May 1974
The Perceiving of the Hidden:
A Tentative Set of Theorems
J. J. Gibson, Cornell University
The World Wide Web distribution of James Gibson’s “Purple Perils” is for scholarly use with the understanding that Gibson did not intend them for publication. References to these essays must cite them explicitly as unpublished manuscripts. Copies may be circulated if this statement is included on each copy.
1. A surface is the interface between a substance and the medium. A surface goes out of existence when it has no substance.
2. An illuminated surface is projected at a fixed point of observation if it has a visual solid angle in the ambient optic array at that point of observation. If it does not but has a solid angle at some other point, it is unprojected in the sense of being hidden or out of sight.
3. For every fixed point of observation the layout of the environment is divided into hidden and unhidden surfaces. For every persisting surface the points of observation are divided into two sets, those at which it is hidden and those in which it is not.
4. An object hides both its far side and the ground behind it.
5. The hidden side of an object turns into the unhidden side, and vice versa, when the object is rotated. A part of the ground is covered and another part is uncovered when the object is displaced.
6. The hidden parts of the surface layout come into sight and the unhidden parts go out of sight as the point of observation moves.
7. Given motion and locomotion, any persisting surface that goes out of sight will, sooner or later, come into sight, and vice versa. Every movement that makes a surface go out of sight has an opposite that makes it come into sight. This is the law of reversible occlusion. But a surface that goes out of existence at one time will not come into existence at another.
8. At all times, although surfaces go from the hidden to the unhidden state and the reverse, they are divided by the loci of occlusion, that is, by occluding edges and convexities. Observers perceive these loci of occlusion along with the continuation of the unhidden into the hidden.
9. The distant parts of an open terrain can become unprojected at a point of observation by the gradual diminution of their visual solid angles to zero, at the horizon. The surface of an object can become unprojected at a point of observation by the optimal minification of its visual angle to zero. This transformation is reversible.
10. A surface may become unprojected at all points of observation when its topological integrity is lost in any of several ways. But this kind of event is not reversible. A surface may be formed in any of several ways and thus come to be projected at some points of observation, but the latter processes are not the opposite of the former.
11. The perceiving of all the surfaces of the environment, including the hidden ones, should be distinguished from the visualizing of surfaces that do not now exist.
12. An observer can be oriented to a hidden surface in his habitat without “seeing” it. He can “visualize” it (in this terminology) to the extent that he can perceive it behind an occluding edge, or behind a connected sequence of occluding edges. This explains why he can point to it.
13. At any given time some points of observation in the medium are occupied and the remainder are unoccupied. But one set can go into the other. For every point of observation there is a different optic array, but for moving points of observation the same information is available to all observers as invariants over time.