Captioned cartoon drawings offering an overview of universal order as they deal with various phenomena are combined with scientific commentary

    Drawing on the insights of towering figures like Karl Popper and Thomas Kuhn, Lewens shows how key questions in science matter, often in personal, practical and political ways.

    But your pleasure and prowess at games, gambling, and other numerically related pursuits can be heightened with this entertaining volume, in which the authors offer a fascinating view of some of the lesser-known and more imaginative aspects of mathematics.A brief and breezy explanation of the new language of mathematics precedes a smorgasbord of such thought-provoking subjects as the googolplex (the largest definite number anyone has yet bothered to conceive of); assorted geometries — plane and fancy; famous puzzles that made mathematical history; and tantalizing paradoxes. Gamblers receive fair warning on the laws of chance; a look at rubber-sheet geometry twists circles into loops without sacrificing certain important properties; and an exploration of the mathematics of change and growth shows how calculus, among its other uses, helps trace the path of falling bombs.Written with wit and clarity for the intelligent reader who has taken high school and perhaps college math, this volume deftly progresses from simple arithmetic to calculus and non-Euclidean geometry. It “lives up to its title in every way [and] might well have been merely terrifying, whereas it proves to be both charming and exciting." — Saturday Review of Literature.

      “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.”—Nina MacLaughlin, Boston Globe “Engaging, eminently readable . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.”—Judith Goodstein, American Scientist  Harvard geometer and Fields medalist Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers readers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.

    Shows how any proof can be understood as a sequence of techniques. Covers the full range of techniques used in proofs, such as the contrapositive, induction, and proof by contradiction. Explains how to identify which techniques are used and how they are applied in the specific problem. Illustrates how to read written proofs with many step-by-step examples. Includes new, expanded appendices related to discrete mathematics, linear algebra, modern algebra and real analysis.

    Astronomer John Barrow takes an intriguing look at the limits of science, who argues that there are things that are ultimately unknowable, undoable, or unreachable.

    Offers 365 daily inspirational thoughts from The Road Less Traveled and The Different Drum that focus on the challenges of everyday life.

    A genius who throughout his life solved complex mathematical calculations in his head, and a writer gifted with an inimitable style, Poincaré rose to the challenge of interpreting the philosophy of science to scientists and nonscientists alike. His lucid and welcoming prose made him the Carl Sagan of his time. This volume collects his three most important books: Science and Hypothesis (1903); The Value of Science (1905); and Science and Method (1908).

    Physics and Beyond contains Heisenberg’s most sophisticated statements of his philosophy of quantum theory, and is also a watershed inspiration for the contemporary pragmatist philosophy of science that prevails in academia today.

    Readers will progress from building a basic physics engine to creating intelligent moving objects and complex systems, setting the foundation for further experiments in generative design. Subjects covered include forces, trigonometry, fractals, cellular automata, self-organization, and genetic algorithms. The book's examples are written in Processing, an open-source language and development environment built on top of the Java programming language. On the book's website (http://www.natureofcode.com), the examples run in the browser via Processing's JavaScript mode.

    In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.

    Bronowski was both a distinguished mathematician and a poet, a philosopher of science and a literary critic who wrote a well-known study of William Blake. Dr. Bronowski's very career was founded on the premise of an intimate connection between science and the humanities, disciplines which are still generally thought to be worlds apart.The Common Sense of Science, a book which remains as topical today as it was when it first appeared twenty-five years ago, articulates and develops Bronowski's provocative idea that the sciences and the arts fundamentally share the same imaginative vision.

    Without knowledge, scientific enquiry is meaningless and we can’t begin to analyse the world around us. What is knowledge? How do you know you are not dreaming? Should we trust our senses? Presuming no prior experience of philosophy, this book covers everything in the topic from scepticism and possible worlds to Kant’s transcendentalism. Clear and readable, Epistemology: A Beginner’s Guide is essential reading for students and aspiring thinkers.

    Is there a God? How can we explain the presence of evil? Do humans, or human souls, live on after death? Is there a hell? The following lectures examine these eternal questions and present the most compelling arguments for and against God's existence, the seeming conflicts between religion and science, and the different truth-claims of the world's most popular religions. By delving into the major characteristics of world religions, including Judaism, Christianity, Islam, Hinduism, and Buddhism, mankind's association with the many different varieties of religious practice is brought to light. Above all, Faith and Reason: The Philosophy of Religion lays the groundwork for a rational approach to pursuing questions of faith - and at the same time provides a better understanding of religion's ongoing importance in the realm of human experience.

    Literally. This book does not aim to make your life carefree, to make your problems disappear, to turn you into a saint free from blemish or blame. In fact, you may end up utterly bewildered by The Mystery Experience at times. But you will also be intrigued. Curious.Questioning. Loving. Loved. Overjoyed. Seduced out of the numbness of banality. And most importantly, awake. Gloriously awake, and full of wonder. Philosopher and author Tim Freke leads us on a journey through the nature of the 'Mystery Experience', via quantum physics, Gnosticism, the essence of Tao, meditation, Walt Whitman, Greek mythology, Buddhism, Dub Punk musician Jah Wobble, and Carl Jung. But what is the 'Mystery Experience'? You can taste it by simply focusing your attention on the mystery. But what is the mystery? The mystery is life. The mystery is the journey. The mystery is you. The mystery is me. The mystery makes you want to say, simply: WOW. No one has the answers, but asking the questions is what makes us come alive. Wherever you're coming from, you will find this journey rewarding. The only real requirement is that you're willing to wonder about life - to be curious and open - to be an explorer. Now prepare to leave base camp, because we're about to set off on a grand adventure.