Gödelian Undecidability in Chaotic Dynamics: Fractals, Entropy, and Unprovable Truths — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Gödel's incompleteness theorems prove any consistent formal system containing arithmetic has undecidable true statements; chaotic dynamical systems exhibit undecidable properties via fractal trajectories and information entropy. MATH: Gödel's first theorem: ∃ G such that ⊬ G and ⊬ ¬G (in system S). Second theorem: Con(S) ⇒ ⊬ Con(S). For chaotic systems: Lyapunov exponent λ > 0; fractal dimension D (e.g., Hausdorff dimension); information entropy H = -∑ p_i log p_i. CONNECTION: Fractal trajectories link to self-similarity ratios (e.g., 0.618 in golden-mean cascades). Undecidability mirrors the gap between rational approximation (0.382, 0.618) and irrational truth. No direct base-60 or crystallographic symmetry found. DEPTH: 9 — Foundational limit on knowledge, unifying logical undecidability with dynamical chaos via fractal geometry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171804407
Cites:
Cited by:
Related to: