Behavioral and Brain Sciences

Open Peer Commentary
Saunders & van Brakel: Colour categorization

Logic, physics, physiology, and topology of color

H. M. Hubey a1
a1 Departments of Mathematics, Computer Science, and Physics, Montclair State University, Upper Montclair, NJ 07043


This commentary starts with a simplified Cartesian vector space of the tristimulus theory of color. This vector space is then further simplified so that bitstrings are used to represent the vector space. The Commission Internationale de l'Eclairage (CIE) diagram is shown to follow directly and simply from this vector space. The Berlin & Kay results are shown to agree quite well with the vector space and the two-dimensional version of it, especially if the dimensions are normalized to take into account the sensitivity of the eye to the different wavelengths comprising color. There is asymmetry with respect to the colors and a similar asymmetry in vocalic phonemes; these effects can be explained in terms of physiology. The (in)famous problem of the color channels is given a unified treatment at various levels. An eight-valued color algebra is created, with addition and multiplication corresponding to additive and subtractive blending of colors. Finally, it is shown that the discrete Hamming metric for colors has a natural toroidal topology.