March 1976
A Note on the Argument from Equivalent Configurations
J. J. Gibson, Cornell University
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Since the era of the Princeton distorted rooms and the Ames demonstrations, together with the Helmholtzian revival that accompanied it, the argument from equivalent configurations has been widely accepted as proving that a projection (or a retinal image) cannot specify a unique solid “object ” in the world. Ecological optics makes the claim that the information in an ambient optic array does uniquely specify the layout of environmental surfaces at a point of observation (e.g., Perceptual Systems, Fig. 10.6 and p.109). Does the argument from equivalent configurations refute the claim of ecological optics?
The argument is usually accompanied by a diagram of a visual solid angle at a fixed point of observation with an envelope going out to infinity. Any planar section of this envelope yields a “form.” There is an infinite set of equivalent forms within the envelope. Therefore, the distance and the slant of any particular surface-form are not specified. The argument can be extended to include the five adjacent solid angles coming to a peephole from the facing surfaces of a room, or it can be applied to a set of equivalent “tunnels” as in the experiment of Gibson, Purdy, and Lawrence (1955) with monocular vision and a fixed head.
But can the argument be extended from an angular optic array to the ambient optic array? Does an equivalent set of possible objects within the envelope of a solid imply an equivalent set of possible environments in the spherical “angle” of 360 ? Although forms do not specify objects does an array of “forms within forms” nevertheless specify the subordinate parts of a real world? If a frozen outline does not specify an object what about a transforming outline? And what if there are transformations within transformations down to the tiniest visual angles detectable? I have argued that the perspective transformation of a frozen optic array would “disambiguate” it but this argument is still based on projective geometry and it does not go deep enough.
The argument from equivalent configurations assumes that the perception of the world consists of a field of adjacent forms none of which has a definite distance and slant, plus the determination of the distance and the slant of each form in the patchwork independently of the others. The size and stage of each “object” will then be determined. The question is what are the “cues” for distance and slant?
Ecological optics assumes that the distances and slants of the surfaces of the world are all determined at once, interdependently, since they are relative to “here” and are related to one another. Ecological optics assumes that the environment is full of things at different levels and that the ambient light is full of invariant structures at different levels. The question to ask is what information about things can be picked up? For example:
1. Is there information in a visual solid angle to specify the shape and size of the surface from which the light comes? The answer is no.
2. Is there information in a patchwork of visual solid angles to specify the layout of the surfaces from which the light comes? What if the patchwork is “nested”? What if regular gradients appear in the patchwork? The answer is: the specification increases.
3. Is there information in a “closed” patchwork of nested solid angles to specify the layout of the surrounding surfaces facing the point of observation? Yes, still more information, or so I believe. The above is a fixed ambient optic array, one that specifies no change of surface layout and no movement of the point of observation. Moreover, the surfaces specified do not include any that are “hidden.” What if the array undergoes change?
4. Is there a specific disturbance of the structure of an ambient array to specify a particular change of layout, i.e., an event? Yes. (For example, there is a disturbance that specifies change of slant of a surface, i.e., rotation, Gibson & Gibson, 1957).
5. Is there a kind of disturbance of structure of the ambient array that specifies a displacement of the point of observation but no change of the layout of surfaces? Yes. It gives rise to “visual kinesthesis.” (Gibson, Olum, & Rosenblatt, 1955).
6. Is there a kind of disturbance that specifies the occlusion of one surface by another and the reverse? Yes. (For example the translation of a surface in front of its background, an event, or the concealing of one surface by another by “motion parallax,” a locomotion.) Note that in this case one perceives both something that varies, occlusion, and something that does not vary, the occluding edge (Gibson, Kaplan, Reynolds & Wheeler, 1969).
7. Is there a kind of disturbance of the structure of a sample of the ambient array that specifies the head-turning of the observer himself? Yes. Thus the environment outside the field of view is specified after sampling.
Evidently the argument from equivalent configurations is irrelevant to the claim of ecological optics. It has to do with “forms” in the array and the muddle of distance and slant perception. Ecological optics has to do with structures in the array, disturbances, of structure, and invariants of structure, and with what they specify.