Admittedly real life wasn’t like that. But only, they argued, because we didn’t have enough data to be certain.Then the cracks began to appear. It proved impossible to predict exactly how three planets orbiting each other would move. Meteorologists discovered that the weather was truly chaotic – so dependent on small variations that it could never be predicted for more than a few days out. And the final nail in the coffin was quantum theory, showing that everything in the universe has probability at its heart.That gives human beings a problem. We understand the world through patterns. Randomness and probability will always be alien to us. But it’s time to plunge into this fascinating, shadowy world, because randomness crops up everywhere. Probability and statistics are the only way to get a grip on nature’s workings. They may even seal the fate of free will and predict how the universe will end.Forget Newton’s clockwork universe. Welcome to Dice World.

    He solidified his standing as the nation's foremost political forecaster with his near perfect prediction of the 2012 election. Silver is the founder and editor in chief of FiveThirtyEight.com. Drawing on his own groundbreaking work, Silver examines the world of prediction, investigating how we can distinguish a true signal from a universe of noisy data. Most predictions fail, often at great cost to society, because most of us have a poor understanding of probability and uncertainty. Both experts and laypeople mistake more confident predictions for more accurate ones. But overconfidence is often the reason for failure. If our appreciation of uncertainty improves, our predictions can get better too. This is the "prediction paradox": The more humility we have about our ability to make predictions, the more successful we can be in planning for the future.In keeping with his own aim to seek truth from data, Silver visits the most successful forecasters in a range of areas, from hurricanes to baseball, from the poker table to the stock market, from Capitol Hill to the NBA. He explains and evaluates how these forecasters think and what bonds they share. What lies behind their success? Are they good-or just lucky? What patterns have they unraveled? And are their forecasts really right? He explores unanticipated commonalities and exposes unexpected juxtapositions. And sometimes, it is not so much how good a prediction is in an absolute sense that matters but how good it is relative to the competition. In other cases, prediction is still a very rudimentary-and dangerous-science.Silver observes that the most accurate forecasters tend to have a superior command of probability, and they tend to be both humble and hardworking. They distinguish the predictable from the unpredictable, and they notice a thousand little details that lead them closer to the truth. Because of their appreciation of probability, they can distinguish the signal from the noise.

    For two decades, John Mighton has developed strategies for fostering intellectual potential in all children through learning math. Math, Mighton says, provides us with mental tools of incredible power. When we learn math we learn to see patterns, to think logically and systematically, to draw analogies, to perceive risk, to understand cause and effect--among many other critical skills. Yet we tolerate and in fact expect a vast performance gap in math among students, and live in a world where many adults aren't equipped with these crucial tools. This learning gap is unnecessary, dangerous and tragic, he cautions, and it has led us to a problem of intellectual poverty which is apparent everywhere--in fake news, political turmoil, floundering economies, even in erroneous medical diagnoses. In All Things Being Equal, Mighton argues that math study is an ideal starting point to break down social inequality and empower individuals to build a smarter, kinder, more equitable world. Bringing together the latest cognitive research and incremental learning strategies, Mighton goes deep into the classroom and beyond to offer a hopeful--and urgent--vision for a numerate society.

    Suitable for a two semester course in complex analysis, or as a supplementary text for an advanced course in function theory, this book aims to give students a good foundation of complex analysis and provides a basis for solving problems in mathematics, physics, engineering and many other sciences.

    A meld of history and science, this book is a group portrait of some of the greatest minds who ever lived as they wrestled with nature’s most sweeping mysteries. The answers they uncovered still hold the key to how we understand the world.At the end of the seventeenth century—an age of religious wars, plague, and the Great Fire of London—when most people saw the world as falling apart, these earliest scientists saw a world of perfect order. They declared that, chaotic as it looked, the universe was in fact as intricate and perfectly regulated as a clock. This was the tail end of Shakespeare’s century, when the natural land the supernatural still twined around each other. Disease was a punishment ordained by God, astronomy had not yet broken free from astrology, and the sky was filled with omens. It was a time when little was known and everything was new. These brilliant, ambitious, curious men believed in angels, alchemy, and the devil, and they also believed that the universe followed precise, mathematical laws—-a contradiction that tormented them and changed the course of history.The Clockwork Universe is the fascinating and compelling story of the bewildered geniuses of the Royal Society, the men who made the modern world.

    Sousa discusses the cognitive mechanisms for learning mathematics and the environmental and developmental factors that contribute to mathematics difficulties. This award-winning text examines:Children's innate number sense and how the brain develops an understanding of number relationships Rationales for modifying lessons to meet the developmental learning stages of young children, preadolescents, and adolescents How to plan lessons in PreK-12 mathematics Implications of current research for planning mathematics lessons, including discoveries about memory systems and lesson timing Methods to help elementary and secondary school teachers detect mathematics difficulties Clear connections to the NCTM standards and curriculum focal points

    But behind it all, there is an even more fundamental driver: Food.In Animal, Vegetable, Junk, trusted food authority Mark Bittman offers a panoramic view of how the frenzy for food has driven human history to some of its most catastrophic moments, from slavery and colonialism to famine and genocide—and to our current moment, wherein Big Food exacerbates climate change, plunders our planet, and sickens its people. Even still, Bittman refuses to concede that the battle is lost, pointing to activists, workers, and governments around the world who are choosing well-being over corporate greed and gluttony, and fighting to free society from Big Food’s grip.Sweeping, impassioned, and ultimately full of hope, Animal, Vegetable, Junk reveals not only how food has shaped our past, but also how we can transform it to reclaim our future.

    When he died in London in 1727 he was so renowned he was given a state funeral—an unheard-of honor for a subject whose achievements were in the realm of the intellect. During the years he was an irascible presence at Trinity College, Cambridge, Newton imagined properties of nature and gave them names—mass, gravity, velocity—things our science now takes for granted. Inspired by Aristotle, spurred on by Galileo’s discoveries and the philosophy of Descartes, Newton grasped the intangible and dared to take its measure, a leap of the mind unparalleled in his generation.James Gleick, the author of Chaos and Genius, and one of the most acclaimed science writers of his generation, brings the reader into Newton’s reclusive life and provides startlingly clear explanations of the concepts that changed forever our perception of bodies, rest, and motion. Ideas so basic to the twenty-first century we literally take them for granted.

    From the Difference Engine to magic squares and from the Fibonacci rabbits to Fermat's Last Theorem, this book features the weird world of numbers, imaginary, real or infinite.

    We often overlook the historical link between mathematics and technological advances, says Stewart—but this connection is integral to any complete understanding of human history.Equations are modeled on the patterns we find in the world around us, says Stewart, and it is through equations that we are able to make sense of, and in turn influence, our world. Stewart locates the origins of each equation he presents—from Pythagoras's Theorem to Newton's Law of Gravity to Einstein's Theory of Relativity—within a particular historical moment, elucidating the development of mathematical and philosophical thought necessary for each equation's discovery. None of these equations emerged in a vacuum, Stewart shows; each drew, in some way, on past equations and the thinking of the day. In turn, all of these equations paved the way for major developments in mathematics, science, philosophy, and technology. Without logarithms (invented in the early 17th century by John Napier and improved by Henry Briggs), scientists would not have been able to calculate the movement of the planets, and mathematicians would not have been able to develop fractal geometry. The Wave Equation is one of the most important equations in physics, and is crucial for engineers studying the vibrations in vehicles and the response of buildings to earthquakes. And the equation at the heart of Information Theory, devised by Claude Shannon, is the basis of digital communication today.An approachable and informative guide to the equations upon which nearly every aspect of scientific and mathematical understanding depends, In Pursuit of the Unknown is also a reminder that equations have profoundly influenced our thinking and continue to make possible many of the advances that we take for granted.

    But what we eat affects more than our bodies; it also affects our brains. And recent studies have shown that diet can have a profound impact on mental health conditions ranging from ADHD to depression, anxiety, sleep disorders, OCD, dementia and beyond.A triple threat in the food space, Dr. Uma Naidoo is a board-certified psychiatrist, nutrition specialist, and professionally trained chef. In This Is Your Brain on Food, she draws on cutting-edge research to explain the many ways in which food contributes to our mental health, and shows how a sound diet can help treat and prevent a wide range of psychological and cognitive health issues.Packed with fascinating science, actionable nutritional recommendations, and delicious, brain-healthy recipes, This Is Your Brain on Food is the go-to guide to optimizing your mental health with food.

    Based on a National Magazine Award-winning article, this masterful biography of Hungarian-born Paul Erdos is both a vivid portrait of an eccentric genius and a layman's guide to some of this century's most startling mathematical discoveries.

    This book upends the conventional approach to math, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. What awaits readers is a freewheeling tour of the inimitable joys and unsolved mysteries of this curiously powerful subject.Like the classic math allegory Flatland, first published over a century ago, or Douglas Hofstadter's Godel, Escher, Bach forty years ago, there has never been a math book quite like Math Without Numbers. So many popularizations of math have dwelt on numbers like pi or zero or infinity. This book goes well beyond to questions such as: How many shapes are there? Is anything bigger than infinity? And is math even true? Milo Beckman shows why math is mostly just pattern recognition and how it keeps on surprising us with unexpected, useful connections to the real world.The ambitions of this book take a special kind of author. An inventive, original thinker pursuing his calling with jubilant passion. A prodigy. Milo Beckman completed the graduate-level course sequence in mathematics at age sixteen, when he was a sophomore at Harvard; while writing this book, he was studying the philosophical foundations of physics at Columbia under Brian Greene, among others.

    Eat Wheat is a scientific and clinically-proven approach to addressing food intolerances. After 3.4 million years of eating wheat and only 500,000 years of hunting meat, humans are actually genetically better equipped to eat wheat than meat. This book is your guide to safely bringing wheat and dairy back into your diet. Dr. John Douillard, a former NBA nutrition expert and creator of LifeSpa.com, and author of 6 health books, addresses the underlying cause of the gluten-free epidemic. Eat Wheat explains how a breakdown in digestion has damaged the intestinal wall and leaked undigested foods and environmental toxins into the body’s lymphatic system, causing “grain brain” symptoms and food allergies. Although eliminating wheat and dairy from your diet may help your symptoms, it is a a temporary solution. Eat Wheat addresses the root cause: the inability to digest well and break down harmful pollutants and toxins that can lead to more serious health concerns. Backed by more than 600 scientific studies, Eat Wheat is a revolutionary guidebook to regaining your digestive strength. Eat Wheat will: Reveal hidden science on the benefits of wheat and dairy Help you navigate around food toxins in modern wheat and dairy Retrain your body to digest wheat and dairy again Flush congested lymphatics linked to food intolerance symptoms Teach you to follow natural digestive circadian cycles Help bring your blood sugar back into balance Teach you proven exercise and detox techniques to re-boot strong digestion and achieve optimal health and vitality

    This accessible and easy-to-follow guide examines the health risks posed by typical Western eating habits and explains how a diet rich in vegetables, fruits, whole grains, legumes, mushrooms, nuts, seeds, herbs and spices can lead to lower blood pressure, healthy weight management, and longer life.Their flexible, customizable approach to eating challenges the conventional idea of breakfast, lunch, and dinner and focuses instead on soups, salads, sides, and sweets. With 100 delicious recipes to choose from, The Healthspan Solution make adopting a plant-based lifestyle simple and sustainable.- Evidence-based research on the scientific underpinnings of the healthspan diet - Easy-to-follow guidelines simplify food choices without being restrictive - Beautifully photographed recipes offer options and flexibility Praise for The Healthspan Solution "Ray and Julieanna didn't write a fad diet book. It's about making a permanent lifestyle transformation. The magic is I still can eat anything I want. The trick is what I want has profoundly changed. They did the trick for me and saved my life--now let them help you."--Penn Jillette, Las Vegas entertainer and magician"Ray is a scientific visionary and Julieanna is a master of nutrition. Together they've written a fact-based recipe book for longevity that belongs in every kitchen. Buy it."--David Sinclair, PhD, AO, Professor of Genetics, Harvard Medical School"Working with Julieanna and Ray has given me a profoundly new understanding of how food impacts health and how what we eat is often dictated by social influences. I'm excited to be a part of their effort to push to this message out to a far bigger audience."--Cyan Banister, angel investor and entrepreneur"Julieanna and Ray are an incredible team. While others have sought to demonstrate the adequacy of an exclusively plant-sourced diet, they teach how it can be superior and mimics longevity research."--Rich Roll, plant-powered ultra athlete and author