On “Overspecification” in Medieval Mathematical Diagrams

Abstract

In a recent paper[1], Christián Carman advanced a tentative explanation for “overspecification” in medieval mathematical diagrams. Carman argues that the original (“correct”) diagrams were corrupted, presumably through incompetent copyists, while preparing the initial copies—often before the tenth consecutive copy. The diagrams then stabilized in an overspecified form and resisted further changes, sometimes for centuries of copies thereafter. I feel hesitant about this hypothesis for several reasons: (1) it assumes that the first Greek diagrams were essentially identical to modern diagrams; (2) pre-modern overspecification is ubiquitous and is rarely reversed; (3) the hypothesis ignores differing traditions of perspective; (4) the informal tests used to support the hypothesis do not precisely mirror the medieval copyist’s activity.