According to our own cognitive map [Table 11.1]... it would seem that a fully developed formal-operational stage has not appeared in the art of any culture except that of post-Renaissance Western art... . Now if defining the history of art in terms of cognitive stages is of any value, it is to the extent that it may contribute to explaining the importance of this development specifically, of an increase in the autonomy of forms to the point where even abstract forms devoid of content can be constructed and manipulated. (Compare, in this regard, Uccello's drawing of a chalice [Figure 11.1] with Sol LeWitt's open modular cubes [Figure 11.2], or Leonardo's War Machine [Figure 11.3] with Malevich's Suprematist Elements [Figure 11.4].⁴ .. In making the seemingly paradoxical assertion that these contemporary works, which when viewed on their own appear to be visually much simpler than a Renaissance painting, are in reality more complex, I refer to the complexity which is occasioned by the Modern paradigm viewed as a whole, and to the infinite number of systems which it is able to generate. The Renaissance paradigm derives from a single, closed logical system - perspective - which is repeated over and over again in every picture in much the same way, so that every picture is rigidly bound and dictated by the rules of the system. The Modern paradigm is characterized by its openness and by the infinite number of possibilities and positions which can be taken. [Gablik 1976 p. 44-5]

Stages of cognitive development	Spatial characteristics	Megaperiods of art history
ENACTIVE MODE
Preoperational stage:	Topological relations:	Ancient & Medieval
The stage at which representations are characterized by static imagery and space is subjectively organized. Psychical and physical ideas are not yet dissociated	Distance between objects is based on their proximity to one another on a two-dimensional plane which only takes height and breadth into account. Absence of depth, no unified global space which conserves size and distance.	(including Græco-Byzantine, ancient Oriental, Egyptian, archaic Greek, and early medieval)
ICONIC MODE
Concrete-operational stage:	Projective & Euclidean relations:	The Renaissance
The stage at which representation can arrange all spatial figures in coordinate systems. Representation is still attached to its perceptual content, however. The emergence of perspective as a formal logic, applicable to any content whatsoever, but still confined to empirical reality and to the concrete features of the perceptual world.	Based on the static viewpoint of a single observer. Separation of observer and world.
SYMBOLIC MODE
Formal-operational stage:	Indeterminate atmospheric space	The Modern period
The stage at which hypothetical deductive, logico-mathematical, and propositional systems emerge, constructed and manipulated as independent relational entities without reference to empirical reality.	(late Monet, Cubism, Rothko): Space as an all-over extension in which all points are of equal status and are relative to each other. No dominance of volume over void. (Pollock)	(including late Impressionism, Cubism, Formalism, Serial art, art governed by logical systems and by propositional thinking)