He believes that we should investigate what makes some countries more capable than others. Complex products—from films to robots, apps to automobiles—are a physical distillation of an economy’s knowledge, a measurable embodiment of its education, infrastructure, and capability. Economic wealth accrues when applications of this knowledge turn ideas into tangible products; the more complex its products, the more economic growth a country will experience.A radical new interpretation of global economics, Why Information Grows overturns traditional assumptions about the development of economies and the origins of wealth and takes a crucial step toward making economics less the dismal science and more the insightful one.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    And two giants at the foundations of modern science were converging, step-by-step, on the answer: Albert Einstein, an young, obscure German physicist experimenting with measuring time using telegraph networks and with the coordination of clocks at train stations; and the renowned mathematician Henri Poincaré, president of the French Bureau of Longitude, mapping time coordinates across continents. Each found that to understand the newly global world, he had to determine whether there existed a pure time in which simultaneity was absolute or whether time was relative.Esteemed historian of science Peter Galison has culled new information from rarely seen photographs, forgotten patents, and unexplored archives to tell the fascinating story of two scientists whose concrete, professional preoccupations engaged them in a silent race toward a theory that would conquer the empire of time.

    Despite early success in the corporate world, his first attempt to pursue his entrepreneurial dream ended in rejection. Jia was crushed and spiraled into a period of deep self-doubt. But he realized that his fear of rejection was a bigger obstacle than any single rejection would ever be, and he needed to find a way to cope with being told no without letting it destroy him. Thus was born his "100 days of rejection" experiment, during which he willfully sought rejection on a daily basis - from requesting a lesson in sales from a car salesman (no) to asking a flight attendant if he could make an announcement on the loudspeaker (yes) to his famous request to get Krispy Kreme doughnuts in the shape of Olympic rings (yes, with a viral video to prove it).Jia learned that even the most preposterous wish may be granted if you ask in the right way, and here he shares the secret of successful asking, how to pick targets, and how to tell when an initial no can be converted into something positive. But more important, he learned techniques for steeling himself against rejection and ways to develop his own confidence - a plan that can't be derailed by a single setback.Filled with great stories and valuable insight, Rejection Proof is a fun and thoughtful examination of how to overcome fear and dare to live more boldly.

    From the early Greek influences to the Middle Ages and the Renaissance to the end of the 19th century, trace the fascinating foundation of mathematics as it developed through the ages. Aristotle, Galileo, Kepler, Newton: you know the names. Now here's what they really did, and the effect their discoveries had on our culture, all explained in a way the layperson can understand. Begin with the basis of arithmetic (Plato and the introduction of geometry), and discover why the use of Arabic numerals was critical to the development of both commerce and science. The development of calculus made space travel a reality, while the abacus prefigured the computer. The greats examined in depth include Leonardo da Vinci, a brilliant mathematician as well as artist; Pascal, who laid out the theory of probabilities; and Fermat, whose intriguing theory has only recently been solved.

    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.

    The shift toward automation is about to create a tsunami of unemployment. Not in the distant future—now. One recent estimate predicts 45 million American workers will lose their jobs within the next twelve years—jobs that won't be replaced. In a future marked by restlessness and chronic unemployment, what will happen to American society? In The War on Normal People, Andrew Yang paints a dire portrait of the American economy. Rapidly advancing technologies like artificial intelligence, robotics and automation software are making millions of Americans' livelihoods irrelevant. The consequences of these trends are already being felt across our communities in the form of political unrest, drug use, and other social ills. The future looks dire-but is it unavoidable? In The War on Normal People, Yang imagines a different future—one in which having a job is distinct from the capacity to prosper and seek fulfillment. At this vision's core is Universal Basic Income, the concept of providing all citizens with a guaranteed income-and one that is rapidly gaining popularity among forward-thinking politicians and economists. Yang proposes that UBI is an essential step toward a new, more durable kind of economy, one he calls "human capitalism."

    Astrophysicist Adam Frank traces the question of alien life and intelligence from the ancient Greeks to the leading thinkers of our own time, and shows how we as a civilization can only hope to survive climate change if we recognize what science has recently discovered: that we are just one of ten billion trillion planets in the Universe, and it’s highly likely that many of those planets hosted technologically advanced alien civilizations. What’s more, each of those civilizations must have faced the same challenge of civilization-driven climate change.Written with great clarity and conviction, Light of the Stars builds on the inspiring work of pioneering scientists such as Frank Drake and Carl Sagan, whose work at the dawn of the space age began building the new science of astrobiology; Jack James, the Texas-born engineer who drove NASA’s first planetary missions to success; Vladimir Vernadsky, the Russian geochemist who first envisioned the Earth’s biosphere; and James Lovelock and Lynn Margulis, who invented Gaia theory. Frank recounts the perilous journey NASA undertook across millions of miles of deep space to get its probes to Venus and Mars, yielding our first view of the cosmic laws of planets and climate that changed our understanding of our place in the universe.Thrilling science at the grandest of scales, Light of the Stars explores what may be the largest question of all: What can the likely presence of life on other worlds tell us about our own fate?

    Snyder exposes the political passions, religious impulses, friendships, rivalries, and love of knowledge—and power—that drove these extraordinary men.  Whewell (who not only invented the word “scientist,” but also founded the fields of crystallography, mathematical economics, and the science of tides), Babbage (a mathematical genius who invented the modern computer), Herschel (who mapped the skies of the Southern Hemisphere and contributed to the invention of photography), and Jones (a curate who shaped the science of economics) were at the vanguard of the modernization of science.  This absorbing narrative of people, science and ideas  chronicles the intellectual revolution inaugurated by these men, one that continues to mold our understanding of the world around us and of our place within it.  Drawing upon the voluminous correspondence between the four men over the fifty years of their work, Laura J. Snyder shows how friendship worked to spur the men on to greater accomplishments, and how it enabled them to transform science and help create the modern world.

    The city had been dumping barely treated sewage into its harbor, coating the seafloor with a layer of "black mayonnaise." Fisheries collapsed, wildlife fled, and locals referred to floating tampon applicators as "beach whistles." But before the plant could start operating, a team of divers had to make a perilous journey to the end of a 10-mile tunnel-devoid of light and air-to complete the construction. Five went in; two never came out. Drawing on hundreds of interviews and thousands of documents, award-winning reporter Neil Swidey re-creates the tragedy and its aftermath in an action-packed narrative. The climax comes when the hard-partying DJ Gillis and his friend Billy Juse trade jobs at a pivotal moment in the mission, sentencing one diver to death and the other to a trauma-induced heroin addiction that eventually lands him in prison. Trapped Under the Sea reminds us that behind every bridge, highway, dam, and tunnel-behind the infrastructure that makes modern life possible-lies unsung bravery and extraordinary sacrifice.

    Ask them the meaning of 'relativity' and few of them will be able to tell you what it is.The basic principles of relativity have not changed since Russell first published his lucid guide for the general reader. The ABC of Relativity is Bertrand Russell's most brilliant work of scientific popularisation. With marvellous lucidity he steers the reader who has no knowledge of maths or physics through the subtleties of Einstein's thinking. In easy, assimilable steps, he explains the theories of special and general relativity and describes their practical application to, amongst much else, discoveries about gravitation and the invention of the hydrogen bomb.

    Rucker acquaints us with Godel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations.Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Godel's incompleteness theorems. His personal encounters with Godel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.

    Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be "computable," creating the field of computability theory in the process, a foundation of present-day computer programming.The book expands Turing's original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing's statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others.Interwoven into the narrative are the highlights of Turing's own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of "gross indecency," and his early death by apparent suicide at the age of 41.

    Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues π and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.-- "Notices of the American Mathematical Society"

    How can it be possible that the world we see is not objective reality? And how can our senses be useful if they are not communicating the truth? Hoffman grapples with these questions and more over the course of this eye-opening work.Ever since Homo sapiens has walked the earth, natural selection has favored perception that hides the truth and guides us toward useful action, shaping our senses to keep us alive and reproducing. We observe a speeding car and do not walk in front of it; we see mold growing on bread and do not eat it. These impressions, though, are not objective reality. Just like a file icon on a desktop screen is a useful symbol rather than a genuine representation of what a computer file looks like, the objects we see every day are merely icons, allowing us to navigate the world safely and with ease.The real-world implications for this discovery are huge. From examining why fashion designers create clothes that give the illusion of a more “attractive” body shape to studying how companies use color to elicit specific emotions in consumers, and even dismantling the very notion that spacetime is objective reality, The Case Against Reality dares us to question everything we thought we knew about the world we see.