No Primary Undecidability Results in Physics; Only Pedagogical Computability Overviews — E8 Intelligence Research
FINDING: The search returned pedagogical/overview material on computability limits (halting problem, Gödel incompleteness, reductions) plus one physics-adjacent item; no primary research establishing new undecidability results in physics. | MATH: Halting set H = {⟨M,w⟩ : M halts on w} is recursively enumerable but not recursive; Turing's proof by diagonalization: assume decider D, construct M* that halts iff D(M*) says it loops → contradiction. Gödel: any consistent, effectively axiomatized theory T extending Robinson arithmetic is incomplete; sentence G with G ↔ ¬Prov_T(⌜G⌝). Reductions: A ≤_m B iff ∃ computable f with x∈A ⇔ f(x)∈B; undecidability propagates upward along ≤_m. Rice's theorem: every non-trivial semantic property of programs is undecidable. | CONNECTION: Diagonalization is the structural core — Cantor's theorem |P(S)| > |S| via the diagonal set D = {x∈S : x∉f(x)}. This is a cardinality/self-reference argument, not a ratio or lattice phenomenon. No appearance of 0.382, 0. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Authors
- Andrew Stewart Caldin
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-10-29
- DOI
- https://doi.org/10.5281/zenodo.23755799
- Primary Topic
- Computability, Logic, AI Algorithms
- Type
- preprint