Historian Jacqueline Stedall shows that mathematical ideas are far from being fixed, but are adapted and changed by their passage across periods and cultures. The book illuminates some of the varied contexts in which people have learned, used, and handed on mathematics, drawing on fascinating case studies from a range of times and places, including early imperial China, the medieval Islamic world, and nineteenth-century Britain. By drawing out some common threads, Stedall provides an introduction not only to the mathematics of the past but to the history of mathematics as a modern academic discipline.

    "One of today's best popularizers of science." —Kirkus Reviews.Loyal readers of the monthly "Universe" essays in Natural History magazine have long recognized Neil deGrasse Tyson's talent for guiding them through the mysteries of the cosmos with stunning clarity and almost childlike enthusiasm. Here, Tyson compiles his favorite essays across a myriad of cosmic topics. The title essay introduces readers to the physics of black holes by explaining the gory details of what would happen to your body if you fell into one. "Holy Wars" examines the needless friction between science and religion in the context of historical conflicts. "The Search for Life in the Universe" explores astral life from the frontiers of astrobiology. And "Hollywood Nights" assails the movie industry's feeble efforts to get its night skies right. Known for his ability to blend content, accessibility, and humor, Tyson is a natural teacher who simplifies some of the most complex concepts in astrophysics while simultaneously sharing his infectious excitement about our universe.

    Galileo's own beautifully lucid arguments are used in this volume to show how his scientific method was utterly divorced from the Aristotelian approach to physics; it was based on a search not for causes but for laws. Galileo's methods had an overwhelming significance for the development of modern physics, and they led to a final parting of the ways between science and philosophy. Now, in this extraordinary and concise introduction, Drake provides a stimulating view of Galileo's life and works, providing a fresh perspective on Galileo's methodology and his final incrimination.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    A fun and fascinating look at great scientific paradoxes.   Throughout history, scientists have come up with theories and ideas that just don't seem to make sense.  These we call paradoxes.  The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds.  For example, how can a cat be both dead and alive at the same time?  Why will Achilles never beat a tortoise in a race, no matter how fast he runs?  And how can a person be ten years older than his twin?   With elegant explanations that bring the reader inside the mind of those who've developed them, Al-Khalili helps us to see that, in fact, paradoxes can be solved if seen from the right angle.  Just as surely as Al-Khalili narrates the enduring fascination of these classic paradoxes, he reveals their underlying logic.  In doing so, he brings to life a select group of the most exciting concepts in human knowledge.  Paradox is mind-expanding fun.

    Their work has uncovered a number of the universe’s more surprising secrets, and many believe further wonders remain hidden within the theory’s tangle of equations, waiting to be exposed. In this sweeping narrative of science and culture, astrophysicist Pedro Ferreira brings general relativity to life through the story of the brilliant physicists, mathematicians, and astronomers who have taken up its challenge. For these scientists, the theory has been both a treasure trove and an enigma, fueling a century of intellectual struggle and triumph.. Einstein’s theory, which explains the relationships among gravity, space, and time, is possibly the most perfect intellectual achievement of modern physics, yet studying it has always been a controversial endeavor. Relativists were the target of persecution in Hitler’s Germany, hounded in Stalin’s Russia, and disdained in 1950s America. Even today, PhD students are warned that specializing in general relativity will make them unemployable. Despite these pitfalls, general relativity has flourished, delivering key insights into our understanding of the origin of time and the evolution of all the stars and galaxies in the cosmos. Its adherents have revealed what lies at the farthest reaches of the universe, shed light on the smallest scales of existence, and explained how the fabric of reality emerges. Dark matter, dark energy, black holes, and string theory are all progeny of Einstein’s theory. We are in the midst of a momentous transformation in modern physics. As scientists look farther and more clearly into space than ever before, The Perfect Theory reveals the greater relevance of general relativity, showing us where it started, where it has led, and where it can still take us.

    It had to be found. But projects as big as CERN’s Large Hadron Collider don’t happen without incredible risks – and occasional skullduggery. In the definitive account of this landmark event, Caltech physicist and acclaimed science writer Sean Carroll reveals the insights, rivalry, and wonder that fuelled the Higgs discovery, and takes us on a riveting and irresistible ride to the very edge of physics today.

    Indeed, without religion, our lives are left without meaning and are likely to degenerate into moral chaos. In this Very Short Introduction, philosopher Stephen Law explains why these claims are false and why humanism--though a rejection of religion--nevertheless provides both a moral basis and a meaning for our lives. Indeed, Law shows that humanism is a quite positive alternative to religion. The humanist is not simply one who denies the truth of religious belief, but one who believes we can enjoy meaningful, purposeful, and good lives without religion. And far from embracing moral nihilism, humanists are often deeply committed people, to be found at the forefront of many important ethical campaigns. Law goes on to show how the term humanism is used in a variety of ways. Marx described himself as a humanist but the Pope has also expressed support for what he calls humanism. Law argues for humanism as it is most commonly understood--as a positive, moral form of atheism.

    Nearly every regime today claims to be democratic, but not all democracies allow free politics, and free politics existed long before democratic franchises. This book is a short account of the history of the doctrine and practice of democracy, from ancient Greece and Rome through the American, French, and Russian revolutions, and of the usages and practices associated with it in the modern world. It argues that democracy is a necessary but not asufficient condition for good government, and that ideas of the rule of law, and of human rights, should in some situations limit democratic claims.

    Discussing not only the main academic theories, but also the practical problems and issues, Wilkinson considers key normative questions, such as how the international state system might be reformed so that international relations are improved.

    It examines the impact of the revolution on society as a whole--on different classes, ethnic groups, the army, men and women, youth. Its centralconcern is to understand how one structure of domination was replaced by another. The book registers the primacy of politics, but situates political developments firmly in the context of massive economic, social, and cultural change. Since the fall of Communism there has been much reflection on thesignificance of the Russian Revolution. The book rejects the currently influential, liberal interpretation of the revolution in favor of one that sees it as rooted in the contradictions of a backward society which sought modernization and enlightenment and ended in political tyranny.

    With a new preface about the significance of the discovery of the Higgs particle, A Universe from Nothing uses Krauss’s characteristic wry humor and wonderfully clear explanations to take us back to the beginning of the beginning, presenting the most recent evidence for how our universe evolved—and the implications for how it’s going to end. Provocative, challenging, and delightfully readable, this is a game-changing look at the most basic underpinning of existence and a powerful antidote to outmoded philosophical, religious, and scientific thinking.

    The author illustrates important aspects of Africa's history with a range of fascinating historical examples, drawn from over 5 millennia across this vast continent. The multitude of topics that the reader will learn about in this succinct work include the unity and diversity of African cultures, slavery, religion, colonial conquest, the diaspora, and the importance of history in understanding contemporary Africa. The book examines questions such as: Who invented the idea of "Africa"? How is African history pieced together, given such a lack of documentary evidence? How did Africa interact with the world 1,000 years ago? Africa has been known as 'the cradle of mankind', and its recoverable history stretches back to the Pharaohs. But the idea of studying African history is itself new, and the authors show why it is still contested and controversial. This VSI, the first concise work of its kind, will prove essential reading for anyone interested in the African continent and the diversity of human history.

    Our Big Bang, our distant future, parallel worlds, the sub-atomic and intergalactic - none of them are what they seem. But there is a way to understand this immense strangeness - mathematics. Seeking an answer to the fundamental puzzle of why our universe seems so mathematical, Tegmark proposes a radical idea: that our physical world not only is described by mathematics, but that it is mathematics. This may offer answers to our deepest questions: How large is reality? What is everything made of? Why is our universe the way it is?Table of ContentsPreface 1 What Is Reality? Not What It Seems • What’s the Ultimate Question? • The Journey Begins Part One: Zooming Out 2 Our Place in Space Cosmic Questions • How Big Is Space? • The Size of Earth • Distance to the Moon • Distance to the Sun and the Planets • Distance to the Stars • Distance to the Galaxies • What Is Space? 3 Our Place in TimeWhere Did Our Solar System Come From? • Where Did theGalaxies Come From? • Where Did the Mysterious MicrowavesCome From? • Where Did the Atoms Come From? 4 Our Universe by NumbersWanted: Precision Cosmology • Precision Microwave-Background Fluctuations • Precision Galaxy Clustering • The Ultimate Map of Our Universe • Where Did Our Big Bang Come From? 5 Our Cosmic Origins What’s Wrong with Our Big Bang? • How Inflation Works • The Gift That Keeps on Giving • Eternal Inflation 6 Welcome to the Multiverse The Level I Multiverse • The Level II Multiverse • Multiverse Halftime Roundup Part Two: Zooming In 7 Cosmic Legos Atomic Legos • Nuclear Legos • Particle-Physics Legos • Mathematical Legos • Photon Legos • Above the Law? • Quanta and Rainbows • Making Waves • Quantum Weirdness • The Collapse of Consensus • The Weirdness Can’t Be Confined • Quantum Confusion 8 The Level III Multiverse The Level III Multiverse • The Illusion of Randomness • Quantum Censorship • The Joys of Getting Scooped • Why Your Brain Isn’t a Quantum Computer • Subject, Object and Environment • Quantum Suicide • Quantum Immortality? • Multiverses Unified • Shifting Views: Many Worlds or Many Words? Part Three: Stepping Back 9 Internal Reality, External Reality and Consensus Reality External Reality and Internal Reality • The Truth, the Whole Truth and Nothing but the Truth • Consensus Reality • Physics: Linking External to Consensus Reality 10 Physical Reality and Mathematical Reality Math, Math Everywhere! • The Mathematical Universe Hypothesis • What Is a Mathematical Structure? 11 Is Time an Illusion? How Can Physical Reality Be Mathematical? • What Are You? • Where Are You? (And What Do You Perceive?) • When Are You? 12 The Level IV Multiverse Why I Believe in the Level IV Multiverse • Exploring the Level IV Multiverse: What’s Out There? • Implications of the Level IV Multiverse • Are We Living in a Simulation? • Relation Between the MUH, the Level IV Multiverse and Other Hypotheses •Testing the Level IV Multiverse 13 Life, Our Universe and Everything How Big Is Our Physical Reality? • The Future of Physics • The Future of Our Universe—How Will It End? • The Future of Life •The Future of You—Are You Insignificant? Acknowledgments Suggestions for Further Reading Index

    In this Very Short Introduction, Robert C. Allen shows how the interplay of geography, globalization, technological change, and economic policy has determined the wealth and poverty of nations. Allen shows how the industrial revolution was Britain's path-breaking response to the challenge of globalization. Western Europe and North America joined Britain to form a club of rich nations, pursuing four polices--creating a national market by abolishing internal tariffs and investing in transportation, erecting an external tariff to protect their fledgling industries from British competition, creating banks to stabilize the currency and mobilize domestic savings for investment, and promoting mass education to prepare people for industrial work. Together these countries pioneered new technologies that have made them ever richer. A few countries--Japan, Soviet Russia, South Korea, Taiwan, and perhaps China--have caught up with the West through creative responses to the technological challenge and with Big Push industrialization that has achieved rapid growth through coordinated investment.

    Everything. Yet, in recent years discoveries in physics and cosmology have led a number of scientists to conclude that our universe may be one among many. With crystal-clear prose and inspired use of analogy, Brian Greene shows how a range of different “multiverse” proposals emerges from theories developed to explain the most refined observations of both subatomic particles and the dark depths of space: a multiverse in which you have an infinite number of doppelgängers, each reading this sentence in a distant universe; a multiverse comprising a vast ocean of bubble universes, of which ours is but one; a multiverse that endlessly cycles through time, or one that might be hovering millimeters away yet remains invisible; another in which every possibility allowed by quantum physics is brought to life. Or, perhaps strangest of all, a multiverse made purely of math.Greene, one of our foremost physicists and science writers, takes us on a captivating exploration of these parallel worlds and reveals how much of reality’s true nature may be deeply hidden within them. And, with his unrivaled ability to make the most challenging of material accessible and entertaining, Greene tackles the core question: How can fundamental science progress if great swaths of reality lie beyond our reach?Sparked by Greene’s trademark wit and precision, The Hidden Reality is at once a far-reaching survey of cutting-edge physics and a remarkable journey to the very edge of reality—a journey grounded firmly in science and limited only by our imagination.