The term “complexity” can be misleading, however, because what makes West’s discoveries so beautiful is that he has found an underlying simplicity that unites the seemingly complex and diverse phenomena of living systems, including our bodies, our cities and our businesses. Fascinated by issues of aging and mortality, West applied the rigor of a physicist to the biological question of why we live as long as we do and no longer. The result was astonishing, and changed science, creating a new understanding of energy use and metabolism: West found that despite the riotous diversity in the sizes of mammals, they are all, to a large degree, scaled versions of each other. If you know the size of a mammal, you can use scaling laws to learn everything from how much food it eats per day, what its heart-rate is, how long it will take to mature, its lifespan, and so on. Furthermore, the efficiency of the mammal’s circulatory systems scales up precisely based on weight: if you compare a mouse, a human and an elephant on a logarithmic graph, you find with every doubling of average weight, a species gets 25% more efficient—and lives 25% longer. This speaks to everything from how long we can expect to live to how many hours of sleep we need. Fundamentally, he has proven, the issue has to do with the fractal geometry of the networks that supply energy and remove waste from the organism's body. West's work has been game-changing for biologists, but then he made the even bolder move of exploring his work's applicability to cities. Cities, too, are constellations of networks and laws of scalability relate with eerie precision to them. For every doubling in a city's size, the city needs 15% less road, electrical wire, and gas stations to support the same population. More amazingly, for every doubling in size, cities produce 15% more patents and more wealth, as well as 15% more crime and disease. This broad pattern lays the groundwork for a new science of cities. Recently, West has applied his revolutionary work on cities and biological life to the business world. This investigation has led to powerful insights into why some companies thrive while others fail. The implications of these discoveries are far-reaching, and are just beginning to be explored. Scale is a thrilling scientific adventure story about the elemental natural laws that bind us together in simple but profound ways. Through the brilliant mind of Geoffrey West, we can envision how cities, companies and biological life alike are dancing to the same simple, powerful tune, however diverse and unrelated they are to each other.From the Hardcover edition.

    Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh's algorithmic approach emphasizes problem-solving techniques. The Seventh Edition reflects user and reviewer feedback on both content and organization.

    "A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

    *Includes some of Martin's most colorful quotes. *Includes a Bibliography for further reading. "If people want to think I get drunk and stay out all night, let 'em. That's how I got here, you know." - Dean Martin A lot of ink has been spilled covering the lives of history's most influential figures, but how much of the forest is lost for the trees? In Charles River Editors' American Legends series, readers can get caught up to speed on the lives of America's most important men and women in the time it takes to finish a commute, while learning interesting facts long forgotten or never known. Like Frank Sinatra, Dean Martin is an American legend for his longevity and success across a garden variety of different platforms. Martin began as a nightclub singer, performed in a comedy act, starred in films, recorded hit albums, and capped his career by serving as a television host. In fact, there may be no star who was better able to transcend the different avenues of entertainment. Martin's success was made all the more amazing by the fact that he never had to change his personality or persona to find success in his different endeavors. From the beginning, Martin's public persona remained largely unchanged. He grew more famous and wealthy, but he always remained the smooth-talking Italian with the easy charm and the cool veneer. As Jerry Lewis noted in his memoirs about Martin, "Dean had this uncanny way of making everything bad look like it wasn't all that bad." If anything, Martin suggested that no matter the circumstances, people can always face their situation with leisurely charm. Martin's versatility is unprecedented even today, an era in which stars routinely alternate between film and musical careers. Martin was able to simultaneously work across different media at the same time; even after rising to fame as a singer, he continued to perform with Jerry Lewis and star in films. But after his film career took off, he continued to perform the crooning style of music that had made him famous and had long since been outdated. While other actors were forced to drastically alter their persona to keep up with the times, Martin's ability to fuse suave glamour with an everyday ordinariness ensured he didn't need to transform anything. Martin's life and career are often compared to his close friend and contemporary Frank Sinatra, and for good reason. Both came from proud Italian families, both were cohorts in the famed Rat Pack in the 1960s, and they each maintained success even late in their careers. However, Sinatra's career was filled with far more ups and downs than Martin, and his public image experienced highs and lows along with it. It's also somewhat ironic that it was Martin who Anglicized his name but remained a bigger Italian icon than Sinatra. They each began their careers as Italian crooners, but Martin maintained his style while Sinatra adopted a brasher, more "All-American" singing method. Martin never strayed far from his humble background, even as he became one of America's biggest stars. American Legends: The Life of Dean Martin profiles the life and career of one of America's most famous performers. Along with pictures of important people, places, and events, you will learn about Dean Martin like you never have before, in no time at all.

    Above all it fizzes with a dizzying mix of deliciously vital ideas. . . A staggering achievement' Tim HarfordThe smartphones in our pockets and computers like brains. The vagaries of game theory and evolutionary biology. Self-replicating moon bases and nuclear weapons. All bear the fingerprints of one remarkable man: John von Neumann.Born in Budapest at the turn of the century, von Neumann is one of the most influential scientists to have ever lived. His colleagues believed he had the fastest brain on the planet - bar none. He was instrumental in the Manhattan Project and helped formulate the bedrock of Cold War geopolitics and modern economic theory. He created the first ever programmable digital computer. He prophesied the potential of nanotechnology and, from his deathbed, expounded on the limits of brains and computers - and how they might be overcome.Taking us on an astonishing journey, Ananyo Bhattacharya explores how a combination of genius and unique historical circumstance allowed a single man to sweep through so many different fields of science, sparking revolutions wherever he went.Insightful and illuminating, The Man from the Future is a thrilling intellectual biography of the visionary thinker who shaped our century.

    It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. He presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to science and social development. Woven together in a tapestry of entertaining stories, scientific curiosities, and educational insights, the book more than lives up to the title Trigonometric Delights.Maor, whose previous books have demystified the concept of infinity and the unusual number "e," begins by examining the "proto-trigonometry" of the Egyptian pyramid builders. He shows how Greek astronomers developed the first true trigonometry. He traces the slow emergence of modern, analytical trigonometry, recounting its colorful origins in Renaissance Europe's quest for more accurate artillery, more precise clocks, and more pleasing musical instruments. Along the way, we see trigonometry at work in, for example, the struggle of the famous mapmaker Gerardus Mercator to represent the curved earth on a flat sheet of paper; we see how M. C. Escher used geometric progressions in his art; and we learn how the toy Spirograph uses epicycles and hypocycles.Maor also sketches the lives of some of the intriguing figures who have shaped four thousand years of trigonometric history. We meet, for instance, the Renaissance scholar Regiomontanus, who is rumored to have been poisoned for insulting a colleague, and Maria Agnesi, an eighteenth-century Italian genius who gave up mathematics to work with the poor--but not before she investigated a special curve that, due to mistranslation, bears the unfortunate name "the witch of Agnesi." The book is richly illustrated, including rare prints from the author's own collection. Trigonometric Delights will change forever our view of a once dreaded subject.

    In Third Thoughts Steven Weinberg casts a wide net: from the cosmological to the personal, from astronomy, quantum mechanics, and the history of science to the limitations of current knowledge, the art of discovery, and the rewards of getting things wrong.Winner of the Nobel Prize in Physics and author of the classic The First Three Minutes, Weinberg shares his views on some of the most fundamental and fascinating aspects of physics and the universe. But he does not seclude science behind disciplinary walls, or shy away from politics, taking on what he sees as the folly of manned spaceflight, the harms of inequality, and the importance of public goods. His point of view is rationalist, realist, reductionist, and devoutly secularist.Weinberg is that great rarity, a prize-winning physicist who is entertaining and accessible. The essays in Third Thoughts, some of which appear here for the first time, will engage, provoke, and inform--and never lose sight of the human dimension of scientific discovery and its consequences for our endless drive to probe the workings of the cosmos.

    It comprises non-technical essays on every aspect of the vast subject, including articles by scores of eminent mathematicians and other thinkers.

    Since the publication of the First Edition over thirty years ago, Div, Grad, Curl, and All That has been widely renowned for its clear and concise coverage of vector calculus, helping science and engineering students gain a thorough understanding of gradient, curl, and Laplacian operators without required knowledge of advanced mathematics.

    Robert Oppenheimer, Freeman Dyson has composed an autobiography unlike any other. Dyson evocatively conveys the thrill of a deep engagement with the world-be it as scientist, citizen, student, or parent. Detailing a unique career not limited to his groundbreaking work in physics, Dyson discusses his interest in minimizing loss of life in war, in disarmament, and even in thought experiments on the expansion of our frontiers into the galaxies.

    He decried the internment of Japanese-Americans in World War Two, agitated against nuclear weapons, promoted vitamin C as a cure for the common cold and researched the idea of DNA.

    It features a visual presentation, designed to encourage learning; revised exercises to ensure clarity, balance and relevance; and clear commentary on the difficult subject of critical multivariable calculus topics.

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    The selections range from his earliest days as a theoretical physicist to his death in 1955; from such subjects as relativity, nuclear war or peace, and religion and science, to human rights, economics, and government.

    Volume Two dramatizes the lives of Omar Khayyam, Albert Einstein, Ada Lovelace, and others.Book Details: Format: Paperback Publication Date: 6/20/1995 Pages: 152 Reading Level: Age 8 and Up