It addresses science and philosophy, explores the underlying nature of reality, the state of our society and culture, the influence of the mainstream media, the nature of free will and a number of other topics. Each of these examinations contributes an angle to an emerging idea gestalt that challenges present mainstream views and behaviors and offers a sane alternative. The book is organized as a series of short and self-contained essays, most of which can be read in under one hour.

    Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: ..". all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999..". the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals."

    Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his little finger told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.

    Beginning with his humble origins in Australia, Doherty shares his early interests and describes his award-winning, influential work with Rolf Zinkernagel on T-cells and the nature of immune defense. In prose that is amusing and astute, Doherty offers a rare insider's look at the realities of being a research scientist. He lucidly explains his own scientific work and the selection, funding, and organization of research projects; the major problems science hopes to solve; and the rewards of a career in scientific research. For Doherty, science plays an important role in improving the world, and he argues that scientists need to do a better job of making their work more accessible to the public. He concludes with tips on how to win a Nobel Prize, including advice on being persistent, generous, and culturally aware.

    They expect objects to obey principles of physics, and they're startled when things disappear or defy gravity. Yet they can also read emotions and respond with anger, sympathy, and joy. In Descartes' Baby, Bloom draws on a wealth of scientific discoveries to show how these two ways of knowing give rise to such uniquely human traits as humor, disgust, religion, art, and morality. How our dualist perspective, developed throughout our lives, profoundly influences our thoughts, feelings, and actions is the subject of this richly rewarding book.

    Responding to Tarby's questions, Badiou takes us on a journey that interrogates and explores the four conditions of philosophy: politics, love, art and science. In all these domains, events occur that bring to light possibilities that were invisible or even unthinkable; they propose something to us. Everything then depends on how the possibility opened up by the event is grasped, elaborated and embedded in the world - this is what Badiou calls a 'truth procedure'. The event creates a possibility but there then has to be an effort - a group effort in the case of politics, an individual effort in the case of love or art - for this possibility to become real and inscribed in the world. As he explains his thinking on politics, love, art and science, Badiou takes stock of his major works, reflects on their central themes and arguments and looks forward to the questions he plans to address in his future writings. The book concludes with a short introduction to Badiou's philosophy by Fabien Tarby. For anyone wishing to understand the work of one of the most widely read and influential philosophers writing today, this small book will be an indispensable guide.

    Ariew's introduction places the correspondence in historical context and discusses the vibrant philosophical climate of the times. Appendices provide those selections from the works of Newton that Clarke frequently refers to in the correspondence. A bibliography is also included.

    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.

    Imagine peeling an apple in your mind. Take the subway without trying to get anywhere. The simple meditations in this book have the potential to shake us awake from our preconceived certainties: our own identity, the stability of the outside world, the meanings of words. At once entertaining and startling, irreverent and wise, this book will provoke moments of awareness for readers in any situation and in all walks of life. Enter the space of your favorite painting. Watch someone sleeping. The world won't look the same again.

    Why do people—even identical twins reared in the same home—differ so much in personality? Armed with an inquiring mind and insights from evolutionary psychology, Judith Rich Harris sets out to solve the mystery of human individuality.

    Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject.'W.W. Sawyer's deep understanding of how we learn and his lively, practical approach have made this an ideal introduction to mathematics for generations of readers. By starting at the level of simple arithmetic and algebra and then proceeding step by step through graphs, logarithms and trigonometry to calculus and the dizzying world of imaginary numbers, the book takes the mystery out of maths. Throughout, Sawyer reveals how theory is subordinate to the real-life applications of mathematics - the Pyramids were built on Euclidean principles three thousand years before Euclid formulated them - and celebrates the sheer intellectual stimulus of mathematics at its best.

    The Golden Section—otherwise known as phi, the golden mean, or the golden ratio—is one of the most elegant and beautiful rations in the universe.Defined as a line segment divided into two unequal parts, such that the ratio of the shorter portion to the longer portion is the same as the ratio of the longer portion to the whole, it pops up throughout nature—in water, DNA, the proportions of fish and butterflies, and the number of teeth we possess—as well as in art and architecture, music, philosophy, science, and mathematics.Beautifully illustrated, The Golden Section tells the story of this remarkable construct and its wide-ranging impact on civilization and the natural world.

    With a foreword by ESA astronaut Tim Peake.Started at the Royal Institution (RI) in 1825 by Michael Faraday, the Christmas Lectures have been broadcast on television since the 1960s and have formed part of the British Christmas tradition for generations. First devised to attract young people to the magic of science through spectacular demonstrations, they are now watched by millions of people around the world every year.Drawing on the incredible archive at the RI, which is packed full of handwritten notebooks, photographs and transcripts, this book will focus on thirteen of the most captivating Lectures given at the RI on space and time, taking a look at what we thought we knew then and what has been discovered since.

    

    Our beliefs constitute a large part of our knowledge of the world. We have beliefs about objects, about culture, about the past, and about the future. We have beliefs about other people, and we believe that they have beliefs as well. We use beliefs to predict, to explain, to create, to console, to entertain. Some of our beliefs we call theories, and we are extraordinarily creative at constructing them. Theories of quantum mechanics, evolution, and relativity are examples. But so are theories about astrology, alien abduction, guardian angels, and reincarnation. All are products (with varying degrees of credibility) of fertile minds trying to find explanations for observed phenomena. In this book, Nils Nilsson examines beliefs: what they do for us, how we come to hold them, and how to evaluate them. We should evaluate our beliefs carefully, Nilsson points out, because they influence so many of our actions and decisions.Some of our beliefs are more strongly held than others, but all should be considered tentative and changeable. Nilsson shows that beliefs can be quantified by probability, and he describes networks of beliefs in which the probabilities of some beliefs affect the probabilities of others. He argues that we can evaluate our beliefs by adapting some of the practices of the scientific method and by consulting expert opinion. And he warns us about "belief traps"--holding onto beliefs that wouldn't survive critical evaluation. The best way to escape belief traps, he writes, is to expose our beliefs to the reasoned criticism of others.