Narrative Anthology and Axiomatic Relations:

Result: The evolution of artificial intelligence (AI) can be formalized through a system of nonlinear differential equations that describe the dynamics of its development and integration: dAI/dt = α(I) + β(T) + γ(C) - δ(R) Where: AI: State of artificial intelligence t: Time α(I): Function of technological innovation β(T): Function of integration into various sectors γ(C): Function of cultural impact δ(R): Function of resistances and limitations The human-machine interaction (HMI) evolves according to: d(HMI)/dt = ε(AI) * ζ(U) - η(B) Where: HMI: State of human-machine interaction ε(AI): Function of AI capabilities ζ(U): Function of human adaptability η(B): Function of technological and cognitive barriers The democratization of AI (D) follows: dD/dt = θ(A) + λ(E) - μ(C) Where: θ(A): Function of accessibility of AI tools λ(E): Function of education and training μ(C): Function of costs and complexity These equations describe a complex dynamic system that models the evolution of AI and its impact on society, highlighting the interconnections between technological innovation, sectoral integration, cultural impact, and accessibility.