January 23, 2023 10:35 MCCII20 Draft Draft Machine Cognition, Control and Embodiment on Landscapes of Fog, Friction and Selection Rodrick Wallace Division of Epidemiology The New York State Psychiatric Institute, Box 47 1051 Riverside Drive New York, NY 10032 USA rodrick.wallace@gmail.com,rodrick.wallace@nyspi.columbia.edu Real-world cognitive structures – embodied biological, machine or composite entities – are inherently unstable by virtue of the ‘topological information’ imposed upon them by external circumstance, adversarial intent, and other persistent ‘selection pressures’. Consequently, under the Data Rate Theorem, they must be constantly controlled by em- bedding regulators. For example, blood pressure and the stream of consciousness require persistent delicate regulation in higher organisms. Here, using the Rate Distortion Theo- rem of information theory, we derive a form of the Data Rate Theorem of control theory that characterizes such instability for adiabatically stationary nonergodic systems and uncover novel forms of cognitive dynamics under stochastic challenge. These range from aperiodic stochastic amplification to Yerkes-Dodson signal transduction and outright system collapse. The analysis, deliberately closely adapted from recent purely biolog- ical studies, leads toward new statistical tools for data analysis, uncovering groupoid symmetry-breaking phase transition analogs to Fisher Zeros in physical systems that may be important for studies of machine intelligence under real-world, hence embodied, interaction. Key Words: cognition, control theory, information theory, phase transition, stability, stochastic burden, symmetry-breaking 1. Introduction Extending formal arguments previously restricted to biological phenomena – in particular Wallace (2023a Ch. 3, closely followed here) – many real-world, real-time cognitive processes, be they biological, machine or composite, are both embodied and inherently unstable. That is, much like a vehicle moving along a twisting, pot- holed roadway, these processes must be closely regulated by a ‘driver’ providing control information at a rate greater than the underlying road generates it’s own ‘topological information’ (e.g., Nair et al. 2007). The human ‘stream of conscious- ness’ is restrained by social and cultural as well as more common neuropsychologi- cal ‘riverbanks’ for successful confrontation and circumvention of powerful selection pressures at both individual and group scales of organization (e.g., Wallace 2022a). Blood pressure rises and falls according to need, but must be held within critical limits for individual survival. Similarly, immune systems conduct routine cellular 1