Complementarity in Bistable Perception

The idea of complementarity already appears in William James’ (1890a, p. 206) Principles of Psychology in the chapter on “the relations of minds to other things”. Later, in 1927, Niels Bohr introduced complementarity as a fundamental concept in quantum mechanics. It refers to properties (observables) that a system cannot have simultaneously, and which cannot be simultaneously measured with arbitrarily high accuracy. Yet, in the context of classical physics they would both be needed for an exhaustive description of the system. In contrast to the concept of a “complement” in mathematics, which refers to the negation of a proposition, complementarity refers to properties that are not simply negations of each other. A nice example is mentioned by James (1890b, p. 284): “The true opposites of belief . . . are doubt and inquiry, not disbelief.” Disbelief would be the complement of belief in the Boolean sense, while doubt and inquiry are concepts that are complementary to belief. Another pertinent example for complementarity may be “learning” and “knowing” in data processing systems. In addition to James and Bohr, Wolfgang Pauli was one of those scientists who always thought that the idea of complementarity is significant far beyond the objectively measurable realms of physics. In quantum mechanics, complementarity is mostly used in the context of observables such as “momentum” and “position” which are, technically speaking, non-commuting observables. Although complementarity soon became an important ingredient in the so-called Copenhagen interpretation of quantum theory, there exists no rigorous and unique mathematical definition of complementarity which all scientists agree upon. There are many definitions which all