“They are both brilliantly original and outsiders,” the narrator tells us. “They are both besotted with mathematics. But for all their devotion, mathematics is indifferent, unaltered by any of their dramas . . . Against indifference, I want to tell their stories.” Which she does in a haunting, incantatory voice, the two lives unfolding in parallel narratives that overlap in the magnitude of each man’s achievement and demise: Gödel, delusional and paranoid, would starve himself to death; Turing, arrested for homosexual activities, would be driven to suicide. And they meet as well in the narrator’s mind, where facts are interwoven with her desire and determination to find meaning in the maze of their stories: two men devoted to truth of the highest abstract nature, yet unable to grasp the mundane truths of their own lives.A unique amalgam of luminous imagination and richly evoked historic character and event—A Madman Dreams of Turing Machines is a story about the pursuit of truth and its effect on the lives of two men. A story of genius and madness, incredible yet true.

    In a short life of thirty-two years, Shankaracharya not only revived Hinduism, but also created the organisational structure for its perpetuation through the mathas he established in Sringeri, Dwaraka, Puri and Jyotir Mathas.Adi Shankaracharaya: Hinduism’s Greatest Thinker is a meticulously researched and comprehensive account of his life and philosophy. Highly readable, and including a select anthology of Shankaracharya’s seminal writing, the book also examines the startling endorsement that contemporary science is giving to his ideas today. A must read for people across the ideological spectrum, this book reminds readers about the remarkable philosophical underpinning of Hinduism, making it one of the most vibrant religions in the world.

    As he wanders the land year upon year, Raymo gathers the revelations embedded in the geological and cultural history of this wild and ancient place. "When I called out for the Absolute, I was answered by the wind," Raymo writes. "If it was God's voice in the wind, then I heard it." In poetic prose grounded in a mind trained to discover fact, Honey from Stone enters the wonder of the material world in search of our deepest nature.

    His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Equally legendary were Gö's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first popular biography of this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life. After describing his childhood in the Moravian capital of Brno, the authors trace the arc of Gö's remarkable career, from the famed Vienna Circle, where philosophers and scientists debated notions of truth, to the Institute for Advanced Study in Princeton, New Jersey, where he lived and worked until his death in 1978. In the process, they shed light on Gö's contributions to mathematics, philosophy, computer science, artificial intelligence -- even cosmology -- in an entertaining and accessible way.

    Composed of such luminaries as Kurt Gödel and Rudolf Carnap, and stimulated by the works of Ludwig Wittgenstein and Karl Popper, the Vienna Circle left an indelible mark on science.Exact Thinking in Demented Times tells the often outrageous, sometimes tragic, and never boring stories of the men who transformed scientific thought. A revealing work of history, this landmark book pays tribute to those who dared to reinvent knowledge from the ground up.

    According to the author, these trends sought to create a unified conceptual apparatus as a common basis for the whole of human knowledge.Because these new developments in logical thought tended to perfect and sharpen the deductive method, an indispensable tool in many fields for deriving conclusions from accepted assumptions, the author decided to widen the scope of the work. In subsequent editions he revised the book to make it also a text on which to base an elementary college course in logic and the methodology of deductive sciences. It is this revised edition that is reprinted here.Part One deals with elements of logic and the deductive method, including the use of variables, sentential calculus, theory of identity, theory of classes, theory of relations and the deductive method. The Second Part covers applications of logic and methodology in constructing mathematical theories, including laws of order for numbers, laws of addition and subtraction, methodological considerations on the constructed theory, foundations of arithmetic of real numbers, and more. The author has provided numerous exercises to help students assimilate the material, which not only provides a stimulating and thought-provoking introduction to the fundamentals of logical thought, but is the perfect adjunct to courses in logic and the foundation of mathematics.

    A brilliantly clear and penetrating exposition of developments in physical science and mathematics brought about by the advent of non-Euclidean geometries, including in-depth coverage of the foundations of geometry, the theory of time, Einstein's theory of relativity and its consequences, other key topics.

    How can today's computers perform such a bewildering variety of tasks if computing is just glorified arithmetic? The answer, as Martin Davis lucidly illustrates, lies in the fact that computers are essentially engines of logic. Their hardware and software embody concepts developed over centuries by logicians such as Leibniz, Boole, and Godel, culminating in the amazing insights of Alan Turing. The Universal Computer traces the development of these concepts by exploring with captivating detail the lives and work of the geniuses who first formulated them. Readers will come away with a revelatory understanding of how and why computers work and how the algorithms within them came to be.

    In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes, everyday examples, and ruminations on history, literature, and more, Tammet allows us to share his unique insights and delight in the way numbers, fractions, and equations underpin all our lives. Inspired by the complexity of snowflakes, Anne Boleyn's eleven fingers, or his many siblings, Tammet explores questions such as why time seems to speed up as we age, whether there is such a thing as an average person, and how we can make sense of those we love. Thinking In Numbers will change the way you think about math and fire your imagination to see the world with fresh eyes.

    His famous paper, Theology and Falsification, was first presented at a meeting of the Oxford Socratic Club chaired by C. S. Lewis and went on to become the most widely reprinted philosophical publication of the last five decades. Flew earned his fame by arguing that one should presuppose atheism until evidence of a God surfaces. He now believes that such evidence exists, and There Is a God chronicles his journey from staunch atheism to believer.For the first time, this book will present a detailed and fascinating account of Flew's riveting decision to revoke his previous beliefs and argue for the existence of God. Ever since Flew's announcement, there has been great debate among atheists and believers alike about what exactly this "conversion" means. There Is a God will finally put this debate to rest.This is a story of a brilliant mind and reasoned thinker, and where his lifelong intellectual pursuit eventually led him: belief in God as designer.

    Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

    Far from the thankless, pointless exercises they are often thought to be, mathematics and logic are indispensable guides to ridding ourselves of dominant opinions and making possible an access to truths, or to a human experience of the utmost value. That is why mathematics may well be the shortest path to the true life, which, when it exists, is characterized by an incomparable happiness.

    First published in 1954, it details his experiences when taking mescaline. The book takes the form of Huxley's recollection of a mescaline trip that took place over the course of an afternoon in May 1953. The book takes its title from a phrase in William Blake's 1793 poem 'The Marriage of Heaven and Hell'. Huxley recalls the insights he experienced, which range from the "purely aesthetic" to "sacramental vision". He also incorporates later reflections on the experience and its meaning for art and religion.

    In 1935, aged 22, he developed the mathematical theory upon which all subsequent stored-program digital computers are modeled.At the outbreak of hostilities with Germany in September 1939, he joined the Government Codebreaking team at Bletchley Park, Buckinghamshire and played a crucial role in deciphering Engima, the code used by the German armed forces to protect their radio communications. Turing's work on the versionof Enigma used by the German navy was vital to the battle for supremacy in the North Atlantic. He also contributed to the attack on the cyphers known as Fish, which were used by the German High Command for the encryption of signals during the latter part of the war. His contribution helped toshorten the war in Europe by an estimated two years.After the war, his theoretical work led to the development of Britain's first computers at the National Physical Laboratory and the Royal Society Computing Machine Laboratory at Manchester University.Turing was also a founding father of modern cognitive science, theorizing that the cortex at birth is an unorganized machine which through training becomes organized into a universal machine or something like it. He went on to develop the use of computers to model biological growth, launchingthe discipline now referred to as Artificial Life.The papers in this book are the key works for understanding Turing's phenomenal contribution across all these fields. The collection includes Turing's declassified wartime Treatise on the Enigma; letters from Turing to Churchill and to codebreakers; lectures, papers, and broadcasts which opened upthe concept of AI and its implications; and the paper which formed the genesis of the investigation of Artifical Life.

    Science in the Soul brings together forty-two essays, polemics, and paeans--all written with Dawkins's characteristic erudition, remorseless wit, and unjaded awe of the natural world.Though it spans three decades, this book couldn't be more timely or more urgent. Elected officials have opened the floodgates to prejudices that have for half a century been unacceptable or at least undercover. In a passionate introduction, Dawkins calls on us to insist that reason take center stage and that gut feelings, even when they don't represent the stirred dark waters of xenophobia, misogyny, or other blind prejudice, should stay out of the voting booth. And in the essays themselves, newly annotated by the author, he investigates a number of issues, including the importance of empirical evidence, and decries bad science, religion in the schools, and climate-change deniers.Dawkins has equal ardor for "the sacred truth of nature" and renders here with typical virtuosity the glories and complexities of the natural world. Woven into an exploration of the vastness of geological time, for instance, is the peculiar history of the giant tortoises and the sea turtles--whose journeys between water and land tell us a deeper story about evolution. At this moment, when so many highly placed people still question the fact of evolution, Dawkins asks what Darwin would make of his own legacy--"a mixture of exhilaration and exasperation"--and celebrates science as possessing many of religion's virtues--"explanation, consolation, and uplift"--without its detriments of superstition and prejudice.In a world grown irrational and hostile to facts, Science in the Soul is an essential collection by an indispensable author.Praise for Science in the Soul"Compelling . . . rendered in gloriously spiky and opinionated prose . . . [Dawkins is] one of the great science popularizers of the last half-century."--The Christian Science Monitor "Dawkins is a ferocious polemicist, a defender of reason and enemy of superstition."--John Horgan, Scientific American