Perceptual Coherence : Hearing and Seeing

14 Perceptual Coherence
must judge whether two shapes can be matched by simple rigid rotations or
reflections. But often the new stimulus is a more complex transformation of
the original one, such as matching baby to adult pictures or matching an
instrument or singer at one pitch to an instrument or singer at a different
pitch. In both of these cases, the perception of whether the two pictures or
two sounds came from the same source must depend on the creation of
a trajectory that allows the observer to predict how people age or how a
novel note would sound. I would argue that the correspondence problem is
harder for listening because sounds at different pitches and loudness often
change in nonmonotonic ways due to simultaneous variation in the excitation
and resonant filters. The transformation simultaneously defines inclusion
and exclusion: the set of pictures and sounds that come from one
object and those that come from other objects.
Inherent Limitations on Certainty
Heisenberg’s uncertainty principle states that there is an inevitable trade-off
between precision in the knowledge of a particle’s position and precision
in the knowledge of the momentum of the same particle. Niels Bohr
broadened this concept by arguing that two perspectives may be necessary
to understand a phenomenon, and yet the measurement of those two perspectives
may require fundamentally incompatible experimental procedures
(Greenspan, 2001). These ideas can be understood to set limits on the
resolution of sensory systems. For vision, there is a reciprocal limitation
for space and time (and, as illustrated in chapter 2, a reciprocal limitation
between spatial frequency and spatial orientation). Resolution is equivalent
to the reliability or uncertainty of the measurement; increasing the resolution
reduces the “blur” of the property. The resolution can be defined as the
square root of the variance of repeated measurements. 2
For audition, there is a reciprocal limitation between resolution in frequency
and in time. To simultaneously measure the duration and frequency
of a short segment, the resolution of duration restricts the resolution of the
spectral components and vice versa. Suppose we define the resolution of
frequency and time so that (∆F)(∆T) = 1. 3 Thus, a temporal resolution of
1/100 s restricts our frequency resolution to 100 Hz so that it would be impossible
to distinguish between two sounds that differ by less than 100 Hz.
Gabor (1946) has discussed how to achieve an optimal balance between
frequency and space or time uncertainty in the sense of minimizing the
2. In chapter 9, we will see that resolution also determines the optimal way to combine
auditory and visual information.
3. In general, (∆F)(∆T) = constant, and the value of the constant is determined by the
shape of the distributions and the definitions of the width (i.e., the resolution) of the frequency
and time distributions.