Amir Aczel, critically acclaimed author of Fermat's Last Theorem, takes us into the heart of science's greatest mystery. In January 1998, astronomers found evidence that the cosmos is expanding at an ever-increasing rate. The way we perceive the universe was changed forever. The most compelling theory cosmologists could find to explain this phenomenon was Einstein's cosmological constant, a theory he conceived--and rejected---over eighty years ago. Drawing on newly discovered letters of Einstein--many translated here for the first time--years of research, and interviews with prominent mathematicians, cosmologists, physicists, and astronomers, Aczel takes us on a fascinating journey into "the strange geometry of space-time," and into the mind of a genius. Here the unthinkable becomes real: an infinite, ever-expanding, ever-accelerating universe whose only absolute is the speed of light. Awesome in scope, thrilling in detail, God's Equation is storytelling at its finest.

    With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change.The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.From the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal.

    In a book of unprecedented scope, McGilchrist draws on a vast body of recent brain research, illustrated with case histories, to reveal that the difference is profound—not just this or that function, but two whole, coherent, but incompatible ways of experiencing the world. The left hemisphere is detail oriented, prefers mechanisms to living things & is inclined to self-interest. The right hemisphere has greater breadth, flexibility & generosity. This division helps explain the origins of music & language, & casts new light on the history of philosophy, as well as on some mental illnesses. The 2nd part of the book takes a journey thru the history of Western culture, illustrating the tension between these two worlds as revealed in the thought & belief of thinkers & artists, from Aeschylus to Magritte. He argues that, despite its inferior grasp of reality, the left hemisphere is increasingly taking precedence in the modern world, with potentially disastrous consequences.List of IllustrationsAcknowledgmentsIntroductionAsymmetry and the brain --What do the two hemispheres 'do'? --Language, truth and music --The nature of the two worlds --The primacy of the right hemisphere --The triumph of the left hemisphere --Imitation and the evolution of culture --The ancient world --The Renaissance and the Reformation --The Enlightenment --Romanticism and the Industrial Revolution --The modern and post-modern worldsConclusionNotes BibliographyIndex

    Covers textual and linguistic matters; mathematical analyses of Euclid's ideas; commentators; refutations, supports, extrapolations, reinterpretations and historical notes. Vol. 1 includes Introduction, Books 1-2: Triangles, rectangles.

    In the past, discoveries often had to wait for the rise of the next generation to see questions in a new light and let go of old truisms. Today, in a world that is defined by a rapid rate of change, staying on the cutting edge has as much to do with shedding outdated notions as adopting new ones. In this spirit, John Brockman, publisher of the online salon Edge.org ("the world's smartest website"—The Guardian), asked 175 of the world's most influential scientists, economists, artists, and philosophers: What scientific idea is ready for retirement?Jared Diamond explores the diverse ways that new ideas emerge * Nassim Nicholas Taleb takes down the standard deviation * Richard Thaler and novelist Ian McEwan reveal the usefulness of "bad" ideas * Steven Pinker dismantles the working theory of human behavior * Richard Dawkins renounces essentialism * Sherry Turkle reevaluates our expectations of artificial intelligence * Physicist Andrei Linde suggests that our universe and its laws may not be as unique as we think * Martin Rees explains why scientific understanding is a limitless goal * Alan Guth rethinks the origins of the universe * Sam Harris argues that our definition of science is too narrow * Nobel Prize winner Frank Wilczek disputes the division between mind and matter * Lawrence Krauss challenges the notion that the laws of physics were preordained * plus contributions from Daniel Goleman, Mihaly Csikszentmihalyi, Nicholas Carr, Rebecca Newberger Goldstein, Matt Ridley, Stewart Brand, Sean Carroll, Daniel C. Dennett, Helen Fisher, Douglas Rushkoff, Lee Smolin, Kevin Kelly, Freeman Dyson, and others.

    Birth of a Theorem is Villani’s own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career.But you don’t have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn’t simplify or overexplain; rather, it invites readers into collaboration. Villani’s diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You’re privy to the dining-hall conversations at the world’s greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker’s whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.

    Having just completed his masterpiece, The General Theory of Relativity—which provided a brand-new theory of gravity and promised a new perspective on the cosmos as a whole—he set out at once to share his excitement with as wide a public as possible in this popular and accessible book.Here published for the first time as a Penguin Classic, this edition of Relativity features a new introduction by bestselling science author Nigel Calder.

    From the transistor to the laser, it s hard to find an aspect of modern life that hasn t been touched by Bell Labs. Why did so many transformative ideas come from Bell Labs? In "The Idea Factory," Jon Gertner traces the origins of some of the twentieth century s most important inventions and delivers a riveting and heretofore untold chapter of American history. At its heart this is a story about the life and work of a small group of brilliant and eccentric men Mervin Kelly, Bill Shockley, Claude Shannon, John Pierce, and Bill Baker who spent their careers at Bell Labs. Their job was to research and develop the future of communications. Small-town boys, childhood hobbyists, oddballs: they give the lie to the idea that Bell Labs was a grim cathedral of top-down command and control.Gertner brings to life the powerful alchemy of the forces at work behind Bell Labs inventions, teasing out the intersections between science, business, and society. He distills the lessons that abide: how to recruit and nurture young talent; how to organize and lead fractious employees; how to find solutions to the most stubbornly vexing problems; how to transform a scientific discovery into a marketable product, then make it even better, cheaper, or both. Today, when the drive to invent has become a mantra, Bell Labs offers us a way to enrich our understanding of the challenges and solutions to technological innovation. Here, after all, was where the foundational ideas on the management of innovation were born. "The Idea Factory" is the story of the origins of modern communications and the beginnings of the information age a deeply human story of extraordinary men who were given extraordinary means time, space, funds, and access to one another and edged the world into a new dimension."

    It clears the air of many confused notions . . . and lays the groundwork for exhaustive study of the basic problem of music theory and aesthetics, the relationship between pattern and meaning."—David Kraehenbuehl, Journal of Music Theory  "This is the best study of its kind to have come to the attention of this reviewer."—Jules Wolffers, The Christian Science Monitor "It is not too much to say that his approach provides a basis for the meaningful discussion of emotion and meaning in all art."—David P. McAllester, American Anthropologist "A book which should be read by all who want deeper insights into music listening, performing, and composing."—Marcus G. Raskin, Chicago Review

    But the so-called Dark Ages also gave us the first universities, eyeglasses, and mechanical clocks, proving that the Middle Ages were home to a vibrant scientific culture.In The Light Ages, Cambridge science historian Seb Falk takes us on an immersive tour of medieval science through the story of one fourteenth-century monk, John of Westwyk. From multiplying Roman numerals to navigating by the stars, curing disease, and telling time with an ancient astrolabe, we learn emerging science alongside Westwyk, while following the gripping story of the struggles and successes of an ordinary man in a precarious world. An enlightening history that argues that these times weren’t so dark after all, The Light Ages shows how medieval ideas continue to color how we see the world today.

    But the discoveries of the last few decades have changed all that, conjuring up instead a universe brimming with unpredictability, creativity, and chance. Writing with exceptional grace and clarity, Thuan vividly describes these important scientific discoveries, intriguing new theories about chaos, gravity, strange attractors, fractals, symmetry, superstrings, and the strangeness of atoms. Equally important, he reveals how these discoveries have shaped our view of the universe--for instance, how quantum mechanics brought indeterminism to the subatomic universe. Thuan deftly describes quantum mechanics, discusses its relationship to the theories of relativity (which deal inability to accept it. Indeed, throughout Chaos and Harmony, he makes clear as never before the mind-bending ideas of modern physics, such as the effect of gravity on time (it slows it down), the impossibility of crossing the speed-of-light barrier (it would actually reverse time), the role of fractals as the language of nature, and the unreasonable effectiveness of mathematics in understanding the universe. From the subatomic world to the vast realm of quasars and galaxies, from the nature of mathematics to the fractal characteristics of the human circulatory system, Trinh Xuan Thuan takes us on a breathtaking tour of the universe. With striking examples and clear, plain language, he shows how science has actually restored mystery to the world around us--a world of symmetry and chaos, contingency and creativity.

    Abbott published a brilliant novel about mathematics and philosophy that charmed and fascinated all of England. As both a witty satire of Victorian society and a means by which to explore the fourth dimension, Flatland remains a tour de force. Now, British mathematician and accomplished science writer Ian Stewart has written a fascinating, modern sequel to Abbott's book. Through larger-than-life characters and an inspired story line, Flatterland explores our present understanding of the shape and origins of the universe, the nature of space, time, and matter, as well as modern geometries and their applications. The journey begins when our heroine, Victoria Line, comes upon her great-great-grandfather A. Square's diary, hidden in the attic. The writings help her to contact the Space Hopper, who becomes her guide and mentor through eleven dimensions. Along the way, we meet Schröger's Cat, The Charming Construction Entity, The Mandelblot (who lives in Fractalia), and Moobius the one-sided cow. In the tradition of Alice in Wonder-land and The Phantom Toll Booth, this magnificent investigation into the nature of reality is destined to become a modern classic.

    A preeminent scholar, writer, and teacher, he has had a profound influence on millions of people. To him, mythology was the "song of the universe, the music of the spheres." With Bill Moyers, one of America's most prominent journalists, as his thoughtful and engaging interviewer, The Power Of Myth touches on subjects from modern marriage to virgin births, from Jesus to John Lennon, offering a brilliant combination of intelligence and wit.

    Far from being simply a tool for the preservation of music, the technology is a catalyst. This is the clear message of Capturing Sound, a wide-ranging, deeply informative, consistently entertaining history of recording's profound impact on the musical life of the past century, from Edison to the Internet.In a series of case studies, Mark Katz explores how recording technology has encouraged new ways of listening to music, led performers to change their practices, and allowed entirely new musical genres to come into existence. An accompanying CD, featuring thirteen tracks from Chopin to Public Enemy, allows readers to hear what Katz means when he discusses music as varied as King Oliver's "Dippermouth Blues," a Jascha Heifetz recording of a Brahms Hungarian Dance, and Fatboy Slim's "Praise You."

    With this volume spanning from her punk fanzine roots to her landmark piece on R. Kelly's past, The First Collection leaves no doubt why The New York Times has called Hopper's work "influential." Not merely a selection of two decades of Hopper's most engaging, thoughtful, and humorous writing, this book documents the last 20 years of American music making and the shifting landscape of music consumption. The book journeys through the truths of Riot Grrrl's empowering insurgence, decamps to Gary, IN, on the eve of Michael Jackson's death, explodes the grunge-era mythologies of Nirvana and Courtney Love, and examines emo's rise. Through this vast range of album reviews, essays, columns, interviews, and oral histories, Hopper chronicles what it is to be truly obsessed with music. The pieces in The First Collection send us digging deep into our record collections, searching to re-hear what we loved and hated, makes us reconsider the art, trash, and politics Hopper illuminates, helping us to make sense of what matters to us most.