An examination of Infinity — in history and science — with excursions into literature, philosophy and religion, written by one of the most successful writers of popular science. Infinity is surely the strangest idea that humans have ever thought. Where did it come from and what is it telling us about our Universe? Can there actually be infinities? Or is infinity just a label for something that is never reached, no matter how long you go on counting? Can you do an infinite number of things in a finite amount of time? Is the universe infinite? But infinity is also the place where things happen that don’t. All manner of strange paradoxes and fantasies characterize an infinite universe. So what is it like to live in a Universe where nothing is original, where you can live forever, where anything that can be done, is done, over and over again? These are some of the deep questions that the idea of the Infinite pushes us to ask. Throughout history, the Infinite has been a dangerous idea. Many have lost their lives, their careers, or their freedom for talking about it. The Infinite Book will take you on a tour of these dangerous questions and the strange answers that scientists, mathematicians, philosophers, and theologians have come up with to deal with its threats to our sanity. As prolific science writer and physicist Barrow regularly remarks, infinity is not merely the smallest or biggest thing, or the longest time imaginable: it's a quality that is unimaginable. It's thus a paradox that mathematicians, physicists, and philosophers have discovered quite a bit about infinity, albeit with different degrees of certitude. As also related in David Foster Wallace's Everything and More: A Compact History of Infinity (2003), Barrow recounts the career of German mathematician Georg Cantor, whose explorations of set theory resulted in fundamental proofs about infinities (some are bigger than others, for example). However joyous such discoveries are to the numbers masters, physicists' encounters with infinities are less rapturous because they hint at deficiencies in general relativity; hence their joy over string theory, which eliminates infinities that arise in calculations about the big bang and black holes. Performing with his customary fluency and accessibility, Barrow imparts for general readers a feeling for the nub of thought about the mathematical, cosmic, ethical, and theological implications of infinity. Gilbert Taylor Copyright © American Library Association. All rights reserved “Highly engaging. . . . [Barrow] brings his charm and wit to bear. . . . [He] introduces novel twists and turns, and presents [the] material in refreshing ways.”– Nature "Eloquent. . . . Succinct. . . . Barrow [has the] remarkable ability to provide clear, concise, engaging and distinctly finite explanations–even when describing some fairly advanced concepts. . . . [An] engaging read."– San Francisco Chronicle "Clever and insightful. . . . [A] lively history of infinity through the ages."– Entertainment Weekly “Entertaining. . . . Remarkably lucid and not the least mind-boggling. . . . His clear, engaging style manages to illuminate abstruse matters.... This is a useful guide to an endlessly fascinating subject.” – American Scientist From the Trade Paperback edition. John Barrow is Research Professor of Mathematical Sciences in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. He is the author of several bestselling books including: Theories of Everything , Impossibility , and The Book of Nothing . chapter one Much Ado about Everything ‘On a clear day you can see forever.’ –Alan Lerner THE ROUGH GUIDE TO INFINITY ‘If there is a Universal and Supreme Conscience I am an idea in it. After I have died God will go on remembering me, and to be remembered by God, to have my consciousness sustained by the Supreme Conscience, is not that, perhaps, to be immortal? – Miguel de Unamuno There is something about infinity and books. Never-ending stories, libraries that contain all possible books, books that contain everything that has ever happened, and everything that hasn’t; books that write themselves, books about themselves, books about there being no books, and books that end before they’ve begun. So you should be no more surprised to find yourself reading a book about infinity than I am to be writing one. But for something that you can’t buy on the internet, ‘infinity’ is strangely ubiquitous. It turns up in church sermons, mathematics lectures at all the best universities, popular science books about ‘Life, the Universe and Everything’, and mysticism the world over, while historians remind us that people have been burnt at the stake for talking about it. It is at once the staple of the mystic contemplation of reality – ‘make me one with everything’ as the mystic said to the hamburger vendor – and the familiar territory of science fiction and fantasy. Can all these t