The qibla learning curve

Claim (verbatim)

The qibla learning curve. Joins experience-curve economics to Islamic mathematical geography. In manufacturing, quality improves as a power law of cumulative output — the experience curve — because every unit produced teaches its producers. Every mosque is such a unit: it must face Mecca, its measurable orientation error is an output-quality score, and a region's dated mosques form a quality series spanning eight centuries. As zij astronomical tables and qibla-determination methods diffused, builders converged on the true bearing, so orientation error should fall as a power law in cumulative regional mosque construction — sacred accuracy as a learning curve. The conjecture predicts, in two independent regions (the Swahili coast; al-Andalus and the Maghrib), median errors shrinking from fifteen degrees or more before 1000 CE to a few degrees after 1400, a learning exponent in the classic range, and improvement arriving as regional step changes after documented arrivals of tables and instruments, rather than as uniform secular drift.

Prediction clause (verbatim)

For dated mosques with published measured orientations in two independent regions (the Swahili coast; al-Andalus and the Maghrib), the median absolute deviation from the true great-circle qibla falls from >=15 degrees before 1000 CE to <=6 degrees after 1400; error versus cumulative regional dated-mosque count fits a power law with learning exponent 0.2-0.5; and improvements arrive as regional step changes following documented arrivals of astronomical tables and qibla instruments, rather than as a uniform secular drift.

Kill-dataset (verbatim)

Kill: published archaeoastronomical orientation surveys of dated mosques (East African coast; Iberian and Maghribi corpora). No error decline over time, or errors behaving as an undirected random walk, kills it.

Novelty / leakage triage

already answered in the literature

The connection is established historiography with a quantitative regional precedent: David King's foundational work documents mosque misalignment and the diffusion of increasingly accurate mathematical qibla methods from the 9th century (the conjecture names him), an Anatolian study already performs a regional multi-century measured-orientation-error analysis (1150-1590), and an early-period accuracy study covers 622-900 CE. The experience-curve formalization (power-law exponent vs cumulative regional output) and the two named regions were not located, but error-declining-with-method-diffusion is the standing account.

Predictions

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