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.

    In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

    It describes how the laws and discoveries of information theory now support controversial revisions to Darwinian evolution, begin to unravel the mysteries of language, memory and dreams, and stimulate provocative ideas in psychology, philosophy, art, music, computers and even the structure of society. Perhaps its most fascinating and unexpected surprise is the suggestion the order and complexity may be as natural as disorder and disorganization. Contrary to the entropy principle, which implies that order is the exception and confusion the rule, information theory asserts that order and sense can indeed prevail against disorder and nonsense. From the simplest forms of organic life to the words used to express our most complex ideas, from our genes to our dreams, from microcomputers to telecommunications, virtually everything around us follows simple rules of information. Life and the material world, like language, remain "grammatical." Grammatical man inhabits a grammatical universe.

    E. Cummings's biographer, include his most popular poems, spanning his earliest creations, his vivacious linguistic acrobatics, up to his last valedictory sonnets. Also featured are thirteen drawings, oils, and watercolors by Cummings, most of them never before published.The selection includes most of the favorites plus many fresh and surprising examples of Cummings's several poetic styles. The corrected texts established by George J. Firmage have been used throughout.

    Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

    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.

    Who invented zero? Why are there 60 seconds in a minute? Can a butterfly's wings really cause a storm on the far side of the world? In 50 concise essays, Professor Tony Crilly explains the mathematical concepts that allow use to understand and shape the world around us.

    Their visionary answers flow from the frontiers of psychology, philosophy, economics, physics, sociology, and more. Surprising and enlightening, these insights will revolutionize the way you think about yourself and the world.Contributors include:Daniel Kahneman on the “focusing illusion”Jonah Lehrer on controlling attentionRichard Dawkins on experimentationAubrey De Grey on conquering our fear of the unknownMartin Seligman on the ingredients of well-beingNicholas Carr on managing “cognitive load”Steven Pinker on win-win negotiatingDaniel Goleman on understanding our connection to the natural worldMatt Ridley on tapping collective intelligenceLisa Randall on effective theorizingBrian Eno on “ecological vision”J. Craig Venter on the multiple possible origins of life  Helen Fisher on temperamentSam Harris on the flow of thoughtLawrence Krauss on living with uncertainty

    Yet in The Science of Interstellar, Kip Thorne, the physicist who assisted Nolan on the scientific aspects of Interstellar, shows us that the movie’s jaw-dropping events and stunning, never-before-attempted visuals are grounded in real science. Thorne shares his experiences working as the science adviser on the film and then moves on to the science itself. In chapters on wormholes, black holes, interstellar travel, and much more, Thorne’s scientific insights—many of them triggered during the actual scripting and shooting of Interstellar—describe the physical laws that govern our universe and the truly astounding phenomena that those laws make possible.Interstellar and all related characters and elements are trademarks of and © Warner Bros. Entertainment Inc. (s14).

    Part I describes questions and issues about mathematics that have motivated philosophers since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in the thought of such philosophers as Plato, Aristotle, Kant, and Mill. Part III covers the three major positions held throughout the twentieth century: the idea that mathematics is logic (logicism), the view that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV brings the reader up-to-date with a look at contemporary developments within the discipline.This sweeping introductory guide to the philosophy of mathematics makes these fascinating concepts accessible to those with little background in either mathematics or philosophy.

    Taking examples from sources as diverse as Plato and Steven Spielberg, author Julian Baggini presents abstract philosophical issues in concrete terms, suggesting possible solutions while encouraging readers to draw their own conclusions: Lively, clever, and thought-provoking, The Pig That Wants to Be Eaten is a portable feast for the mind that is sure to satisfy any intellectual appetite.

    Examining heroic myths in the light of modern psychology, it considers not only the patterns and stages of mythology but also its relevance to our lives today--and to the life of any person seeking a fully realized existence.Myth, according to Campbell, is the projection of a culture's dreams onto a large screen; Campbell's book, like Star Wars, the film it helped inspire, is an exploration of the big-picture moments from the stage that is our world. It is a must-have resource for both experienced students of mythology and the explorer just beginning to approach myth as a source of knowledge.

    This omnibus collection includes all of the author’s early poetry as well as the Four Quartets, Old Possum’s Book of Practical Cats, and the plays Murder in the Cathedral, The Family Reunion, and The Cocktail Party.

    Attracted by the simplicity and clarity of his writing, readers of all ages and backgrounds have found in Professor Gombrich a true master, and one who combines knowledge and wisdom with a unique gift for communicating his deep love of the subject. The Story of Art, one of the most famous and popular books on art ever written, has been a world bestseller for over four decades. Attracted by the simplicity and clarity of his writing, readers of all ages and backgrounds have found in Professor Gombrich a true master, and one who combines knowledge and wisdom with a unique gift for communicating his deep love of the subject.For the first time in many years the book has been completely redesigned. The illustrations, now in colour throughout, have all been improved and reoriginated, and include six fold-outs. The text has been revised and updated where appropriate, and a number of significant new artists have been incorporated. The bibliographies have been expanded and updated, and the maps and charts redrawn. The Story of Art has always been admired for two key qualities: it is a pleasure to read and a pleasure to handle. In these respects the new edition is true to its much-loved predecessors: the text runs as smoothly as ever and the improved illustrations are always on the page where the reader needs them. In its new edition, this classic work continues its triumphant progress tirelessly for yet another generation, to remain the title of first choice for any newcomer to art or the connoisseur. The Story of Art has always been admired for two key qualities: it is a pleasure to read and a pleasure to handle. In these respects the new edition is true to its much-loved predecessors: the text runs as smoothly as ever and the improved illustrations are always on the page where the reader needs them. In its new edition, this classic work continues its triumphant progress tirelessly for yet another generation, to remain the title of first choice for any newcomer to art or the connoisseur.

    His illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty. Mathematics is the language of size, shape, and order—a language Hogben shows one can both master and enjoy.