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.

    In this hilarious essay, originally published in the collection A Supposedly Fun Thing I'll Never Do Again, he ventures to the Illinois State Fair, where he examines butter sculptures, munches on corndogs, and swaps stories with local exhibitors. As he wanders through this endlessly fascinating world, Wallace's one-of-a-kind blend of humor and insight is on full display. "Getting Away from Already Being Pretty Much Away from It All" is an uproarious and ultimately unforgettable foray into a classic part of American life and culture.

    Author Paul Copan has observed that many of these questions emerge as "anti-truth claims" that are part of today's skeptical mind-set. Christians defending their faith often hear slogans and questions such as:Ž It's all relativeŽ Everything is one with the Divine; all else is illusionŽ The Gospels contradict each otherŽ Why would a good God create hell?This book provides incisive answers to slogans related to truth and reality; theism, pantheism/Eastern religion, and naturalism; and doctrinal issues such as the incarnation and truth of Scripture. Each of the twenty-two chapters provides succinct answers and summary points for countering the arguments. Copan's book is accessible for all Christians who want to defend the plausibility of Christianity in the marketplace of ideas. It also includes helpful summary sections, additional resources, and additional documentation in the endnotes for review and discussion.

    Tracing the exchange of ideas between history's key philosophers, The Great Conversation: A Historical Introduction to Philosophy, Fifth Edition, demonstrates that while constructing an argument or making a claim, one philosopher almost always has others in mind. The book addresses the fundamental questions of human life: Who are we? What can we know? How should we live? and What sort of reality do we inhabit? The fifth edition retains the distinctive feature of previous editions: author Norman Melchert provides a generous selection of excerpts from major philosophical works and makes them more easily understandable to students with his lucid and engaging explanations. Ranging from the Pre-Socratics to Derrida and Quine, the selections are organized historically and include four complete works: Plato's Euthyphro, Apology, and Crito, and Descartes' Meditations on First Philosophy. The author's commentary offers a rich intellectual and cultural context for the philosophical ideas conveyed in the excerpts. Extensive cross-referencing shows students how philosophers respond appreciatively or critically to the thoughts of other philosophers. The text is enhanced by two types of exercises--Basic Questions and For Further Thought--and more than sixty illustrations.New to the Fifth Edition: * A new chapter (25) on Simone de Beauvoir and her contributions to philosophy * New material on Buddhist, Muslim, and Jewish thinkers, including profiles of the Buddha, Avicenna (Ibn Sina), Averro�s (Ibn Rushd), and Maimonides (Moses ben Maimon) * A new profile of Jean-Jacques Rousseau * Improved translations of several of Plato's works, including Protagoras, Gorgias, Phaedo, Symposium, Meno, and the Republic * Review questions that are now dispersed throughout the chapters (instead of at chapter ends) to follow relevant passages and facilitate classroom discussion * Thirteen new images, including seven explanatory cartoons that help students understand key concepts * A revised Instructor's Manual and Test Bank--available both on CD and in a printed version--containing essential points, teaching suggestions, and multiple-choice, short-answer, and essay exam questionsThe Great Conversation, Fifth Edition, is also available in two paperback volumes to suit your course needs. Volume I: Pre-Socratics through Descartes includes chapters 1-13 of the combined volume, while Volume II: Descartes through Derrida and Quine includes chapters 12-26.

    Patton and Kevin Cannon introduce us to the grand tradition of examined living. With the wisecracking Heraclitus as our guide, we travel down the winding river of philosophy, meeting influential thinkers from nearly three millennia of Western thought and witnessing great debates over everything from ethics to the concept of the self to the nature of reality.Combining Cannon's playful artistry and Patton's humorous, instructive prose, The Cartoon Introduction to Philosophy puts the fun back into the quest for fundamental truths, imparting a love of wisdom to anyone willing to grab a paddle and join the ride.

    Shows how our concept of humankind has changed over time and argues our current understanding of what it means to be human has been shaken by new discoveries from science and philosophy.

    This sharply intelligent, consistently provocative book takes the reader on an astonishing, thought-provoking voyage into the realm of delightful uncertainty--a world of paradox in which logical argument leads to contradiction and common sense is seemingly rendered irrelevant.

    Maisel, Monk) calmly tells the tale of how the ancient Greeks formalized the study of mathematics based on Phoenician teachings. Bedtime stories are narrated by the world’s most celebrated voices and written with no beginning, middle, or end so you don’t stay up to hear what happens next. They're interesting enough to give your mind something to focus on, but delivered in a way that encourages sleep. This title is part of the Audible Sleep Collection, exclusive audio experiences created to invite relaxation and sleep. New and free for members.Public Domain (P)2020 Audible

    Using the data they are constantly collecting about where we travel, where we shop, what we buy, and what interests us, they can begin to predict our daily habits, and increasingly we are relinquishing our decision-making to algorithms. Are we giving this up too easily?Without understanding what mathematics can and can't do it is impossible to get a handle on how it is changing our lives. Outnumbered is a journey to the dark side of mathematics, from how it dictates our social media activities to our travel routes. David Sumpter investigates whether mathematics is crossing dangerous lines when it comes to what we can make decisions about.This book will show how math impacts all parts of our lives: from the algorithms that decide whom we interact with to the statistical methods that categorize us as potential criminals. It tests financial algorithms that purport to generate money from nothing, and reveals that we are constantly manipulated by the math used by others, from algorithms choosing the news we hear to automated hospital waiting lists deciding whether we receive treatment.Using interviews with those people working at the cutting edge of mathematical and data research, Outnumbered will explain how math and stats work in the real world, and what we should and shouldn't worry about.

    Why is it better to buy a lottery ticket on a Friday? Why are showers always too hot or too cold? And what's the connection between a rugby player taking a conversion and a tourist trying to get the best photograph of Nelson's Column?These and many other fascinating questions are answered in this entertaining and highly informative book, which is ideal for anyone wanting to remind themselves – or discover for the first time – that maths is relevant to almost everything we do.Dating, cooking, travelling by car, gambling and even life-saving techniques have links with intriguing mathematical problems, as you will find explained here. Whether you have a PhD in astrophysics or haven't touched a maths problem since your school days, this book will give you a fresh understanding of the world around you.

    To Taylor, self-fulfillment, although often expressed in self-centered ways, isn't necessarily a rejection of traditional values and social commitment; it also reflects something authentic and valuable in modern culture. Only by distinguishing what is good in this modern striving from what is socially and politically dangerous, Taylor says, can our age be made to deliver its promise.

    But your pleasure and prowess at games, gambling, and other numerically related pursuits can be heightened with this entertaining volume, in which the authors offer a fascinating view of some of the lesser-known and more imaginative aspects of mathematics.A brief and breezy explanation of the new language of mathematics precedes a smorgasbord of such thought-provoking subjects as the googolplex (the largest definite number anyone has yet bothered to conceive of); assorted geometries — plane and fancy; famous puzzles that made mathematical history; and tantalizing paradoxes. Gamblers receive fair warning on the laws of chance; a look at rubber-sheet geometry twists circles into loops without sacrificing certain important properties; and an exploration of the mathematics of change and growth shows how calculus, among its other uses, helps trace the path of falling bombs.Written with wit and clarity for the intelligent reader who has taken high school and perhaps college math, this volume deftly progresses from simple arithmetic to calculus and non-Euclidean geometry. It “lives up to its title in every way [and] might well have been merely terrifying, whereas it proves to be both charming and exciting." — Saturday Review of Literature.

    Written not from a post-crisis perspective – but from a preventative point of view – this book traces the development of financial derivatives from bonds to credit default swaps, and shows how mathematical formulas went beyond pricing to expand their use to the point where they dwarfed the real economy. You'll learn how the deadly allure of their ice-cold beauty has misled generations of economists and investors, and how continued reliance on these formulas can either assist future economic development, or send the global economy into the financial equivalent of a cardiac arrest. Rather than rehash tales of post-crisis fallout, this book focuses on preventing the next one. By exploring the heart of the shadow economy, you'll be better prepared to ride the rough waves of finance into the turbulent future. Delve into one of the world's least-understood but highest-impact industries Understand the key principles of quantitative finance and the evolution of the field Learn what quantitative finance has become, and how it affects us all Discover how the industry's next steps dictate the economy's future How do you create a quadrillion dollars out of nothing, blow it away and leave a hole so large that even years of "quantitative easing" can't fill it – and then go back to doing the same thing? Even amidst global recovery, the financial system still has the potential to seize up at any moment. The Money Formula explores the how and why of financial disaster, what must happen to prevent the next one.

    In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.

    With over one million downloads per episode, these discussions have clearly hit a nerve, frequently walking a tightrope where either host or guest - and sometimes both - lose their footing, but always in search off a greater understanding of the world in which we live. for Harris, honest conversation, no matter how difficult or controversial, represents the only path to moral and intellectual progress.This book includes a dozen of the best conversations from 'MAKING SENSE', including talks with Daniel Kahneman, Timothy Snyder, Nick Bostrom, and Glen Loury, on topics that range from the nature of consciousness and free will, to politics and extremism, to living ethically. Together they shine a light on what it means to "make sense" in the modern world.RUNNING TIME ⇒ 22hrs.©2020 Sam Harris (P)2020 HarperAudio