Unifying Physics and Psychophysics on the Basis of Symmetry, Least-Action ≈ Simplicity Principle, and Conservation Laws ≈ Veridicality

Abstract

Psychophysics refers to the branch of Experimental Psychology that deals with the study of Sensation and Perception. A consensus has grown up among experts in Psychophysics during the last hundred years that the human being's percepts are inferences that are based on a minimum, or simplicity principle, which is applied to the currently available sensory data. These educated guesses play the critical role in establishing veridical perceptual representations of the 3D environment, where by "veridical" we mean that the percept agrees with what is "out there." These veridical representations cannot be achieved without making use of symmetries, much like those known in Physics, where they are essential for characterizing our physical world and deriving the conservation laws. But, unlike in Physics, the important role that symmetry plays in Psychophysics has only been demonstrated and explained within the last ten years. Symmetries represent regularities in our physical world. These symmetries also serve as the source of the redundancies that are inherent in 3D objects and that make vision possible. The main goal of this paper is to show that the similarity between the mathematical formalisms used in Physics and in Psychophysics is not coincidental, and that exploring this similarity can benefit the sciences called Perception and Cognition. This paper includes a brief tutorial about symmetry groups and their relationship to transformation groups as well as to their invariants. It was included to make this material available to readers who are not familiar with these topics.

Implicit Computation and the Origins of Knowledge

“…There have been previous proposals in cognitive science that are related to implicit computation, as noted below (e.g., Dodwell, 1983;Gallistel, 1990;Hoffman, 1966;Pizlo, 2010Pizlo, , 2019Shepard, 1984Shepard, , 1994. But the intellectual lineage of these ideas can be traced to Helmholtz' (1867) concept of 'unconscious inference ' and Poincaré's (1905) analysis of the perception of space, and ultimately back to Kant.…”

“…If a scaling factor is added, the result is a similarity transformation group (Figure 7) with seven degrees of freedom. The angles between triples of points are invariant under the action of a similarity group, which means that the shape of 3D objects are preserved (Pizlo, 2010(Pizlo, , 2019. The similarity group describes the viewpoint invariance that an observer perceives while moving through an environment with objects.…”

“…Recently, he has proposed that symmetry plays an analogous role in physics and psychophysics, and that a 'least action' principle, fundamental in physics, connects mental representations with the outside world (Pizlo, 2019). Pizlo's proposals are similar to implicit computation as attempts to specify the priors imposed by the visual system that solve the problem of 3D shape perception.…”

The Concept of Symmetry and the Theory of Perception

“…But the visual data that come from the retinal image are 2D. It follows that the problem of inferring 3D interpretation from a 2D image is an ill-posed inverse problem (Poggio et al, 1985 ; Pizlo, 2001 , 2019 ). By ill-posed, we mean here that a 2D image does not specify a unique 3D interpretation.…”

“…Symmetry and its invariance properties are essential in human vision, as well as in other cognitive functions. Without symmetry, vision, as we know it, would not exist (Pizlo, 2019 ). By the time the reader finishes reading this paper, they should become familiar with the multiple facets of symmetry and invariance.…”