Seeing the impossible and building the likely

Abstract

Young & Deregowski (1981) state that the reason for some subjects' failure to perceive 'impossible' figures as confusing is probably that they do not integrate the stimuli, even though they see elements of the figures as depicting spatial arrangements. This suggests that such subjects should also tend to build distorted models of geometrical structures. This hypothesis was tested in the course of the present experiment. The results support the hypothesis.

Real space and represented space: Cross-cultural perspectives

“…Stimuli incorporating such configurations of lines are likely to be perceived as 3D (that is, they are 2/3d) when other stimuli, such as those of Hudson's test, are not. This conjecture is in agreement not only with the results provided by the Construction Task, but also with those obtained using an entirely different task (Deregowski & Bentley 1986) involving the same "geometric" principles: Subjects must adjust simple callipers, made of square timber batten, to indicate the angle made by the main lines of figures such as Figure 19a and b. The angle of the examples shown is clearly the same, but it is not seen as the same by those observers who see (a) as being flat (it could not possibly be seen otherwise) and (b) as 2/3d.…”

“…This suggests that the less sophisticated of Young and Deregowski's (1981) subjects might not have failed to notice the contradictions among various elements of the trident but noticed them and were unconcerned about them. This is an unlikely eventuality, because Deregowski and Bentley's (1987) study of Kxoe (Bushmen) children shows that those who find the "impossible" trident easy to copy tend to build distorted models of geometric figures. Thus, poor ability to integrate the stimuli appears to affect both tasks and, paradoxically, whilst helping the subjects in performing one of them, hinders them in the other.…”

“…a Figure 19. Two of the drawings to which subjects set the arms of wooden callipers used in the Kwengo Callipers Test (Deregowski & Bentley 1986). A subject who sees the bottom figure as depicting a 3D object is likely to see the angle between the represented arms as larger than that of the top figure.…”

“…Deregowski touches on the manipulation of space several times when he mentions spatial memory; he discusses perceptual skills briefly and then, at greater length, the use of various construction and replication tasks. One such task, using callipers to replicate angles shown in 2D as "flat" without depth cues and as "solid" in oblique projection (Deregowski & Bentley 1986) meets both imagery and problem-solving requirements. However, Deregowski mentions that the "flat" figure could only be seen as flat.…”

An Investigation on Primary School Students’ 3d Geometric Thinking

“…3D geometric objects are generally represented by actual physical objects, objects in the computer environment and drawings on paper (Gutiérrez, 1992). In order to understand the representations on paper, which are most commonly used in schools, the depth in the drawing and the elements of the object must be recognized, and the object must be visualized as a whole (Deregowski, & Bentley, 1987). Therefore, it can be said that the representation that requires the utmost mental processing is the representation through drawing.…”