But through it all they persisted, motivated by the promise of a better life in which they could gather and worship God in their own ways. A collection of ragtag ships carried them across the ocean, among them The Mayflower. Crammed into the ship's hull, 102 people made this most famous pilgrimage. Besieged by illness and Indians and, many of them believed, witches, the Pilgrims eventually flourished, building up colonies and establishing their own rules for the practice of religion. Here is their dramatic story.

    But now, with the aid of high-speed computers, scientists have been able to penetrate a reality that is changing the way we perceive the universe. Their findings -- the basis for chaos theory -- represent one of the most exciting scientific pursuits of our time.No better introduction to this find could be found than John Briggs and F. David Peat's Turbulent Mirror. Together, they explore the many faces of chaos and reveal how its law direct most of the processes of everyday life and how it appears that everything in the universe is interconnected -- discovering an "emerging science of wholeness."Turbulent Mirror introduces us to the scientists involved in study this endlessly strange field; to the theories that are turning our perception of the world on its head; and to the discoveries in mathematics, biology, and physics that are heralding a revolution more profound than the one responsible for producing the atomic bomb. With practical applications ranging from the control of traffic flow and the development of artifical intelligence to the treatment of heart attacks and schizophrenia, chaos promises to be an increasingly rewarding area of inquiry -- of interest to everyone.

    Mathematics, Applied & Natural Sciences

    A definitive biography presents a portrait of the Nobel Prize-winning philosopher, uses unpublished letters, manuscripts, and papers that reveal his philosophical creativity, social conscience, and erotic drives.

    Although it presents the main ideas of quantum theory essentially in nonmathematical terms, it follows these with a broad range of specific applications that are worked out in considerable mathematical detail. Addressed primarily to advanced undergraduate students, the text begins with a study of the physical formulation of the quantum theory, from its origin and early development through an analysis of wave vs. particle properties of matter. In Part II, Professor Bohm addresses the mathematical formulation of the quantum theory, examining wave functions, operators, Schrödinger's equation, fluctuations, correlations, and eigenfunctions.Part III takes up applications to simple systems and further extensions of quantum theory formulation, including matrix formulation and spin and angular momentum. Parts IV and V explore the methods of approximate solution of Schrödinger's equation and the theory of scattering. In Part VI, the process of measurement is examined along with the relationship between quantum and classical concepts.Throughout the text, Professor Bohm places strong emphasis on showing how the quantum theory can be developed in a natural way, starting from the previously existing classical theory and going step by step through the experimental facts and theoretical lines of reasoning which led to replacement of the classical theory by the quantum theory.

    It describes how the laws and discoveries of information theory now support controversial revisions to Darwinian evolution, begin to unravel the mysteries of language, memory and dreams, and stimulate provocative ideas in psychology, philosophy, art, music, computers and even the structure of society. Perhaps its most fascinating and unexpected surprise is the suggestion the order and complexity may be as natural as disorder and disorganization. Contrary to the entropy principle, which implies that order is the exception and confusion the rule, information theory asserts that order and sense can indeed prevail against disorder and nonsense. From the simplest forms of organic life to the words used to express our most complex ideas, from our genes to our dreams, from microcomputers to telecommunications, virtually everything around us follows simple rules of information. Life and the material world, like language, remain "grammatical." Grammatical man inhabits a grammatical universe.

    With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change.The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.From the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal.

    Wolfram lets the world see his work in A New Kind of Science, a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modeling complex systems. On the frontier of complexity science since he was a boy, Wolfram is a champion of cellular automata--256 "programs" governed by simple nonmathematical rules. He points out that even the most complex equations fail to accurately model biological systems, but the simplest cellular automata can produce results straight out of nature--tree branches, stream eddies, and leopard spots, for instance. The graphics in A New Kind of Science show striking resemblance to the patterns we see in nature every day. Wolfram wrote the book in a distinct style meant to make it easy to read, even for nontechies; a basic familiarity with logic is helpful but not essential. Readers will find themselves swept away by the elegant simplicity of Wolfram's ideas and the accidental artistry of the cellular automaton models. Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. --Therese Littleton

    The author believes that there are such things as "The Mathematics of Life" and "The Mathematics of Art," and that the two coincide. Using simple mathematical formulas, most as basic as Pythagoras' theorem and requiring only a very limited knowledge of mathematics, Professor Ghyka shows the fascinating relationships between geometry, aesthetics, nature, and the human body.Beginning with ideas from Plato, Pythagoras, Archimedes, Ockham, Kepler, and others, the author explores the outlines of an abstract science of space, which includes a theory of proportions, an examination of "the golden section," a study of regular and semi-regular polyhedral, and the interlinking of these various shapes and forms. He then traces the transmission of this spatial science through the Pythagorean tradition and neo-Pythagorism, Greek, and Gothic canons of proportion, the Kabbala, Masonic traditions and symbols, and modern applications in architecture, painting, and decorative art. When we judge a work of art, according to his formulation, we are making it conform to a pattern whose outline is laid down in simple geometrical figures; and it is the analysis of these figures both in art and nature that forms the core of Professor Ghyka's book. He also shows this geometry at work in living organisms. The ample illustrations and figures give concrete examples of the author's analysis: the Great Pyramid and tomb of Rameses IV, the Parthenon, Renaissance paintings and architecture, the work of Seurat, Le Corbusier, and flowers, shells, marine life, the human face, and much more.For the philosopher, scientist, archaeologist, art historian, biologist, poet, and artist as well as the general reader who wants to understand more about the fascinating properties of numbers and geometry, and their relationship to art and life, this is a thought-provoking book.

    Widely praised and much-discussed, this classic book explores how cooperation can emerge in a world of self-seeking egoists—whether superpowers, businesses, or individuals—when there is no central authority to police their actions. The problem of cooperation is central to many different fields. Robert Axelrod recounts the famous computer tournaments in which the “cooperative” program Tit for Tat recorded its stunning victories, explains its application to a broad spectrum of subjects, and suggests how readers can both apply cooperative principles to their own lives and teach cooperative principles to others.

    Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.

    That explains why what many of us long for is simplicity: a life that can be more pared down, peaceful, and focused on the essentials.But finding simplicity is not always easy; it isn’t just a case of emptying out our closets or trimming back commitments in our diaries. True simplicity requires that we understand the roots of our distractions – and develop a canny respect for the stubborn reasons why things can grow complex and overwhelming.This book is a guide to the simpler lives we crave and deserve. It considers how we might achieve simplicity across a range of areas. Along the way, we learn about Zen Buddhism, modernist architecture, monasteries, psychoanalysis, and why we probably don’t need more than three good friends or a few treasured belongings.It isn’t enough that our lives should look simple; they need to be simple from the inside. This book takes a psychological approach, guiding us towards less contorted hearts and minds. We have for too long been drowning in excess and clutter from a confusion about our aspirations; A Simpler Life helps us tune out the static and focus on what properly matters to us.

    Of course, it’s not all cooking; we’ll also run the New York and Chicago marathons, pay visits to Cinderella and Lewis Carroll, and even get to the bottom of a tomato’s identity as a vegetable. This is not the math of our high school classes: mathematics, Cheng shows us, is less about numbers and formulas and more about how we know, believe, and understand anything, including whether our brother took too much cake.At the heart of How to Bake Pi is Cheng’s work on category theory—a cutting-edge “mathematics of mathematics.” Cheng combines her theory work with her enthusiasm for cooking both to shed new light on the fundamentals of mathematics and to give readers a tour of a vast territory no popular book on math has explored before. Lively, funny, and clear, How to Bake Pi will dazzle the initiated while amusing and enlightening even the most hardened math-phobe.

    A masterpiece of technical exposition, it was the basic textbook of astronomy for more than a thousand years, and still is the main source for our knowledge of ancient astronomy. This translation, based on the standard Greek text of Heiberg, makes the work accessible to English readers in an intelligible and reliable form. It contains numerous corrections derived from medieval Arabic translations and extensive footnotes that take account of the great progress in understanding the work made in this century, due to the discovery of Babylonian records and other researches. It is designed to stand by itself as an interpretation of the original, but it will also be useful as an aid to reading the Greek text.

    A child prodigy, Pascal made essential additions to Descartes's work at age sixteen. By age nineteen, he had invented the world's first mechanical calculator. But despite his immense contributions to modern science and mathematical thinking, it is Pascal's wager with God that set him apart from his peers as a man fully engaged with both religious and scientific pursuits.One night in 1654, Pascal had a visit from God, a mystical experience that changed his life. Struggling to explain God's existence to others, Pascal dared to apply his mathematical work to religious faith, playing dice with divinity: he argued for the existence of God, basing his position not on rigorous logical principles as did Aquinas or Anselm of Canterbury, but on outcomes—his famous wager. By applying to the existence of God the same rules that governed the existence and position of the universe itself, Pascal sounded the death knell for medieval "certainties" and paved the way for modern thinking.