes:

"... using calculus was as much an act of faith as declaring a belief in god."

This absurd statement was almost certainly made without thinking. After all, even though early mathematicians could not explain why the calculus worked - at least not with rigorous logic - they could demonstrate that it *did* work. Furthermore, anyone could use it. A person didn't have to believe in calculus or work themselves into an emotional frenzy to calculate the volume of a sphere. The same cannot, of course, be said of god.

This could have been a really great book. The subject matter and story of zero are fascinating. Unfortunately, Seife uses too many analogies that are either poor, extreme, or misleading. And his persistent tendency toward exaggeration was a real distraction for me. For these reasons I'd not recommend the book to someone not already somewhat knowledgeable about mathematics and physics - I think it would be too confusing. For those who can read between the lines of poetic hyperbole, though, I think the book is worthwhile.

It may well be the most potent force in the universe. The Greeks were scared to death of it. Aristotle wouldn't permit it(and the Catholic Church's vice-grip on Aristotelianism held Western science and mathematics back for centuries). But this force does not discriminate; it delights in tripping up secular science as well. Certain forms of mathematics must ignore it in order to work. String theory basically pretends it isn't there. It is, as stated on the book jacket, "a timebomb ticking in the heart of astrophysics."

Zero.

Charles Seife's history of zero(and of infinity, which is awfully close to the same thing, as Seife elegantly demonstrates)is one of the most interesting and thought-provoking books I have read in a long time. There are mathematical and scientific equations and concepts aplenty here, but they were not daunting for this manifestly un-mathematic non-scientist. Seife has a fascinating story to tell and he tells it with enthusiasm. I cannot recommend Zero too highly.

Quite a few books recently have chosen the history of zero and the vacuum as their subject, and Seife's book is the clunker of the group. He has the dubious honor of bringing a tabloid style to math writing; his pages are replete with hyberbole and lame puns, as well as sometimes potty-mouthed in-jokes about mathematicians and various historical personages (Martin Luther in particular) that simply do not belong here.

This might be a pardonable sin, but Seife combines this problem with two others that are less forgivable-- frequent errors and outright arrogance. I could go on at length, but a review in the Notices of the American Mathematical Society captures the problems best. (...)

As Gray points out in the review, Seife says contradictory things about the Mayan calendar, in one place claiming that it is more consistent than the Gregorian (by including a zero year in the calendar) but then showing how the mixing of 3 different calendars led to confusion about the days. At one point the book also notes how zero was an ancient concept beginning thousands of years before the first civilization, but later suggests it started just a few centuries before Christ in the Fertile Crescent. Seife's book is full of these maddening little errors, which together suggest that he was not thorough in his research and proofreading.

Seife's discussion of the history of calculus is woeful, as Gray further notes. Seife conflates the history of Newtonian calculus with its representation in differential equation form, and exaggerates the importance of the indeterminate expression-- 0/0-- and its confrontation via L'Hopital's rule, in establishing the foundation of the calculus.

The last third of the book, which moves into cosmology and physics, is simply awful; Seife has no idea what he's talking about, and his discussions are based either on totally outdated information or misconceptions of one kind or another. He states that "a black hole is a point." This is totally wrong! Even the singularity-- which had for a while been considered something like a point-- is probably not a point, as work in the past decade on quantum gravity has shown; and in any case, the black hole itself is a collapsed object and is not modeled as a point. Most disappointingly of all, Seife almost completely skips over the total alteration of the physical vacuum based on quantum physics-- this is precisely why "zero" and the "vacuum" are so interesting these days, *because* the vacuum is known to be such a vibrant place, but Seife's book totally misses this. As Gray goes on to point out, the fundamental flaw with Seife's sloppy book is that it wants less "to instruct" the reader than to get the reader "to marvel," so the book is high on flash and poor on substance.

I'd strongly encourage anyone to read Gray's review, as it goes into much more depth that can be provided here. The only "dangerous idea" of Seife's book is the possibility that it might wind up recommended in school classrooms, leading students and teachers down the path of misinformation.

I am emphatically NOT a math person - in fact I avoid math whenever possible. I started this book essentially under duress from a friend. It came as rather a shock that it was not only interesting, but understandable - even enjoyable.

I always considered numbers static quantitative figures, used for counting and for plugging into formulas when forced. I never considered that numbers could have an impact on religion, philosophy, and science. They're just numbers - they don't do anything. But in reality, there was a cosmological shift required to accept a number that we take for granted. By following a chronological "biography" of zero, you see that the concepts of zero and infinity have caused as much intrigue, politicking, and murder as either love or money ever has. You see how civilizations, religions, and rulers rose and fell partly based on their acceptance of numbers. The impact of the concepts of nothingness and infinity continues today and the book gives insight into some really interesting concepts - wormholes in space/time, the nature of the universe, etc.

There is some math, but the theories are clearly and wittily explained - even if you don't crunch the numbers, you'll get the concepts. And you can console yourself with the thought that you're in good company - even Einstein used a cosmological constant to make his formulas work out!(It's in the book.) The author clearly knows and loves his subject, and does a great job of sharing his enthusiasm with the reader.

Zero: The Biography of a Dangerous Idea is a book based on an intriguing idea, the history of zero. It's
something that most of us don't often contemplate. Some of us may know that zero, at least as a place holder,
was invented/discovered by the Mayans, but beyond that most of us haven't a clue. At least I hadn't.

Charles Seife begins his discourse with the earliest history of numbers. Counted things first appear in the
archaeological record as marks on bones in the the stone age. Early civilizations had little use for a concept
of zero; one rarely counts no apples or no sheep, etc. Ancient Egyptian mathematics seems to have been limited to measuring land areas and calendaric time for which zero in their method was unnecessary. In fact, it is the early calendar's persistent lack of zero in day and year counting that led to the confusion over when the 21st century started. The Babylonians likewise used
math for celestial observation and calendars, but they also introduced zero as a place holder which simplified the writing of numbers and doing simple arithmetic.

It is among the Greek philosophers that Seife sees an outright distaste for the concept of zero as nothing, a void. It conflicted with their particular notions of the universe and how it operated. Their aversion to it seems to have
carried over into the Mediaeval European period by way of the offended established principles of the church.
Seife follows the history of zero to modern times and discusses some of the ways that zero and infinity are
the same and some of the ways that they oppose one another. He brings both quantum mechanics and relativity theory into the discussion, revealing some of the ways that looking at zero and infinity have led to advances in physics in more recent times.

The author is a science writer with an MS in mathematics. As a journalist his style is both enjoyable and readable, making a complex subject more accessible to the average individual--that is, he doesn't bog one down with a lot of complicated equations. I'm no math wiz by any means, but I understood his thesis in its
entirety. Those who've studied math in greater depth may find the book a little patronizing or at least a little too heavy on the verbal form and a little too light on the math.

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.

Here is a mostly enjoyable work of popular science in which we learn the true power of zero, which is far from nothing. The odd mathematical properties of zero have had vast implications in the development of math and science, and even intellectual and cultural development around the world. Zero is extremely important for, and even dangerous to, time-tested conceptions of reality. Most of this book provides a perfectly enjoyable history of zero as an idea. However, Charles Seife falls into the trap that often afflicts pop science books, in that he tries to soup up his narrative by claiming that his subject (zero) is connected to just about everything else in the universe. Seife's attempted connection to matters of both western and eastern religion stretch the limits of believability, as do his attempts to tie the numerical version of zero to vast concepts of the void and infinity in science and philosophy. Therefore, the book gets farther and farther away from the history of the idea of zero, which is inherent in the book's title, and gets stuck in esoteric matters of advanced physics and calculus. At this point Seife is reduced to non-sequiturs about how zero is still a part of the discussion, although you wouldn't really think so otherwise. This is still a quite successful work of popular science (and math), though Seife can't quite find the proper balance between zero and infinity – that is, an infinite belief in the importance of zero in everything the reader knows or conceives. [~doomsdayer520~]

I can't recommend this book highly enough. For everyone who has ever struggled with mathematics, this book shows that through history mathematicians also had their struggles with what might appear to be the simplest of numbers, zero. While focusing squarely on the history of zero, the book leaves the reader with so much more. By the end, you have an appreciation for the subtlety and beauty of mathematics. To illustrate, in one chapter Seife tells how a the student of the famous Gauss, using ideas found by a Frenchman who was imprisoned in Russia, found that zero and infinity are twins diguised as opposites.

Seife's writing is clear and engaging. I read this book much like I might read a well woven spy thriller, finding myself spending that extra few minutes indulging in luxurious reading rather than proceeding with mundane necessities of life (i.e., sleep).

And, as another reviewer has done, to contrast this book with another recent volume on the same topic, Kaplan's The Nothing that Is, the differences are remarkable. Succinctly, it is the difference between an enjoyable read and a grinding burden. Kaplan's book is unfocused, leaving the reader confused about where in time or space the historical events are occuring. Kaplan's side trips of literary fancy were very distracting to me and added little to the story. And story is the key. In Zero, Seife is telling a story and clearly enjoying telling it on its own terms. Kaplan did not tell a story, leaving the reader wondering why any particular part is being told. I understood from the start what Kaplan was trying to do, and I was bewildered that he failed so horribly. Seife's is, hands down, the better book on the subject of the history of zero.

A chore to make it through. Seife's account of the history of the acceptance of zero is mildly interesting, but very repetitive. Seife repeatedly makes value judgements and then doesn't justify them (For example, he complains many times about the damage that the exclusion of zero has done to the calendar, without ever going into detail about why anyone should care as much as he seems to about the supposed damage).

Seife should have stuck to history though; his attempts to tie together disparate areas of physics with zero as rhetorical glue amount to little more than annoying handwaving.