Proceedings of the Annual Meeting of the Cognitive Science Society

The development of mathematical marking conventions from prehistory to the present is characterized by a trendfrom conventions with more iconic relationships to concrete structures of the physical world (such as more pictorial ancient landsurveying marks) to marking systems with less-iconic relationships to physical structures (that represent numbers, operations,infinity, and other more abstract concepts). We propose how certain constraints of perception-cognition induced conventionsthat made more-iconic (pictorial) marks controversial. These became too conceptually ambiguous to convey more abstractconceptual categories during the formalization of mathematics: Iconic properties of ancient proto-mathematical conventionsrecruited lower level perceptual capabilities developed to perceive-act in a concrete world of occluded surfaces-edges andwere suitable for conveying concrete structures (such as landforms during surveying). However, these were too conceptuallyambiguous to convey more abstract conceptual categories that emerged when mathematics was formalized because a (pictured)concrete structure can fall under many possible conceptual categories