The demonstration has mainly two purposes: First, it shall show that a forward model can serve as a building block that allows to use simulation either for planning actions or for perceiving space. Such an approach does not need a world representation based on a coordinate frame, or any one-to-one mapping from the world to an internal representation (Grush, 2004; Hesslow, 2002; Möller, 1999; Jirenhed et al., 2001).
Second, the demonstration shall show how the mastery of sensorimotor relations, which is proposed by Möller (1999) and O'Regan and Noë (2001) to be the basis of visual perception, might lead to an understanding of the geometry of the surrounding (section 1.4.3). In particular, in one task, it is shown that this mastery can take advantage of the spatial symmetry. Thus, symmetry can be perceived (detected) without having a sensory representation that reflects this symmetry, as in the thought experiment with the perception of a straight line (O'Regan and Noë, 2001), see section 1.4.3.