The Discovery of Algorithmic Probability

This paper will describe a voyage of discovery — the discovery of Algorithmic Probability. But before I describe that voyage —a few words about motivation. Motivation in science is roughly of two kinds: In one, the motivation is discovery itself — the joy of “going where no one has gone before” — the excitement of creating new universes and exploring them. Another kind of motivation is the achievement of a previously defined larger goal, and there may be many subsidiary discoveries on the path to this goal. In my own case both kinds of motivation were very strong. I first experienced the pure joy of mathematical discovery when I was very young — learning algebra. I didn’t really see why one of the axioms was “obvious”, so I tried reversing it and exploring the resultant system. For a few hours I was in this wonderful never-never land that I myself had created! The joy of exploring it only lasted until it became clear that my new axiom wouldn’t work, but the motivation of the joy of discovery continued for the rest of my life. The motivation for the discovery of Algorithmic Probability was somewhat different. It was the result of “goal motivated discovery” — like the discovery of the double helix in biology, but with fewer people involved and relatively little political skullduggery. The goal I set grew out of my early interest in science and mathematics. I found that while the discoveries of the past were interesting to me, I was