A fun and fascinating look at great scientific paradoxes.   Throughout history, scientists have come up with theories and ideas that just don't seem to make sense.  These we call paradoxes.  The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds.  For example, how can a cat be both dead and alive at the same time?  Why will Achilles never beat a tortoise in a race, no matter how fast he runs?  And how can a person be ten years older than his twin?   With elegant explanations that bring the reader inside the mind of those who've developed them, Al-Khalili helps us to see that, in fact, paradoxes can be solved if seen from the right angle.  Just as surely as Al-Khalili narrates the enduring fascination of these classic paradoxes, he reveals their underlying logic.  In doing so, he brings to life a select group of the most exciting concepts in human knowledge.  Paradox is mind-expanding fun.

    In his fascinating new book, he writes with characteristic clarity and personal awareness as he sheds light on the mysteries of savants' incredible mental abilities, and our own. Tammet explains that the differences between savant and non-savant minds have been exaggerated; his astonishing capacities in memory, math and language are neither due to a cerebral supercomputer nor any genetic quirk, but are rather the results of a highly rich and complex associative form of thinking and imagination. Autistic thought, he argues, is an extreme variation of a kind that we all do, from daydreaming to the use of puns and metaphors."Embracing the Wide Sky" combines meticulous scientific research with Tammet's detailed descriptions of how his mind works to demonstrate the immense potential within us all. He explains how our natural intuitions can help us to learn a foreign language, why his memories are like symphonies, and what numbers and giraffes have in common. We also discover why there is more to intelligence than IQ, how optical illusions fool our brains, and why too much information can make you dumb.Many readers will be particularly intrigued by Tammet's original ideas concerning the genesis of genius and exceptional creativity. He illustrates his arguments with examples as diverse as the private languages of twins, the compositions of poets with autism, and the breakthroughs, and breakdowns, of some of history's greatest minds. "Embracing the Wide Sky" is a unique and brilliantly imaginative portrait of how we think, learn, remember and create, brimming with personal insights and anecdotes, and explanations of the most up-to-date, mind-bending discoveries from fields ranging from neuroscience to psychology and linguistics. This is a profound and provocative book that will transform our understanding and respect for every kind of mind.

    In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Godel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

    Vygotsky analyzes the relationship between words and consciousness, arguing that speech is social in its origins and that only as children develop does it become internalized verbal thought.Now Alex Kozulin has created a new edition of the original MIT Press translation by Eugenia Hanfmann and Gertrude Vakar that restores the work's complete text and adds materials that will help readers better understand Vygotsky's meaning and intentions. Kozulin has also contributed an introductory essay that offers new insight into the author's life, intellectual milieu, and research methods.

    In addition to showing how recent metaphysics has drifted away from connection with all other serious scholarly inquiry as a result of not heeding this restriction, they demonstrate how to build a metaphysics compatible with current fundamental phsyics ("ontic structural realism"), which, when combined with their metaphysics of the special sciences ("rainforest realism"), can be used to unify physics with the other sciences without reducing these sciences to physics intself. Taking science metaphysically seriously, Ladyman and Ross argue, means that metaphysicians must abandon the picture of the world as composed of self-subsistent individual objects, and the paradigm of causation as the collision of such objects. Every Thing Must Go also assesses the role of information theory and complex systems theory in attempts to explain the relationship between the special sciences and physics, treading a middle road between the grand synthesis of thermodynamics and information, and eliminativism about information. The consequences of the author's metaphysical theory for central issues in the philosophy of science are explored, including the implications for the realism vs. empiricism debate, the role of causation in scientific explanations, the nature of causation and laws, the status of abstract and virtual objects, and the objective reality of natural kinds

    Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

    All of us can remember a moment as a child when time became a personal reality, when we realized what a "year" was, or asked ourselves when "now" happened. Common sense says time moves forward, never backward, from cradle to grave. Nevertheless, Einstein said that time is an illusion. Nature's laws, as he and Newton defined them, describe a timeless, deterministic universe within which we can make predictions with complete certainty. In effect, these great physicists contended that time is reversible and thus meaningless.

    A meld of history and science, this book is a group portrait of some of the greatest minds who ever lived as they wrestled with nature’s most sweeping mysteries. The answers they uncovered still hold the key to how we understand the world.At the end of the seventeenth century—an age of religious wars, plague, and the Great Fire of London—when most people saw the world as falling apart, these earliest scientists saw a world of perfect order. They declared that, chaotic as it looked, the universe was in fact as intricate and perfectly regulated as a clock. This was the tail end of Shakespeare’s century, when the natural land the supernatural still twined around each other. Disease was a punishment ordained by God, astronomy had not yet broken free from astrology, and the sky was filled with omens. It was a time when little was known and everything was new. These brilliant, ambitious, curious men believed in angels, alchemy, and the devil, and they also believed that the universe followed precise, mathematical laws—-a contradiction that tormented them and changed the course of history.The Clockwork Universe is the fascinating and compelling story of the bewildered geniuses of the Royal Society, the men who made the modern world.

    S. Ramachandran is at the forefront of his field-so much so that Richard Dawkins dubbed him the "Marco Polo of neuroscience." Now, in a major new work, Ramachandran sets his sights on the mystery of human uniqueness. Taking us to the frontiers of neurology, he reveals what baffling and extreme case studies can teach us about normal brain function and how it evolved. Synesthesia becomes a window into the brain mechanisms that make some of us more creative than others. And autism--for which Ramachandran opens a new direction for treatment--gives us a glimpse of the aspect of being human that we understand least: self-awareness. Ramachandran tackles the most exciting and controversial topics in neurology with a storyteller's eye for compelling case studies and a researcher's flair for new approaches to age-old questions. Tracing the strange links between neurology and behavior, this book unveils a wealth of clues into the deepest mysteries of the human brain.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    In treating cognition as problem solving, Andy Clark suggests, we may often abstract too far from the very body and world in which our brains evolved to guide us. Whereas the mental has been treated as a realm that is distinct from the body and the world, Clark forcefully attests that a key to understanding brains is to see them as controllers of embodied activity. From this paradigm shift he advances the construction of a cognitive science of the embodied mind.

    Cheng is a mathematician, so she knows how to make an airtight argument. But even for her, logic sometimes falls prey to emotion, which is why she still fears flying and eats more cookies than she should. If a mathematician can't be logical, what are we to do? In this book, Cheng reveals the inner workings and limitations of logic, and explains why alogic--for example, emotion--is vital to how we think and communicate. Cheng shows us how to use logic and alogic together to navigate a world awash in bigotry, mansplaining, and manipulative memes. Insightful, useful, and funny, this essential book is for anyone who wants to think more clearly.

    Its flexible organization (with all chapters complete and self-contained) allows instructors the freedom to cover the topics they want in the order they choose.

    Is stoicism right for you? What can you learn from these ancient masters? Stoicism: Ultimate Handbook to Stoic Philosophy, Wisdom and Way of Life describes the core philosophies of the stoics: • Control What You Can • Emotions and Outcomes Exist Within • Honesty is a Virtue • Hope Never Dies • Knowledge Will Save You • Mindfulness is Important • Seek Morals, Not Awards • Stop On Time • Every Day Is A New Day You'll also learn the 4 Cardinal Virtues Of Stoicism: • Wisdom • Courage • Justice • Temperance What can Stoicism do for you in your everyday life? Stoicism: Ultimate Handbook to Stoic Philosophy, Wisdom and Way of Life also describes how Stoicism can help you in today's world. This ancient tradition can help you through tough times by teaching you to build your mental and physical strength and be a great leader. Also, you'll find that most religions agree with the philosophies and practices of Stoicism. Practicing Stoicism can help you cope with many negative emotions: • Stress • Judgment • Anger • Worry • Incompetence • Disappointment Download Stoicism: Ultimate Handbook to Stoic Philosophy, Wisdom and Way of Life NOW to find out about this amazing tradition that has stood the test of time. You'll be so glad you did!

    In this indispensable volume, a primer for the information age, Hans Christian von Baeyer presents a clear description of what information is, how concepts of its measurement, meaning, and transmission evolved, and what its ever-expanding presence portends for the future. Information is poised to replace matter as the primary stuff of the universe, von Baeyer suggests; it will provide a new basic framework for describing and predicting reality in the twenty-first century. Despite its revolutionary premise, von Baeyer's book is written simply in a straightforward fashion, offering a wonderfully accessible introduction to classical and quantum information. Enlivened with anecdotes from the lives of philosophers, mathematicians, and scientists who have contributed significantly to the field, Information conducts readers from questions of subjectivity inherent in classical information to the blurring of distinctions between computers and what they measure or store in our quantum age. A great advance in our efforts to define and describe the nature of information, the book also marks an important step forward in our ability to exploit information--and, ultimately, to transform the nature of our relationship with the physical universe. (20040301)