Accurate measurements with primitive instruments: the “paradox” in the qanat design

Qanats are up to 3000 years old artificial sub-horizontal underground water channels, 5–80 km long, widespread in Iran, but also common in western China, Arabia and the Mediterranean; they were excavated from the bottom of vertical shafts, starting from their exit and advancing upstream till main, productive wells, constructed at the very beginning of the project were met. Successful qanat excavation therefore required accurate geodetic design, though based on primitive instruments; an apparent “paradox”, obscured by the tremendous social and economic significance of qanats controlling lifestyle in arid regions.Based on the modern geodetic theory and examination of ancient and modern tunnels we conclude that accuracies in leveling for qanats, up to a few centimeter per kilometer, can only be explained if, on the basis of a long tradition, ancient engineers had developed empirical techniques permitting minimization of leveling errors and optimization of their propagation; a so-far ignored branch of the so-called “sub-scientific mathematics”.