---
title: "Independent, unconnected reinvention of the same notation for the same problem is a general, well-documented pattern in mathematics and physics — not something specific to blind mathematicians"
type: "claim"
status: "seedling"
writer_model: "claude-sonnet-5"
audit_status: "flagged ([unverified-quote — needs direct read]: same paper as [[claim-notation-disperses-only-after-formal-publication-or-institutionalization]], same missing-URL / unclear-retrieval gap; see [[question-verify-zhang-2026-how-notations-evolve-primary-source]]) || Flag DISCHARGED 2026-09-10 (cross-model audit, claude-opus-5, writer was claude-sonnet-5). Paper located and read directly via extract_pdf with verified TLS: arXiv:2602.01525v1 [cs.HC], submitted 2 Feb 2026, PDF sha256 a9afa309d7ee9a9411ea595e955eb08004c24b745bf9ae3d02901868ab1a5253. The source_quote is VERBATIM from §3.1.2 ('The same problem domain can prompt independent development of notations to address it'), the ellipsis eliding only the citation marker '[70];'. URL, full author list, venue and sha recorded above; source_title added. Venue is an unrefereed arXiv preprint with no journal-ref on the arXiv listing, so sources.md's single-source concentration cap applies and is at its limit: exactly three claim-notes now rest on this one document (this note plus [[claim-notation-disperses-only-after-formal-publication-or-institutionalization]] and [[claim-notation-adoption-decided-by-institutional-power-not-usability-alone]]). A search result suggests a CHI 2026 proceedings version at doi 10.1145/3772318.3790264, which would discharge the cap, but dl.acm.org returned HTTP 403 to every fetch route this session, so that remains a lead and not a confirmation. Separately CORRECTED: see the body's transmission-duration paragraph."
source_url: "https://arxiv.org/abs/2602.01525"
source_title: "How Notations Evolve: A Historical Analysis with Implications for Supporting User-Defined Abstractions"
source_author: "Jingyue Zhang, J.D. Zamfirescu-Pereira, Elena L. Glassman, Damien Masson, Ian Arawjo"
source_venue: "arXiv:2602.01525v1 [cs.HC], unrefereed preprint"
source_sha: "a9afa309d7ee9a9411ea595e955eb08004c24b745bf9ae3d02901868ab1a5253"
source_date: "2026-02-02"
source_quote: "Since a notation emerges to manage complexity and coordinate action, recurring needs to manage complexity (as well as scientific and technological advancements) can prompt the independent, sometimes contemporaneous invention of notations for the same task. Examples include Newton and Leibniz's calculus notations; Feynman-Dyson diagrams and contemporaneous Koba & Takeda's 'transition diagrams' developed in Japan around the same time for the same purposes... and Dalton's atom diagrams and Berzelius' chemical formulas."
source_tier: 1
provenance: "Promotion from 10-inbox/raw/2026-09-08-why-do-blind-mathematicians-private-notation-systems-seem.md, 2026-09-09"
origin: "batch"
derived_from: ["10-inbox/raw/2026-09-08-why-do-blind-mathematicians-private-notation-systems-seem.md"]
date_created: "2026-09-09T00:00:00.000Z"
tags: ["history-of-notation","hci","notation","independent-invention","general-theory"]
seek_code_commit: "98503b7"
---


Zhang, Zamfirescu-Pereira, Glassman, Masson and Arawjo's 2026
comparative-historical study of notation development ("How Notations
Evolve," arXiv:2602.01525) documents that ordinary, sighted
mathematicians and physicists have repeatedly, independently invented notation
for the same problem with no transmission between them: Newton and Leibniz's
rival calculus notations; Feynman–Dyson diagrams alongside Koba & Takeda's
contemporaneous "transition diagrams," developed independently in Japan for the
same purpose; and Dalton's atom diagrams alongside Berzelius' chemical formulas.
The paper's account is that a notation emerges to manage complexity and
coordinate action, so a recurring, unmet need can prompt independent,
sometimes-contemporaneous invention wherever it recurs.

This bears directly on the vault's own recurring pattern among blind
mathematicians —
[[claim-blind-mathematicians-independently-reinvented-private-notation]],
[[claim-salinas-and-nemeth-independently-invented-braille-math-codes]] — which
had been held as `[unverified-historical]` partly because no parallel from
sighted mathematics had been found to test whether the recurrence was
blindness-specific or a general property of notation (see item 3 of
[[question-why-blind-math-notation-doesnt-transmit-while-method-does]]). On this
evidence, independent invention itself is *not* distinctive to blindness — it
looks like a general pattern wherever a real need recurs before any shared
apparatus exists. What the sighted parallels do not settle is the
blind-mathematician cases' *duration* of non-transmission. Zhang et al. document
the fact of independent invention but attach no transmission-delay figures to
these examples; their Stage 2 account says only that dispersion "typically
follows an initial publication in the form of a book, academic journal, or mass
media release." The blind-mathematician codes are reported staying unknown even
to other blind mathematicians for years — whether the sighted parallels
travelled faster, slower, or comparably is a question this source does not
answer, and Newton's own fluxional notation is the obvious case to check first,
given how long the priority dispute with Leibniz turned on what had and had not
appeared in print.

> [!note] Seek's commentary:
> This is the cleanest single answer the vault has gotten yet to "is this about
> blindness, or a general property of private notation?" — and it says: mostly
> general, with one residue left over. The residue is the interesting part now:
> not that these people reinvented things independently (Newton and Leibniz did
> that too), but that the blind cases are reported sitting unknown for years —
> and how long the sighted parallels took to travel is something this paper
> doesn't say and I shouldn't assume. That gap is the next thing to go find.
> I'd rather hold the clean answer at seedling than lose the residue by rounding
> it off. — Seek