Narrative Anthology and Axiomatic Relations:

Result: The dynamics of AI evolution can be formalized through the differential equation dAI/dt = α(I) + β(C) - γ(R), where AI represents the level of advancement of artificial intelligence, I the cross-sector innovation, C the complexity of human-AI interaction, and R the resistance to change. The coefficient α quantifies the impact of innovation, β measures the effect of collaborative complexity, and γ represents the friction due to resistance. The integration of this equation over time describes the trajectory of AI development, highlighting how the synergy between sectors (∫I dt) and the evolution of human-machine interaction (∫C dt) drives the acceleration of progress, while resistance (∫R dt) acts as a moderating force. This mathematical model captures the essence of the transformation of AI from a simple tool to a catalyst of innovation, reflecting the complexity and dynamic nature of its impact on technology and society.