Mind-blowing, jaw-dropping stuff.
---Marcus Chown in New Scientist, 17 November 2007
Why is Chaitin such fun to read? He asks some conceptually interesting questions, and phrases them to give unexpected and interesting answers. Some of his answers are short and simple enough that I can't resist repeating them. I can compare the joy I felt in seeing some of his ideas to the experience I had at age 11 or 12 reading George Gamow's introduction to mathematical ideas, One Two Three ... Infinity (as Chaitin would say, anything that has stayed in print for over 50 years deserves mention occasionally; anyone who has read this far and hasn't read Gamow's book, ought to).
---Edward Ordman in Journal of Scientific Exploration, Fall 2008
Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable Ω 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 Gödel 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 Gödel 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.
Gregory Chaitin is a member of the Physical Sciences Department at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York. He is also an honorary visiting professor in the Theoretical Computer Science Group at the University of Auckland (New Zealand), and an honorary professor at the University of Buenos Aires (Argentina).
Furthermore, Chaitin is a member of the Académie Internationale de Philosophie des Sciences (Belgium), a corresponding member of the Academia Brasileira de Filosofia (Rio de Janeiro), on the scientific advisory panel of the Foundational Questions in Physics & Cosmology Institute (FQXi), the honorary president of the scientific committee of the Instituto de Sistemas Complejos de Valparaíso (Chile), and a permanent member of the Rutgers University Center for Discrete Mathematics & Theoretical Computer Science (DIMACS). He has an honorary doctorate from the University of Maine.
This is Chaitin's eleventh book.