Thinking About Godel And Turing: Essays On Complexity, 1970-2007
A Hardback edition by Gregory J. Chaitin in English (Apr 10, 2007)
$199.80 + FREE delivery
Short Description: Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable number, a concrete example of irreducible complexity in pure... Read more
Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as Goedel and Turing.This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size complexity or algorithmic information content in order to shed further light on the fundamental work of Goedel and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his information-theoretic approach to metamathematics suggests a quasi-empirical view of mathematics that emphasizes the similarities rather than the differences between mathematics and physics. He also develops his own brand of digital philosophy, which views the entire universe as a giant computation, and speculates that perhaps everything is discrete software, everything is 0's and 1's.Chaitin's fundamental mathematical work will be of interest to philosophers concerned with the limits of knowledge and to physicists interested in the nature of complexity.
Thinking About Godel And Turing: Essays On Complexity, 1970-2007 Hardback edition by Gregory J. Chaitin
- Gregory J. Chaitin
- World Scientific Publishing Co Pte Ltd
- Publication date
- Apr 10, 2007
- Product dimensions
- 184 x 259 x 19mm
On the Difficulty of Computations; Information-Theoretic Computational Complexity; Randomness and Mathematical Proof; Godel's Theorem and Information; Randomness in Arithmetic; Paradoxes of Randomness; Complexity and Leibniz; The Limits of Reason; How Real Are Real Numbers?; Is Incompleteness a Serious Problem?; How Much Information Can There Be in a Real Number?; and other papers.