By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist. Einstein endorsed this result reluctantly but he could find no way to refute it, since then, neither has anyone else. Yet cosmologists and philosophers alike have proceeded as if this discovery was never made. In A World Without Time, Palle Yourgrau sets out to restore Godel to his rightful place in history, telling the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue the brilliant work they did together.

      “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.”—Nina MacLaughlin, Boston Globe “Engaging, eminently readable . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.”—Judith Goodstein, American Scientist  Harvard geometer and Fields medalist Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers readers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.

    Leibniz' Monadology, one of the most important pieces of the Leibniz corpus, is at once one of the great classics of modern philosophy & one of its most puzzling productions. Because the essay is written in so compactly condensed a fashion, for almost three centuries it has baffled & beguiled those who read it for the first time. Nicholas Rescher accompanies the text of the Monadology section-by-section with relevant excerpts from some of Leibniz' widely scattered discussions of the matters at issue. The result serves a dual purpose of providing a commentary of the Monadology by Leibniz himself, while at the same time supplying an exposition of his philosophy using the Monadology as an outline. The book contains all the materials that even the most careful study of this text could require: a detailed overview of the philosophical background of the work & of its bibliographic ramifications; a presentation of the original French text together with a new, closely faithful English translation; a selection of other relevant Leibniz texts; & a detailed commentary. Rescher also provides a survey of Leibniz' use of analogies & three separate indices of key terms & expressions, Leibniz' French terminology, & citations. Rescher's edition of the Monadology presents Leibniz' ideas faithfully, accurately & accessibly, making it especially valuable to scholars & students alike.

    In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.

    After mulling over the lessons he's learned, the places he's been, and all the miracles and strange occurrences he's witnessed over the course of an enduring career in Hollywood and on the stage, he arrived at one simple rule for living a long and good life: don't die.It's the only one-size-fits-all advice, Shatner argues in Live Long and..: What I Might Have Learned Along the Way, because everyone has a unique life--but, to help us all out, he's more than willing to share stories from his unique life. With a combination of pithy humor and thoughtful vulnerability, Shatner lays out his journey from childhood to peak stardom and all the bumps in the road. (Sometimes the literal road, as in the case of his 2,400-mile motorcycle trip across the country with a bike that didn't function.)William Shatner is one of our most beloved entertainers, and he intends never to stop entertaining. His funny, provocative, and poignant reflections offer an unforgettable read about a remarkable man.

    Called by some, "the theory of everything," superstrings may solve a problem that has eluded physicists for the past 50 years, the final unification of the two great theories of the twentieth century, general relativity and quantum field theory. Now, here is a thoroughly revised, second edition of a course-tested comprehensive introductory graduate text on superstrings which stresses the most current areas of interest, not covered in other presentations, including: - Four-dimensional superstrings - Kac-Moody algebras - Teichm�ller spaces and Calabi-Yau manifolds - M-theory Membranes and D-branes - Duality and BPS relations - Matrix models The book begins with a simple discussion of point particle theory, and uses Feynman path integrals to unify the presentation of superstrings. It has been updated throughout, and three new chapters on M-theory have been added. Prerequisites are an acquaintance with quantum mechanics and relativity.

    

    Misty Knight and Colleen Wing use their underworld connections and government funding to lead them into battle.

    Indeed, numbers are part of every discipline in the sciences and the arts.With 350 illustrations, including diagrams, photographs and computer imagery, the book chronicles the centuries-long search for the meaning of numbers by famous and lesser-known mathematicians, and explains the puzzling aspects of the mathematical world. Topics include:The earliest ideas of numbers and counting Patterns, logic, calculating Natural, perfect, amicable and prime numbers Numerology, the power of numbers, superstition The computer, the Enigma Code Infinity, the speed of light, relativity Complex numbers The Big Bang and Chaos theories The Philosopher's Stone. The Book of Numbers shows enthusiastically that numbers are neither boring nor dull but rather involve intriguing connections, rivalries, secret documents and even mysterious deaths.

    Julia Diggins masterfully recreates the atmosphere of ancient times, when men, using three simple tools, the string, the straightedge, and the shadow, discovered the basic principles and constructions of elementary geometry. Her book reveals how these discoveries related to the early civilizations of Mesopotamia, Egypt, and Greece.The fabric of the story is woven out of archeological and historical records and legends about the major men of mathematics. By reconstructing the events as they might have happened, Diggins enables the attentive reader to easily follow the pattern of reasoning that leads to an ingenious proof of the Pythagorean theorem, an appreciation of the significance of the Golden Mean in art and architecture, and the construction of the five regular solids.Out of print for 34 years, Julia Diggins' classic book is back and is a must-read for middle school students or for parents helping their children through their first geometry course. You will be fascinated with the graphic illustrations and written depiction of how the knowledge and wisdom of so many cultures helped shape our civilization today. This book is popular with teachers and parents who use Jamie York's Making Math Meaningful curriculum books.

    Day...." The articles narrated here are "My Escape From Slavery" (1881) and "Reconstruction" (1866). - Summary by Lee Smalley

    It has an algebra and trigonometry prerequisite, but calculus is preferred.

    The objective here is to explain science in a simple, attractive and fun form that is open to all.The first axiom of this approach was set out as follows: “We believe in the magic of science. We hope to show you that sci-ence is not a secret art, accessible only to a dedicated few. It involves learning about nature and society, and aspects of our existence which affect us all, and which we should all therefore have the chance to understand. We shall interpret science for those who might not speak its language fluently, but want to understand its meaning. We don’t teach, we just tell stories about the beginnings of science, the natural phenomena and the underlying principles through which they occur, and the lives of the people who discovered them.”The aim of the writings collected in this series is to present some key scientific events, ideas and personalities in the form of short stories that are easy and fun to read. Scientific and philo-sophical concepts are explained in a way that anyone may under-stand. Each story may be read separately, but at the same time they all band together to form a wide-ranging introduction to the history of science and areas of contemporary scientific research, as well as some of the recurring problems science has encountered in history and the philosophical dilemmas it raises today.Review“If I were the only survivor on a remote island and all I had with me were this book, a Swiss army knife and a bottle, I would throw the bottle into the sea with the note: ‘Don’t worry, I have everything I need.’”— Ciril Horjak, alias Dr. Horowitz, a comic artist“The writing is understandable, but never simplistic. Instructive, but never patronizing. Straightforward, but never trivial. In-depth, but never too intense.”— Ali Žerdin, editor at Delo, the main Slovenian newspaper“Does science think? Heidegger once answered this question with a decisive No. The writings on modern science skillfully penned by Sašo Dolenc, these small stories about big stories, quickly convince us that the contrary is true. Not only does science think in hundreds of unexpected ways, its intellectual challenges and insights are an inexhaustible source of inspiration and entertainment. The clarity of thought and the lucidity of its style make this book accessible to anyone … in the finest tradition of popularizing science, its achievements, dilemmas and predicaments.”— Mladen Dolar, philosopher and author of A Voice and Nothing More“Sašo Dolenc is undoubtedly one of our most successful authors in the field of popular science, possessing the ability to explain complex scientific achievements to a broader audience in a clear and captivating way while remaining precise and scientific. His collection of articles is of particular importance because it encompasses all areas of modern science in an unassuming, almost light-hearted manner.”— Boštjan Žekš, physicist and former president of the Slovenian Academy of Sciences and Arts

    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.

    40 illustrations throughout.