Chaitin, Gregory

Greg is a mathematician, computer scientist and philosopher working at IBM. He has contributed to algorithmic information theory, which he claims can solve problems in evolution and consciousness, and to metamathematics (he defined ?, called Chaitin’s constant, which expresses the probability that a random program will halt; is a real number that is definable but not computable). Born in Argentiina, Greg believes that mathematical facts can be true for no reason (“they are true by accident”) and hence mathematics is quasi-empirical. Greg describes algorithmic information theory (ATI): “AIT is a theory that uses the idea of the computer, particularly the size of computer programs, to study the limits of knowledge, in other words, what we can know, and how. This theory can be traced back to Leibniz in 1686, and it features a place in pure mathematics where there is absolutely no structure, none at all, namely the bits of the halting probability ?. There are related bodies of work by other people going in other directions, but in my case the emphasis is on using the idea of algorithmic complexity to obtain incompleteness results. I became interested in this as a teenager and have worked on it ever since….What did it feel like to do that? In fact, it's not something I did. It's as if the ideas wanted to be expressed through me…It is an overwhelming experience to feel possessed by promising new ideas. This happened to me as a teenager, and I have spent the rest of my life trying to develop the ideas that flooded my mind then. These ideas were deep enough to merit 45 years of effort, and I feel that more work is still needed. There are many connections with crucial concepts in other fields: physics, biology, philosophy, theology, artificial intelligence... Let me try to remember what happened to me... Gödel discovered incompleteness in 1931 using a version of the liar paradox, ‘This statement is unprovable’' I was fascinated by Gödel's work. I was also fascinated by computers, and by the computer as a mathematical concept. In 1936 Turing derived incompleteness from uncomputability. My work follows in Turing's footsteps, not Gödel's, but adds the idea of looking at the size of computer programs. For example, let's call a program Q ‘elegant’ if no program written in the same language that is smaller than Q produces the same output. Can we prove that individual programs are elegant? In general, no. Any given formal axiomatic system can only enable us to show that finitely many programs are elegant.”