Quantum Cognition: Hilbert-Space Probability for Human Decision-Making — E8 Intelligence Research

FINDING: Quantum cognition applies Hilbert-space probability (complex amplitudes) to model human decision-making under uncertainty and context effects, replacing classical Kolmogorov probability with non-commutative operator logic. | MATH: Core formalism: state vector |ψ⟩ ∈ ℂⁿ; decision observable with spectral decomposition = Σᵢ λᵢ |eᵢ⟩⟨eᵢ|; probability p(λᵢ) = |⟨eᵢ|ψ⟩|² (Born rule). Context effects via non-commutativity: [Â, B̂] ≠ 0 → order-dependent probabilities. Interference term: p(A then B) = p(A)p(B) + 2√(p(A)p(B))·cos(δ), where δ is the phase difference between probability amplitudes — the quantum analog of the classical conjunction fallacy correction. | CONNECTION: The interference term cos(δ) directly maps to the golden-ratio family when δ = 2π/5 (72°) → cos(72°) = (√5−1)/4 = 0.309; δ = π/5 (36°) → cos(36°) = φ/2 = 0.809; δ = 2π/10 → cos(36°) again. More critically, the Hilbert-space dimension ℂⁿ with n = 2 (qubit) yields the Bloch sphere — whose equatorial projection co Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com