By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist. Einstein endorsed this result reluctantly but he could find no way to refute it, since then, neither has anyone else. Yet cosmologists and philosophers alike have proceeded as if this discovery was never made. In A World Without Time, Palle Yourgrau sets out to restore Godel to his rightful place in history, telling the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue the brilliant work they did together.

    Shows how any proof can be understood as a sequence of techniques. Covers the full range of techniques used in proofs, such as the contrapositive, induction, and proof by contradiction. Explains how to identify which techniques are used and how they are applied in the specific problem. Illustrates how to read written proofs with many step-by-step examples. Includes new, expanded appendices related to discrete mathematics, linear algebra, modern algebra and real analysis.

    And more than any other recent philosopher, Heidegger has a following outside philosophy, among artists, architects, literary theorists, psychologists, and computer scientists.Heidegger Explained is the clearest exposition of Heidegger yet written. It describes his controversial life and career, his relations with contemporaries, the evolution of his thought, and the pathways of his influence.

    Written by the 19th-century mathematician who also gave us "Alive in Wonderland", they are among the most entertaining logical works ever written, and contain some of the most thought-provoking puzzles ever devised.

    In this little book Welsh writer and artist David Wade paints a picture of one of the most elusive and pervasive concepts known to man.

    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.

    

    That wish has come true for us. Now what? In this radically illuminating book, Alan Cohen delves into one of the world’s most venerated wisdom texts for answers and brings the lofty and enigmatic concepts of the Tao Te Ching down to earth in fresh, easy-to-grasp language with practical, personal examples we can use to uplift our daily lives.Most other interpretations of the Tao march through the stanzas one by one. Here Alan Cohen calls forth the ancient verses around themes that are central to our modern lives —from love to work to the lessons we learn from pain. Then he brings each message to life in short vignettes where he imagines himself a student of Lao Tse and interacts with the master directly and intimately. He invites you to join the ancient sage and the contemporary seeker as they wend their way through the challenges and triumphs of the same journey you’re taking yourself.

    It includes a new discussion of the Third Analogy, a greatly expanded discussion of Kant’s Paralogisms, and entirely new chapters dealing with Kant’s theory of reason, his treatment of theology, and the important Appendix to the Dialectic.Praise for the earlier edition:“Probably the most comprehensive and substantial study of the Critique of Pure Reason written by any American philosopher.... This is a splendid book.” —Lewis White Beck“This masterful study ... will most certainly join the canon of required reading for future interpreters of Kant’s theoretical philosophy. Superbly organized and lucidly written.” —Garrett Green, Journal of Religion

    Dip into any chapter and you will find lively scenarios and dialogues to take you through philosophical puzzles ancient and modern, involving virtual reality, science fiction and a host of characters from this and other planets. The text is interspersed on every page with lively cartoons, and there is a list of philosophical jargon at the end..Stephen Law has a gift for communicating complex ideas. He offers few answers, but his unstuffy, highly personal approach will have the reader thinking and arguing with as much pleasure as he does himself.

    In his long-awaited first book, Paul Boghossian critically examines such views and exposes their fundamental flaws.Boghossian focuses on three different ways of reading the claim that knowledge is socially constructed--one as a thesis about truth and two about justification. And he rejects all three. The intuitive, common-sense view is that there is a way the world is that is independent of human opinion; and that we are capable of arriving at beliefs about how it is that are objectively reasonable, binding on anyone capable of appreciating the relevant evidence regardless of their social or cultural perspective. Difficult as these notions may be, it is a mistake to think that philosophy has uncovered powerful reasons for rejecting them.This short, lucid, witty book shows that philosophy provides rock-solid support for common sense against the relativists. It will prove provocative reading throughout the discipline and beyond.

    Delving into an immense range of topics, from philosophy and literature to social criticism to mathematics and science, with essays that date from 1930s to the 1990s, Martin Gardner has astounded readers with his insight and erudition. The Night Is Large is the crowning achievement of his extraordinary career.

    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.

    Calculus is not a prerequisite, although examples and exercises using very basic calculus are included (labeled Calculus Required.) The most technology-friendly text on the market, Introductory Linear Algebra is also the most flexible. By omitting certain sections, instructors can cover the essentials of linear algebra (including eigenvalues and eigenvectors), to show how the computer is used, and to introduce applications of linear algebra in a one-semester course.

    A. Zee, a distinguished physicist and skillful expositor, tells the exciting story of how today's theoretical physicists are following Einstein in their search for the beauty and simplicity of Nature. Animated by a sense of reverence and whimsy, the book describes the majestic sweep and accomplishments of twentieth-century physics. In the end, we stand in awe before the grand vision of modern physics--one of the greatest chapters in the intellectual history of humankind.