It was studied from antiquity to the Renaissance as a way of glimpsing the nature of reality. Geometry is number in space; music is number in time; and comology expresses number in space and time. Number, music, and geometry are metaphysical truths: life across the universe investigates them; they foreshadow the physical sciences.Quadrivium is the first volume to bring together these four subjects in many hundreds of years. Composed of six successful titles in the Wooden Books series-Sacred Geometry, Sacred Number, Harmonograph, The Elements of Music, Platonic & Archimedean Solids, and A Little Book of Coincidence-it makes ancient wisdom and its astonishing interconnectedness accessible to us today.Beautifully produced in six different colors of ink, Quadrivium will appeal to anyone interested in mathematics, music, astronomy, and how the universe works.

    The other books in the series are The Black Swan, Antifragile,and The Bed of Procrustes.

    The work of English clergyman, educator and Shakespearean scholar Edwin A. Abbott (1838-1926), it describes the journeys of A. Square [sic – ed.], a mathematician and resident of the two-dimensional Flatland, where women-thin, straight lines-are the lowliest of shapes, and where men may have any number of sides, depending on their social status.Through strange occurrences that bring him into contact with a host of geometric forms, Square has adventures in Spaceland (three dimensions), Lineland (one dimension) and Pointland (no dimensions) and ultimately entertains thoughts of visiting a land of four dimensions—a revolutionary idea for which he is returned to his two-dimensional world. Charmingly illustrated by the author, Flatland is not only fascinating reading, it is still a first-rate fictional introduction to the concept of the multiple dimensions of space. "Instructive, entertaining, and stimulating to the imagination." — Mathematics Teacher.

    Though the answers may seem simple, their profound implications make the prisoner's dilemma one of the great unifying concepts of science. Watching players bluff in a poker game inspired John von Neumann--father of the modern computer and one of the sharpest minds of the century--to construct game theory, a mathematical study of conflict and deception. Game theory was readily embraced at the RAND Corporation, the archetypical think tank charged with formulating military strategy for the atomic age, and in 1950 two RAND scientists made a momentous discovery.Called the prisoner's dilemma, it is a disturbing and mind-bending game where two or more people may betray the common good for individual gain. Introduced shortly after the Soviet Union acquired the atomic bomb, the prisoner's dilemma quickly became a popular allegory of the nuclear arms race. Intellectuals such as von Neumann and Bertrand Russell joined military and political leaders in rallying to the preventive war movement, which advocated a nuclear first strike against the Soviet Union. Though the Truman administration rejected preventive war the United States entered into an arms race with the Soviets and game theory developed into a controversial tool of public policy--alternately accused of justifying arms races and touted as the only hope of preventing them.A masterful work of science writing, Prisoner's Dilemma weaves together a biography of the brilliant and tragic von Neumann, a history of pivotal phases of the cold war, and an investigation of game theory's far-reaching influence on public policy today. Most important, Prisoner's Dilemma is the incisive story of a revolutionary idea that has been hailed as a landmark of twentieth-century thought.

    Even as they bring ease to our lives, these programs are stealing something essential from us.Drawing on psychological and neurological studies that underscore how tightly people’s happiness and satisfaction are tied to performing hard work in the real world, Carr reveals something we already suspect: shifting our attention to computer screens can leave us disengaged and discontented.From nineteenth-century textile mills to the cockpits of modern jets, from the frozen hunting grounds of Inuit tribes to the sterile landscapes of GPS maps, The Glass Cage explores the impact of automation from a deeply human perspective, examining the personal as well as the economic consequences of our growing dependence on computers.With a characteristic blend of history and philosophy, poetry and science, Carr takes us on a journey from the work and early theory of Adam Smith and Alfred North Whitehead to the latest research into human attention, memory, and happiness, culminating in a moving meditation on how we can use technology to expand the human experience.

    "A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

    Capturing the tone of students exchanging ideas among themselves, this unique guide also explains how calculus is taught, how to get the best teachers, what to study, and what is likely to be on exams—all the tricks of the trade that will make learning the material of first-semester calculus a piece of cake. Funny, irreverent, and flexible, How to Ace Calculus shows why learning calculus can be not only a mind-expanding experience but also fantastic fun.

    At the dawn of the Industrial Revolution in eighteenth-century England, standards of measurement were established, giving way to the development of machine tools—machines that make machines. Eventually, the application of precision tools and methods resulted in the creation and mass production of items from guns and glass to mirrors, lenses, and cameras—and eventually gave way to further breakthroughs, including gene splicing, microchips, and the Hadron Collider.Simon Winchester takes us back to origins of the Industrial Age, to England where he introduces the scientific minds that helped usher in modern production: John Wilkinson, Henry Maudslay, Joseph Bramah, Jesse Ramsden, and Joseph Whitworth. It was Thomas Jefferson who later exported their discoveries to the fledgling United States, setting the nation on its course to become a manufacturing titan. Winchester moves forward through time, to today’s cutting-edge developments occurring around the world, from America to Western Europe to Asia.As he introduces the minds and methods that have changed the modern world, Winchester explores fundamental questions. Why is precision important? What are the different tools we use to measure it? Who has invented and perfected it? Has the pursuit of the ultra-precise in so many facets of human life blinded us to other things of equal value, such as an appreciation for the age-old traditions of craftsmanship, art, and high culture? Are we missing something that reflects the world as it is, rather than the world as we think we would wish it to be? And can the precise and the natural co-exist in society?

    From the first lesson to the last, each chapter introduces games of increasing complexity and then teaches the game theoretical tools necessary to solve them. Inside, you will find: All the basics fully explained, including pure strategy Nash equilibrium, mixed strategy Nash equilibrium, the mixed strategy algorithm, how to calculate payoffs, strict dominance, weak dominance, iterated elimination of strictly dominated strategies, iterated elimination of weakly dominated strategies, and more! Dozens of games solved, including the prisoner's dilemma, stag hunt, matching pennies, zero sum games, battle of the sexes/Bach or Stravinsky, chicken/snowdrift, pure coordination, deadlock, and safety in numbers! Crystal clear, line-by-line calculations of every step, with more than 200 images so you don't miss a thing! Tons of applications: war, trade, game shows, and duopolistic competition. Quick, efficient, and to the point, Game Theory 101: The Basics is perfect for introductory game theory, intermediate microeconomics, and political science.

    Raymond M. Smullyan — a celebrated mathematician, logician, magician, and author — presents a logical labyrinth of more than 200 increasingly complex problems. The puzzles delve into Gödel’s undecidability theorem and other examples of the deepest paradoxes of logic and set theory. Detailed solutions follow each puzzle.

    Delving further, Shulman unearthed the surprising story behind the invention of the telephone: a tale of romance, corruption, and unchecked ambition. Bell furtively—and illegally—copied part of Elisha Gray’s invention in the race to secure what would become the most valuable U.S. patent ever issued. And afterward, as Bell’s device led to the world’s largest monopoly, the American Telephone and Telegraph Company, he hid his invention’s illicit beginnings. In The Telephone Gambit, Shulman challenges the reputation of an icon of invention, rocks the foundation of a corporate behemoth, and offers a probing meditation on how little we know about our own history.

    One of them, the Prussian aristocrat Alexander von Humboldt, negotiates savanna and jungle, travels down the Orinoco, tastes poisons, climbs the highest mountain known to man, counts head lice, and explores every hole in the ground. The other, the barely socialized mathematician and astronomer Carl Friedrich Gauss, does not even need to leave his home in Göttingen to prove that space is curved. He can run prime numbers in his head. He cannot imagine a life without women, yet he jumps out of bed on his wedding night to jot down a mathematical formula. Von Humboldt is known to history as the Second Columbus. Gauss is recognized as the greatest mathematical brain since Newton. Terrifyingly famous and more than eccentric in their old age, the two meet in Berlin in 1828. Gauss has hardly climbed out of his carriage before both men are embroiled in the political turmoil sweeping through Germany after Napoleon’s fall.Already a huge best seller in Germany, Measuring the World marks the debut of a glorious new talent on the international scene.

    Yet The Origin of Species (1859) is also a humane and inspirational vision of ecological interrelatedness, revealing the complex mutual interdependencies between animal and plant life, climate and physical environment, and—by implication—within the human world. Written for the general reader, in a style which combines the rigour of science with the subtlety of literature, The Origin of Species remains one of the founding documents of the modern age.

    . . Nothing less than a major contribution to the scientific culture of this world." — The New York Times Book ReviewThis major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems.Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference."This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science

    As a flight director in NASA’s Mission Control, Kranz witnessed firsthand the making of history. He participated in the space program from the early days of the Mercury program to the last Apollo mission, and beyond. He endured the disastrous first years when rockets blew up and the United States seemed to fall further behind the Soviet Union in the space race. He helped to launch Alan Shepard and John Glenn, then assumed the flight director’s role in the Gemini program, which he guided to fruition. With his teammates, he accepted the challenge to carry out President John F. Kennedy’s commitment to land a man on the Moon before the end of the 1960s. Kranz recounts these thrilling historic events and offers new information about the famous flights. What appeared as nearly flawless missions to the Moon were, in fact, a series of hair-raising near misses. When the space technology failed, as it sometimes did, the controllers’ only recourse was to rely on their skills and those of their teammates. He reveals behind-the-scenes details to demonstrate the leadership, discipline, trust, and teamwork that made the space program a success. A fascinating firsthand account by a veteran mission controller of one of America’s greatest achievements, Failure is Not an Option reflects on what has happened to the space program and offers his own bold suggestions about what we ought to be doing in space now.