Computation and its Limits

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OUP Oxford, Mar 15, 2012 - Science - 248 pages
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Computation 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 Introduction
1
2 What is computation?
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
Bibliography
216
Index
226
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About the author (2012)

Paul Cockshott was educated at McMaster, Manchester, Heriot-Watt, and Edinburgh Universities. He trained originally as an economist and continues to be interested in the area. He later studied computer science, obtaining his PhD in the same from Edinburgh University. Dr Cockshott has worked in industry for ICL on hardware verification and for Memex on the design of database machines. He has also been a research worker and lecturer at the universities of Edinburgh, Heriot-Watt, Glasgow, and Strathclyde. He is currently Reader in Computer Science at the University of Glasgow. Lewis M. Mackenzie is a Senior Lecturer in Computing Science at the University of Glasgow. His research interests are in machine architectures and the performance modelling of communication systems. Dr Mackenzie's recently published work has involved the modelling of traffic patterns in a variety of scenarios from regular wormhole-switched multi-computer interconnects to mobile ad-hoc wireless networks (MANETs). Greg Michaelson studied Computer Science at the University of Essex and the University of St Andrews, working as a real-time programmer at Scottish Gas in between. He then taught at Napier College and the University of Glasgow, before joining Heriot-Watt University in 1983, where he gained his PhD. He was Head of Computer Science from 2003-8 and promoted to Professor in 2006. Dr Michaelson's research interests encompass formally motivated computing, in particular the design, implementation, and analysis of programming languages for multi-process systems. He published his first novel in 2008.