What type of rectangle is a square?

Walter Gerbino, University of Trieste, Italy

Since Mach (1872), the phenomenal shape of the square has intrigued scientists interested in perceptual organization. I will argue that bisection – a classical psychophysical method (Plateau 1872) – can shed light on the inner structure of phenomenal shape. Consider the family of rectangles with vertical/horizontal sides and variable aspect ratio, including the square as a singularity. Participants were required to adjust a variable rectangle until its size appeared intermediate between those of two extreme rectangles (one about three times larger than the other). Two adjustment continua were contrasted: constant aspect ratio vs. grassfire. Surprisingly, bisection of the square (whose size change is compatible with both models) was inconsistent with the bisection of constant-ratio rectangles, while fully consistent with that of grassfire rectangles. The phenomenal shape of the square seems related to an implicit growth that destroys form while maintaining Ebenbreite (Morinaga 1941; Metzger, 1953).