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e455696
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Zero is powerful because it is infinity's twin. They are equal and opposite, yin and yang. They are equally paradoxical and troubling. The biggest questions in science and religion are about nothingness and eternity, the void and the infinite, zero and infinity. The clashes over zero were the battles that shook the foundations of philosophy, of science, of mathematics, and of religion. Underneath every revolution lay a zero - and an infinit..
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Charles Seife |
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8713c3d
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We tend to shy away from data that challenges our assumptions, that erodes our preconceptions. Getting rid of our wrong ideas is a painful and difficult process, yet it's that very process that makes data truly useful. A fact becomes information when it challenges our assumptions. These challenges are the raw material that forces our ideas to evolve, our tastes to change, our minds to grow.
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Charles Seife |
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728d270
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There are many ways to generate numerical falsehoods from data, many ways to create proofiness from even valid meaurements. Causuistry distorts the relationships between two sets of numbers. Randumbness creates patterns where none are to be found. Regression to the moon disguises nonsense in mathematical-looking lines or equations or formulae, making even the silliest ideas seem respectable. Such as the one described by this formula: Callip..
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Charles Seife |
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7701ad0
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Bad information is a disease that attacks the brain. It messes with your head, making you do things that you shouldn't, causing you to make wrong decisions. Just as a potent virus co-opts your cells' machinery, bad information can co-opt your behavior. It can alter the way you interact with the world and, as a result, it can change the world.
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Charles Seife |
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7854ff7
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The body, the house of the spirit, is under the power of pleasure and pain," explains a god. "And if a man is ruled by his body then this man can never be free."
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Charles Seife |
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d8c86d6
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My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. How do I know this? I have studied it...I have followed its roots, so to speak, to the first infallible cause of all created things. --GEORG CANTOR
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Charles Seife |
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51f14ac
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As mathematicians were uncovering the connection between zero and infinity, physicists began to encounter zeros in the natural world; zero crossed over from mathematics to physics. In thermodynamics a zero became an uncrossable barrier: the coldest temperature possible. In Einstein's theory of general relativity, a zero became a black hole, a monstrous star that swallows entire suns. In quantum mechanics, a zero is responsible for a bizarre..
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Charles Seife |
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0aefd72
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When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science. --WILLIAM THOMSON, LORD KELVIN
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Charles Seife |
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39dfc4e
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With news and data that is tailored to our prejudices, we deprive ourselves of true information. We wind up wallowing in our own false ideas, reflected back at us by the media. The news is ceasing to be a window unto the world; it is becoming a mirror that allows us to gaze only upon our own beliefs.
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Charles Seife |
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9e8d71b
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Where there is the Infinite there is joy. There is no joy in the finite. --THE CHANDOGYA UPANISHAD
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Charles Seife |
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f88e027
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Not only does the media fail to challenge our preconceptions - instead reinforcing them as media outlets try to cater to smaller audiences - but we all are able to find small groups of people who share and fortify the beliefs we have, no matter how quirky or outright wrong they might be. Ironically, all this interconnection is isolating us. We are becoming solipsists, trapped in worlds of our own creation.
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Charles Seife |
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56ce0a9
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A bad idea, a wrong piece of information, a digital brain-altering virus can spread at the speed of light through the internet and quickly find a home among a dispersed but digitally interconnected group of true believers. This group acts as a reservoir for the bad idea, allowing it to gather strength and reinfect people; as the group grows, the belief, no matter how crazy, becomes more and more solidly established among the faithful.
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Charles Seife |
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f587bb1
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Skinnerian conditioning, crossed with social pressure, is now an ever-present invisibly hand that tries to manipulate all of your actions on the internet. This is the hand that is making you act against your own self-interest. Once you recognize it, you see it everywhere, hovering over you, trying to make you click your mouse or press buttons on your smartphone, giving up your valuable time, money, or information in return for little or not..
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Charles Seife |
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5dc2b38
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Skinnerian conditioning, crossed with social pressure, is now an ever-present invisible hand that tries to manipulate all of your actions on the internet. This is the hand that is making you act against your own self-interest. Once you recognize it, you see it everywhere, hovering over you, trying to make you click your mouse or press buttons on your smartphone, giving up your valuable time, money, or information in return for little or not..
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Charles Seife |
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ff6a529
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Just as it's important to take the changing value of a dollar into account when comparing spending over time, it's important to take doctors' changing diagnoses into account when looking at disease trends
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Charles Seife |
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4a075b1
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Digital information has an unbelievably high R0 [basic reproductive rate], and this means that it's hard to stop once it emerges. It spreads from person to person - even those at a great distance - incredibly quickly, thanks to its high transmissibility and the high interconnectedness of digital society. Once it escapes into the wild, it's all but impossible to stop its spread. This is wonderful, so long as the information is correct and us..
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Charles Seife |
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0feb11d
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The Mayan system made more sense than the Western system does. Since the Western calendar was created at a time when there was no zero, we never see a day zero, or a year zero. This apparently insignificant omission caused a great deal of trouble; it kindled the controversy over the start of the millenium. The Mayans would never have argued about whether 2000 or 2001 was the first year in the twenty-first century. But it was not the Mayans ..
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Charles Seife |
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7bfcabc
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The Greeks couldn't do this neat little mathematical trick. They didn't have the concept of a limit because they didn't believe in zero. The terms in the infinite series didn't have a limit or a destination; they seemed to get smaller and smaller without any particular end in sight. As a result, the Greeks couldn't handle the infinite. They pondered the concept of the void but rejected zero as a number, and they toyed with the concept of th..
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Charles Seife |
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5c44558
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The infinite zero of a black hole-mass crammed into zero space, curving space infinitely-punches a hole in the smooth rubber sheet. The equations of general relativity cannot deal with the sharpness of zero. In a black hole, space and time are meaningless.
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Charles Seife |
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5b43cd4
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See appendix A for a proof that Winston Churchill was a carrot.
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mathematics
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Charles Seife |
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05a51cd
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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--..
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Charles Seife |
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011cf1c
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Quantum mechanics has a similar problem, a problem related to the zero-point energy. The laws of quantum mechanics treat particles such as the electron as points; that is, they take up no space at all. The electron is a zero-dimensional object, and its very zerolike nature ensures that scientists don't even know the electron's mass or charge.
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Charles Seife |
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a209673
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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^2. This simple formula relates mass and energy: the mass of an object is equivalent to a certain amount of energy. (In fact, particle physics don't measure the mass 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 mass is .511 MeV [mil..
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Charles Seife |
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61d09ac
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The electron that scientists see in the laboratory-the electron that physicists, chemists, and engineers have known and loved for decades-is an impostor. It is not the true electron. The true electron is hidden in a shroud of particles, made up of the zero-point fluctuations, those particles that constantly pop in and out of existence. As an electron sits in the vacuum, it occasionally absorbs or spits out one of these particles, such as a ..
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Charles Seife |
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b69a6ac
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In string theory, zero has been banished from the universe; there is no such thing as zero distance or zero time. This solves all the infinity problems of quantum mechanics.
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Charles Seife |
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This is the definition of the infinite: it is something that can stay the same size even when you subtract from it.
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Charles Seife |
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0084858
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Banishing zero also solves the infinity problems in general relativity. If you imagine a black hole as a string, no longer do objects fall through a rip in the fabric of space-time. Instead, a particle loop approaching a black-hole loop stretches out and touches the black hole. The two loops tremble, tear, and form one loop: a slightly more massive black hole. (Some theorists believe that the act of merging a particle to a black hole create..
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Charles Seife |
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e8fc474
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Removing zero from the universe might seem like a drastic step, but strings are much more tractable than dots; by eliminating zero, string theory smooths out the discontinuous, particle-like nature of quantum mechanics and mends the gashes torn in general relativity by black holes. With these problems patched over, the two theories are no longer incompatible. Physicists began to think that string theory would unify quantum mechanics with re..
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Charles Seife |
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45a836c
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In Cantor's mind there were an infinite number of infinities-the transfinite numbers-each nested in the other. Aleph 0 is smaller than Aleph 1, which is smaller than Aleph 2, which is smaller than Aleph 3, and so forth. At the top of the chain sits the ultimate infinity that engulfs all other infinities: God, the infinity that defies all comprehension.
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Charles Seife |
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fa3e6b7
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In the battle between Kronecker and Cantor, Cantor would ultimately prevail. Cantor's theory would show that Kronecker's precious integers-and even the rational numbers-were nothing at all. They were an infinite zero.
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Charles Seife |
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1c67c42
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Christianity initially rejected zero, but trade would soon demand it. The man who reintroduced zero to the West was Leonardo of Pisa. The son of an Italian trader, he traveled to northern Africa. There the young man-better known as Fibonacci-learned Mathematics from the Muslims and soon became a good mathematician in his own right.
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Charles Seife |
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1dd8812
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Though the Casimir force-a mysterious, phantom force exerted by nothing at all-seems like science fiction, it exists. It is a tiny force and very difficult to measure, but in 1995 the physicist Steven Lamoreaux measured the Casimir effect directly. By putting two gold-covered plates on a sensitive twist-measuring device, he determined how much force it took to counteract the Casimir force between them. The answer-about the weight of one sli..
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Charles Seife |
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6a2b241
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Zero dwells at the juxtaposition of quantum mechanics and relativity; zero lives where the two theories meet, and zero causes the two theories to clash. A black hole is a zero in the equations of general relativity; the energy of the vacuum is a zero in the mathematics of quantum theory. The big bang, the most puzzling event in the history of the universe, is a zero in both theories. The universe came from nothing-and both theories break do..
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Charles Seife |
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4047c33
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In 1933, the Indian Subrahmanyan Chandrasekhar realized that the Pauli exclusion principle had only a limited ability to fight against the squeeze of gravity. As pressure in the star increases, the Pauli exclusion principle states that ekectrons inside must move faster and faster to avoid one another. But there's a speed limit: electrons cannot move faster than the speed of light, so if you put enough pressure on a lump of matter, electrons..
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Charles Seife |
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f743e81
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Further calculations showed that when collapsing stars are a little more massive than the Chandrasekhar limit, the pressure of the resulting neutrons-similar to the pressure of electrons-can stave off collapse for a little while; this is what happens in a neutron star. At this point, the star is so dense that every teaspoon weighs hundreds of millions of tons. There is a limit, though, to even the pressure that neutrons can bear. Some astro..
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Charles Seife |
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ca8b05d
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The key to a black hole's strange properties is the way it curves space-time. A black hole takes up no space at all, but it still has mass. Since the black hole has mass, it causes space-time to curve. Normally, this would not cause a problem. As you approach a heavy star, the curvature gets greater and greater, but once you have passed the outer edge of the star itself, the curvature decreases again, bottoming out at the center of the star..
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Charles Seife |