Do illusory effects cumulate? It has often been suggested that several geometric illusions can be combined into a single display (Gillam, 1991; Schiffman, 1990). Here we ask what actually happens when two illusions are combined. There are several possibilities. The illusions can simply reaffirm each other. In this case, if one illusion made a line look 10% bigger than another, adding a second illusion that also made the line look 10% bigger would make no change. The second illusion would simply reaffirm the results of the first Alternatively, the effects of two illusions that work in the same direction could accumulate. In this case combining the two illusions would make the line look more than 10% bigger. Consider now combining two "antagonistic" illusions, one making the line look bigger, and the other making the line look smaller. If illusion effects are cumulative, antagonistic illusions could cancel each other out
The purpose of the present study is to compare the illusory effects in two isolated figures to effects in a figure that combines the two. The illusions that were used were the Ponzo (Fig 1A) and the Miiller-Lyer (Fig 1B and 1C) figures. These were combined to form two new figures (Fig 1D and IE). In the first combined figure (1 D), the illusory effects of the Ponzo act in the same direction as those of the MiillerLyer component. That is, both components encourage overestimation of the top bar. If illusory effects are cumulative we would expect a stronger illusion in this combined figure than in the isolated ones. In the second combined figure (1 E) the components act antagonistically: Whereas the Ponzo favors overestimation of the top segment, the Miiller-Lyer favors its underestimation. If the cumulative model is correct, there would be a weaker illusion in the combined figure than in the isolated figures.