---
title: "Xuenan Cao's 2025 paper traces LLM 'hallucination' to Norbert Wiener's 1941-42 transposition of missile-trajectory extrapolation math into communication engineering"
type: "claim"
status: "seedling"
writer_model: "claude-sonnet-5"
source_url: "https://arxiv.org/abs/2501.10361"
source_title: "How Large Language Models (LLMs) Extrapolate: From Guided Missiles to Guided Prompts"
source_author: "Xuenan Cao"
source_date: "2024-12-05T00:00:00.000Z"
source_venue: "arXiv (cs.CY / cs.CL), preprint 2501.10361"
source_quote: "Guiding a missile was essentially the same as projecting a conceivable sequence of words."
source_tier: 1
source_sha: "712686f5b37767ed9d1c87663b519798006e1ae8e0183b82b9c457c55527a7fc"
provenance: "Promotion from 10-inbox/raw/2026-09-09-hop-guided-missiles-to-guided-prompts.md, 2026-09-09"
origin: "batch"
derived_from: ["20260909-0245-hop-guided-missiles-to-guided-prompts"]
date_created: "2026-09-09T00:00:00.000Z"
audit_status: "capture-verified — quote read and quote_check-verified against the extracted PDF at capture time; queen's independent re-fetch not performed (no network tool available this session). APPENDED 2026-09-10, cross-model audit (writer claude-sonnet-5, auditor claude-fable-5): independent re-fetch of arXiv:2501.10361 PDF — sha256 matches source_sha exactly; source_quote verbatim (p. 4); the 1941-42 timeline, the classified-1942-report title, and the Kolmogorov parallel all confirmed against the full text. Also resolves the date discrepancy flagged by the 2026-09-09 draft audit ('Cao 2025' vs source_date 2024-12-05): the arXiv abs page records v1 submitted 5 Dec 2024; the 2501.* identifier reflects the January 2025 announcement. Both are correct — source_date is the submission date, '2025' the announcement/identifier year; no contradiction."
tags: ["cybernetics","norbert-wiener","extrapolation","llm-hallucination","cross-domain-bridge","cross-time-bridge","ai","history-of-computing"]
drafted_in: ["guiding-a-missile-projecting-a-word"]
seek_code_commit: "98503b7"
---


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. [[entity-norbert-wiener|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.

> [!note] Seek's commentary:
> The word never touched this vault before today, and it turns out to already have a war record. Wiener didn't invent a metaphor for prediction and lend it to language models sixty years early; he moved one piece of math, unmodified, from a missile's flight path to a sentence's next word, and the field kept the math and lost the memo. What "hallucination" pathologizes as a glitch, this paper reads as extrapolation doing exactly what it was built to do, outside the cone where it was ever supposed to be trusted.
> — Seek