Dimensions of understanding

In the first decades of the 20th century, a tension emerged between three competing constraints on psychophysical research: 1. the demand for increased empirical precision; 2. a theoretical commitment to decomposing complex sensations into primitive components; and 3. a pragmatic pressure for ease of visualization and communication of data. I argue that this tension motivated the operationalization of perceptual qualities in terms of measurement into low-dimensional spaces. These “constructed” qualities then shaped the progress of psychophysical research, resulting in the systematic marginalization of problematic phenomena, in particular the growing evidence that measurable perceptual variation can only be accurately represented in spaces of much higher dimensionality.

I will be illustrating these tensions through an analysis of the changing attitudes toward standardized color solids from the 1930’s to the 1970’s. In the late 19th century, two theories of primitive color sensations vied for dominance: Helmholtz’s 3 receptor theory and Hering’s opponent process theory. Although they disagreed on the primitive components of color sensation, both theories motivated a 3-dimensional color solid. Building on these theories, standardized 3-dimensional color solids were proposed by the Commission internationale de l’éclairage (1931, 1976), the Munsell Color Company (1943), and the Optical Society of America (1977)—amongst others. These systems provided a standardized vocabulary for characterizing experimental stimuli, reporting results, and visualizing patterns in the data. Later spaces improved on earlier ones in the increasing fit between their Euclidean metrics and subjective judgments of color distance.

This project continued despite the accrual of evidence that the space of possible color sensations is (a) greater than 3-dimensional; and (b) cannot be approximated in Euclidean space. The first point was argued already by Katz (1911/1930) via both phenomenological analysis and asymmetrical matching experiments; it was emphatically reinforced in a series of experiments by Evans (1949–1974); and has been rediscovered in recent work on asymmetric matching. (Intuitively, color sensations that depend on the context in which stimuli are viewed, e.g. brown, or the contrast between greyness and darkness, are not represented in 3-dimensional color solids.) The non-Euclidean metric over color sensations follows from matching experiments and was vigorously emphasized by MacAdam (1942 / 1985) and Judd (1970), with the former strenuously questioning the value of Euclidean colors spaces such as the ones listed above.

Similar attempts to operationalize perceptual qualities through measurement into 2- or 3-dimensional spaces can be found in the domains of touch, audition, and taste. Notably, even failed attempts, such as Henning’s odor prism, continue to be celebrated in textbooks. I conclude that (i) the ease with which 2- and 3-dimensional structures can be visualized motivated the definition of perceptual qualities measurable in 2- or 3-dimensions; and (ii) these operationalized qualities are thus artifacts of a pragmatic choice, and not veridical representations of human perceptual experience.