However, it is one of the basic principles of quantum theory, the most widely accepted explanation of the subatomic world - and one of the fascinating subjects dealt with in Equations of Eternity.

    Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the humanist idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos.What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

    The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics and in general ontology.

    presidential elections have been won by the second most popular candidate. The reason was a "spoiler"--a minor candidate who takes enough votes away from the most popular candidate to tip the election to someone else. The spoiler effect is more than a glitch. It is a consequence of one of the most surprising intellectual discoveries of the twentieth century: the "impossibility theorem" of Nobel laureate economist Kenneth Arrow. The impossibility theorem asserts that voting is fundamentally unfair--a finding that has not been lost on today's political consultants. Armed with polls, focus groups, and smear campaigns, political strategists are exploiting the mathematical faults of the simple majority vote. In recent election cycles, this has led to such unlikely tactics as Republicans funding ballot drives for Green spoilers and Democrats paying for right-wing candidates' radio ads. Gaming the Vote shows that there is a solution to the spoiler problem that will satisfy both right and left. A systemcalled range voting, already widely used on the Internet, is the fairest voting method of all, according to computer studies. Despite these findings, range voting remains controversial, and Gaming the Vote assesses the obstacles confronting any attempt to change the American electoral system. The latest of several books by William Poundstone on the theme of how important scientific ideas have affected the real world, Gaming the Vote is a wry exposé of how the political system really works, and a call to action.

     During fourteen years, from 1955 to 1969, the Soviet Union and the United States of America were engaged in a dramatic race against each other to conquer space. This period encompassed dramatic victories, humbling defeats, and more than one tragedy. This is a story of human courage and ingenuity at its best and political maneuvering at its worst, of almost unbelievable technological progress undertaken with the object not just of advancing human knowledge but also of proving the superiority of one country over another. Inside you will read about... ✓ From Missiles to Rockets ✓ Russia Takes the Lead ✓ Early American Failures ✓ The First Men in Space ✓ Fatalities on Both Sides ✓ The Moon Landing And much more! The space race culminated in man setting foot upon the moon, but each milestone on the way to that final goal was bitterly contested. Two powerful nations pledged a substantial part of their national resources to beat the other in a scientific and technological race to be the first to achieve new records. In terms of contests between major powers, there has never been anything quite as dramatic, public, and sustained as the space race; it remains one of the most fascinating and engaging episodes of the Cold War.

    Who invented zero? Why are there 60 seconds in a minute? Can a butterfly's wings really cause a storm on the far side of the world? In 50 concise essays, Professor Tony Crilly explains the mathematical concepts that allow use to understand and shape the world around us.

    It doesn't matter how small the tunnel is you never know what's around the bend ... You don't know if it's abandoned, you don't know if it's booby trapped and you don't know why the tunnel is there in the first place."They were young, they were Australian, they were Army engineers and they were the first allied soldiers to risk their lives in the darkness of the Vietcong tunnels of South Vietnam. Staring death squarely in the face every day, not only did they follow their enemy down into these unknown underground labyrinths, but matched the Vietcong's jungle warfare skills and defused thousands of their clever booby traps.Off duty, it was a different story. The bad boys of 3 Field Troop were a boozing, brawling, bonking bunch of larrikins, who cut a swathe through the bars and brothels of Saigon, fought American Military Police to a standstill, built a secret casino and booby-trapped their own HQ to teach their officers a lesson.Thrilling, inspiring and action packed, this is the true story of the unsung heroes of Australia's war in Vietnam. Living up to their motto of 'We Make and We Break', they created the legend of the Tunnel Rats.

    It is the mathematical method for the analysis of things that change, and since in the natural world we are surrounded by change, the development of calculus was a huge breakthrough in the history of mathematics. But it is also something of a mathematical adventure, largely because of the way infinity enters at virtually every twist and turn...In The Calculus Story David Acheson presents a wide-ranging picture of calculus and its applications, from ancient Greece right up to the present day. Drawing on their original writings, he introduces the people who helped to build our understanding of calculus. With a step by step treatment, he demonstrates how to start doing calculus, from the very beginning.

    He solidified his standing as the nation's foremost political forecaster with his near perfect prediction of the 2012 election. Silver is the founder and editor in chief of FiveThirtyEight.com. Drawing on his own groundbreaking work, Silver examines the world of prediction, investigating how we can distinguish a true signal from a universe of noisy data. Most predictions fail, often at great cost to society, because most of us have a poor understanding of probability and uncertainty. Both experts and laypeople mistake more confident predictions for more accurate ones. But overconfidence is often the reason for failure. If our appreciation of uncertainty improves, our predictions can get better too. This is the "prediction paradox": The more humility we have about our ability to make predictions, the more successful we can be in planning for the future.In keeping with his own aim to seek truth from data, Silver visits the most successful forecasters in a range of areas, from hurricanes to baseball, from the poker table to the stock market, from Capitol Hill to the NBA. He explains and evaluates how these forecasters think and what bonds they share. What lies behind their success? Are they good-or just lucky? What patterns have they unraveled? And are their forecasts really right? He explores unanticipated commonalities and exposes unexpected juxtapositions. And sometimes, it is not so much how good a prediction is in an absolute sense that matters but how good it is relative to the competition. In other cases, prediction is still a very rudimentary-and dangerous-science.Silver observes that the most accurate forecasters tend to have a superior command of probability, and they tend to be both humble and hardworking. They distinguish the predictable from the unpredictable, and they notice a thousand little details that lead them closer to the truth. Because of their appreciation of probability, they can distinguish the signal from the noise.

    More people in Western Europe thought quantitatively in the sixteenth century than in any other part of the world, enabling them to become the world's leaders. With amusing detail and historical anecdote, Alfred Crosby discusses the shift from qualitative to quantitative perception that occurred during the late Middle Ages and Renaissance. Alfred W. Crosby is the author of five books, including the award-winning Ecological Imperialism: The Biological Expansion of Europe, 900-1900 (Cambridge, 1986)

    For real.If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel.Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry," from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.

    Illustrated.

    Yet you'd have to fly every day for the next 26,000 years to assure yourself of dying in a crash. A leisurely canoe ride is more than 100 times deadlier. Think city streets are unsafe? You're more likely to come to harm in your own home, where every year you stand a 1 in 650 chance of being injured by your bed, mattress, or pillows—and each year 800 Americans die in accidents involving soft furnishings.We live in a world governed by fear, where packets of peanuts "may contain nuts" and children must be ever on the alert to "stranger danger." And yet, life expectancy has never been higher. Crime rates have plunged. Even unintentional injuries are down. So if we're so safe, why are we so afraid?How to Live Dangerously is a hilarious, straight-talking look at the things that terrify us. It considers life's real risks, not to mention the often ridiculous methods we've contrived to keep ourselves "safe." It encourages you to ignore fearmongers and embrace a new kind of freedom, in which we all worry a little less—and live a whole lot more.

    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.

    Wilczek’s groundbreaking work in quantum physics was inspired by his intuition to look for a deeper order of beauty in nature. In fact, every major advance in his career came from this intuition: to assume that the universe embodies beautiful forms, forms whose hallmarks are symmetry—harmony, balance, proportion—and economy. There are other meanings of “beauty,” but this is the deep logic of the universe—and it is no accident that it is also at the heart of what we find aesthetically pleasing and inspiring.Wilczek is hardly alone among great scientists in charting his course using beauty as his compass. As he reveals in A Beautiful Question, this has been the heart of scientific pursuit from Pythagoras, the ancient Greek who was the first to argue that “all things are number,” to Galileo, Newton, Maxwell, Einstein, and into the deep waters of twentiethcentury physics. Though the ancients weren’t right about everything, their ardent belief in the music of the spheres has proved true down to the quantum level. Indeed, Wilczek explores just how intertwined our ideas about beauty and art are with our scientific understanding of the cosmos.Wilczek brings us right to the edge of knowledge today, where the core insights of even the craziest quantum ideas apply principles we all understand. The equations for atoms and light are almost literally the same equations that govern musical instruments and sound; the subatomic particles that are responsible for most of our mass are determined by simple geometric symmetries. The universe itself, suggests Wilczek, seems to want to embody beautiful and elegant forms. Perhaps this force is the pure elegance of numbers, perhaps the work of a higher being, or somewhere between. Either way, we don’t depart from the infinite and infinitesimal after all; we’re profoundly connected to them, and we connect them. When we find that our sense of beauty is realized in the physical world, we are discovering something about the world, but also something about ourselves.Gorgeously illustrated, A Beautiful Question is a mind-shifting book that braids the age-old quest for beauty and the age-old quest for truth into a thrilling synthesis. It is a dazzling and important work from one of our best thinkers, whose humor and infectious sense of wonder animate every page. Yes: The world is a work of art, and its deepest truths are ones we already feel, as if they were somehow written in our souls.