The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    Greene, who recently launched World Science U, which offers free online science courses, explains what it is that's so "elegant" about string theory while lamenting the possible limits of what dogs (and by implication humans) can ever hope to understand about the universe. The interview was conducted by Rivka Galchen, an acclaimed fiction writer and journalist, named by The New Yorker as one of 20 Writers Under 40. Cover design by Adil Dara Kim.

    He was one of the leading pioneers of the greatest revolution in twentieth-century science: quantum mechanics. The youngest theoretician ever to win the Nobel Prize for Physics, he was also pathologically reticent, strangely literal-minded and legendarily unable to communicate or empathize. Through his greatest period of productivity, his postcards home contained only remarks about the weather.Based on a previously undiscovered archive of family papers, Graham Farmelo celebrates Dirac's massive scientific achievement while drawing a compassionate portrait of his life and work. Farmelo shows a man who, while hopelessly socially inept, could manage to love and sustain close friendship.The Strangest Man is an extraordinary and moving human story, as well as a study of one of the most exciting times in scientific history.'A wonderful book . . . Moving, sometimes comic, sometimes infinitely sad, and goes to the roots of what we mean by truth in science.' Lord Waldegrave, Daily Telegraph

    Our Big Bang, our distant future, parallel worlds, the sub-atomic and intergalactic - none of them are what they seem. But there is a way to understand this immense strangeness - mathematics. Seeking an answer to the fundamental puzzle of why our universe seems so mathematical, Tegmark proposes a radical idea: that our physical world not only is described by mathematics, but that it is mathematics. This may offer answers to our deepest questions: How large is reality? What is everything made of? Why is our universe the way it is?Table of ContentsPreface 1 What Is Reality? Not What It Seems • What’s the Ultimate Question? • The Journey Begins Part One: Zooming Out 2 Our Place in Space Cosmic Questions • How Big Is Space? • The Size of Earth • Distance to the Moon • Distance to the Sun and the Planets • Distance to the Stars • Distance to the Galaxies • What Is Space? 3 Our Place in TimeWhere Did Our Solar System Come From? • Where Did theGalaxies Come From? • Where Did the Mysterious MicrowavesCome From? • Where Did the Atoms Come From? 4 Our Universe by NumbersWanted: Precision Cosmology • Precision Microwave-Background Fluctuations • Precision Galaxy Clustering • The Ultimate Map of Our Universe • Where Did Our Big Bang Come From? 5 Our Cosmic Origins What’s Wrong with Our Big Bang? • How Inflation Works • The Gift That Keeps on Giving • Eternal Inflation 6 Welcome to the Multiverse The Level I Multiverse • The Level II Multiverse • Multiverse Halftime Roundup Part Two: Zooming In 7 Cosmic Legos Atomic Legos • Nuclear Legos • Particle-Physics Legos • Mathematical Legos • Photon Legos • Above the Law? • Quanta and Rainbows • Making Waves • Quantum Weirdness • The Collapse of Consensus • The Weirdness Can’t Be Confined • Quantum Confusion 8 The Level III Multiverse The Level III Multiverse • The Illusion of Randomness • Quantum Censorship • The Joys of Getting Scooped • Why Your Brain Isn’t a Quantum Computer • Subject, Object and Environment • Quantum Suicide • Quantum Immortality? • Multiverses Unified • Shifting Views: Many Worlds or Many Words? Part Three: Stepping Back 9 Internal Reality, External Reality and Consensus Reality External Reality and Internal Reality • The Truth, the Whole Truth and Nothing but the Truth • Consensus Reality • Physics: Linking External to Consensus Reality 10 Physical Reality and Mathematical Reality Math, Math Everywhere! • The Mathematical Universe Hypothesis • What Is a Mathematical Structure? 11 Is Time an Illusion? How Can Physical Reality Be Mathematical? • What Are You? • Where Are You? (And What Do You Perceive?) • When Are You? 12 The Level IV Multiverse Why I Believe in the Level IV Multiverse • Exploring the Level IV Multiverse: What’s Out There? • Implications of the Level IV Multiverse • Are We Living in a Simulation? • Relation Between the MUH, the Level IV Multiverse and Other Hypotheses •Testing the Level IV Multiverse 13 Life, Our Universe and Everything How Big Is Our Physical Reality? • The Future of Physics • The Future of Our Universe—How Will It End? • The Future of Life •The Future of You—Are You Insignificant? Acknowledgments Suggestions for Further Reading Index

    With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot. Holt offers a painless and playful introduction to many of our most beautiful but least understood ideas, from Einsteinian relativity to string theory, and also invites us to consider why the greatest logician of the twentieth century believed the U.S. Constitution contained a terrible contradiction--and whether the universe truly has a future.

    There, at its center, the fusion of 620 million tons of hydrogen every second generates an unfathomable amount of energy. By replicating even a tiny piece of the Sun’s power on Earth, we can secure all the heat and energy we would ever need.Nuclear fusion scientists have pursued this simple yet extraordinary ambition for decades. Skeptics say it will never work but, as A Piece of the Sun makes clear, large-scale nuclear fusion is scientifically possible—and has many advantages over other options. Fusion is clean, green and virtually limitless and Clery argues passionately and eloquently that the only thing keeping us from proving its worth is our politicians’ shortsightedness. The world energy industry is worth trillions of dollars, divert just a tiny fraction of that into researching fusion and we would soon know if it is workable.Timely and authoritative, A Piece of the Sun is a rousing call-to-arms to seize this chance of avoiding the looming energy crisis.

    It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.

    Conflict between humans and machines is seen as inevitable and its outcome all too predictable.In this groundbreaking book, distinguished AI researcher Stuart Russell argues that this scenario can be avoided, but only if we rethink AI from the ground up. Russell begins by exploring the idea of intelligence in humans and in machines. He describes the near-term benefits we can expect, from intelligent personal assistants to vastly accelerated scientific research, and outlines the AI breakthroughs that still have to happen before we reach superhuman AI. He also spells out the ways humans are already finding to misuse AI, from lethal autonomous weapons to viral sabotage.If the predicted breakthroughs occur and superhuman AI emerges, we will have created entities far more powerful than ourselves. How can we ensure they never, ever, have power over us? Russell suggests that we can rebuild AI on a new foundation, according to which machines are designed to be inherently uncertain about the human preferences they are required to satisfy. Such machines would be humble, altruistic, and committed to pursue our objectives, not theirs. This new foundation would allow us to create machines that are provably deferential and provably beneficial.In a 2014 editorial co-authored with Stephen Hawking, Russell wrote, "Success in creating AI would be the biggest event in human history. Unfortunately, it might also be the last." Solving the problem of control over AI is not just possible; it is the key that unlocks a future of unlimited promise.

    Thus began one of the boldest scientific projects in history, the Search for Extraterrestrial Intelligence (SETI). But after a half century of scanning the skies, astronomers have little to report but an eerie silence—eerie because many scientists are convinced that the universe is teeming with life. The problem, argues the leading physicist-astrobiologist Paul Davies, is that we’ve been looking in the wrong place, at the wrong time & in the wrong way. Davies should know. For more than three decades, he's been closely involved with SETI & now chairs its Post-Detection Taskgroup, charged with deciding what to do if we’re confronted with evidence of alien intelligence. In this extraordinary book, he shows how SETI has lost its edge & offers a new exciting road map for the future. Davies believes our search so far has been overly anthropocentric: we tend to assume an alien species will look, think & behave like us. He argues that we need to be far more expansive in our efforts, & in this book he completely redefines the search, challenging existing ideas of what form an alien intelligence might take, how it might try to communicate with us & how we should respond if it does. A provocative & mind-expanding journey, The Eerie Silence will thrill fans of science & science fiction alike.

    To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok.In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years—at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information (Alan Turing's role in breaking Germany's Enigma code during World War II), and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security.Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.

    Astronomy 101 cuts out the boring details and lengthy explanations, and instead, gives you a lesson in astronomy that keeps you engaged as you discover what's hidden beyond our starry sky. From the Big Bang and nebulae to the Milky Way and Sir Isaac Newton, this celestial primer is packed with hundreds of entertaining astronomy facts, charts, and photographs you won't be able to get anywhere else. So whether you’re looking to unravel the mystery behind black holes, or just want to learn more about your favorite planets, Astronomy 101 has all the answers—even the ones you didn’t know you were looking for.

    Explaining why the whole is sometimes smarter than the sum of its parts, Johnson presents surprising examples of feedback, self-organization, and adaptive learning. How does a lively neighborhood evolve out of a disconnected group of shopkeepers, bartenders, and real estate developers? How does a media event take on a life of its own? How will new software programs create an intelligent World Wide Web? In the coming years, the power of self-organization -- coupled with the connective technology of the Internet -- will usher in a revolution every bit as significant as the introduction of electricity. Provocative and engaging, Emergence puts you on the front lines of this exciting upheaval in science and thought.

    The book also provides a balanced presentation of time-varying and static fields, preparingstudents for employment in today's industrial and manufacturing sectors. Streamlined to facilitate student understanding, this edition features worked examples in every chapter that explain how to use the theory presented in the text to solve different kinds of problems. Numerical methods, including MATLAB and vector analysis, are also included to help students analyzesituations that they are likely to encounter in industry practice. Elements of Electromagnetics, Fifth Edition, is designed for introductory undergraduate courses in electromagnetics.

    Everything. Yet, in recent years discoveries in physics and cosmology have led a number of scientists to conclude that our universe may be one among many. With crystal-clear prose and inspired use of analogy, Brian Greene shows how a range of different “multiverse” proposals emerges from theories developed to explain the most refined observations of both subatomic particles and the dark depths of space: a multiverse in which you have an infinite number of doppelgängers, each reading this sentence in a distant universe; a multiverse comprising a vast ocean of bubble universes, of which ours is but one; a multiverse that endlessly cycles through time, or one that might be hovering millimeters away yet remains invisible; another in which every possibility allowed by quantum physics is brought to life. Or, perhaps strangest of all, a multiverse made purely of math.Greene, one of our foremost physicists and science writers, takes us on a captivating exploration of these parallel worlds and reveals how much of reality’s true nature may be deeply hidden within them. And, with his unrivaled ability to make the most challenging of material accessible and entertaining, Greene tackles the core question: How can fundamental science progress if great swaths of reality lie beyond our reach?Sparked by Greene’s trademark wit and precision, The Hidden Reality is at once a far-reaching survey of cutting-edge physics and a remarkable journey to the very edge of reality—a journey grounded firmly in science and limited only by our imagination.

    It is a book for those who were part of Apollo and want to recapture the experience and for those of a new generation who want to know how it was done. It is an opinion shared by many Apollo veterans. Republished in 2004 with a new Foreword by the authors.