But ask what it means, and the result will be a brawl. For a century, most physicists have followed Niels Bohr's Copenhagen interpretation and dismissed questions about the reality underlying quantum physics as meaningless. A mishmash of solipsism and poor reasoning, Copenhagen endured, as Bohr's students vigorously protected his legacy, and the physics community favored practical experiments over philosophical arguments. As a result, questioning the status quo long meant professional ruin. And yet, from the 1920s to today, physicists like John Bell, David Bohm, and Hugh Everett persisted in seeking the true meaning of quantum mechanics. What Is Real? is the gripping story of this battle of ideas and of the courageous scientists who dared to stand up for truth.

    In Code Breaking , Rudolf Kippenhahn offers readers both an exciting chronicle of cryptography and a lively exploration of the cryptographer’s craft. Rich with vivid anecdotes from a history of coding and decoding and featuring three new chapters, this revised and expanded edition makes the often abstruse art of deciphering coded messages accessible to the general reader and reveals the relevance of codes to our everyday high-tech society. A stylishly written, meticulously researched adventure, Code Breaking explores the ways in which communication can be obscured and, like magic, made clear again.

    Harlen Bretz walked the dry scabland channels of eastern Washington in the 1920s, it dawned on him that he was viewing a landscape sculpted by water. Lots of water. A flood of catastrophic proportions. Glacial Lake Missoula and Its Humongous Floods tells the gripping tale of a huge Ice Age lake that drained suddenly--not just once but repeatedly--and reshaped the landscape of the Northwest. The narrative follows the path of the floodwaters as they raged from western Montana across the Idaho Panhandle, then scoured through eastern Washington and down the Columbia Gorge to the Pacific Ocean. This is also the story of geologists grappling with scientific controversy--"of how personalities, pride, and prejudice sometimes superseded scientific evidence."

    Indeed, many physicists today believe that there are other dimensions beyond the four of our space-time, and that a unified vision of the various forces of nature can be achieved, if we consider that everything we see around us, from the trees to the stars are nothing but vibrations in hyperspace. Hyperspace theory - and its more recent derivation, superstring theory - is the eye of this revolution. In this book, Michio Kaku shows us a fascinating panorama, which completely changes our view of the cosmos, and takes us on a dazzling journey through new dimensions: wormholes connecting parallel universes, time machines, "baby universes" and more. Similar wonders are emerging in some pages in which everything is explained with elegant simplicity and where the mathematical formulation is replaced by imaginative illustrations that allow the problems to be visualized. The result is a very entertaining and surprising book, which even leaves behind the greatest fantasies of the old science fiction authors.

    The Platonic-Pythagorean tradition looked on nature in geometric terms with the conviction that the cosmos was constructed according to the principles of mathematical order, while the mechanical philosophy conceived of nature as a huge machine and sought to explain the hidden mechanisms behind phenomena. Pursuing different goals, these two movements of thought tended to conflict with each other, and more than the obviously mathematical sciences were affected - the influence spread as far as chemistry and the life sciences. As this book demonstrates, the full fruition of the scientific revolution required a resolution of the tension between the two dominant trends.

    Brian Greene, one of the world's leading string theorists, peels away the layers of mystery surrounding string theory to reveal a universe that consists of eleven dimensions, where the fabric of space tears and repairs itself, and all matter—from the smallest quarks to the most gargantuan supernovas—is generated by the vibrations of microscopically tiny loops of energy.Today physicists and mathematicians throughout the world are feverishly working on one of the most ambitious theories ever proposed: superstring theory. String theory, as it is often called, is the key to the Unified Field Theory that eluded Einstein for more than thirty years. Finally, the century-old antagonism between the large and the small-General Relativity and Quantum Theory-is resolved. String theory proclaims that all of the wondrous happenings in the universe, from the frantic dancing of subatomic quarks to the majestic swirling of heavenly galaxies, are reflections of one grand physical principle and manifestations of one single entity: microscopically tiny vibrating loops of energy, a billionth of a billionth the size of an atom. In this brilliantly articulated and refreshingly clear book, Greene relates the scientific story and the human struggle behind twentieth-century physics' search for a theory of everything.Through the masterful use of metaphor and analogy, The Elegant Universe makes some of the most sophisticated concepts ever contemplated viscerally accessible and thoroughly entertaining, bringing us closer than ever to understanding how the universe works.

    The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

    Peter Bernstein has written a comprehensive history of man's efforts to understand risk and probability, beginning with early gamblers in ancient Greece, continuing through the 17th-century French mathematicians Pascal and Fermat and up to modern chaos theory. Along the way he demonstrates that understanding risk underlies everything from game theory to bridge-building to winemaking.

    A simple web search picks out a handful of relevant needles from the world's biggest haystack: the billions of pages on the World Wide Web. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers; and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease? This is the first book to answer that question in language anyone can understand, revealing the extraordinary ideas that power our PCs, laptops, and smartphones. Using vivid examples, John MacCormick explains the fundamental "tricks" behind nine types of computer algorithms, including artificial intelligence (where we learn about the "nearest neighbor trick" and "twenty questions trick"), Google's famous PageRank algorithm (which uses the "random surfer trick"), data compression, error correction, and much more. These revolutionary algorithms have changed our world: this book unlocks their secrets, and lays bare the incredible ideas that our computers use every day.

    It presents the important traditional content of mineralogy including crystallography, chemical bonding, controls on mineral structure, mineral stability, and crystal growth to provide a foundation that enables students to understand the nature and occurrence of minerals. Physical, optical, and X-ray powder diffraction techniques of mineral study are described in detail, and common chemical analytical methods are outlined as well. Detailed descriptions of over 100 common minerals are provided, and the geologic context within which these minerals occur is emphasized. Appendices provide tables and diagrams to help students with mineral identification, using both physical and optical properties. Numerous line drawings, photographs, and photomicrographs help make complex concepts understandable. Introduction to Mineralogy not only provides specific knowledge about minerals but also helps students develop the intellectual tools essential for a solid, scientific education. This comprehensive text is useful for undergraduate students in a wide range of mineralogy courses.

    You experience it passing every day when you watch clocks tick, bread toast, and children grow. But most physicists see things differently, from Newton to Einstein to today’s quantum theorists. For them, time isn’t real. You may think you experience time passing, but they say it’s just an illusion.Lee Smolin, author of the controversial bestseller The Trouble with Physics, argues this limited notion of time is holding physics back. It’s time for a major revolution in scientific thought. The reality of time could be the key to the next big breakthrough in theoretical physics.What if the laws of physics themselves were not timeless? What if they could evolve? Time Reborn offers a radical new approach to cosmology that embraces the reality of time and opens up a whole new universe of possibilties. There are few ideas that, like our notion of time, shape our thinking about literally everything, with major implications for physics and beyond—from climate change to the economic crisis. Smolin explains in lively and lucid prose how the true nature of time impacts our world.

    Combine this with thoughtful and thorough apparatus, and Philosophy of Science: The Central Issues is the most flexible and comprehensive collection ever created for undergraduate courses.

    This is the amazing story of how the "map problem" was solved.The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little need to limit how many colors they used. But the problem set off a frenzy among professional mathematicians and amateur problem solvers, among them Lewis Carroll, an astronomer, a botanist, an obsessive golfer, the Bishop of London, a man who set his watch only once a year, a California traffic cop, and a bridegroom who spent his honeymoon coloring maps. In their pursuit of the solution, mathematicians painted maps on doughnuts and horseshoes and played with patterned soccer balls and the great rhombicuboctahedron. It would be more than one hundred years (and countless colored maps) later before the result was finally established. Even then, difficult questions remained, and the intricate solution--which involved no fewer than 1,200 hours of computer time--was greeted with as much dismay as enthusiasm.Providing a clear and elegant explanation of the problem and the proof, Robin Wilson tells how a seemingly innocuous question baffled great minds and stimulated exciting mathematics with far-flung applications. This is the entertaining story of those who failed to prove, and those who ultimately did prove, that four colors do indeed suffice to color any map.

    In Denialism, New Yorker staff writer Michael Specter reveals that Americans have come to mistrust institutions and especially the institution of science more today than ever before. For centuries, the general view had been that science is neither good nor bad—that it merely supplies information and that new information is always beneficial. Now, science is viewed as a political constituency that isn’t always in our best interest. We live in a world where the leaders of African nations prefer to let their citizens starve to death rather than import genetically modified grains. Childhood vaccines have proven to be the most effective public health measure in history, yet people march on Washington to protest their use. In the United States a growing series of studies show that dietary supplements and “natural” cures have almost no value, and often cause harm. We still spend billions of dollars on them. In hundreds of the best universities in the world, laboratories are anonymous, unmarked, and surrounded by platoons of security guards—such is the opposition to any research that includes experiments with animals. And pharmaceutical companies that just forty years ago were perhaps the most visible symbol of our remarkable advance against disease have increasingly been seen as callous corporations propelled solely by avarice and greed. As Michael Specter sees it, this amounts to a war against progress. The issues may be complex but the choices are not: Are we going to continue to embrace new technologies, along with acknowledging their limitations and threats, or are we ready to slink back into an era of magical thinking? In Denialism, Specter makes an argument for a new Enlightenment, the revival of an approach to the physical world that was stunningly effective for hundreds of years: What can be understood and reliably repeated by experiment is what nature regarded as true. Now, at the time of mankind’s greatest scientific advances—and our greatest need for them—that deal must be renewed.

    Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.