For a thousand years, infinity has proven to be a difficult and illuminating challenge for mathematicians and theologians. It certainly is 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? Is matter infinitely divisible into ever-smaller pieces? But infinity is also the place where things happen that don't. All manner of strange paradoxes and fantasies characterize an infinite universe. If our Universe is infinite then an infinite number of exact copies of you are, at this very moment,…mehr
For a thousand years, infinity has proven to be a difficult and illuminating challenge for mathematicians and theologians. It certainly is 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? Is matter infinitely divisible into ever-smaller pieces? But infinity is also the place where things happen that don't. All manner of strange paradoxes and fantasies characterize an infinite universe. If our Universe is infinite then an infinite number of exact copies of you are, at this very moment, reading an identical sentence on an identical planet somewhere else in the Universe. Now Infinity is the darling of cutting edge research, the measuring stick used by physicists, cosmologists, and mathematicians to determine the accuracy of their theories. From the paradox of Zeno's arrow to string theory, Cambridge professor John Barrow takes us on a grand tour of this most elusive of ideas and describes with clarifying subtlety how this subject has shaped, and continues to shape, our very sense of the world in which we live. The Infinite Book is a thoroughly entertaining and completely accessible account of the biggest subject of them all-infinity.
Preface 1 Much Ado about Everything The Rough Guide to Infinity Intimations of the Infinite Zeno Hour 2 Infinity, Almost and Actual, Fictitious and Factual Darkness at Noon A Purely Aristotelian Relationship Infinity and God A Little Kant 3 Welcome to the Hotel Infinity Hotels Experiences of the Hotel Infinity The Hotel Infinity’s Accounts 4 Infinity Is Not a Big Number An Immaculate Misconception Albert of Saxony’s Paradox Galileo’s Paradox Cadmus and Harmonia Terminator 0, 1⁄2, and 1 Countable Infinities Uncountable Infinities The Towering Infinito 5 The Madness of Georg Cantor Cantor and Son The Chronicle of Kronecker Cantor, God, and Infinity – the Trinity with Affinity All’s Sad that Ends Bad 6 Infinity Comes in Three Flavours Triple Top Let’s Get Physical Naked Infinities The Great Blue Yonder Infinity on the Back Foot 7 Is the Universe Infinite? Everything That Is Cosmology Goes Underground Bent Universes The Problem of Topology The Problem of Uniformity The Problem of Acceleration Where Does This Leave Us? The Shining 8 The Infinite Replication Paradox A Universe Where Nothing Is Original The Great Escape The Temporal Version – Been There, Done That The Never-ending Story The Ethics of the Infinite 9 Worlds Without End Other Worlds in History Out of This World Inflation – Here, There, and Everywhere Conscious Interventions – Men in Black Simulated Universes How Should We Then Live? 10 Making Infinity Machines Super-tasks Rubbing Thomson’s Lamp Some Norse Code The End-game Problem Relativity and the Amazing Shrinking Man A Matter of Timing Newtonian Super-tasks Relativistic Super-tasks Big Bangs and Big Crunches 11 Living Forever Childhood’s End The Sociology of Eternity The Problem-Page of the Unending Future The Strange, Familiar, and Forgotten Incestuous Time Travel The Grandmother Paradox Consistent Histories Tourists From the Future Time Travellers in the Financial World: Perpetual Money Machines Why You Can’t Change the Past Infinity – Where Will It All End? Notes Index
Preface 1 Much Ado about Everything The Rough Guide to Infinity Intimations of the Infinite Zeno Hour 2 Infinity, Almost and Actual, Fictitious and Factual Darkness at Noon A Purely Aristotelian Relationship Infinity and God A Little Kant 3 Welcome to the Hotel Infinity Hotels Experiences of the Hotel Infinity The Hotel Infinity’s Accounts 4 Infinity Is Not a Big Number An Immaculate Misconception Albert of Saxony’s Paradox Galileo’s Paradox Cadmus and Harmonia Terminator 0, 1⁄2, and 1 Countable Infinities Uncountable Infinities The Towering Infinito 5 The Madness of Georg Cantor Cantor and Son The Chronicle of Kronecker Cantor, God, and Infinity – the Trinity with Affinity All’s Sad that Ends Bad 6 Infinity Comes in Three Flavours Triple Top Let’s Get Physical Naked Infinities The Great Blue Yonder Infinity on the Back Foot 7 Is the Universe Infinite? Everything That Is Cosmology Goes Underground Bent Universes The Problem of Topology The Problem of Uniformity The Problem of Acceleration Where Does This Leave Us? The Shining 8 The Infinite Replication Paradox A Universe Where Nothing Is Original The Great Escape The Temporal Version – Been There, Done That The Never-ending Story The Ethics of the Infinite 9 Worlds Without End Other Worlds in History Out of This World Inflation – Here, There, and Everywhere Conscious Interventions – Men in Black Simulated Universes How Should We Then Live? 10 Making Infinity Machines Super-tasks Rubbing Thomson’s Lamp Some Norse Code The End-game Problem Relativity and the Amazing Shrinking Man A Matter of Timing Newtonian Super-tasks Relativistic Super-tasks Big Bangs and Big Crunches 11 Living Forever Childhood’s End The Sociology of Eternity The Problem-Page of the Unending Future The Strange, Familiar, and Forgotten Incestuous Time Travel The Grandmother Paradox Consistent Histories Tourists From the Future Time Travellers in the Financial World: Perpetual Money Machines Why You Can’t Change the Past Infinity – Where Will It All End? Notes Index
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