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

Kosslyn et al., 1995). “There is good evidence that the brain depicts representations
literally, using space on the cortex to represent space in the world” (Kosslyn,
Thompson, & Ganis, 2006, p. 15).
Another notion of distributed representation considered by van Gelder (1991)
was the coarse code (Feldman & Ballard, 1982; Hinton, McClelland, & Rumelhart,
1986). Again, a coarse code is typically presented as distinguishing connectionist
networks from classical models. A coarse code is extended in the sense that multiple
processors are required to do the representing. These processors have two properties.
First, their receptive fields are wide—that is, they are very broadly tuned,
so that a variety of circumstances will lead to activation in a processor. Second,
the receptive fields of different processors overlap. In this kind of representation,
a high degree of accuracy is possible by pooling the responses of a number of
broadly tuned (i.e., coarse) processors (Dawson, Boechler, & Orsten, 2005; Dawson,
Boechler, & Valsangkar-Smyth, 2000).
While coarse coding is an important kind of representation in the connectionist
literature, once again it is possible to find examples of coarse coding in classical
models as well. For example, one way that coarse coding of spatial location is
presented by connectionists (Hinton, McClelland, & Rumelhart, 1986) can easily be
recast in terms of Venn diagrams. That is, each non-empty set represents the coarse
location of a target in a broad spatial area; the intersection of overlapping nonempty
sets provides more accurate target localization.
However, classical models of syllogistic reasoning can be cast in similar fashions
that include Euler circles and Venn diagrams (Johnson-Laird, 1983). Indeed,
Johnson-Laird’s (1983) more modern notion of mental models can themselves be
viewed as an extension of these approaches: syllogistic statements are represented
as a tableau of different instances; the syllogism is solved by combining (i.e., intersecting)
tableaus for different statements and examining the relevant instances that
result. In other words, mental models can be considered to represent a classical
example of coarse coding, suggesting that this concept does not necessarily distinguish
connectionist from classical theories.
After his more detailed analysis of the concept, van Gelder (1991) argued that
a stronger notion of distributed is required, and that this can be accomplished by
invoking the concept of superposition. Two different concepts are superposed if the
same resources are used to provide their representations. “Thus in connectionist
networks we can have different items stored as patterns of activity over the same
set of units, or multiple different associations encoded in one set of weights” (p. 43).
Van Gelder (1991) pointed out that one issue with superposition is that it must
be defined in degrees. For instance, it may be the case that not all resources are
used simultaneously to represent all contents. Furthermore, operationalizing the
notion of superposition depends upon how resources are defined and measured.
340 Chapter 7