Fig. 5. Outline for a critical test to falsify the template-matching hypothesis. If a fish trained to discriminate a disk from an upright triangle has stored a template of the disk and selects other patterns by matching them with this template, then it could be made to fail in discriminating a disk and a triangle if they are appropriately rescaled. If both are of the same size and both fit within the hypothetical template, then the quantities L, T and M (see Fig. 4) that quantify the quality of the matching are the same for both patterns. Consequently, the fish should fail to discriminate them. This conclusion holds irrespective of the particular way in which L, T and M are combined to assess the match.