FESTSCHRIFT VOLUMES

Greg Chaitin, September 2007

Cristian S Calude

RANDOMNESS AND COMPLEXITY, FROM LEIBNIZ TO CHAITIN

This book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays.

From Leibniz to Chaitin will inform and give pleasure to many diverse readerships. Logicians, philosophers and programmers, teachers and students, specialists and amateurs will find much to learn, to conjure with and, yes, perhaps to be inflamed by. Such is as should be, given the nature of Greg Chaitin's magnificent obsession, technical prowess, personal generosity and willingness to court controversy. It is hard to imagine a better sexagecimal birthday present for a scientist who perfectly exemplifies his own maxim

"To me, you understand something only if you can program it. (You, not someone else!)"

---Jonathan Borwein, FRSC, is a co-author of Mathematics by Experiment: Plausible Reasoning in the 21st Century.

Any volume that would do justice to Gregory Chaitin must be technically impeccable, philosophically daring, mathematically both deep and playful, and so intellectually exciting as to remind a lover of the world of mathematics what the love is all about. This is such a volume.

---Rebecca Goldstein is a MacArthur Fellow and the author of The Mind-Body Problem, Strange Attractors, and Incompleteness: The Proof and Paradox of Kurt Gödel.

Review in New Scientist

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.