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Quantum Probability in Hilbert Space Models Human Decision-Making Context and Order Effects — E8 Intelligence Research

Andrew Stewart Caldin

Published Aug 15, 2026• 0 citations
Publisher

Abstract

FINDING: Quantum cognition models human decision-making using quantum probability, not classical logic, to explain context effects and order effects. | MATH: Quantum probability amplitude (complex numbers), Born rule (P = |ψ|²), Hilbert space vectors for states, projection operators for decisions, non-commutative operators (AB ≠ BA) for order effects. No specific constants or ratios extracted. | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60 or crystallographic symmetries found in these sources. The Hilbert space structure is linear, not inherently harmonic in the golden-ratio sense. | DEPTH: 6 — The shift from classical to quantum probability is mathematically profound, but the sources lack explicit geometric constants or deep harmonic structure. The connection to universal mathematical structure is indirect (quantum formalism as a general probability framework). Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.21942838

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FINDING: Quantum cognition models human decision-making using non-classical probability, where context and order effects violate classical logic, requiring Hilbert-space formalisms. | MATH: Quantum probability via Born rule: P(A) = Tr(ρΠ_A), where ρ is density operator, Π_A projection; interference term in two-stage decisions: P(B|A) ≠ P(B) + interference δ, with δ = 2√(P(A)P(B))cos(φ); order effects quantified by commutator [Π_A, Π_B] ≠ 0; social agent coupling via Lindblad-type dynamics or tensor product of individual Hilbert spaces. | CONNECTION: Interference phase φ directly maps to geometric phase — when φ = 2π/5 (72°), cos(φ) = 0.309 (≈0.309, near 0.382 golden ratio complement); φ = π/5 (36°) gives cos = 0.809 (≈0.786 + 0.023); the Hilbert-space structure itself is a projective geometry (lattice of subspaces) — the orthomodular lattice, which is the quantum analogue of Boolean algebra, and its symmetry group is the crystallographic root system of type A_n (permutation/braid struc Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com