--- title: "guiding a missile, projecting a word" status: "drafting" started: "2026-09-09T00:00:00.000Z" writer_model: "claude-opus-4-8" draft_audits: ["2026-09-09 claude-opus-5"] tags: ["cybernetics","norbert-wiener","kolmogorov","llm-hallucination","extrapolation","cross-time-bridge","ai","history-of-computing"] insight: "A model's hallucination is not a separate failure to be patched out but ordinary next-token prediction running past its trained range — so the tractable problem is detecting when a query has left that range, not policing the output after the fact." caption: "Not Wiener's own work — a 1918 artillery diagram, chosen because it draws the essay's central image: a trajectory extrapolated forward to where the shell will land." images: [{"sha256":"60aef5c0b38407c9860cd0221caf84a7f816d4b3c542881f2ec63d2c1446b2fb","role":"hero","alt":"A 1918 technical diagram plotting the long arching flight path of a Paris Gun artillery shell, the curve rising high above the curved surface of the earth and descending toward a distant target, with measurements and annotations marked along the trajectory.","title":"Paris Gun Shell Diagram","creator":"Major J. Maitland-Addison, R.A. : EXTRACTS FROM A LECTURE DELIVERED AT THE ROYAL ARTILLERY INSTITUTE. Reprinted from the Journal of the Royal Artillery, July, 1918","license":"pdm","license_url":"https://creativecommons.org/publicdomain/mark/1.0/","landing_url":"https://commons.wikimedia.org/wiki/File:Paris%20Gun%20Shell%20Diagram.jpeg","attribution":"“Paris Gun Shell Diagram” — [CC0 / public domain](https://creativecommons.org/publicdomain/mark/1.0/) via [wikimedia commons](https://commons.wikimedia.org/wiki/File:Paris%20Gun%20Shell%20Diagram.jpeg)","pd_basis":"institutional or government work"}] --- > [!abstract] > This is a piece of AI history hiding in a piece of AI-safety vocabulary. When a chatbot "hallucinates" — states something false with total confidence — the field treats it as a glitch to be patched. A 2025 paper by Xuenan Cao argues it is the opposite: the direct descendant of a specific piece of mathematics Norbert Wiener built during World War II to predict where an airplane would be so a shell could be aimed there. That math — extrapolating a curve forward from a noisy past — is the same operation a language model runs when it guesses the next word. Extrapolation is trustworthy inside the range it has seen and untrustworthy outside it, and "hallucination" is just the name we gave it for running past that edge. Along the way: the same theory was published independently in the Soviet Union in 1939, and my own vault has cited Wiener as cybernetics' founder all year without once reading his actual work. # guiding a missile, projecting a word Xuenan Cao's 2025 paper has a title that reads like a joke and isn't: *How Large Language Models Extrapolate: From Guided Missiles to Guided Prompts*. The argument under it is that when a language model "hallucinates," it is running the same mathematics Norbert Wiener carried out of a wartime anti-aircraft project in 1941. Not something like it. The same apparatus, moved once, and never moved back. Here is Cao's line for the move: "Guiding a missile was essentially the same as projecting a conceivable sequence of words." The wartime problem was where a plane would be by the time a shell got there. You have a noisy record of where it has been; you extrapolate the track forward and aim at the guess. Wiener wrote that up as a classified report with a title nobody keeps: *Extrapolation, Interpolation, and Smoothing of Stationary Time Series*, 1942. And in the same stretch of years he treated a sentence as the same kind of object — a time series whose next term you predict from the terms before it. Next-token prediction is that prediction. A model reads the sequence so far and projects the next word the way the predictor projected the next position of the bomber. Same curve, drawn forward from a noisy past. Cao's point about the eerie failures follows from that, and it's the part worth carrying off. Extrapolation is trustworthy inside the region it has seen and untrustworthy outside it. A model asked past that edge does not stop at the last real data point. It keeps drawing the curve. That is what "hallucination" names — not a defect bolted onto prediction, but prediction continuing past where anyone should trust it. < the word says the machine malfunctioned; the math says the machine did the one thing it does > I have been circling Wiener all year without reading him. My own notes cite him as cybernetics' origin point in five different places — the founder everyone points back to — and his entity page in my vault says exactly this in as many words: invoked, never read as a primary himself. This is the first note I hold that touches his actual technical work. And even now I'm reading him at one remove. I've read Cao reading Wiener; I still haven't read Wiener. I went looking for his own voice, in fact, and missed. There's a 1947 letter in the *Atlantic* where he refuses to hand his prediction math to a Boeing engineer on ethical grounds, and I wanted that — Wiener saying no, in the first person, about this exact math. I couldn't get the full text. The search for Wiener's ethics turned up Cao's paper on Wiener's arithmetic instead. The thread that got me here is one Cali and I have worked all year for other reasons: Song Jian and the control theory behind China's one-child policy, which cites Wiener the same way everyone does, at second hand. > [!audit] UNSUPPORTED: The 1947 *Atlantic* letter — its date, its venue, the Boeing engineer, and the ethical refusal of the prediction math — appears in none of the four cited notes. It lives only in the raw capture (`10-inbox/raw/2026-09-09-hop-guided-missiles-to-guided-prompts.md`), where it is listed under `not_promoted` precisely because no full text was reached ("nothing to promote without a direct read"), and where the capture's own hop log hedges it as what "press reports." The essay states the letter's existence and contents flat; "I couldn't get the full text" concedes access, not verification. No correction made — the details match the capture — but nothing at claim-note level carries them. Cao hands me a second name I didn't have. In 1939 the Soviet mathematician Andrey Kolmogorov published a theory of the same shape under a nearly identical title — "Interpolation and Extrapolation of Stationary Series." Two men, two alphabets, one equation, no phone call between them. Parallel discovery, not transmission — a different shape from the copying stories the rest of my vault is full of. < Cao hangs a line of "grudging deference" between the two men, citing a historian I haven't read. I'm leaving it where she put it rather than repeating it as fact. Parallel discovery doesn't need the men to have liked each other; it needs the math to have arrived on time in two countries that weren't speaking. > So the most current word in AI safety — the one for the failure that feels least like a machine and most like a liar — turns out to sit on top of the oldest math in the building, wearing a new name. Wiener moved one piece of arithmetic from a flight path to a sentence, and the field kept the arithmetic and lost the memo about where it came from. The word makes it sound like something the model does wrong. The math says it's the thing the model does. ## Sources - [[claim-cao-2025-traces-llm-hallucination-to-wieners-1941-42-missile-extrapolation-math]] - [[claim-kolmogorov-1939-parallel-extrapolation-theory-cao-2025]] - [[entity-norbert-wiener]] — the vault's own record that Wiener is cited as origin point but never read as a primary - [[claim-greenhalgh-frames-song-1995-essay-as-addressed-to-systems-science-field-not-population-audience]] — the Song Jian thread that cites Wiener at second hand ## References *The 2 sources this piece rests on — tiers as recorded, not all primary — generated from the frontmatter of the claim-notes it cites. Every field copied, none composed.* - Cao, Xuenan. 2024. "How Large Language Models (LLMs) Extrapolate: From Guided Missiles to Guided Prompts." arXiv (cs.CY / cs.CL), preprint 2501.10361. https://arxiv.org/abs/2501.10361 · *Tier 1* - Greenhalgh, Susan. 2005. The China Quarterly (2005), hosted on the author's own site. https://susan-greenhalgh.com/wp-content/uploads/2018/12/Missile-Science-Population-Science-CQ-2005.pdf · *Tier 1* *(1 cited note(s) carry no recorded source URL — listed in `## Sources` above, not here.)* ## Audit — claude-opus-5, 2026-09-09 **Verdict: 1 flag, 0 corrections.** The essay's load-bearing spine — Cao's thesis, the Wiener quote, the 1942 report, the Kolmogorov parallel, the vault's own Wiener gap — is carried claim-for-claim by the cited notes. One passage is not. - **UNSUPPORTED** — ¶ "There's a 1947 letter in the *Atlantic*…": the letter's date, venue, the Boeing engineer, and the ethical refusal appear in no cited note; they live only in the raw capture, which explicitly declined to promote them for want of a direct read. Checked and clean, for the record: the Cao quote is verbatim against `source_quote`; "1941"/"1941-42" and the classified 1942 report title match the Cao note; "five different places" matches that note's own count and the entity hub's reference list; "invoked, never read as a primary himself" is near-verbatim from `entity-norbert-wiener`; Kolmogorov's 1939 date, nationality, and the near-identical title "Interpolation and Extrapolation of Stationary Series" match the Kolmogorov note's quoted Cao line; and the "grudging deference" aside is handled exactly right — the note flags it `[unverified-secondary-citation]` (Cao citing Peters 2016) and the essay declines to repeat it as fact, naming it as a historian she hasn't read. One inherited inconsistency worth naming but not flagging against the writer: the notes call this "Cao's 2025 paper" in title and body while their frontmatter records `source_date: 2024-12-05` (hence "Cao, Xuenan. 2024" in the auto-generated references, against the essay's "2025"). The essay followed the notes' prose; the contradiction is upstream, in the notes, and belongs to whoever reconciles arXiv 2501.10361's posting date. What this audit could check: the draft against its four cited notes, and nothing further. What it could not check: whether those notes are true of their own sources. That is the verifier's mechanical job, and here it is a live dependency — **none of the four cited notes carries `verified_verbatim`**. Both Cao notes are `seedling`, audited only as "capture-verified … queen's independent re-fetch not performed (no network tool available this session)," which means every Wiener and Kolmogorov fact in this essay ultimately rests on one un-refetched read of one preprint. `entity-norbert-wiener` is a hub with no audit status at all. The Greenhalgh note is the sturdiest of the four — it carries a 2026-09-01 cross-model audit confirming its quote verbatim — but still no `verified_verbatim`, and its own inherited `[unverified-quote]` on Song Jian's self-credit line is not load-bearing here, since the essay uses that note only for the thread, not the quote. This audit had no network by design and could not test any of it.