What is the Meaning of Shape? - Gestalt Theory

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GESTALT THEORY, Vol. 33, No.3/4 the shape, i.e. without the rotation the square as a singularity could not be perceived. As soon as they are defined, square and rotation organize themselves asymmetrically as suggested by the two previous descriptions. ! " # Fig. 2 A square (a), a rotated square (b) and a diamond (c) 3.2.3. Diamond By increasing the rotation of Fig. 2b up to 45° as shown in Fig. 2c, both the happening (rotation) and the square are replaced by another one-word description: a diamond. This outcome is unexpected, if compared with the square of Fig. 2a. It represents a hard problem for an invariant features hypothesis. In fact, if shapes are defined by virtue of attributes invariant over rotations, then the two shapes of Figs. 2a and 2c should be perceived as having the same shape. Therefore, the square and the diamond demonstrate that different shape rotations cannot be perceived as having the same shape. Figs. 2a and 2c show the so-called Mach’s square/diamond illusion (Mach, 1914/1959; Schumann, 1900), according to which the same geometrical figure is perceived as a square when its sides are vertical and horizontal, but as a diamond when they are diagonal. From a phenomenal point of view, it is more correct to state that the square is perceived when the sides are vertical and horizontal, while a diamond is seen when its angles or vertices are vertical and horizontal. This description is more appropriate if we consider what emerges more strongly in the two conditions: the sides in the case of the square, and the angles/vertices in the !"#$%&'()''!"#$%#&'(#$$" case $%!&'()'&%*'+*!,(,-'./')%!0*1 of the diamond. We will see in section 5 some important consequences of these phenomenal observations for a better understanding of the meaning of shape. One main effect related to Mach’s square/diamond illusion is the fact that the diamond appears larger than the square. Schumann (1900) suggested that this is related to the fact that visual attention is placed on the vertical-horizontal axes, which are clearly longer in the diamond condition. This explanation is supported by the results of a simple control experiment according to which, by focusing the attention on one side of the diamond rather than on one angle, during the comparison of the size of Fig. 2a and 2c, the apparent size difference between the square and the diamond is strongly reduced or even annulled. 390
391 Pinna, What is the Meaning of Shape? 3.3. The Role of the Frame of Reference in Shape Perception More recent and complex explanations of the square/diamond illusion are based on object-centered reference frames. Rock (1973, 1983; see also Clément & Bukley, 2008), starting from previous Gestalt studies (Asch & Witkin, 1948a, 1948b; Koffka, 1935; Metzger, 1941, 1975), suggested that the perceived shape is a description relative to a perceptual frame of reference, i.e. the visual system prefers gravitational axes over retinal or head axes. In other words, Rock considered Mach’s square/diamond illusion as a clear evidence that a shape is perceived in relation to an environmental frame of reference where gravity defines the reference orientation, at least in the absence of intrinsic axes in the object itself. If the environmental orientation of the figure changes with respect to the two figures, the description of one shape does not match the description stored in memory for the other shape, therefore the observer fails to perceive the equivalence of the two figures. The stimulus factors important in determining the intrinsic reference frame are: gravitational orientation; directional symmetry (Pinna, 2010b; Pinna & Reeves, 2009); axes of reflectional symmetry, configural orientation (Attneave, 1968; Palmer, 1980) and axes of elongation (Marr & Nishihara, 1978; Palmer, 1975a, 1983, 1985; Rock, 1973). These factors rule the relation between shape and orientation as it happens in other phenomena (e.g., the rod-and-frame and Kopfermann’s effects; Davi & Profitt, 1993; Kopfermann, 1930; see also Marr & Nishihara, 1978; Palmer, 1975b, 1989, 1999; Witkins & Asch, 1948). These explanations contain some serious limits especially within the context of phenomenology. More particularly, they cannot account for the reason why we perceive a square, a diamond or a rotated square without invoking names and descriptions stored in memory. More specifically, they do not say anything about what changes phenomenally inside the shape properties when axes of reflection, gravitation and other factors change and about which shape properties switch when a square switches to a diamond. These limits are accompanied by the following questions: why are two names/ descriptions (square and diamond) stored so differently? Are they stored as different names because they are perceived differently or are they perceived differently because they are stored in memory with different names/descriptions? These last questions are not trivial because they are related to the important problem of the primary role of visual perception over the higher cognitive processes (see Kanizsa, 1980, 1985, 1991). This implies that the difference between square and diamond can be accounted for within the domain of vision alone and in terms of perceptual organization of shape attributes. In addition to these issues, the previous hypotheses cannot explain what shapes, such as squares, diamonds or rotated squares, are, and, even more generally, they
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