Quantum cognition emerged as an important discipline of mathematical psychology during the last two decades. Using abstract analogies between mental phenomena and the formal framework of physical quantum theory, quantum cognition demonstrated its ability to resolve several puzzles from cognitive psychology , issued in the bounded rationality research program . Until now, quantum cognition essentially exploited ideas from projective (Hilbert space) geometry, such as quantum probability or quantum similarity. However, many powerful tools provided by physical quantum theory, such as symmetry groups and their representation theories, particularly local gauge symmetries and their connection to physical forces, have not been utilized in the field of quantum cognition research sofar. This is somewhat astonishing as "mental forces" or "mental energies" appear as important metaphorical concepts in cognitive science. One particular example is music psychology, where static or dynamic tonal attraction phenomena are computationally often modeled in terms of metaphorical forces. Inspired by seminal work by Guerino Mazzola on the connection between musical forces and symmetries in tonal music, our study aims at elucidating and reconciling musical forces in the framework of quantum cognition. Based on the fundamental transposition symmetry of tonal music, as reflected by the circle of fifths, we develop different wave function descriptions over this underlying tonal space, governed by a Schr\"odinger equation containing different interaction energies. We present quantum models for static and dynamic tonal attraction and compare them with traditional computational models in musicology. Our approach turns out to be more parsimonious and of greater explanatory power than symbolic models of music perception.
Quantum cognition emerged as an important discipline of mathematical psychology during the last two decades. Using abstract analogies between mental phenomena and the formal framework of physical quantum theory, quantum cognition demonstrated its ability to resolve several puzzles from cognitive psychology . Until now, quantum cognition essentially exploited ideas from projective (Hilbert space) geometry, such as quantum probability or quantum similarity. However, many powerful tools provided by physical quantum theory, such as symmetry groups and their representation theories, particularly local gauge symmetries and their connection to physical forces, have not been utilized in the field of quantum cognition research sofar. This is somewhat astonishing as "mental forces" or "mental energies" appear as important metaphorical concepts in cognitive science. One particular example is music psychology, where static or dynamic tonal attraction phenomena are computationally often modeled in terms of metaphorical forces. Inspired by seminal work by Guerino Mazzola on the connection between musical forces and symmetries in tonal music, our study aims at elucidating and reconciling musical forces in the framework of quantum cognition. Based on the fundamental transposition symmetry of tonal music, as reflected by the circle of fifths, we develop different wave function descriptions over this underlying tonal space, governed by a Schr\"odinger equation containing different interaction energies. We present quantum models for static and dynamic tonal attraction and compare them with traditional computational models in musicology. Our approach replicates and also improves predictions based on symbolic models of music perception.
D
, issued in the bounded rationality research program
R
turns out to be more parsimonious and of greater explanatory power than
replicates and also improves predictions based on