C. Escher and composer Johann Sebastian Bach, discussing common themes in their work and lives. At a deeper level, the book is a detailed and subtle exposition of concepts fundamental to mathematics, symmetry, and intelligence. Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself. In response to confusion over the book's theme, Hofstadter has emphasized that GEB is not about mathematics, art, and music but rather about how cognition and thinking emerge from well-hidden neurological mechanisms.

    Whether you were the king's court astrologer or a farmer marking the best time for planting, timekeeping and numbers really mattered. Mistake a numerical pattern of petals and you could be poisoned. Lose the rhythm of a sacred dance or the meter of a ritually told story and the intricately woven threads that hold life together were spoiled. Ignore the celestial clock of equinoxes and solstices, and you'd risk being caught short of food for the winter. Shesso's friendly tone and clear grasp of the information make the math "go down easy" in this marvelous book.BONUS: This book has over 100 illustrations! Click on the Google Preview link to get a glimpse.Excerpt from Math for Mystics: “It’s our collective malaise: Post-Traumatic Math Disorder.“Yet despite how we personally feel about mathematics, our distant ancestors willingly used numbers as pathways into the great patterns of Nature, avenues to understanding the Universe and their own place in it. Many ancient cultures had specific gods and goddesses they credited with inventing mathematical skills. With the aid of divine inspiration and assistance, humans nourished this numerical invention, continually pushing their skills and seeking greater clarity of expression. “Our starting point may seem like a Zero. But for now, before looking at numbers and math, let’s simply see it as a circle. No matter what our spiritual practice, we each live within the circle of creation, each within the circle—the cohesiveness—of our own form...” From John Michael Greer, Grand Archdruid, Ancient Order of Druids in America and author of The Druidry Handbook:“As thoughtful as it is readable, Renna Shesso’s Math for Mystics is the book I wish I had when I first started trying to make sense of the mathematics that underlie so much of modern magic and traditional occult lore. Not the least of its virtues is the way it makes magical number theory accessible even to those who think they don’t like or can’t handle math. It provides a first-rate introduction to a fairly neglected branch of magical lore.”

    In this lively book of essays, Stephen Wolfram takes the reader along on some of his most surprising and engaging intellectual adventures in science, technology, artificial intelligence and language design.

    A basic idea that proved elusive for hundreds of years and bent the minds of the greatest thinkers in the world, the algorithm is what made the modern world possible. Without the algorithm, there would have been no computer, no Internet, no virtual reality, no e-mail, or any other technological advance that we rely on every day.In The Advent of the Algorithm, David Berlinski combines science, history, and math to explain and explore the intriguing story of how the algorithm was finally discovered by a succession of mathematicians and logicians, and how this paved the way for the digital age. Beginning with Leibniz and culminating in the middle of the twentieth century with the groundbreaking work of Gödel and Turing, The Advent of the Algorithm is an epic tale told with clarity and imaginative brilliance.

    Boldt has helped thousands of readers find personal satisfaction in their work and personal lives. Now he applies these principles to the subject of abundance: How do we achieve material wealth without sacrificing our souls?In The Tao of Abundance, Boldt applies ancient wisdom to modern times, presenting eight guiding principles from Taoist philosophy geared to help readers make practical life changes that will bring them a truer and deeper sense of abundance. Boldt encourages readers to strike a balance between material and spiritual wealth--not to favor one over the other--and argues that increased material wealth comes as a natural byproduct of psychological fulfillment. With exercises designed to help readers find their own balance between societal demands and their own deepest desires, this helpful, inspiring book offers the chance to experience a new feeling of abundance in all aspects of life.

    The Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included.Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises.

    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.

    40 illustrations throughout.

    Theories that contain time as a simple quantity form the basis of our understanding of many scientific disciplines, yet the debate rages on: why does there seem to be a direction to time, an arrow of time pointing from past to future?In The Arrow of Time, a major bestseller in England, Dr. Peter Coveney, a research scientist, and award-winning journalist Dr. Roger Highfield, demonstrate that the commonsense view of time agrees with the most advanced scientific theory. Time does in fact move like an arrow, shooting forward into what is genuinely unknown, leaving the past immutably behind. The authors make their case by exploring three centuries of science, offering bold reinterpretations of Newton's mechanics, Einstein's special and general theories of relativity, quantum mechanics, and advancing the insights of James Gleick's Chaos.

    Presenting to the world his remarkable observations using the recently invented telescope--the craters of the moon, the satellites of Jupiter--Galileo dramatically challenged our idea of the perfection of the heavens and the centrality of the Earth in the universe. Indeed, the appearance of the little book is regarded as one of the great moments in the history of science. Planned to coincide with the 400th anniversary of the publication of the Starry Messenger, this is a major new biography of Galileo, a fresh and much more rounded view of the great scientist than found in earlier works. Unlike previous biographers, Heilbron shows us that Galileo was far more than a mathematician: he was deeply knowledgeable in the arts, an expert on the epic poet Ariosto, a fine lutenist. More important, Heilbron notes that years of reading the poets and experimenting with literary forms were not mere sidebars--they enabled Galileo to write clearly and plausibly about the most implausible things. Indeed, Galileo changed the world not simply because he revolutionized astronomy, but because he conveyed his discoveries so clearly and crisply that they could not be avoided or denied. If ever a discoverer was perfectly prepared to make and exploit his discovery, it was the dexterous humanist Galileo aiming his first telescope at the sky. In Galileo, John Heilbron captures not only the great scientist, but also the creative, artistic younger man who would ultimately become the champion of Copernicus, the bête-noire of the Jesuits, and the best-known of all martyrs to academic freedom.

    Illogical Atheism comprises a comprehensive four-part analysis of the deep-seated philosophical tensions in the New Atheist agenda and serves as one of but a handful of important books seeking to alert the public consciousness toward the propagandist maneuvers of the the Freethinking community's most prominent figureheads. No stone is left unturned as Jinn takes all Four Famed Horsemen to task.

    Written by two of the field's true pioneers, Spacetime Physics can extend and enhance coverage of specialty relativity in the classroom. This thoroughly up-to-date, highly accessible overview covers microgravity, collider accelerators, satellite probes, neutron detectors, radioastronomy, and pulsars.  The chapter on general relativity with new material on gravity waves, black holes, and cosmology.

    In this book, author Fred Heeren tells why even Einstein had to revise his thinking to bring it in line with the Bible's claims. Through Heeren's interviews with Steven Hawking and Nobel prize-winning physicists, you'll learn why many leading cosmologists today are bringing God into the equation.

    . . . [His] arguments are often lively and entertaining.--Los Angeles TimesIn Not in His Image John Lamb Lash explains how a little-known messianic sect propelled itself into a dominant world power, systematically wiping out the great Gnostic spiritual teachers, the Druid priests, and the shamanistic healers of Europe and North Africa. Early Christians burned libraries and destroyed temples in an attempt to silence the ancient truth-tellers and keep their own secrets. But as Lash reveals the truth cannot be hidden or destroyed.Not in His Image delves deeply into the shadows of ancient Gnostic writings to reconstruct the story early Christians tried to scrub from the pages of history, exploring the richness of the ancient European Pagan spirituality-the Pagan Mysteries, the Great Goddess, Gnosis, the myths of Sophia and Gaia.Long before the birth of Christianity, monotheism was an anomaly; Europe and the Near East flourished under the divine guidance of Sophia, the ancient goddess of wisdom. The Earth was the embodiment of Sophia and thus sacred to the people who sought fulfillment in her presence. This ancient philosophy was threatening to the emerging salvation-based creed of Christianity that was based on patriarchal dominion over the Earth and lauded personal suffering as a path to the afterlife. As Derrick Jensen points out in the afterword, in Lash's hands Jesus Christ emerges as the agent provocateur of the ruling classes.Sometimes a book changes the world. Not in His Image is such a book. It is clear, stimulating, well-researched, and sure to outrage the experts. . . . Get it. Improve not just your own life, but civilization's chances for survival.--Roger Payne, author of Among Whales

    Such is the case right now with our wounded feeling function- our inability to find joy, worth, and meaning in life. Robert A. Johnson, the celebrated author of 'He, She', and 'We', revisits two medieval tales and illuminates how this feeling function has become a casualty of our modern times.Johnson tells the story of the Wounded Fisher King from the Grail Myth to illustrate the anxiety and loneliness that plague men. From the folktale of the Handless Maiden, he explains the very different frustrations of women and describes how these disparities in the way we suffer account for much of the tension and miscommunication between men and women. His insightful analysis shows that these two stories, created centuries ago, are even more relevant today.Robert A. Johnson, a noted lecturer and Jungian analyst, is also the author of 'He, She, We, Inner Work, Ecstasy, Transformation', and 'Owning Your Own Shadow'.