I derive from celestial phenomena the forces of gravity with which bodies tend to the sun and other planets.

    But recent technological advances have made the question both practical and urgent. A brilliantly imaginative group of physicists at Oxford University have risen to the challenge. This is their story. At long last, there is a sensible way to think about quantum mechanics. The new view abolishes the need to believe in randomness, long-range spooky forces, or conscious observers with mysterious powers to collapse cats into a state of life or death. But the new understanding comes at a price: we must accept that we live in a multiverse wherein countless versions of reality unfold side-by-side. The philosophical and personal consequences of this are awe-inspiring.The new interpretation has allowed imaginative physicists to conceive of wonderful new technologies: measuring devices that effectively share information between worlds and computers that can borrow the power of other worlds to perform calculations. Step by step, the problems initially associated with the original many-worlds formulation have been addressed and answered so that a clear but startling new picture has emerged.Just as Copenhagen was the centre of quantum discussion a lifetime ago, so Oxford has been the epicenter of the modern debate, with such figures as Roger Penrose and Anton Zeilinger fighting for single-world views, and David Deutsch, Lev Vaidman and a host of others for many-worlds.An independent physicist living in Oxford, Bruce has had a ringside seat to the debate. In his capable hands, we understand why the initially fantastic sounding many-worlds view is not only a useful way to look at things, but logically compelling. Parallel worlds are as real as the distant galaxies detected by the Hubble Space Telescope, even though the evidence for their existence may consist only of a few photons.

    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.

    - This is the best kind of popular science: informed, impassioned, and highly accessible.- Compare it to Stephen Hawking's The Universe in a Nutshell, but broader in scope and much more readable.- A crossover for the Young Adult market, now in the perfect format.

    Professor Resnick presents a fundamental and unified development of the subject with unusually clear discussions of the aspects that usually trouble beginners. He includes, for example, a section on the common sense of relativity. His presentation is lively and interspersed with historical, philosophical and special topics (such as the twin paradox) that will arouse and hold the reader's interest. You'll find many unique features that help you grasp the material, such as worked-out examples, summary tables, thought questions and a wealth of excellent problems. The emphasis throughout the book is physical. The experimental background, experimental confirmation of predictions, and the physical interpretation of principles are stressed. The book treats relativistic kinematics, relativistic dynamics, and relativity and electromagnetism and contains special appendices on the geometric representation of space-time and on general relativity. Its organization permits an instructor to vary the length and depth of his treatment and to use the book either with or following classical physics. These features make it an ideal companion for introductory course

    This book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. Includes exercises. 1976 edition.

    Seemingly random events -- the flapping of a flag, a storm-driven wave striking the shore, a pinball's path -- often appear to have no order, no rational pattern. Explicating the theory of chaos and the consequences of its principal findings -- that actual, precise rules may govern such apparently random behavior -- has been a major part of the work of Edward N. Lorenz. In The Essence of Chaos, Lorenz presents to the general reader the features of this "new science," with its far-reaching implications for much of modern life, from weather prediction to philosophy, and he describes its considerable impact on emerging scientific fields.Unlike the phenomena dealt with in relativity theory and quantum mechanics, systems that are now described as "chaotic" can be observed without telescopes or microscopes. They range from the simplest happenings, such as the falling of a leaf, to the most complex processes, like the fluctuations of climate. Each process that qualifies, however, has certain quantifiable characteristics: how it unfolds depends very sensitively upon its present state, so that, even though it is not random, it seems to be. Lorenz uses examples from everyday life, and simple calculations, to show how the essential nature of chaotic systems can be understood. In order to expedite this task, he has constructed a mathematical model of a board sliding down a ski slope as his primary illustrative example. With this model as his base, he explains various chaotic phenomena, including some associated concepts such as strange attractors and bifurcations.As a meteorologist, Lorenz initially became interested in the field of chaos because of its implications for weather forecasting. In a chapter ranging through the history of weather prediction and meteorology to a brief picture of our current understanding of climate, he introduces many of the researchers who conceived the experiments and theories, and he describes his own initial encounter with chaos.A further discussion invites readers to make their own chaos. Still others debate the nature of randomness and its relationship to chaotic systems, and describe three related fields of scientific thought: nonlinearity, complexity, and fractality. Appendixes present the first publication of Lorenz's seminal paper "Does the Flap of a Butterfly's Wing in Brazil Set Off a Tornado in Texas?"; the mathematical equations from which the copious illustrations were derived; and a glossary.

    AI is also behind self-driving cars, predictive policing, and autonomous weapons that can kill without human intervention. These and other AI applications raise complex ethical issues that are the subject of ongoing debate. This volume in the MIT Press Essential Knowledge series offers an accessible synthesis of these issues. Written by a philosopher of technology, AI Ethics goes beyond the usual hype and nightmare scenarios to address concrete questions.Mark Coeckelbergh describes influential AI narratives, ranging from Frankenstein's monster to transhumanism and the technological singularity. He surveys relevant philosophical discussions: questions about the fundamental differences between humans and machines and debates over the moral status of AI. He explains the technology of AI, describing different approaches and focusing on machine learning and data science. He offers an overview of important ethical issues, including privacy concerns, responsibility and the delegation of decision making, transparency, and bias as it arises at all stages of data science processes. He also considers the future of work in an AI economy. Finally, he analyzes a range of policy proposals and discusses challenges for policymakers. He argues for ethical practices that embed values in design, translate democratic values into practices and include a vision of the good life and the good society.

    This change is being driven by powerful new cognitive tools, enabled by the internet, which are greatly accelerating scientific discovery. There are many books about how the internet is changing business or the workplace or government. But this is the first book about something much more fundamental: how the internet is transforming the nature of our collective intelligence and how we understand the world.Reinventing Discovery tells the exciting story of an unprecedented new era of networked science. We learn, for example, how mathematicians in the Polymath Project are spontaneously coming together to collaborate online, tackling and rapidly demolishing previously unsolved problems. We learn how 250,000 amateur astronomers are working together in a project called Galaxy Zoo to understand the large-scale structure of the Universe, and how they are making astonishing discoveries, including an entirely new kind of galaxy. These efforts are just a small part of the larger story told in this book--the story of how scientists are using the internet to dramatically expand our problem-solving ability and increase our combined brainpower.This is a book for anyone who wants to understand how the online world is revolutionizing scientific discovery today--and why the revolution is just beginning.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    40 illustrations throughout.

    Richard Rorty, a Princeton professor who had contributed to the analytic tradition in philosophy, was now attempting to shrug off all the central problems with which it had long been preoccupied. After publication, the Press was barely able to keep up with demand, and the book has since gone on to become one of its all-time best-sellers in philosophy. Rorty argued that, beginning in the seventeenth century, philosophers developed an unhealthy obsession with the notion of representation. They compared the mind to a mirror that reflects reality. In their view, knowledge is concerned with the accuracy of these reflections, and the strategy employed to obtain this knowledge--that of inspecting, repairing, and polishing the mirror--belongs to philosophy. Rorty's book was a powerful critique of this imagery and the tradition of thought that it spawned. He argued that the questions about truth posed by Descartes, Kant, Hegel, and modern epistemologists and philosophers of language simply couldn't be answered and were, in any case, irrelevant to serious social and cultural inquiry. This stance provoked a barrage of criticism, but whatever the strengths of Rorty's specific claims, the book had a therapeutic effect on philosophy. It reenergized pragmatism as an intellectual force, steered philosophy back to its roots in the humanities, and helped to make alternatives to analytic philosophy a serious choice for young graduate students. Twenty-five years later, the book remains a must-read for anyone seriously concerned about the nature of philosophical inquiry and what philosophers can and cannot do to help us understand and improve the world.

    Knuth, whose massive contributions to computing have led others to nickname him "The Father of Computer Science"—and whose religious faith led him to understand a fascinating analysis of the Bible called the 3:16 project. In this series of six spirited, informal lectures, Knuth explores the relationships between his vocation and his faith, revealing the unique perspective that his work with computing has lent to his understanding of God.His starting point is the 3:16 project, an application of mathematical "random sampling" to the books of the Bible. The first lectures tell the story of the project's conception and execution, exploring its many dimensions of language translation, aesthetics, and theological history. Along the way, Knuth explains the many insights he gained from such interdisciplinary work. These theological musings culminate in a surprising final lecture tackling the ideas of infinity, free will, and some of the other big questions that lie at the juncture of theology and computation.Things a Computer Scientist Rarely Talks About, with its charming and user-friendly format—each lecture ends with a question and answer exchange, and the book itself contains more than 100 illustrations—is a readable and intriguing approach to a crucial topic, certain to edify both those who are serious and curious about their faiths and those who look at the science of computation and wonder what it might teach them about their spiritual world.Includes "Creativity, Spirituality, and Computer Science," a panel discussion featuring Harry Lewis, Guy L. Steele, Jr., Manuela Veloso, Donald E. Knuth, and Mitch Kapor.

    In Higher Superstition scientists Paul Gross and Norman Levitt raise serious questions about the growing criticism of science by humanists and social scientists on the "academic left." This paperback edition of Higher Superstition includes a new afterword by the authors.

    Sometimes our best efforts can result in the opposite of what we want over time. How can we avoid these unwanted results? If we apply conventional thinking to complex issues, we often maintain or increase the very problems we want to fix. There is, however, a solution to get the desired results. Think in Systems is a concise information manual offering high-level problem-solving methods for personal and global issues. The book presents the main features of systems thinking in an understandable and everyday manner, helping you to develop this skill top analysts and world leaders use. If you thought that complex thinking is only for people who deal with complex issues like running a company or country, think again. Every issue is complex. Running out of gas is a simple problem, but I’m sure you’re dealing with much greater headaches on a daily basis. Your life is a system. Everything that is connected to your system (life) is a part of it. However, you are just a subsystem in the larger picture. Your town, country, the world, the solar system are all bigger systems you are a part of. These systems are interconnected. Whatever you do will affect the system and whatever the system does will affect your life. Systems can have positive and negative effect on your life – or on the life of people generally. The greatest problems like hunger, war, and poverty are all failures in the system. Similarly, fights with your loved ones, being stuck in a rut at your job are also system failures. They are not only your fault. Thus they can’t be fixed with a simple cause-effect thinking. Learn to use systems thinking in your business, relationships, friendships, and general political, socio-economic, and environmental issues. Systems thinking boosts your critical thinking skills, makes you more logical, enhances your analytical abilities, and makes you more creative. Systems thinking won’t put extra pressure on your cognition. Quite the contrary, you’ll have fewer headaches knowing that you surely didn’t miss any detail when you tried to solve a problem. "We cannot solve our problems with the same thinking we used when we created them." Albert Einstein • Learn the main aspects, concepts, and models of systems thinking. • Design models and systems maps to solve your problems • Find solutions to your underlying problems, not just the symptoms • Improve your mental health, wealth, and relationships Systems thinking is a relatively new discipline which doesn’t get the exposure it deserves. However, our world grows more connected, interdependent and complex with each passing day. Becoming a systems thinker will help you to overcome your confusion and fear of missing the whole picture, and help you find more effective solutions to your personal (and if you are up to it), global problems. •Widen your understanding of international economic, political, and socio-economic affairs •Manage your business better •The most helpful materials, books, and experts to learn even more about systems thinking Identify your problems more accurately. Find solutions to your problems, don’t just treat the symptoms.