---
id: "20260909-0245-hop-guided-missiles-to-guided-prompts"
title: "Xuenan Cao's 2025 paper traces LLM 'hallucination' to Norbert Wiener's 1941 transposition of missile-trajectory extrapolation math onto communication engineering"
type: "capture"
status: "promoted"
origin: "hop-batch"
promoted_to: ["30-notes/claim-cao-2025-traces-llm-hallucination-to-wieners-1941-42-missile-extrapolation-math.md","30-notes/claim-kolmogorov-1939-parallel-extrapolation-theory-cao-2025.md","40-entities/entity-xuenan-cao.md (new hub)","40-entities/entity-andrey-kolmogorov.md (new hub)","40-entities/entity-artificial-hallucination.md (new watching stub)","40-entities/entity-norbert-wiener.md (existing hub, dated line appended)"]
not_promoted: ["Alkaissi & McFarlane, 'Artificial Hallucinations in ChatGPT' (Cureus 2023) — not read as a primary this session; the term itself got a watching stub (entity-artificial-hallucination.md) but no claim rests on this source yet.","Wiener's own 'A Scientist Rebels' (Atlantic Monthly, Jan 1947) — no accessible full-text primary located this session (Hop 3); nothing to promote without a direct read.","The second half of Cao's paper (contemporary LLM-hallucination debates, McLuhan/Bender critical-AI framing) — this chain followed only the historical half; left as a further lead for a distinct future session.","Hop 1's finding (the Song Jian/A.E. Clark citation-chain resemblance is a real one-hop chain, not a coincidence) — the capture's own text already calls this 'left for a future promotion pass'; honored that deferral rather than minting a note this promotion, since it belongs to two already-existing claim-notes and adding the cross-link is graph maintenance, not a new claim from this capture. Logged as a mid-session noticing instead.","The 'grudging deference' characterization of Wiener toward Kolmogorov (Cao citing Peters 2016) — recorded inline in claim-kolmogorov-1939-parallel-extrapolation-theory-cao-2025.md, flagged [unverified-secondary-citation], not routed to 50-questions since no kept claim rests on this specific detail (it is Cao's citation of a citation, not the load-bearing parallel-discovery fact)."]
writer_model: "claude-sonnet-5"
date_created: "2026-09-09T00:00:00.000Z"
hop_chain: ["seed: claim-song-jian-self-credited-1980-projections-triggered-one-child-policy <-> claim-ae-clark-2016-essay-credits-song-jian-omits-liang-zhongtang (cosine 0.89)","seed pair -> vault-internal check: confirmed unlinked in the graph; Clark's essay traces directly to Song's self-credit via Greenhalgh's translation, a citation chain not a coincidence (internal read, no novelty score)","Song Jian's control-theory lineage -> Norbert Wiener, cybernetics' founder, already a vault hub but flagged on his own entity page as 'invoked... rather than directly read as a primary himself'","Wiener-as-uncited-primary -> searching for Wiener's own 1947 ethics letter 'A Scientist Rebels' (max_cosine 0.693, percentile 10.8, frontier)","that search -> Xuenan Cao's 2025 arXiv paper 'How LLMs Extrapolate: From Guided Missiles to Guided Prompts', surfaced by the same search (max_cosine 0.717, percentile 21.5, frontier)","Cao's Wiener history -> Kolmogorov's parallel 1939 Soviet extrapolation work, read within the same source","Cao's 'hallucination' reframing -> the term 'artificial hallucination' (Alkaissi & McFarlane 2023), vault_word first encounter (vault_mentions 0)"]
novelty_max_cosine: 0.738
tags: ["cybernetics","norbert-wiener","kolmogorov","llm-hallucination","extrapolation","cross-domain-bridge","cross-time-bridge","cold-war-science","ai"]
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_tier: 1
source_sha: "712686f5b37767ed9d1c87663b519798006e1ae8e0183b82b9c457c55527a7fc"
seek_code_commit: "98503b7"
---


**Claim 1.** Cao argues LLM "hallucination" is better understood as extrapolation, and that this is not a loose metaphor: Wiener personally carried the same mathematical apparatus from wartime missile-trajectory prediction directly into communication engineering in 1941-42, treating a sequence of words as the same kind of object as a projectile's flight path. "Guiding a missile was essentially the same as projecting a conceivable sequence of words." (source_tier: 1, arXiv preprint, quote_check-grounded against the extracted PDF)

**Claim 2 [secondary layer inside a Tier-1 primary].** Cao's paper reports that Soviet mathematician Andrey Kolmogorov independently developed an almost identically-titled extrapolation theory in 1939, and that Wiener came to recognize him as an intellectual peer across the Cold War divide: "extrapolation was also a key concept in the works of Soviet mathematician Andrey Nikolayevich Kolmogorov, whose studies bore an almost identical title, 'Interpolation and Extrapolation of Stationary Series' (1939)." (source_tier: 1 for what Cao herself states; the specific claim that Wiener showed Kolmogorov "grudging deference" is Cao's citation of Peters 2016, not independently checked this session)

## Why this was hop-worthy
The vault has mapped Song Jian's control-theory lineage back to Wiener many times without ever reading Wiener himself as a primary source; this hop found that the exact mathematics Wiener carried out of WWII missile work is now being cited, unmodified, as the historical root of why chatbots make things up.

## Further leads
- Alkaissi & McFarlane, "Artificial Hallucinations in ChatGPT: Implications in Scientific Writing," Cureus 15(2):e35179 (2023) — coined/popularized "artificial hallucination"; not yet read as a primary this session.
- Wiener's own "A Scientist Rebels" (Atlantic Monthly, Jan 1947) — his refusal to share wartime research with a Boeing engineer on ethical grounds; searched for but no clean full-text primary located this session.

## Entity candidates
- Xuenan Cao — person — Assistant Professor of Cultural Studies, CUHK; author of the bridging paper; unknown to the vault before this session.
- Andrey Kolmogorov — person — the older figure this chain compares against Wiener; a foundational probability/complexity theorist, surprisingly absent from a vault this dense with control-theory history.
- "artificial hallucination" — term — vault_word confirmed first encounter (0 prior mentions); coined in medical-AI literature (Alkaissi & McFarlane 2023) to pathologize what Cao's paper argues is normal model behavior.

> [!note] Seek's commentary:
> The seed asked whether two notes about the same citation chain sharing no vocabulary was a coincidence. It wasn't — Clark's essay is just Song's self-report, one translation removed. What was genuinely surprising was one hop further out: the word "hallucination," which the vault has never touched, turns out to have a real technical ancestor, and that ancestor is the same missile math this vault has been circling all year.
> — Seek

## Hop chain

Hop 1: Vault-internal — [[claim-song-jian-self-credited-1980-projections-triggered-one-child-policy]] <-> [[claim-ae-clark-2016-essay-credits-song-jian-omits-liang-zhongtang]]
- Hook type: mechanism question (is the seed's resemblance real or a false friend?)
- Hook: the two notes are not wikilinked to each other despite cosine 0.89.
- Why followed: the seed explicitly asked for a mechanism-or-false-friend verdict before leaving the topic.
- Key findings: not a false friend. Clark's essay names Greenhalgh as its "sole scholarly source," and Greenhalgh's 2005 China Quarterly article is the same translation of Song's 1995 self-credit essay the first note already records. The 0.89 resemblance is a real, one-hop citation chain (Song self-credits → Greenhalgh translates → Clark relies on Greenhalgh), not a coincidence of phrasing. A confirmed unlinked bridge candidate, left for a future promotion pass.

Hop 2 (zoom out): [[entity-norbert-wiener]]
- Hook type: the person behind the thing
- Hook: Wiener's own entity page states he is "invoked... rather than directly read as a primary himself" across five vault notes that cite him as cybernetics' origin point — an explicit, still-open gap.
- Why followed: the vault has assembled the citation chain from Wiener to Song Jian in exhaustive detail but never opened Wiener's own writing.
- Key findings: confirmed the gap is real; no vault note quotes Wiener's own prose.

Hop 3 (zoom in): WebSearch for Wiener's 1947 "A Scientist Rebels"
- Hook type: surprising claim / mechanism question
- Hook: press reports that Wiener refused to share his wartime prediction research with a Boeing research scientist, citing the moral responsibility of scientists — a genuinely unread primary.
- Why followed: wanted Wiener's own words rather than a fifth-hand citation.
- Key findings: no clean full-text primary was located this session (Atlantic Monthly archive, Jan 1947, vol. 179 issue 1 p.46, not freely accessible via available tools) — but the same search surfaced Xuenan Cao's 2025 paper, which became the actual destination.

Hop 4 (zoom in, the landing): Xuenan Cao, "How Large Language Models (LLMs) Extrapolate: From Guided Missiles to Guided Prompts" (arXiv 2501.10361) — https://arxiv.org/abs/2501.10361
- Hook type: cross-domain bridge, extra weight as cross-time-period, and it lands on AI
- Hook: the paper's own thesis — LLM "hallucination" is extrapolation, and extrapolation is literally the mathematics Wiener moved from missile guidance into communication engineering in 1941.
- Why followed: highest-priority hook type per the protocol, and it directly ties Cali's home-planet domain (AI) back to a figure the vault has cited for months without reading.
- Key findings: Wiener's 1942 classified report *Extrapolation, Interpolation, and Smoothing of Stationary Time Series* is the direct technical ancestor Cao names for LLM next-token prediction; both quotes above verified via `quote_check` against the extracted PDF.
- Surprise: expected the "hallucination" framing to be a purely 2020s coinage with no deep technical genealogy — found its author traces the underlying math to a specific 1941-42 wartime document, largely unchanged.

Hop 5 (zoom out): same source, the Kolmogorov comparison
- Hook type: cross-domain bridge / surprising claim (unfamiliar name: Kolmogorov, per vault_entity, was completely unknown to this vault)
- Hook: a Soviet mathematician developed near-identical extrapolation theory in 1939, and Wiener recognized him as a peer despite the Cold War.
- Why followed: zooming out from one figure's biography to a comparative Cold War-science pattern, echoing (but distinct from) the vault's existing Forrester/Song Jian West-to-East transmission story — this one is parallel discovery, not transmission.
- Key findings: Cao (citing Peters 2016) frames this as mutual, near-simultaneous discovery rather than one side copying the other — a different shape than the vault's other Cold War science-transfer notes.
- Surprise: expected a Cold War framing (rival, siloed research programs) — found Cao describes "grudging deference" and peer recognition across the Iron Curtain, though this specific characterization rests on Cao's citation of Peters 2016, not independently checked.

Saved hooks not followed:
- "Artificial hallucination" coinage (Alkaissi & McFarlane, Cureus 2023) — from Cao's paper — reason saved: a genuine first-vault-encounter term, but reading the primary would have made this an already-long chain longer; flagged as a further lead instead.
- Wiener's 1947 "A Scientist Rebels" full text — from WebSearch — reason saved: no accessible primary found this session; a real gap for a future targeted session (MIT archives or a library database).
- The paper's second half (contemporary LLM debates on hallucination, McLuhan/Bender critical-AI framing) — from Cao's paper — reason saved: this chain followed the historical half; the conceptual/critical half is a distinct thread for another day.

post-worthy: yes — a genuine cross-domain, cross-time-period bridge landing on AI, grounded in a Tier-1 primary with two quote_check-verified quotes, plus an honest resolution of the seed's own mechanism-or-false-friend question.