He shows that the scientists of ancient and medieval times not only did not understand what we understand about the world—they did not understand what there is to understand, or how to understand it. Yet over the centuries, through the struggle to solve such mysteries as the curious backward movement of the planets and the rise and fall of the tides, the modern discipline of science eventually emerged. Along the way, Weinberg examines historic clashes and collaborations between science and the competing spheres of religion, technology, poetry, mathematics, and philosophy.An illuminating exploration of the way we consider and analyze the world around us, To Explain the World is a sweeping, ambitious account of how difficult it was to discover the goals and methods of modern science, and the impact of this discovery on human knowledge and development.

    His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Equally legendary were Gö's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first popular biography of this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life. After describing his childhood in the Moravian capital of Brno, the authors trace the arc of Gö's remarkable career, from the famed Vienna Circle, where philosophers and scientists debated notions of truth, to the Institute for Advanced Study in Princeton, New Jersey, where he lived and worked until his death in 1978. In the process, they shed light on Gö's contributions to mathematics, philosophy, computer science, artificial intelligence -- even cosmology -- in an entertaining and accessible way.

    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.

    Each expresses a perspective on the Sciences.

    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.

    He begins with Copernicus, during the Renaissance, when science replaced mysticism as a means of explaining the workings of the world, and he continues through the centuries, creating an unbroken genealogy of not only the greatest but also the more obscure names of Western science, a dot-to-dot line linking amateur to genius, and accidental discovery to brilliant deduction.By focusing on the scientists themselves, Gribbin has written an anecdotal narrative enlivened with stories of personal drama, success and failure. A bestselling science writer with an international reputation, Gribbin is among the few authors who could even attempt a work of this magnitude. Praised as “a sequence of witty, information-packed tales” and “a terrifi c read” by The Times upon its recent British publication, The Scientists breathes new life into such venerable icons as Galileo, Isaac Newton, Albert Einstein and Linus Pauling, as well as lesser lights whose stories have been undeservedly neglected. Filled with pioneers, visionaries, eccentrics and madmen, this is the history of science as it has never been told before.From the Hardcover edition.

    It certainly is the strangest idea that humans have ever thought. Where did it come from and what is it telling us about our Universe? Can there actually be infinities? Is matter infinitely divisible into ever-smaller pieces? But infinity is also the place where things happen that don't. All manner of strange paradoxes and fantasies characterize an infinite universe. If our Universe is infinite then an infinite number of exact copies of you are, at this very moment, reading an identical sentence on an identical planet somewhere else in the Universe. Now Infinity is the darling of cutting edge research, the measuring stick used by physicists, cosmologists, and mathematicians to determine the accuracy of their theories. From the paradox of Zeno’s arrow to string theory, Cambridge professor John Barrow takes us on a grand tour of this most elusive of ideas and describes with clarifying subtlety how this subject has shaped, and continues to shape, our very sense of the world in which we live. The Infinite Book is a thoroughly entertaining and completely accessible account of the biggest subject of them all–infinity.

    New to this third edition are expanded coverage of such important topics as surface boundary interfaces, improved discussions of such physical and mathematical laws as the Law of Biot and Savart and the Euler Momentum Integral. A very important new section on Computational Fluid Dynamics has been added for the very first time to this edition. Expanded and improved end-of-chapter problems will facilitate the teaching experience for students and instrutors alike. This book remains one of the most comprehensive and useful texts on fluid mechanics available today, with applications going from engineering to geophysics, and beyond to biology and general science. * Ample, useful end-of-chapter problems.* Excellent Coverage of Computational Fluid Dynamics.* Coverage of Turbulent Flows.* Solutions Manual available.

    What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted.Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics.From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

    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.

    More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

    It was studied from antiquity to the Renaissance as a way of glimpsing the nature of reality. Geometry is number in space; music is number in time; and comology expresses number in space and time. Number, music, and geometry are metaphysical truths: life across the universe investigates them; they foreshadow the physical sciences.Quadrivium is the first volume to bring together these four subjects in many hundreds of years. Composed of six successful titles in the Wooden Books series-Sacred Geometry, Sacred Number, Harmonograph, The Elements of Music, Platonic & Archimedean Solids, and A Little Book of Coincidence-it makes ancient wisdom and its astonishing interconnectedness accessible to us today.Beautifully produced in six different colors of ink, Quadrivium will appeal to anyone interested in mathematics, music, astronomy, and how the universe works.

    Bridging the chasm between educational and social history, this book was one of the first to examine developments in higher education in the context of the social, economic, and political forces that were shaping the nation at large.Surveying higher education from the colonial era through the mid-twentieth century, Rudolph explores a multitude of issues from the financing of institutions and the development of curriculum to the education of women and blacks, the rise of college athletics, and the complexities of student life. In his foreword to this new edition, John Thelin assesses the impact that Rudolph's work has had on higher education studies. The new edition also includes a bibliographic essay by Thelin covering significant works in the field that have appeared since the publication of the first edition.At a time when our educational system as a whole is under intense scrutiny, Rudolph's seminal work offers an important historical perspective on the development of higher education in the United States.

    This network has been called a greater invention than the steam engine, comparable only to the development of the printing press.Robert P. Crease traces the evolution of this international system from the use of flutes to measure distance in the dynasties of ancient China and figurines to weigh gold in West Africa to the creation of the French metric and British imperial systems. The former prevailed, with the United States one of three holdout nations. Into this captivating history Crease weaves stories of colorful individuals, including Thomas Jefferson, an advocate of the metric system, and American philosopher Charles S. Peirce, the first to tie the meter to the wavelength of light. Tracing the dynamic struggle for ultimate precision, World in the Balance demonstrates that measurement is both stranger and more integral to our lives than we ever suspected.

    The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and in the process venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.