Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Godel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a so-called exponential diophantine equation."

In The Unknowable I use LISP to compare my work on incompleteness with that of G6del and Turing, and in The Limits of Mathematics I use LISP to discuss my work on incompleteness in more detail. In this book we'll use LISP to explore my theory of randomness, called algorithmic information theory (AIT). And when I say "explore" I mean it This book is full of exercises for the reader, ranging from the mathematical equivalent oftrivial "fin ger warm-ups" for pianists, to substantial programming projects, to questions I can formulate precisely but don't know how to answer, to questions that I...

G. J. Chaitin is at the IBM Thomas J. Watson Research Center in New York. He has shown that God plays dice not only in quantum mechanics, but even in the foundations of mathematics, where Chaitin discovered mathematical facts that are true for no reason, that are true by accident. This book collects his most wide-ranging and non-technical lectures and interviews, and it will be of interest to anyone concerned with the philosophy of mathematics, with the similarities and differences between physics and mathematics, or with the creative process and mathematics as an art.
"Chaitin has put a...

This essential companion to Chaitins highly successful The Limits of Mathematics, gives a brilliant historical survey of important work on the foundations of mathematics. The Unknowable is a very readable introduction to Chaitins ideas, and includes software (on the authors website) that will enable users to interact with the authors proofs. -Chaitins new book, The Unknowable, is a welcome addition to his oeuvre. In it he manages to bring his amazingly seminal insights to the attention of a much larger audience His work has deserved such treatment for a long time.- JOHN ALLEN PAULOS, AUTHOR...

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.

As a teenager, Greg created independently of Kolmogorov and Solomonoff, what we call today algorithmic information theory, a sub- ject of which he is the main architect. His 1965 paper on gedanken experiments on automata, which he wrote when he was in high school, is still of interest today. He was also heavily involved in IBM, where he has worked for almost thirty years, on the development of RISC technology. Greg's results are widely quoted. My favorite portrait of Greg can be found in John Horgan's-a writer for Scientific American-1996 book The End 01 Science. Greg has gotten many honors....