University of Virginia Library

10 The invention of perspective and the
evolution of art

In this last chapter, I will discuss three views of the place
of perspective in the history of art: those of Panofsky,
Goodman, and Gablik. The first two are relativists and
claim that perspective is a convention of representation
adopted during the Renaissance. Gablik has proposed an
interesting parallel between the development of cognitive
abilities in children and the evolution of art.

In his book on The Renaissance Rediscovery of Linear Perspective,
Samuel Edgerton wrote a masterly exposition of
Panofsky's seminal article “Die Perspektive als 'symbolische
Form' ” (Panofsky, 1924/25) and of its reception
among scholars interested in perspective. I will quote extensively
from his discussion because it serves so well to
introduce the points I wish to make in conclusion.

However, Panofsky's essay did contain one egregious error.
With ingenious reasoning, the author tried to show that the
ancient Greeks and Romans — Euclid and Vitruvius in particular
— conceived of the visual world as curved, and that since the
retina is in fact a concave surface, we do indeed tend to see
straight lines as curved. ...

Panofsky's essay, particularly in recent years, has come under
criticism from scientists, as well as from E. H. Gombrich [1969,
1976, 1980] and other scientific-minded art historians. Writers
on optics and perceptual psychology such as James J. Gibson
[1971], G. ten Doesschate [1964], and M. H. Pirenne [1952–3]
have challenged Panofsky for his subjective curvature hypothesis
and denial that linear perspective has a catholic or “ultimate”
veracity. They are especially put off by Panofsky's reference to
perspective as a “symbolic form,” which is to say, a mere convention...
Unfortunately, Panofsky never explained definitively
just what he meant by the phrase “symbolic form.”
However, he certainly has in mind a more subtle meaning than
a “system of conventions [like][1] versification in poetry.” [This
is how Pirenne summarized Panofsky's theory.] Indeed, Professor
Pirenne and other scientist critics misunderstand the ingenuity
of Panofsky's approach as much as they find Panofsky
himself misunderstood classical optics and modern perceptual
psychology. (1975, pp. 153–5)

Edgerton proceeds to show how Panofsky's notion of
symbolic form is inspired by Ernst Cassirer's Kantian philosophy,
which he capsulates as follows:

In the 15th century, there emerged mathematically ordered
“systematic space,” infinite, homogeneous, and isotropic, making
possible the advent of linear perspective ... Linear perspective,
whether “truth” or not, thus became the symbolic form
of the Italian Renaissance because it reflected the general world
view of the Italian people at this particular moment in history.
(1975, pp. 156, 157–8)

As Edgerton so well explains, Panofsky's position was
not blithely relativistic: It is more important to understand
why the artists of the Renaissance were interested in perspective
than to determine whether it is the “correct”
method of representation. In this book, I have attempted
to convey the variety as well as subtlety of the reasons
why Renaissance artists were interested in perspective. I
hope I have persuaded the reader that “truth” was not at
stake here. To be sure, perspective was a system that enabled
artists to represent space according to geometric rules.
Mainly, however, it was a framework within which originality
without arbitrariness[2] could be achieved.

Nelson Goodman took the issue a step further by marshaling
all his philosophical arguments in support of the
relativistic conception of perspective. Goodman's sustained
analysis of the notions of representation, realism,
and resemblance is also an impassioned defense of the argument
that perspective is not an absolute standard of fidelity,
that it is but one of many methods of representation.
According to Goodman, depictions are analogous to descriptions,
and descriptions need not resemble the things
they describe. Indeed, sometimes they cannot resemble the
thing they are describing because that thing simply doesn't
exist (e.g., a unicorn). Why then do we think that a picture
should resemble the thing it represents? Goodman answers
that conventions of representation are responsible for this
misapprehension. From the correct observation that a picture
usually resembles other pictures of the same kind of
thing, we tend to infer that a picture resembles the kind
of thing it represents. The key argument is here: Goodman
asks himself whether

the most realistic picture is the one that provides the greatest
amount of pertinent information. But this hypothesis can be
quickly and completely refuted. Consider a realistic picture,
painted in ordinary perspective and normal color, and a second
picture just like the first except that the perspective is reversed
and each color is replaced by its complementary. The second
picture, appropriately interpreted, yields exactly the same information
as the first. ... The alert absolutist will argue that for
the second picture but not the first we need a key. Rather, the
difference is that for the first the key is already at hand. For
proper reading of the second picture, we have to discover rules
of interpretation and apply them deliberately. Reading of the
first is by virtually automatic habit; practice has rendered the
symbols so transparent that we are not aware of any effort, of
any alternatives, or of making any interpretation at all. (1976,
pp. 35–6)

I believe that I have provided us with the tools to refute
Goodman's radical relativism.[3] I have shown that perspective
is not a thoroughgoing, arbitrary application of
the geometric system of central projection. Rather, it is a
geometric system tempered by what perception can or
cannot do. It has evolved into a system adapted to the
capabilities of our perceptual system. To respond, Goodman
would have to claim that what perception can do
depends on what it learned to do, and that there is no limit
to what perception can learn. But that argument is false.
There are clear limits to the extent of perceptual rearrangement
(induced by wearing prisms, mirrors, and other devices
that modify the form of the optical information
reaching our eyes) to which human beings can adapt. We
cannot arbitrarily change the way we perceive optical information,
nor can we arbitrarily change our motor responses
to it, regardless of the amount of time or effort
we might invest in doing so (Welch, 1978, pp. 277-9).

We have seen that Panofsky's view on the conventionality
of perspective may not have been as extreme as some
have interpreted it to be because it does not exaggerate the
importance of the role played by the “correct” representation
of space in Renaissance art. We have also seen that

Goodman's view, on the other hand, is the most radical
position on this matter that one can take precisely because
it makes the “correctness” of perspective into a central
issue, thereby impoverishing our understanding of perspective
in Renaissance art rather than enriching it. We
turn now to a third view, which shares some of the features
of Goodman's approach. Suzi Gablik, in her book Progress
in Art, has presented a cultural analog of the classical embryological
law, “ontogeny recapitulates phylogeny,” according
to which an embryo, in the course of its maturation,
goes through stages during which it takes on the appearances
of its evolutionary ancestors. Gablik has proposed a
similar law for the evolution of art, which I call “sophogeny
recapitulates ontogeny,” namely, that the evolution
of cultural wisdom parallels the development of the individual.
I will argue that Gablik, to make her point, emphasizes
only one of the goals of Renaissance perspective
— the representation of objects in space — and that she implies
that art cannot achieve this goal without being rigid
and inflexible, rule-bound and lacking in true conceptual
autonomy.

Gablik's point of departure is the theory of cognitive
development of Jean Piaget, the celebrated Swiss psychologist.
Piaget proposed that it is possible to discover
milestones in the development of thinking, perception,
problem solving, and all the other cognitive abilities. He
distinguished three major stages in cognitive development.
In the preoperational stage (which ends at about 5 years of
age), children have a very poor grasp of causality and reversibility.
For instance, if you pour a liquid from a tall,
narrow glass to fill a squat, short one of equal capacity,
refill the tall glass with liquid, and then ask a preoperational
child which glass contains more liquid, the child will say
that the taller glass contains more. The child does not
understand the concepts of conservation (of the amount of
fluid) and of compensation (the trade-off of height for area
of the cross section), which are physical expressions of the
formal concept of reversibility. In the concrete-operational
stage (which runs to about the age of 10), children understand
the reversibility underlying certain physical operations

Table 10-1. Stage of cognitive development and megaperiods of art history.

                   

Stages of cognitive development	Spatial characteristics	Megaperiods of art history
ENACTIVE MODE
Preoperational stage:	Topological relations:	Ancient and 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 Graeco-Byzantine, ancient Oriental, Egyptian, archaic Greek, and early medieval)
ICONIC MODE
Concrete-operational stage:	Projective and 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)

but are unable to deal with the logical concepts that
are their abstract representation. Finally, in the formal-operational
stage, children can understand abstract logical and
mathematical structures that underly reality.

At this point, we should let Gablik speak for herself:

Gablik can make her case only if she can demonstrate that
Renaissance artists used perspective rigidly and concretely:

The belief that the universe is ordered and rationally explicable
in terms of geometry was part of a deterministic world-picture
which viewed nature as stable and unchanging, and considered
that mastery of it could be achieved by universal mathematical
principles. The spatial illusionism of one-point perspective reflected
a world which was permanent and fixed in its ways,
modelled on an absolute space and time unrelated to any outward
circumstance. One has only to look at [paintings by] Piero della
Francesca [see Figure 10-5] or ... Bellini [see Figure 10-6] to
sense this immutability of things: a world is portrayed in which

[ILLUSTRATION]

Figure 10-3. Leonardo da Vinci, A
War Machine (Codex Atlanticus,
Folio 387r). Drawing.

[ILLUSTRATION]

Figure 10-4. Kasimir Malevich:
Left: Suprematist Elements: Two
Squares (1913). Pencil. Sheet:
19¾ × 14¼″. Composition:
6¾ × 11¼″. Collection, The Museum
of Modern Art, New York.
Right: Suprematist Element: Circle
(1913). Pencil. Sheet:
18½ × 14⅜″. Composition:
11½ × 11⅛″. Collection, The
Museum of Modern Art, New
York.

chance and indeterminacy play no part. From this vantage point,
we can see how a totally mathematized philosophy of nature
was the dominant influence on the course of Western painting,
and how these processes of mathematics offer themselves as a
bridge from one stage in the development of art to the next.

In the Renaissance, geometry was truth and all nature was a
vast geometrical system. (The book of nature, Galileo wrote, is
written in geometrical characters.) Perspective images were based
on observation, but they were rationalized and structured by

[ILLUSTRATION]

Figure 10-5. Piero della Francesca
(attrib. doubtful), Perspective of
an Ideal City (ca. 1470). Panel.
Galleria Nazionale delle Marche,
Palazzo Ducale, Urbino.

mathematics. For Alberti in 1435, the first requirement of a
painter was to know geometry; and Piero, in De Prospettiva
Pingendi, virtually identified painting with perspective, writing
three treatises to show how the visible world could be reduced
to mathematical order by the principles of perspective and solid
geometry. (1976, p. 70)

These views stress the rigidity, the rationality, and the
immutability of the laws of perspective. Undoubtedly, there
is some truth in Gablik's portrait of an era fascinated by
geometry. But fascination is not fetishism. During the
Renaissance, geometry was always subordinate to perception:
I have shown how the geometry of central projection
was routinely violated to counteract its perceptually unacceptable
effects. We have seen that perspective was far
from being a single, closed, logical system that was repeated
over and over. Gablik has produced a caricature of
Renaissance art, which even with regard to its use of perspective
was far from being rigid and uncompromising.
To be sure, perspective was used for a representational
purpose, and in that respect it remained tied to the concrete
objects it served to represent. But it also served to explore
other aspects of experience. Indeed, it is possible to make
a case against Gablik's position by applying a slightly different
set of Piagetian concepts. Taking my analysis of the
effects of perspective as a point of departure, one might
argue that the Renaissance artists were exploring the nature
of egocentrism and ways of using perspective to free oneself
from one's special vantage point. To do so is a sign of
one's ability to transcend egocentrism. One might argue
that the Cubists were engaged in a similar exploration, but
can one say that they were, in this respect, more advanced

[ILLUSTRATION]

Figure 10-6. Gentile Bellini,
Procession of the Relic of the
True Cross (1496). Canvas. Accademia,
Venice.

than were the Renaissance artists? And certainly one would
not claim that Sol LeWitt's sculpture is part of such an
investigation. I am convinced that by carefully selecting
the dimensions along which comparisons between different
periods of art were made, one could develop an argument
that any period in art is more advanced than all
the others.[5]

We have disagreed with Goodman; perspective is not
mere convention. We have disagreed with Gablik; sophogeny
does not recapitulate ontogeny. And Panofsky was
mistaken on some matters. But Panofsky had an extremely
useful formulation of the importance of perspective: It
served as symbolic form. Even though perspective has a
very sturdy geometric and perceptual foundation, which
makes it, in some sense, the best method to represent space
on a flat surface, the question of whether perspective is
“true” is far less important than the inquiry about how

perspective was put to use by Renaissance artists in an
artistic context. I have tried to answer this question and
to show that these uses were far removed from the oversimplified
view of perspective as a procrustean system
in the service of crass illusionism. Perspective often enabled
the Renaissance artist to cast the deeply religious contents
of his art in a form that could produce in the viewer spiritual
effects that could not have been achieved by any other
formal means. In that sense, perspective should be viewed
as “symbolic form.”