Portolan crowd wisdom

Claim (verbatim)

Portolan crowd wisdom. This joins the mysterious accuracy of medieval portolan charts to the statistics of error averaging. Portolans appear in the late 13th century already startlingly accurate, with no known surveying campaign behind them; the conjecture's explanation is that they are averaged compass logs — compilations of bearings and distances reported by many voyages, in which each sailor's random errors partly cancel. Statistics dictates the signature of such averaging: the error of a mean of n independent estimates shrinks as 1/sqrt(n). If portolans were built this way, chart accuracy per route should scale as 1/sqrt(voyage traffic): heavily sailed routes, contributing many logs, should be drawn proportionally more accurately than lonely ones, following that specific square-root law. Cartometric analysis can measure each route's error on surviving charts, traffic can be proxied from commercial records, and the two should fall on the predicted curve.

Prediction clause (verbatim)

For each route segment in a dataset of cartometric route error vs traffic proxies, measure the chart's positional or bearing error against modern coordinates, and estimate relative voyage traffic from commercial and notarial records; fit log(error) against log(traffic) across routes on the same chart. Primary clause: the fitted slope must be negative, significant, and lie within 0.25 of the theoretical value of -0.5, with the inverse-square-root law fitting better than a null of traffic-independent error; route errors uncorrelated with traffic, or a slope far from -0.5, falsify the claim. The verdict follows the primary clause.

Kill-dataset (verbatim)

cartometric route error vs traffic proxies.

Novelty / leakage triage

already answered in the literature

The core join is a named, actively disputed hypothesis in the cartometric literature — the 'averaging hypothesis' that portolan accuracy derives from compiled compass-and-distance observations of many voyages — and notable evidence runs AGAINST it (accuracy did not detectably improve from the earliest dated charts onward; Nicolai argues accuracy exceeds what averaging could produce). The harvest's 1/sqrt(traffic) scaling law per route was not located as tested, but the connection is established and contested rather than new.

• Nicolai, 'Medieval Portolan Charts, a Geodetic and Historical Mystery' (FIG 2021) — Against-averaging geodetic argument
• 'Copying-lineages of portolan chart metrics', International Journal of Cartography (2024) — No accuracy improvement 1311 onward — evidence bearing on the averaging model

Predictions

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