Computation and its Limits

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. Introduction -- What Is Computation? -- Mechanical Computers And Their Limits -- Logical Limits To Computing -- Heat, Information, And Geometry -- Quantum Computers -- Beyond The Logical Limits Of Computing? -- Hypercomputing Proposals. Paul Cockshott, Lewis M. Mackenzie, Greg Michaelson. Includes Bibliographical References (p. [216]-225) And Index. Although we are entirely unaware of it, computation is central to all aspects of our existences. Every day we solve, or try to solve, a myriad of problems, from the utterly trivial to the bafflingly complex. This book explains why it is possible to do computation and what the ultimate limits of it are, as understood by modern science.