|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|