This book will lead you down the rabbit hole in search of something we can point to, hang our hats on and say this is real, On the way, Jim Baggott examines some of the things that have been said about reality by a few of the world's greatest thinkers-from the philosophers of ancient Greece to modern scientists and social theorists. Jim Baggott is the author of The Meaning of Quantum Physics and Beyond Measure: Modern Physics, Philosophy, and Quantum Theory, both published by Oxford University Press. He lives in England.

    The Golden Section—otherwise known as phi, the golden mean, or the golden ratio—is one of the most elegant and beautiful rations in the universe.Defined as a line segment divided into two unequal parts, such that the ratio of the shorter portion to the longer portion is the same as the ratio of the longer portion to the whole, it pops up throughout nature—in water, DNA, the proportions of fish and butterflies, and the number of teeth we possess—as well as in art and architecture, music, philosophy, science, and mathematics.Beautifully illustrated, The Golden Section tells the story of this remarkable construct and its wide-ranging impact on civilization and the natural world.

    

    - help is finally at hand. That help comes in the comfortingly accessible form of Stephen Trombley's Short History of Western Thought, which outlines the 2,500-year history of European ideas from the philosophers of Classical Antiquity to the thinkers of today, No major representative of any significant strand of Western thought escapes Trombley's attention: the Christian Scholastic theologians of the Middle Ages, the great philosophers of the Enlightenment, the German idealists from Kant to Hegel; the utilitarians Bentham and Mill; the transcendentalists Emerson and Thoreau; Kierkegaard and the existentialists; the analytic philosophers Russell, Moore, Whitehead and Wittgenstein; and - last but not least - the four shapers-in-chief of our modern world: the philosopher, historian and political theorist Karl Marx; the naturalist Charles Darwin, proposer of the theory of evolution; Sigmund Freud, the father of psychoanalysis; and the theoretical physicist Albert Einstein, begetter of the special and general theories of relativity and founder of post-Newtonian physics.

    But a dispute over its discovery sowed the seeds of discontent between two of the greatest scientific giants of all time - Sir Isaac Newton and Gottfried Wilhelm Leibniz." "Today Newton and Leibniz are generally considered the twin independent inventors of calculus. They are both credited with giving mathematics its greatest push forward since the time of the Greeks. Had they known each other under different circumstances, they might have been friends. But in their own lifetimes, the joint glory of calculus was not enough for either and each declared war against the other, openly and in secret." This long and bitter dispute has been swept under the carpet by historians - perhaps because it reveals Newton and Leibniz in their worst light - but The Calculus Wars tells the full story in narrative form for the first time. This history ultimately exposes how these twin mathematical giants were brilliant, proud, at times mad, and in the end completely human.

    The attacks have come not only from traditional conservatives but increasingly from the postmodern left. In this essay, Stephen Hicks presents and dissects the philosophical arguments made by the postmoderns for speech restrictions and responds with a vigorous and updated liberal case for free speech.

    Beautifully illustrated with old engravings as well as contemporary imagery, Sacred Number introduces basic counting systems; significant numbers from major religious texts; the importance of astronomy, geometry, and music to number quality; how numbers affect architecture. Lundy explains why the ideas of Pythagoras still resonate, and she profiles each number from one to ten to show its distinct qualities: why, for example, the golden section is associated with five, and seven with the Virgin Mary.

    Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject.'W.W. Sawyer's deep understanding of how we learn and his lively, practical approach have made this an ideal introduction to mathematics for generations of readers. By starting at the level of simple arithmetic and algebra and then proceeding step by step through graphs, logarithms and trigonometry to calculus and the dizzying world of imaginary numbers, the book takes the mystery out of maths. Throughout, Sawyer reveals how theory is subordinate to the real-life applications of mathematics - the Pyramids were built on Euclidean principles three thousand years before Euclid formulated them - and celebrates the sheer intellectual stimulus of mathematics at its best.

    In this new, innovative overview textbook, the authors put special emphasis on the deep ideas of mathematics, and present the subject through lively and entertaining examples, anecdotes, challenges and illustrations, all of which are designed to excite the student's interest. The underlying ideas include topics from number theory, infinity, geometry, topology, probability and chaos theory. Throughout the text, the authors stress that mathematics is an analytical way of thinking, one that can be brought to bear on problem solving and effective thinking in any field of study.

    The text is divided into three parts: the problems posed for anthropology by universals; six important studies that have forced anthropologists to rethink; and the distinctions between linguistic, cultural and social universals.

    Twenty-two years later, he did. April 1945 – Berlin. The world had been at war for more than five-and-a-half years – approximately seventy million people were dead across the globe. The epicentre of the twelve-year-old Third Reich was now surrounded, enveloped by bitter Soviet forces hardened by Nazi barbarity in the east over the last four years. As the buildings were blasted into rubble, pounded by Russian guns and bombs, before their troops and tanks, Hitler was hunkered down in his last headquarters – the dark and damp bunker under the Reich Chancellery. As the Third Reich began to crumble as fast as the city’s buildings, what was the state of mind of the tyrant? Only his closest and fanatical allies saw the collapse, none more so than Hitler’s servants, Otto Gunsche and Heinz Linge – two individuals which witnessed the final act of their regime. An act tinged over the last ten days in late April with selfish betrayal, increasingly forlorn hope, pleas, desperation and eventually suicide. As the Soviets closed in with impending vigour, in the concrete tomb below ground and under the thunderous booms of the petrifying battle for Berlin, the mind of the dictator disintegrated into drugs, delusion and a determination to die. Not by the enemy bullet but one of his own. This is the story of the people who held a unique place in world history – the ones who were there when the nightmare of Nazism and the horrors which accompanied it was finally banished as a dark chapter in the story of the human race.

    Starting a war 'to promote freedom and democracy' could in certain though rare circumstances be a justified act; but in the case of the Second Gulf War that began in 2003, which involved reacting to criminals hiding in one country (Al Qaeda in Afghanistan or Pakistan) by invading another country (Iraq), one of the main fronts has, dismayingly, been the home front, where the War on Terror takes the form of a War on Civil Liberties in the spurious name of security. To defend 'freedom and democracy', Western governments attack and diminish freedom and democracy in their own country. By this logic, someone will eventually have to invade the US and UK to restore freedom and democracy to them.'In this lucid and timely book, Grayling sets out what's at risk, engages with the arguments for and against examining the cases made by Isaiah Berlin and Ronald Dworkin on the one hand, and Roger Scruton and John Gray on the other, and finally proposes a different way to respond that makes defending the civil liberties on which western society is founded the cornerstone for defeating terrorism.

    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

    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.

    But Vidal was also a terrific conversationalist; indeed Dick Cavett once described him as “the best talker since Oscar Wilde.” Vidal was never more eloquent, or caustic, than when let loose on his favorite topic: the history and politics of the United States.This book is made up from four interviews conducted with his long-time interlocutor, the writer and radio host Jon Wiener, in which Vidal grapples with matters evidently close to his heart: the history of the American Empire, the rise of the National Security State, and his own life in politics, both as a commentator and candidate.The interviews cover a twenty-year span, from 1988 to 2008, when Vidal was at the height of his powers. His extraordinary facility for developing an argument, tracing connections between past and present, and drawing on an encyclopedic knowledge of America’s place in the world, are all on full display. And, of course, it being Gore Vidal, an ample sprinkling of gloriously acerbic one-liners is also provided.