However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

    We are addicted to prediction, desperate for certainty about the future. But the complexity of modern life won’t provide that; experts in forecasting are reluctant to look more than 400 days out. History doesn’t repeat itself and even genetics won’t tell you everything you want to know. Ineradicable uncertainty is now a fact of life. In complex environments, efficiency is a hazard not a help; being robust is the better, safer option. Drawing on a wide array of people and places, Margaret Heffernan looks at long-term projects developed over generations that could never have been planned the way that they have been run. Experiments, led by individuals and nations, discover new possibilities and options. Radical exercises in forging new futures with wildly diverse participants allow everyone to create outcomes together that none could do alone. Existential crises reveal the vital social component in resilience. Death is certain, but how we approach it impacts the future of those we leave behind. And preparedness – doing everything today that you might need for tomorrow – provides the antidote to passivity and prediction. Ranging freely through history and from business to science, government to friendships, this refreshing book challenges us to resist the false promises of technology and efficiency and instead to mine our own creativity and humanity for the capacity to create the futures we want and can believe in.

    Such systems--whether political parties, stock markets, or ant colonies--present some of the most intriguing theoretical and practical challenges confronting the social sciences. Engagingly written, and balancing technical detail with intuitive explanations, Complex Adaptive Systems focuses on the key tools and ideas that have emerged in the field since the mid-1990s, as well as the techniques needed to investigate such systems. It provides a detailed introduction to concepts such as emergence, self-organized criticality, automata, networks, diversity, adaptation, and feedback. It also demonstrates how complex adaptive systems can be explored using methods ranging from mathematics to computational models of adaptive agents. John Miller and Scott Page show how to combine ideas from economics, political science, biology, physics, and computer science to illuminate topics in organization, adaptation, decentralization, and robustness. They also demonstrate how the usual extremes used in modeling can be fruitfully transcended.

    In the past, discoveries often had to wait for the rise of the next generation to see questions in a new light and let go of old truisms. Today, in a world that is defined by a rapid rate of change, staying on the cutting edge has as much to do with shedding outdated notions as adopting new ones. In this spirit, John Brockman, publisher of the online salon Edge.org ("the world's smartest website"—The Guardian), asked 175 of the world's most influential scientists, economists, artists, and philosophers: What scientific idea is ready for retirement?Jared Diamond explores the diverse ways that new ideas emerge * Nassim Nicholas Taleb takes down the standard deviation * Richard Thaler and novelist Ian McEwan reveal the usefulness of "bad" ideas * Steven Pinker dismantles the working theory of human behavior * Richard Dawkins renounces essentialism * Sherry Turkle reevaluates our expectations of artificial intelligence * Physicist Andrei Linde suggests that our universe and its laws may not be as unique as we think * Martin Rees explains why scientific understanding is a limitless goal * Alan Guth rethinks the origins of the universe * Sam Harris argues that our definition of science is too narrow * Nobel Prize winner Frank Wilczek disputes the division between mind and matter * Lawrence Krauss challenges the notion that the laws of physics were preordained * plus contributions from Daniel Goleman, Mihaly Csikszentmihalyi, Nicholas Carr, Rebecca Newberger Goldstein, Matt Ridley, Stewart Brand, Sean Carroll, Daniel C. Dennett, Helen Fisher, Douglas Rushkoff, Lee Smolin, Kevin Kelly, Freeman Dyson, and others.

    The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

    Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

    Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal. Features include: The use of boxes to strengthen the narrative: pieces that provide historical context, descriptions of how the algorithms are used in practice, and excursions for the mathematically sophisticated.Carefully chosen advanced topics that can be skipped in a standard one-semester course, but can be covered in an advanced algorithms course or in a more leisurely two-semester sequence.An accessible treatment of linear programming introduces students to one of the greatest achievements in algorithms. An optional chapter on the quantum algorithm for factoring provides a unique peephole into this exciting topic. In addition to the text, DasGupta also offers a Solutions Manual, which is available on the Online Learning Center.Algorithms is an outstanding undergraduate text, equally informed by the historical roots and contemporary applications of its subject. Like a captivating novel, it is a joy to read. Tim Roughgarden Stanford University

    Trolling. Conspiracies. Social media pile-ons. Campus intolerance. On the surface, these recent additions to our daily vocabulary appear to have little in common. But together, they are driving an epistemic crisis: a multi-front challenge to America's ability to distinguish fact from fiction and elevate truth above falsehood.In 2016 Russian trolls and bots nearly drowned the truth in a flood of fake news and conspiracy theories, and Donald Trump and his troll armies continued to do the same. Social media companies struggled to keep up with a flood of falsehoods, and too often didn't even seem to try. Experts and some public officials began wondering if society was losing its grip on truth itself. Meanwhile, another new phenomenon appeared: "cancel culture." At the push of a button, those armed with a cellphone could gang up by the thousands on anyone who ran afoul of their sanctimony.In this pathbreaking book, Jonathan Rauch reaches back to the parallel eighteenth-century developments of liberal democracy and science to explain what he calls the "Constitution of Knowledge"--our social system for turning disagreement into truth.By explicating the Constitution of Knowledge and probing the war on reality, Rauch arms defenders of truth with a clearer understanding of what they must protect, why they must do--and how they can do it. His book is a sweeping and readable description of how every American can help defend objective truth and free inquiry from threats as far away as Russia and as close as the cellphone.

    . .he believes these ideas to be accessible to the audience he wantsto reach, and he writes so that they are. -- NatureIf you want to encourage anyone's interest in math, get them TheMathematical Universe. * New Scientist

    Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations--as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal relevance that explores the great variety of applications and importance of symmetry.

    For centuries, the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. Zero follows this number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe and its apotheosis as the mystery of the black hole. Today, zero lies at the heart of one of the biggest scientific controversies of all time, the quest for the theory of everything. Elegant, witty, and enlightening, Zero is a compelling look at the strangest number in the universe and one of the greatest paradoxes of human thought.

    The story of information begins in a time profoundly unlike our own, when every thought and utterance vanishes as soon as it is born. From the invention of scripts and alphabets to the long-misunderstood talking drums of Africa, Gleick tells the story of information technologies that changed the very nature of human consciousness. He provides portraits of the key figures contributing to the inexorable development of our modern understanding of information: Charles Babbage, the idiosyncratic inventor of the first great mechanical computer; Ada Byron, the brilliant and doomed daughter of the poet, who became the first true programmer; pivotal figures like Samuel Morse and Alan Turing; and Claude Shannon, the creator of information theory itself. And then the information age arrives. Citizens of this world become experts willy-nilly: aficionados of bits and bytes. And we sometimes feel we are drowning, swept by a deluge of signs and signals, news and images, blogs and tweets. The Information is the story of how we got here and where we are heading.

    I just wish I had known all of this twelve years ago...'When you speak to the likes of Dylan Wiliam, Doug Lemov, Daisy Christodoulou, Kris Boulton and the Bjorks, you are bound to learn a thing or two. But when he started his Mr Barton Maths Podcast, Craig Barton wasn't expecting to have his whole outlook on teaching and learning turned upside down. How I Wish I'd Taught Maths is the story of an experienced and successful maths teacher's journey into the world of research, and what it looks like in the classroom.Along the way we meet practical, easy-to-implement strategies including Supercharged Worked Examples, Silent Teacher, SSDD problems, low-stakes quizzes, diagnostic questions, Purposeful Practice, self-explanations, harnessing the power of the hypercorrection effect, how to (and how not to) teach problem-solving and much more. No matter your experience, teaching style or favourite number, every maths teacher will find something to think about in this book.

    "Nonsense," says the sensible Bernard Suits: "playing a game is a voluntary attempt to overcome unnecessary obstacles." The short book Suits wrote demonstrating precisely that is as playful as it is insightful, as stimulating as it is delightful. Suits not only argues that games can be meaningfully defined; he also suggests that playing games is a central part of the ideal of human existence, so games belong at the heart of any vision of Utopia. Originally published in 1978, The Grasshopper is now re-issued with a new introduction by Thomas Hurka and with additional material (much of it previously unpublished) by the author, in which he expands on the ideas put forward in The Grasshopper and answers some questions that have been raised by critics.

    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.