Computation and its Limits - Tapa dura

Mathematics, computer science, physics - and even biology - are now beginning to converge. This delightful book, beautifully illustrated, shows the physics of computation and the theory of computation as two sides of the same coin. We are witnessing a paradigm shift, the birth of a fruitful new interdisciplinary point of view. (Gregory Chaitin, author of Proving Darwin: Making Biology Mathematical)

This book provides a unique and important presentation of the factors that have, do and will limit the science of computation. A most stimulating, scholarly and entertaining synthesis of history, logic, mathematics and science. (Stephen Barnett, University of Strathclyde, Glasgow, UK)

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.