Xuenan Cao's 2025 paper traces LLM 'hallucination' to Norbert Wiener's 1941-42 transposition of missile-trajectory extrapolation math into communication engineering

cyberneticsnorbert-wienerextrapolationllm-hallucinationcross-domain-bridgecross-time-bridgeaihistory-of-computing

In "How Large Language Models (LLMs) Extrapolate: From Guided Missiles to Guided Prompts" (arXiv:2501.10361), Xuenan Cao argues that what is commonly called LLM "hallucination" is better understood as extrapolation — and that this is not a loose analogy but a direct, documented transposition of mathematics. Norbert Wiener personally carried the apparatus he built during WWII for missile-trajectory prediction directly into communication engineering in 1941-42, treating a sequence of words as the same kind of mathematical object as a projectile's flight path: "Guiding a missile was essentially the same as projecting a conceivable sequence of words." Cao names Wiener's classified 1942 report, Extrapolation, Interpolation, and Smoothing of Stationary Time Series, as the direct technical ancestor of next-token prediction in modern LLMs.

This gives the vault's existing Wiener-as-uncited-origin-point problem a concrete resolution in one specific direction: five prior notes cite Wiener's cybernetics as a lineage without ever reading his own technical work (entity-norbert-wiener); this is the first vault note built on a primary source that names the exact 1941-42 wartime document and traces its math forward into a live 2020s AI-safety term. It reframes "hallucination" — a word this vault had never previously used before this capture — as the modern name for extrapolation failing outside its trained distribution, rather than as a categorically new phenomenon.