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.

    Some went on to create governments that were accountable to their constituents. We take these institutions for granted, but they are absent or are unable to perform in many of today’s developing countries—with often disastrous consequences for the rest of the world.Francis Fukuyama, author of the bestselling The End of History and the Last Man and one of our most important political thinkers, provides a sweeping account of how today’s basic political institutions developed. The first of a major two-volume work, The Origins of Political Order begins with politics among our primate ancestors and follows the story through the emergence of tribal societies, the growth of the first modern state in China, the beginning of the rule of law in India and the Middle East, and the development of political accountability in Europe up until the eve of the French Revolution.Drawing on a vast body of knowledge—history, evolutionary biology, archaeology, and economics—Fukuyama has produced a brilliant, provocative work that offers fresh insights on the origins of democratic societies and raises essential questions about the nature of politics and its discontents.

    It can offer examples to inform our decisions and guesses about the consequences of our actions. But we should be wary of looking to history for dogmatic lessons.We should distrust those who abuse history when they call on it to justify unreasonable claims to land, for example, or restitution. MacMillan illustrates how dangerous history can be in the hands of nationalistic or religious or ethnic leaders who use it to foster a sense of grievance and a desire for revenge.

    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.

    One of the most influential figures of the twentieth century, he transformed philosophy and can lay claim to being one of the greatest philosophers of all time. He was a Nobel Prize winner for Literature and was imprisoned several times as a result of his pacifism. His views on religion, education, sex, politics and many other topics, made him one of the most read and revered writers of the age. This, his autobiography, is one of the most compelling and vivid ever written. This one-volume, compact paperback edition contains an introduction by the politician and scholar, Michael Foot, which explores the status of this classic nearly 30 years after the publication of the final volume.

    The book was based on a course of public lectures delivered by Schrödinger in February 1943 at Trinity College, Dublin. Schrödinger's lecture focused on one important question: "how can the events in space and time which take place within the spatial boundary of a living organism be accounted for by physics and chemistry?" In the book, Schrödinger introduced the idea of an "aperiodic crystal" that contained genetic information in its configuration of covalent chemical bonds. In the 1950s, this idea stimulated enthusiasm for discovering the genetic molecule and would give both Francis Crick and James Watson initial inspiration in their research.

    Full of insights, arguments and philosophical perspectives, the book covers an amazing array of topics. Beginning in antiquity with Democritus, it progresses through logic and set theory, computability and complexity theory, quantum computing, cryptography, the information content of quantum states and the interpretation of quantum mechanics. There are also extended discussions about time travel, Newcomb's Paradox, the anthropic principle and the views of Roger Penrose. Aaronson's informal style makes this fascinating book accessible to readers with scientific backgrounds, as well as students and researchers working in physics, computer science, mathematics and philosophy.

    The conversion of energy on Earth ranges from terra-forming forces of plate tectonics to cumulative erosive effects of raindrops. Life on Earth depends on the photosynthetic conversion of solar energy into plant biomass. Humans have come to rely on many more energy flows—ranging from fossil fuels to photovoltaic generation of electricity—for their civilized existence. In this monumental history, Vaclav Smil provides a comprehensive account of how energy has shaped society, from pre-agricultural foraging societies through today's fossil fuel–driven civilization.Humans are the only species that can systematically harness energies outside their bodies, using the power of their intellect and an enormous variety of artifacts—from the simplest tools to internal combustion engines and nuclear reactors. The epochal transition to fossil fuels affected everything: agriculture, industry, transportation, weapons, communication, economics, urbanization, quality of life, politics, and the environment. Smil describes humanity's energy eras in panoramic and interdisciplinary fashion, offering readers a magisterial overview. This book is an extensively updated and expanded version of Smil's Energy in World History (1994). Smil has incorporated an enormous amount of new material, reflecting the dramatic developments in energy studies over the last two decades and his own research over that time.

    Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his little finger told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.

    The book opens with an assessment of different sociologies of knowledge from Mannheim to Foucault and beyond, and goes on to discuss intellectuals as a social group and the social institutions (especially universities and academies) which encouraged or discouraged intellectual innovation. Then, in a series of separate chapters, Burke explores the geography, anthropology, politics and economics of knowledge, focusing on the role of cities, academies, states and markets in the process of gathering, classifying, spreading and sometimes concealing information. The final chapters deal with knowledge from the point of view of the individual reader, listener, viewer or consumer, including the problem of the reliability of knowledge discussed so vigorously in the seventeenth century. One of the most original features of this book is its discussion of knowledges in the plural. It centres on printed knowledge, especially academic knowledge, but it treats the history of the knowledge 'explosion' which followed the invention of printing and the discovery of the world beyond Europe as a process of exchange or negotiation between different knowledges, such as male and female, theoretical and practical, high-status and low-status, and European and non-European. Although written primarily as a contribution to social or socio-cultural history, this book will also be of interest to historians of science, sociologists, anthropologists, geographers and others in another age of information explosion.

    In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Godel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

    Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

    Mandelbrot, one of the century's most influential mathematicians, is world-famous for making mathematical sense of a fact everybody knows but that geometers from Euclid on down had never assimilated: Clouds are not round, mountains are not cones, coastlines are not smooth. To these classic lines we can now add another example: Markets are not the safe bet your broker may claim. In his first book for a general audience, Mandelbrot, with co-author Richard L. Hudson, shows how the dominant way of thinking about the behavior of markets-a set of mathematical assumptions a century old and still learned by every MBA and financier in the world-simply does not work. As he did for the physical world in his classic The Fractal Geometry of Nature, Mandelbrot here uses fractal geometry to propose a new, more accurate way of describing market behavior. The complex gyrations of IBM's stock price and the dollar-euro exchange rate can now be reduced to straightforward formulae that yield a far better model of how risky they are. With his fractal tools, Mandelbrot has gotten to the bottom of how financial markets really work, and in doing so, he describes the volatile, dangerous (and strangely beautiful) properties that financial experts have never before accounted for. The result is no less than the foundation for a new science of finance.

    The horror of the First World War is still fresh for the protagonists of Time of the Magicians, each of whom finds himself at a crucial juncture. Benjamin, whose life is characterized by false starts and unfinished projects, is trying to flee his overbearing father and floundering in his academic career, living hand to mouth as a critic. Wittgenstein, by contrast, has dramatically decided to divest himself of the monumental fortune he stands to inherit, as a scion of one of the wealthiest industrial families in Europe, in search of absolute spiritual clarity. Meanwhile, Heidegger, having managed to avoid combat in war by serving instead as a meteorologist, is carefully cultivating his career, aligning himself with the great Edmund Husserl and renouncing his prior Catholic associations. Finally, Cassirer is working furiously on the margins of academia, applying himself intensely to his writing and the possibility of a career at Hamburg University. The stage is set for a great intellectual drama, which will unfold across the next decade. The lives and ideas of this extraordinary philosophical quartet will converge as they become world historical figures. But as the Second World War looms on the horizon, their fates will be very different.Wolfram Eilenberger stylishly traces the paths of these remarkable and turbulent lives, which feature not only philosophy but some of the most important economists, politicians, journalists, and artists of the century, including John Maynard Keynes, Hannah Arendt, and Bertrand Russell. In doing so, he tells a gripping story about some of history's most ambitious and passionate thinkers, and illuminates with rare clarity and economy their brilliant ideas, which all too often have been regarded as enigmatic or opaque.

    Written in short, carefully numbered paragraphs of extreme brilliance, it captured the imagination of a generation of philosophers. For Wittgenstein, logic was something we use to conquer a reality which is in itself both elusive and unobtainable. He famously summarized the book in the following words: 'What can be said at all can be said clearly; and what we cannot talk about we must pass over in silence.' David Pears and Brian McGuinness received the highest praise for their meticulous translation. The work is prefaced by Bertrand Russell's original introduction to the first English edition.