Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

    Too often, textbooks turn the fascinating systems, processes, and figures of anatomy into tedious discourse that even Leonardo Da Vinci would reject. This easy-to-read guide cuts out the boring details, and instead, provides you with a compelling lesson in anatomy. Covering every aspect of anatomical development and physiology, each chapter details the different parts of the human body, how systems are formed, and disorders that could disrupt bodily functions. You'll unravel the mysteries of anatomy with unique, accessible elements like: Detailed charts of each system in the body Illustrations of cross sections Unique profiles of the most influential figures in medical history From cell chemistry to the respiratory system, Anatomy 101 is packed with hundreds of entertaining facts that you can't get anywhere else!

    Cells are built out of molecular circuits that perform logical operations, as electronic devices do, but with unique properties. Bray argues that the computational juice of cells provides the basis of all the distinctive properties of living systems: it allows organisms to embody in their internal structure an image of the world, and this accounts for their adaptability, responsiveness, and intelligence.In Wetware, Bray offers imaginative, wide-ranging and perceptive critiques of robotics and complexity theory, as well as many entertaining and telling anecdotes. For the general reader, the practicing scientist, and all others with an interest in the nature of life, the book is an exciting portal to some of biology’s latest discoveries and ideas.

    But now, with the aid of high-speed computers, scientists have been able to penetrate a reality that is changing the way we perceive the universe. Their findings -- the basis for chaos theory -- represent one of the most exciting scientific pursuits of our time.No better introduction to this find could be found than John Briggs and F. David Peat's Turbulent Mirror. Together, they explore the many faces of chaos and reveal how its law direct most of the processes of everyday life and how it appears that everything in the universe is interconnected -- discovering an "emerging science of wholeness."Turbulent Mirror introduces us to the scientists involved in study this endlessly strange field; to the theories that are turning our perception of the world on its head; and to the discoveries in mathematics, biology, and physics that are heralding a revolution more profound than the one responsible for producing the atomic bomb. With practical applications ranging from the control of traffic flow and the development of artifical intelligence to the treatment of heart attacks and schizophrenia, chaos promises to be an increasingly rewarding area of inquiry -- of interest to everyone.

    In the mid-1970s, scientists began using DNA sequences to reexamine the history of all life. Perhaps the most startling discovery to come out of this new field—the study of life’s diversity and relatedness at the molecular level—is horizontal gene transfer (HGT), or the movement of genes across species lines. It turns out that HGT has been widespread and important. For instance, we now know that roughly eight percent of the human genome arrived not through traditional inheritance from directly ancestral forms, but sideways by viral infection—a type of HGT.David Quammen chronicles these discoveries through the lives of the researchers who made them—such as Carl Woese, the most important little-known biologist of the twentieth century; Lynn Margulis, the notorious maverick whose wild ideas about “mosaic” creatures proved to be true; and Tsutomu Wantanabe, who discovered that the scourge of antibiotic-resistant bacteria is a direct result of horizontal gene transfer, bringing the deep study of genome histories to bear on a global crisis in public health.

    He asks how today's scientists can claim to predict future climate events when even three-day forecasts prove a serious challenge. Can we predict and control epidemics? Can we accurately foresee our financial future? Or will we only find out about tomorrow when tomorrow arrives?

    It is a ‘ must’ book for those in every branch of science . . . in addition, economists, politicians, statesmen, and businessmen cannot afford to overlook cybernetics and its tremendous, even terrifying implications. "It is a beautifully written book, lucid, direct, and despite its complexity, as readable by the layman as the trained scientist." -- John B. Thurston, "The Saturday Review of Literature" Acclaimed one of the "seminal books . . . comparable in ultimate importance to . . . Galileo or Malthus or Rousseau or Mill," "Cybernetics" was judged by twenty-seven historians, economists, educators, and philosophers to be one of those books published during the "past four decades", which may have a substantial impact on public thought and action in the years ahead." -- Saturday Review

    and a Professor of Life Sciences at UCLA who is immersed in the debate on religion. In Anarchy Evolution, Graffin puts forth his bold ideas about “naturalism” and the connection between science religion and art. In this provocative and timely book, Graffin tackles head on the “intellectual dishonestly” of creationism; he also shares compelling stories about his childhood and how science saved him when he ran into trouble as a teenager. Anarchy Evolution will appeal to the fans of Bad Religion (which as sold over 2.8 million albums) as well as readers of Richard Dawkins and Christopher Hitchens. The book coincides with a major national Bad Religion reunion tour that will start in October of 2010.

    In question-and-answer format, Polkinghorne and his collaborator Nicholas Beale offer their highly informed opinions about some of the most frequently asked of these questions. Readers can follow their own paths through the book, selecting questions that interest them and looking at the additional material if they choose. This unique book will help Christians clarify their beliefs regarding difficult issues and better face challenges--from within and from others--to their faith.

    But what if everything we’ve been taught to believe about aging is wrong? What if we could choose our lifespan? In this groundbreaking book, Dr. David Sinclair, leading world authority on genetics and longevity, reveals a bold new theory for why we age. As he writes: “Aging is a disease, and that disease is treatable.” This book takes us to the frontlines of research many from Dr. David Sinclair’s own lab at Harvard—that demonstrate how we can slow down, or even reverse, aging. The key is activating newly discovered vitality genes, the descendants of an ancient genetic survival circuit that is both the cause of aging and the key to reversing it.

    It was the dawn of a new era in artificial intelligence: a machine capable of beating the reigning human champion at this most cerebral game. That moment was more than a century in the making, and in this breakthrough book, Kasparov reveals his astonishing side of the story for the first time. He describes how it felt to strategize against an implacable, untiring opponent with the whole world watching, and recounts the history of machine intelligence through the microcosm of chess, considered by generations of scientific pioneers to be a key to unlocking the secrets of human and machine cognition. Kasparov uses his unrivaled experience to look into the future of intelligent machines and sees it bright with possibility. As many critics decry artificial intelligence as a menace, particularly to human jobs, Kasparov shows how humanity can rise to new heights with the help of our most extraordinary creations, rather than fear them. Deep Thinking is a tightly argued case for technological progress, from the man who stood at its precipice with his own career at stake.

    In The First Idea, Stanley Greenspan and Stuart Shanker explore this missing link and offer brilliant new insights into two longstanding questions: how human beings first create symbols and how these abilities evolved and were transmitted across generations over millions of years. From fascinating research into the intelligence of both human infants and apes, they identify certain cultural practices that are vitally important if we are to have stable and reflective future societies.

    In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Godel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

    They develop an interpretation of quantum mechanics which gives a clear, intuitive understanding of its meaning and in which there is a coherent notion of the reality of the universe without assuming a fundamental role for the human observer. With the aid of new concepts such as active information together with non-locality, they provide a comprehensive account of all the basic features of quantum mechanics, including the relativistic domain and quantum field theory. It is shown that, with the new approach, paradoxical or unsatisfactory features associated with the standard approaches, such as the wave-particle duality and the collapse of the wave function, do not arise. Finally, the authors make new suggestions and indicate some areas in which one may expect quantum theory to break down in a way that will allow for a test. The Undivided Universe is an important book especially because it provides a different overall world view which is neither mechanistic nor reductionist. This view will ultimately have radical implications not only in physics but also in our general approach to all areas of life.

    It is precisely because of the unreliability of vision, of memory, of wanting to believe, of induced belief ... that the Sufis say that an objective perception must be acquired before even familiar things can be seen as they are. "Seeker After Truth" goes beyond the familiar "first do this, then do that" style of handbook, transporting the reader to new ranges of perception, according to his or her capacity. Among the many assumptions questioned are: the objective worth of deep emotional feelings; the superiority of man's social habits over those of rats, and the origin of those habits; the evils of deceit ... The magazine Literary Review said about it: "This book ... is food for many different kinds of study - a book unlike anything our society has produced until recently, in its richness, its unexpectedness, its capacity to shock us into seeing ourselves as others see us, both personally and as a society."