His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.

    Explaining how such basic concepts as number and magnitude, space and force were developed, the great French mathematician refutes the skeptical position that modern scientific method and its results are wholly factitious. The places of rigorous logic and intuitive leaps are both established by an analysis of contrasting methods of idea-creation in individuals and in modern scientific traditions. The nature of hypothesis and the role of probability are investigated with all of Poincaré's usual fertility of insight.Partial contents: On the nature of mathematical reasoning. Magnitude and experiment. Space: non-Euclidean geometrics, space and geometry, experiment and geometry. Force: classical mechanics, relative and absolute motion, energy and thermodynamics. Nature: hypotheses in physics, the theories of modern physics, the calculus of probabilities, optics and electricity, electro-dynamics."Poincaré's was the last man to take practically all mathematics, both pure and applied as his province. Few mathematicians have had the breadth of philosophic vision that Poincaré's had, and none is his superior in the gift of clear exposition." — Men of Mathematics, Eric Temple Bell, Professor of Mathematics, University of Cambridge

    A scholar, wit, lawyer and statesman, he wrote widely on politics, philosophy and science - declaring early in his career that 'I have taken all knowledge as my province'. In this, his most famous work, he considers a diverse range of subjects, such as death and marriage, ambition and atheism, in prose that is vibrant and rich in Renaissance learning. Bacon believed that rhetoric - the force of eloquence and persuasion - could lead the mind to the pure light of reason, and his own rhetorical genius is nowhere better expressed than in these vivid essays.

            The stories are divided into three sections: The Age of Fable or Stories of Gods and Heroes (first published in 1855); The Age of Chivalry (1858), which contains King Arthur and His Knights, The Mabinogeon, and The Knights of English History; and Legends of Charlemagne or Romance of the Middle Ages (1863). For the Greek myths, Bulfinch drew on Ovid and Virgil, and for the sagas of the north, from Mallet's Northern Antiquities. He provides lively versions of the myths of Zeus and Hera, Venus and Adonis, Daphne and Apollo, and their cohorts on Mount Olympus; the love story of Pygmalion and Galatea; the legends of the Trojan War and the epic wanderings of Ulysses and Aeneas; the joys of Valhalla and the furies of Thor; and the tales of Beowulf and Robin Hood. The tales are eminently readable. As Bulfinch wrote, "Without a knowledge of mythology much of the elegant literature of our own language cannot be understood and appreciated. . . . Our book is an attempt to solve this problem, by telling the stories of mythology in such a manner as to make them a source of amusement."Thomas Bulfinch, in his day job, was a clerk in the Merchant's Bank of Boston, an undemanding position that afforded him ample leisure time in which to pursue his other interests. In addition to serving as secretary of the Boston Society of Natural History, he thoroughly researched the myths and legends and copiously cross-referenced them with literature and art. As such, the myths are an indispensable guide to the cultural values of the nineteenth century; however, it is the vigor of the stories themselves that returns generation after generation to Bulfinch.

    From the sudden expansion of a cloud of gas to the cooling of hot metal--everything is moved or restrained by four simple laws. Written by Peter Atkins, one of the world's leading authorities on thermodynamics, this powerful and compact introduction explains what these four laws are and how they work, using accessible language and virtually no mathematics. Guiding the reader a step at a time, Atkins begins with Zeroth (so named because the first two laws were well established before scientists realized that a third law, relating to temperature, should precede them--hence the jocular name zeroth), and proceeds through the First, Second, and Third Laws, offering a clear account of concepts such as the availability of work and the conservation of energy. Atkins ranges from the fascinating theory of entropy (revealing how its unstoppable rise constitutes the engine of the universe), through the concept of free energy, and to the brink, and then beyond the brink, of absolute zero. About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    In those twelve months, Einstein shattered many cherished scientific beliefs with five extraordinary papers that would establish him as the world's leading physicist. This book brings those papers together in an accessible format. The best-known papers are the two that founded special relativity: On the Electrodynamics of Moving Bodies and Does the Inertia of a Body Depend on Its Energy Content? In the former, Einstein showed that absolute time had to be replaced by a new absolute: the speed of light. In the second, he asserted the equivalence of mass and energy, which would lead to the famous formula E = mc2.The book also includes On a Heuristic Point of View Concerning the Production and Transformation of Light, in which Einstein challenged the wave theory of light, suggesting that light could also be regarded as a collection of particles. This helped to open the door to a whole new world--that of quantum physics. For ideas in this paper, he won the Nobel Prize in 1921.The fourth paper also led to a Nobel Prize, although for another scientist, Jean Perrin. On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat concerns the Brownian motion of such particles. With profound insight, Einstein blended ideas from kinetic theory and classical hydrodynamics to derive an equation for the mean free path of such particles as a function of the time, which Perrin confirmed experimentally. The fifth paper, A New Determination of Molecular Dimensions, was Einstein's doctoral dissertation, and remains among his most cited articles. It shows how to calculate Avogadro's number and the size of molecules.These papers, presented in a modern English translation, are essential reading for any physicist, mathematician, or astrophysicist. Far more than just a collection of scientific articles, this book presents work that is among the high points of human achievement and marks a watershed in the history of science. Coinciding with the 100th anniversary of the miraculous year, this new paperback edition includes an introduction by John Stachel, which focuses on the personal aspects of Einstein's youth that facilitated and led up to the miraculous year.

    Based on a major conference sponsored by the National Academy of Sciences and the Smithsonian Institution, Biodiversity creates a systematic framework for analyzing the problem and searching for possible solutions.

    Offering time-tested problems, conceptual and visual pedagogy, and a state-of-the-art media package, this 11th edition looks to the future of university physics, in terms of both content and approach.