## Computation and its LimitsComputation and its Limits is an innovative cross-disciplinary investigation of the relationship between computing and physical reality. It begins by exploring the mystery of why mathematics is so effective in science and seeks to explain this in terms of the modelling of one part of physical reality by another. Going from the origins of counting to the most blue-skies proposals for novel methods of computation, the authors investigate the extent to which the laws of nature and of logic constrain what we can compute. In the process they examine formal computability, the thermodynamics of computation, and the promise of quantum computing. |

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### Contents

1 | |

6 | |

3 Mechanical computers and their limits | 28 |

4 Logical limits to computing | 47 |

5 Heat information and geometry | 83 |

6 Quantum computers | 128 |

7 Beyond the logical limits of computing? | 173 |

8 Hypercomputing proposals | 187 |

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### Other editions - View all

Computation and Its Limits W. Paul Cockshott,Paul Cockshott,Lewis M Mackenzie,Gregory Michaelson Limited preview - 2012 |

Computation and its Limits Paul Cockshott,Lewis M Mackenzie,Gregory Michaelson No preview available - 2012 |

Computation and Its Limits W. Paul Cockshott,Paul Cockshott,Lewis M Mackenzie,Gregory Michaelson No preview available - 2012 |

### Common terms and phrases

adiabatic algorithms allow analogue computer Antikythera arbitrary argument arithmetic assume basis calculations chip Church–Turing thesis circuit classical clock CMOS components construct corresponding counting cycle defined device Eberbach electron encoding energy levels entangled entropy equilibrium error example expression false false false true finite number given Gödel halt halting problem heat Hilbert space hypercomputer implement infinite infinity initial integer Interaction Machines internal energy light limits logic macroscopic mathematical measurement memory microstates multiple natural numbers observed output particles Peano Peano arithmetic photons physical possible predictions problem properties propositional logic quantum circuit quantum computer quantum gates quantum mechanics quantum system quantum theory qubits real numbers recursive function result rotation rules sequence sheep shown in Fig space SUCC(X Suppose symbol tape temperature theorem thermal thermodynamic tokens true false truth table Turing Machine unitary operator variable vector velocity wavelength Wegner wheel wires