Franklin (1992) argues that a more detailed account of how the SRS receives input and how nonspatial information about objects is associated with knowledge of the objects' spatial locations in the SRS is required. Franklin also questions the validity of proposing absolute coordinate representations and the stage at which differential access to spatial information occurs. I attempt to expand the SRS account encompassing these issues.
2.1 The SRS receives basic information concerning distance and relative direction from the visual perceptual system. Visual information is necessarily derived in an egocentric framework but can be used to compute allocentric location. To determine an object's egocentric coordinates, the individual must estimate the object's distance from the self and it's angular displacement relative to some body axis (presumably the front). These two pieces of information can be used by the SRS to calculate egocentric coordinates through trigonometric calculations. Perception of distance and angular displacement is accomplished by species-specific sensory mechanisms (Gallistel, 1990a, pp. 110-118). In species with well developed visual senses, such as humans, distance can be estimated using a number of cues, including binocular disparity, parallax, and various monocular cues. Visual direction can be derived from geometric relations between an object and the direction of gaze of the two eyes (Ono, 1990).
2.2 Gallistel (1990a, pp. 106-109) describes a set of simple geometric calculations for deriving the location of an object in an allocentric coordinate space from egocentric perception. These calculations require only the egocentric coordinates of the object and the coordinates of the organism in the allocentric frame of reference. Thus, an individual must maintain on-line knowledge of its position in the allocentric space, a process referred to as "dead reckoning" (Gallistel, 1990a). Dead reckoning can be accomplished in several ways, but there is evidence that people accomplish it by summing direction vectors (based on kinesthetic, vestibular, and visual feedback) as they move through the allocentric space (Landau, Spelke, & Gleitman, 1984).
2.3 The SRS would require the same inputs from the language system; this is a much trickier problem, however, because linguistic descriptions provide much less precise information about distance and angle, or omit it altogether. Thus, when I say the chair is to my left, it is unclear whether I mean that the chair is exactly ninety degrees off my midline; and I have not indicated how far away the chair is. So it is impossible to position the chair in a coordinate space on the basis of just this information. Thus, creating a spatial model requires assumptions based on general knowledge.
2.4 How can such assumptions be made? I don't have a detailed proposal, but one way could be to use scene schemas that provide information about the configuration of objects in familiar places. Explicitly combining discourse information with a schema might allow one to create a single determinate spatial model of a scene that is somewhat arbitrary but likely to be reasonably accurate. Another possibility is that the SRS might accommodate indeterminacies by marking a range of locations as potential positions. Thus, if the chair is to my left, I could mark a range of distances from a few inches away to nine or ten feet, taking into account that one usually interacts with furniture in relatively small rooms.
3.1 Little information about objects need be directly stored by the SRS. Many theorists have argued that separate systems handle object recognition and classification (the "what" system) and object localization (the "where" system) (e.g., Landau & Jackendoff, in press; O'Keefe & Nadel 1978; Rueckl, Cave, & Kosslyn, 1988). This idea has received a good deal of empirical support. Lesion studies with primates indicate that the inferior temporal cortex is involved in pattern and object recognition but not spatial localization (Ungerleider & Mishkin, 1982). On the other hand, the inferior parietal cortex performs localization tasks but not object recognition. The double dissociation between these two physical systems and their effects on recognition and localization tasks implies that each is involved in processing a separate form of visual information about objects (Ungerleider & Mishkin, 1982, pp. 560-563). Likewise, Farah, Hammond, Levine, and Calvanio (1988) found that selective damage to the inferior temporal lobes in humans impairs ability on shape and object recognition tasks but not on localization tasks. Also, as noted in Bryant (1992, section 3.3), neurological evidence suggests that areas of the mammalian hippocampus and parietal cortex are specialized for coding place in egocentric or allocentric spaces (Feigenbaum & Rolls, 1991; Kesner, Farnsworth, & DiMattia, 1989; O'Keefe & Nadel, 1978; Tamura, Ono, Fukuda, & Nakamura, 1990).
3.2 Recently, Landau and Jackendoff (in press) have analyzed spatial concepts contained in spatial language. They note that spatial prepositions require little or no information about objects to convey spatial relations. For example, to say that A is above B, or A is near B requires no information about what A or B are or look like. Even prepositions such as along or inside only require information about a few selected dimensions. One can use spatial prepositions to describe the layout of objects in space almost completely independently of what those objects are. Landau and Jackendoff conclude, and I agree, that this suggests language users access a purely spatial representational system when comprehending linguistic descriptions of space.
3.3 In reply to Franklin's question about how the SRS interfaces with nonspatial knowledge, I would say that the mind keeps distinct spatial and nonspatial knowledge. The SRS must maintain some token for each object represented in the SRS that is either directly associated with an object representation in another system or can be looked up in one's general knowledge. The SRS need not store any information, however, beyond location in space.
4.1 Franklin questions the assumption that the SRS uses absolute coordinate representations, so I would like to clarify why this assumption was made. Gallistel (1990b) offers a concise definition of a representation as a "functioning isomorphism" or formal correspondence between two systems, such that operations in one system produce conclusions about the other. To have a representation of space is to have an internal system with operations that allow inferences about the external world. According to this definition, absolute coordinate systems and relativistic ones are equally legitimate representations of space. Relativistic representations, however, capture only some of the aspects of physical space available in a coordinate representation. A representation that encodes only relationships between objects lacks information about position independent of objects.
4.2 One major goal of the study of spatial cognition should be to determine the level of isomorphism between spatial representations and physical space. The SRS account starts out with the assumption that internal spatial models have a coordinate structure that corresponds to the coordinate structure of real space, independent of any object or the relationships between objects. Different frames of reference correspond to different origin points in real space. A coordinate system is a richer and more powerful representation than a relativistic representation because it allows an individual to perform geometric operations on locations (including empty locations) rather than only on objects in relation to other objects.
4.3 What is the level of correspondence between internal spatial representations and real space? Little research has directly approached this question in humans, perhaps because it is taken for granted that humans have fairly accurate knowledge of the geometric properties of their environment. This issue, however, has been central in the study of animal spatial cognition. An animal's spatial representation need by no means correspond to all aspects of physical space to be useful in guiding the animal's behavior. For example, Cheng and Gallistel (1984) report evidence that digger wasps represent the location of their nests in terms of the intersection of lines between pairs of landmarks, excluding much of the metric and geometric information in the environment.
4.4 The following are a few examples of the geometric power of animals' spatial representations. Wilkie (1989) trained pigeons to peck at keys arranged in a three-by-three matrix after short delays. The pigeons' place confusions could be predicted by a two-dimensional Euclidean scaling solution, but not by non-Euclidean solutions. This demonstrates that the pigeons' representation preserved the geometric relations of the keys. Likewise, Cheng (1986) found evidence that rats use the geometric relations between objects and the shape of their surroundings to search for food and that they code metric and left-right information as well. Animals can even communicate geometric information. Honey bee foragers recruit other bees at the nest by means of a "dance" that specifies the location of food. Gould (1990) made the interesting observation that bees ignore dances that specify an impossible food location such as a point over a lake. He suggested that the bees evaluate communicated locations in terms of spatial addresses in a cognitive map.
4.5 Few studies have tested the geometric power of human spatial representations directly; one example is a study by Landau, Spelke, and Gleitman (1984). They examined the ability of a blind child, Kelli, to learn layouts of objects by walking routes between them. With relatively little practice, Kelli was able to infer novel routes that required precise geometric knowledge about the layout. The authors concluded that to accomplish this task Kelli's spatial representation must have contained metric and geometric information. Furthermore, Kelli demonstrated knowledge of "places" in space that contained no objects and she could infer geometric relations between objects and those empty locations. This implies that she was representing the environment in terms of an internal coordinate space rather than a set of inter-related landmarks.
5.1 The issue of differential access to spatial relations is perhaps the most difficult to approach. There is a growing body of literature that demonstrates that people have faster, and perhaps more accurate, access to certain spatial relations than others (e.g., Bryant, Franklin, & Tversky, 1992; Franklin & Tversky, 1990; Glenberg, Meyer, & Lindem, 1985; Hintzman, O'Dell, & Arndt, 1982; Morrow, Greenspan, & Bower, 1987), but there remains the question of why. In dealing with such effects in text comprehension, researchers have proposed that readers use certain spatial relations as cues to foreground objects and characters (Glenberg et al., 1985; Morrow et al., 1987). There is some evidence, however, that people may also have differential access to spatial directions when perceiving scenes (Hintzman et al., 1982; Logan, 1991). This suggests instead that certain spatial relations have special status in cognition.
5.2 At this point, I would like to speculate that differential access serves an adaptive function. Franklin and Tversky's (1990) spatial framework analysis predicts the accessibility of spatial directions on the basis of features of the environment (gravity), the human body (physical and perceptual asymmetries), and the interaction of the two (canonical posture), but they offer no rationale for why mental spatial models should be influenced by these features. To answer this question, we need to explore how the regularities of the environment and the human body affect how well individuals survive and reproduce.
5.3 Environmental features that affect an individual's ability to interact with the environment successfully should become internalized in the mental processes that deal with those regularities as a consequence of natural selection. Any individual born with a predisposition to take advantage of, or learn about, environmental regularities will have a survival and reproductive advantage. This argument can be applied to the issue of differential access to spatial directions (although I am doing so in a post hoc way here). The gravitational (up/down) axis is highly accessible in one's spatial framework. We can speculate that this is because the gravitational axis plays such an important role in structuring the physical environment and the SRS is tuned to code information along this dimension more accurately. People also access objects in front of them faster than objects behind them. Because our perceptual and behavioral organs are oriented frontward, the decision to face something marks that object as the focus of our perception and action. Favoring front relative to back may convey the advantage of speeding responses to the most salient object in the environment, the one the individual has oriented toward.
5.4 To answer Franklin's question about whether the SRS is required to produce differential access: I assume the SRS is involved in guiding perception and can hence influence the accessibility of perceived objects and locations. This does not rule out the possibility that visual and perceptual systems themselves have not also been tuned to environmental regularities through natural selection. However, the locus of differential access to spatial dimensions should be at the SRS because this system is specialized for representing those dimensions and guiding behavior in space.
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