Zero: The Biography of a Dangerous Idea

Rating:
Summary: Amusing Review of our Ancestors' Failings...
Review: Charles Seife is a great writer with humongous science and history knowledge. In "Zero," he manages easily to keep the reader interested in the (already interesting) subjects of nothing and everything. Definitely written for the more casual reader, he explains the original mathematicians' faults in dealing with irrationals, zero, and infinity, and explains proven and theoretical uses for the latter two in everyday science well.

For readers heavily interested in the subjects of physics and mathematics and their histories, Seife provides an extensive bibliography that will satisfy anyone's cravings for more knowledge. While Seife may not go into great detail in his chapters, he provides an excellent introduction to the topic, preparing the reader for more studies later on.

"Zero" is definitely a dangerous idea, more in the sense of its rejection and its historical struggle for eventual acceptance. Just as amazing as this idea is the book which should be read by any one even mildly interested in numerology and mathematics.

Rating:
Summary: Zero by charles Seife
Review: The work contains various theories about the number zero.
The study of zero has fascinated thinkers from Ancient Rome to
the Americas. Zero did not fit into the Pythagorean framework.
Saint Augustine defined it as formlessness without definition.
The number has a role in the quadratic formula. The work
contains many possible interpretation of the number zero in
philosophy, mathematics and academe. It is highly recommended
for a wide constiency in academe.

Rating:
Summary: Theme based on false premise about Aristotle's ideas
Review: 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.

Rating:
Summary: A very engaging, interesting, and enlightening read
Review: 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.

Rating:
Summary: Zero is not just a number, its a way of life
Review: A very interesting book. The Author shows how mindsets, philosophies and cultures had to change to enable the Zero to be accepted. The West overlooked then resisted the idea of zero.
When the zero idea took hold and was finally accepted it affected everything from Aristoteloism, to commerce, to Art. Even the biblical creation stories took on a different light.
Art in the West during the Renaissance gained a major improvement
as the sense of perspective was developed. This vanishing point within a painting is the equivalnt of the introduction of Zero into the art world .
I would read other books by this author, interesting history, The book moves right along, I like the Author's style, plenty of background, but always stayed the coure. I believe an audio book
is probably not the correct format for this information. I would have liked to have seen the test portraying some of the
equtions.

Rating:
Summary: Popular Intro to the Zero
Review: 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:
Summary: A very engaging, interesting, and enlightening read
Review: 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.

Rating:
Summary: Amusing Review of our Ancestors' Failings...
Review: Charles Seife is a great writer with humongous science and history knowledge. In "Zero," he manages easily to keep the reader interested in the (already interesting) subjects of nothing and everything. Definitely written for the more casual reader, he explains the original mathematicians' faults in dealing with irrationals, zero, and infinity, and explains proven and theoretical uses for the latter two in everyday science well.

For readers heavily interested in the subjects of physics and mathematics and their histories, Seife provides an extensive bibliography that will satisfy anyone's cravings for more knowledge. While Seife may not go into great detail in his chapters, he provides an excellent introduction to the topic, preparing the reader for more studies later on.

"Zero" is definitely a dangerous idea, more in the sense of its rejection and its historical struggle for eventual acceptance. Just as amazing as this idea is the book which should be read by any one even mildly interested in numerology and mathematics.

Rating:
Summary: Jumbled mess of ideas
Review: 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.

Rating:
Summary: Learned a lot from this book
Review: 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 didn’t seem well-written and was disorganized, especially later on. The quotes early in the chapters often didn’t make much sense, and some of the figures should’ve had legendsâ€"they were sometimes tough to follow and make sense out of. But I still learned a lot from this book.