But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

    Includes such gems as:? There are 42 eyes in a deck of cards, and 42 dots on a pair of dice ? In order to fill in a map so that neighboring regions never get the same color, one never needs more than four colors ? Hells Angels use the number 81 in their insignia because the initials H and A are the eighth and first numbers in the alphabet respectively

    Escher -- goes to some of the strangest spots imaginable. It takes us to a place where the purely intellectual enters our daily world: where our outraged senses, overloaded with grocery bills, the price of gas, and what to eat for lunch, are expected to absorb really bizarre ideas. And no better guide to this weird universe exists than the brilliant thinker Clifford A. Pickover, the 21st century's answer to Buckminster Fuller. Come along as Pickover traces the origins of the Mobius strip from the mid-1800s, when the visionary scientist Dr. August Mobius became the first to describe the properties of one-sided surfaces, to the present, where it is an integral part of mathematics, magic, science, art, engineering, literature, and music. It has become a metaphor for change, strangeness, looping, and rejuvenation. Touching on everything from molecules and metal sculptures to postage stamps, architectural structures, and models of our entire universe, The Mobius Strip is lavishly illustrated and gives readers a glimpse into other worlds and new ways of thinking as Pickover reaches across cultures and dimensions.

    Through the eyes of a curious scientist, she watched her mind deteriorate whereby she could not walk, talk, read, write, or recall any of her life. Because of her understanding of the brain, her respect for the cells in her body, and an amazing mother, Jill completely recovered. In My Stroke of Insight, she shares her recommendations for recovery and the insight she gained into the unique functions of the two halves of her brain. When she lost the skills of her left brain, her consciousness shifted away from normal reality where she felt "at one with the universe." Taylor helps others not only rebuild their brains from trauma, but helps those of us with normal brains better understand how we can consciously influence the neural circuitry underlying what we think, how we feel and how we react to life's circumstances.

    At nine he started working on an original theory in astrophysics that experts believe may someday put him in line for a Nobel Prize, and at age twelve he became a paid researcher in quantum physics. But the story of Kristine’s journey with Jake is all the more remarkable because his extraordinary mind was almost lost to autism. At age two, when Jake was diagnosed, Kristine was told he might never be able to tie his own shoes. The Spark is a remarkable memoir of mother and son. Surrounded by “experts” at home and in special ed who tried to focus on Jake’s most basic skills and curtail his distracting interests—moving shadows on the wall, stars, plaid patterns on sofa fabric—Jake made no progress, withdrew more and more into his own world, and eventually stopped talking completely. Kristine knew in her heart that she had to make a change. Against the advice of her husband, Michael, and the developmental specialists, Kristine followed her instincts, pulled Jake out of special ed, and began preparing him for mainstream kindergarten on her own. Relying on the insights she developed at the daycare center she runs out of the garage in her home, Kristine resolved to follow Jacob’s “spark”—his passionate interests. Why concentrate on what he couldn’t do? Why not focus on what he could? This basic philosophy, along with her belief in the power of ordinary childhood experiences (softball, picnics, s’mores around the campfire) and the importance of play, helped Kristine overcome huge odds. The Barnetts were not wealthy people, and in addition to financial hardship, Kristine herself faced serious health issues. But through hard work and determination on behalf of Jake and his two younger brothers, as well as an undying faith in their community, friends, and family, Kristine and Michael prevailed. The results were beyond anything anyone could have imagined. Dramatic, inspiring, and transformative, The Spark is about the power of love and courage in the face of overwhelming obstacles, and the dazzling possibilities that can occur when we learn how to tap the true potential that lies within every child, and in all of us.

    Goodbye, Little Rock and Roller is an inventive and original book from Nashville singer/songwriter Chapman, who uses twelve of her most resonant songs as entry points to many of her life's adventures. Not a memoir, but a map of the places Chapman's been and what went through her mind as she was traveling there, this book is funny and tender, warm and exuberant. Raised a debutante in Spartanburg, South Carolina, the daughter of a mill owner and firmly part of proper society, Chapman became a rocker at a time when women weren't yet picking up electric guitars. She is "a living example," as one reviewer wrote, "of the triumph of rock and roll over good breeding."From New Year's Eve in 1978 when Jerry Lee Lewis gave Chapman advice on how to live life ("I mean it's one thing when your mother says 'Honey don't you think you'd better slow down?' But when The Killer voices his concern....") to the time her black maid Cora Jeter took the seven-year-old to see Elvis, Goodbye, Little Rock and Roller goes to the moments when the influences on Chapman's songwriting and psyche were cemented. And it winningly reveals how the creative process comes from life: one of Chapman's favorite songs was written after waking up facedown in her underpants in her front-yard vegetable garden. Revealing intimate rock and roll moments and memories of a South Carolina childhood, Marshall Chapman is a fresh voice firmly in the Southern tradition.

    So began a relationship that almost wrecked her life.Barber's fascinating memoir takes us beyond this bizarre episode, revealing how it left her with an abiding mistrust of men which paradoxically led her to a promiscuous life-style at university until she met her husband-to-be. An Education tells how she went on to work for seven years at daring (for the times) men's magazine Penthouse before beginning her starry days as the Demon Barber - Britain's most entertaining and most feared interviewer. The book ends with an extraordinarily moving account of the early death of her husband. Her writing is refreshingly frank and funny.

    Winner of a Pulitzer Prize, he has written more than forty-five plays, including True West, Fool for Love, and Buried Child. Shepard has also appeared in more than fifty films, beginning with Terrence Malick's Days of Heaven, and was nominated for an Academy Award for his performance in The Right Stuff. Despite the publicity his work and life have attracted, however, Shepard remains a strongly private man who has said many times that he will never write a memoir. But he has written intensively about his inner life and creative work to his former father-in-law and housemate, Johnny Dark, who has been Shepard's closest friend, surrogate brother (they're nearly the same age), and even artistic muse for forty-five years and counting.Two Prospectors gathers nearly forty years of correspondence and transcribed conversations between Shepard and Dark. In these gripping, sometimes gut-wrenching letters, the men open themselves to each other with amazing honesty. Shepard's letters give us the deepest look we may ever get into his personal philosophy and creative process, while in Dark's letters we discover insights into Shepard's character that only an intimate friend could provide. The writers also reflect on the books and authors that stimulate their thinking, their relationships with women (including Shepard's anguished decision to leave his wife and son--Dark's stepdaughter and grandson--for actress Jessica Lange), personal struggles, and accumulating years. Illustrated with Dark's candid, revealing photographs of Shepard and their mutual family across many years, as well as facsimiles of numerous letters, Two Prospectors is a compelling portrait of a complex friendship that has anchored both lives for decades, a friendship also poignantly captured in Treva Wurmfeld's film, Shepard & Dark.

    Or the "Phantom of Fine Hall," a figure many students had seen shuffling around the corridors of the math and physics building wearing purple sneakers and writing numerology treatises on the blackboards. The Phantom was John Nash, one of the most brilliant mathematicians of his generation, who had spiraled into schizophrenia in the 1950s. His most important work had been in game theory, which by the 1980s was underpinning a large part of economics. When the Nobel Prize committee began debating a prize for game theory, Nash's name inevitably came up—only to be dismissed, since the prize clearly could not go to a madman. But in 1994 Nash, in remission from schizophrenia, shared the Nobel Prize in economics for work done some 45 years previously.Economist and journalist Sylvia Nasar has written a biography of Nash that looks at all sides of his life. She gives an intelligent, understandable exposition of his mathematical ideas and a picture of schizophrenia that is evocative but decidedly unromantic. Her story of the machinations behind Nash's Nobel is fascinating and one of very few such accounts available in print (the CIA could learn a thing or two from the Nobel committees).

    For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. In Everyday Calculus, Oscar Fernandez shows us how to see the math in our coffee, on the highway, and even in the night sky.Fernandez uses our everyday experiences to skillfully reveal the hidden calculus behind a typical day's events. He guides us through how math naturally emerges from simple observations-how hot coffee cools down, for example-and in discussions of over fifty familiar events and activities. Fernandez demonstrates that calculus can be used to explore practically any aspect of our lives, including the most effective number of hours to sleep and the fastest route to get to work. He also shows that calculus can be both useful-determining which seat at the theater leads to the best viewing experience, for instance-and fascinating-exploring topics such as time travel and the age of the universe. Throughout, Fernandez presents straightforward concepts, and no prior mathematical knowledge is required. For advanced math fans, the mathematical derivations are included in the appendixes.Whether you're new to mathematics or already a curious math enthusiast, Everyday Calculus invites you to spend a day discovering the calculus all around you. The book will convince even die-hard skeptics to view this area of math in a whole new way.

    Using playing cards, a newspaper, the back of an envelope, a Sudoku, some pennies and of course a pair of socks, Rob Eastaway shows how maths can demonstrate its secret beauties in even the most mundane of everyday objects. Among the many fascinating curiosities in these pages, you will discover the strange link between limericks and rabbits, an apparently 'fair' coin game where the odds are massively in your favour, why tourist boards can't agree on where the centre of Britain is, and how simple paper folding can lead to a Jurassic Park monster. With plenty of ideas you'll want to test out for yourself, this engaging and refreshing look at mathematics is for everyone.

    This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth--mathematicians whose achievements are comparable to those of Bach in music or Shakespeare in literature. William Dunham lucidly presents the definitions, theorems, and proofs. Students of literature read Shakespeare; students of music listen to Bach, he writes. But this tradition of studying the major works of the masters is, if not wholly absent, certainly uncommon in mathematics. This book seeks to redress that situation.Like a great museum, The Calculus Gallery is filled with masterpieces, among which are Bernoulli's early attack upon the harmonic series (1689), Euler's brilliant approximation of pi (1779), Cauchy's classic proof of the fundamental theorem of calculus (1823), Weierstrass's mind-boggling counterexample (1872), and Baire's original category theorem (1899). Collectively, these selections document the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching--a story of genius triumphing over some of the toughest, most subtle problems imaginable.Anyone who has studied and enjoyed calculus will discover in these pages the sheer excitement each mathematician must have felt when pushing into the unknown. In touring The Calculus Gallery, we can see how it all came to be.

    Underpinning both math and science, it is the foundation of every major advancement in knowledge since the time of the ancient Greeks. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between math and the real world. Ultimately, Mazur argues, logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.

    Edgar Hoover by a member of his personal staff—his former assistant, Paul Letersky—offers unprecedented, “clear-eyed and compelling” (Mark Olshaker, coauthor of Mindhunter) insight into an American legend.The 1960s and 1970s were arguably among America’s most turbulent post-Civil War decades. While the Vietnam War continued seemingly without end, protests and riots ravaged most cities, the Kennedys and MLK were assassinated, and corruption found its way to the highest levels of politics, culminating in Watergate. In 1965, at the beginning of the chaos, twenty-two-year-old Paul Letersky was assigned to assist the legendary FBI director J. Edgar Hoover who’d just turned seventy and had, by then, led the Bureau for an incredible forty-one years. Hoover was a rare and complex man who walked confidently among the most powerful. His personal privacy was more tightly guarded than the secret “files” he carefully collected—and that were so feared by politicians and celebrities. Through Letersky’s close working relationship with Hoover, and the trust and confidence he gained from Hoover’s most loyal senior assistant, Helen Gandy, Paul became one of the few able to enter the Director’s secretive—and sometimes perilous—world. Since Hoover’s death half a century ago, millions of words have been written about the man and hundreds of hours of TV dramas and A-list Hollywood films produced. But until now, there has been virtually no account from someone who, for a period of years, spent hours with the Director on a daily basis. Balanced, honest, and keenly observed, this “vivid, foibles-and-all portrait of the fabled scourge of gangsters, Klansmen, and communists” (The Wall Street Journal) sheds new light on one of the most powerful law enforcement figures in American history.

    Randall Riese has exhaustively covered every aspect of her life--from her rise to stardom and her stunning career on Broadway and in film, to her relationship with her mother and with her son, her political involvement, and her numerous lovers. Includes 16 pages of fabulous photographs.