Why are Geometric Proofs (Usually) “Non-Visual”? We asked this question as
a way to explore the similarities and differences between diagrams and text (visual
thinking versus language thinking). Traditional text-based proofs are considered
(by many to be) more rigorous than diagrams alone. In this paper we focus on
human perceptual-cognitive characteristics that may encourage textual modes for
proofs because of the ergonomic affordances of text relative to diagrams. We suggest
that visual-spatial perception of physical objects, where an object is perceived
with greater acuity through foveal vision rather than peripheral vision, is similar
to attention navigating a conceptual visual-spatial structure. We suggest that attention
has foveal-like and peripheral-like characteristics and that textual modes
appeal to what we refer to here as foveal-focal attention, an extension of prior
work in focused attention
