Computational irreducibility as the foundation of agency: A formal model connecting undecidability to autonomous behavior in complex systems

Abstract

This article presents a formal model demonstrating that genuine autonomy, the ability of a system to self-regulate and pursue objectives, fundamentally implies computational unpredictability from an external perspective. I establish precise mathematical connections, proving that for any truly autonomous system, questions about its future behavior are fundamentally undecidable. This formal undecidability, rather than mere complexity, grounds a principled distinction between autonomous and non-autonomous systems. My framework integrates insights from computational theory and biology, particularly regarding emergent agency and computational irreducibility, to explain how novel information and purpose can arise within a physical universe. The findings have significant implications for artificial intelligence, biological modeling, and philosophical concepts like free will.