Graphics and Quantum Mechanics—The Necker Cube as a Quantum-like Two-Level System Giorgio Benedek 1,2(&) and Giuseppe Caglioti 3 1 Dipartimento di Scienza dei Materiali, Università di Milano-Bicocca, Via R. Cozzi 55, 20125 Milan, Italy giorgio.benedek@unimib.it 2 Donostia International Physics Center (DIPC), P. M. de Lardizàbal 4, 20018 San Sebastian, Spain 3 Dipartimento di Energia, Politecnico di Milano, Campus Leonardo, via Ponzio 34, 20133 Milan, Italy Abstract. A simulation of the dynamic perception of the Necker cube in terms of a two-level quantum system, e.g. that of the hydrogen tunneling states of the ammonia molecules associated with the 24 GHz maser frequency, indicates that the neuro-physiological transformation leading, through a symmetry reduction, to perceptual reversal is controlled by the principles of quantum mechanics. An elementary neuro-physiological action similar to the Planck constant at a mesoscopic level is introduced. Keywords: Two-level quantum and quantum-like systems  Ambiguous figures  Principle of superposition  Symmetry reduction  Tunneling Chemical and graphic barriers  Perception  Mind  The unconscious 1 Introduction The objective of this contribution is to discuss some points of contact between graphics, geometry, quantum mechanics and perception psychology. Specifically: (i) to show that the main features of the dynamic perception of the Necker cube can be illustrated rigorously with the language of quantum mechanics, and (ii) to show that a careful analysis of the process enabling the observer of a Necker cube (or of a painting of kinetic art) to perceive it dynamically, can help to understand the nature of the transformation produced in an isolated quantum structure by the act of measurement. The Necker cube (1832) is the paradigmatic example of a planar graph with an inversion symmetry center (Fig. 1a) which can be perceived also as a 3D object in two different equally probable ways, depending on whether the lower (Fig. 1b) or the upper square (Fig. 1c) is viewed in front or in the rear, respectively. The operations trans- forming the Necker cube (NC) into the two tridimensional cubes as seen in an axonometric representation are actually a symmetry reduction promoted by a mental action: the new 3D objects lose the original inversion symmetry of the planar graph and acquire an orientation. The two possible ways of perceiving the NC and the © Springer International Publishing AG, part of Springer Nature 2019 L. Cocchiarella (Ed.), ICGG 2018—Proceedings of the 18th International Conference on Geometry and Graphics, Advances in Intelligent Systems and Computing 809, pp. 161–172, 2019. https://doi.org/10.1007/978-3-319-95588-9_12