## Beyond reason: eight great problems that reveal the limits of scienceA 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). |

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### Contents

Where Reason Cannot Go | 1 |

Impossible Machines | 11 |

Unreachable Speeds | 35 |

Copyright | |

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algebraic numbers algorithm appear arithmetic atom attractor axioms beam behavior Bell's inequality Bell's theorem called cell century chaos complexity conservation of energy consists constructable number Cook's theorem Copenhagen interpretation decision problem detector developed digits discovered distance DNA computers dynamical systems Einstein electrons equation ether example experiment expression formula Godel number grimbliks halt happens Hilbert Hobbes instance integers length logical Lorenz Mandelbrot set math mathematician mathematics measure meters moving natural numbers nondeterministic nondeterministic algorithm NP complete Orffyreus particles particular pendulum perpetual motion machine phase space photon photon passes physical physicist polarization polynomial polynomial-time position predicted produce proof Proof(x propositions prove quantum mechanics ramp rational numbers real numbers Redheffer represent result rollers satisfiability problem sequence simply slit solution solve speed of light squaring the circle Suppose symbol tape theorem theory tion transformation triangle true Turing machine turn variable velocity wheel words