According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.

    Ariew's introduction places the correspondence in historical context and discusses the vibrant philosophical climate of the times. Appendices provide those selections from the works of Newton that Clarke frequently refers to in the correspondence. A bibliography is also included.

    Now William Dunham gives them the attention they deserve.Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.

    That transition is the basis of this book. In From Science to God, he blends physics, psychology, and philosophy to reach a new worldview in which consciousness is a fundamental quality of creation. Russell shows how all the ingredients for this worldview are in place; it remains only to put the pieces together and explore the new picture of reality that emerges. Integrating a deep knowledge of science with his own experiences of meditation, Russell arrives at a universe similar to that described by many mystics — one in which the inner and outer worlds no longer conflict. The bridge between them, he shows, is light, and this book invites readers to cross that bridge to find new meaning in God and a deeper significance in spiritual practice.

    Their insights shook our perception of who we are and where we stand in the world, and in their wake have left an uneasy coexistence: science vs. religion, faith vs. empirical inquiry. Which is the keeper of truth? Which is the true path to understanding reality?After forty years of study with some of the greatest scientific minds, as well as a lifetime of meditative, spiritual, and philosophic study, the Dalai Lama presents a brilliant analysis of why all avenues of inquiry—scientific as well as spiritual—must be pursued in order to arrive at a complete picture of the truth. Through an examination of Darwinism and karma, quantum mechanics and philosophical insight into the nature of reality, neurobiology and the study of consciousness, the Dalai Lama draws significant parallels between contemplative and scientific examinations of reality.This breathtakingly personal examination is a tribute to the Dalai Lama’s teachers—both of science and spirituality. The legacy of this book is a vision of the world in which our different approaches to understanding ourselves, our universe, and one another can be brought together in the service of humanity.

    Join us on a journey through how we understand the Universe, from its most basic particles and forces, to planets, stars and galaxies, and back through cosmic history to the birth of the cosmos. Conflicting notions about our place in the Universe are defined, defended and critiqued from scientific, philosophical and religious viewpoints. The authors' engaging and witty style addresses what fine-tuning might mean for the future of physics and the search for the ultimate laws of nature. Tackling difficult questions and providing thought-provoking answers, this volumes challenges us to consider our place in the cosmos, regardless of our initial convictions.

    Most know Richard Feynman for the hilarious anecdotes and exploits in his best-selling books Surely You're Joking, Mr. Feynman! and What DoYou Care What Other People Think? But not always obvious in those stories was his brilliance as a pure scientist—one of the century's greatest physicists. With this book and CD, we hear the voice of the great Feynman in all his ingenuity, insight, and acumen for argument. This breathtaking lecture—"The Motion of the Planets Around the Sun"—uses nothing more advanced than high-school geometry to explain why the planets orbit the sun elliptically rather than in perfect circles, and conclusively demonstrates the astonishing fact that has mystified and intrigued thinkers since Newton: Nature obeys mathematics. David and Judith Goodstein give us a beautifully written short memoir of life with Feynman, provide meticulous commentary on the lecture itself, and relate the exciting story of their effort to chase down one of Feynman's most original and scintillating lectures.

    Our memory is unreliable; we can't multiply large sums in our heads; advertising manipulates our judgment; we tend to distrust people who are different from us; supernatural beliefs and superstitions are hard to shake; we prefer instant gratification to long-term gain; and what we presume to be rational decisions are often anything but. Drawing on striking examples and fascinating studies, neuroscientist Dean Buonomano illuminates the causes and consequences of these "bugs" in terms of the brain's innermost workings and their evolutionary purposes. He then goes one step further, examining how our brains function-and malfunction-in the digital, predator-free, information-saturated, special effects-addled world that we have built for ourselves. Along the way, Brain Bugs gives us the tools to hone our cognitive strengths while recognizing our inherent weaknesses.

    Good stories are full of life: they engage our emotions and have subtlety and nuance, but they lack rigor and the truths they tell are elusive and subject to debate. As ways of understanding the world around us, numbers and stories seem almost completely incompatible. Once Upon a Number shows that stories and numbers aren't as different as you might imagine, and in fact they have surprising and fascinating connections. The concepts of logic and probability both grew out of intuitive ideas about how certain situations would play out. Now, logicians are inventing ways to deal with real world situations by mathematical means -- by acknowledging, for instance, that items that are mathematically interchangeable may not be interchangeable in a story. And complexity theory looks at both number strings and narrative strings in remarkably similar terms. Throughout, renowned author John Paulos mixes numbers and narratives in his own delightful style. Along with lucid accounts of cutting-edge information theory we get hilarious anecdotes and jokes; instructions for running a truly impressive pyramid scam; a freewheeling conversation between Groucho Marx and Bertrand Russell (while they're stuck in an elevator together); explanations of why the statistical evidence against OJ Simpson was overwhelming beyond doubt and how the Unabomber's thinking shows signs of mathematical training; and dozens of other treats. This is another winner from America's favorite mathematician.

    We tour the Vatican's meteorite collection and learn how astronomy progresses despite its dearth of tactile evidence. It seeks to prove that not all religion is hostile to science.

    Everyday experience cannot prepare us for the sub-atomic world, where quantum effects become all-important. Here, particles can look like waves, and vice versa; electrons seem to lose their identity and instead take on a shifting, unpredictable appearance that depends on how they are being observed; and a single photon may sometimes behave as if it could be in two places at once. In the world of quantum mechanics, uncertainty and ambiguity become not just unavoidable, but essential ingredients of science -- a development so disturbing that to Einstein "it was as if God were playing dice with the universe." And there is no one better able to explain the quantum revolution as it approaches the century mark than David Lindley. He brings the quantum revolution full circle, showing how the familiar and trustworthy reality of the world around us is actually a consequence of the ineffable uncertainty of the subatomic quantum world -- the world we can't see.

    Drawing from years of teaching modern physics to nonscientists, Wolfson explains in a lively, conversational style the simple principles underlying Einstein's theory.Relativity, Wolfson shows, gave us a new view of space and time, opening the door to questions about their flexible nature: Is the universe finite or infinite? Will it expand forever or eventually collapse in a "big crunch"? Is time travel possible? What goes on inside a black hole? How does gravity really work? These questions at the forefront of twenty-first-century physics are all rooted in the profound and sweeping vision of Albert Einstein's early twentieth-century theory. Wolfson leads his readers on an intellectual journey that culminates in a universe made almost unimaginably rich by the principles that Einstein first discovered.

    Original, well researched, and well documented by distinguished sources, The Field is a book of hope and inspiration for today's world.

    However, it is one of the basic principles of quantum theory, the most widely accepted explanation of the subatomic world - and one of the fascinating subjects dealt with in Equations of Eternity.

    Its rules and pieces have served as a metaphor for society including military strategy, mathematics, artificial intelligence, literature, and the arts. It has been condemned as the devil’s game by popes, rabbis, and imams, and lauded as a guide to proper living by different popes, rabbis, and imams. In his wide-ranging and ever fascinating examination of chess, David Shenk gleefully unearths the hidden history of a game that seems so simple yet contains infinity. From its invention somewhere in India around 500 A.D., to its enthusiastic adoption by the Persians and its spread by Islamic warriors, to its remarkable use as a moral guide in the Middle Ages and its political utility in the Enlightenment, to its crucial importance in the birth of cognitive science and its key role in the new aesthetic of modernism in 20th century art, to its 21st century importance to the development of artificial intelligence and use as a teaching tool in inner-city America, chess has been a remarkably omnipresent factor in the development of civilization. Indeed as Shenk shows, some neuroscientists believe that playing chess may actually alter the structure of the brain, that it may for individuals be what it has been for civilization: a virus that makes us smarter.From the Hardcover edition.