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

arXiv: https://arxiv.org/abs/2505.04646 · HTML: https://mlsanity.com/paper/2505.04646/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 60 references that are in the map.
- First posted on arXiv 5 May 2025.

## Builds on (most cited first, 5 of 5)

- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [When the map is better than the territory](https://mlsanity.com/paper/1612.09592/) (2016)
- [Emergence and Causality in Complex Systems: A Survey on Causal Emergence and Related Quantitative Studies](https://mlsanity.com/paper/2312.16815/) (2023)
- [A Turing test for free will](https://mlsanity.com/paper/1310.3225/) (2013)
- [Understanding Biology in the Age of Artificial Intelligence](https://mlsanity.com/paper/2403.04106/) (2024)

## Built on by (most cited first, 2 of 2)

- [Contextual Memory Intelligence -- A Foundational Paradigm for Human-AI Collaboration and Reflective Generative AI Systems](https://mlsanity.com/paper/2506.05370/) (2025)
- [Active Inference Agency Formalization, Metrics, and Convergence Assessments](https://mlsanity.com/paper/2603.21319/) (2026)

## Abstract (arXiv)

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.