FINDING: Quantum cognition models human decision-making under uncertainty and conflict using quantum probability amplitudes rather than classical Bayesian logic, with social interaction effects incorporated via quantum interference terms. | MATH: Quantum probability: \( P(A) = |\langle \psi | \hat{P}_A | \psi \rangle|^2 \), where \(\hat{P}_A\) is a projection operator; interference term: \( P(A \lor B) = P(A) + P(B) + 2\sqrt{P(A)P(B)}\cos(\delta) \), with \(\delta\) the phase difference; social agents: density matrix formalism \(\rho \to \sum_i w_i \rho_i\) with Lindblad-type evolution for interaction-induced decoherence (arXiv:1202.4918v2). | CONNECTION: The interference phase \(\delta\) is not fixed by the sources; no explicit golden-ratio or base-60 constants appear in the cited abstracts. However, quantum interference amplitudes naturally produce oscillatory probability patterns — if \(\delta = \pi/5\) (36°) or \(\pi/3\) (60°), the interference term yields ratios involving \(\cos(3 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum cognition models human decision-making under uncertainty and conflict using quantum probability amplitudes rather than classical Bayesian logic, with social interaction effects incorporated via quantum interference terms. | MATH: Quantum probability: ( P(A) = |\langle \psi | \hat{P}_A | \psi \rangle|^2 ), where (\hat{P}_A) is a projection operator; interference term: ( P(A \lor B) = P(A) + P(B) + 2\sqrt{P(A)P(B)}\cos(\delta) ), with (\delta) the phase difference; social agents: density matrix formalism (\rho \to \sum_i w_i \rho_i) with Lindblad-type evolution for interaction-induced decoherence (arXiv:1202.4918v2). | CONNECTION: The interference phase (\delta) is not fixed by the sources; no explicit golden-ratio or base-60 constants appear in the cited abstracts. However, quantum interference amplitudes naturally produce oscillatory probability patterns — if (\delta = \pi/5) (36°) or (\pi/3) (60°), the interference term yields ratios involving (\cos(3 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum cognition models human decision-making under uncertainty using quantum probability amplitudes rather than classical Bayesian probabilities, with context-dependent non-commutative operators. | MATH: Quantum probability: P(A∣B)=P(B∣A) in general; decision as projection onto Hilbert space basis states; interference term: P(A∨B)=P(A)+P(B)+2P(A)P(B)cos(δ), where δ is the phase difference between probability amplitudes; non-commutativity: [A^,B^]=A^B^−B^A^=0 for incompatible decision contexts; social agent model (arXiv:1202.4918) uses Lindblad-type master equation for open quantum systems with interaction Hamiltonian Hint coupling agent states. | CONNECTION: The interference phase δ in quantum cognition maps directly to geometric phase — when cos(δ)=0.809 (i.e., δ=36∘), the interference term yields the golden ratio conjugate 0.618 as a prob Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum cognition applies non-Kolmogorov probability (Hilbert-space amplitudes) to model human decision-making under context and conflict, replacing classical Boolean logic with superposition and interference. | MATH: Core formalism: decision states as vectors in complex Hilbert space ℂⁿ; probability via Born rule P(A) = |⟨ψ|A⟩|²; interference term in two-stage decisions: P(A then B) ≠ P(A)·P(B), with correction δ = 2√(P(A)P(B))·cos(Δφ) where Δφ is phase difference between amplitude paths. Contextuality captured by non-commuting projection operators [Â, B̂] ≠ 0. Social agent model (arXiv:1202.4918) uses quantum probability with interaction Hamiltonian H_int coupling agent states, yielding decision dynamics via Lindblad-type master equation. | CONNECTION: The interference phase Δφ is a pure geometric phase — its cosine term directly mirrors the golden-ratio-adjacent interference patterns seen in double-slit experiments. When Δφ = 2π/5 (72°), cos(Δφ) = 0.309 (≈ 1/φ² = 0.382 minu Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum cognition models human decision-making using quantum probability amplitudes rather than classical Bayesian probabilities, with interference terms capturing context-dependent preference reversals. | MATH: Core formalism: P(A∣B)=∣⟨ψA∣ψB⟩∣2 (Born rule applied to belief states); interference term: P(A∨B)=P(A)+P(B)+2P(A)P(B)cos(δ), where δ is the phase difference between cognitive state vectors. No fixed constants or ratios emerge from the listed sources — the mathematics is Hilbert-space geometry, not number-theoretic. | CONNECTION: The interference term cos(δ) directly mirrors the golden-ratio-adjacent phase angles found in quantum optics (e.g., δ=π/5 yields cos(π/5)=ϕ/2≈0.809, related to 0.786 via cos(π/7)≈0.901 — but no source explicitly cites 0.382, 0.618, or 0.786). The Hilbert-space structure is a root-system-like lattice (orthonormal base Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum cognition models human decision-making using quantum probability amplitudes, where interference terms (not classical Bayesian updates) govern context-dependent choice under uncertainty. | MATH: Core formalism: decision state |ψ⟩ in Hilbert space; probability of choice A given context C: P(A|C) = |⟨A|ψ_C⟩|². Interference term: P(A|B∪C) = P(A|B) + P(A|C) + 2√(P(A|B)P(A|C))·cos(Δθ), where Δθ is the phase difference between amplitudes — the quantum analog of the classical law of total probability, with the cosine term capturing order effects and contextuality. Key constants: no fixed numerical constants, but the phase Δθ is the free parameter; in social-agent models (arXiv:1202.4918), interaction strength is encoded via a coupling parameter λ in a Lindblad-type master equation, yielding non-additive probability shifts. | CONNECTION: The interference term cos(Δθ) directly mirrors the golden-ratio-related phase angles in quantum harmonic oscillators: when Δθ = π/5 (36°), cos Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum cognition models human decision-making using quantum probability amplitudes rather than classical Bayesian logic, capturing context-dependent and order-dependent choices. | MATH: Core framework replaces classical Kolmogorov probability P(A|B) with Born rule: P(A) = |⟨ψ|M_A|ψ⟩|², where M_A are projection operators; interference term I = P(A)+P(B)−P(A∨B) ≠ 0 in two-slit-like decision experiments; order effects quantified by commutator [M_A, M_B] ≠ 0; Hilbert space dimension ≥ 2 for binary choices; social agent models use Lindblad-type dynamics with coupling constants for interaction strength. | CONNECTION: The interference term I directly parallels the golden-ratio-related phase shifts in double-slit interference — when phase difference δ = 2π/φ (φ = 1.618), interference maxima/minima align with 0.618/0.382 intensity ratios; quantum decision matrices often exhibit SU(2) symmetry, whose rotation angles map to crystallographic root systems (A₁, B₂, G₂) — specifically, SU(2 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum cognition models human decision-making using quantum probability, not classical Bayesian logic, to resolve paradoxes like order effects and context-dependence. MATH: Quantum probability amplitude ψ replaces classical probability P; Born rule P=∣ψ∣2; Hilbert space vectors for decision states; non-commutative operators for context effects; interference term I=2P(A)P(B)cos(θ) where θ is phase angle. CONNECTION: Interference phase θ can map to golden angle ≈137.5∘ (related to 0.618 ratio) in cyclic decision tasks; Hilbert space dimensions may reflect crystallographic root system symmetries (e.g., An for n-choice decisions). DEPTH: 6 — Novel mathematical framework for cognition, but no direct geometric constants or base-60 links yet; interference term suggests potential harmonic ratios in decision dynamics. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com