Readers will find excerpts from bestsellers such as Douglas R. Hofstadter's Gödel, Escher, Bach, Francis Crick's Life Itself, Loren Eiseley's The Immense Journey, Daniel Dennett's Darwin's Dangerous Idea, and Rachel Carson's The Sea Around Us. There are classic essays ranging from J.B.S. Haldane's "On Being the Right Size" and Garrett Hardin's "The Tragedy of the Commons" to Alan Turing's "Computing Machinery and Intelligence" and Albert Einstein's famed New York Times article on "Relativity." And readers will also discover lesser-known but engaging pieces such as Lewis Thomas's "Seven Wonders of Science," J. Robert Oppenheimer on "War and Physicists," and Freeman Dyson's memoir of studying under Hans Bethe.A must-read volume for all science buffs, The Oxford Book of Modern Science Writing is a rich and vibrant anthology that captures the poetry and excitement of scientific thought and discovery.One of New Scientist's Editor's Picks for 2008.

    And it is ignorance--not knowledge--that is the true engine of science.Most of us have a false impression of science as a surefire, deliberate, step-by-step method for finding things out and getting things done. In fact, says Firestein, more often than not, science is like looking for a black cat in a dark room, and there may not be a cat in the room. The processis more hit-or-miss than you might imagine, with much stumbling and groping after phantoms. But it is exactly this not knowing, this puzzling over thorny questions or inexplicable data, that gets researchers into the lab early and keeps them there late, the thing that propels them, the verydriving force of science. Firestein shows how scientists use ignorance to program their work, to identify what should be done, what the next steps are, and where they should concentrate their energies. And he includes a catalog of how scientists use ignorance, consciously or unconsciously--aremarkable range of approaches that includes looking for connections to other research, revisiting apparently settled questions, using small questions to get at big ones, and tackling a problem simply out of curiosity. The book concludes with four case histories--in cognitive psychology, theoreticalphysics, astronomy, and neuroscience--that provide a feel for the nuts and bolts of ignorance, the day-to-day battle that goes on in scientific laboratories and in scientific minds with questions that range from the quotidian to the profound.Turning the conventional idea about science on its head, Ignorance opens a new window on the true nature of research. It is a must-read for anyone curious about science.

    At the same time adjacent portions of philosophy and logic are discussed. To the existence of what objects may a given scientific theory be said to be committed? And what considerations may suitably guide us in accepting or revising such ontological commitments? These are among the questions dealt with in this book, particular attention being devoted to the role of abstract entities in mathematics. There is speculation on the mechanism whereby objects of one sort or another come to be posited a process in which the notion of identity plays an important part."This volume of essays has a unity and bears throughout the imprint of Quine's powerful and original mind. It is written with the felicity in the choice of words which makes everything that Quine writes a pleasure to read, and which ranks him among the best contemporary writers on abstract subjects." (Cambridge Review)"Professor Quine's challenging and original views are here for the first time presented as a unity. The chief merit of the book is the heart-searching from which it arose and to which it will give rise. In vigour, conciseness, and clarity, it is characteristic of its author." (Oxford Magazine)

    Keying Einstein's crucial discoveries to the simple mental images that inspired them, Michio Kaku finds a revealing new way to discuss his ideas, and delivers an appealing and always accessible introduction to Einstein's work.

    Birth of a Theorem is Villani’s own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career.But you don’t have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn’t simplify or overexplain; rather, it invites readers into collaboration. Villani’s diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You’re privy to the dining-hall conversations at the world’s greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker’s whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.

    But it was C. P. Snow's Rede lecture of 1959 that brought it to prominence and began a public debate that is still raging in the media today. This 50th anniversary printing of The Two Cultures and its successor piece, A Second Look (in which Snow responded to the controversy four years later) features an introduction by Stefan Collini, charting the history and context of the debate, its implications and its afterlife. The importance of science and technology in policy run largely by non-scientists, the future for education and research, and the problem of fragmentation threatening hopes for a common culture are just some of the subjects discussed.

    This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round.Why one and two weren't considered numbers by the ancient Greeks.Why squares show up so often in goddess art and board games.What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster a cathedral, and much more.

    W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by "Vooster " V. Beman.

    This sharply intelligent, consistently provocative book takes the reader on an astonishing, thought-provoking voyage into the realm of delightful uncertainty--a world of paradox in which logical argument leads to contradiction and common sense is seemingly rendered irrelevant.

    Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

    Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts, mathematical discussions, and the application of complex numbers and functions to important problems.

    Heisenberg’s principle implied that scientific quantities/concepts do not have absolute, independent meaning, but acquire meaning only in terms of the experiments used to measure them. This proposition, undermining the cherished belief that science could reveal the physical world with limitless detail and precision, placed Heisenberg in direct opposition to the revered Albert Einstein. The eminent scientist Niels Bohr, Heisenberg’s mentor and Einstein’s long-time friend, found himself caught between the two.Uncertainty chronicles the birth and evolution of one of the most significant findings in the history of science, and portrays the clash of ideas and personalities it provoked. Einstein was emotionally as well as intellectually determined to prove the uncertainty principle false. Heisenberg represented a new generation of physicists who believed that quantum theory overthrew the old certainties; confident of his reasoning, Heisenberg dismissed Einstein’s objections. Bohr understood that Heisenberg was correct, but he also recognized the vital necessity of gaining Einstein’s support as the world faced the shocking implications of Heisenberg’s principle.

    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.

    The era covered by this book, 1950 to 1990, was surely one of the golden ages of science as well as the American university.Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period Stanislav Ulam (who, together with Edward Teller, signed the patent application for the hydrogen bomb), Solomon Lefschetz (Chairman in the 50s of the Princeton mathematics department), William Feller (one of the founders of modern probability theory), Jack Schwartz (one of the founders of computer science), and many others.Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. After the publication of the essay "The Pernicious Influence of Mathematics upon Philosophy" (reprinted six times in five languages) the author was blacklisted in analytical philosophy circles. Indiscrete Thoughts should become an instant classic and the subject of debate for decades to come."Read Indiscrete Thoughts for its account of the way we were and what we have become; for its sensible advice and its exuberant rhetoric."--The Mathematical Intelligencer"Learned, thought-provoking, politically incorrect, delighting in paradox, and likely to offend but everywhere readable and entertaining."--The American Mathematical Monthly"It is about mathematicians, the way they think, and the world in which the live. It is 260 pages of Rota calling it like he sees it... Readers are bound to find his observations amusing if not insightful. Gian-Carlo Rota has written the sort of book that few mathematicians could write. What will appeal immediately to anyone with an interest in research mathematics are the stories he tells about the practice of modern mathematics."--MAA Reviews"

    Chance and Necessity is a philosophical statement whose intention is to sweep away as both false and dangerous the animist conception of man that has dominated virtually all Western worldviews from primitive cultures to those of dialectical materialists. He bases his argument on the evidence of modern biology, which indisputably shows, that man is the product of chance genetic mutation. With the unrelenting logic of the scientist, he draws upon what we now know (and can theorize) of genetic structure to suggest an new way of looking at ourselves. He argues that objective scientific knowledge, the only reliable knowledge, denies the concepts of destiny or evolutionary purpose that underlie traditional philosophies. He contends that the persistence of those concepts is responsible for the intensifying schizophrenia of a world that accepts, and lives by, the fruits of science while refusing to face its moral implications. Dismissing as "animist" not only Plato, Hegel, Bergson and Teilhard de Chardin but Spencer and Marx as well, he calls for a new ethic that will recognize the distinction between objective knowledge and the realm of values--an ethic of knowledge that can, perhaps, save us from our deepening spiritual malaise, from the new age of darkness he sees coming.PrefaceOf strange objects Vitalisms and animisms Maxwell's demons Microscopic cyberneticsMolecular ontogenesis Invariance and perturbationsEvolution The frontiers The kingdom and the darknessAppendixes