Hand argues that extraordinarily rare events are anything but. In fact, they’re commonplace. Not only that, we should all expect to experience a miracle roughly once every month.     But Hand is no believer in superstitions, prophecies, or the paranormal. His definition of “miracle” is thoroughly rational. No mystical or supernatural explanation is necessary to understand why someone is lucky enough to win the lottery twice, or is destined to be hit by lightning three times and still survive. All we need, Hand argues, is a firm grounding in a powerful set of laws: the laws of inevitability, of truly large numbers, of selection, of the probability lever, and of near enough.     Together, these constitute Hand’s groundbreaking Improbability Principle. And together, they explain why we should not be so surprised to bump into a friend in a foreign country, or to come across the same unfamiliar word four times in one day. Hand wrestles with seemingly less explicable questions as well: what the Bible and Shakespeare have in common, why financial crashes are par for the course, and why lightning does strike the same place (and the same person) twice. Along the way, he teaches us how to use the Improbability Principle in our own lives—including how to cash in at a casino and how to recognize when a medicine is truly effective.     An irresistible adventure into the laws behind “chance” moments and a trusty guide for understanding the world and universe we live in, The Improbability Principle will transform how you think about serendipity and luck, whether it’s in the world of business and finance or you’re merely sitting in your backyard, tossing a ball into the air and wondering where it will land.

    One simply could not put a numerical value on the likelihood that a particular event would occur. Even the outcome of something as simple as a dice roll or the likelihood of showers instead of sunshine was thought to lie in the realm of pure, unknowable chance.The issue remained intractable until Blaise Pascal wrote to Pierre de Fermat in 1654, outlining a solution to the “unfinished game” problem: how do you divide the pot when players are forced to end a game of dice before someone has won? The idea turned out to be far more seminal than Pascal realized. From it, the two men developed the method known today as probability theory.In The Unfinished Game, mathematician and NPR commentator Keith Devlin tells the story of this correspondence and its remarkable impact on the modern world: from insurance rates, to housing and job markets, to the safety of cars and planes, calculating probabilities allowed people, for the first time, to think rationally about how future events might unfold.

    Many of these students are extremely intelligent and hardworking, but even the best will, at some point, struggle with the demands of making the transition to advanced mathematics. Some have difficulty adjusting to independent study and to learning from lectures. Other struggles, however, are more fundamental: the mathematics shifts in focus from calculation to proof, so students are expected to interact with it in different ways. These changes need not be mysterious - mathematics education research has revealed many insights into the adjustments that are necessary - but they are not obvious and they do need explaining.This no-nonsense book translates these research-based insights into practical advice for a student audience. It covers every aspect of studying for a mathematics degree, from the most abstract intellectual challenges to the everyday business of interacting with lecturers and making good use of study time. Part 1 provides an in-depth discussion of advanced mathematical thinking, and explains how a student will need to adapt and extend their existing skills in order to develop a good understanding of undergraduate mathematics. Part 2 covers study skills as these relate to the demands of a mathematics degree. It suggests practical approaches to learning from lectures and to studying for examinations while also allowing time for a fulfilling all-round university experience.The first subject-specific guide for students, this friendly, practical text will be essential reading for anyone studying mathematics at university.

    Bronowski was both a distinguished mathematician and a poet, a philosopher of science and a literary critic who wrote a well-known study of William Blake. Dr. Bronowski's very career was founded on the premise of an intimate connection between science and the humanities, disciplines which are still generally thought to be worlds apart.The Common Sense of Science, a book which remains as topical today as it was when it first appeared twenty-five years ago, articulates and develops Bronowski's provocative idea that the sciences and the arts fundamentally share the same imaginative vision.

    Mythologized and misunderstood, lauded and loathed, a girl from the suburbs who became a proud symbol of cosmopolitanism, Sontag left a legacy of writing on art and politics, feminism and homosexuality, celebrity and style, medicine and drugs, radicalism and Fascism and Freudianism and Communism and Americanism, that forms an indispensable key to modern culture. She was there when the Cuban Revolution began, and when the Berlin Wall came down; in Vietnam under American bombardment, in wartime Israel, in besieged Sarajevo. She was in New York when artists tried to resist the tug of money—and when many gave in. No writer negotiated as many worlds; no serious writer had as many glamorous lovers. Sontag tells these stories and examines the work upon which her reputation was based. It explores the agonizing insecurity behind the formidable public face: the broken relationships, the struggles with her sexuality, that animated—and undermined—her writing. And it shows her attempts to respond to the cruelties and absurdities of a country that had lost its way, and her conviction that fidelity to high culture was an activism of its own. Utilizing hundreds of interviews conducted from Maui to Stockholm and from London to Sarajevo—and featuring nearly one hundred images—Sontag is the first book based on the writer’s restricted archives, and on access to many people who have never before spoken about Sontag, including Annie Leibovitz. It is a definitive portrait—a great American novel in the form of a biography.

    An enduring cultural icon, she came to symbolize a new kind of woman, one who successfully combined marriage & motherhood with a career & scholarship with a singular concern for its role in the lives of ordinary people. Even today, when memoirs of successful women scientists & scholars remain scarce, Blackberry Winter, 1st published in '72, provides a rare glimpse of a pioneering woman's formative journey. In her chapters "On Being a Granddaughter" & "The Pattern My Family Made Me," Mead examines the wisdom she gained from her maternal grandmother as well as the inheritance she recieved from her ancestors, & how her upbringing fueled her desire for a fulfilling career that would reflect her own emerging values. We are treated to captivating portraits of bohemian life in NYC in the '20s; her early days at the American Museum of Natural History, where she met her longtime mentor, Franz Boas, & friend, Ruth Benedict; & 1st field trip to study adolescent girls in Samoa. Near the book's end, in "On Being a Grandmother," she reflects on the legacy she leaves her descendants, indeed, all of humanity. This autobiography, reissued for a new generation of readers, will appeal to any eager to discover a woman of our century who made her way in a world seldom hospitable to the dreams & accomplishments of women.

    Gerard 't Hooft was closely involved in many of the advances in modern theoretical physics that led to improved understanding of elementary particles, and this is a first-hand account of one of the most creative and exciting periods of discovery in the history of physics. Using language a layperson can understand, this narrative touches on many central topics and ideas, such as quarks and quantum physics; supergravity, superstrings and superconductivity; the Standard Model and grand unification; eleven-dimensional space time and black holes. This fascinating personal account of the past thirty years in one of the most dramatic areas in twentieth-century physics will be of interest to professional physicists and physics students, as well as the educated general reader with an interest in one of the most exciting scientific detective stories ever.

    Widely praised for providing a lucid and historically informed account of Wittgenstein's core philosophical concerns.Demonstrates the continuity between Wittgenstein's early and later writings.Provides a persuasive argument for the unity of Wittgenstein's thought.Kenny also assesses Wittgenstein's influence in the latter part of the twentieth century.Inside:PrefaceAbbreviations in References to Works by WittgensteinBiographical Sketch of Wittgenstein's PhilosophyThe Legacy of Frege & RussellThe Criticism of PrincipiaThe Picture Theory of the PropositionThe Metaphysics of Logical AtomismThe Dismantling of Logical AtomismAnticipation, Intentionality & VerificationUnderstanding, Thinking & MeaningLanguage-GamesPrivate LanguagesOn Scepticism & CertaintyThe Continuity of Wittgenstein's PhilosophySuggestions for Further ReadingIndex

    A stirring collection of never-before-seen photographs of the Kennedy family presented in this seminal work by JFK's personal photographer, Jacques Lowe.

    Although his writings on philosophical aesthetics have shown him to be a leading authority in the field, his defence of political conservatism has marked him out in academic circles as public enemy number one. Whether it is Scruton's opinions that get up the nose of his critics, or the wit and erudition with which he expresses them, there is no doubt that their noses are vastly distended by his presence, and constantly on the verge of a collective sneeze. Contrary to orthodox opinion, however, Roger Scruton is a human being, and Gentle Regrets contains the proof of it - a quiet, witty but also serious and moving account of the ways in which life brought him to think what he thinks, and to be what he is. His moving vignettes of his childhood and later influences illuminate this book. Love him or hate him, he will engage you in an argument that is both intellectually stimulating and informed by humour.

    It resurrects from the vaults of neglect the polymath Jerome Cardano, a Milanese of the sixteenth century. Who is he? A gambler and blasphemer, inventor and chancer, plagued by demons and anxieties, astrologer to kings, emperors and popes. This stubborn and unworldly man was the son of a lawyer and a brothel keeper, but also a gifted physician and the unacknowledged discoverer of the mathematical foundations of quantum physics. That is the argument of this charming and intoxicatingly clever book, which is truly original in its style, and in the manner of the modernists embodies in its very form its theories about the world.'The Quantum Astrologer’s Handbook' is a science book with the panache of a novel, for readers of Carlo Rovelli or Umberto Eco. It is a work of and about genius.

    Grayling extends the range of his previous two books to show how much understanding people can gain about themselves and their world by reflecting on the lessons offered by science, the arts (including literature) and history. Covering subjects as diverse as Jane Austen's EMMA, the Rosetta Stone, Shakespeare, the Holocaust, quantum physics, Galileo, and even alien abductions, A..C. Grayling's latest collection is a rich source for reflection and contemplation over the mysteries of life.

    Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

    As we enter the year 2000, zero is once again making its presence felt. Nothing itself, it makes possible a myriad of calculations. Indeed, without zero mathematicsas we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean? Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story, taking us back to Sumerian times, and then to Greece and India, piecing together the way the idea of a symbol for nothing evolved. Kaplan shows us just how handicapped our ancestors were in trying to figurelarge sums without the aid of the zero. (Try multiplying CLXIV by XXIV). Remarkably, even the Greeks, mathematically brilliant as they were, didn't have a zero--or did they? We follow the trail to the East where, a millennium or two ago, Indian mathematicians took another crucial step. By treatingzero for the first time like any other number, instead of a unique symbol, they allowed huge new leaps forward in computation, and also in our understanding of how mathematics itself works. In the Middle Ages, this mathematical knowledge swept across western Europe via Arab traders. At first it was called dangerous Saracen magic and considered the Devil's work, but it wasn't long before merchants and bankers saw how handy this magic was, and used it to develop tools likedouble-entry bookkeeping. Zero quickly became an essential part of increasingly sophisticated equations, and with the invention of calculus, one could say it was a linchpin of the scientific revolution. And now even deeper layers of this thing that is nothing are coming to light: our computers speakonly in zeros and ones, and modern mathematics shows that zero alone can be made to generate everything.Robert Kaplan serves up all this history with immense zest and humor; his writing is full of anecdotes and asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far beyond the scope of scientific specialists. For Kaplan, the history of zero is a lens for looking notonly into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. Thebeauty of mathematics is that even though we invent it, we seem to be discovering something that already exists.The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture. A tour de force of science history, The Nothing That Is takes us through the hollow circle that leads to infinity.

    This long out-of-paint autobiography provides insight into the genesis of Bunuel's films and conveys his frank opinions on dwarves, Catholicism, the Marquis de Sade, food, and smoking, not to mention his recipe for a good dry martini!