Incompleteness and Artificial Intelligence

The implications of Gödel incompleteness for artificial intelligence have been studied many times before (e.g. [8]), as has the relation between Kolmogorov complexity and incompleteness (e.g. [3, 2]). In this paper we look at the relationship between these from a new angle. We start by considering the prediction of computable sequences of bounded complexity, an ability which would be fundamental to an artificial intelligence. We then show that although very powerful algorithms exist which can solve this problem, they are necessarily very complex. From this, we then prove that it is impossible to find any of these powerful algorithms due to Gödel incompleteness. This places serious limitations on our ability to understand and analyse intelligent systems using mathematics, and adds a new perspective on the relation between artificial intelligence, complexity and Gödel incompleteness.