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3 The effectiveness of
Brunelleschi's peepshow

Brunelleschi's friends were amazed at the compelling
impression of depth they experienced when they looked
at his panel through the peephole in its back. How compelling
could it have been? In this chapter, we will see that
Brunelleschi had discovered an almost optimal technique
to wrest an illusion of depth from a picture painted on a
flat surface.

If one wishes to gauge the intensity of an experience of
depth induced by a picture, it is best to compare it to the
most effective technique available: the stereoscope. Figure
3-1 shows a stereoscopic pair of drawings prepared by Sir
Charles Wheatstone in 1831 to demonstrate his discovery
of the basis of stereoscopic vision to the Royal Society
(Wheatstone, 1838). If you look at them as instructed in
the caption, only one picture will be seen by each eye, and
you will experience the full strength of the effect. To understand
the effect, hold an object in your hand and look
at it first with one eye and then with the other. Because
each eye sees the object from a slightly different vantage
point, the object casts a somewhat different image on the
retina of each eye. Nevertheless, when both eyes are open
we see only one object; we do not see double as we might
naively expect. Of course, the visual system cannot fuse
two images that are very different. To see how limited is
our ability to fuse disparate images, hold up your two
hands, side by side, a few inches apart, their backs facing
your eyes, index fingers pointing up, about half a foot
before your nose, and focus on one of your fingers. Make
sure that you can see both fingers clearly. If you can't,

[ILLUSTRATION]

Figure 3-1. Wheatstone's stereoscopic
drawing. Take a piece of thin
cardboard (an index card will do)
roughly 4 by 6 in. (10 by 15 cm).
Place the book on a table, hold the
card vertically between the two pictures
(with its short dimension
against the page), touch your nose to
the card, and look at the right-hand
drawing with your right eye and at
the left-hand drawing with your left
eye. Relax. The two drawings will
appear to merge and you will see the
object in depth.

move them closer to each other. Now slowly move the
hand at which you were looking closer or further away.
Over a short distance, both fingers will remain in focus,
but after your hand has moved about an inch you will
notice that the finger at rest looks double. This is because
the visual system can only fuse the two disparate images
that a single object casts on the two retinae if the so-called
retinal disparity between these two images is not too large.
The retinal disparity of the finger you were looking at
remained zero while the retinal disparity of the other finger
grew as you moved it away. Wheatstone demonstrated
that if retinal disparity is small the two images not only
fuse but also give rise to a most compelling experience of
depth, called stereopsis.[1]

What is the function of stereoscopic vision? It gives us
the ability to accurately gauge and compare distances in
our immediate environment, approximately within range
of a long jump, that is, a range of a few yards. For instance,
you will find it extremely difficult — indeed almost impossible
— to perform a task requiring fine perceptual-motor
coordination at close range (such as threading a
needle) with one eye closed.

There was a time when psychologists, impressed with
the critical role played by stereoscopic vision in the performance
of such perceptual — motor skills, thought that the
world appeared flat when seen through one eye. The truth
is that one-eyed people are not really handicapped at all
when it comes to visual tasks that require them to aim
action toward long-range targets, such as throwing a ball
or landing an airplane. From this observation concerning
our ability to effectively gauge depth with one eye, we
might predict that a monocularly viewed picture that projects
onto the retina the same image as might be projected
by a three-dimensional scene would be seen in depth, because
the picture would then be a projective surrogate for the
scene. A projective surrogate was considered by Gibson

(1954) to be a special case of the more general class of
surrogates:

A surrogate will be defined as a stimulus produced by another
individual which is relatively specific to some object, place, or
event not at present affecting the sense organs of the perceiving
individual. (pp. 5–6)

Surrogates fall into two classes: conventional and nonconventional.
The nonconventional surrogates can also be
subdivided:

It is easy to create a projective surrogate: One draws a
picture in rigorous perspective and places the observer's
eye at the picture's center of projection. Unfortunately,
the expectation that an exact projective surrogate would
be seen in depth is not confirmed. Although we usually
interpret such a picture as the representation of a three-dimensional
scene when we view it from the appropriate
vantage point, the impression is no more compellingly
three-dimensional than if we viewed the picture from a
different vantage point. The vividness of stereopsis is absent
from this experience. Thus to view a rigorous perspective
picture from its center of projection is not enough
to transform our impression of a picture that represents
depth into an experience almost indistinguishable from the
perception of objects deployed in depth. At this point, we
might conclude that only disparate images seen by the two
eyes can produce the sort of vivid experience of depth we
are discussing. Such a conclusion would be premature, as
we shall presently see. Indeed, one might say that the reason
we do not see vivid depth in pictures (whether viewed
with one eye or two) is not because they fail to fulfill the
necessary conditions for such perception, but rather because
pictures bear two kinds of incompatible information,
namely, information about the three-dimensional scene they
represent, as well as information about their own two-dimensionality.
It follows that if we could rid ourselves of

[ILLUSTRATION]

Figure 3-2. Fra Andrea Pozzo,
Saint Ignatius Being Received
into Heaven (1691–4). Fresco.
Ceiling of the Church of
Sant'Ignazio, Rome.

the latter, the former information should produce a vivid
and compelling experience of depth, as striking as stereopsis.

One way to reduce the noticeability of the surface of a
picture is to have the spectator view the picture from a
long distance away. If the picture is so large as to enable
the spectator to view the picture from afar, stereoscopic
vision, which can under some conditions diminish the experience
of depth by supplying us with information regarding
the flatness of the picture plane, is ineffectual
because of the distance. Indeed, it is unlikely that stereoscopic
cues can tell us much about the flatness or the orientation
of a picture that is more than 200 cm. (about 2
yd.) away from us (Ono and Comerford, 1977). So if the
spectator's eyes are approximately at the center of projection
of the picture and the picture plane is distant, we
should perceive the picture in vivid depth. The typical
work of art based on this principle is a wall or ceiling
painting. It represents a scene in an architectural setting
that, even though imaginary, is a continuation of the real
architecture of the hall. The best example is Pozzo's ceiling
fresco in the Church of Sant'Ignazio in Rome (Figure 32).
The painting is a very precise central projection of an
imaginary architecture onto the hemicylindrical ceiling of
the church, which uses a center of projection at the eye
level of a person standing on a yellow marble disc in the
middle of the nave.[2] Maurice Henri Pirenne in his important

book Optics, Painting, and Photography (1970) writes
about Pozzo's ceiling:

The Pozzo ceiling is the culmination of a tradition of
illusionistic painted architectures begun by Mantegna.[3] In
the Ducal Palace in Mantua (Figure 3-3), he had painted
an illusionistic parapet that appears to break through the
ceiling. Around it, in extreme foreshortening, we see several
putti[4] precariously perched on a narrow ledge and other
figures peering down over the parapet. Almost half a century
later, Peruzzi undertook a far more ambitious exercise
in illusionistic imaginary architecture. On the walls of a
room on the second floor of the Roman villa he designed
for Agostino Chigi, the Pope's banker, he painted frescoes
that represent balconies from which one can see beautiful
views of Rome (Figure 3-4).

Neither of these works is extensive enough to provide an
illusion as powerful as Pozzo's, nor did either artist prescribe
an ideal vantage point from which the painting ought
to be seen.

A second way to diminish the impact of cues for flatness
was discovered about the middle of the seventeenth century
when there flourished in the Netherlands a popular
art — the “perspectyfkas,” the perspective cabinet. Some
of its practitioners were major artists of the Delft School,
such as Pieter de Hooch and Jan Vermeer.[5] Pirenne describes
one of them:

Why is it “hardly possible to tell on which surface of the
cabinet the various parts are painted”? Is it only due to the
removal of stereoscopic cues to the disposition of the internal
walls of the box? We should also consider the possibility
that it is due to the peephole itself.

To understand peepholes, we must first deal with certain
properties of lenses, which also apply to the lens of the
eye. Consider a lens and a film (Figure 3-6). Consider also
a field of object points (the gray region in panel A of Figure
3-6), the images of which are formed on the film by the
lens. Even the best of lenses introduces some blur; in other
words, the image of a point on an object is a circular region
called the circle of confusion. The object points for which
the circle of confusion is minimal are said to be in the focus
plane. Object points that are less in focus than those in the
focus plane, but are not objectionably blurred, are said to
be in focus (panels B and C of Figure 3-6). The distance
between the nearest object point that is in focus and the
farthest object point that is in focus is called the depth of
field of that lens.

Just as the distance of the focal plane of most camera
lenses can be varied from infinity to a few feet, the visual
system can change the shape of the eye's lens (a process
called accommodation) and thereby vary the distance of the
focal plane of the eye (over a greater range than most
camera lenses). If an object is fairly close to the eye (say,
less than 10 ft. away), the accommodation of the eye can
be a source of information regarding the distance of the
object; that is, the accommodation of the eye can serve as
a range finder.

Cameras have diaphragms that make it possible to mask
off part of the lens, to change the aperture size; similarly,
the iris can change the size of the pupil. The smaller the
aperture or pupil size, the less light hits the film or the
retina. Changing the aperture size also affects depth of
field. The smaller it is, the greater the depth of field (see
Figure 3-6, panels D and E). Now if a peephole is so small
that it effectively reduces the size of the pupil, it is called
an artificial pupil. An artificial pupil can enhance pictorial
depth by increasing depth of field and thus minimizing the

[ILLUSTRATION]

Figure 3-6. Focus and depth of field

value of information about distance derived from accommodation.
For instance, when one looks into a relatively
small perspective cabinet (as most are), the eye must focus
on the painted surfaces inside the box; because the range
is small, one might expect accommodation to disclose the
distance of the painted surfaces and thereby diminish the
illusion. This may be so, but if the peephole is very small,
we should expect the viewer's depth of field to be increased.
In such a case, the painting would be nicely in
focus even if the eye accommodated so that its focus plane
would be at the distance one might expect the walls of a
real room to be.

In addition to affecting the depth of field, a peephole can
also reduce information about the flatness of a painting just
by truncating the visual field — by removing from sight
the immediate foreground, surrounding objects, the picture's
margin, and the unfocused (but possibly important)
sight of one's nose (see Schlosberg, 1941, and Hagen and
Jones, 1978).

So Brunelleschi's use of a peephole in his first demonstration
was instrumental in producing a compelling experience
of depth for two reasons: First, it increased the
effectiveness of the illusion by forcing the viewer to place
his or her eye at the center of projection of the perspective
(thus making the picture a projective surrogate for the
scene); second, it reduced the viewer's information regarding
the flatness of the picture plane.

There is another aspect of Brunelleschi's technique that
merits discussion. Although Brunelleschi's peepshow was
similar to seventeenth-century perspective cabinets, it appears
to have anticipated certain techniques for the enhancement
of depth in monocularly viewed pictures that
were not discovered until the first two decades of this
century. Here is Harold Schlosberg's (1941) summary of
these discoveries:

For our purposes, it is most important to note that a similar
effect can be achieved by “looking at a picture monocularly
in a mirror. The mirror seems to break up the surface cues
and may well have less obvious effects, such as destroying

[ILLUSTRATION]

Figure 3-7. Experimental apparatus
for Smith and Smith's experiment.

orientation” (Schlosberg, 1941, p. 603). This is exactly what
Brunelleschi did.

In addition to all this nonexperimental evidence regarding
the impact of Brunelleschi's peepshow, it has been
shown in experiments that a proper central projection can
be mistaken for a real scene if viewed monocularly from
the center of projection. For instance, Smith and Smith
(1961) asked subjects to throw a ball at a target in a room
that they could view through a peephole (see Figure 3-7).
Two groups of subjects threw the ball at a target in a real
room. The subjects in one group were actually able to see
the room through the peephole, whereas the subjects in
the other group thought they were looking at the room
but actually were looking at a photograph of the room.
When subjects looked through the peephole at the real
room, their throws were on the average quite accurate;
when subjects looked through the peephole at a photograph
of the room, the average throw was not systematically
longer or shorter, but it was considerably more
variable.[6] But what is more important than the similar
accuracies of the throws was the absence of any awareness
on the part of subjects that they had been seeing photographs
in the viewing apparatus. In other words, neither
in their performance of the ball-throwing task nor in their
interpretation of the situation did the participants show
any sign that the picture looked different from an actual
room. And this implies that the Brunelleschi peephole can
give rise to an illusion so strong that it could properly be
called a delusion. We will return to this point in
Chapter 5.