How can we predict and explain the phenomena of nature? What are the limits to this knowledge process? The central issues of prediction, explanation, and mathematical modeling, which underlie all scientific activity, were the focus of a conference organized by the Swedish Council for the Planning and Coordination of Research, held at the Abisko Research Station in May of 1989. At this forum, a select group of internationally known scientists in physics, chemistry, biology, economics, sociology and mathematics discussed and debated the ways in which prediction and explanation interact with mathematical modeling in their respective areas of expertise. Beyond Belief is the result of this forum, consisting of 11 chapters written specifically for this volume. The multiple themes of randomness, uncertainty, prediction and explanation are presented using (as vehicles) several topical areas from modern science, such as morphogenetic fields, Boscovich covariance, and atmospheric variability. This multidisciplinary examination of the foundational issues of modern scientific thought and methodology will offer stimulating reading for a very broad scientific audience.
Kurt Gödel was an intellectual giant. His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Shattering hopes that logic would, in the end, allow us a complete understanding of the universe, Gödel's theorem also raised many provocative questions: What are the limits of rational thought? Can we ever fully understand the machines we build? Or the inner workings of our own minds? How should mathematicians proceed in the absence of complete certainty about their results? Equally legendary were Gödel'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 book for a general audience on this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life.
By the author of The Cambridge Quintet, John L. Casti's new book continues the tradition of combining science fact with just the right dose of fiction. Part novel, part science â€" wholly informative and entertaining. In the fall of 1933 the newly founded Institute for Advanced Study in Princeton, New Jersey, welcomed its first faculty member, Albert Einstein. With this superstar on the roster, the Institute was able to attract many more of the greatest scholars, scientists, and poets from around the world. It was to be an intellectual haven, a place where the most brilliant minds on the planet, sheltered from the outside world's cares and calamities, could study and collaborate and devote their time to the pure and exclusive pursuit of knowledge. For many of them, it was the "one, true, platonic heaven." Over the years, key figures at the Institute began to question the limits to what science could tell us about the world, pondering the universal secrets it might unlock. Could science be the ultimate source of truth; or are there intrinsic limits, built into the very fabric of the universe, to what we can learn? In the late 1940's and early 1950's, this important question was being asked and pondered upon by some of the Institute's deepest thinkers. Enter the dramatis personae to illuminate the science and the philosophy of the time. Mathematical logician Kurt Godel was the unacknowledged Grant Exalted Ruler of this platonic estate â€" but he was a ruler without a scepter as he awaited the inexplicably indefinite postponement of his promotion to full, tenured professor. Also in residence was his colleague, the Hungarian-American polymath, John van Neumann, developer of game theory, the axiomatic foundations of quantum mechanics, and the digital computer â€" stymied by the Institute's refusal to sanction his bold proposal to actually build a computer. One of Godel's closest friends figures large in this story: Albert Einstein, by common consensus the greatest physicist the 20th century had ever known. And, of course, the director the Institute, J. Robert Oppenheimer, the father of the atomic bomb, must by necessity be key to any story that focuses in on this time and place. Author Casti elegantly sets the stage and then masterfully directs this impressive cast of charactersâ€"with able assists by many "minor-character" icons like T. S. Eliot, Wolfgang Pauli, Freeman Dyson, and David Bohm, to tell a story of science, history, and ideas. As we watch events unfold (some of which are documented fact while others are creatively imagined fiction), we are witness to the discussions and deliberations of this august group… privy to wide-ranging conversations on thinking machines, quantum logic, biology as physics, weather forecasting, the structure of economic systems, the distinction between mathematics and natural science, the structure of the universe, and the powers of the human mind â€" all centered around the question of the limits to scientific knowledge. Imaginatively conceived and artfully executed, The One True Platonic Heaven is an accessible and intriguing presentation of some of the deepest scientific and philosophical ideas of the 20th century.
This book is about intersections among science, philosophy, and literature. It bridges the gap between the traditional “cultures” of science and the humanities by constituting an area of interaction that some have called a “third culture.” By asking questions about three disciplines rather than about just two, as is customary in research, this inquiry breaks new ground and resists easy categorization. It seeks to answer the following questions: What impact has the remapping of reality in scientific terms since the Copernican Revolution through thermodynamics, relativity theory, and quantum mechanics had on the way writers and thinkers conceptualized the place of human culture within the total economy of existence? What influence, on the other hand, have writers and philosophers had on the doing of science and on scientific paradigms of the world? Thirdly, where does humankind fit into the total picture with its uniquely moral nature? In other words, rather than privileging one discipline over another, this study seeks to uncover a common ground for science, ethics, and literary creativity. Throughout this inquiry certain nodal points emerge to bond the argument cogently together and create new meaning. These anchor points are the notion of movement inherent in all forms of existence, the changing concepts of evil in the altered spaces of reality, and the creative impulse critical to the literary work of art as well as to the expanding universe. This ambitious undertaking is unified through its use of phenomena typical of chaos and complexity theory as so many leitmotifs. While they first emerged to explain natural phenomena at the quantum and cosmic levels, chaos and complexity are equally apt for explaining moral and aesthetic events. Hence, the title “Remapping Reality” extends to the reconfigurations of the three main spheres of human interaction: the physical, the ethical, and the aesthetic or creative.
Mood Matters" makes the radical assertion that all social events ranging from fashions in music and art to the rise and fall of civilizations are biased by the attitudes a society holds toward the future. When the "social mood" is positive and people look forward to the future, events of an entirely different character tend to occur than when society is pessimistic. The book presents many examples from every walk of life in support of this argument. In addition, methods are given to actually measure the social mood and to project it into the future in order to forecast what’s likely or not over varying periods of time. Casti's writing is a pleasure to read and its contents an eye-opener. "They [the chapters] tell an engrossing story, and the mystery heightens as it goes. . . . it's chatty and knowing." Greg Benford, Physicist and science-fiction writer, author of "Timescape" and "Deep Time" "I am struck by how thought-provoking it all is. I am sure that your book will draw a lot of attention" Tor Norretranders, Science writer, author of "The Generous Man" and "The User Illusion".
Die beiden ursprünglich 1992 veröffentlichten Bände liegen nun in zusammengefaßter Paperback-Form vor. Reality Rules beleuchten die Syntax und die Semantik der Sprache, in der mathematische Modellierungsregeln niedergelegt werden. Eine Vielzahl von Beispielen zeigt praktische Anwendungen auf; auch ein Lösungsband zur Unterstützung des Selbststudiums ist erhältlich.
Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution. In models involving such perturbations, it is natural to assume these perturbations act instantaneously or in the form of impulses. As a consequence, impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. There are also many different studies in biology and medicine for which impulsive differential equations provide good models. During the last 10 years, the authors have been responsible for extensive contributions to the literature on impulsive differential inclusions via fixed point methods. This book is motivated by that research as the authors endeavor to bring under one cover much of those results along with results by other researchers either affecting or affected by the authors' work. The questions of existence and stability of solutions for different classes of initial value problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems. In addition, since differential equations can be viewed as special cases of differential inclusions, significant attention is also given to relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simpler beginnings as well.
How did life on Earth get started? Can we duplicate human thought in a computing machine? How do children acquire language? Ten years ago, in PARADIGMS LOST, John L. Casti looked at the state of play with these and a handful of other eternal questions, outlining the competing answers on offer and describing the scientists who advocated them. In PARADIGMS REGAINED Casti recounts the huge leaps science has made since then, and how new theories and candidate answers have emerged for almost all the big questions. As we enter the twenty-first century, PARADIGMS REGAINED provides an excellent summary of what we understand about key scientific issues.
Casti Tours offers the most spectacular vistas of modern applied mathematics."-- Nature Mathematical modeling is about rules--the rules of reality. Reality Rules explores the syntax and semantics of the language in which these rules are written, the language of mathematics. Characterized by the clarity and vision typical of the author's previous books, Reality Rules is a window onto the competing dialects of this language--in the form of mathematical models of real-world phenomena--that researchers use today to frame their views of reality. Moving from the irreducible basics of modeling to the upper reaches of scientific and philosophical speculation, Volumes 1 and 2, The Fundamentals and The Frontier, are ideal complements, equally matched in difficulty, yet unique in their coverage of issues central to the contemporary modeling of complex systems. Engagingly written and handsomely illustrated, Reality Rules is a fascinating journey into the conceptual underpinnings of reality itself, one that examines the major themes in dynamical system theory and modeling and the issues related to mathematical models in the broader contexts of science and philosophy. Far-reaching and far-sighted, Reality Rules is destined to shape the insight and work of students, researchers, and scholars in mathematics, science, and the social sciences for generations to come. Of related interest . . . ALTERNATE REALITIES Mathematical Models of Nature and Man John L. Casti A thoroughly modern account of the theory and practice of mathematical modeling with a treatment focusing on system-theoretic concepts such as complexity, self-organization, adaptation, bifurcation, resilience, surprise and uncertainty, and the mathematical structures needed to employ these in a formal system. 1989 0-471-61842-X 493pp.
Mood Matters" makes the radical assertion that all social events ranging from fashions in music and art to the rise and fall of civilizations are biased by the attitudes a society holds toward the future. When the "social mood" is positive and people look forward to the future, events of an entirely different character tend to occur than when society is pessimistic. The book presents many examples from every walk of life in support of this argument. In addition, methods are given to actually measure the social mood and to project it into the future in order to forecast what’s likely or not over varying periods of time. Casti's writing is a pleasure to read and its contents an eye-opener. "They [the chapters] tell an engrossing story, and the mystery heightens as it goes. . . . it's chatty and knowing." Greg Benford, Physicist and science-fiction writer, author of "Timescape" and "Deep Time" "I am struck by how thought-provoking it all is. I am sure that your book will draw a lot of attention" Tor Norretranders, Science writer, author of "The Generous Man" and "The User Illusion".
By 1949, the idea of duplicating human thought processes in a computer was starting to surface, as the outgrowth of code-breaking work done by Alan Turing and others in Britain during the Second World War. This ingenious work of speculative scientific fiction reconstructs what might have been said during the animated conversation flowing around Snow's rooms that fateful in Cambridge. The quintet's debate anticipates all of the basic questions which have surrounded artificial intelligence in the fifty years since. Can a machine think or merely process information? Is the brain simply a symbol-processing machine, as Turing suggests, and if so, what is the nature of meaning? Can there be, as Wittgenstein proposes, no thought without language, and no language without the social interaction of human beings?
By the author of The Cambridge Quintet, John L. Casti's new book continues the tradition of combining science fact with just the right dose of fiction. Part novel, part science â€" wholly informative and entertaining. In the fall of 1933 the newly founded Institute for Advanced Study in Princeton, New Jersey, welcomed its first faculty member, Albert Einstein. With this superstar on the roster, the Institute was able to attract many more of the greatest scholars, scientists, and poets from around the world. It was to be an intellectual haven, a place where the most brilliant minds on the planet, sheltered from the outside world's cares and calamities, could study and collaborate and devote their time to the pure and exclusive pursuit of knowledge. For many of them, it was the "one, true, platonic heaven." Over the years, key figures at the Institute began to question the limits to what science could tell us about the world, pondering the universal secrets it might unlock. Could science be the ultimate source of truth; or are there intrinsic limits, built into the very fabric of the universe, to what we can learn? In the late 1940's and early 1950's, this important question was being asked and pondered upon by some of the Institute's deepest thinkers. Enter the dramatis personae to illuminate the science and the philosophy of the time. Mathematical logician Kurt Godel was the unacknowledged Grant Exalted Ruler of this platonic estate â€" but he was a ruler without a scepter as he awaited the inexplicably indefinite postponement of his promotion to full, tenured professor. Also in residence was his colleague, the Hungarian-American polymath, John van Neumann, developer of game theory, the axiomatic foundations of quantum mechanics, and the digital computer â€" stymied by the Institute's refusal to sanction his bold proposal to actually build a computer. One of Godel's closest friends figures large in this story: Albert Einstein, by common consensus the greatest physicist the 20th century had ever known. And, of course, the director the Institute, J. Robert Oppenheimer, the father of the atomic bomb, must by necessity be key to any story that focuses in on this time and place. Author Casti elegantly sets the stage and then masterfully directs this impressive cast of charactersâ€"with able assists by many "minor-character" icons like T. S. Eliot, Wolfgang Pauli, Freeman Dyson, and David Bohm, to tell a story of science, history, and ideas. As we watch events unfold (some of which are documented fact while others are creatively imagined fiction), we are witness to the discussions and deliberations of this august group… privy to wide-ranging conversations on thinking machines, quantum logic, biology as physics, weather forecasting, the structure of economic systems, the distinction between mathematics and natural science, the structure of the universe, and the powers of the human mind â€" all centered around the question of the limits to scientific knowledge. Imaginatively conceived and artfully executed, The One True Platonic Heaven is an accessible and intriguing presentation of some of the deepest scientific and philosophical ideas of the 20th century.
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