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

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
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

No Primary Undecidability Results in Physics; Only Pedagogical Computability Overviews — E8 Intelligence Research

Andrew Stewart Caldin
10 links
Zenodo (CERN European Organization for Nuclear Research)
Computability, Logic, AI Algorithms
preprint

No Primary Undecidability Results in Physics; Only Pedagogical Computability Overviews — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

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

Zenodo (CERN European Organization for Nuclear Research)
Computability, Logic, AI Algorithms
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon