MERLIN SCIENCE — Computability Limits vs. Open Problems: Two Impossibility Classes in M — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: There's a result I want to walk you through, and it's not a new theorem. It's a taxonomy. Mathematics has two fundamentally different kinds of impossibility, and we keep confusing them. The first class is computability limits. These are problems no computer can ever solve, not because we lack cleverness or hardware, but because the solution provably does not exist. Turing's halting problem is the canonical example. No total computable function decides whether an arbitrary program halts on an arbitrary input. The proof is diagonalization, and it closed Hilbert's Entscheidungsproblem as a corollary. This boundary is permanent. It is not a frontier that moves. The second class is different. These are problems that are solvable in principle but open to all human and machine effort. Collatz is the archetype. Take any positive integer. If even, halve it. If odd, triple it and add one. The conjecture says every orbit reaches one. It has been verified computationally to roughly two to the si Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223674036