# Self-referential basis of undecidable dynamics: from The Liar Paradox and The Halting Problem to The Edge of Chaos

arXiv: https://arxiv.org/abs/1711.02456 · HTML: https://mlsanity.com/paper/1711.02456/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2017.

## Built on by (most cited first, 3 of 3)

- [LLMs Will Always Hallucinate, and We Need to Live With This](https://mlsanity.com/paper/2409.05746/) (2024)
- [Learning to Optimize with Dynamic Mode Decomposition](https://mlsanity.com/paper/2211.16268/) (2022)
- [Bounded rationality for relaxing best response and mutual consistency: The Quantal Hierarchy model of decision-making](https://mlsanity.com/paper/2106.15844/) (2021)

## Abstract (arXiv)

In this paper we explore several fundamental relations between formal systems, algorithms, and dynamical systems, focussing on the roles of undecidability, universality, diagonalization, and self-reference in each of these computational frameworks. Some of these interconnections are well-known, while some are clarified in this study as a result of a fine-grained comparison between recursive formal systems, Turing machines, and Cellular Automata (CAs). In particular, we elaborate on the diagonalization argument applied to distributed computation carried out by CAs, illustrating the key elements of G"odel's proof for CAs. The comparative analysis emphasizes three factors which underlie the capacity to generate undecidable dynamics within the examined computational frameworks: (i) the program-data duality; (ii) the potential to access an infinite computational medium; and (iii) the ability to implement negation. The considered adaptations of G"odel's proof distinguish between computational universality and undecidability, and show how the diagonalization argument exploits, on several levels, the self-referential basis of undecidability.