James E. Cutting of Cornell University discusses the perception of pictorial space, particularly the differential rotation effect observed by Goldstein (1987). This effect refers to the apparent rotation of objects in a picture as the viewer moves around it. Goldstein found that objects pointing directly at the viewer rotate more than those pointing at other angles. He did not provide a theoretical model for this effect, but Cutting proposes one based on affine geometry and the analyses of La Gournerie (1859). This model suggests that pictorial space can be transformed by shears, compressions, and dilations according to the viewer's position relative to the picture. Representational pictures, especially photographs, have a dual nature: they portray objects in a specific environment and are themselves objects. This duality leads to certain perceived relations about objects in a picture being influenced by the viewer's position relative to the picture surface. For example, the eyes and arms of portrait subjects appear to follow the viewer as they move around a gallery. This phenomenon is well-documented in historical and modern examples, such as the portraits of Kitchener and Uncle Sam. Goldstein (1987) conducted experiments to study this effect, presenting slanted pictures to observers and asking them to judge spatial relations. His results showed systematic changes in perceived orientation with the viewer's position. Cutting argues that these results can be explained by affine geometry, which accounts for the distortions in pictorial space due to the viewer's position and the properties of the picture. Cutting also discusses the effects of lens length on pictorial depth, noting that longer lenses compress depth, which can affect the perceived orientation of objects in a picture. He applies this analysis to Goldstein's experiments, showing how depth compression and misperceptions of angles can account for some of the observed results. Cutting's model of affine geometry provides a framework for understanding the differential rotation effect and other aspects of pictorial perception. He argues that this model explains Goldstein's data well, including the perceived orientation of lines and eye glances. He also discusses the distinction between perceived orientation, spatial layout, and projection, arguing that affine geometry can account for all three aspects of pictorial space perception. Cutting concludes that affine geometry is a useful tool for understanding the perception of pictorial space and that it provides a solid foundation for understanding the differential rotation effect and other related phenomena.James E. Cutting of Cornell University discusses the perception of pictorial space, particularly the differential rotation effect observed by Goldstein (1987). This effect refers to the apparent rotation of objects in a picture as the viewer moves around it. Goldstein found that objects pointing directly at the viewer rotate more than those pointing at other angles. He did not provide a theoretical model for this effect, but Cutting proposes one based on affine geometry and the analyses of La Gournerie (1859). This model suggests that pictorial space can be transformed by shears, compressions, and dilations according to the viewer's position relative to the picture. Representational pictures, especially photographs, have a dual nature: they portray objects in a specific environment and are themselves objects. This duality leads to certain perceived relations about objects in a picture being influenced by the viewer's position relative to the picture surface. For example, the eyes and arms of portrait subjects appear to follow the viewer as they move around a gallery. This phenomenon is well-documented in historical and modern examples, such as the portraits of Kitchener and Uncle Sam. Goldstein (1987) conducted experiments to study this effect, presenting slanted pictures to observers and asking them to judge spatial relations. His results showed systematic changes in perceived orientation with the viewer's position. Cutting argues that these results can be explained by affine geometry, which accounts for the distortions in pictorial space due to the viewer's position and the properties of the picture. Cutting also discusses the effects of lens length on pictorial depth, noting that longer lenses compress depth, which can affect the perceived orientation of objects in a picture. He applies this analysis to Goldstein's experiments, showing how depth compression and misperceptions of angles can account for some of the observed results. Cutting's model of affine geometry provides a framework for understanding the differential rotation effect and other aspects of pictorial perception. He argues that this model explains Goldstein's data well, including the perceived orientation of lines and eye glances. He also discusses the distinction between perceived orientation, spatial layout, and projection, arguing that affine geometry can account for all three aspects of pictorial space perception. Cutting concludes that affine geometry is a useful tool for understanding the perception of pictorial space and that it provides a solid foundation for understanding the differential rotation effect and other related phenomena.