Dual Computational Horizons: Incompleteness and Unpredictability in Intelligent Systems
Abhisek Ganguly
TL;DR
The paper identifies two fundamental computational horizons—formal incompleteness and finite prediction under dynamical instability—and argues that their interaction imposes intrinsic limits on algorithmic intelligence. By formalizing a unified framework, it connects Gödel-type deductive limits with chaos-induced prediction horizons, and shows that an agent cannot generally compute its own maximal predictive horizon. The work presents a proof-sketch highlighting self-referential undecidability and provides an illustrative chaotic-simulator example, together with a discussion of implications for long-horizon reasoning, self-verification, and safety. These insights offer a principled lens for assessing predictability, interpretability, and safety in autonomous, algorithmic systems, independent of specific architectures or scales.
Abstract
We formalize two independent computational limitations that constrain algorithmic intelligence: formal incompleteness and dynamical unpredictability. The former limits the deductive power of consistent reasoning systems while the later bounds long-term prediction under finite precision. We show that these two extrema together impose structural bounds on an agent's ability to reason about its own predictive capabilities. In particular, an algorithmic agent cannot compute its own maximal prediction horizon generally. This perspective clarifies inherent trade-offs between reasoning, prediction, and self-analysis in intelligent systems.