The question of how space, including the third dimension, is represented in the human mind is doubtless of major importance to the behavioral and brain sciences. The bicoded map proposed by Jeffery et al. constitutes an interesting candidate representation. However, it seems unlikely that it captures more than one very specific type of the multitude of spatial representations available to humans. To assume that the bicoded map is more than a special case is to misjudge the nature of spatial representations.
Even in one or two dimensions, mental representations of spatial information are usually neither as metric nor as consistent as assumed in the bicoded map. More often, humans use so-called qualitative representations. Such representations abstract from a continuous property (e.g., distance) by partitioning it and distinguishing only between classes that are defined by these partitions (e.g., near and far in the case of distance; see Forbus Reference Forbus2011). Empirical behavioral (Knauff et al. Reference Knauff, Rauh, Renz, Hirtle and Frank1997) and neuroscientific (Sereno et al. Reference Sereno, Pitzalis and Martinez2001) as well as computational (Krumnack et al. Reference Krumnack, Bucher, Nejasmic, Nebel and Knauff2011) studies have shown that humans are prone to employing qualitative, non-metric spatial representations. Furthermore, human spatial representations suffer from systematic distortions that lead to misrepresentations of, for example, distance (McNamara & Diwadkar Reference McNamara and Diwadkar1997) and orientation (Moar & Bower Reference Moar and Bower1983). According to these properties, mental spatial representations are often better viewed not as cognitive maps, but as cognitive collages (Tversky Reference Tversky, Frank and Campari1993): combinations and overlays of qualitative, non-metric representations of parts and aspects of the overall represented space. In addition, organization of human memory has been found to favor representation structures that are economic in the sense of minimizing storage space and processing requirements for representing a given body of knowledge, both for semantic knowledge generally (Collins & Quillian Reference Collins and Quillian1969) and for spatial knowledge in particular (McNamara Reference McNamara1986; Stevens & Coupe Reference Stevens and Coupe1978).
Given these properties of human spatial representations, it seems unlikely that the bicoded map constitutes more than one out of many representations employed by humans. A more comprehensive view on human spatial representations that includes the bicoded map as a special case is provided by our framework of scalable spatial representation structures (Schultheis & Barkowsky Reference Schultheis and Barkowsky2011; Schultheis et al. Reference Schultheis, Bertel, Barkowsky, Seifert, Barkowsky, Knauff, Ligozat and Montello2007). According to this conception, representations are constructed such that they remain as simple as possible given the current task demands. If the task demand changes, the representations are adapted accordingly and, thus, the representations scale to and with the current task requirements. This on-demand scaling can occur with respect to several aspects of the representations.
First, scaling can occur with respect to the types of spatial knowledge that are represented (e.g., distance, topology, orientation). Evidence from psychological and artificial intelligence research (reviewed in Schultheis et al. Reference Schultheis, Bertel, Barkowsky, Seifert, Barkowsky, Knauff, Ligozat and Montello2007) indicates that mental representations of spatial information are best viewed as being composed of several distinct, knowledge-type–specific representation structures. Such knowledge-type–specific representation structures contribute to the scalability of spatial representations. If a certain situation provides or requires only knowledge about orientations between objects, only a representation structure specialized for representing orientation knowledge will be employed. If the consideration of further types of knowledge such as topology becomes necessary, further representation structures that are specialized for representing topological knowledge will be added to the overall spatial representation.
Second, each knowledge-type–specific representation is subject to scaling such that (a) only task-relevant entities are included in the representation and (b) the granularity of the representation, that is, its ability to distinguish between different relations, changes with task demands. Since the granularity of a representation is directly related to how coarsely or finely the represented spatial continuum is partitioned, spatial representations are also scalable in terms of how qualitative or metric they are.
Finally, spatial representations are scalable with respect to the number of dimensions that are encoded. Although a two-dimensional representation may be considered the most common form of spatial representation, one-dimensional representations can be sufficient and even superior to two-dimensional representations in certain contexts (e.g., route representations; MacEachren Reference MacEachren1986).
When viewed in the framework of scalable representation structures, the conception of the bicoded map as the predominant mental representation appears too restrictive. It seems implausible to assume that the spatial plane is always represented metrically while the vertical dimension is always exclusively represented qualitatively; which dimensions are represented and how fine-grained the representation is depend on the demands of the current spatial task. For example, when planning a bike trip, the plane may not be represented, but the vertical dimension may be instantiated by a fine-grained (perhaps metric) representation of slope and elevation, because this may constitute the most important information for planning the bike route. On the other hand, if required by the task, humans may construct a full three-dimensional volumetric mental representation. Research on air traffic controllers, for instance, suggests that experienced controllers form a continuous “functional picture of the momentary traffic situation” that allows them “to interpret very complex dynamic constellations within a few seconds” (Eyferth et al. Reference Eyferth, Niessen and Spaeth2003, p. 415).
That there is little empirical evidence for metric representations of the vertical dimension or a three-dimensional volumetric representation is, therefore, more indicative of the necessity than of the ability to maintain and employ such representation structures. For many spatial tasks it is sufficient to exclude construction of a representation of the vertical, because the vertical information is (a) irrelevant to the task or (b) partly redundant with horizontal information (e.g., in slanted terrain, moving in certain directions implies certain elevation changes). Due to this lack of a necessity to represent vertical information in much detail (if at all) in many situations, the data reviewed in the target article do not allow unequivocally ruling out alternative representations to the bicoded map. Given the above considerations, the framework of scalable representation structures provides a much more convincing account of human mental spatial representations than does the overly specific bicoded map.
The question of how space, including the third dimension, is represented in the human mind is doubtless of major importance to the behavioral and brain sciences. The bicoded map proposed by Jeffery et al. constitutes an interesting candidate representation. However, it seems unlikely that it captures more than one very specific type of the multitude of spatial representations available to humans. To assume that the bicoded map is more than a special case is to misjudge the nature of spatial representations.
Even in one or two dimensions, mental representations of spatial information are usually neither as metric nor as consistent as assumed in the bicoded map. More often, humans use so-called qualitative representations. Such representations abstract from a continuous property (e.g., distance) by partitioning it and distinguishing only between classes that are defined by these partitions (e.g., near and far in the case of distance; see Forbus Reference Forbus2011). Empirical behavioral (Knauff et al. Reference Knauff, Rauh, Renz, Hirtle and Frank1997) and neuroscientific (Sereno et al. Reference Sereno, Pitzalis and Martinez2001) as well as computational (Krumnack et al. Reference Krumnack, Bucher, Nejasmic, Nebel and Knauff2011) studies have shown that humans are prone to employing qualitative, non-metric spatial representations. Furthermore, human spatial representations suffer from systematic distortions that lead to misrepresentations of, for example, distance (McNamara & Diwadkar Reference McNamara and Diwadkar1997) and orientation (Moar & Bower Reference Moar and Bower1983). According to these properties, mental spatial representations are often better viewed not as cognitive maps, but as cognitive collages (Tversky Reference Tversky, Frank and Campari1993): combinations and overlays of qualitative, non-metric representations of parts and aspects of the overall represented space. In addition, organization of human memory has been found to favor representation structures that are economic in the sense of minimizing storage space and processing requirements for representing a given body of knowledge, both for semantic knowledge generally (Collins & Quillian Reference Collins and Quillian1969) and for spatial knowledge in particular (McNamara Reference McNamara1986; Stevens & Coupe Reference Stevens and Coupe1978).
Given these properties of human spatial representations, it seems unlikely that the bicoded map constitutes more than one out of many representations employed by humans. A more comprehensive view on human spatial representations that includes the bicoded map as a special case is provided by our framework of scalable spatial representation structures (Schultheis & Barkowsky Reference Schultheis and Barkowsky2011; Schultheis et al. Reference Schultheis, Bertel, Barkowsky, Seifert, Barkowsky, Knauff, Ligozat and Montello2007). According to this conception, representations are constructed such that they remain as simple as possible given the current task demands. If the task demand changes, the representations are adapted accordingly and, thus, the representations scale to and with the current task requirements. This on-demand scaling can occur with respect to several aspects of the representations.
First, scaling can occur with respect to the types of spatial knowledge that are represented (e.g., distance, topology, orientation). Evidence from psychological and artificial intelligence research (reviewed in Schultheis et al. Reference Schultheis, Bertel, Barkowsky, Seifert, Barkowsky, Knauff, Ligozat and Montello2007) indicates that mental representations of spatial information are best viewed as being composed of several distinct, knowledge-type–specific representation structures. Such knowledge-type–specific representation structures contribute to the scalability of spatial representations. If a certain situation provides or requires only knowledge about orientations between objects, only a representation structure specialized for representing orientation knowledge will be employed. If the consideration of further types of knowledge such as topology becomes necessary, further representation structures that are specialized for representing topological knowledge will be added to the overall spatial representation.
Second, each knowledge-type–specific representation is subject to scaling such that (a) only task-relevant entities are included in the representation and (b) the granularity of the representation, that is, its ability to distinguish between different relations, changes with task demands. Since the granularity of a representation is directly related to how coarsely or finely the represented spatial continuum is partitioned, spatial representations are also scalable in terms of how qualitative or metric they are.
Finally, spatial representations are scalable with respect to the number of dimensions that are encoded. Although a two-dimensional representation may be considered the most common form of spatial representation, one-dimensional representations can be sufficient and even superior to two-dimensional representations in certain contexts (e.g., route representations; MacEachren Reference MacEachren1986).
When viewed in the framework of scalable representation structures, the conception of the bicoded map as the predominant mental representation appears too restrictive. It seems implausible to assume that the spatial plane is always represented metrically while the vertical dimension is always exclusively represented qualitatively; which dimensions are represented and how fine-grained the representation is depend on the demands of the current spatial task. For example, when planning a bike trip, the plane may not be represented, but the vertical dimension may be instantiated by a fine-grained (perhaps metric) representation of slope and elevation, because this may constitute the most important information for planning the bike route. On the other hand, if required by the task, humans may construct a full three-dimensional volumetric mental representation. Research on air traffic controllers, for instance, suggests that experienced controllers form a continuous “functional picture of the momentary traffic situation” that allows them “to interpret very complex dynamic constellations within a few seconds” (Eyferth et al. Reference Eyferth, Niessen and Spaeth2003, p. 415).
That there is little empirical evidence for metric representations of the vertical dimension or a three-dimensional volumetric representation is, therefore, more indicative of the necessity than of the ability to maintain and employ such representation structures. For many spatial tasks it is sufficient to exclude construction of a representation of the vertical, because the vertical information is (a) irrelevant to the task or (b) partly redundant with horizontal information (e.g., in slanted terrain, moving in certain directions implies certain elevation changes). Due to this lack of a necessity to represent vertical information in much detail (if at all) in many situations, the data reviewed in the target article do not allow unequivocally ruling out alternative representations to the bicoded map. Given the above considerations, the framework of scalable representation structures provides a much more convincing account of human mental spatial representations than does the overly specific bicoded map.