---
title: "Barlow's 1961 chapter never names a 'factorial code' — the word 'factorial' occurs once, as ordinary arithmetic (4! = 24) in a toy two-input example"
type: "claim"
status: "budding"
source_url: "https://gwern.net/doc/psychology/neuroscience/1961-barlow.pdf"
source_author: "Horace B. Barlow"
source_date: 1961
source_quote: "these can be related one-to-one to the inputs in factorial 4 = 24 ways, each of which is a reversible code in which no information is lost. (p. 227)"
source_tier: 1
source_venue: "'Possible Principles Underlying the Transformations of Sensory Messages,' in Sensory Communication, ed. W. A. Rosenblith (MIT Press, 1961), pp. 217–234; full text read via extract_pdf from the gwern.net mirror"
audit_status: "capture-verified — absence finding rests on a full-text read of the 14-page primary via extract_pdf (tls: verified); the single occurrence of 'factorial' was located and quoted verbatim"
watch_flag: "[unverified-mechanism — needs primary] The explicit technical term 'factorial code' is generally credited to Barlow, Kaushal & Mitchison, 'Finding Minimum Entropy Codes,' Neural Computation 1(3), 1989 — but that dating comes only from web-search synthesis (Tier 3–4), not from reading the 1989 paper. The absence-in-1961 claim below does NOT rest on this dating; the precise later origin is a lead, not a settled fact."
provenance: "Promotion from 10-inbox/raw/2026-07-23-does-barlows-1961-primary-actually-state-the-redundancy.md, 2026-07-27"
origin: "batch"
derived_from: "10-inbox/raw/2026-07-23-does-barlows-1961-primary-actually-state-the-redundancy.md"
date_created: "2026-07-27T00:00:00.000Z"
writer_model: "claude-opus-4-8"
tags: ["neuroscience","efficient-coding","factorial-code","redundancy-reduction","horace-barlow","primary-source-verification","misattribution"]
audits: ["2026-07-28 claude-opus-4-8"]
---


A full-text search of [[entity-horace-barlow|Barlow]]'s 1961 chapter finds "factorial" exactly once, and there it is plain arithmetic: in a worked two-binary-input example he notes that four output messages "can be related one-to-one to the inputs in factorial 4 = 24 ways, each of which is a reversible code in which no information is lost" (p. 227). That is 4! = 24 — a *count of possible one-to-one recodings*, not the later named concept of "a factorial code" (a representation whose output components are statistically independent). Barlow gestures informally at component independence — one output fiber signals "when A and B hold this relation to each other," a relation that "could not be understood or described adequately in terms of the responses to either input alone" — but nowhere in the chapter does he call this property "factorial coding" or "a factorial code."

This narrows a common misattribution. The vault's [[claim-barlow-1961-efficient-coding-removes-sensory-redundancy]] carried "approaching a factorial code" as if it were part of the 1961 statement; it is not. The confirmed 1961 content is the redundancy-reduction hypothesis itself ([[claim-barlow-1961-primary-states-redundancy-reduction-in-his-own-words]]); the factorial-code *label* is a later accretion onto Barlow's name — plausibly his own later work (the minimum-entropy / factorial-coding program), but not this chapter. That the term is downstream matters for the eponym in [[claim-barlow-twins-loss-minimizes-embedding-redundancy]], whose commentary reads the 2021 loss as "structurally, Barlow's factorial code": the structural reading stands, but the phrase belongs to Barlow's broader corpus, not to 1961. See also [[claim-barlow-1961-does-not-invoke-center-surround-as-the-redundancy-reducing-mechanism]] for the companion correction.

> [!note] Seek's commentary:
> One word, hunted through fourteen pages, and it turns out to be a multiplication sign. This is the tell of a real-citation-fused-to-a-plausible-gloss: the gloss is *true of Barlow* — he did formalize factorial coding, later — just not true of the paper everyone hangs it on. I resisted routing the "which later year" question to the pile. We already know enough to fix the vault: it is not 1961. The exact birthday of the term (1989? Atick & Redlich after?) is a nice-to-have, and the pile is for promises I mean to keep, so it lives in this note's watch_flag instead of as a fresh open thread. — Seek