Beautifully illustrated with old engravings as well as contemporary imagery, Sacred Number introduces basic counting systems; significant numbers from major religious texts; the importance of astronomy, geometry, and music to number quality; how numbers affect architecture. Lundy explains why the ideas of Pythagoras still resonate, and she profiles each number from one to ten to show its distinct qualities: why, for example, the golden section is associated with five, and seven with the Virgin Mary.

    Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

    a great book to read

    Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics -- the universal language of science -- keep the masterpieces of the subject hidden behind a veil?"The Universe in Zero Words" tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society -- from the elementary (1+1 = 2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E = mc^2) to the arcane (Hamilton's quaternion equations). Mackenzie, who has been called a "popular-science ace" by Booklist magazine, lucidly explains what each equation means, who discovered it (and how), and how it has affected our lives.(From the jacket copy.)Note: The Princeton University Press version (black cover) is for sale in the English-speaking world outside Australia. The Newsouth Press version (blue cover) is for sale in Australia. The two versions are identical except for the covers.

    This adventure in science and imagination, which the Medical Tribune said might herald "a Copernican revolution for the life sciences," leads the reader through unexplored jungles and uncharted aspects of mind to the heart of knowledge.In a first-person narrative of scientific discovery that opens new perspectives on biology, anthropology, and the limits of rationalism, The Cosmic Serpent reveals how startlingly different the world around us appears when we open our minds to it.

    But there is one other motive which is as strong as any of these — the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen. Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.

    With this astonishing guidebook, Surfing Through Hyperspace, you need not be a mathematician or an astrophysicist to explore the all-but-unfathomable concepts of hyperspace and higher-dimensional geometry.No subject in mathematics has intrigued both children and adults as much as the idea of a fourth dimension. Philosophers and parapsychologists have meditated on this mysterious space that no one can point to but may be all around us. Yet this extra dimension has a very real, practical value to mathematicians and physicists who use it every day in their calculations. In the tradtion of Flatland, and with an infectious enthusiasm, Clifford Pickover tackles the problems inherent in our 3-D brains trying to visualize a 4-D world, muses on the religious implications of the existence of higher-dimensional consciousness, and urges all curious readers to venture into the unexplored territory lying beyond the prison of the obvious. Pickover alternates sections that explain the science of hyperspace with sections that dramatize mind-expanding concepts through a fictional dialogue between two futuristic FBI agents who dabble in the fourth dimension as a matter of national security. This highly accessible and entertaining approach turns an intimidating subject into a scientific game open to all dreamers.Surfing Through Hyperspace concludes with a number of puzzles, computer experiments and formulas for further exploration, inviting readers to extend their minds across this inexhaustibly intriguing scientific terrain.

    Augustine equate nothingness with the Devil? What tortuous means did 17th-century scientists employ in their attempts to create a vacuum? And why do contemporary quantum physicists believe that the void is actually seething with subatomic activity? You’ll find the answers in this dizzyingly erudite and elegantly explained book by the English cosmologist John D. Barrow.Ranging through mathematics, theology, philosophy, literature, particle physics, and cosmology, The Book of Nothing explores the enduring hold that vacuity has exercised on the human imagination. Combining high-wire speculation with a wealth of reference that takes in Freddy Mercury and Shakespeare alongside Isaac Newton, Albert Einstein, and Stephen Hawking, the result is a fascinating excursion to the vanishing point of our knowledge.

    God in Search of Man combines scholarship with lucidity, reverence, and compassion as Dr. Heschel discusses not man's search for God but God's for man--the notion of a Chosen People, an idea which, he writes, "signifies not a quality inherent in the people but a relationship between the people and God." It is an extraordinary description of the nature of Biblical thought, and how that thought becomes faith.

    Written in exquisite Persian verse, the 'Zafarnama' or 'Epistle of Victory' was a defiant message composed by Guru Gobind Singh, the tenth Sikh Guru, and addressed to the Mughal emperor Aurangzeb.In this brilliant new translation, Navtej Sarna brings to life the valiant voice of Guru Gobind Singh and the power of his poetic genius in a passionate disavowal of tyranny that remains ever relevant.

    Either a profoundly psychotic episode or a galvanizing glimpse into the true nature of time & mind, McKenna is a spellbinding storyteller, providing plenty of down-to-earth reasons for preserving the planet.Preface1 The Call of the Secret2 Into the Devil's Paradise3 Along a Ghostly Trail 4 Camped by a Doorway 5 A Brush with the Other6 Kathmandu Interlude 7 A Violet Psychofluid8 The Opus Clarified 9 A Conversation Over Saucers10 More on the Opus 11 The Experiment at La Chorrera12 In the Vortex 13 At Play in the Fields of the Lord14 Looking Backward 15 A Saucer Full of Secrets16 Return 17 Waltzing the Enigma18 Say What Does It Mean?19 The Coming of the Strophariad20 The Hawaiian Connection EpilogueAcknowledgmentsFurther Reading

    Hidden in the caves at Qumran by the Essenes, a Jewish sect in existence before and during the time of Jesus, the Scrolls have transformed our understanding of the Hebrew Bible, early Judaism, and the origins of Christianity. This fully revised edition of the classic English translation by Geza Vermes, the world's leading scholar on the subject, offers an astonishing look into the organization, customs, and beliefs of the community at Qumran. Enhanced by much previously unpublished material and a new preface, this will remain the authoritative translation of the Dead Sea Scrolls for years to come.

    Drawing on years of research & on thinkers from Plato to Jung, Tarnas explores the planetary correlations of epochal events like the French Revolution, the world wars & 9/11. Whether read as astrology updated for the quantum age or as a contemporary classic of spirituality, Cosmos & Psyche is an important work of sophistication & learning. importance.Preface1 The transformation of the cosmos. The birth of the modern selfThe dawn of a new universe Two paradigms of historyForging the self, disenchanting the worldThe cosmological situation today 2 In search of a deeper order. Two suitors: a parableThe interior quest Synchronicity & its implicationsThe archetypal cosmos3 Through the archetypal telescope. The evolving traditionArchetypal principlesThe planets Forms of correspondence Personal transit cycles Archetypal coherence & concrete diversityAssessing patterns of correlation 4 Epochs of revolution. From the French Revolution to the 1960sSynchronic & diachronic patterns in historyScientific & technological revolutionsAwakenings of the DionysianThe liberation of natureReligious rebellion & erotic emancipationFilling in the cyclical sequence The individual & the collectiveA larger view of the sixties5 Cycles of crisis & contraction. World Wars, Cold War & 9/11Historical contrasts & tensionsConservative empowermentSplitting, evil & terror"Moby Dick" & nature's depthHistorical determinism, realpolitik & apocalypseMoral courage, facing the shadow & the tension of oppositesParadigmatic works of artForging deep structures 6 Cycles of creativity & expansion. Opening new horizons Convergences of scientific breakthroughsSocial & political rebellions & awakeningsQuantum leaps & peak experiencesFrom Copernicus to DarwinMusic & literatureIconic moments & cultural milestonesGreat heights & shadowsHidden births 7 Awakenings of spirit & soul. Epochal shifts of cultural visionSpiritual epiphanies & the emergence of new religionsUtopian social visions Romanticism, imaginative genius & cosmic epiphanyRevelations of the numinous The great awakening of the Axial Age The late 20th century & the turn of the millennium8 Towards a new heaven & a new earth. Understanding the past, creating the futureObservations on future planetary alignmentsSources of the world orderEpilogueNotesSourcesAcknowledgmentsIndex

    Graced with opening words by His Holiness The Dalai Lama, the Penguin Deluxe Edition of The Tibetan Book of the Dead is "immaculately rendered in an English both graceful and precise." Translated with the close support of leading contemporary masters and hailed as “a tremendous accomplishment,” this book faithfully presents the insights and intentions of the original work. It includes one of the most detailed and compelling descriptions of the after-death state in world literature, practices that can transform our experience of daily life, guidance on helping those who are dying, and an inspirational perspective on coping with bereavement.

    Helplessness in the face of disease and human disaster helped to perpetuate this belief in magic and the supernatural. As Keith Thomas shows, England during these years resembled in many ways today's underdeveloped areas. The English population was exceedingly liable to pain, sickness, and premature death; many were illiterate; epidemics such as the bubonic plague plowed through English towns, at times cutting the number of London's inhabitants by a sixth; fire was a constant threat; the food supply was precarious; and for most diseases there was no effective medical remedy. In this fascinating and detailed book, Keith Thomas shows how magic, like the medieval Church, offered an explanation for misfortune and a means of redress in times of adversity. The supernatural thus had its own practical utility in daily life. Some forms of magic were challenged by the Protestant Reformation, but only with the increased search for scientific explanation of the universe did the English people begin to abandon their recourse to the supernatural. Science and technology have made us less vulnerable to some of the hazards which confronted the people of the past. Yet Religion and the Decline of Magic concludes that if magic is defined as the employment of ineffective techniques to allay anxiety when effective ones are not available, then we must recognize that no society will ever be free from it.