If perceived shape is a compromise of perceptual facts creating the simplest perceptual experience, space is seen when depth is the simplest percept. Most of the examples that Arnheim discusses regarding space relate to the simplest evocations of depth in two-dimensions. He states that "there is no such thing as a strictly flat, two-dimensional image" (AaVP, 219) and proceeds to develop his taxonomy of lines - object lines, hatch lines, contour (and we can add "crack" lines; see Massironi, 2002). Interestingly, Arnheim does not report on experiments he well knew that explored the limiting conditions of space, those by his Berlin colleague Wolfgang Metzger on the Ganzfeld. Just as Arnheim sought out the simplest mark, Metzger investigated the simplest spatial experience. In the absence of differentiation of the visual field, object perception ceases and reverts to a sense of pure extensity. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[left: from Wolfgang Metzger, "Optische Untersuchungen am Ganzfeld." Psychologische Forschung 13 (1930) : 6-29."; right: James Turrell, Breathing Light, 2013, Biennale, Venice] 

 

Not surprisingly, such meta-experiences have been of special importance to artists like James Turrell, who have sought to understand the strange phenomenology of colored environments. Thus, where Arnheim directed his psychological tools at mostly pictorial content, contemporary artists have been fascinated by the break down of experience and its transformative potential. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[Fred Sandback, Untitled, 1967, 45.7 x 172.4 x 45.7 cm, Grey elastic cord,  http://www.annemarie-verna.ch/gallery/exhibitions/Fred_Sandback_2012/]

 

Arnheim's most interesting observation on lines was the object line. Using an example from Klee, Arnheim noted that "the lines are perceived as one-dimensional objects, as thought they were wrought in iron or made of some other solid material" (AaVP, 219). Such object lines are sometimes found in the graphic works of Keith Haring. Perhaps more interesting are three-dimensional examples, where this limiting condition of linearity is played out in space. The yarn lines of Fred Sandback do not trace out any representational forms but they do alternate between self-sufficient object and form-building contour with the simple use of a taut line.

 

Lines are not only the simplest forms; they become figures to the ground of their surrounding space. Arnheim was interested in how modernists had reduced space to its minimal suggestion. Artists after modernism turned centralized space into an emblem of Renaissance rationalism and the means for laying bare the very mechanisms that Arnheim had explained. Drawings by Sol Lewitt blandly stake out spaces that seem at first sight to be rigorous but become puns on the human proclivity to read depth into marks. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[Jan Dibbets, Perspective Correction, My Studio I, 2: Square with 2 Diagonals on Wall, 1969; http://www.moma.org/collection/works/173247?locale=en] 

 

A mainstay of theory after Arnheim has been the kind of perspective that more radically tricks us, the central demonstration being the anamorphosis. Arnheim explains such effects in the Ames room to show how simplicity wins out over knowledge in perceiving depth. Artists like Jan Dibbets on the other hand prominently display cases of anamorphosis in their art as a way of forcing the incorrigibility of the illusion to linger. Its very persistence is its power.