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Let us start with a seemingly unrelated field to that described in the article by Yair et al. (1) in PNAS. The field of psychophysics deals with the relationships between physical stimuli and mental phenomena. An excellent example is the scientific community’s early efforts to study the human perception of color. Scientists have been intrigued by visual awareness of colors, trying to understand our interpretation of colors and attempting to quantify human perception with simple equations. Roughly speaking, one could divide these efforts into axiomatic ones that gave birth to the Young, Maxwell, Helmholtz, and, later on, Schrödinger so-called “inductive color line elements” and the empirical color arc-lengths that reflected the effort to virtually embed measurements of human color perception into a simple, often Euclidean, domain. In fact, the latter school of thought, of treating the problem empirically rather than axiomatically, is probably one of the earliest attempts to apply a manifold learning technique to study a psychophysical phenomenon. The outcome was the insightful observation that human color perception is 3D, while most birds probably have (and most dinosaurs probably had) a color perception manifold of higher dimensions and most other mammals share a lower dimensional space for the (lack of) perception of color. One of the analysis tools used to arrive at this important observation is known as multidimensional scaling (MDS), and is related to the famous principal component analysis machinery that is commonly used in big data representation, for which various modern generalizations exist. While axiomatic realizations of studying the color receptors in the eye lead Maxwell (2) to the understanding that color images could be synthesized by a linear …

From understanding of color perception to dynamical systems by manifold learning