But there is one other motive which is as strong as any of these — the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen. Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.

    Amazingly, he completed the task in an intense six weeks, and Eine kurze Weltgeschichte für junge Leser was published in Vienna to immediate success, and is now available in seventeen languages across the world. Toward the end of his long life, Gombrich embarked upon a revision and, at last, an English translation. A Little History of the World presents his lively and involving history to English-language readers for the first time. Superbly designed and freshly illustrated, this is a book to be savored and collected. In forty concise chapters, Gombrich tells the story of man from the stone age to the atomic bomb. In between emerges a colorful picture of wars and conquests, grand works of art, and the spread and limitations of science. This is a text dominated not by dates and facts, but by the sweep of mankind's experience across the centuries, a guide to humanity's achievements and an acute witness to its frailties. The product of a generous and humane sensibility, this timeless account makes intelligible the full span of human history.

    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

    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

    James Cleaves II seek to answer the most crucial question in science: How did life begin? They trace the trials and triumphs of the iconoclastic scientists who have sought to solve the mystery, from Darwin’s theory of evolution to Crick and Watson’s unveiling of DNA. This fascinating exploration not only examines the origin-of-life question, but also interrogates the very nature of scientific discovery and objectivity.

    In this narrative, Walter Isaacson explains how his mind worked and the mysteries of the universe that he discovered.

    Life remains the only way to make life. Are we still missing a vital ingredient in its creation?      Like Richard Dawkins' The Selfish Gene, which provided a new perspective on how evolution works, Life on the Edge alters our understanding of our world's fundamental dynamics. Bringing together first-hand experience at the cutting edge of science with unparalleled gifts of explanation, Jim Al-Khalili and Johnjoe Macfadden reveal that missing ingredient to be quantum mechanics; the phenomena that lie at the heart of this most mysterious of sciences. Drawing on recent ground-breaking experiments around the world, each chapter in Life on the Edge engages by illustrating one of life's puzzles: How do migrating birds know where to go? How do we really smell the scent of a rose? How do our genes copy themselves with such precision? Life on the Edge accessibly reveals how quantum mechanics can answer these probing questions of the universe. Guiding the reader through the rapidly unfolding discoveries of the last few years, Al-Khalili and McFadden communicate the excitement of the explosive new field of quantum biology and its potentially revolutionary applications, while offering insights into the biggest puzzle of all: what is life? As they brilliantly demonstrate in these groundbreaking pages, life exists on the quantum edge.

    But gravitational waves – ripples in the fabric of space and time – are unrelenting, passing through barriers that stop light dead.At the two 4-kilometre long LIGO observatories in the US, scientists developed incredibly sensitive detectors, capable of spotting a movement 100 times smaller than the nucleus of an atom. In 2015 they spotted the ripples produced by two black holes spiralling into each other, setting spacetime quivering.This was the first time black holes had ever been directly detected – and it promises far more for the future of astronomy. Brian Clegg presents a compelling story of human technical endeavour and a new, powerful path to understand the workings of the universe.Brian Clegg’s most recent books are The Reality Frame (Icon, 2017), What Colour is the Sun? (Icon, 2016) and Ten Billion Tomorrows (St Martin’s Press, 2016). His Dice World and A Brief History of Infinity were both longlisted for the Royal Society Prize for Science Books. He has also written Big Data for the Hot Science series. Brian has written for numerous publications including The Wall Street Journal, Nature, BBC Focus, Physics World, The Times and The Observer. Brian is editor of popularscience.co.uk and blogs at brianclegg.blogspot.com.

    It’ll have you scratching your head wondering why we even bother to go to school.Think Magellan was the first man to circumnavigate the globe, baseball was invented in America, Henry VIII had six wives, Mount Everest is the tallest mountain? Wrong, wrong, wrong, and wrong again. You’ll be surprised at how much you don’t know! Check out THE BOOK OF GENERAL IGNORANCE for more fun entries and complete answers to the following:How long can a chicken live without its head?About two years.What do chameleons do?They don’t change color to match the background. Never have; never will. Complete myth. Utter fabrication. Total Lie. They change color as a result of different emotional states.How many legs does a centipede have?Not a hundred.How many toes has a two-toed sloth?It’s either six or eight.Who was the first American president?Peyton Randolph.What were George Washington’s false teeth made from?Mostly hippopotamus.What was James Bond’s favorite drink?Not the vodka martini.

    It far surpasses any previous explanation of Relativity for laypersons.

    The prolonged encounter between the Cro-Magnons and the archaic Neanderthals and between 45,000 and 30,000 years ago was one of the defining moments of history. The Neanderthals survived for some 15,000 years in the face of the newcomers, but were finally pushed aside by the Cro-Magnons' vastly superior intellectual abilities and cutting-edge technologies, which allowed them to thrive in the intensely challenging climate of the Ice Age.What do we know about this remarkable takeover? Who were the first modern Europeans and what were they like? How did they manage to thrive in such an extreme environment? And what legacy did they leave behind them after the cold millennia? The age of the Cro-Magnons lasted some 30,000 years?longer than all of recorded history. Cro-Magnon is the story of a little known, yet seminal, chapter of human experience.

    Massive in its scope, and yet totally accessible, A HISTORY OF KNOWLEDGE covers not only all the great theories and discoveries of the human race, but also explores the social conditions, political climates, and individual men and women of genius that brought ideas to fruition throughout history."Crystal clear and concise...Explains how humankind got to know what it knows."Clifton FadimanSelected by the Book-of-the-Month Club and the History Book Club

    Two of the three-Nicolaus Copernicus and Charles Darwin-are widely known and heralded for their breakthroughs. The third, James Hutton, never received the same recognition, yet he profoundly changed our understanding of the earth and its dynamic forces. Hutton proved that the earth was likely millions of years old rather than the biblically determined six thousand, and that it was continuously being shaped and re-shaped by myriad everyday forces rather than one cataclysmic event. In this expertly crafted narrative, Jack Repcheck tells the remarkable story of this Scottish gentleman farmer and how his simple observations on his small tract of land led him to a theory that was in direct confrontation with the Bible and that also provided the scientific proof that would spark Darwin's theory of evolution. It is also the story of Scotland and the Scottish Enlightenment, which brought together some of the greatest thinkers of the age, from David Hume and Adam Smith to James Watt and Erasmus Darwin. Finally, it is a story about the power of the written word. Repcheck argues that Hutton's work was lost to history because he could not describe his findings in graceful and readable prose. (Unlike Darwin's Origin of the Species, Hutton's one and only book was impenetrable.) A marvelous narrative about a little-known man and the science he founded, The Man Who Found Time is also a parable about the power of books to shape the history of ideas.

    Johnson takes us to those times when the world seemed filled with mysterious forces, when scientists were dazzled by light, by electricity, and by the beating of the hearts they laid bare on the dissecting table. We see Galileo singing to mark time as he measures the pull of gravity, and Newton carefully inserting a needle behind his eye to learn how light causes vibrations in the retina. William Harvey ties a tourniquet around his arm and watches his arteries throb above and his veins bulge below, proving that blood circulates. Luigi Galvani sparks electrical currents in dissected frog legs, wondering at the twitching muscle fibers, and Ivan Pavlov makes his now-famous dogs salivate at ascending chord progressions.For all of them, diligence was rewarded. In an instant, confusion was swept aside and something new about nature leaped into view. In bringing us these stories, Johnson restores some of the romance to science, reminding us of the existential excitement of a single soul staring down the unknown.

    We may know a bit about Napoleon or Joan of Arc or Louis XIV, but for most of us that's about it. In my own three schools we were taught only about the battles we won: Crécy and Poitiers, Agincourt and Waterloo. The rest was silence. So here is my attempt to fill in the blanks... John Julius Norwich (at 88) has finally written the book he always wanted to write, the extremely colourful story of the country he loves best. From frowning Roman generals and belligerent Gallic chieftains, to Charlemagne (hated by generations of French children taught that he invented schools) through Marie Antoinette and the storming of the Bastille to Vichy, the Resistance and beyond, FRANCE is packed with heroes and villains, adventures and battles, romance and revolution. Full of memorable stories and racy anecdotes, this is the perfect introduction to the country that has inspired the rest of the world to live, dress, eat -- and love better.