The Stick-in-Water Illusion
J. J. Gibson, Cornell University
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The following principles of optical stimulus information can be derived from ecological optics and perspective geometry (Ware, Modern Perspective). We are interested in the relation between the materialedge of an object (stick) and the corresponding optical line in a field of view (optic array).This line is called the “perspective” of the edge. Edges in the world are only perceived because they have perspectives in the array (ambient light converging to the station point of an observer).
1. In a uniform medium of air, the perspective of an edge that is geometrically straight (whatever the position of the object) is a line that is optically straight. Hence the straightness of an objective edge (in a uniform medium) can always be detected (and with considerable acuity).
The same is true in a uniform medium of water.
In any uniform medium, likewise, the perspective of a curved edge is a curved line (and the perspective of a bent edge is a bent line) for any position of the edge except the special case called “edge-on”. Theamount of curvature (or bending) of the edge does not correspond to that of the line, however, except in the special case called “frontal plane”.
With any rotation of a straight edge around itself as an axis, the corresponding perspective remains a straight line. But with rotations of curved or bent edges the amount of curvature or bending is altered.
In a uniform medium, therefore, the straightness of an edge can be distinguished from non-straightness by an invariant property of any stationary perspective of this edge, that is, in any pictorial (frozen) array, without having to see the object in motion. (But other properties of an object, of course, can not be so distinguished.)
2. Consider now a motionless straight-edged stick with one portion in air and another portion in water, the air-water interface being a plane. Whenever the edge is not perpendicular to that plane the perspective of the straight edge will be a bent line (by refraction of light rays at the air-water boundary). This constitutes information for perception of a bent edge. Such perception is illusory (false). We are accustomed to say that the stick “appears” bent, and that we can only “know” that it is straight (by remembering its appearance in the air medium or by inference from understanding of the laws of refraction).
3. We now ask: is there higher-order information in the optic array from a moving stick partly immersed in water for the discrimination of its edges as straight or bent? Can something in the motions of a bent line ever specify a straight edge? This information would be in conflict with the pictorial or perspective information described above.
The answer is yes. When the straight stick-in-water is rotated around its longitudinal axis the perspectives of its edges remain unaltered. The lines corresponding to its edges are bent, to be sure, but they are unaltered by rotation and this invariant independently specifies a straight-edged stick as against a bent stick. There is mathematical information for the straightness of the edge over and above the perspective representation that holds with a uniform medium.
4. We can now determine experimentally whether, and at what age, children will detect this invariant for the stick-in-water. If they separate the perspective information for a bent stick the concurrent mathematical information for a straight stick-in-water, they will have achieved some apprehension of the difference between “apparent” and “real”.