96 Foundations of Visual Perception
attributes many geometric illusions of size to this sort of mis-
application of rules. For example, the illusions of size in per-
spective renderings of a scene, such as the Ponzo illusion, are
attributed to the irrepressible but inappropriate application of
the putative standard rule for computing size on the basis of
visual angle and perceived distance.
All cases of misrepresentation do heavy work, but the con-
trasting theories depend on different forms of misrepresenta-
tion to promote their aims. Consider the theories of direct
perception and cognitive constructivism. The ecological real-
ist turns for support to examples of the first kind, which break
the link between the environment and optical input. By de-
coupling the distal state from the optical state while preserv-
ing the spatiotemporal optical structure, as in the optical
tunnel (Gibson, 1979, Figure 9.2, p. 154), the ecological real-
ist means to demonstrate that information is a property of
optical structure and that perception is the pickup of informa-
tion in optical structure. The advocates of the theory of direct
perception are of course deeply distrustful of misrepresenta-
tions of the third kind (rules are applied under conditions for
which they are inappropriate). They contend that these cases
are artifacts of special situations and cannot illuminate the
workings of ordinary seeing. Occasionally, advocates of di-
rect theory have suggested that a special theory, a theory of
judgment and decision making under uncertainty, is needed
for perceptual misrepresentations of the third kind.
The cognitive constructivist, on the other hand, relies
heavily on misrepresentations of the third kind. Indeed, these
instances of misrepresentations form the core of the empir-
ical case for cognitive constructivism. It is supposed that
these perceptual misrepresentations disclose the workings of
the hidden processes that govern perception. According to the
cognitive constructivist, the processes that underlie veridical
and illusory perception are the same, and these processes are
revealed by misrepresentations of the third kind. The cogni-
tive constructivist doubts that the demonstrations of the first
kind can, in fact, be interpreted in the manner urged by the
advocate of direct theory.
Although it has been often suggested that investigations of
misrepresentation can be decisive for theories of perception,
only infrequently do analyses of misrepresentation test com-
peting hypotheses originating in rival general theoretical ori-
entations. The more common practice is to offer examples of
misrepresentation as elements in a confirmation strategy
(Nickerson, 1998). The misrepresentations of choice serve as
existence proofs of some fundamental postulate of the theo-
retical approach. The confirmation strategy acts as a directive
influence in selecting the class of misrepresentation for in-
vestigation and a disincentive that discourages consideration
of contrasting accounts generated by rival theories.
PSYCHOPHYSICAL METHODSThe purpose of the remainder of this chapter is to introduce the
reader to a selection of experimental techniques and tools for
theory construction. Wherever possible we do this by referring
new concepts to contemporary experiments and theories. In
this way, the reader will understand the ideas in context. We
recommend the following textbooks and chapters for the
reader who wishes to pursue topics introduced in this section:
Gescheider (1997), Hartmann (1998), Link (1992), Luce and
Krumhansl (1988), Macmillan and Creelman (1991), and
Swets (1996).
Psychophysical methods are indispensable to the advance-
ment of perceptual research. Baird and Noma (1978, p. 1) put
it well:Psychophysics is commonly defined as the quantitative branch
of the study of perception, examining the relations between ob-
served stimuli and responses and the reasons for those relations.
This is, however, a very narrow view of the influence it has had
on much of psychology. Since its inception, psychophysics has
been based on the assumption that the human perceptual system
is a measuring instrument yielding results (experiences, judg-
ments, responses) that may be systematically analyzed. Because
of its long history (over 100 years [in 1978]), its experimental
methods, data analyses, and models of underlying perceptual
and cognitive processes have reached a high level of refinement.
For this reason, many techniques originally developed in psy-
chophysics have been used to unravel problems in learning,
memory, attitude measurement, and social psychology. In addi-
tion, scaling and measurement theory have adapted these meth-
ods and models to analyze decision making in contexts entirely
divorced from perception.After Fechner (1860/1996) developed psychophysics, two
kinds of questions were asked: (a) How sensitive are ob-
servers to intensities of stimulation? and (b) How intense do
certain amounts of stimulation appear to observers? The first
question is about thresholds,the second about scaling.Given
the magnitude of these two fields of research and the number
of research tools each has spawned, we have chosen to focus
on the more fundamental problem of observer sensitivity.
The notion of threshold comes from Leibniz’s New Essays
on Human Understanding(1765/1981):I would prefer to distinguish between perception and being
aware. For instance, a perception of light or colour of which we
are aware is made up of many minute perceptions of which we are
unaware; and a noise which we perceive but do not attend to is
brought within reach of our awareness by a tiny increase or addi-
tion. If the previous noise had no effect on the soul, this minute
addition would have none either, nor would the total. (book 2,
chap. 9, p. 134; see also Leibniz, 1989, p. 295.)