Computational Irreducibility as the Foundation of Agency: A Formal Model Connecting Undecidability to Autonomous Behavior in Complex Systems

TL;DR

This paper introduces a formal model linking computational irreducibility to autonomous behavior, showing that truly autonomous systems are fundamentally unpredictable and undecidable in their future states.

Contribution

It establishes a rigorous mathematical connection between undecidability and autonomy, integrating computational theory and biology to explain emergent agency.

Findings

Autonomous systems exhibit undecidable future behavior.

Computational irreducibility underpins genuine autonomy.

Implications for AI, biology, and philosophy of free will.

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. we 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. our 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.