Historical records are first found in Babylon and Egypt, and after two millennia the arithmetical astronomy of the Babylonians merged with the Greek geometrical approach to culminate in the Almagest of Ptolemy. This legacy was transmitted to the Latin West via Islam, and led to Copernicus's claim that the Earth is in motion. In justifying this Kepler converted astronomy into a branch of dynamics, leading to Newton's universal law of gravity. The book concludes with eighteenth- and nineteenth-century applications of Newton's law, and the first explorations of the universe of stars.

    Federal Reserve Bank sneezes the global economy catches cold, read this book," writes John L. Casti (Santa Fe Institute). This "cogent and engaging" (Nature) work presents the fundamental principles of the emerging field of "small-worlds" theory—the idea that a hidden pattern is the key to how networks interact and exchange information, whether that network is the information highway or the firing of neurons in the brain. Mathematicians, physicists, computer scientists, and social scientists are working to decipher this complex organizational system, for it may yield a blueprint of dynamic interactions within our physical as well as social worlds.Highlighting groundbreaking research behind network theory, "Mark Buchanan's graceful, lucid, nontechnical and entertaining prose" (Mark Granovetter) documents the mounting support among various disciplines for the small-worlds idea and demonstrates its practical applications to diverse problems—from the volatile global economy or the Human Genome Project to the spread of infectious disease or ecological damage. Nexus is an exciting introduction to the hidden geometry that weaves our lives so inextricably together.

    Increasingly, the decisions that affect our lives--where we go to school, whether we can get a job or a loan, how much we pay for health insurance--are being made not by humans, but by machines. In theory, this should lead to greater fairness: Everyone is judged according to the same rules.But as mathematician and data scientist Cathy O'Neil reveals, the mathematical models being used today are unregulated and uncontestable, even when they're wrong. Most troubling, they reinforce discrimination--propping up the lucky, punishing the downtrodden, and undermining our democracy in the process.

    The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on a large scale, and the development of a variety of new theoretical tools has allowed us to extract new knowledge from many different kinds of networks.The study of networks is broadly interdisciplinary and important developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas.Subjects covered include the measurement and structure of networks in many branches of science, methods for analyzing network data, including methods developed in physics, statistics, and sociology, the fundamentals of graph theory, computer algorithms, and spectral methods, mathematical models of networks, including random graph models and generative models, and theories of dynamical processes taking place on networks.

    Wolfram lets the world see his work in A New Kind of Science, a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modeling complex systems. On the frontier of complexity science since he was a boy, Wolfram is a champion of cellular automata--256 "programs" governed by simple nonmathematical rules. He points out that even the most complex equations fail to accurately model biological systems, but the simplest cellular automata can produce results straight out of nature--tree branches, stream eddies, and leopard spots, for instance. The graphics in A New Kind of Science show striking resemblance to the patterns we see in nature every day. Wolfram wrote the book in a distinct style meant to make it easy to read, even for nontechies; a basic familiarity with logic is helpful but not essential. Readers will find themselves swept away by the elegant simplicity of Wolfram's ideas and the accidental artistry of the cellular automaton models. Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. --Therese Littleton

    This short and accessible introduction provides an invaluable tool with which to think about the ethical values that lie at the heart of medicine.Tony Hope deals with thorny moral issues, including euthanasia and the morality of killing. He also explores political questions, such as how we can make sure health care resources are distributed fairly. Each chapter in the book considers a different issue, for example, genetics, modern reproductive technologies, resource allocation, mental health, and medical research. Each section also discusses controversial questions such as: Who should have access to reproductive technology? Is it right to fund expensive drug treatment for individuals? Should treatment for mental illness be imposed on patients without their consent? Considering a wide range of questions of medical ethics, this Very Short Introduction will help to explain some of the confusing issues facing the field of medicine today.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    Japanese goods and cultural products--from animated movies and computer games to cars, semiconductors, and management techniques--are consumed around the world. In many ways, Japan is an icon of the modern world, and yet it remains something of an enigma to many, who see it as a confusing montage of the alien and the familiar, the ancient and modern. This Very Short Introduction explodes the myths and explores the reality of modern Japan, offering a concise, engaging, and accessible look at the history, economy, politics, and culture of this fascinating nation. It examines what the term modern means to the Japanese, debunks the notion that Japan went through a period of total isolation from the world, and explores the continuity between pre- and post-war Japan. Anyone curious about this intriguing country will find a wealth of insight and information in these pages.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam

    Plants have also become essential to humans not only in the form of cereal crops, fruit, and vegetables, but in their many other uses in wood and paper, and in providing medicines. In this Very Short Introduction Timothy Walker, Director of the Botanical Gardens in Oxford, provides a concise account of the nature of plants, their variety and classification, their evolution, and their aesthetic and practical value, stressing the need for their conservation for future generations.

    From Edward Lorenz’s discovery of the Butterfly Effect, to Mitchell Feigenbaum’s calculation of a universal constant, to Benoit Mandelbrot’s concept of fractals, which created a new geometry of nature, Gleick’s engaging narrative focuses on the key figures whose genius converged to chart an innovative direction for science. In Chaos, Gleick makes the story of chaos theory not only fascinating but also accessible to beginners, and opens our eyes to a surprising new view of the universe.

    Jan Westerhoff shows that the question "what is real?" is not some esoteric puzzle that only philosophers ponder. Scientists also ask this question when they investigate whether candidates for the fundamental constituents of matter are actually "out there" or just a mere abstraction from a successful theory and cognitive scientists ask it when trying to find out which set of the bewildering array of data processed by our brain could constitute the basis for the self.

    Yet there is much more to the debate than theclash of these extremes. As Thomas Dixon shows in this balanced and thought-provoking introduction, a whole range of views, subtle arguments, and fascinating perspectives can be found on this complex and centuries-old subject. He explores the key philosophical questions that underlie the debate, but also highlights the social, political, and ethical contexts that have made the tensions between science and religion such a fraught and interesting topic in the modern world. Dixon emphasizes how the modern conflict between evolution and creationism is quintessentially an American phenomenon, arising from the culture and history of the United States, as exemplified through the ongoing debates about how to interpret the First-Amendment's separation of church and state. Along the way, he examines landmark historical episodes such as the Galileo affair, Charles Darwin's own religious andscientific odyssey, the Scopes Monkey Trial in Tennessee in 1925, and the Dover Area School Board case of 2005, and includes perspectives from non-Christian religions and examples from across the physical, biological, and social sciences.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundredsof key topics, from philosophy to Freud, quantum theory to Islam.

    A complex system--such as an economy or a tropical ecosystem--consists of interacting adaptive entities that produce dynamic patterns and structures. Diversity plays a different role in a complex system than it does in an equilibrium system, where it often merely produces variation around the mean for performance measures. In complex adaptive systems, diversity makes fundamental contributions to system performance.Scott Page gives a concise primer on how diversity happens, how it is maintained, and how it affects complex systems. He explains how diversity underpins system level robustness, allowing for multiple responses to external shocks and internal adaptations; how it provides the seeds for large events by creating outliers that fuel tipping points; and how it drives novelty and innovation. Page looks at the different kinds of diversity--variations within and across types, and distinct community compositions and interaction structures--and covers the evolution of diversity within complex systems and the factors that determine the amount of maintained diversity within a system. Provides a concise and accessible introduction Shows how diversity underpins robustness and fuels tipping points Covers all types of diversity The essential primer on diversity in complex adaptive systems

    But what are thoughts? How does the brain--billions of tiny neurons and synapses--accomplish thought? In this compelling Very Short Introduction, Tim Bayne offers a compact but wide-ranging account of the nature of thought, drawing upon philosophy, psychology, neuroscience, and anthropology. Bayne touches on a stimulating array of topics. Does thinking occur in public or is it a purely private affair? Do young children and non-human animals think? Is human thought the same everywhere, or are there culturally specific modes of thought? What is the relationship between thought and language? What kind of responsibility do we have for our thoughts? In what ways can the process of thinking go wrong? Beginning with questions about what thought is and what distinguishes it from other kinds of mental states, he explores the logical structures of thought as well as the mechanisms that make thought possible. In sum, this book provides an engaging survey of what we know--and what we don't know--about one of the most central of human capacities. About the Series: Oxford's Very Short Introductions series offers concise and original introductions to a wide range of subjects--from Islam to Sociology, Politics to Classics, Literary Theory to History, and Archaeology to the Bible. Not simply a textbook of definitions, each volume in this series provides trenchant and provocative--yet always balanced and complete--discussions of the central issues in a given discipline or field. Every Very Short Introduction gives a readable evolution of the subject in question, demonstrating how the subject has developed and how it has influenced society. Eventually, the series will encompass every major academic discipline, offering all students an accessible and abundant reference library. Whatever the area of study that one deems important or appealing, whatever the topic that fascinates the general reader, the Very Short Introductions series has a handy and affordable guide that will likely prove indispensable.

    The book was based on a course of public lectures delivered by Schrödinger in February 1943 at Trinity College, Dublin. Schrödinger's lecture focused on one important question: "how can the events in space and time which take place within the spatial boundary of a living organism be accounted for by physics and chemistry?" In the book, Schrödinger introduced the idea of an "aperiodic crystal" that contained genetic information in its configuration of covalent chemical bonds. In the 1950s, this idea stimulated enthusiasm for discovering the genetic molecule and would give both Francis Crick and James Watson initial inspiration in their research.

    Most of the time this math works quietly behind the scenes . . . until it doesn't. All sorts of seemingly innocuous mathematical mistakes can have significant consequences.Math is easy to ignore until a misplaced decimal point upends the stock market, a unit conversion error causes a plane to crash, or someone divides by zero and stalls a battleship in the middle of the ocean.Exploring and explaining a litany of glitches, near misses, and mathematical mishaps involving the internet, big data, elections, street signs, lotteries, the Roman Empire, and an Olympic team, Matt Parker uncovers the bizarre ways math trips us up, and what this reveals about its essential place in our world. Getting it wrong has never been more fun.