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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.

Throughout history, some books have changed the world. They have transformed the way we see ourselves - and each other. They have inspired debate, dissent, war and revolution. They have enlightened, outraged, provoked and comforted. They have enriched lives - and destroyed them. Now Penguin brings you the works of the great thinkers, pioneers, radicals and visionaries whose ideas shook civilization and helped make us who we are. The Father of Existentialism, Kierkegaard transformed philosophy with his conviction that we must all create our own nature; in this great work of religious anxiety, he argues that a true understanding of God can only be attained by making a personal 'leap of faith'.

Paperback. Pub Date :2013-06-06 Pages: 544 Language: English Publisher: Penguin Books The hottest thinker in the world Bryan Appleyard. Sunday TimesIn The Black Swan. Taleb showed us that highly improbable and unpredictable events underlie almost everything about our world ... Here Taleb stands uncer-tainty on its head. making it desirable. even necessary The antifragile is beyond the resilient or robust The resil-ient resists shocks and stays the same; the antifragile gets better and better.Just as human bones get stronger when subjected to stress and tension. many things in life benefit from stress. disorder. volatility. and turmoil. What Taleb has identified and calls antifragile are things that not only gain from chaos but need it in order to survive and flourish.Whats more . the antifragile is immune to prediction errors and protected from adverse events. Why is the cit...

'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.

There is a logical flaw in the statistical methods used across experimental science. This fault is not a minor academic quibble: it underlies a reproducibility crisis now threatening entire disciplines. In an increasingly statistics-reliant society, this same deeply rooted error shapes decisions in medicine, law, and public policy with profound consequences. The foundation of the problem is a misunderstanding of probability and its role in making inferences from observations.Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it. He highlights how influential nineteenth- and twentieth-century figures developed a statistical methodology they claimed was purely objective in order to silence critics of their political agendas, including eugenics.Clayton provides a clear account of the mathematics and logic of probability, conveying complex concepts accessibly for readers interested in the statistical methods that frame our understanding of the world. He contends that we need to take a Bayesian approach―that is, to incorporate prior knowledge when reasoning with incomplete information―in order to resolve the crisis. Ranging across math, philosophy, and culture, Bernoulli’s Fallacy explains why something has gone wrong with how we use data―and how to fix it.

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.

The Perennial Philosophy is defined by its author as "The metaphysic that recognizes a divine Reality substantial to the world of things and lives and minds." With great wit and stunning intellect, Aldous Huxley examines the spiritual beliefs of various religious traditions and explains them in terms that are personally meaningful.

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.

Voltaire's Philosophical Dictionary, first published in 1764, is a series of short, radical essays - alphabetically arranged - that form a brilliant and bitter analysis of the social and religious conventions that then dominated eighteenth-century French thought. One of the masterpieces of the Enlightenment, this enormously influential work of sardonic wit - more a collection of essays arranged alphabetically, than a conventional dictionary - considers such diverse subjects as Abraham and Atheism, Faith and Freedom of Thought, Miracles and Moses. Repeatedly condemned by civil and religious authorities, Voltaire's work argues passionately for the cause of reason and justice, and criticizes Christian theology and contemporary attitudes towards war and society - and claims, as he regards the world around him: 'common sense is not so common'.

Famous the world over for the creative brilliance of his insights into the physical world, Nobel Prize-winning physicist Richard Feynman also possessed an extraordinary talent for explaining difficult concepts to the nonscientist. QED--the edited version of four lectures on quantum electrodynamics that Feynman gave to the general public at UCLA as part of the Alix G. Mautner Memorial Lecture series--is perhaps the best example of his ability to communicate both the substance and the spirit of science to the layperson.The focus, as the title suggests, is quantum electrodynamics (QED), the part of the quantum theory of fields that describes the interactions of the quanta of the electromagnetic field-light, X rays, gamma rays--with matter and those of charged particles with one another. By extending the formalism developed by Dirac in 1933, which related quantum and classical descriptions of the motion of particles, Feynman revolutionized the quantum mechanical understanding of the nature of particles and waves. And, by incorporating his own readily visualizable formulation of quantum mechanics, Feynman created a diagrammatic version of QED that made calculations much simpler and also provided visual insights into the mechanisms of quantum electrodynamic processes.In this book, using everyday language, spatial concepts, visualizations, and his renowned "Feynman diagrams" instead of advanced mathematics, Feynman successfully provides a definitive introduction to QED for a lay readership without any distortion of the basic science. Characterized by Feynman's famously original clarity and humor, this popular book on QED has not been equaled since its publication.