This essential companion to Chaitin's successful books The Unknowable and The Limits of Mathematics, presents the technical core of his theory of program-size complexity. The two previous volumes are more concerned with applications to meta-mathematics. LISP is used to present the key algorithms and to enable computer users to interact with the authors proofs and discover for themselves how they work. The LISP code for this book is available at the author's Web site together with a Java applet LISP interpreter. "No one has looked deeper and farther into the abyss of randomness and its role in...

The author, G. J. Chaitin, shows that God plays dice not only in quantum mechanics but also in the foundations of mathematics. According to Chaitin there exist mathematical facts that are true for no reason. This fascinating and provocative text contains a collection of his most wide-ranging and non-technical lectures and interviews. It will be of interest to anyone concerned with the philosophy of mathematics, the similarities and differences between physics and mathematics, and mathematics as art.