The Concept of Symmetry and the Theory of Perception

Zygmunt Pizlo; J Acacio de Barros

doi:10.3389/fncom.2021.681162

The Concept of Symmetry and the Theory of Perception

Front Comput Neurosci. 2021 Aug 23:15:681162. doi: 10.3389/fncom.2021.681162. eCollection 2021.

Authors

Zygmunt Pizlo¹, J Acacio de Barros²

Affiliations

¹ Department of Cognitive Sciences, University of California, Irvine, Irvine, CA, United States.
² School of Humanities and Liberal Studies, San Francisco State University, San Francisco, CA, United States.

Abstract

Perceptual constancy refers to the fact that the perceived geometrical and physical characteristics of objects remain constant despite transformations of the objects such as rigid motion. Perceptual constancy is essential in everything we do, like recognition of familiar objects and scenes, planning and executing visual navigation, visuomotor coordination, and many more. Perceptual constancy would not exist without the geometrical and physical permanence of objects: their shape, size, and weight. Formally, perceptual constancy and permanence of objects are invariants, also known in mathematics and physics as symmetries. Symmetries of the Laws of Physics received a central status due to mathematical theorems of Emmy Noether formulated and proved over 100 years ago. These theorems connected symmetries of the physical laws to conservation laws through the least-action principle. We show how Noether's theorem is applied to mirror-symmetrical objects and establishes mental shape representation (perceptual conservation) through the application of a simplicity (least-action) principle. This way, the formalism of Noether's theorem provides a computational explanation of the relation between the physical world and its mental representation.

Keywords: Noether's theorem; conservation laws; human perception; invariance and symmetry; least-action principle; perceptual constancy.