Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his little finger told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.

    You experience it passing every day when you watch clocks tick, bread toast, and children grow. But most physicists see things differently, from Newton to Einstein to today’s quantum theorists. For them, time isn’t real. You may think you experience time passing, but they say it’s just an illusion.Lee Smolin, author of the controversial bestseller The Trouble with Physics, argues this limited notion of time is holding physics back. It’s time for a major revolution in scientific thought. The reality of time could be the key to the next big breakthrough in theoretical physics.What if the laws of physics themselves were not timeless? What if they could evolve? Time Reborn offers a radical new approach to cosmology that embraces the reality of time and opens up a whole new universe of possibilties. There are few ideas that, like our notion of time, shape our thinking about literally everything, with major implications for physics and beyond—from climate change to the economic crisis. Smolin explains in lively and lucid prose how the true nature of time impacts our world.

    Now, in What the Dog Saw, he brings together, for the first time, the best of his writing from The New Yorker over the same period. Here you'll find the bittersweet tale of the inventor of the birth control pill, and the dazzling creations of pasta sauce pioneer Howard Moscowitz. Gladwell sits with Ron Popeil, the king of the American kitchen, as he sells rotisserie ovens, and divines the secrets of Cesar Millan, the "dog whisperer" who can calm savage animals with the touch of his hand. He explores intelligence tests and ethnic profiling and why it was that employers in Silicon Valley once tripped over themselves to hire the same college graduate.

    In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy.In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.

    This ideal guide shows us how mathematics can illuminate the human condition.

    The term “complexity” can be misleading, however, because what makes West’s discoveries so beautiful is that he has found an underlying simplicity that unites the seemingly complex and diverse phenomena of living systems, including our bodies, our cities and our businesses. Fascinated by issues of aging and mortality, West applied the rigor of a physicist to the biological question of why we live as long as we do and no longer. The result was astonishing, and changed science, creating a new understanding of energy use and metabolism: West found that despite the riotous diversity in the sizes of mammals, they are all, to a large degree, scaled versions of each other. If you know the size of a mammal, you can use scaling laws to learn everything from how much food it eats per day, what its heart-rate is, how long it will take to mature, its lifespan, and so on. Furthermore, the efficiency of the mammal’s circulatory systems scales up precisely based on weight: if you compare a mouse, a human and an elephant on a logarithmic graph, you find with every doubling of average weight, a species gets 25% more efficient—and lives 25% longer. This speaks to everything from how long we can expect to live to how many hours of sleep we need. Fundamentally, he has proven, the issue has to do with the fractal geometry of the networks that supply energy and remove waste from the organism's body. West's work has been game-changing for biologists, but then he made the even bolder move of exploring his work's applicability to cities. Cities, too, are constellations of networks and laws of scalability relate with eerie precision to them. For every doubling in a city's size, the city needs 15% less road, electrical wire, and gas stations to support the same population. More amazingly, for every doubling in size, cities produce 15% more patents and more wealth, as well as 15% more crime and disease. This broad pattern lays the groundwork for a new science of cities. Recently, West has applied his revolutionary work on cities and biological life to the business world. This investigation has led to powerful insights into why some companies thrive while others fail. The implications of these discoveries are far-reaching, and are just beginning to be explored. Scale is a thrilling scientific adventure story about the elemental natural laws that bind us together in simple but profound ways. Through the brilliant mind of Geoffrey West, we can envision how cities, companies and biological life alike are dancing to the same simple, powerful tune, however diverse and unrelated they are to each other.From the Hardcover edition.

    xn + yn = zn, where n represents 3, 4, 5, ...no solution"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations.  What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years.  In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it.  Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

    Taking as territory everything from the Big Bang to the rise of civilization, Bryson seeks to understand how we got from there being nothing at all to there being us. To that end, he has attached himself to a host of the world’s most advanced (and often obsessed) archaeologists, anthropologists, and mathematicians, travelling to their offices, laboratories, and field camps. He has read (or tried to read) their books, pestered them with questions, apprenticed himself to their powerful minds. A Short History of Nearly Everything is the record of this quest, and it is a sometimes profound, sometimes funny, and always supremely clear and entertaining adventure in the realms of human knowledge, as only Bill Bryson can render it. Science has never been more involving or entertaining.

    Asimov takes the reader on a rousing mental trip into the world of mathematics, physics, chemistry, biology, and astronomy.

    In this little book Welsh writer and artist David Wade paints a picture of one of the most elusive and pervasive concepts known to man.

    Now, two science professors give us the tools to dismantle misinformation and think clearly in a world of fake news and bad data.It's increasingly difficult to know what's true. Misinformation, disinformation, and fake news abound. Our media environment has become hyperpartisan. Science is conducted by press release. Startup culture elevates bullshit to high art. We are fairly well equipped to spot the sort of old-school bullshit that is based in fancy rhetoric and weasel words, but most of us don't feel qualified to challenge the avalanche of new-school bullshit presented in the language of math, science, or statistics. In Calling Bullshit, Professors Carl Bergstrom and Jevin West give us a set of powerful tools to cut through the most intimidating data.You don't need a lot of technical expertise to call out problems with data. Are the numbers or results too good or too dramatic to be true? Is the claim comparing like with like? Is it confirming your personal bias? Drawing on a deep well of expertise in statistics and computational biology, Bergstrom and West exuberantly unpack examples of selection bias and muddled data visualization, distinguish between correlation and causation, and examine the susceptibility of science to modern bullshit.We have always needed people who call bullshit when necessary, whether within a circle of friends, a community of scholars, or the citizenry of a nation. Now that bullshit has evolved, we need to relearn the art of skepticism.

    In Homo Deus, he looked to our future. Now, one of the most innovative thinkers on the planet turns to the present to make sense of today's most pressing issues.How do computers and robots change the meaning of being human? How do we deal with the epidemic of fake news? Are nations and religions still relevant? What should we teach our children?Yuval Noah Harari's 21 Lessons for the 21st Century is a probing and visionary investigation into today's most urgent issues as we move into the uncharted territory of the future. As technology advances faster than our understanding of it, hacking becomes a tactic of war, and the world feels more polarized than ever, Harari addresses the challenge of navigating life in the face of constant and disorienting change and raises the important questions we need to ask ourselves in order to survive.In twenty-one accessible chapters that are both provocative and profound, Harari builds on the ideas explored in his previous books, untangling political, technological, social, and existential issues and offering advice on how to prepare for a very different future from the world we now live in: How can we retain freedom of choice when Big Data is watching us? What will the future workforce look like, and how should we ready ourselves for it? How should we deal with the threat of terrorism? Why is liberal democracy in crisis?Harari's unique ability to make sense of where we have come from and where we are going has captured the imaginations of millions of readers. Here he invites us to consider values, meaning, and personal engagement in a world full of noise and uncertainty. When we are deluged with irrelevant information, clarity is power. Presenting complex contemporary challenges clearly and accessibly, 21 Lessons for the 21st Century is essential reading.

    Exploring issues that range from faith to prayer to evil to immortality, and far beyond, Garnder challenges the discerning reader with fundamental questions of classical philosophy and life's greater meanings.Recalling such philosophers was Wittgenstein and Arendt, The Whys of Philosophical Scrivener embodies Martin Garner's unceasing interest and joy in the impenetrable mysteries of life.

    At the same time adjacent portions of philosophy and logic are discussed. To the existence of what objects may a given scientific theory be said to be committed? And what considerations may suitably guide us in accepting or revising such ontological commitments? These are among the questions dealt with in this book, particular attention being devoted to the role of abstract entities in mathematics. There is speculation on the mechanism whereby objects of one sort or another come to be posited a process in which the notion of identity plays an important part."This volume of essays has a unity and bears throughout the imprint of Quine's powerful and original mind. It is written with the felicity in the choice of words which makes everything that Quine writes a pleasure to read, and which ranks him among the best contemporary writers on abstract subjects." (Cambridge Review)"Professor Quine's challenging and original views are here for the first time presented as a unity. The chief merit of the book is the heart-searching from which it arose and to which it will give rise. In vigour, conciseness, and clarity, it is characteristic of its author." (Oxford Magazine)

    Raymond M. Smullyan — a celebrated mathematician, logician, magician, and author — presents a logical labyrinth of more than 200 increasingly complex problems. The puzzles delve into Gödel’s undecidability theorem and other examples of the deepest paradoxes of logic and set theory. Detailed solutions follow each puzzle.