Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once - setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

This book is devoted to the problems involved in modern human diet, as it changes from the time of the Neolithic revolution some 12,000 years ago and have a great impact on human health. The book offers an entirely new concept of the genome, cells and body interaction which explains the increase in population of the degenerative diseases frequency such as cancer, diabetes and many others. Systematic approach to the genome and its interaction with food formalized as the work of a strange attractor metabolism. This approach points to new direction for the study of metabolism of food and the importance of general principles associated with life origin and existence of living matter. The book is useful to anyone interested in issues of nutrition and provides an invaluable tool to assess the superfoods and dietary supplements in various commercial forms available on the market. In addition, this book will help understand the quality of the products offered in supermarkets and to develop proper dieting strategy to each section of population. After reading this book, anyone can become a professional in matters of food and diets, and to conduct itself independent research in this area.

This book presents leading-edge research on artificial life, cellular automata, chaos theory, cognition, complexity theory, synchronisation, fractals, genetic algorithms, information systems, metaphors, neural networks, non-linear dynamics, parallel computation and synergetics. The unifying feature of this research is the tie to chaos and complexity.

An integrated coverage of probability, statistics, Monte Carlo simulation, inferential statistics, design of experiments, systems reliability, fitting random data to models, analysis of variance, stochastic processes, and stochastic differential equations. The author for first time presents an introduction to the broad field of applied engineering uncertainty analysis in one comprehensive, friendly, coverage. Each concept is illustrated with several examples of relevance in engineering applications (no cards, colored balls, or dice). This edition includes new research advances in nonlinear stochastic equations; simple methods to solve and graph boundary-value problems in several dimensions; 478 pages; 177 solved examples; 147 proposed problems; 174 illustrations, 69 short computer programs; and 51 data and statistical tables. AEROSPACE (from the Royal Aeronautical Society): ..".an integrated, balanced, and clear presentation to probability, statistics, stochastic models, and stochastic differential equations. The aim is to demonstrate to the reader that the fundamental principles are inherently simple and that the methods are practical and extremely useful in everyday engineering analysis or design. The book succeeds admirably in these aims." QUALITY AND RELIABILITY INTERNATIONAL: ..".discusses uncertainty in engineering... The essential differences are beautifully explained, providing a philosophical and practical basis for the rest of the book. This essential introduction is lacking in most books on statistics applications in engineering ...Overall, the book presents clear and interesting descriptions and explanations. The level of mathematics is appropriate to reasonably numerate engineers, and the use of spreadsheets and Maple enhance the practical value to engineers. I strongly recommend this book to design and systems engineers..." STOCHASTIC ENVIRONMENTAL RESEARCH ANS RISK ASSESSMENT: ..".written in a clear and easy-to-understand manner. It requires no prior background in statistics... it has numerous solved practical examples... and a significant amount of new material. The emphasis is on concepts and their illustration, and the author has made a concerted effort in avoiding lengthy derivations and this is an attractive feature from a student's perspective."

"You believe in a God who plays dice, and I in complete law and order", Albert Einstein. The science of chaos is forcing scientists to rethink Einstein's fundamental assumptions regarding the way the universe behaves. Chaos theory has already shown that simple systems, obeying precise laws, can nevertheless act in a random manner. Perhaps God plays dice within a cosmic game of complete law and order. "Does God Play Dice?" reveals a strange universe in which nothing may be as it seems. Familiar geometrical shapes such as circles and ellipses give way to infinitely complex structures known as fractals, the fluttering of a butterfly's wings can change the weather, and the gravitational attraction of a creature in a distant galaxy can change the fate of the solar system. This revised and updated edition includes three completely new chapters on the prediction and control of chaotic systems. It also incorporates new information regarding the solar system and an account of complexity theory. This text aims to make the complex mathematics of chaos accessible and entertaining.

There is a growing interest on the part of undergraduate and graduate students and investigators in applying fractals and chaos (nonlinear dynamics) to a variety of problems in biology and medicine. This book explains fractals and chaos and illustrates their use with examples from biomedical research. The author presents the material in a unique style that doesn't require a strong background in mathematics. The ideas are presented in a straightforward way without technical jargon. One concept at a time is explained in a set of facing pages, with text on the left page and graphics on the right page. The graphics pages can be copied directly on to transparencies for teaching.

Chaos theory challenges the presumption that the cosmos is orderly, linear, and predictable--but it does not imply pure randomness and chance events. Rather, chaos-informed postmodernist analysis introduces a new vision by celebrating unexpected, surprise, ironic, contradictory, and emergent elements. Scholars in many disciplines are taking this perspective as an alternative to the entrenched structural functionalism and empiricism rooted in linear science. In the early 1990s studies began to emerge applying chaos theory to criminology, law, and social change. This book brings together some of the key thinkers in these areas. Part I situates chaos theory as a constitutive thread in contemporary critical thought in criminology and law. It seeks to provide the reader with a sensitivity to how chaos theory fits within the postmodern perspective and an understanding of its conceptual tools. Part II comprises chapters on applying the chaos perspective to critical criminology and law and, beyond, to peacemaking. Part III presents studies in chaos-informed perspectives on new social movement theory, social change, and the development of social justice. While the book emphasizes the usefulness of the conceptual tools of chaos theory in critical criminology and law, its ultimate goal goes beyond theory-building to provide vistas for understanding the contemporary social scene and for the development of the new just society.

"SCIENCE JOURNALISM AT ITS BEST. . . An impeccably researched, amazingly up-to-date, crisply written and well-illustrated survey."
--Nature
At the cutting edge of the sciences, a dynamic new concept is emerging: complexity. In this groundbreaking new book, Peter Coveney and Roger Highfield explore how complexity in mathematics, physics, biology, chemistry, and even the social sciences is transforming not only the way we think about the universe, but also the very assumptions that underlie conventional science.
Complexity is a watchword for a new way of thinking about the behavior of interacting units, whether they are atoms, ants in a colony, or neurons firing in a human brain. The rise of the electronic computer provided both the key and the catalyst to our exploration of complexity.
A new generation of computers that runs on light and exploits the bizarre properties of quantum mechanics promises to deepen our understanding still further. The advances we have already witnessed are spectacular. The authors take us inside laboratories where scientists are evolving the genetic molecules that enabled life to emerge on earth and generating universes teeming with virtual creatures in cyber-space. We witness the utterly realistic behavior of a school of virtual fish--computer-generated replicas that have been trained to swim gracefully, hunt for food, and scatter at the approach of a leopard shark.
Compelling in its clarity, far-reaching in its implications, vibrant with the excitement of new discovery, Frontiers of Complexity is an arresting account of how far science has come in the past fifty years and an essential guide to the rapidly approaching future.
"[A] MARVELOUS AND COMPREHENSIVE WORK . . . Virtually any scientist or interested lay reader will find this book engrossing, edifying and inspiring."
--Publishers Weekly (starred review)

"Chaos Theory" is a revolutionary approach to understanding and forecasting the behavior of complex systems. The theory, which utilizes nonlinear mathematics to identify the underlying rules of evolving systems, provides extraordinary insights into the dynamics of the financial markets. In so doing, Dr. Chorafas explores a variety of new approaches that provide an entirely new perspective on financial market analysis and forecasting. Topics in this book include: the concepts and mathematics of chaos theory; using nonlinear equations and fractals to forecast the currency market; genetic algorithms and neural networks.

Das Buch wendet sich an Leser, die - uber die rein computergraphische Darstellung hinaus - an einer analytischen Untersuchung von chaotischen und nichtchaotischen Differenzen- und Differentialgleichungssystemen interessiert sind. Breiter Raum wird der Durchrechnung von Beispielen gegeben. Dargestellt werden zunachst qualitative Methoden als auch solche, die das Auffinden von Attraktoren, Bifurkationen etc. und deren Klassifikation in Abhangigkeit von den Systemparametern gestatten. Der letzte Teil schliesslich widmet sich der quantitativen Beschreibung chaotischer Systeme. Dazu werden zuerst die Begriffe Chaos und Fraktal exakt definiert und dann die verschiedenen fraktalen Dimensionen, Lyapunov-Exponenten, Entropien etc. eingefuhrt und durch Beispiele begrundet."

These are exciting times for mathematics, science, and technology. One of the fields that has been receiving great attention is Chaos Theory. Actually, this is not a single discipline, but a potpourri of nonlinear dynamics, nonequilibrium thermodynamics, information theory, and fractal geometry. In the less than two decades that Chaos Theory has become a major part of mathematics and physics, it has become evident that the old paradigm of determinism is insufficient if we are to understand - and perhaps solve - real life problems. Curiously, many of these problems are deterministic, but they are intertwined with randomness and chance. Thus the deterministic laws of physics coexist with the laws of probability. Consequently, uncertainty arises and unpredictability occurs, characteristic of complex systems. In its short lifetime Chaos Theory has already helped us gain insights into problems that in the past we found intractable. Examples of such problems include weather, turbulence, cardiological and neurophysiological episodes, economic restructuring, financial transactions, policy analysis, and decision making. Admittedly, we can as yet solve only relatively simple problems, but much progress has been made and we are now able to observe complex problems from new vantage points that provide us with numerous benefits. One such benefit is the universality of Chaos Theory in its applicability to different situations, which enables us to look at communal problems in an interdisciplinary manner, so that persons of different backgrounds can communicate with one another. Chaos Theory also enables us to reason in a holistic manner, rather than being constrained by simplistic reductionism.Finally, it is gratifying that the mathematics is not intimidating, and one can accomplish much with a personal computer or even a handheld calculator.

These 28 contributions by leading researchers - from such diverse disciplines as chemistry, biology, physics, mathematics, and physiology - describe recent experiments, numerical simulations, and theoretical analyses of the formation of spatial patterns in chemical and biological systems.Chemical patterns have been systematically studied since the field was established by Alan Turing's landmark 1952 paper, "The chemical basis for morphogenesis," yet only recently have new experimental techniques and numerical analyses of reaction-diffusion equations opened the way to understanding stationary and traveling wave patterns.This collection summarizes the exciting developments in this rapidly growing field. It shows that some biological patterns have been found to be strikingly similar to patterns found in simple, well-controlled laboratory chemical systems, that new chemical reactor designs make it possible to sustain chemical patterns and to study transitions between different kinds of patterns, and that nearly 40 years after Turing's paper, the patterns predicted by Turing have finally been observed in laboratory experiments.Harry L. Swinney is Sid Richardson Foundation Regents Chair, Department of Physics, and Director of the Center for Nonlinear Dynamics at the University of Texas at Austin. Valentin I. Krinsky is Head of the Autowave Laboratory, Institute of Biological Physics, Academy of Sciences, Pushchino, USSR.Chapters cover: Spiral, Ring, and Scroll Patterns: Experiments. Spiral, Ring, and Scroll Patterns: Theory and Simulations. Fronts and Turing Patterns. Waves and Patterns in Biological Systems.

This volume contains the proceedings of a highly successful AMS Short Course on Chaos and Fractals, held during the AMS Centennial Celebration in Providence, Rhode Island in August 1988. Chaos and fractals have been the subject of great interest in recent years and have proven to be useful in a variety of areas of mathematics and the sciences. The purpose of the short course was to provide a solid introduction to the mathematics underlying the notions of chaos and fractals. The papers in this book range over such topics as dynamical systems theory, Julia sets, the Mandelbrot set, attractors, the Smale horseshoe, calculus on fractals, and applications to data compression. The authors represented here are some of the top experts in this field. Aimed at beginning graduate students, college and university mathematics instructors, and non-mathematics researchers, this book provides readable expositions of several exciting topics of contemporary research.

While many books have discussed methodological advances in nonlinear dynamical systems theory (NDS), this volume is unique in its focus on NDS's role in the development of psychological theory. After an introductory chapter covering the fundamentals of chaos, complexity and other nonlinear dynamics, subsequent chapters provide in-depth coverage of each of the specific topic areas in psychology. A concluding chapter takes stock of the field as a whole, evaluating important challenges for the immediate future. The chapters are written by experts in the use of NDS in each of their respective areas, including biological, cognitive, developmental, social, organizational and clinical psychology. Each chapter provides an in-depth examination of theoretical foundations and specific applications and a review of relevant methods. This edited collection represents the state of the art in NDS science across the disciplines of psychology.

Dieses Lehrbuch bietet eine grundlegende Einfuhrung in chaotische Systeme, welche keinerlei Abstriche an mathematischer Exaktheit macht. Der Text umfasst einerseits in ansprechender Tiefe die klassischen theoretischen Gesichtspunkte der dynamischen Systeme, wobei alle wesentlichen Beispiele der Literatur ausuhrlich behandelt werden. Daneben befasst er sich mit moderneren Fragestellungen, wie etwa nach der Natur der Berechenbarkeit oder der Verlasslichkeit des Computers. Die Abgrenzung zu fortgeschrittenen Methoden ist klar gegeben durch den Ausschluss statistischer Methoden.

Zu den Kernphanomenen werden kurze, aber vollstandige Programme in der Programmiersprache Mathematica angegeben, welche leicht zu verstehen sind und die man fur das individuelle Experimentieren leicht ubernehmen und anpassen kann. Uber 180 Beispiele und Ubungsaufgaben veranschaulichen das Material und vertiefen das Verstandnis des Lesers. Biographien von historischen Schlusselpersonlichkeiten bereichern den Text."

This book presents new international research on artificial life, cellular automata, chaos theory, cognition, complexity theory, synchronisation, fractals, genetic algorithms, information systems, metaphors, neural networks, non-linear dynamics, parallel computation and synergetics. The unifying feature of this research is the tie to chaos and complexity.

This book presents the latest leading-edge international research on artificial life, cellular automata, chaos theory, cognition, complexity theory, synchronisation, fractals, genetic algorithms, information systems, metaphors, neural networks, non-linear dynamics, parallel computation and synergetics. The unifying feature of this research is the tie to chaos and complexity.

This collection of fifteen research papers explores the implications of chaos and complexity in physical, chemical, and biological systems for philosophical and theological issues regarding God's action in the world. It resulted from the second of five international research conferences being co-sponsored by the Vatican Observatory, Rome, and the Center for Theology and the Natural Sciences, Berkeley. The overarching goal is to contribute to constructive theology as it engages current research in the natural sciences and to investigate the philosophical and theological elements in ongoing theoretical research in the natural sciences.