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

    Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life. In A Mind for Numbers, Dr. Oakley lets us in on the secrets to effectively learning math and science—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn math. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. A Mind for Numbers shows us that we all have what it takes to excel in math, and learning it is not as painful as some might think!

    With the sophisticated algorithms in this book, you can write smart programs to access interesting datasets from other web sites, collect data from users of your own applications, and analyze and understand the data once you've found it.Programming Collective Intelligence takes you into the world of machine learning and statistics, and explains how to draw conclusions about user experience, marketing, personal tastes, and human behavior in general -- all from information that you and others collect every day. Each algorithm is described clearly and concisely with code that can immediately be used on your web site, blog, Wiki, or specialized application. This book explains:Collaborative filtering techniques that enable online retailers to recommend products or media Methods of clustering to detect groups of similar items in a large dataset Search engine features -- crawlers, indexers, query engines, and the PageRank algorithm Optimization algorithms that search millions of possible solutions to a problem and choose the best one Bayesian filtering, used in spam filters for classifying documents based on word types and other features Using decision trees not only to make predictions, but to model the way decisions are made Predicting numerical values rather than classifications to build price models Support vector machines to match people in online dating sites Non-negative matrix factorization to find the independent features in a dataset Evolving intelligence for problem solving -- how a computer develops its skill by improving its own code the more it plays a game Each chapter includes exercises for extending the algorithms to make them more powerful. Go beyond simple database-backed applications and put the wealth of Internet data to work for you. "Bravo! I cannot think of a better way for a developer to first learn these algorithms and methods, nor can I think of a better way for me (an old AI dog) to reinvigorate my knowledge of the details."-- Dan Russell, Google "Toby's book does a great job of breaking down the complex subject matter of machine-learning algorithms into practical, easy-to-understand examples that can be directly applied to analysis of social interaction across the Web today. If I had this book two years ago, it would have saved precious time going down some fruitless paths."-- Tim Wolters, CTO, Collective Intellect

    So why do we know so little about how to get them right?Big, life-altering decisions matter so much more than the decisions we make every day, and they're also the most difficult: where to live, whom to marry, what to believe, whether to start a company, how to end a war. There's no one-size-fits-all approach for addressing these kinds of conundrums. Steven Johnson's classic Where Good Ideas Come From inspired creative people all over the world with new ways of thinking about innovation. In Farsighted, he uncovers powerful tools for honing the important skill of complex decision-making. While you can't model a once-in-a-lifetime choice, you can model the deliberative tactics of expert decision-makers. These experts aren't just the master strategists running major companies or negotiating high-level diplomacy. They're the novelists who draw out the complexity of their characters' inner lives, the city officials who secure long-term water supplies, and the scientists who reckon with future challenges most of us haven't even imagined. The smartest decision-makers don't go with their guts. Their success relies on having a future-oriented approach and the ability to consider all their options in a creative, productive way. Through compelling stories that reveal surprising insights, Johnson explains how we can most effectively approach the choices that can chart the course of a life, an organization, or a civilization. Farsighted will help you imagine your possible futures and appreciate the subtle intelligence of the choices that shaped our broader social history.

    But what is it physically? And where is it really? Our mental map of the network is as blank as the map of the ocean that Columbus carried on his first Atlantic voyage. The Internet, its material nuts and bolts, is an unexplored territory. Until now.In Tubes, journalist Andrew Blum goes inside the Internet's physical infrastructure and flips on the lights, revealing an utterly fresh look at the online world we think we know. It is a shockingly tactile realm of unmarked compounds, populated by a special caste of engineer who pieces together our networks by hand; where glass fibers pulse with light and creaky telegraph buildings, tortuously rewired, become communication hubs once again. From the room in Los Angeles where the Internet first flickered to life to the caverns beneath Manhattan where new fiber-optic cable is buried; from the coast of Portugal, where a ten-thousand-mile undersea cable just two thumbs wide connects Europe and Africa, to the wilds of the Pacific Northwest, where Google, Microsoft, and Facebook have built monumental data centers—Blum chronicles the dramatic story of the Internet's development, explains how it all works, and takes the first-ever in-depth look inside its hidden monuments.This is a book about real places on the map: their sounds and smells, their storied pasts, their physical details, and the people who live there. For all the talk of the "placelessness" of our digital age, the Internet is as fixed in real, physical spaces as the railroad or telephone. You can map it and touch it, and you can visit it. Is the Internet in fact "a series of tubes" as Ted Stevens, the late senator from Alaska, once famously described it? How can we know the Internet's possibilities if we don't know its parts?Like Tracy Kidder's classic The Soul of a New Machine or Tom Vanderbilt's recent bestseller Traffic, Tubes combines on-the-ground reporting and lucid explanation into an engaging, mind-bending narrative to help us understand the physical world that underlies our digital lives.

    Reveals how to run an online business profitably in spite of the Internet's inherently free culture, disseminating the principles of a ''priceless economy'' in six categories that pertain to advertising, labor exchange, and advanced-version fees.

    Today's researchers are continuing to confirm the remarkable, life-giving properties of true extra-virgin, and "extra-virgin Italian" has become the highest standard of quality.But what if this symbol of purity has become deeply corrupt? Starting with an explosive article in The New Yorker, Tom Mueller has become the world's expert on olive oil and olive oil fraud-a story of globalization, deception, and crime in the food industry from ancient times to the present, and a powerful indictment of today's lax protections against fake and even toxic food products in the United States. A rich and deliciously readable narrative, Extra Virginity is also an inspiring account of the artisanal producers, chemical analysts, chefs, and food activists who are defending the extraordinary oils that truly deserve the name "extra-virgin."

    It's a "Brotopia," where men hold all the cards and make all the rules. Vastly outnumbered, women face toxic workplaces rife with discrimination and sexual harassment, where investors take meetings in hot tubs and network at sex parties.In this powerful exposé, Bloomberg TV journalist Emily Chang reveals how Silicon Valley got so sexist despite its utopian ideals, why bro culture endures despite decades of companies claiming the moral high ground (Don't Be Evil! Connect the World!)--and how women are finally starting to speak out and fight back.Drawing on her deep network of Silicon Valley insiders, Chang opens the boardroom doors of male-dominated venture capital firms like Kleiner Perkins, the subject of Ellen Pao's high-profile gender discrimination lawsuit, and Sequoia, where a partner once famously said they "won't lower their standards" just to hire women. Interviews with Facebook COO Sheryl Sandberg, YouTube CEO Susan Wojcicki, and former Yahoo! CEO Marissa Mayer--who got their start at Google, where just one in five engineers is a woman--reveal just how hard it is to crack the Silicon Ceiling. And Chang shows how women such as former Uber engineer Susan Fowler, entrepreneur Niniane Wang, and game developer Brianna Wu, have risked their careers and sometimes their lives to pave a way for other women.Silicon Valley's aggressive, misogynistic, work-at-all costs culture has shut women out of the greatest wealth creation in the history of the world. It's time to break up the boys' club. Emily Chang shows us how to fix this toxic culture--to bring down Brotopia, once and for all.

    Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor.

    In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

    An impassioned critique of K 12 mathematics education, it outlined how we shortchange students by introducing them to math the wrong way. Here Lockhart offers the positive side of the math education story by showing us how math should be done. "Measurement "offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living.In conversational prose that conveys his passion for the subject, Lockhart makes mathematics accessible without oversimplifying. He makes no more attempt to hide the challenge of mathematics than he does to shield us from its beautiful intensity. Favoring plain English and pictures over jargon and formulas, he succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable. His elegant discussion of mathematical reasoning and themes in classical geometry offers proof of his conviction that mathematics illuminates art as much as science.Lockhart leads us into a universe where beautiful designs and patterns float through our minds and do surprising, miraculous things. As we turn our thoughts to symmetry, circles, cylinders, and cones, we begin to see that almost anyone can do the math in a way that brings emotional and aesthetic rewards. "Measurement" is an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work."

    These topics lie at the heart of many exciting areas of contemporary science and engineering - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics, and cryptography. This textbook introduces theory in tandem with applications. Information theory is taught alongside practical communication systems, such as arithmetic coding for data compression and sparse-graph codes for error-correction. A toolbox of inference techniques, including message-passing algorithms, Monte Carlo methods, and variational approximations, are developed alongside applications of these tools to clustering, convolutional codes, independent component analysis, and neural networks. The final part of the book describes the state of the art in error-correcting codes, including low-density parity-check codes, turbo codes, and digital fountain codes -- the twenty-first century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, David MacKay's groundbreaking book is ideal for self-learning and for undergraduate or graduate courses. Interludes on crosswords, evolution, and sex provide entertainment along the way. In sum, this is a textbook on information, communication, and coding for a new generation of students, and an unparalleled entry point into these subjects for professionals in areas as diverse as computational biology, financial engineering, and machine learning.

    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.

    It is so important that it provides the fundamental underpinning of all modern sciences. Without it, we'd have no nuclear power or nuclear bombs, no lasers, no TV, no computers, no science of molecular biology, no understanding of DNA, no genetic engineering—at all. John Gribbin tells the complete story of quantum mechanics, a truth far stranger than any fiction. He takes us step-by-step into an ever more bizarre and fascinating place—requiring only that we approach it with an open mind. He introduces the scientists who developed quantum theory. He investigates the atom, radiation, time travel, the birth of the universe, superconductors and life itself. And in a world full of its own delights, mysteries and surprises, he searches for Schrödinger's Cat—a search for quantum reality—as he brings every reader to a clear understanding of the most important area of scientific study today—quantum physics.

    In the four main sections of the book, Stein tells the stories of the mathematical thinkers who discerned some of the most fundamental aspects of our universe. From their successes and failures, delusions, and even duels, the trajectories of their innovations—and their impact on society—are traced in this fascinating narrative. Quantum mechanics, space-time, chaos theory and the workings of complex systems, and the impossibility of a "perfect" democracy are all here. Stein's book is both mind-bending and practical, as he explains the best way for a salesman to plan a trip, examines why any thought you could have is imbedded in the number π , and—perhaps most importantly—answers one of the modern world's toughest questions: why the garage can never get your car repaired on time.Friendly, entertaining, and fun, How Math Explains the World is the first book by one of California's most popular math teachers, a veteran of both "math for poets" and Princeton's Institute for Advanced Studies. And it's perfect for any reader wanting to know how math makes both science and the world tick.