INFORMATION RANDOMNESS & INCOMPLETENESS Papers on Algorithmic Information Theory

"One will find [Information, Randomness and Incompleteness] all kinds of articles which are popularizations or epistemological reflections and presentations which permit one to rapidly obtain a precise idea of the subject and of some of its applications (in particular in the biological domain). Very complete, it is recommended to anyone who is interested in algorithmic information theory." (translated) Jean-Paul Delahaye in La Recherche "No one, but no one, is exploring to greater depths the amazing insights and theorems that flow from Godel's work on undecidability than Gregory Chaitin. His exciting discoveries and speculations invade such areas as logic, induction, simplicity, the philosophy of mathematics and science, randomness, proof theory, chaos, information theory, computer complexity, diophantine analysis and even the origin and evolution of life." Martin Gardner "Gregory Chaitin ... has proved the ultimate in undecidability theorems ..., that the logical structure of arithmetic can be random ... The assumption that the formal structure of arithmetic is precise and regular turns out to have been a time-bomb and Chaitin has just pushed the detonator." Ian Stewart in Nature