David Hestenes' conformal mapping in Geometric Algebra is an extraordinary achievement of modern algebra with profound implications for the ontology of mathematics, or what mathematics is, as well as for visual perception and spatial consciousness that exhibit a striking resemblance to Hestenes' conformal mapping. Unfortunately the mathematics of Hestenes' conformal mapping is extraordinarily abstruse, as is the Geometric Algebra by which it is defined, which place this fascinating concept generally beyond the reach of the non-specialist. It turns out however that both Hestenes' conformal geometry, as well as the Geometric Algebra on which it is based, are fundamentally visuospatial concepts, and thus they can be presented in simple intuitive terms that do not require deep knowledge of algebra.