Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    Sci-fi makes it look so easy. Receive a distress call from Alpha Centauri? No problem: punch the warp drive and you're there in minutes. Facing a catastrophe that can't be averted? Just pop back in the timestream and stop it before it starts. But for those of us not lucky enough to live in a science-fictional universe, are these ideas merely flights of fancy—or could it really be possible to travel through time or take shortcuts between stars? Cutting-edge physics may not be able to answer those questions yet, but it does offer up some tantalizing possibilities. In Time Travel and Warp Drives, Allen Everett and Thomas A. Roman take readers on a clear, concise tour of our current understanding of the nature of time and space—and whether or not we might be able to bend them to our will. Using no math beyond high school algebra, the authors lay out an approachable explanation of Einstein's special relativity, then move through the fundamental differences between traveling forward and backward in time and the surprising theoretical connection between going back in time and traveling faster than the speed of light. They survey a variety of possible time machines and warp drives, including wormholes and warp bubbles, and, in a dizzyingly creative chapter, imagine the paradoxes that could plague a world where time travel was possible—killing your own grandfather is only one of them! Written with a light touch and an irrepressible love of the fun of sci-fi scenarios—but firmly rooted in the most up-to-date science, Time Travel and Warp Drives will be a delightful discovery for any science buff or armchair chrononaut.

    Unended Quest recounts these moments and many others in the life of one of the most influential thinkers of the twentieth century, providing an indispensable account of the ideas that influenced him most. As an introduction to Popper's philosophy, Unended Quest also shines. Popper lucidly explains the central ideas in his work, making this book ideal for anyone coming to Popper's life and work for the first time.

    Hofstadter's collection of quirky essays is unified by its primary concern: to examine the way people perceive and think.

    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.

    Today we are at the brink of discoveries that should soon reveal the deepest secrets of the universe.Alpha and Omega is a dispatch from the front lines of the cosmological revolution that is being waged at observatories and laboratories around the world-in Europe, in America, and even in Antarctica--where scientists are actually peering into both the cradle of the universe and its grave. Scientists--including galaxy hunters and microwave eavesdroppers, gravity theorists and atom smashers, all of whom are on the trail of dark matter, dark energy, and the growing inhabitants of the particle zoo-now know how the universe will end and are on the brink of understanding its beginning. Their findings will be among the greatest triumphs of science, even towering above the deciphering of the human genome.This is the book you need to help understand the frequent front-page headlines heralding dramatic cosmological discoveries. It makes cutting-edge science both crystal clear and wonderfully exciting.

    nd its place within a grander scheme, one of the most creative and original of contemporary scientists draws together recent advances in astrophysics and up-to-the-minute research to cast a piercing light on man's place in the cosmos.

    How do scientists look at chance, or randomness, and chaos in physical systems? In answering this question for a general audience, Ruelle writes in the best French tradition: he has produced an authoritative and elegant book--a model of clarity, succinctness, and a humor bordering at times on the sardonic.

    This discussion paves the way for an outline of epistemological methods in which the rationalism of thinkers like Descartes, Leibniz and Kant is compared to the empiricism of Locke and Hume.Over the course of the book, in a manner that is careful and methodic but never dull, Jeans marshals the evidence for his startling conclusion: recent discoveries in astronomy, mathematics, sub-atomic physics and other disciplines have washed away the scientific basis of many older philosophic discussions. Such long-standing problems as causality, free will and determinism, the nature of space and time, materialism and mentalism must be considered anew int he light of new knowledge and information attained by 20th-century physical science. Even then, however, Jeans cautions against drawing any positive conclusions, pointing out that both physics and philosophy are both relatively young and that we are still, in Newton's words, like children playing with pebbles on the sea-shore, while the great ocean of truth rolls, unexplored, beyond our reach.Although first published nearly 40 years ago, nothing in physics has happened to affect Jean's account in this book; it remains remarkably fresh and undated, a classic exposition of the philosophical implications of scientific knowledge.

    Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.

    Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics -- the universal language of science -- keep the masterpieces of the subject hidden behind a veil?"The Universe in Zero Words" tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society -- from the elementary (1+1 = 2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E = mc^2) to the arcane (Hamilton's quaternion equations). Mackenzie, who has been called a "popular-science ace" by Booklist magazine, lucidly explains what each equation means, who discovered it (and how), and how it has affected our lives.(From the jacket copy.)Note: The Princeton University Press version (black cover) is for sale in the English-speaking world outside Australia. The Newsouth Press version (blue cover) is for sale in Australia. The two versions are identical except for the covers.

    This time physicist Robert Gilmore takes us on a journey with Dorothy, following the yellow building block road through the land of the Wizard of Quarks. Using characters and situations based on the Wizard of Oz story, we learn along the way about the fascinating world of particle physics. Classes of particles, from quarks to leptons are shown in an atomic garden, where atoms and molecules are produced. See how Dorothy, The Tin Geek, and the Cowardly Lion experience the bizarre world of subatomic particles.

    

    Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

    It defines our experience of the world; it echoes through our every waking hour. Time is the very foundation of conscious experience. Yet as familiar as it is, time is also deeply mysterious. We cannot see, hear, smell, taste, or touch it. Yet we do "feel" it--or at least we "think" we feel it. No wonder poets, writers, philosophers, and scientists have grappled with time for centuries.In his latest book, award-winning science writer Dan Falk chronicles the story of how humans have come to understand time over the millennia, and by drawing from the latest research in physics, psychology, and other fields, Falk shows how that understanding continues to evolve. "In Search of Time" begins with our earliest ancestors' perception of time and the discoveries that led--with much effort--to the Gregorian calendar, atomic clocks, and "leap seconds." Falk examines the workings of memory, the brain's remarkable "bridge across time," and asks whether humans are unique in their ability to recall the past and imagine the future. He explores the possibility of time travel, and the paradoxes it seems to entail. Falk looks at the quest to comprehend the beginning of time and how time--and the universe--may end. Finally, he examines the puzzle of time's "flow," and the remarkable possibility that the passage of time may be an illusion.Entertaining, illuminating, and ultimately thought provoking, "In Search of Time "reveals what some of our most insightful thinkers have had to say about time, from Aristotle to Kant, from Newton to Einstein, and continuing with the brightest minds of today.