## Visual illusions

According to Gregory (1970, 1980), many classic visual illusions can be explained by assuming that previous knowledge derived from the perception of three-dimensional objects is applied inappropriately to the perception of two-dimensional figures. For example, people typically see a given object as having a constant size by taking account of its apparent distance (see Chapter 2). Size constancy means that an object is perceived as having the same size whether it is looked at from a short or a long distance away. This constancy contrasts with the size of the retinal image, which becomes progressively smaller as an object recedes into the distance. Gregory's (1970, 1980) misapplied size-constancy theory argues that this kind of perceptual processing is applied wrongly to produce several illusions.

The basic ideas in the theory can be understood with reference to the Ponzo illusion (see Figure 3.2). The long lines in the Figure look like railway lines or the edges of a road receding into the distance. Thus, the top horizontal line can be seen as further away from us than the bottom horizontal line. As rectangles A and B are the same size in the retinal image, the more distant rectangle (A) must actually be larger than the nearer one.

Misapplied size-constancy theory can also explain the Muller-Lyer illusion; see Figure 3.3). The vertical lines in the two figures are the same length. However, the vertical line on the left looks longer than the one in the figure on the right. According to Gregory (1970), the Muller-Lyer figures can be thought of as simple perspective drawings of three-dimensional objects. The left figure looks like the inside corners of a room, whereas the right figure is like the outside corners of a building. Thus, the vertical line in the left figure is in some sense further away from us than its fins, whereas the vertical line in the right figure is closer to us than its fins. Because the size of the retinal image is the same for both vertical lines, the principle of size constancy tells us that the line that is further away (i.e., the one in the left figure) must be longer. This is precisely the Muller-Lyer illusion. However, this explanation only works on the assumption that all fin tips of both figures are in the same plane, and it is not at all clear why perceivers would make this assumption (Georgeson, personal communication).

Gregory argued that figures such as the Ponzo and the Muller-Lyer are treated in many ways as three-dimensional objects. Why, then, do they seem flat and two-dimensional? According to Gregory, cues to

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