The Transformational Approach

The notion of transformation originated in geometry. A transformation is a function that maps a set of points onto another set. Transformations preserve certain geometric properties, but change others. In the nineteenth century, geometer Felix Klein (Klein, 1939) used transformations to define classes of geometric properties. For instance, euclidean properties are those properties remaining invariant after any euclidean transformation, which consists of a displacement optionally coupled with a reflection. Cheng and Gallistel (1984) took this idea to the psychology of spatial cognition. Transformations were effected on spaces to test what classes of geometric properties rats were sensitive to. The geometric module was discovered using this approach.