It requires, in short, an understanding of probability. In this Very Short Introduction, John Haigh introduces the ideas of probability--and the different philosophical approaches to probability--and gives a brief account of the history of development of probability theory, from Galileo and Pascal to Bayes, Laplace, Poisson, and Markov. He describes the basic probability distributions and discusses a wide range of applications in science, economics, and a variety of other contexts such as games and betting. He concludes with an intriguing discussion of coincidences and some curious paradoxes.

    Even the simplest system of cause and effect can be subject to chaos, denying us accurate predictions of its behaviour, and sometimes giving rise to astonishing structures of large-scale order. Our growing understanding of Chaos Theory is having fascinating applications in the real world - from technology to global warming, politics, human behaviour, and even gambling on the stock market. Leonard Smith shows that we all have an intuitive understanding of chaotic systems. He uses accessible maths and physics (replacing complex equations with simple examples like pendulums, railway lines, and tossing coins) to explain the theory, and points to numerous examples in philosophy and literature (Edgar Allen Poe, Chang-Tzu, Arthur Conan Doyle) that illuminate the problems. The beauty of fractal patterns and their relation to chaos, as well as the history of chaos, and its uses in the real world and implications for the philosophy of science are all discussed in this Very Short Introduction.

    Featuring many striking photos, this Very Short Introduction offers a fascinating portrait of the unique world of each planet as well as an illuminating discussion of moons, asteroids, and Trans-Neptunian objects. Leading planetary scientist David A. Rothery, who has chaired the European Space Agency's Mercury surface and composition working group since 2007, gives a stimulating overview of the origin, nature, and evolution of our Solar System, including the controversial issues of what qualifies as a planet, and what conditions are required for a planetary body to support life. He explains how the surfaces of planets and moons have been sculpted by geology, weather, and impacts by meteors and asteroids. Rothery shows how our knowledge has advanced over the centuries, and how it has expanded at a dramatic rate in recent years, going far beyond our Solar System to explore planets orbiting distant stars.

    Travel fast enough and you could weigh as much as a jumbo jet, be flattened thinner than a CD without feeling a thing-and live forever! As for the angles of a triangle, they do not always have to add up to 180 degrees. And then, of course, there are black holes. These are but a few of the extraordinary consequences of Einstein's theory of relativity. It is now over a hundred years since he made these discoveries, and yet the general public is still largely unaware of them. Filled with illuminating anecdotes and fascinating accounts of experiments, this book aims to introduce the interested lay person to the subject of relativity in a way which is accessible and engaging and at the same time scientifically rigorous. With relatively few mathematical equations--nothing more complicated than the Pythagoras's Theorem--this VSI packs a lot time into very little space, and for anyone who has felt intimidated by Einstein's groundbreaking theory, it offers the perfect place to start. 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.

    In this Very Short Introduction, Peter M. Higgins, a renowned popular-science writer, unravels the world of numbers, demonstrating its richness and providing an overview of all the number types that feature in modern science and mathematics. Indeed, Higgins paints a crystal-clear picture of the number world, showing how the modern number system matured over many centuries, and introducing key concepts such as integers, fractions, real and imaginary numbers, and complex numbers. Higgins sheds light on such fascinating topics as the series of primes, describing how primes are now used to encrypt confidential data on the internet. He also explores the infinite nature of number collections and explains how the so-called real numbers knit together to form the continuum of the number line. Written in the fashion of Higgins' highly popular science paperbacks, Numbers accurately explains the nature of numbers and how so-called complex numbers and number systems are used in calculations that arise in real problems.

    Not only are galaxies fascinatingastronomical structures in themselves, but their study has revealed much of what we know today about the cosmos, providing a window on the Big Bang and the origins of the Universe. Gribben looks at our own Milky Way Galaxy in detail, from the different kinds of stars that are born within it, tothe origins of its magnificent spiral structure. Perhaps most interesting, Gribben describes the many exciting discoveries have been made about our own galaxy and about those beyond: how a supermassive black hole lurks at the center of every galaxy, how enormous forces are released when galaxiescollide, how distant galaxies provide a window on the early Universe, and how the formation of young galaxies shed needed light on the mysteries of Cold Dark Matter.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.

    It explains what algorithms do, how they are used, the risks associated with using them, and why governments should be concerned. Important areas arehighlighted, such as Stream Ciphers, block ciphers, public key algorithms, digital signatures, and applications such as e-commerce. This book highlights the explosive impact of cryptography on modern society, with, for example, the evolution of the internet and the introduction of more sophisticatedbanking methods.

    The authors introduce the general reader to some of the most important basic findings, concepts, and procedures of evolutionary biology, as it has developed since the first publications of Darwin and Wallace on the subject, over 140 years ago. They show how evolution provides a unifying set of principles for the whole of biology and sheds light on the relation of human beings to the universe and each other.

    Allen and Cowling start with the simple "prokaryotic" cell--cells with no nucleus--and show how the bodies of more complex plants and animals consist of billions of "eukaryotic" cells, of varying kinds, adapted to fill different roles--red blood cells, muscle cells, branched neurons. The authors also show that each cell is an astonishingly complex chemical factory, the activities of which we have only begun to unravel in the past fifty years.

    The book begins with a guide to what matter is made up of and how it evolved, and goes on to describe the fascinating and cutting-edge techniques used to study it. The author discusses particles such as quarks, electrons, and the neutrino, and exotic matter and antimatter. He also investigates the forces of nature, accelerators and detectors, and the intriguing future of particle physics. This book is essential reading for general readers interested in popular science, students of physics, and scientists at all levels.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.

    The book describes dramatic breakthroughs in our knowledge of how sleep occurs, what it does, and what happens to our health if we do not have enough. The authors consider the impact of modern society, examining the relationship between sleep and our 24/7 culture.

    This book gives a lucid, exciting, and accessible account of the surprising and counterintuitive ideas that shape our understanding of the sub-atomic world. It does not disguise the problems of interpretation that still remain unsettled 75 years after the initial discoveries. The main text makes no use of equations, but there is a Mathematical Appendix for those desiring stronger fare. Uncertainty, probabilistic physics, complementarity, the problematic character of measurement, and decoherence are among the many topics discussed. This volume offers the reader access to one of the greatest discoveries in the history of physics and one of the outstanding intellectual achievements of the twentieth century.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.

    Historian Jacqueline Stedall shows that mathematical ideas are far from being fixed, but are adapted and changed by their passage across periods and cultures. The book illuminates some of the varied contexts in which people have learned, used, and handed on mathematics, drawing on fascinating case studies from a range of times and places, including early imperial China, the medieval Islamic world, and nineteenth-century Britain. By drawing out some common threads, Stedall provides an introduction not only to the mathematics of the past but to the history of mathematics as a modern academic discipline.

    The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understandingof paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questionsabout the mathematical community (such as Is it true that mathematicians burn out at the age of 25?) It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.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.

    But how much do these types of entertainment really tell us about recent scientific discoveries and the latest research into the world of the dinosaur?This is the first book explain how scientists have been able to put together a picture of how dinosaurs looked, what they ate, and how they moved and interacted with each other. Taking a new approach to the subject, David Norman combines different areas of science, such as anatomy, genetics, forensics, and engineering design, to piece together the latest evidence of how animal life evolved on earth. Norman engagingly lays out the history of dinosaur research, from the speculation over ancient myths about dragons, to the latest virtual reality animation sequences and engineering design analysis. He also discusses the role that informed speculation and luck has played in many of the major discoveries.This book is a fantastic introduction for those just beginning to take an interest in dinosaurs and a must-read for true dinosaur-lovers who want to know not just the latest theories and discoveries, but how scientists achieved them.