Zero Quotes

“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 infinity.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“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.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“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”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“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 source of energy-infinite and ubiquitous, present even in the deepest vacuum-and a phantom force exerted by nothing at all.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“Where there is the Infinite there is joy. There is no joy in the finite. —THE CHANDOGYA UPANISHAD”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“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”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“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 the infinite but refused to allow infinity-numbers that are infinitely small and infinitely large-anywhere near the realm of numbers. This is the biggest failure in Greek mathematics, and it is the only thing that kept them from discovering calculus.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“See appendix A for a proof that Winston Churchill was a carrot.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“This is the definition of the infinite: it is something that can stay the same size even when you subtract from it.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“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 down when they try to explain the origin of the cosmos.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“Nature speaks in equations.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“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.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“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.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“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. Take any number on the plane. For the sake of argument, we'll choose i/2. Square it. Cube it. Raise it to the fourth power. The fifth. The sixth. The seventh. Keep multiplying. It slowly spirals toward zero like water down a drain. What happens to 2i? The exact opposite. Square it. Cube it. Raise it to the fourth power. It spirals outward. But on the number sphere, the two curves are duplicates of each other; they are mirror images. All numbers in the complex plane suffer this fate. They are drawn inexorably toward 0 or toward infinity. The only numbers that escape are the ones that are equally distant from the two rivals-the numbers on the equator, like 1, -1, and i. These numbers, pulled by the tug of both zero and infinity, spiral around on the equator forever and ever, never able to escape the grasp of either. (You can see this on your calculator. Enter a number- any number. Square it. Square it again. Do it again and again; the number will quickly zoom toward infinity or toward zero, except if you entered 1 or -1 to begin with. There is no escape.)”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“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, leaving a vast trail of destruction in its wake. It might be so bad that every one of our atoms would be torn apart during the apocalypse.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“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 who formed our calendar; it was the Egyptians and, later, the Romans. For this reason, we are stuck with a troublesome, zero-free calendar.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“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.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“However, if we do discover a complete theory, it should in time be understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists, and just ordinary people, be able to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason—for we would know the mind of God.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“But if there were some sort of quantum sail, a one-way mirror that reflected virtual particles on one side but let them pass unhindered through the other, the vacuum energy would push the whole object toward the unreflective half of the sail. Millis admits that nobody has any clue how to do this.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“Today most mathematicians accept the continuum hypothesis as true, though some study non-Cantorian transfinite numbers where the continuum hypothesis is taken to be false.)”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“a mathematician could show how a triangle’s angles sum to 180 degrees, or any other geometric fact. On the other hand, calculus was based on faith.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“There was neither non-existence nor existence then; there was neither the realm of space nor the sky which is beyond. What stirred? Where? —THE RIG VEDA”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“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.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“December 31, 1999—not so for December 31, 2000. Everybody celebrated the turn of the millennium on the wrong date.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“The number-shape duality in Greek numbers made it easy; after all, zero didn’t”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“In other words, the diagonal of that square is irrational—and nowadays we recognize that number as the square root of two.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“Zero was the solution to the problem. By around 300 BC the Babylonians had started using two slanted wedges, , to represent an empty space, an empty column on the abacus. This placeholder mark made it easy to tell which position a symbol was in.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“wolf bone was the Stone Age equivalent of a supercomputer.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“Pythagoras concluded that ratios govern not only music but also all other types of beauty. To the Pythagoreans, ratios and proportions controlled musical beauty, physical beauty, and mathematical beauty. Understanding nature was as simple as understanding the mathematics of proportions.”
― Charles Seife, Zero: The Biography of a Dangerous Idea

“December 31, 1999, is the evening when the great odometer in the sky clicks ahead.”
― Charles Seife, Zero: The Biography of a Dangerous Idea