Invariants

Invariants are the mathematical heart of Gibson's theory. As the observer moves through the environment, the ambient optic array transforms continuously: textures expand and contract, surfaces rotate in perspective, occlusion boundaries shift. Amid these transformations, certain higher-order properties remain unchanged — the ratio between the observer's height and the apparent elevation of distant objects, the rate of change of a texture gradient, the topological relationships among surfaces. These invariants specify the layout of the environment with mathematical precision. Perception, in Gibson's account, is the detection of invariants: the perceptual system extracts what persists across transformations rather than processing each momentary array as an independent stimulus. The concept is what makes direct perception mathematically tenable — the information is not merely suggestive of the environment's structure; it specifies that structure through the invariants that emerge in the flow of exploratory action.