Inconsistent Images

The University of Adelaide Australia
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Perspective is all around us, not just on the way to the horizon. It is a “one eye” phenomenon, in contrast with the depth of focus that stereoscopy (two eyes) affords. Perspective can be seen wherever the head moves. But it is not a matter of where the eye lines up: for example, look one way but point a camera another way, at right angles say, then the camera will register perspective.

Perspective plays a role in many impossible images. Reutersvärd did not use it in his Opus 1, but he did later; and Escher and Penrose certainly used it, in such a way as to reinforce the effect of the impossible occlusions on which the paradoxes depend. On the other hand, it proves difficult, perhaps impossible, to construct a paradox of “pure perspective”, that is depending on nothing but perspective for its paradoxicality. This is in line with the conjecture that occlusion illusions are the sole source of visual paradox. Of course, a good purely-perspectival paradox would bury that conjecture. The nearest we have been able to get along this direction can be seen in the top left-hand-side image of the gallery below, which is also the most recently drawn of those displayed (31/08/07, click for enlargement). On the right hand side of this image there seem to be two competing perspectives associated with beams that are joined up, which is surely impossible. It is left to the viewer to decide whether this fits the bill as a paradox of pure perspective.

Interestingly, when occlusion and perspective clash, occlusion seems to be the inevitable winner. The two images below illustrate this point. The left-hand image lines up the perspective with the occlusion, whereas the right-hand image clashes them, but the result is that the blue face with the superior occlusion looks to be in front, so that the object ceases to look like a cube, the front face is simply smaller.

Having raised the question of whether perspective by itself can generate paradox, we note that nonetheless there are many striking effects that can be generated by combining perspective with other images of impossibility. The following gallery of perspectival drawings, drawn by Steve Leishman, exploit the technique. Click on the thumbnails to get enlarged images.

Chris Mortensen

A Gallery of Impossible Persectives by Steve Leishman

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