Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

    This third edition of the successful textbook provides a fresh look at key topics in metaphysics and includes two new chapters on time and causation.Wherever possible, Loux links contemporary views to their classical sources in the history of philosophy. This new edition also keeps the user-friendly format, the chapter overviews summarizing the main topics and examples to clarify difficult concepts.

    The journey is the joy, and Emily Thomas a terrific guide." - Mike ParkerHow can we think more deeply about our travels?This was the question that inspired Emily Thomas' journey into the philosophy of travel. Part philosophical ramble, part travelogue, The Meaning of Travel begins in the Age of Discovery, when philosophers first started taking travel seriously. It meanders forward to consider Montaigne on otherness, John Locke on cannibals, and Henry Thoreau on wilderness.On our travels with Thomas, we discover the dark side of maps, how the philosophy of space fuelled mountain tourism, and why you should wash underwear in woodland cabins... We also confront profound issues, such as the ethics of 'doom tourism' (travel to 'doomed' glaciers and coral reefs), and the effect of space travel on human significance in a leviathan universe.The first ever exploration of the places where history and philosophy meet, this book will reshape your understanding of travel.

    Contemporary research in the empirical neurosciences and recent research in the philosophy of mind and the philosophy of science are used to illuminate fundamental questions concerning the relation between abstract cognitive theory and substantive neuroscience.

    In this book van Fraassen develops an alternative to scientific realism by constructing and evaluating three mutually reinforcing theories.

    And this language is mathematics." In The Language of Mathematics, award-winning author Keith Devlin reveals the vital role mathematics plays in our eternal quest to understand who we are and the world we live in. More than just the study of numbers, mathematics provides us with the eyes to recognize and describe the hidden patterns of life—patterns that exist in the physical, biological, and social worlds without, and the realm of ideas and thoughts within.Taking the reader on a wondrous journey through the invisible universe that surrounds us—a universe made visible by mathematics—Devlin shows us what keeps a jumbo jet in the air, explains how we can see and hear a football game on TV, allows us to predict the weather, the behavior of the stock market, and the outcome of elections. Microwave ovens, telephone cables, children's toys, pacemakers, automobiles, and computers—all operate on mathematical principles. Far from a dry and esoteric subject, mathematics is a rich and living part of our culture. An exploration of an often woefully misunderstood subject, The Language of Mathematics celebrates the simplicity, the precision, the purity, and the elegance of mathematics.

    His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.

    The emphasis is, instead, on the myriad ways in which the universe presents itself to us--and how, as observers and participants in its processes, we respond to it. "Life, like a dome of many-colored glass," wrote Percy Bysshe Shelley, "stains the white radiance of eternity." The author seeks here to explore the variety that gives life its beauty.Taken from Dyson's recent public lectures--delivered to audiences with no specialized knowledge in hard sciences--the book begins with a consideration of the practical and political questions surrounding biotechnology. As he seeks how best to explain the place of life in the universe, Dyson then moves from the ethical to the purely scientific. The book concludes with an attempt to understand the implications of biology for philosophy and religion.The pieces in this collection touch on numerous disciplines, from astronomy and ecology to neurology and theology, speaking to the lay reader as well as to the scientist. As always, Dyson's view of human nature and behavior is balanced, and his predictions of a world to come serve primarily as a means for thinking about the world as it is today.

    Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations--as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal relevance that explores the great variety of applications and importance of symmetry.

    Whether discussing Greek art and thought, vindicating the church’s battle with Galileo, exploring the development of quantum physics or exposing the dogmatism of Karl Popper, Feyerabend defends a relativist and historicist notion of the sciences. The appeal to reason, he insists, is empty, and must be replaced by a notion of science that subordinates it to the needs of citizens and communities.Provocative, polemical and rigorously argued, Farewell to Reason will infuriate Feyerabend’s critics and delight his many admirers.

    Imperfect Thirst includes beautiful love poems and approaches elemental subjects with a remarkable balance of good nature and holy dread: recollections of childhood, snapshots of impassive cruelty, reflections on art and nature. This energetic collection will prove once again why Galway Kinnell is one of America's masters of the art.

     Euclid in living color   Nearly a century before Mondrian made geometrical red, yellow, and blue lines famous, 19th century mathematician Oliver Byrne employed the color scheme for the figures and diagrams in his most unusual 1847 edition of Euclid's Elements. The author makes it clear in his subtitle that this is a didactic measure intended to distinguish his edition from all others: “The Elements of Euclid in which coloured diagrams and symbols are used instead of letters for the greater ease of learners.” As Surveyor of Her Majesty’s Settlements in the Falkland Islands, Byrne had already published mathematical and engineering works previous to 1847, but never anything like his edition on Euclid. This remarkable example of Victorian printing has been described as one of the oddest and most beautiful books of the 19th century. Each proposition is set in Caslon italic, with a four-line initial, while the rest of the page is a unique riot of red, yellow, and blue. On some pages, letters and numbers only are printed in color, sprinkled over the pages like tiny wild flowers and demanding the most meticulous alignment of the different color plates for printing. Elsewhere, solid squares, triangles, and circles are printed in bright colors, expressing a verve not seen again on the pages of a book until the era of Dufy, Matisse, and Derain.

    Its Philosophy 101 for everyone who knows not to take all this heavy stuff too seriously. Some of the Big Ideas are Existentialism (what do Hegel and Bette Midler have in common?), Philosophy of Language (how to express what its like being stranded on a desert island with Halle Berry), Feminist Philosophy (why, in the end, a man is always a man), and much more. Finally it all makes sense!

    Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host--call him Monty Hall--opens a different door, alwayschoosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door? In this light-hearted yet ultimately serious book, Jason Rosenhouse explores the history of this fascinating puzzle. Using a minimum ofmathematics (and none at all for much of the book), he shows how the problem has fascinated philosophers, psychologists, and many others, and examines the many variations that have appeared over the years. As Rosenhouse demonstrates, the Monty Hall Problem illuminates fundamental mathematical issuesand has abiding philosophical implications. Perhaps most important, he writes, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.

    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.