Reversed dimensional analysis in psychophysics

Abstract

It is argued that dimensional analysis (from physics) can be applied in psychophysics in the same manner as in physics, provided that the dimensions of sensations are interpreted in the sense of reversed dimensional analysis, which allows for extracting dimensions from data. A dimension obtained by this method, referred to as phenomenological dimension, is similar to a fractal dimension. The examples discussed show that, if the dimension of sensation in Stevens' psychophysical law for time duration (Ψ = Cn, n ≈ 1.15) is interpreted as a phenomenological dimension, such a dimension can be traced even in short-term memory data. It is suggested that dimensions obtained via reversed dimensional analysis may serve as a link between physical and psychological variables and as a basis for developing the notion of dimension in psychology.