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Quantum Cognition: Born Rule and Non-Commutative Operators in Decision Dynamics — E8 Intelligence Research

Andrew Stewart Caldin

Published Aug 6, 2026• 0 citations
Publisher

Abstract

FINDING: Quantum cognition models use Born rule probabilities and non-commutative operators to describe human decision dynamics, with a derivation of the Born rule from measurement models. | MATH: Born rule: \( P(a) = |\langle a|\psi\rangle|^2 \); non-commutative operators \([A,B] \neq 0\); Hilbert space structure; probability amplitudes. | CONNECTION: No explicit geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618), base-60, or crystallographic symmetries found in the provided sources. The Born rule derivation (arXiv:2408.06375v4) uses quantum measurement theory, not harmonic or lattice geometry. | DEPTH: 4 — The Born rule derivation is mathematically rigorous but does not reveal new geometric constants or symmetries. The quantum cognition application is interdisciplinary but mathematically standard (Hilbert space, complex amplitudes). No profound geometric harmony link. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.21818365

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