Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be "computable," creating the field of computability theory in the process, a foundation of present-day computer programming.The book expands Turing's original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing's statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others.Interwoven into the narrative are the highlights of Turing's own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of "gross indecency," and his early death by apparent suicide at the age of 41.

    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.

    The Golden Bough" describes our ancestors' primitive methods of worship, sex practices, strange rituals and festivals. Disproving the popular thought that primitive life was simple, this monumental survey shows that savage man was enmeshed in a tangle of magic, taboos, and superstitions. Revealed here is the evolution of man from savagery to civilization, from the modification of his weird and often bloodthirsty customs to the entry of lasting moral, ethical, and spiritual values.

    Beautifully illustrated, it remains one of those rare works of scholarship which the general reader simply cannot afford to ignore.

    A concise, and delightful introduction to Vedanta, the philosophical backbone of Hinduism.Written with verve and charm by a Western nun for a Western audience, this brief book gives a comprehensive overview of Vedanta philosophy while emphasizing its practical Western application.

    The highly readable texts and over 800 beautiful full-color images come together in a unique way to convey hidden dimensions of meaning. Each of the ca. 350 essays examines a given symbol’s psychic background, and how it evokes psychic processes and dynamics. Etymological roots, the play of opposites, paradox and shadow, the ways in which diverse cultures have engaged a symbolic image—all these factors are taken into consideration.Authored by writers from the fields of psychology, religion, art, literature, and comparative myth, the essays flow into each other in ways that mirror the psyche’s unexpected convergences. There are no pat definitions of the kind that tend to collapse a symbol; a still vital symbol remains partially unknown, compels our attention and unfolds in new meanings and manifestations over time. Rather than merely categorize, The Book of Symbols illuminates how to move from the visual experience of a symbolic image in art, religion, life, or dreams to directly experiencing its personal and psychological resonance.The Book of Symbols sets new standards for thoughtful exploration of symbols and their meanings, and will appeal to a wide range of readers: artists, designers, dreamers and dream interpreters, psychotherapists, self-helpers, gamers, comic book readers, religious and spiritual searchers, writers, students, and anyone curious about the power of archetypal images.

    A meld of history and science, this book is a group portrait of some of the greatest minds who ever lived as they wrestled with nature’s most sweeping mysteries. The answers they uncovered still hold the key to how we understand the world.At the end of the seventeenth century—an age of religious wars, plague, and the Great Fire of London—when most people saw the world as falling apart, these earliest scientists saw a world of perfect order. They declared that, chaotic as it looked, the universe was in fact as intricate and perfectly regulated as a clock. This was the tail end of Shakespeare’s century, when the natural land the supernatural still twined around each other. Disease was a punishment ordained by God, astronomy had not yet broken free from astrology, and the sky was filled with omens. It was a time when little was known and everything was new. These brilliant, ambitious, curious men believed in angels, alchemy, and the devil, and they also believed that the universe followed precise, mathematical laws—-a contradiction that tormented them and changed the course of history.The Clockwork Universe is the fascinating and compelling story of the bewildered geniuses of the Royal Society, the men who made the modern world.

    Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations. As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics. Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself. Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery. Dr. Michael Guillen is Instructor of Physics and Mathematics in the Core Curriculum Program at Harvard University.

    Eliade traces manifestations of the sacred from primitive to modern times in terms of space, time, nature, and the cosmos. In doing so he shows how the total human experience of the religious man compares with that of the nonreligious. This book of great originality and scholarship serves as an excellent introduction to the history of religion, but its perspective also encompasses philosophical anthropology, phenomenology, and psychology. It will appeal to anyone seeking to discover the potential dimensions of human existence.

    

    Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life. In A Mind for Numbers, Dr. Oakley lets us in on the secrets to effectively learning math and science—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn math. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. A Mind for Numbers shows us that we all have what it takes to excel in math, and learning it is not as painful as some might think!

    Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life.Stephen Budiansky’s Journey to the Edge of Reason is the first biography to fully draw upon Gödel’s voluminous letters and writings—including a never-before-transcribed shorthand diary of his most intimate thoughts—to explore Gödel’s profound intellectual friendships, his moving relationship with his mother, his troubled yet devoted marriage, and the debilitating bouts of paranoia that ultimately took his life. It also offers an intimate portrait of the scientific and intellectual circles in prewar Vienna, a haunting account of Gödel’s and Jewish intellectuals’ flight from Austria and Germany at the start of the Second World War, and a vivid re-creation of the early days of Princeton’s Institute for Advanced Study, where Gödel and Einstein both worked.Eloquent and insightful, Journey to the Edge of Reason is a fully realized portrait of the odd, brilliant, and tormented man who has been called the greatest logician since Aristotle, and illuminates the far-reaching implications of Gödel’s revolutionary ideas for philosophy, mathematics, artificial intelligence, and man’s place in the cosmos.

    You'll find out how to unknot your DNA, how to count like a supercomputer and how to become famous for solving mathematics' most challenging problem.

    Now, in this lucid and accessibly written book, Philip Ball applies state-of-the-art scientific understanding from the fields of biology, chemistry, geology, physics, and mathematics to these ancient mysteries, revealing how nature's seemingly complex patterns originate in simple physical laws. Tracing the history of scientific thought about natural patterns, Ball shows how common presumptions--for example, that complex form must be guided by some intelligence or that form always follows function--are erroneous and continue to mislead scientists today. He investigates specific patterns in depth, revealing that these designs are self-organized and that simple, local interactions between component parts produce motifs like spots, stripes, branches, and honeycombs. In the process, he examines the mysterious phenomenon of symmetry and why it appears--and breaks--in similar ways in different systems. Finally, he attempts to answer this profound question: why are some patterns universal? Illustrations throughout the text, many in full color, beautifully illuminate Ball's ideas.

    Jason Ā. Josephson-Storm argues that as broad cultural history goes, this narrative is wrong, as attempts to suppress magic have failed more often than they have succeeded. Even the human sciences have been more enchanted than is commonly supposed. But that raises the question: How did a magical, spiritualist, mesmerized Europe ever convince itself that it was disenchanted? Josephson-Storm traces the history of the myth of disenchantment in the births of philosophy, anthropology, sociology, folklore, psychoanalysis, and religious studies. Ironically, the myth of mythless modernity formed at the very time that Britain, France, and Germany were in the midst of occult and spiritualist revivals. Indeed, Josephson-Storm argues, these disciplines’ founding figures were not only aware of, but profoundly enmeshed in, the occult milieu; and it was specifically in response to this burgeoning culture of spirits and magic that they produced notions of a disenchanted world.   By providing a novel history of the human sciences and their connection to esotericism, The Myth of Disenchantment dispatches with most widely held accounts of modernity and its break from the premodern past.