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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.

Product Description 'I'll stop doing it as soon as I understand what I'm doing.' Somewhere between a historical account and work of philosophy, Socrates' Defence details the final plea of Plato's beloved mentor. Introducing Little Black Classics: 80 books for Penguin's 80th birthday. Little Black Classics celebrate the huge range and diversity of Penguin Classics, with books from around the world and across many centuries. They take us from a balloon ride over Victorian London to a garden of blossom in Japan, from Tierra del Fuego to 16th-century California and the Russian steppe. Here are stories lyrical and savage; poems epic and intimate; essays satirical and inspirational; and ideas that have shaped the lives of millions. Plato (474 BC-347 BC). Plato's works available in Penguin Classics are Republic, The Last Days of Socrates, The Laws, Phaedrus, Protagoras and Meno, Timaeus and Critias, Theaetetus, Early Socratic Dialogues, The Symposium and Gorgias. About the Author Plato (474 BC-347 BC). Plato's works available in Penguin Classics are Republic, The Last Days of Socrates, The Laws, Phaedrus, Protagoras and Meno, Timaeus and Critias, Theaetetus, Early Socratic Dialogues, The Symposium and Gorgias.

For readers of E. H. Gombrich’s A Little History of the World, an equally irresistible volume that brings history’s greatest philosophers to life“A primer in human existence: philosophy has rarely seemed so lucid, so important, so worth doing and so easy to enter into. . . . A wonderful introduction for anyone who’s ever felt curious about almost anything.”—Sarah Bakewell, author of How To Live: A Life of Montaigne in One Question and Twenty Attempts at an AnswerPhilosophy begins with questions about the nature of reality and how we should live. These were the concerns of Socrates, who spent his days in the ancient Athenian marketplace asking awkward questions, disconcerting the people he met by showing them how little they genuinely understood. This engaging book introduces the great thinkers in Western philosophy and explores their most compelling ideas about the world and how best to live in it.In forty brief chapters, Nigel Warburton guides us on a chronological tour of the major ideas in the history of philosophy. He provides interesting and often quirky stories of the lives and deaths of thought-provoking philosophers from Socrates, who chose to die by hemlock poisoning rather than live on without the freedom to think for himself, to Peter Singer, who asks the disquieting philosophical and ethical questions that haunt our own times.Warburton not only makes philosophy accessible, he offers inspiration to think, argue, reason, and ask in the tradition of Socrates. A Little History of Philosophy presents the grand sweep of humanity’s search for philosophical understanding and invites all to join in the discussion.

'Grayling brings satisfying order to daunting subjects' Steven Pinker 'An enthusiastic thinker who embraces humour, common sense and lucidity' Independent _______________ From the eminent philosopher, an authoritative exploration of the great questions of how to live 'There is a question everyone has to ask and answer - in fact, has to keep on asking and keep on answering. It is, 'How should I live my life?' meaning, 'What values shall I live by? 'What sort of person should I be? What shall I aim for?' The great majority of people do not ask this question, they merely answer it unthinkingly, by adopting conventional views of life and what matters in it...' From Stoics to existentialists, in philosophy and literature, discussion of the philosophy of life -- of love and death, of courage, fortitude and wisdom -- challenges us all to think about what kinds of life are truly worth living. In this summation of a lifetime thinking and writing about this great question, A. C. Grayling explores with clarity and depth the ideas that each of us must use in answering it for ourselves. Drawing on the lives, experiences and works of a fantastically eclectic range of thinkers -- taking in not only philosophers such as Confucius, Seneca and Nietzsche, but also authors from Shakespeare to Ursula LeGuin, and modern thinkers such as Martha Nussbaum and Bernard Williams - Philosophy and Life brings together wisdom from across eras and continents in a tour de force on the philosophy of being human in a complicated world.

In a single work of colossal scope one of the world’s greatest scientists has given us a complete and unrivalled guide to the glories of the universe.The Road to Reality is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader — for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book.Roger Penrose’s purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections. Rarely less than challenging, the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams.The Road to Reality was a Sunday Times top-ten bestseller in the hardcover edition, with over 40,000 copies sold.

One of the major philosophical texts of the 20th century, Process and Reality is based on Alfred North Whitehead’s influential lectures that he delivered at the University of Edinburgh in the 1920s on process philosophy.Whitehead’s master work in philsophy, Process and Reality propounds a system of speculative philosophy, known as process philosophy, in which the various elements of reality into a consistent relation to each other. It is also an exploration of some of the preeminent thinkers of the seventeenth and eighteenth centuries, such as Descartes, Newton, Locke, and Kant.The ultimate edition of Whitehead’s magnum opus, Process and Reality is a standard reference for scholars of all backgrounds.

A profoundly beautiful and uniquely insightful description of the universe, Benedict de Spinoza's Ethics is one of the masterpieces of Enlightenment-era philosophy.Published shortly after his death, the Ethics is undoubtedly Spinoza's greatest work - an elegant, fully cohesive cosmology derived from first principles, providing a coherent picture of reality, and a guide to the meaning of an ethical life. Following a logical step-by-step format, it defines in turn the nature of God, the mind, the emotions, human bondage to the emotions, and the power of understanding - moving from a consideration of the eternal, to speculate upon humanity's place in the natural order, the nature of freedom and the path to attainable happiness. A powerful work of elegant simplicity, the Ethics is a brilliantly insightful consideration of the possibility of redemption through intense thought and philosophical reflection. The Ethics is presented in the standard translation of the work by Edwin Curley. This edition also includes an introduction by Stuart Hampshire, outlining Spinoza's philosophy and placing it in context.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.

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.

The story of philosophy is an epic tale: an exploration of the ideas, views and teachings of some of the most creative minds known to humanity. But since the long-popular classic Bertrand Russell's History of Western Philosophy, first published in 1945, there has been no comprehensive and entertaining, single-volume history of this great intellectual journey.With his characteristic clarity and elegance A. C. Grayling takes the reader from the world-views and moralities before the age of the Buddha, Confucius and Socrates, through Christianity's dominance of the European mind to the Renaissance and Enlightenment, and on to Mill, Nietzsche, Sartre, and philosophy today. And, since the story of philosophy is incomplete without mention of the great philosophical traditions of India, China and the Persian-Arabic world, he gives a comparative survey of them too.Intelligible for students and eye-opening for philosophy readers, he covers epistemology, metaphysics, ethics, aesthetics, logic, the philosophy of mind, the philosophy of language, political philosophy and the history of debates in these areas of enquiry, through the ideas of the celebrated philosophers as well as less well-known influential thinkers. He also asks what we have learnt from this body of thought, and what progress is still to be made.The first authoritative and accessible single-volume history of philosophy for decades, remarkable for its range and clarity, this is a landmark work.

In 1913, a young unschooled Indian clerk wrote a letter to G H Hardy, begging the pre-eminent English mathematician's opinion on several ideas he had about numbers. Realising the letter was the work of a genius, Hardy arranged for Srinivasa Ramanujan to come to England. Thus began one of the most improbable and productive collaborations ever chronicled. With a passion for rich and evocative detail, Robert Kanigel takes us from the temples and slums of Madras to the courts and chapels of Cambridge University, where the devout Hindu Ramanujan, 'the Prince of Intuition,' tested his brilliant theories alongside the sophisticated and eccentric Hardy, 'the Apostle of Proof'. In time, Ramanujan's creative intensity took its he died at the age of thirty-two and left behind a magical and inspired legacy that is still being plumbed for its secrets today.