Scale-invariance as a unifying psychological principle.

How can the classical psychological laws be explained and unified? It is proposed here that scale-invariance is a unifying principle. Distributions of many environmental magnitudes are observed to be scale invariant; that is, the statistical structure of the world remains the same at different measurement scales [Mandelbrot, B., 1982. The Fractal Geometry of Nature (2nd Edn.). W.H. Freeman, San Francisco, CA; Bak, P., 1997. How Nature Works: The Science of Self-organized Criticality. Oxford University Press, Oxford, UK]. We hypothesise that the perceptual-motor system reflects and preserves these scale invariances. This allows derivation of several of the most widely applicable psychological laws governing perception and action across domains and species (Weber's, Stevens', Fitts' and Piéron's Laws). We suggest that these fundamental laws reflect accommodation of the perceptuo-motor system to the scale-invariant physical world and therefore have a common foundation.