The Greek lapse rate

Claim (verbatim)

The Greek lapse rate. Joins atmospheric physics to colonial sociolinguistics: just as pressure thins exponentially with altitude at a fixed scale height, Greek thinned with river distance up the Nile from Alexandria at a fixed exponential scale length. The mechanism is demand decay: Greek was the language of administration and of the export economy centred on the metropolitan port, and the payoff to drawing up a document in Greek rather than an Egyptian language — Demotic or Coptic — fell off steadily with every river-kilometre from that centre. The conjecture predicts that the log-odds of a dated document being Greek declines roughly linearly with up-river distance of its findspot, with a scale length of a few hundred river-kilometres, and that this slope stays stable from Ptolemaic to Roman times even as the overall Greek level shifts. The Fayum, a Greek settler enclave, is the pre-registered exception, predicted to sit well above the fitted line.

Prediction clause (verbatim)

In papyri.info, the log-odds that a dated document is Greek rather than Egyptian-language (Demotic or Coptic) declines approximately linearly with up-river distance of the findspot from Alexandria, with a scale length of 300-600 river-km; the fitted slope is stable within +/-30% between Ptolemaic (300-30 BCE) and Roman (30 BCE-300 CE) strata even as the overall Greek level shifts. Pre-registered exception: the Arsinoite nome (Fayum), a Greek settler enclave, is excluded and predicted to sit more than 1 log-odds unit above the fitted line.

Kill-dataset (verbatim)

Kill: papyri.info language and findspot metadata joined to river distances from a standard gazetteer. A flat or non-monotonic distance profile outside the Fayum, or slopes differing by more than x2 between strata, kills it.

Novelty / leakage triage

no prior formulation located (search dated 2026-07-05)

Single-site language-choice studies exist (Pathyris) and modern sociolinguistics has distance-decay/reaction-diffusion language-shift models (PNAS 2017; linguistic fronts), but no source was located regressing Greek-vs-Egyptian log-odds on river distance in papyrological findspot data. No prior formulation located (search dated 2026-07-05).

• Vandorpe, 'Greek or Egyptian? The Language Choice in Ptolemaic Documents from Pathyris' — Single-site language-choice study
• 'Quantifying the driving factors for language shift in a bilingual region', PNAS 114 (2017) — The borrowed model class, modern data

Predictions

No prediction registered yet.