People everywhere have heard of Waldorf schools, Biodynamic farming, Camphill Villages, and other innovations of the Austrian philosopher Rudolf Steiner (1861-1925). Indeed, Steiner-as an architect, artist, teacher, and agriculturalist-ranks among the most creative and prolific figures of the early twentieth century, pioneering work in alternative education, holistic health, and environmental research. While his accomplishments are felt all over the world, few people understand this unusual figure. Steiner's own writings and lectures fill several bookcases, intimidating those who would like to know more. Works on Steiner are often dense and "insider" in tone, further deterring the curious. No popular biography, written by a sympathetic but critical outsider, has been available. Gary Lachman's Rudolf Steiner provides this missing introduction. Along with telling Steiner's story and placing Steiner in his historical context, Lachman's book presents Steiner's key ideas in a readable, accessible manner. In particular, Lachman considers the spread of Steiner's most popular projects, which include Waldorf schools-one of the leading forms of alternative education-and Biodynamic farming-a popular precursor to organic farming. He also traces Steiner's beginnings as a young intellectual in the ferment of fin de si?cle culture, to his rise as a thought leader within the influential occult movement of Theosophy, to the founding of his own metaphysical teaching called Anthroposophy. Finally, the book illustrates how Steiner's methods are put into practice today, and relates Steiner's insights into cosmology to the work of current thinkers. Rudolf Steiner is a full-bodied portrait of one of the most original philosophical and spiritual luminaries of the last two centuries, and gives those interested in the history of ideas the opportunity to discover one of the most underappreciated figures of the twentieth century.

    Even the simplest system of cause and effect can be subject to chaos, denying us accurate predictions of its behaviour, and sometimes giving rise to astonishing structures of large-scale order. Our growing understanding of Chaos Theory is having fascinating applications in the real world - from technology to global warming, politics, human behaviour, and even gambling on the stock market. Leonard Smith shows that we all have an intuitive understanding of chaotic systems. He uses accessible maths and physics (replacing complex equations with simple examples like pendulums, railway lines, and tossing coins) to explain the theory, and points to numerous examples in philosophy and literature (Edgar Allen Poe, Chang-Tzu, Arthur Conan Doyle) that illuminate the problems. The beauty of fractal patterns and their relation to chaos, as well as the history of chaos, and its uses in the real world and implications for the philosophy of science are all discussed in this Very Short Introduction.

    John Dee (1527–1608) resolved that worldly knowledge could no longer provide him the wisdom he desired. He turned his attention to magick, and in 1582 he and his clairvoyant partner Edward Kelley made contact with a number of spiritual entities who identified themselves as angles—the same angels that communicated with Adam, Enoch, and the patriarchs of the Old Testament. Over the next three years three distinct magical systems were revealed to Dee and Kelley. The third, thanks largely to efforts from the adepts of the Hermetic Order of the Golden Dawn and the 20th-century practices of Aleister Crowley, is now widely known as Enochian Magick.Enochian Vision Magick includes extensive background and historical notes, explores the foundation for the creation of the Enochian Magick system, and provides readers with a step-by-step process for using it.

    The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understandingof paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questionsabout the mathematical community (such as Is it true that mathematicians burn out at the age of 25?) It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundredsof key topics, from philosophy to Freud, quantum theory to Islam.

    Includes Crowley's "An Initiated Interpretation of Ceremonial Magic," his version of "The Bornless Ritual," Enochian translations of some of the Goetic invocations, an introduction, and notes. Illustrated. Smythe-sewn and printed on acid-free paper.

    It deals with one powerful obsession that preoccupied Escher: what he called "the regular division of the plane," the puzzlelike interlocking of birds, fish, lizards, and other natural forms in continuous patterns. Schattschneider asks, "How did he do it?" She answers the question by analyzing Escher's notebooks." Visions of Symmetry includes many of Escher's masterworks, as well as hundreds of lesser-known examples of his work. This new edition also features a foreward and an illustrated epilogue that reveals new information about Escher's inspiration and shows how his ideas of symmetry have influenced mathematicians, computer scientists, and contemporary artists.

    His breaking of the German U-boat Enigma cipher in World War II ensured Allied-American control of the Atlantic. But Turing's vision went far beyond the desperate wartime struggle. Already in the 1930s he had defined the concept of the universal machine, which underpins the computer revolution. In 1945 he was a pioneer of electronic computer design. But Turing's true goal was the scientific understanding of the mind, brought out in the drama and wit of the famous "Turing test" for machine intelligence and in his prophecy for the twenty-first century.Drawn in to the cockpit of world events and the forefront of technological innovation, Alan Turing was also an innocent and unpretentious gay man trying to live in a society that criminalized him. In 1952 he revealed his homosexuality and was forced to participate in a humiliating treatment program, and was ever after regarded as a security risk. His suicide in 1954 remains one of the many enigmas in an astonishing life story.

    He lives in Atlanta, Georgia, with his wife Jan and their two teenage children Charity and John. At the age of sixteen as a junior in high school, he first heard the message of the Christian gospel and yielded his life to Christ. Dr. Craig pursued his undergraduate studies at Wheaton College (B.A. 1971) and graduate studies at Trinity Evangelical Divinity School (M.A. 1974; M.A. 1975), the University of Birmingham (England) (Ph.D. 1977), and the University of Munich (Germany) (D.Theol. 1984). From 1980-86 he taught Philosophy of Religion at Trinity, during which time he and Jan started their family. In 1987 they moved to Brussels, Belgium, where Dr. Craig pursued research at the University of Louvain until 1994.

    Its first followers guarded them as priceless treasures. After an increasingly rigid hierarchy began to bury these truths in the early centuries A.D., they were known only to a few initiates, who communicated them privately, often in obscure language. In Esoteric Christianity, Besant's aim is to restore the secret truths underlying Christian doctrine. As public interest grows in the Gnostic Gospels and the mystical side of Christianity, Besant's remarkable book, first published in 1901, is attracting new attention.

    However, it is one of the basic principles of quantum theory, the most widely accepted explanation of the subatomic world - and one of the fascinating subjects dealt with in Equations of Eternity.

    But for those of us who left math behind in high school, the numbers and figures hurled at us as we go about our days can sometimes leave us scratching our heads and feeling as if we’re fumbling through a mathematical minefield. In this eye-opening and extraordinarily accessible book, mathemati­cian Kit Yates illuminates hidden principles that can help us understand and navigate the chaotic and often opaque surfaces of our world. In The Math of Life and Death, Yates takes us on a fascinating tour of everyday situations and grand-scale applications of mathematical concepts, including exponential growth and decay, optimization, statistics and probability, and number systems. Along the way he reveals the mathematical undersides of controversies over DNA testing, medical screening results, and historical events such as the Chernobyl disaster and the Amanda Knox trial. Readers will finish this book with an enlightened perspective on the news, the law, medicine, and history, and will be better equipped to make personal decisions and solve problems with math in mind, whether it’s choosing the shortest checkout line at the grocery store or halting the spread of a deadly disease.

    Cox and Forshaw's contention? There is no need for quantum mechanics to be viewed this way. There is a lot of mileage in the 'weirdness' of the quantum world, and it often leads to confusion and, frankly, bad science. The Quantum Universe cuts through the Wu Li and asks what observations of the natural world made it necessary, how it was constructed, and why we are confident that, for all its apparent strangeness, it is a good theory.The quantum mechanics of The Quantum Universe provide a concrete model of nature that is comparable in its essence to Newton’s laws of motion, Maxwell’s theory of electricity and magnetism, and Einstein’s theory of relativity.

    presents some of the most famous mathematical proofs in a charming book that will appeal to nonmathematicians and math experts alike. Grasp in an instant why Pythagoras's theorem must be correct. Follow the ancient Chinese proof of the volume formula for the frustrating frustum, and Archimedes' method for finding the volume of a sphere. Discover the secrets of pi and why, contrary to popular belief, squaring the circle really is possible. Study the subtle art of mathematical domino tumbling, and find out how slicing cones helped save a city and put a man on the moon.

    Eros and Magic in the Renaissance challenges this view, providing an in-depth scholarly explanation of the workings of magic and showing that magic continues to exist in an altered form even today.Renaissance magic, according to Ioan Couliano, was a scientifically plausible attempt to manipulate individuals and groups based on a knowledge of motivations, particularly erotic motivations. Its key principle was that everyone (and in a sense everything) could be influenced by appeal to sexual desire. In addition, the magician relied on a profound knowledge of the art of memory to manipulate the imaginations of his subjects. In these respects, Couliano suggests, magic is the precursor of the modern psychological and sociological sciences, and the magician is the distant ancestor of the psychoanalyst and the advertising and publicity agent.In the course of his study, Couliano examines in detail the ideas of such writers as Giordano Bruno, Marsilio Ficino, and Pico della Mirandola and illuminates many aspects of Renaissance culture, including heresy, medicine, astrology, alchemy, courtly love, the influence of classical mythology, and even the role of fashion in clothing.Just as science gives the present age its ruling myth, so magic gave a ruling myth to the Renaissance. Because magic relied upon the use of images, and images were repressed and banned in the Reformation and subsequent history, magic was replaced by exact science and modern technology and eventually forgotten. Couliano's remarkable scholarship helps us to recover much of its original significance and will interest a wide audience in the humanities and social sciences.

    D. Williams wrote this entertaining, witty introduction for the nonscientist, game theory was still a somewhat mysterious subject familiar to very few scientists beyond those researchers, like himself, working for the military. Now, over thirty years after its original publication as a Rand Corporation research study, his light-hearted though thoroughly effective primer is the recognized classic introduction to an increasingly applicable discipline. Used by amateurs, professionals, and students throughout the world in the classroom, on the job, and for personal amusement, the book has been through ten printings, and has been translated into at least five languages (including Russian and Japanese).Revised, updated, and available for the first time in an inexpensive paperback edition, The Compleat Strategyst is a highly entertaining text essential for anyone interested in this provocative and engaging area of modern mathematics. In fully illustrated chapters complete with everyday examples and word problems, Williams offers readers a working understanding of the possible methods for selecting strategies in a variety of situations, simple to complex. With just a basic understanding of arithmetic, anyone can grasp all necessary aspects of two-, three-, four-, and larger strategy games with two or more sets of inimical interests and a limitless array of zero-sum payoffs.As research and study continues not only in this new discipline but in the related areas of statistics, probability and behavioral science, understanding of games, decision making, and the development of strategies will be increasingly important. In the areas of economics, sociology, politics, and the military, game theory is sure to have an even wider impact. For students and amateurs fascinated by game theory's implications there is no better, immediately applicable, or more entertaining introduction to the subject than this engaging text by the late J. D. Williams, Professor of Mathematics at Princeton University and a member of the Research Council of The Rand Corporation.