Essentially, you make an initial guess, and then get more data to improve it. Bayes Theorem, or Bayes Rule, has a ton of real world applications, from estimating your risk of a heart attack to making recommendations on Netflix But It Isn't That Complicated This book is a short introduction to Bayes Theorem. It is only 15 pages long, and is intended to show you how Bayes Theorem works as quickly as possible. The examples are intentionally kept simple to focus solely on Bayes Theorem without requiring that the reader know complicated probability distributions. If you want to learn the basics of Bayes Theorem as quickly as possible, with some easy to duplicate examples, this is a good book for you.

    What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.This sixtieth anniversary edition includes not only the original text but also an introduction by Harold Kuhn, an afterword by Ariel Rubinstein, and reviews and articles on the book that appeared at the time of its original publication in the New York Times, tthe American Economic Review, and a variety of other publications. Together, these writings provide readers a matchless opportunity to more fully appreciate a work whose influence will yet resound for generations to come.

    In The Master Algorithm, Pedro Domingos lifts the veil to give us a peek inside the learning machines that power Google, Amazon, and your smartphone. He assembles a blueprint for the future universal learner--the Master Algorithm--and discusses what it will mean for business, science, and society. If data-ism is today's philosophy, this book is its bible.

    At a summer tea party in Cambridge, England, a guest states that tea poured into milk tastes different from milk poured into tea. Her notion is shouted down by the scientific minds of the group. But one man, Ronald Fisher, proposes to scientifically test the hypothesis. There is no better person to conduct such an experiment, for Fisher is a pioneer in the field of statistics.The Lady Tasting Tea spotlights not only Fisher's theories but also the revolutionary ideas of dozens of men and women which affect our modern everyday lives. Writing with verve and wit, David Salsburg traces breakthroughs ranging from the rise and fall of Karl Pearson's theories to the methods of quality control that rebuilt postwar Japan's economy, including a pivotal early study on the capacity of a small beer cask at the Guinness brewing factory. Brimming with intriguing tidbits and colorful characters, The Lady Tasting Tea salutes the spirit of those who dared to look at the world in a new way.

    In this lively and groundbreaking new book, economist Ian Ayres shows how today's best and brightest organizations are analyzing massive databases at lightening speed to provide greater insights into human behavior. They are the Super Crunchers. From internet sites like Google and Amazon that know your tastes better than you do, to a physician's diagnosis and your child's education, to boardrooms and government agencies, this new breed of decision makers are calling the shots. And they are delivering staggeringly accurate results. How can a football coach evaluate a player without ever seeing him play? Want to know whether the price of an airline ticket will go up or down before you buy? How can a formula outpredict wine experts in determining the best vintages? Super crunchers have the answers. In this brave new world of equation versus expertise, Ayres shows us the benefits and risks, who loses and who wins, and how super crunching can be used to help, not manipulate us.Gone are the days of solely relying on intuition to make decisions. No businessperson, consumer, or student who wants to stay ahead of the curve should make another keystroke without reading Super Crunchers.

    Illustrating his points with examples, and supporting them with the latest research findings, he documents the cognitive, social, and motivational processes that distort our thoughts, beliefs, judgments and decisions. In a rapidly changing world, the biases and stereotypes that help us process an overload of complex information inevitably distort what we would like to believe is reality. Awareness of our propensity to make these systematic errors, Gilovich argues, is the first step to more effective analysis and action.

    do it? How should you flip your mattress to get the maximum wear out of it? How does Google search the Internet? How many people should you date before settling down? Believe it or not, math plays a crucial role in answering all of these questions and more.Math underpins everything in the cosmos, including us, yet too few of us understand this universal language well enough to revel in its wisdom, its beauty — and its joy. This deeply enlightening, vastly entertaining volume translates math in a way that is at once intelligible and thrilling. Each trenchant chapter of The Joy of x offers an “aha!” moment, starting with why numbers are so helpful, and progressing through the wondrous truths implicit in π, the Pythagorean theorem, irrational numbers, fat tails, even the rigors and surprising charms of calculus. Showing why he has won awards as a professor at Cornell and garnered extensive praise for his articles about math for the New York Times, Strogatz presumes of his readers only curiosity and common sense. And he rewards them with clear, ingenious, and often funny explanations of the most vital and exciting principles of his discipline.Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight in The Joy of x.

    Many of our wisest policy-makers, activists, scientists, and philosophers agree that the only problem with empathy is that we don’t have enough of it.Nothing could be farther from the truth, argues Yale researcher Paul Bloom. In AGAINST EMPATHY, Bloom reveals empathy to be one of the leading motivators of inequality and immorality in society. Far from helping us to improve the lives of others, empathy is a capricious and irrational emotion that appeals to our narrow prejudices. It muddles our judgment and, ironically, often leads to cruelty. We are at our best when we are smart enough not to rely on it, but to draw instead upon a more distanced compassion.Basing his argument on groundbreaking scientific findings, Bloom makes the case that some of the worst decisions made by individuals and nations—who to give money to, when to go to war, how to respond to climate change, and who to imprison—are too often motivated by honest, yet misplaced, emotions. With precision and wit, he demonstrates how empathy distorts our judgment in every aspect of our lives, from philanthropy and charity to the justice system; from medical care and education to parenting and marriage. Without empathy, Bloom insists, our decisions would be clearer, fairer, and—yes—ultimately more moral.Brilliantly argued, urgent and humane, AGAINST EMPATHY shows us that, when it comes to both major policy decisions and the choices we make in our everyday lives, limiting our impulse toward empathy is often the most compassionate choice we can make.

    Why don't facts work? Why, that is, did the obviously intelligent man beside him sincerely believe in Adam and Eve, the Garden of Eden and a six-thousand-year-old Earth, in spite of the evidence against them? It was the start of a journey that would lead Storr all over the world--from Texas to Warsaw to the Outer Hebrides--meeting an extraordinary cast of modern heretics whom he tries his best to understand. He goes on a tour of Holocaust sites with David Irving and a band of neo-Nazis; experiences his own murder during past-life regression hypnosis; discusses the looming One World Government with iconic climate skeptic Lord Monckton; and investigates the tragic life and death of a woman who believed her parents were high priests in a baby-eating cult. Using a unique mix of highly personal memoir, investigative journalism, and the latest research from neuroscience and experimental psychology, Storr reveals how the stories we tell ourselves about the world invisibly shape our beliefs, and how the neurological "hero maker" inside us all can so easily lead to self-deception, toxic partisanship, and science denial.

    Over years of groundbreaking experiments, he has distilled remarkable discoveries significant enough to become the bedrock of a whole new scientific field: social physics. Humans have more in common with bees than we like to admit: We’re social creatures first and foremost. Our most important habits of action—and most basic notions of common sense—are wired into us through our coordination in social groups. Social physics is about idea flow, the way human social networks spread ideas and transform those ideas into behaviors. Thanks to the millions of digital bread crumbs people leave behind via smartphones, GPS devices, and the Internet, the amount of new information we have about human activity is truly profound. Until now, sociologists have depended on limited data sets and surveys that tell us how people say they think and behave, rather than what they actually do. As a result, we’ve been stuck with the same stale social structures—classes, markets—and a focus on individual actors, data snapshots, and steady states. Pentland shows that, in fact, humans respond much more powerfully to social incentives that involve rewarding others and strengthening the ties that bind than incentives that involve only their own economic self-interest. Pentland and his teams have found that they can study patterns of information exchange in a social network without any knowledge of the actual content of the information and predict with stunning accuracy how productive and effective that network is, whether it’s a business or an entire city. We can maximize a group’s collective intelligence to improve performance and use social incentives to create new organizations and guide them through disruptive change in a way that maximizes the good. At every level of interaction, from small groups to large cities, social networks can be tuned to increase exploration and engagement, thus vastly improving idea flow.  Social Physics will change the way we think about how we learn and how our social groups work—and can be made to work better, at every level of society. Pentland leads readers to the edge of the most important revolution in the study of social behavior in a generation, an entirely new way to look at life itself.

    Most of the time this math works quietly behind the scenes . . . until it doesn't. All sorts of seemingly innocuous mathematical mistakes can have significant consequences.Math is easy to ignore until a misplaced decimal point upends the stock market, a unit conversion error causes a plane to crash, or someone divides by zero and stalls a battleship in the middle of the ocean.Exploring and explaining a litany of glitches, near misses, and mathematical mishaps involving the internet, big data, elections, street signs, lotteries, the Roman Empire, and an Olympic team, Matt Parker uncovers the bizarre ways math trips us up, and what this reveals about its essential place in our world. Getting it wrong has never been more fun.

      Statistics are everywhere, as integral to science as they are to business, and in the popular media hundreds of times a day. In this age of big data, a basic grasp of statistical literacy is more important than ever if we want to separate the fact from the fiction, the ostentatious embellishments from the raw evidence -- and even more so if we hope to participate in the future, rather than being simple bystanders. In The Art of Statistics, world-renowned statistician David Spiegelhalter shows readers how to derive knowledge from raw data by focusing on the concepts and connections behind the math. Drawing on real world examples to introduce complex issues, he shows us how statistics can help us determine the luckiest passenger on the Titanic, whether a notorious serial killer could have been caught earlier, and if screening for ovarian cancer is beneficial. The Art of Statistics not only shows us how mathematicians have used statistical science to solve these problems -- it teaches us how we too can think like statisticians. We learn how to clarify our questions, assumptions, and expectations when approaching a problem, and -- perhaps even more importantly -- we learn how to responsibly interpret the answers we receive. Combining the incomparable insight of an expert with the playful enthusiasm of an aficionado, The Art of Statistics is the definitive guide to stats that every modern person needs.

    He asked them to disclose something that, for scientific reasons, worries them—particularly scenarios that aren't on the popular radar yet. Encompassing neuroscience, economics, philosophy, physics, psychology, biology, and more—here are 150 ideas that will revolutionize your understanding of the world.Steven Pinker uncovers the real risk factors for war * Mihaly Csikszentmihalyi peers into the coming virtual abyss * Nobel laureate Frank Wilczek laments our squandered opportunities to prevent global catastrophe * Seth Lloyd calculates the threat of a financial black hole * Alison Gopnik on the loss of childhood * Nassim Nicholas Taleb explains why firefighters understand risk far better than economic "experts" * Matt Ridley on the alarming re-emergence of superstition * Daniel C. Dennett and george dyson ponder the impact of a major breakdown of the Internet * Jennifer Jacquet fears human-induced damage to the planet due to "the Anthropocebo Effect" * Douglas Rushkoff fears humanity is losing its soul * Nicholas Carr on the "patience deficit" * Tim O'Reilly foresees a coming new Dark Age * Scott Atran on the homogenization of human experience * Sherry Turkle explores what's lost when kids are constantly connected * Kevin Kelly outlines the looming "underpopulation bomb" * Helen Fisher on the fate of men * Lawrence Krauss dreads what we don't know about the universe * Susan Blackmore on the loss of manual skills * Kate Jeffery on the death of death * plus J. Craig Venter, Daniel Goleman, Virginia Heffernan, Sam Harris, Brian Eno, Martin Rees, and more

    But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place."Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct--including the revelation that ants can actually count how many steps they've taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games.Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize. Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. "Here's Looking at Euclid "is a rare gem that brings the beauty of math to life.

    How have we achieved so much despite understanding so little? Cognitive scientists Steven Sloman and Philip Fernbach argue that we survive and thrive despite our mental shortcomings because we live in a rich community of knowledge. The key to our intelligence lies in the people and things around us. We're constantly drawing on information and expertise stored outside our heads: in our bodies, our environment, our possessions, and the community with which we interact--and usually we don't even realize we're doing it. The human mind is both brilliant and pathetic. We have mastered fire, created democratic institutions, stood on the moon, and sequenced our genome. And yet each of us is error prone, sometimes irrational, and often ignorant. The fundamentally communal nature of intelligence and knowledge explains why we often assume we know more than we really do, why political opinions and false beliefs are so hard to change, and why individually oriented approaches to education and management frequently fail. But our collaborative minds also enable us to do amazing things. This book contends that true genius can be found in the ways we create intelligence using the world around us.