Charles Seife

Ever since my teacher in 4th grade asked the class what was one divided by zero and I said infinity.....and was roundly condemned, on the grounds that a) it was meaningless to divide by zero and b) "you can't divide by zero" .........I've been on a mild personal quest to prove the teacher wrong. So I've had a bit of an unhealthy interest in the concept of zero and this book certainly caught my attention. I thought it would have all the answers. Well it has a few and bits of it are show more interesting. For example, it was interesting to me to find that the Babylonians invented the concept; the Greeks banned it; the Hindus worshipped its and the Christian church used it to fend of heretics until forced to accept it. I found that there is almost as much about infinity in this book as there is about zero.....both concepts have proved especially puzzling.
Seife suggests that now-days everybody knows that zero can't really sit anywhere on the number line, because it has a definite numerical value its own. It is the number that separates the positive numbers from the negative numbers. It is an even number, and it is an integer that precedes one. Zero must sit in its rightful place on the number line; before one and after negative one. Nowhere else makes any sense. Yet zero sits at the end of the computer and at the bottom of the telephone because we ways start counting with one. And, I must say, in Australia out building levels start at zero (or more usually "ground-level") but in Japan there is no zero level....ground level is One, etc.
The widespread usage of zero entered Europe via trade and commercial usage and in the end the governments had to relent in the face of commercial pressure. The Arabic notation was allowed into Italy and soon spread throughout Europe. Zero had arrived -as had the void. The Aristotelian wall was crumbling, thanks to the influence of the Muslims and the Hindus, and by the 1400s even the staunchest European supporters of Aristotelianism had their doubts. Thomas Bradwardine, who was to become archbishop of Canterbury, tried to disprove atomism, Aristotle's old nemesis. At the same time, he wondered whether his own logic was faulty, since he based his arguments on geometry, whose infinitely divisible lines automatically reject atomism. However, the battle against Aristotle was far from over. If Aristotle were to fall, the proof of God -a bulwark of the church - was no longer valid. A new proof was needed.Worse yet, if the universe were infinite, then there could be no centre. How could Earth, then, be the centre of the universe? The answer was found in zero.
With the introduction of calculus by Newton and Leibniz, mathematicians had a wonderful tool that seemed to give the right answers bu nobody could explain how those infinitesimals disappeared when squared; they just accepted the fact because making them vanish at the right time gave the correct answer. Nobody worried about dividing by zero when.... conveniently ignoring the rules of mathematics....... explained everything from the fall of an apple to the orbits of the planets in the sky. Though it gave the right answer, using calculus was as much an act of faith as declaring a belief in God. (I'm rather reminded of quantum mechanics and quantum chromodynamics).
I've never understood Riemannian mathematics and Seife has the clearest explanation that I've ever seen. Though maybe if I'd actually read some texts about Riemann geometry etc., I would understand it better. Here is part of Siege's explanation: "Riemann imagined a translucent ball sitting atop the complex plane, with the south pole of the ball touching zero. If there were a tiny light at the north pole of the ball, any figures that are marked on the ball would cast shadows on the plane below. The shadow of the equator would be a circle around the origin. The shadow of the southern hemisphere is inside the circle and the shadow of the northern hemisphere is outside (Figure 36). The origin-zero - corresponds to the south pole. Every point on the ball has a shadow on the complex plane; in a sense, every point on the ball is equivalent to its shadow on the plane and vice versa. Every circle on the plane is the shadow of a circle on the ball, and a circle on the ball corresponds to a circle on the plane ... with one exception.If you've got a circle that goes through the north pole of the ball, the shadow is no longer a circle. It is a line. The north pole is like the point at infinity that Kepler and Poncelet imagined. Lines on the plane are simply circles thatmgo through the north pole---the point at infinity. Once Riemann saw that the complex plane (with a point at infinity) was the same thing as a sphere, mathematicians could see multiplication, division, and other, more difficult operations by analyzing the way the sphere deformed and rotated. For instance, multiplying by the number i was equivalent to spinning the sphere 90 degrees clockwise.........And there it is ...on p144 1/0 = infinity and 1/infinity = zero. Was I actually right in 4th grade?
When Seife starts to get into the concepts of the Quantum zero (or the void) he seems to b e moving into slightly mystical territory tho my way of thinking but here is his rationale: How could the vacuum, which has nothing in it, have any energy at all? The answer comes from another equation Einstein's famous E=mc squared. This simple formula relates mass and energy: the mass of an object is equivalent to a certain amount of energy. (In fact, particle physicists don't measure the mast of the electron, say, in kilograms or pounds or any of the usual units of mass or weight. They say that the electron's rest man is 0.511 MeV [million electron volts] -a lump of energy.) The fluctuation in the energy in the vacuum is the same thing as a fluctuation in the amount of mass. Particles are constantly winking in and out of existence, like tiny Cheshire cats. The vacuum is never truly empty. Instead, it is seething with these virtual particles; at every point in space, an infinite number are happily popping up and disappearing. This is the zero-point energy, an infinity in the formulas of quantum the. ory. Interpreted strictly, the zero-point energy is limitless. According to the equations of quantum mechanics, more power than is stored in all the coal mines, oil fields, and nuclear weapons in the world is sitting in the space inside your toaster. When an equation has an infinity in it, physicists usually assume that there is something wrong; the infinity has no physical meaning. The zero-point energy is no different; most scientists ignore it completely. They simply pretend that the zero-point energy is zero, even though they know it is infinite.
It's a convenient fiction, and it usually doesn't matter. However, sometimes it does. In 1948 two Dutch physicists, Hendrick B. G. Casimir and Dik Polder, first realized that the zero-point energy can't always be ignored. The two scientists were studying the forces between atoms when they realized that their measurements didn't match the forces that had been predicted. In a search for an explanation, Casimir realized that he had felt the force of nothing.
Current thinking is that there is no question that the vacuum has energy; the Casimir force is witness to that fact. But is it possible that the energy of the vacuum is truly the lowest possible energy? If not, danger might be lurking in the vacuum. In 1983 two scientists suggested in Nature that tinkering with the energy of the vacuum might cause the universe to self-destruct. The paper argued that our vacuum might be a "false" vacuum in an unnaturally energetic state - like a ball perched precariously on the side of a hill. If we give the vacuum a big enough nudge, it might start rolling down the hill-settling into a lower energy state -and we would not be able to stop it. We would release a huge bubble of energy that expands at the speed of light. Though current thinking seems to dismiss this view as unlikely.
Siege, also veers into string theory...seemingly giving it the "thumbs up" though I have my on my way reservations about such a complex theory which doesn't seem to be testable.
Overall, an interesting book which looks at the concept of zero from multiple perspectives ...and not all mathematical. I give it 3.5 stars. show less

Rather a good book, but it needed a better editor. "as many as 5% of the people who are on death row are not guilty of the crime they committed" is not what the author intended, surely.

He invents or formalizes some good catch phrases for the different kinds of deception he describes: Potemkin numbers, cherry-picking, comparing apples and oranges, apple polishing, randumbness, causuistry, dis-estimation, regression to the moon, risk mismanagement. He also uses a few good technical terms show more invented by other people like absolute malice and pseudoevent. He distinguishes very nicely between systematic and statistical error in polling. He describes how poll questions may be chosen to manipulate rather than discover public opinion. He makes the important, and little made, point that the counting of votes is a kind of measurement with considerable built in inaccuracy, and that the contested 2000 presidential election and the contested 2008 Senate race in Minnesota were, by the same standard we would apply when, e.g., comparing the length of two pencils with a ruler, a draw, and should have been treated that way. He does not support this point w/ enough statistical evidence, he does not prove that the inherent inaccuracy in the vote counting swamped the difference between the counts for the opponents, but his argument that this is another very significant case of dis-estimation is a good one. He discusses the practice of gerrymandering, which probably needs a separate book all its own. I currently live right next to the very first ever gerrymander! He discusses the pathetic misuse of statistics and expert witnesses who use statistics in the courts of law and the grotesque lying of supreme court justices. He discusses statistical propaganda and warfare. He discusses the precise meaning of "margin of error" when that phrase is used by news media.

He is positive about electronic voting and he demands that all the software be open-source! Good for him!

The book has a bunch of endnotes, but alas, no further reading section.

I often feel a tremendous weariness with the news, since it is so full of this utterly vacuous proofiness. Seife has given me a name for what makes me so tired and at least a framework for objecting to it.

Not a partisan book; he seems to have made a very deliberate effort to pick on Republicans and Democrats equally and to point out very clearly with what faciilty opposing candidates swap principles when changing circumstances make it expedient. show less

No other number can do so much damage, so says Charles Seife. He tells you this as he is explaining the Golden Ratio, how Winston Churchill is equal to a vegetable, and how you can make your very own wormhole. Mathematics, religion, philosophy, art, engineering, history: they all connect to zero. Mathematics is a more obvious element, but take religion: Shiva, one of the three gods in the Hindu triumvirate, represents nothing because Shiva's role is to destroy the universe in order to show more perpetually recreate it. Seife goes deep to illustrate the importance of the zero and how, historically, it created as well as calmed chaos. Zero is historical and humorous, informative and even a little emotional. show less

I bought and read this book based on the enthusiastic recommendation of Peter Woit, the outspoken critic of string theory who runs the blog Not Even Wrong. In this unauthorized biography of Stephen Hawking, Charles Seife did a remarkable job of retaining my interest. (Remarkable, because pop science is a genre with which I've not had a lot of luck in the past.) It was fascinating to learn more about the man Stephen Hawking, warts and all. And Seife's descriptions of Hawking's cosmological show more results seemed clear and not dumbed down.

I subtracted half a point from a perfect 5-star rating because of repetition, one of my pet peeves. I think Seife felt he had to repeat some things because he had decided to tell Hawking's story (roughly) in reverse chronological order. That decision was not as annoying as it might have been, but I think the book would have been better without that gimmick. show less