From Edward Lorenz’s discovery of the Butterfly Effect, to Mitchell Feigenbaum’s calculation of a universal constant, to Benoit Mandelbrot’s concept of fractals, which created a new geometry of nature, Gleick’s engaging narrative focuses on the key figures whose genius converged to chart an innovative direction for science. In Chaos, Gleick makes the story of chaos theory not only fascinating but also accessible to beginners, and opens our eyes to a surprising new view of the universe.

    Here, Sokal teams up with Jean Bricmont to expose the abuse of scientific concepts in the writings of today's most fashionable postmodern thinkers. From Jacques Lacan and Julia Kristeva to Luce Irigaray and Jean Baudrillard, the authors document the errors made by some postmodernists using science to bolster their arguments and theories. Witty and closely reasoned, Fashionable Nonsense dispels the notion that scientific theories are mere "narratives" or social constructions, and explored the abilities and the limits of science to describe the conditions of existence.

    Stengers and Prigogine show how the two great themes of classic science, order and chaos, which coexisted uneasily for centuries, are being reconciled in a new and unexpected synthesis.

    But if we were to let go of this fond conviction, Bruno Latour asks, what would the world look like? His book, an anthropology of science, shows us how much of modernity is actually a matter of faith.What does it mean to be modern? What difference does the scientific method make? The difference, Latour explains, is in our careful distinctions between nature and society, between human and thing, distinctions that our benighted ancestors, in their world of alchemy, astrology, and phrenology, never made. But alongside this purifying practice that defines modernity, there exists another seemingly contrary one: the construction of systems that mix politics, science, technology, and nature. The ozone debate is such a hybrid, in Latour’s analysis, as are global warming, deforestation, even the idea of black holes. As these hybrids proliferate, the prospect of keeping nature and culture in their separate mental chambers becomes overwhelming—and rather than try, Latour suggests, we should rethink our distinctions, rethink the definition and constitution of modernity itself. His book offers a new explanation of science that finally recognizes the connections between nature and culture—and so, between our culture and others, past and present.Nothing short of a reworking of our mental landscape, We Have Never Been Modern blurs the boundaries among science, the humanities, and the social sciences to enhance understanding on all sides. A summation of the work of one of the most influential and provocative interpreters of science, it aims at saving what is good and valuable in modernity and replacing the rest with a broader, fairer, and finer sense of possibility.

    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.

    It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.

    Astronomer John Barrow takes an intriguing look at the limits of science, who argues that there are things that are ultimately unknowable, undoable, or unreachable.

    Covers the key historical developments and philosophical themes and topics that have impacted upon our scientific view of the world around us Introduces fundamental conceptual issues, including truth, empirical facts and philosophical/conceptual "facts," falsifiability, and instrumentalism /realism Analyzes the transition from the Aristotelian worldview to the Newtonian worldview Explores challenges to our own western worldview brought on by developments in twentieth-century science, most notably relativity theory and quantum theory

    Of particular importance is the examination of Bayesianism and the new experimentalism, as well as new chapters on the nature of scientific laws and recent trends in the realism versus anti-realism debate."Crisp, lucid and studded with telling examples… As a handy guide to recent alarums and excursions (in the philosophy of science) I find this book vigorous, gallant and useful."New Scientist

    And yet, disturbingly, in today's so-called information age, pseudoscience is burgeoning with stories of alien abduction, channeling past lives, and communal hallucinations commanding growing attention and respect. As Sagan demonstrates with lucid eloquence, the siren song of unreason is not just a cultural wrong turn but a dangerous plunge into darkness that threatens our most basic freedoms.

    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.

    Increasingly, the decisions that affect our lives--where we go to school, whether we can get a job or a loan, how much we pay for health insurance--are being made not by humans, but by machines. In theory, this should lead to greater fairness: Everyone is judged according to the same rules.But as mathematician and data scientist Cathy O'Neil reveals, the mathematical models being used today are unregulated and uncontestable, even when they're wrong. Most troubling, they reinforce discrimination--propping up the lucky, punishing the downtrodden, and undermining our democracy in the process.

    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

    Hollingdale with an introduction by Michael Tanner in Penguin Classics.Beyond Good and Evil confirmed Nietzsche's position as the towering European philosopher of his age. The work dramatically rejects the tradition of Western thought with its notions of truth and God, good and evil. Nietzsche demonstrates that the Christian world is steeped in a false piety and infected with a 'slave morality'. With wit and energy, he turns from this critique to a philosophy that celebrates the present and demands that the individual imposes their own 'will to power' upon the world.This edition includes a commentary on the text by the translator and Michael Tanner's introduction, which explains some of the more abstract passages in Beyond Good and Evil.Frederich Nietzsche (1844-1900) became the chair of classical philology at Basel University at the age of 24 until his bad health forced him to retire in 1879. He divorced himself from society until his final collapse in 1899 when he became insane. A powerfully original thinker, Nietzsche's influence on subsequent writers, such as George Bernard Shaw, D.H. Lawrence, Thomas Mann and Jean-Paul Sartre, was considerable.If you enjoyed Beyond Good and Evil you might like Nietzsche's Thus Spoke Zarathustra, also available in Penguin Classics."One of the greatest books of a very great thinker." —Michael Tanner

    In the paper, Wigner observed that the mathematical structure of a physical theory often points the way to further advances in that theory and even to empirical predictions.