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Quantum Probability Resolves Decision Paradoxes via Non-Commutative Operators — E8 Intelligence Research

Andrew Stewart Caldin

Published Jul 31, 2026• 0 citations
Publisher

Abstract

FINDING: Quantum cognition models human decision-making using quantum probability, not classical Bayesian logic, to resolve paradoxes like order effects and conjunction fallacies. MATH: Quantum probability amplitude: \( P(A) = |\langle \psi | \Pi_A | \psi \rangle|^2 \), where \( |\psi \rangle \) is a state vector in Hilbert space, \( \Pi_A \) a projection operator. Non-commutative operators: \( [\hat{A}, \hat{B}] \neq 0 \) for incompatible questions. No fixed constants or ratios emerge from these sources. CONNECTION: No explicit geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60, crystallographic, or root-system symmetries are reported. The Hilbert space structure is linear, not inherently harmonic. DEPTH: 4 — The framework is mathematically novel (quantum probability in cognition) but lacks direct ties to universal geometric constants or symmetries. It advances understanding of decision-making as a non-classical process but does not reveal new fundamental mathematic Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.21714652

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