In search of an "irrational" idea

A.A. Tyapkin

Alexander Klimets

The article formulates and substantiates the philosophical epistemological principle, which generalizes the principle of complementarity of Bohr to all phenomena of reality. The general complementarity principle is formulated as follows: the rational side of reality and its cognition and its associated irrational side of reality and its cognition are complementary to each other. The general principle of complementarity allows one to search for phenomena of duality in various fields, grouping them according to rational and irrational signs.

Costas Christodoulides, George Christodoulides

Bernadette Bensaude‐Vincent

SUMMARY. — This paper emphasizes the evolution of complementarity, in Niels Bohr's successive formulations of this idea, from 1927 to 1939, despite little, if any change in the definition of the concept with time. In the Como lecture, in 1927, Bohr introduced the idea of « complementary descriptions » in a problematic, polemical way. Against Schrödinger' s interpretation, he stressed the « irrationality » inherent in the quantum postulate. In 1935, Bohr again used complementarity polemically, in his reply to Einstein-Podolsky-Rosen. But far from intending it to convey irrationality this time, he meant to use it instead to prove that quantum mechanics is a complete theory. Finally, I will take up Bohr's attempts to apply complementarity to fundamental problems in biology, psychology, sociology, and so forth. I will argue that the introduction of complementarity outside physics was not motivated by an imperialist ambition of the Copenhagen School, but rather inspired by Bohr's own personal philosophy.

Joshua Knobe

Andreas Wichert, Catarina Moreira, Peter Bruza

Empirical findings from cognitive psychology indicate that, in scenarios under high levels of uncertainty, many people tend to make irrational decisions. To address this problem, models based on quantum probability theory, such as the quantum-like Bayesian networks, have been proposed. However, this model makes use of a Bayes normalisation factor during probabilistic inference to convert the likelihoods that result from quantum interference effects into probability values. The interpretation of this operation is not clear and leads to extremely skewed intensity waves that make the task of prediction of these irrational decisions challenging. This article proposes the law of balance, a novel mathematical formalism for probabilistic inferences in quantum-like Bayesian networks, based on the notion of balanced intensity waves. The general idea is to balance the intensity waves resulting from quantum interference in such a way that, during Bayes normalisation, they cancel each other. With this representation, we also propose the law of maximum uncertainty, which is a method to predict these paradoxes by selecting the amplitudes of the wave with the highest entropy. Empirical results show that the law of balance together with the law of maximum uncertainty were able to accurately predict different experiments from cognitive psychology showing paradoxical or irrational decisions, namely in the Prisoner's Dilemma game and the Two-Stage Gambling Game.