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An accessible and fascinating exploration of how Alan Turing’s mathematical theory gave rise to modern computer science and applications—from the desktops to cell phonesIn 1936, when he was just 24 years old, Alan Turing wrote a remarkable paper in which he outlined the theory of computation, laying out the ideas that underlie all modern computers. This groundbreaking and powerful theory now forms the basis of computer science. In Turing’s Vision, Chris Bernhardt explains the theory for the general reader, beginning with its foundations and systematically building to its surprising conclusions. He also views Turing’s theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turing’s later work, and the birth of the modern computer.Turing wanted to show that there were problems that were beyond any computer’s ability to solve; in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turing’s ideas, Bernhardt examines 3 well-known decision problems to explore the concept of undecidability; investigates theoretical computing machines, including Turing machines; explains universal machines; and proves that certain problems are undecidable, including Turing’s problem concerning computable numbers.

A New York Times bestseller—the outrageous exploits of one of this century's greatest scientific minds and a legendary American original. Richard Feynman, winner of the Nobel Prize in physics, thrived on outrageous adventures. Here he recounts in his inimitable voice his experience trading ideas on atomic physics with Einstein and Bohr and ideas on gambling with Nick the Greek; cracking the uncrackable safes guarding the most deeply held nuclear secrets; accompanying a ballet on his bongo drums; painting a naked female toreador. In short, here is Feynman's life in all its eccentric—a combustible mixture of high intelligence, unlimited curiosity, and raging chutzpah.

Kurt Gödel (1906-1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory and stronger systems, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, the foundations of computation theory, unusual cosmological models, and for the strong individuality of his writings on the philosophy of mathematics. The Collected Works is a landmark resource that draws together a lifetime of creative accomplishment. The first two volumes were devoted to Gödel's publications in full (both in the original and translation). This third volume features a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass, documents that enlarge considerably our appreciation of his scientific and philosophical thought and add a great deal to our understanding of his motivations. Continuing the format of the earlier volumes, the present volume includes introductory notes that provide extensive explanatory and historical commentary on each of the papers, English translations of material originally written in German (some transcribed from Gabelsberger shorthand), and a complete bibliography. A succeeding volume is to contain a comprehensive selection of Gödel's scientific correspondence and a complete inventory of his Nachlass. The books are designed to be accessible and useful to as wide an audience as possible without sacrificing scientific or historical accuracy. The only complete edition available in English, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science.

Boethius was an eminent public figure under the Gothic emperor Theodoric, and an exceptional Greek scholar. When he became involved in a conspiracy and was imprisoned in Pavia, it was to the Greek philosophers that he turned. The Consolation was written in the period leading up to his brutal execution. It is a dialogue of alternating prose and verse between the ailing prisoner and his 'nurse' Philosophy. Her instruction on the nature of fortune and happiness, good and evil, fate and free will, restore his health and bring him to enlightenment. The Consolation was extremely popular throughout medieval Europe and his ideas were influential on the thought of Chaucer and Dante.For more than seventy years, Penguin has been the leading publisher of classic literature in the English-speaking world. With more than 1,700 titles, Penguin Classics represents a global bookshelf of the best works throughout history and across genres and disciplines. Readers trust the series to provide authoritative texts enhanced by introductions and notes by distinguished scholars and contemporary authors, as well as up-to-date translations by award-winning translators.

This book, one of the first full-length studies of the modalities to emerge from the debate to which Saul Kripke, David Lewis, Ruth Marcus, and others are contributing, is an exploration and defense of the notion of modality de re, the idea that objects have both essential and accidental properties. Plantinga develops his argument by means of the notion of possible worlds and ranges over such key problems as the nature of essence, transworld identity, negative existential propositions, and the existence of unactual objects in other possible worlds. He also applies his logical theories to the elucidation of two problems in the philosophy of religion: the problem of evil and the ontological argument.

Contemporary science presents us with the remarkable theory that the universe began to exist about fifteen billion years ago with a cataclysmic explosion called "the Big Bang." The question of whether Big Bang cosmology supports theism or atheism has long been a matter of discussion among the general public and in popular science books, but has received scant attention from philosophers. This book sets out to fill this gap by means of a sustained debate between two philosophers, William Lane Craig and Quentin Smith, who defend opposing positions. Craig argues that the Big Bang that began the universe was created by God, while Smith argues that the Big Bang has no cause. Alternating chapters by the two philosophers criticize and attempt to refute preceding arguments. Their arguments are based on Einstein's theory of relativity and include a discussion of the new quantum cosmology recently developed by Stephen Hawking and popularized in A Brief History of Time.

It has only been a couple of decades since Benoit Mandelbrot published his famous picture of what is now called the Mandelbrot set. That picture, now seeming graphically primitive, has changed our view of the mathematical and physical universe. The properties and circumstances of the discovery of the Mandelbrot Set continue to generate much interest in the research community and beyond. This book contains the hard-to-obtain original papers, many unpublished illustrations dating back to 1979 and extensive documented historical context showing how Mandelbrot helped change our way of looking at the world.

Madness, sexuality, power, knowledge—are these facts of life or simply parts of speech? In a series of works of astonishing brilliance, historian Michel Foucault excavated the hidden assumptions that govern the way we live and the way we think.The Archaeology of Knowledge begins at the level of "things aid" and moves quickly to illuminate the connections between knowledge, language, and action in a style at once profound and personal. A summing up of Foucault's own methodological assumptions, this book is also a first step toward a genealogy of the way we live now.Challenging, at times infuriating, it is an absolutely indispensable guide to one of the most innovative thinkers of our time.

While its tone is playful and frivolous, this book poses tough questions over the nature of religion and belief.Religion provides comfortable responses to the questions that have always beset humankind - why are we here, what is the point of being alive, how ought we to behave? Russell snatches that comfort away, leaving us instead with other, more troublesome alternatives: responsibility, autonomy, self-awareness. He tells us that the time to live is now, the place to live is here, and the way to be happy is to ensure others are happy.

In this classic account of madness, Michel Foucault shows once and for all why he is one of the most distinguished European philosophers since the end of World War II. Madness and Civilization,Foucault's first book and his finest accomplishment, will change the way in which you think about society. Evoking shock, pity and fascination, it might also make you question the way you think about yourself.