标签：#maths

@kungfufk Since the dawn of computing, we have built Artificial Intelligence on a flawed premise: perfect rationality. We brute-force algorithms to find the optimal solution, assuming infinite time and infinite capacity. But humans don't work like that. As Herbert Simon famously coined, we operate on Bounded Rationality. We make decisions based on limited time, limited cognitive capacity, and limited information. What if, instead of forcing AI to be perfectly rational, we created a mathematical equivalent for human processing? What if we modeled human cognition using the laws of physics — wave theory, thermodynamics, and mechanical energy equations — to build a heavy, complex, but highly probabilistic AI engine? Here is a blueprint for a new field of research: Computational Cognitive Mechanics . 1. The Core Equations of Cognitive Processing To model bounded rationality mathematically, we first need to define the relationship between Knowledge ($K$), Cognitive Capacity ($C$), and Processing Time ($T$). Based on human observation, we can establish these foundational proportions: Knowledge vs. Time — The more knowledge you possess, the faster you can generate a decision. $$T \propto \frac{1}{K}$$ Capacity vs. Time — High cognitive capacity (skills, processing power) inversely relates to the time required to solve a problem. $$T \propto \frac{1}{C}$$ Knowledge vs. Capacity — This is the most fascinating limit. Knowledge does not scale linearly with capacity. Gaining true knowledge requires exponential capacity (effort/skill). Therefore, knowledge is roughly proportional to the square root of capacity. $$K \propto \sqrt{C}$$ By integrating these, we can build a baseline processing algorithm for an AI. Instead of giving an AI unlimited time to compute, we cap its computing time based on a synthetic "Knowledge and Capacity" matrix, forcing it to use heuristics — just like a human. 2. Cognitive Wave Theory & FFT: Information as Interference In physics, waves interact throug