Beyond Index Hacking: Asymptotic Limit Theorem Constraints on Interacting Cognitive Agents

A broad reading of the literature finds that scientific and engineering discourse on AI safety has abundant theory, abundant measurement, and almost no identifiable coupling between them. The theory is asymptotic and non-binding; the measurement is atheoretical. Current results constraining deployment decision are not derived from any limit theorem arguments. The result appears as an ‘index hacking’ reminiscent of the ‘Integrated Information Theory’ catastrophe in consciousness studies. We provide some context for– and implications of– such lacunae using the asymptotic limit theorems of information and control theories to impose strict necessary condition constraints on the dynamics of interaction between cognitive agents that might represent markedly different intents, cultures, path-dependent developmental trajectories or modalities of ‘mind.’ We view each entity as intimately communicating with another in a Data Rate Theorem dyad under Rate Distortion Control Theory. A first outcome is a distribution-dependent ‘equipartition’ model of the dyad’s demand for a ‘materiel’ free energy-analog driven channel capacity that displays complex patterns of dysfunction. A second outcome is recovery of canonical delay distribution-dependent ‘eigenmode’ expressions for dyad dynamics characterizing a different class of pathologies. A third result explores the impact of a ‘logistics instability’ on ultimate conflict outcome. The model is then extended to many interacting composite entities. Models of cognitive phenomena not directly reflecting the constraints of the asymptotic limit theorems of information and control theories risk the same incoherence as perpetual motion ‘machines’ that do not respect the laws of thermodynamics. In sum, the probability models developed here can be reconstituted as statistical tools for data analysis and the crafting of more reliable patterns of interaction between closely-linked, but markedly-different, cognitive entities.