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.

    Along the way she considers how to use a chessboard to plan a worldwide dinner party, how to make a chicken-sandwich sandwich, and how to create infinite cookies from a finite ball of dough. Beyond Infinity shows how this little symbol holds the biggest idea of all. "Beyond Infinity is a spirited and friendly guide--appealingly down to earth about math that's extremely far out." --Jordan Ellenberg, author of How Not to Be Wrong "Dr. Cheng . . . has a knack for brushing aside conventions and edicts, like so many pie crumbs from a cutting board." --Natalie Angier, New York Times

    Einstein famously quipped that God does not play dice with the universe, and Schrödinger is equally well known for his thought experiment about the cat in the box who ends up “spread out” in a probabilistic state, neither wholly alive nor wholly dead. Both of these famous images arose from these two men’s dissatisfaction with quantum weirdness and with their assertion that underneath it all, there must be some essentially deterministic world. Even though it was Einstein’s own theories that made quantum mechanics possible, both he and Schrödinger could not bear the idea that the universe was, at its most fundamental level, random.As the Second World War raged, both men struggled to produce a theory that would describe in full the universe’s ultimate design, first as collaborators, then as competitors. They both ultimately failed in their search for a Grand Unified Theory—not only because quantum mechanics is true, but because Einstein and Schrödinger were also missing a key component: of the four forces we recognize today (gravity, electromagnetism, the weak force, and the strong force), only gravity and electromagnetism were known at the time.Despite their failures, though, much of modern physics remains focused on the search for a Grand Unified Theory. As Halpern explains, the recent discovery of the Higgs Boson makes the Standard Model—the closest thing we have to a unified theory—nearly complete. And while Einstein and Schrödinger tried and failed to explain everything in the cosmos through pure geometry, the development of string theory has, in its own quantum way, brought this idea back into vogue. As in so many things, even when he was wrong, Einstein couldn’t help but be right.

    How does Jane Goodall’s relationship with her dog Rusty inform her thinking about our relationship to other species? Which time and place would Jared Diamond most prefer to live in, in light of his work on the role of chance in history? What does driving a sports car have to do with Steven Weinberg’s quest for the “theory of everything”? Physicist and journalist Stefan Klein’s intimate conversations with nineteen of the world’s best-known scientists (including three Nobel Laureates) let us listen in as they talk about their paradigm-changing work—and how it is deeply rooted in their daily lives. • Cosmologist Martin Rees on the beginning and end of the world • Evolutionary biologist Richard Dawkins on egoism and selflessness • Neuroscientist V. S. Ramachandran on consciousness • Molecular biologist Elizabeth Blackburn on aging • Philosopher Peter Singer on morality • Physician and social scientist Nicholas Christakis on human relationships • Biochemist Craig Venter on the human genome • Chemist and poet Roald Hoffmann on beauty

    Visitors to the town often remark about the valley’s peace and beauty—both of which are plentiful. Unlocked doors, front porches, pies cooling in the windows—this is country life at its finest. But visitors don’t always see what lies at the heart of a community. Or just beyond…Deep in the ValleyThe daughter of the town doctor, June Hudson left only to get her medical training, then returned home and followed in her father’s footsteps. Some might say she chose the easy, comfortable route…but June knows better. Her emergency room is wherever she’s needed—or wherever a patient finds her. She is always on call, her work is her life, and these people are her extended family. Which is a good thing, since this is a town where you should have picked your husband in the ninth grade. It’s not exactly the place to meet eligible men—until an undercover DEA agent suddenly starts appearing at all sorts of strange hours. Everybody has secrets down in the valley. Now June has one of her own.Just Over the MountainIn this peaceful community, it’s hard to keep a secret—but Dr. June Hudson has managed to keep one heck of a humdinger. Though visits from undercover DEA agent Jim Post are as clandestine as they are passionate, somehow it fits with her demanding schedule. But how can a secret lover compete with a flesh-and-blood heartthrob from her past? June’s old flame has just returned after twenty years—and he’s divorced. June is seriously rattled. So when the town’s most devoted wife takes buckshot to her husband and some human bones turn up in her aunt Myrna’s backyard, June is almost happy for the distraction. Sooner or later, love will have its way in Grace Valley. It always does.Down by the RiverPeople in town are beginning to notice the bloom in Dr. June Hudson’s cheeks—and the swell of her belly. Happily, DEA agent Jim Post is back in June’s arms for good, newly retired from undercover work and ready for new beginnings. And the community is overflowing with gossip right now. Who is the secret paramour June’s aunt Myrna is hiding? Does the town’s poker-playing pastor have too many aces up his sleeve? But when dangers, from man and nature, rise up with a vengeance to threaten June and the town, this community pulls together and shows what it’s made of. And Jim discovers the true meaning of happiness here in Grace Valley: there really is no place like home.

    This wonderfully accessible book illuminates the professional and personal paths that led him to this remarkable conclusion.All interactions between particles in the universe, Lloyd explains, convey not only energy but also information—in other words, particles not only collide, they compute. And what is the entire universe computing, ultimately? “Its own dynamical evolution,” he says. “As the computation proceeds, reality unfolds.”To elucidate his theory, Lloyd examines the history of the cosmos, posing questions that in other hands might seem unfathomably complex: How much information is there in the universe? What information existed at the moment of the Big Bang and what happened to it? How do quantum mechanics and chaos theory interact to create our world? Could we attempt to re-create it on a giant quantum computer? Programming the Universe presents an original and compelling vision of reality, revealing our world in an entirely new light.

    Then, in 2005, astronomer Mike Brown made the discovery of a lifetime: a tenth planet, Eris, slightly bigger than Pluto. But instead of its resulting in one more planet being added to our solar system, Brown’s find ignited a firestorm of controversy that riled the usually sedate world of astronomy and launched him into the public eye. The debate culminated in the demotion of Pluto from real planet to the newly coined category of “dwarf” planet. Suddenly Brown was receiving hate mail from schoolchildren and being bombarded by TV reporters—all because of the discovery he had spent years searching for and a lifetime dreaming about.Filled with both humor and drama, How I Killed Pluto and Why It Had It Coming is Mike Brown’s engaging first-person account of the most tumultuous year in modern astronomy—which he inadvertently caused. As it guides readers through important scientific concepts and inspires us to think more deeply about our place in the cosmos, it is also an entertaining and enlightening personal story: While Brown sought to expand our understanding of the vast nature of space, his own life was changed in the most immediate, human ways by love, birth, and death. A heartfelt and personal perspective on the demotion of everyone’s favorite farflung planet, How I Killed Pluto and Why It Had It Coming is the book for anyone, young or old, who has ever dreamed of exploring the universe—and who among us hasn’t?

    But Shep Doeleman and a global coalition of scientists are on the cusp of doing just that.With exclusive access to the team, journalist Seth Fletcher spent five years following Shep and an extraordinary cast of characters as they assembled the Event Horizon Telescope, a virtual radio observatory the size of the Earth. He witnessed their struggles, setbacks, and breakthroughs, and along the way, he explored the latest thinking on the most profound questions about black holes. Do they represent a limit to our ability to understand reality? Or will they reveal the clues that lead to the long-sought Theory of Everything?Fletcher transforms astrophysics into something exciting, accessible, and immediate, taking us on an incredible adventure to better understand the complexity of our galaxy, the boundaries of human perception and knowledge, and how the messy human endeavor of science really works.Weaving a compelling narrative account of human ingenuity with excursions into cutting-edge science, Einstein’s Shadow is a tale of great minds on a mission to change the way we understand our universe—and our place in it.

    Using the dialogue form, a genre common in classical philosophical works, Galileo masterfully demonstrates the truth of the Copernican system over the Ptolemaic one, proving, for the first time, that the earth revolves around the sun. Its influence is incalculable. The Dialogue is not only one of the most important scientific treatises ever written, but a work of supreme clarity and accessibility, remaining as readable now as when it was first published. This edition uses the definitive text established by the University of California Press, in Stillman Drake’s translation, and includes a Foreword by Albert Einstein and a new Introduction by J. L. Heilbron.

    Using illustrations and examples from science fiction pulp magazines and comic books, The Amazing Story of Quantum Mechanics explains the fundamental principles of quantum mechanics that underlie the world we live in.Watch a Video

    He proposes that we look at evolution as a battle between genes instead of between whole organisms. We can then view changes in phenotypes—the end products of genes, like eye color or leaf shape, which are usually considered to increase the fitness of an individual—as serving the evolutionary interests of genes.Dawkins makes a convincing case that considering one’s body, personality, and environment as a field of combat in a kind of “arms race” between genes fighting to express themselves on a strand of DNA can clarify and extend the idea of survival of the fittest. This influential and controversial book illuminates the complex world of genetics in an engaging, lively manner.

    Cox comes this insightful new history of the critical Guadalcanal and Solomons campaign at the height of World War II. His previous book, Morning Star, Rising Sun, had found the US Navy at its absolute nadir and the fate of the Enterprise, the last operational US aircraft carrier at this point in the war, unknown. This new volume completes the history of this crucial campaign, combining detailed research with a novelist's flair for the dramatic to reveal exactly how, despite missteps and misfortunes, the tide of war finally turned. By the end of February 1944, thanks to hard-fought and costly American victories in the first and second naval battles of Guadalcanal, the battle of Empress Augusta Bay, and the battle of Cape St George, the Japanese would no longer hold the materiel or skilled manpower advantage. From this point on, although the war was still a long way from being won, the American star was unquestionably on the ascendant, slowly, but surely, edging Japanese imperialism towards its sunset.Jeffrey Cox's analysis and attention to detail of even the smallest events are second to none. But what truly sets this book apart is how he combines this microscopic attention to detail, often unearthing new facts along the way, with an engaging style that transports the reader to the heart of the story, bringing the events on the deep blue of the Pacific vividly to life.

     Have you ever been put off by music theory or thought that it is too hard to learn? If you find yourself in any of this, then this book is what you need. It covers everything that anyone who plays (or wants to play) music and wishes to become a better musician should know. This is the most comprehensive evergreen book on music theory that you'll be able to find, and you will want to keep it forever.Not only that but this book is structured in a way that is very easy to follow and internalize all the concepts explained. You don't have to be a college degree music student in order to understand and use any of this - anyone can do it, even a total beginner! It also doesn't matter what instrument(s) you play - because music theory is universal - nor what is your level of knowledge or playing ability! This book will give you all the information necessary to become a true expert in music theory without frustration and feeling overwhelmed, and this in-turn will have innumerable benefits to your playing! Don't believe me? Just use the look inside feature by clicking on the book cover to get a sneak peak of what you'll learn inside... Get this book now to solve all your problems with music theory and become an expert in this field! Pick up your copy today by clicking on the BUY now button at the top of this page. P.S. For guitar players free bonus gift is included!

    Hazen writes of how the co-evolution of the geosphere and biosphere—of rocks and living matter—has shaped our planet into the only one of its kind in the Solar System, if not the entire cosmos.With an astrobiologist’s imagination, a historian’s perspective, and a naturalist’s passion for the ground beneath our feet, Hazen explains how changes on an atomic level translate into dramatic shifts in Earth’s makeup over its 4.567 billion year existence. He calls upon a flurry of recent discoveries to portray our planet’s many iterations in vivid detail. Through his theory of “co-evolution,” we learn how reactions between organic molecules and rock crystals may have generated Earth’s first organisms, which in turn are responsible for more than two-thirds of the mineral varieties on the planet.The Story of Earth is also the story of the pioneering men and women behind the sciences. Readers will meet black-market meteorite hawkers of the Sahara Desert, the gun-toting Feds who guarded the Apollo missions’ lunar dust, and the World War II Navy officer whose super-pressurized “bomb”—recycled from military hardware—first simulated the molten rock of Earth’s mantle. As a mentor to a new generation of scientists, Hazen introduces the intrepid young explorers whose dispatches from Earth’s harshest landscapes will revolutionize geology.

        Growing up on a ranch in Sterling, Colorado, Frederick Libby mastered the cowboy arts of roping, punching cattle, and taming horses. As a young man he exercised his skills in the mountains and on the ranges of Arizona and New Mexico as well as the Colorado prairie. When World War I broke out, he found himself in Calgary, Alberta, and joined the Canadian army. In France, he transferred to the Royal Flying Corps as an "observer," the gunner in a two-person biplane. Libby shot down an enemy plane on his first day in battle over the Somme, which was also the first day he flew in a plane or fired a machine gun. He went on to become a pilot. He fought against the legendary German aces Oswald Boelcke and Manfred von Richthofen, and became the first American to down five enemy planes. He won the Military Cross for conspicuous gallantry in action.   Libby's memoir of his cowboy days in the last years of the Old West evokes a real-life Cormac McCarthy novel. His description of World War I combines a rattling good account of the air war over France with captivating and sometimes poignant depictions of wartime London, the sorrow for friends lost in combat, and the courage and camaraderie of the Royal Flying Corps. Told in charming, straightforward vernacular, Horses Don't Fly is an unforgettable piece of Americana.