February 1976
Note on the Apprehension of Formless and Timeless Invariants
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 References to these essays must cite them explicitly as unpublished manuscripts.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.
An information-based theory of perception implies a theory of memory, imagination, conception, and thought not based on stored images but on invariants. One can have a memory image or “mental picture” of something, a perspective view of it, but that is not how one necessarily thinks of it. I argued that one can “visualize” something without any particular point of observation from which it is seen (Leonardo, 1974, p.41-42). If so, one is not retrieving any particular percept. Short-term percepts involve the feeling of being at the center of one’s surroundings, of seeing surfaces with different directions from “here”, surfaces at different distances from here, and surfaces at different inclinations to one’s line of sight (optical slant). In addition, one perceives the hiding of farther by nearer surfaces (occlusion). But long-term percepts where the invariants emerge and the perspectives recede do not have these characteristics.
In distinguishing abstract geometry from what he called “sensory” geometry the mathematician Jean Nicod observed the entities of abstract geometry are “everywhere perfectly transparent including the body of the observer himself“, (Foundations of Geometry and Induction, 1930). I think what he meant to say was that the body of the observer, the ego, does not exist in mathematical space; and that the planes and forms therein, unlike the surfaces of the environment, do not reflect light and cannot be seen, as ghost and spirits cannot be seen. But, of course, they can be visualized. We can think about points, lines, and planes, and make diagrams of them (not pictures) and we say they are concepts. Planes, forms, and polyhedrons cannot be hidden; that is what “perfectly transparent” meant. There is no observer to move around in abstract space and open up new vistas, and there are no opaque surfaces to cause vistas.
Geometrical planes are not at different distances from here, at different directions from here, nor are they at different inclinations to the line of sight (cf. Ch. 10 in my Perception of the Visual World, 1950).
The Out-of-Sight Environment. The case of perceiving hidden surfaces and distant parts of the environment is one of apprehension on “visualizing” but it is not at all the same as the case of mathematical visualizing. The hidden surfaces will come into sight with locomotion but the ghostly planes will not. There is always a point of observation at which a surface can be seen but there is no point of observation at which geometrical entities can be seen. One can be oriented to a hidden or distant part of the world in the sense of being able to go there but no one is able to go find a triangle.
The layout of surrounding surfaces is perceived on the basis of quite simple invariants, optical gradients. The layout of hidden and distant surfaces is perceived (or apprehended) on the basis of invariants after locomotion, and by the detecting of occluding edges. The space of geometry is not perceived at all and is not even connected with the surfaces of the environment, but its structure can be visualized and it also is based on invariants, although of still higher order. Surfaces have affordances for behavior; planes do not, but they afford thought.
The Atomic and the Cosmic Levels. What about the world of atomic physics and that of astronomy? The very small and the very large can be visualized in some sense of the term, i.e., apprehended, but not perceived since there are no ordinary invariants in ambient light for perceiving them. Are particles and galaxies like geometric entities? Perhaps, in some ways, but not in others, for our apprehension of them is mediated by instruments, microscopes, and telescopes, and thus they are closer to being perceivable than triangles and circles. But the feeling of being at a point of observation when using such an instrument seems to me to be absent.
The visualizing of objects measures in millimicrons and light years depends on the detecting of invariants, perhaps even more obviously than the perceiving of objects measured in centimeters. But it is not like other kinds of visualizing.
Remembering and Imagining. What about things, events, and persons that have ceased to exist, or that have not yet come into existence? They also can be visualized or thought about or conceived (or whatever) but not seen or perceived. This kind of visualizing has aroused the greatest degree of interest among psychologists and philosophers. It is taken to demonstrate the hypothesis of mental images. There is no existing point of observation at which the object or event can be seen; it cannot be made to come into sight by locomotion, but the feeling of the ego and a point of observation may be present (although, I think, not necessarily).
The invariant of a stimulus flux from the environment must have been extracted in the past if a thing is to be remembered or imagined, although the presently effective stimulus flux does not specify it. The perceptual system is reverberating even if it is not perceiving the immediate environment. The latter, in fact, may scarcely reach awareness, as in cases of dreaming and hallucinating. In a sense the individual isperceiving but perceiving something gone or something to come.
Evidently there are several kinds of visualizing besides visual perceiving. The old terms for these phenomena are inadequate. What are they?