In Are Numbers Real?, Brian Clegg explores the way that math has become more and more detached from reality, and yet despite this is driving the development of modern physics. From devising a new counting system based on goats, through the weird and wonderful mathematics of imaginary numbers and infinity, to the debate over whether mathematics has too much influence on the direction of science, this fascinating and accessible book opens the reader’s eyes to the hidden reality of the strange yet familiar entities that are numbers.

    Book by Waring, Chris

    In this unconventional introduction, physicist Leonard Susskind and hacker-scientist George Hrabovsky offer a first course in physics and associated math for the ardent amateur. Unlike most popular physics books—which give readers a taste of what physicists know but shy away from equations or math—Susskind and Hrabovsky actually teach the skills you need to do physics, beginning with classical mechanics, yourself. Based on Susskind's enormously popular Stanford University-based (and YouTube-featured) continuing-education course, the authors cover the minimum—the theoretical minimum of the title—that readers need to master to study more advanced topics.An alternative to the conventional go-to-college method, The Theoretical Minimum provides a tool kit for amateur scientists to learn physics at their own pace.

    A meld of history and science, this book is a group portrait of some of the greatest minds who ever lived as they wrestled with nature’s most sweeping mysteries. The answers they uncovered still hold the key to how we understand the world.At the end of the seventeenth century—an age of religious wars, plague, and the Great Fire of London—when most people saw the world as falling apart, these earliest scientists saw a world of perfect order. They declared that, chaotic as it looked, the universe was in fact as intricate and perfectly regulated as a clock. This was the tail end of Shakespeare’s century, when the natural land the supernatural still twined around each other. Disease was a punishment ordained by God, astronomy had not yet broken free from astrology, and the sky was filled with omens. It was a time when little was known and everything was new. These brilliant, ambitious, curious men believed in angels, alchemy, and the devil, and they also believed that the universe followed precise, mathematical laws—-a contradiction that tormented them and changed the course of history.The Clockwork Universe is the fascinating and compelling story of the bewildered geniuses of the Royal Society, the men who made the modern world.

    Breaking down the symbols themselves, they pose a series of questions: What is energy? What is mass? What has the speed of light got to do with energy and mass? In answering these questions, they take us to the site of one of the largest scientific experiments ever conducted. Lying beneath the city of Geneva, straddling the Franco-Swiss boarder, is a 27 km particle accelerator, known as the Large Hadron Collider. Using this gigantic machine—which can recreate conditions in the early Universe fractions of a second after the Big Bang—Cox and Forshaw will describe the current theory behind the origin of mass.Alongside questions of energy and mass, they will consider the third, and perhaps, most intriguing element of the equation: 'c' - or the speed of light. Why is it that the speed of light is the exchange rate? Answering this question is at the heart of the investigation as the authors demonstrate how, in order to truly understand why E=mc2, we first must understand why we must move forward in time and not backwards and how objects in our 3-dimensional world actually move in 4-dimensional space-time. In other words, how the very fabric of our world is constructed. A collaboration between two of the youngest professors in the UK, Why Does E=mc2? promises to be one of the most exciting and accessible explanations of the theory of relativity in recent years.

    "A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

    Who invented zero? Why are there 60 seconds in a minute? Can a butterfly's wings really cause a storm on the far side of the world? In 50 concise essays, Professor Tony Crilly explains the mathematical concepts that allow use to understand and shape the world around us.

    Underpinning both math and science, it is the foundation of every major advancement in knowledge since the time of the ancient Greeks. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between math and the real world. Ultimately, Mazur argues, logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.

    It is so important that it provides the fundamental underpinning of all modern sciences. Without it, we'd have no nuclear power or nuclear bombs, no lasers, no TV, no computers, no science of molecular biology, no understanding of DNA, no genetic engineering—at all. John Gribbin tells the complete story of quantum mechanics, a truth far stranger than any fiction. He takes us step-by-step into an ever more bizarre and fascinating place—requiring only that we approach it with an open mind. He introduces the scientists who developed quantum theory. He investigates the atom, radiation, time travel, the birth of the universe, superconductors and life itself. And in a world full of its own delights, mysteries and surprises, he searches for Schrödinger's Cat—a search for quantum reality—as he brings every reader to a clear understanding of the most important area of scientific study today—quantum physics.

    Johnson takes us to those times when the world seemed filled with mysterious forces, when scientists were dazzled by light, by electricity, and by the beating of the hearts they laid bare on the dissecting table. We see Galileo singing to mark time as he measures the pull of gravity, and Newton carefully inserting a needle behind his eye to learn how light causes vibrations in the retina. William Harvey ties a tourniquet around his arm and watches his arteries throb above and his veins bulge below, proving that blood circulates. Luigi Galvani sparks electrical currents in dissected frog legs, wondering at the twitching muscle fibers, and Ivan Pavlov makes his now-famous dogs salivate at ascending chord progressions.For all of them, diligence was rewarded. In an instant, confusion was swept aside and something new about nature leaped into view. In bringing us these stories, Johnson restores some of the romance to science, reminding us of the existential excitement of a single soul staring down the unknown.

    Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

    In this masterfully written and brilliantly informed work of scientific history and explanation, Dr. Thorne, the Feynman Professor of Theoretical Physics at Caltech, leads his readers through an elegant, always human, tapestry of interlocking themes, coming finally to a uniquely informed answer to the great question: what principles control our universe and why do physicists think they know the things they think they know? Stephen Hawking's A Brief History of Time has been one of the greatest best-sellers in publishing history. Anyone who struggled with that book will find here a more slowly paced but equally mind-stretching experience, with the added fascination of a rich historical and human component.

    Hand argues that extraordinarily rare events are anything but. In fact, they’re commonplace. Not only that, we should all expect to experience a miracle roughly once every month.     But Hand is no believer in superstitions, prophecies, or the paranormal. His definition of “miracle” is thoroughly rational. No mystical or supernatural explanation is necessary to understand why someone is lucky enough to win the lottery twice, or is destined to be hit by lightning three times and still survive. All we need, Hand argues, is a firm grounding in a powerful set of laws: the laws of inevitability, of truly large numbers, of selection, of the probability lever, and of near enough.     Together, these constitute Hand’s groundbreaking Improbability Principle. And together, they explain why we should not be so surprised to bump into a friend in a foreign country, or to come across the same unfamiliar word four times in one day. Hand wrestles with seemingly less explicable questions as well: what the Bible and Shakespeare have in common, why financial crashes are par for the course, and why lightning does strike the same place (and the same person) twice. Along the way, he teaches us how to use the Improbability Principle in our own lives—including how to cash in at a casino and how to recognize when a medicine is truly effective.     An irresistible adventure into the laws behind “chance” moments and a trusty guide for understanding the world and universe we live in, The Improbability Principle will transform how you think about serendipity and luck, whether it’s in the world of business and finance or you’re merely sitting in your backyard, tossing a ball into the air and wondering where it will land.

    Indeed, numbers are part of every discipline in the sciences and the arts.With 350 illustrations, including diagrams, photographs and computer imagery, the book chronicles the centuries-long search for the meaning of numbers by famous and lesser-known mathematicians, and explains the puzzling aspects of the mathematical world. Topics include:The earliest ideas of numbers and counting Patterns, logic, calculating Natural, perfect, amicable and prime numbers Numerology, the power of numbers, superstition The computer, the Enigma Code Infinity, the speed of light, relativity Complex numbers The Big Bang and Chaos theories The Philosopher's Stone. The Book of Numbers shows enthusiastically that numbers are neither boring nor dull but rather involve intriguing connections, rivalries, secret documents and even mysterious deaths.

    He shows that the scientists of ancient and medieval times not only did not understand what we understand about the world—they did not understand what there is to understand, or how to understand it. Yet over the centuries, through the struggle to solve such mysteries as the curious backward movement of the planets and the rise and fall of the tides, the modern discipline of science eventually emerged. Along the way, Weinberg examines historic clashes and collaborations between science and the competing spheres of religion, technology, poetry, mathematics, and philosophy.An illuminating exploration of the way we consider and analyze the world around us, To Explain the World is a sweeping, ambitious account of how difficult it was to discover the goals and methods of modern science, and the impact of this discovery on human knowledge and development.