Among the estimated one hundred billion solar systems in the known universe, evolving life is surely abundant. That evolution is a process of becoming in each case. Since Newton, we have turned to physics to assess reality. Butphysics alone cannot tell us where we came from, how we arrived, and why our world has evolved past the point of unicellular organisms to an extremely complex biosphere.Building on concepts from his work as a complex systems researcher at the Santa Fe Institute, Kauffman focuses in particular on the idea of cells constructing themselves and introduces concepts such as constraint closure. Living systems are defined by the concept of organization which has notbeen focused on in enough in previous works. Cells are autopoetic systems that build themselves: they literally construct their own constraints on the release of energy into a few degrees of freedom that constitutes the very thermodynamic work by which they build their own self creating constraints.Living cells are machines that construct and assemble their own working parts. The emergence of such systems-the origin of life problem-was probably a spontaneous phase transition to self-reproduction in complex enough prebiotic systems. The resulting protocells were capable of Darwin's heritablevariation, hence open-ended evolution by natural selection. Evolution propagates this burgeoning organization. Evolving living creatures, by existing, create new niches into which yet further new creatures can emerge. If life is abundant in the universe, this self-constructing, propagating, exploding diversity takes us beyond physics to biospheres everywhere.

    They have dictated how we build, eat, communicate, wage war, create art, travel, and worship. Some, such as stone, iron, and bronze, lend their names to the ages. Others, such as gold, silver, and diamond, contributed to the rise and fall of great empires. How would history have unfolded without glass, paper, steel, cement, or gunpowder?The impulse to master the properties of our material world and to invent new substances has remained unchanged from the dawn of time; it has guided and shaped the course of history. Sass shows us how substances and civilizations have evolved together. In antiquity, iron was considered more precious than gold. The celluloid used in movie film had its origins in the search for a substitute for ivory billiard balls. The same clay used in the pottery of antiquity has its uses in todayâ€s computer chips.Moving from the Stone Age to the Age of Silicon, from the days of prehistoric survival to the cutting edge of nanotechnology, this fascinating and accessible book connects the worlds of minerals and molecules to the sweep of human history, and shows what materials will dominate the century ahead. 19 color illustrations

    40 illustrations throughout.

    It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

    From very simple beginnings he takes us on a thrilling journey to some deep mathematical ideas. On the way, via Kepler and Newton, he explains what calculus really means, gives a brief history of pi, and even takes us to chaos theory and imaginary numbers. Every short chapter is carefully crafted to ensure that no one will get lost on the journey. Packed with puzzles and illustrated by world famous cartoonists, this is one of the most readable and imaginative books on mathematics ever written.

    His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

    This brilliant work heralds the new age of nanotechnology, which will give us thorough and inexpensive control of the structure of matter.  Drexler examines the enormous implications of these developments for medicine, the economy, and the environment, and makes astounding yet well-founded projections for the future.

    It has been developed in response to the need for a text that supports the mastery of this difficult subject. Therefore, in addition to presenting electromagnetics in a concise and logical manner, the text includes end-of-section review questions, worked examples, boxed remarks that alert students to key ideas and tricky points, margin notes, and point-by-point chapter summaries. Examples and applications invite students to solve problems and build their knowledge of electromagnetics. Application topics include: electric motors, transmission lines, waveguides, antenna arrays and radar systems.

    Einstein considered Bergson's theory of time to be a soft, psychological notion, irreconcilable with the quantitative realities of physics. Bergson, who gained fame as a philosopher by arguing that time should not be understood exclusively through the lens of science, criticized Einstein's theory of time for being a metaphysics grafted on to science, one that ignored the intuitive aspects of time. The Physicist and the Philosopher tells the remarkable story of how this explosive debate transformed our understanding of time and drove a rift between science and the humanities that persists today.Jimena Canales introduces readers to the revolutionary ideas of Einstein and Bergson, describes how they dramatically collided in Paris, and traces how this clash of worldviews reverberated across the twentieth century. She shows how it provoked responses from figures such as Bertrand Russell and Martin Heidegger, and carried repercussions for American pragmatism, logical positivism, phenomenology, and quantum mechanics. Canales explains how the new technologies of the period--such as wristwatches, radio, and film--helped to shape people's conceptions of time and further polarized the public debate. She also discusses how Bergson and Einstein, toward the end of their lives, each reflected on his rival's legacy--Bergson during the Nazi occupation of Paris and Einstein in the context of the first hydrogen bomb explosion.The Physicist and the Philosopher reveals how scientific truth was placed on trial in a divided century marked by a new sense of time.Jimena Canales holds the Thomas M. Siebel Chair in the History of Science at the University of Illinois, Urbana-Champaign, and was previously associate professor of the history of science at Harvard University. She is the author of A Tenth of a Second: A History.Review:"In illuminating a historic 1922 debate between Albert Einstein and Henri Bergson about the nature of time, Canales marks a turning point in the power of philosophy to influence science."--Publishers Weekly"Sparks—both incendiary and illuminating—fly from the collision of two giants!"--Booklist, starred review"This fascinating, scholarly, readable look at physics and epistemology will interest readers of science, history, philosophy, and biography."--Library Journal, starred review"Whether or not you agree, this humane and melancholy account of how two talents misunderstood each other will linger in the mind."--New Scientist"[Canales] weaves a tale around Europe and to America. . . . [Her] subject raises important core philosophical issues, like the scope of philosophy itself."--Michael Ruse, The Chronicle of Higher Education"This fascinating book traces a debate about the nature of time. . . . Canales has done a masterful job of research and explication. Her account of the debate is lively, the background of it is interesting, and the debate’s ramifications as filtered through other minds are downright exciting. Anyone interested in physics or philosophy will have a field day with this book."--Kelly Cherry, The Smart Set"Canales does sterling work investigating these engagements . . . [A] stimulating book."--Graham Farmelo, Nature Endorsement: "The Physicist and the Philosopher explores the nature of time, the meaning of relativity, and the place of philosophical thought in a scientific age. Canales aims to reposition Einstein's work in a field of disputation and give Bergson back the significance he had in his contemporaries' minds."--Cathryn Carson, University of California, Berkeley

    Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea.From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.

    "A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

    The presentation stresses analytical methods, concrete examples, and geometric intuition. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory.About the Author:Steven Strogatz is in the Center for Applied Mathematics and the Department of Theoretical and Applied Mathematics at Cornell University. Since receiving his Ph.D. from Harvard university in 1986, Professor Strogatz has been honored with several awards, including the E.M. Baker Award for Excellence, the highest teaching award given by MIT.

    Comparing the key events of the Old Testament with the latest findings in physics, biochemistry, and paleontology, a physicist and theologian shows that science and the Bible can be reconciled to resolve the age-old debates about God.

    Repchecks riveting story tells of the enigmatic genius responsible for one of the most important scientific theories ever--and why it took several decades and a strangers intervention before his groundbreaking On the Revolutions of the Heavenly Spheres was published.

    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.