Text, Terrain, and Algorithms: Searching for Al-Idrisi’s Aqranus with Formal Methods

"Aqranus is a magnificent city located on a high mountain," writes the 12th-century Arab geographer al-Idrisi. Today, historians widely agree that Aqranus refers to the medieval city of Kran whose exact location remains uncertain. In this study, we test competing hypotheses for Kran’s location by modeling spatial references from al-Idrisi in a GIS environment. Al-Idrisi records Aqranus as lying six days of march from Istibuni (modern Ihtiman), 40 miles from Farui (Stara Zagora), and four days of march from Lufisa (Lovech). We operationalize these distances using three progressively realistic spatial methods. First, we apply Euclidean distance buffers. Second, we model anisotropic, slope-dependent travel costs across the landscape. Third, we simulate travel within a reconstructed medieval road network. As model realism increases, the probable location of Aqranus shifts westward. To assess the consistency of al-Idrisi’s account, we also incorporate two Byzantine sources describing Kran as midway between Beroe (Stara Zagora) and Tarnovo (Veliko Tarnovo). Two least-cost path variants from this analysis suggest an alternative location, supporting a more easterly interpretation and challenging the current scholarly consensus. Rather than resolving the mystery, our findings expand the range of plausible candidates and underscore the problem of geocoding historical toponyms even where numerous linguistic and spatial clues are available.