Mind, Body, World- Foundations of Cognitive Science, 2013a

Language acquisition can be described as solving the projection problem:
determining the mapping from primary linguistic data to the acquired grammar
(Baker, 1979; Peters, 1972). When language learning is so construed, the poverty
of the stimulus becomes a problem of underdetermination. That is, the projection
from data to grammar is not unique, but is instead one-to-many: one set of primary
linguistic data is consistent with many potential grammars.
For sighted individuals, our visual experience makes us take visual perception
for granted. We have the sense that we simply look at the world and see it. Indeed,
the phenomenology of vision led artificial intelligence pioneers to expect that building
vision into computers would be a straightforward problem. For instance, Marvin
Minsky assigned one student, as a summer project, the task of programming a computer
to see (Horgan, 1993). However, failures to develop computer vision made it
apparent that the human visual system was effortlessly solving, in real time, enormously
complicated information processing problems. Like language learning,
vision is dramatically underdetermined. That is, if one views vision as the projection
from primary visual data (the proximal stimulus on the retina) to the internal
interpretation or representation of the distal scene, this projection is one-to-many.
A single proximal stimulus is consistent with an infinite number of different interpretations
(Gregory, 1970; Marr, 1982; Pylyshyn, 2003c; Rock, 1983; Shepard, 1990).
One reason that vision is underdetermined is because the distal world is
arranged in three dimensions of space, but the primary source of visual information
we have about it comes from patterns of light projected onto an essentially two
dimensional surface, the retina. “According to a fundamental theorem of topology,
the relations between objects in a space of three dimensions cannot all be preserved
in a two-dimensional projection” (Shepard, 1990, pp. 173–175).
This source of underdetermination is illustrated in Figure 8-1, which illustrates
a view from the top of an eye observing a point in the distal world as it moves from
position X 1
to position Y 1
over a given interval of time.
X 1
X 2
Y 1
Y 2
X 3
X 4
Y 3
A
B
Figure 8-1. Underdetermination of projected movement.
364 Chapter 8