Books by Certain Members of the Physics of Information Group At IBM Research

Books by Gregory Chaitin

Randomness and Complexity The magnificent work of Kurt Gödel and Alan Turing on the limits of knowledge and computation has been an inspiration to a great many people. I have devoted my life to trying to advance an infinitesimal distance on this thorny path by utilizing the concept of complexity, which can be traced back to Leibniz. In these two volumes Cris Calude and I offer to the readers a summary and overview of these attempts of mine, plus some reactions from the community, in the hope that this will encourage further work on these extremely difficult and fundamental questions. ---Greg Chaitin, September 2007	Exploring Randomness This essential companion volume to Chaitin's highly successful books The Unknowable and The Limits of Mathematics, also published by Springer, presents the technical core of his theory of program-size complexity, also known as algorithmic information theory. (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 author's proofs and discover for themselves how they work.
Thinking About 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.	The Limits of Mathematics This book presents the final version of Chaitin's course on the limits of mathematical reasoning. This course uses algorithmic information theory to show that mathematics has serious limitations, and features a new more didactic approach to algorithmic information theory using LISP and Mathematica software. The thesis of the book is that the incompleteness phenomenon discovered by Gödel is much more widespread and serious than hitherto suspected. Also Gödel and Einstein's views on the foundations of mathematics are discussed, and it is suggested that mathematics is quasi-empirical and that experimental mathematics should be used more freely.
Algorithmic Information Theory Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gödel'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.	From Philosophy to Program Size This little book contains the course that I had the pleasure of giving at the Eighth Estonian Winter School in Computer Science (EWSCS '03) held at the beautiful Park Hotel Palmse in Lahemaa National Park, Estonia, from March 2nd through 7th, 2003. There I gave four 90-minute lectures on algorithmic information theory (AIT), which is the theory of program-size complexity. Each of these lectures is one chapter of this book. In these lectures I discuss philosophical applications of AIT, not practical applications. Indeed, I believe AIT has no practical applications. —Gregory Chaitin
Conversations With a Mathematician In this book Gregory Chaitin 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.	The Unknowable This essential companion volume to Chaitin's highly successful "The Limit of Mathematics", also published by Springer, gives a brilliant historical survey of the work this century on the foundations of mathematics, in which the author was a major participation. "The Unknowable" is a very readable and concrete introduction to Chaitin's ideas, and it includes a detailed explanation of the programing language used by Chaitin in both volumes.
Meta Maths: The Quest for Omega Meta Maths is Gregory Chaitin's exuberant account of his discovery of 'omega': the infinitely long, exquisitely complex and utterly incalculable representaion of randomness and unknowability in mathematics.	Japanese Edition of Meta Math