Animal Cognition: Proceedings of the Harry Frank Guggenheim Conference, June 2-4, 1982

By H. L. Roitblat; T. G. Bever et al. | Go to book overview

II. THE POWER OF SPATIAL REPRESENTATION
To pursue the question we have posed, one must have a more formal notion of what kinds of spatial representations there are that tasks may require. We have hinted that the specification may be described by formal geometries, for example order geometry. Geometries are the fruits of hundreds of years of effort to capture precisely the various aspects of our conception of what space is or could be. Geometries provide precise languages for talking about representations of space. It would be ill- advised for psychologists theorizing about animals' spatial representations to ignore these formal languages. It seems likely that any geometry (language) that might be required to describe the spatial representations of animals has already been developed. The task, as we see it, is to select amongst the great number of geometries those that seem reasonable candidates to use in describing animals' spatial representations.
A. PRINCIPLES TO RESTRICT THE RANGE OF GEOMETRIES TO BE CONSIDERED
To select theoretical candidates from all geometries that have been investigated mathematically would prove futile since the field is too large. We believe, however, that with the aid of two plausible principles, the range of geometries to be considered can be drastically reduced. We state these principles briefly, as lack of space prevents full discussion.
1. Principle 1. Animals may have weaker representations of space, but they are unlikely to have systematically wrong ones.

The justification for this principle rests on evolutionary grounds. A radically wrong representation of space is likely to prove harmful in that it would systematically mislead the animal as to the true facts about the world the animal had to navigate. Thus, geometries that are fundamentally wrong in the way in which they represent the world we actually live in (e.g, geometries with Minkowski metrics) should be selected against. By contrast, geometries that do not represent the Euclidean world we experience wrongly, but merely underrepresent it can be useful, as the hypothetical explanation of digger wasp navigation shows. Since these geometries represent correctly those aspects of experienced space that they represent at all, they cannot do harm by misleading the animal. Hence, they seem biologically plausible. (When we say that they represent correctly, we mean that they treat, for example, angles and distances, in a way that corresponds to the way angles and distances work in our Euclidean world, not that they necessarily get the value for a specific distance right.) Principle 1 rules out of court a priori any geometry that represents the world's metric or order properties in a radically wrong fashion.

2. Principle 2. Euclidean geometry is taken to be the most powerful description of local space we have. Should the geometric language required to describe an animal's representation of space be weaker than Euclidean geometry, then we assume that the language

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