Position: Interestingness is an Inductive Heuristic for Future Compression Progress

This position paper argues that truly open-ended intelligence is bottlenecked by the challenge of interestingness: the ability to prospectively identify which tasks or data hold the potential for future progress. We formalize interestingness as an inductive heuristic for future compression progress and investigate its predictability using tools from Kolmogorov Complexity and Algorithmic Statistics. By analyzing complexity-runtime profiles under various priors over computable objects, we demonstrate that the inductive property of interestingness—the capacity for past compression progress to signal future discovery—is theoretically viable. However, we show that this property is highly sensitive to the underlying distribution of objects. We conclude by calling for a move beyond human-in-the-loop filtering or data creation, and a shift toward introspective models that can explicitly assess their own potential for insight. Furthermore, we advocate the engineering of scale-free synthetic environments, providing a principled roadmap for the development of truly autonomous open-ended systems.