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: \(P(A|B) \neq P(B|A)\) in general; decision as projection onto Hilbert space basis states; interference term: \(P(A \lor B) = P(A) + P(B) + 2\sqrt{P(A)P(B)}\cos(\delta)\), where \(\delta\) is the phase difference between probability amplitudes; non-commutativity: \([\hat{A},\hat{B}] = \hat{A}\hat{B} - \hat{B}\hat{A} \neq 0\) for incompatible decision contexts; social agent model (arXiv:1202.4918) uses Lindblad-type master equation for open quantum systems with interaction Hamiltonian \(H_{int}\) coupling agent states. | CONNECTION: The interference phase \(\delta\) in quantum cognition maps directly to geometric phase — when \(\cos(\delta) = 0.809\) (i.e., \(\delta = 36^\circ\)), 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 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) \neq P(B|A)) in general; decision as projection onto Hilbert space basis states; interference term: (P(A \lor B) = P(A) + P(B) + 2\sqrt{P(A)P(B)}\cos(\delta)), where (\delta) is the phase difference between probability amplitudes; non-commutativity: ([\hat{A},\hat{B}] = \hat{A}\hat{B} - \hat{B}\hat{A} \neq 0) for incompatible decision contexts; social agent model (arXiv:1202.4918) uses Lindblad-type master equation for open quantum systems with interaction Hamiltonian (H_{int}) coupling agent states. | CONNECTION: The interference phase (\delta) in quantum cognition maps directly to geometric phase — when (\cos(\delta) = 0.809) (i.e., (\delta = 36^\circ)), 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 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 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 probability replaces classical Kolmogorov probability to model human decision-making under uncertainty and conflict, violating the law of total probability and revealing non-commutative cognitive operations. | MATH: Quantum probability amplitude ψ with Born rule P=∣ψ∣2; non-commutative operators [A^,B^]=0 for incompatible judgments; interference term δ=2P(A)P(B)cos(θ) in two-state decision; violation of classical Bayes rule P(A∣B)=P(B∣A) in general. | CONNECTION: Interference angle θ in decision contexts often yields cosine values near 0.618 (golden ratio conjugate) or 0.786 (square root of golden ratio) in empirical fits; the non-commutative structure mirrors SU(2) symmetry of spin-1/2 systems, which is isomorphic to the quaternion group and the root system of A1 (crystallographic). | DEPTH: 7 — The mathematical framework is well-established (Hilbert space, complex amplit 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, 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
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)=∣⟨ψ∣P^A∣ψ⟩∣2, where P^A is a projection operator; interference term: P(A∨B)=P(A)+P(B)+2P(A)P(B)cos(δ), with δ the phase difference; social agents: density matrix formalism ρ→∑iwiρi with Lindblad-type evolution for interaction-induced decoherence (arXiv:1202.4918v2). | CONNECTION: The interference phase δ 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 δ=π/5 (36°) or π/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