This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

    They forged economic dynasties, built mansions and estates, assembled libraries, endowed charities, and advised a German kaiser and two American presidents. But their very success made the Warburgs lightning rods for anti-Semitism, and their sense of patriotism became increasingly dangerous in a Germany that had declared Jews the enemy.Ron Chernow's hugely fascinating history is a group portrait of a clan whose members were renowned for their brilliance, culture, and personal energy yet tragically vulnerable to the dark and irrational currents of the twentieth century.

    "A stunning memoir from the astronaut who spent a record-breaking year aboard the International Space Station – a candid account of his remarkable voyage, the journeys that preceded it, and his colorful formative years." Inside book cover comments.

    In the spring of 1940, the aspiring but unknown writer Albert Camus and budding scientist Jacques Monod were quietly pursuing ordinary, separate lives in Paris. After the German invasion and occupation of France, each joined the Resistance to help liberate the country from the Nazis, ascended to prominent, dangerous roles, and were very lucky to survive. After the war and through twists of circumstance, they became friends, and through their passionate determination and rare talent, they emerged as leading voices of modern literature and biology, each receiving the Nobel Prize in their respective fields. Drawing upon a wealth of previously unpublished and unknown material gathered over several years of research, Brave Genius tells the story of how each man endured the most terrible episode of the twentieth century and then blossomed into extraordinarily creative and engaged individuals. It is a story of the transformation of ordinary lives into exceptional lives by extraordinary events--of courage in the face of overwhelming adversity, the flowering of creative genius, deep friendship, and of profound concern for and insight into the human condition.

    

    Purchasers are entitled to a free trial membership in the General Books Club where they can select from more than a million books without charge. Subjects: Astronomy; History / General; Juvenile Nonfiction / Science

    Weaving together his immersive interest in people and history with insights gathered from his own experiences, Stephen Wolfram gives an ennobling look at some of the individuals whose ideas and creations have helped shape our world today. Contents includes biographical sketches of: Richard Feynman Kurt Godel Alan Turing John von Neumann George Boole Ada Lovelace Gottfried Leibniz Benoit Mandelbrot Steve Jobs Marvin Minsky Russell Towle Bertrand Russell Alfred Whitehead Richard Crandall Srinivasa Ramanujan Solomon Golomb

    Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles.This completely new translation, the first in 270 years, is based on the third (1726) edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the Principia also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system.The illuminating Guide to the Principia by I. Bernard Cohen, along with his and Anne Whitman's translation, will make this preeminent work truly accessible for today's scientists, scholars, and students.

    Finished only weeks before his death in 1994, it is the self-portrait of one of this century's most original and influential intellectuals.Trained in physics and astronomy, Feyerabend was best known as a philosopher of science. But he emphatically was not a builder of theories or a writer of rules. Rather, his fame was in powerful, plain-spoken critiques of "big" science and "big" philosophy. Feyerabend gave voice to a radically democratic "epistemological anarchism:" he argued forcefully that there is not one way to knowledge, but many principled paths; not one truth or one rationality but different, competing pictures of the workings of the world. "Anything goes," he said about the ways of science in his most famous book, Against Method. And he meant it.Here, for the first time, Feyerabend traces the trajectory that led him from an isolated, lower-middle-class childhood in Vienna to the height of international academic success. He writes of his experience in the German army on the Russian front, where three bullets left him crippled, impotent, and in lifelong pain. He recalls his promising talent as an operatic tenor (a lifelong passion), his encounters with everyone from Martin Buber to Bertolt Brecht, innumerable love affairs, four marriages, and a career so rich he once held tenured positions at four universities at the same time.Although not written as an intellectual autobiography, Killing Time sketches the people, ideas, and conflicts of sixty years. Feyerabend writes frankly of complicated relationships with his mentor Karl Popper and his friend and frequent opponent Imre Lakatos, and his reactions to a growing reputation as the "worst enemy of science."

    But your pleasure and prowess at games, gambling, and other numerically related pursuits can be heightened with this entertaining volume, in which the authors offer a fascinating view of some of the lesser-known and more imaginative aspects of mathematics.A brief and breezy explanation of the new language of mathematics precedes a smorgasbord of such thought-provoking subjects as the googolplex (the largest definite number anyone has yet bothered to conceive of); assorted geometries — plane and fancy; famous puzzles that made mathematical history; and tantalizing paradoxes. Gamblers receive fair warning on the laws of chance; a look at rubber-sheet geometry twists circles into loops without sacrificing certain important properties; and an exploration of the mathematics of change and growth shows how calculus, among its other uses, helps trace the path of falling bombs.Written with wit and clarity for the intelligent reader who has taken high school and perhaps college math, this volume deftly progresses from simple arithmetic to calculus and non-Euclidean geometry. It “lives up to its title in every way [and] might well have been merely terrifying, whereas it proves to be both charming and exciting." — Saturday Review of Literature.

    In 1905 an unknown 26-year-old clerk at the Swiss Patent Office, who had supposedly failed math in school, burst on to the scientific scene and swept away the hidebound theories of the day. The clerk, Albert Einstein, introduced a new and unexpected understanding of the universe and launched the two great revolutions of twentieth-century physics, relativity and quantum mechanics. The obscure origin and wide-ranging brilliance of the work recalled Isaac Newton’s “annus mirabilis” (miracle year) of 1666, when as a 23-year-old seeking safety at his family manor from an outbreak of the plague, he invented calculus and laid the foundations for his theory of gravity. Like Newton, Einstein quickly became a scientific icon--the image of genius and, according to Time magazine, the Person of the Century.The actual story is much more interesting. Einstein himself once remarked that “science as something coming into being ... is just as subjectively, psychologically conditioned as are all other human endeavors.” In this profile, the historian of science L. Randles Lagerstrom takes you behind the myth and into the very human life of the young Einstein. From family rifts and girlfriend troubles to financial hardships and jobless anxieties, Einstein’s early years were typical of many young persons. And yet in the midst of it all, he also saw his way through to profound scientific insights. Drawing upon correspondence from Einstein, his family, and his friends, Lagerstrom brings to life the young Einstein and enables the reader to come away with a fuller and more appreciative understanding of Einstein the person and the origins of his revolutionary ideas.About the cover image: While walking to work six days a week as a patent clerk in Bern, Switzerland, Einstein would pass by the famous "Zytglogge" tower and its astronomical clocks. The daily juxtaposition was fitting, as the relative nature of time and clock synchronization would be one of his revolutionary discoveries in the miracle year of 1905.

    While he was working on his Atomic Energy badge for the Boy Scouts, David’s obsessive attention turned to nuclear energy. Throwing caution to the wind, he plunged into a new project: building a model nuclear reactor in his backyard garden shed.Posing as a physics professor, David solicited information on reactor design from the U.S. government and from industry experts. Following blueprints he found in an outdated physics textbook, David cobbled together a crude device that threw off toxic levels of radiation. His wholly unsupervised project finally sparked an environmental emergency that put his town’s forty thousand suburbanites at risk. The EPA ended up burying his lab at a radioactive dumpsite in Utah. This offbeat account of ambition and, ultimately, hubris has the narrative energy of a first-rate thriller.

    The latter half of our century has seen its own Renaissance - informations technology has changed irrevocable the way we live, work, and think about the world. We are fortunate, therefore, that the authors of Out of Their Minds have been able to talk so candidly with the founders of computer science. In Out of their Minds, readers will hear the Newtons and Euclids of the computer age as they talk about their discoveries in information technology that have changed forever the way we live, work, and think about the world. Based on interviews by freelance writer Cathy Lazere and the expertise of computer scientist Dennis Shasha, Out of their Minds introduces readers to fifteen of the planet's foremost computer scientists, including eight winners of the Turing Award, computing's Nobel Prize. The scientists reveal themselves in fascinating anecdotes about their early inspirations and influences, their contributions to computer science, and their thoughts on its explosive future. These are the programmers whose work

    No other investor--Warren Buffett, Peter Lynch, Ray Dalio, Steve Cohen, or George Soros--can touch his record. Since 1988, Renaissance's signature Medallion fund has generated average annual returns of 66 percent. The firm has earned profits of more than $100 billion; Simons is worth twenty-three billion dollars.Drawing on unprecedented access to Simons and dozens of current and former employees, Zuckerman, a veteran Wall Street Journal investigative reporter, tells the gripping story of how a world-class mathematician and former code breaker mastered the market. Simons pioneered a data-driven, algorithmic approach that's sweeping the world.As Renaissance became a market force, its executives began influencing the world beyond finance. Simons became a major figure in scientific research, education, and liberal politics. Senior executive Robert Mercer is more responsible than anyone else for the Trump presidency, placing Steve Bannon in the campaign and funding Trump's victorious 2016 effort. Mercer also impacted the campaign behind Brexit.The Man Who Solved the Market is a portrait of a modern-day Midas who remade markets in his own image, but failed to anticipate how his success would impact his firm and his country. It's also a story of what Simons's revolution means for the rest of us.