## The danger of visual illusions

Engineering drawing is based on the fact that three-dimensional objects are presented in a two-dimensional form on two-dimensional paper. The potential problems of trying to convey apparent three-dimensional information on two-dimensional flat paper is shown by the two sets of circles in Figure 1.2. The author drew these 12 circles himself, and they are based on a concept by Ramachandran (1988). Because the circles are shaded, each one is seen as either a bump or a depression. In this case, if one's brain interprets the left-hand set of circles as bumps, the right-hand set appears as depressions (and vice versa). During a recent lecture on engineering drawing, I took a vote and two thirds of the student group saw the left-hand set of circles as bumps and the right hand set as depressions. The reason for this is concerned with the shading of the lower part of the circles. Our visual system assumes a single light source. The single light source that we know best is the sun and it shines from above. Thus, the eye sees the left-hand series of circles as bumps because it assumes the illumination is from above. This is not always the case, because in a recent lecture, one third of the students assumed the light source was from below. So much for what the psychologists tell us about the brain!

The facemask in Figure 1.3 is an interesting example of visual illusions (adapted from Ramachandran, 1988). The face appears eerie. Can you guess why this is so without reading any further?

Figure 1.2 Three-dimensional bumps and depressions

Figure 1.3 An eerie face mask

The answer is that it is actually a hollow mask in which the interior is lit from above to produce an eerie impression of a protruding face lit from below. When interpreting shaded images, the brain usually assumes the light is shining from above. Here it rejects that assumption in order to interpret the image as a normal convex object.

The above examples show the difficulties involved in trying to represent three-dimensional information on a two-dimensional piece of paper using shading. A different type of visual illusion is shown in the tri-bar in Figure 1.4. Each of the three corners of the triangle, when considered separately, indicates a valid three-dimensional shape. However, when the tri-bar diagram is considered as an entirety, it becomes an impossible figure. This tri-bar visual illusion was first noted in 1934 by the Swedish artist Oscar Reutersvard. He produced many similar types of drawings of other impossible figures. It was the artist Escher who first bought the knowledge of impossible figures to a much wider audience. He will be particularly remembered for his 'waterfall lithograph' that he produced in 1961. Although channels of water is the subject of his drawing, it is essentially an impossible tri-bar in a different form.

The above visual illusions are created because one is trying to represent a three-dimensional object in a two-dimensional space. However, it is still possible to confuse the eye/brain even when absorbing two-dimensional information because rules of perception are broken. The example in Figure 1.5 was actually handed to me on a street corner. The image was written on a credit card-size piece of paper. The accompanying text read, 'Can you find the answer?'. The problem is that the image breaks one of the pre-conceived rules of perception, which is that the eye normally looks for black information on a white background. In this case the eye sees a jumbled series of shapes and lines. The answer to the question should become obvious when the eye looks for white information on a black background.

Some two-dimensional drawings are termed 'geometrical' illusions because it is the geometric shape and layout that cause distortions. These geometric illusions were discovered in the second half of the 19th century. Three geometric illusions are shown in Figure 1.6. In the 'T' figure, a vertical line and a horizontal line look to be of different lengths yet, in reality, they are exactly the same length. In the figure with the arrows pointing in and out, the horizontal lines look to be of different lengths yet they are equal. In the final figure, the dot is at the mid-point of the horizontal line yet it appears to be off-centre. In all these figures, the eye/brain interprets some parts as different from others. Why this should be so does not seem to be fully understood by psychologists. Gillam (1980/1990) suggests that the effects appear to be related to clues in the size of objects in the three-dimensional world. Although the psychologists