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Searching... | Q173 .D49 2004 | Adult Non-Fiction | Non-Fiction Area | Searching... | Searching... |

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### Summary

### Summary

A mind-bending excursion to the limits of science and mathematics

Are some scientific problems insoluble? In Beyond Reason, internationally acclaimed math and science author A. K. Dewdney answers this question by examining eight insurmountable mathematical and scientific roadblocks that have stumped thinkers across the centuries, from ancient mathematical conundrums such as "squaring the circle," first attempted by the Pythagoreans, to G'del′s vexing theorem, from perpetual motion to the upredictable behavior of chaotic systems such as the weather.

A. K. Dewdney, PhD (Ontario, Canada), was the author of Scientific American′s "Computer Recreations" column for eight years. He has written several critically acclaimed popular math and science books, including A Mathematical Mystery Tour (0-471-40734-8); Yes, We Have No Neutrons (0-471-29586-8); and 200% of Nothing (0-471-14574-2).

### Author Notes

Recreations, his column which appeared in Scientific American for more than eight years. He has been an Associate Professor of Computer Science at the University of Western Ontario in Canada since 1968, and is president of Turing Omnibus, Inc. Among his many books on computer science, science and mathematics are Two Hundred Percent of Nothing (1993), an effort to expose abuses of math and statistics in everyday life and its companion work, Yes, We Have No Neutrons (1997).

Dewdney is also interested in growing and distributing rare native trees, as manifested in his book, Hungry Hollow: The Story of a Natural Place (1998). Hungry Hollow examines the elements of a natural habitat in both time and space.

(Bowker Author Biography)

### Reviews 2

### Booklist Review

Inventors and engineers have invested centuries of effort trying to build a perpetual-motion machine. They have never succeeded, but without their valiant attempts, a particularly piquant chapter would be missing from this new book on scientific impossibilities. Science-writer Dewdney teases illuminating logic and formulas from the despair of physicists who wish to predict how electrons will dance, from the frustration of computer programmers who want to resolve certain types of yes-no questions, and from the embarrassment of meteorologists who would like to predict next week's weather. Rigorous enough to challenge intelligent readers but not so daunting as to overwhelm the nonspecialist, the investigation of each impossibility clarifies the barriers that forbid further progress along certain theoretical paths, limning the conceptual boundaries of science and even reflecting the limitations inherent in the structure of human rationality. Still, Dewdney concedes a catalogue of scientific impossibilities may just provoke some maverick to do what the greatest scientists have always done: enlarge the limits of the possible. --Bryce Christensen Copyright 2004 Booklist

### Publisher's Weekly Review

Dewdney (A Mathematical Mystery Tour), best known for the Scientific American column "Computer Recreations," which he wrote for eight years, sets an impressive goal for himself: "to discover how physical reality depends on mathematical reality, and to examine how mathematical reality manifests itself." He attempts to do this by outlining four problems in the physical realm and four in the mathematical realm that he believes can never be solved. The topics he discusses are largely of great interest to science and math buffs: perpetual motion, the speed of light, Heisenberg's uncertainty principle, chaos theory, squaring the circle, unprovable but true mathematical theorems, "simple" problems that no computer program can solve, and the fact that some mathematical problems would require an infinite amount of computer time to solve. In his chapter on chaos theory, for example, Dewdney does a very nice job of explaining why we will never be able to predict the weather accurately more than four days in advance. The problem throughout the book, however, is that he alternates between colorful prose or explanations of basic terms (such as "primary number") and relatively dense mathematics (transcendental and transfinite numbers), never settling on who the appropriate audience for this study might be. B&w illus. Agent, Linda McKnight. (May) (c) Copyright PWxyz, LLC. All rights reserved

### Table of Contents

Introduction: Where Reason Cannot Go | p. 1 |

Math in the Cosmos | |

1 The Energy Drain: Impossible Machines | p. 11 |

2 The Cosmic Limit: Unreachable Speeds | p. 35 |

3 The Quantum Curtain: Unknowable Particles | p. 59 |

4 The Edge of Chaos: Unpredictable Systems | p. 85 |

Math in the Holos | |

5 The Circular Crypt: Unconstructable Figures | p. 115 |

6 The Chains of Reason: Unprovable Theorems | p. 137 |

7 The Computer Treadmill: Impossible Programs | p. 163 |

8 The Big-O Bottleneck: Intractable Problems | p. 183 |

References | p. 207 |

Further Reading | p. 211 |

Index | p. 213 |