"Multiscale Coordination and Dynamical Similarity"
Multiscale coordination can be defined to be the study of how complex biological systems explicitly utilize layers of physiological organization in the performance of a given task. In the recent years, a number of models have been proposed (by Frank, Daffertshoffer, et.al.) that address the issue of multiscale coordination from the perspective of non-extensive statistical mechanics and coupled oscillator models. The key pegs in their approach is morphological reductionism (the neural layer is seen to be more “privileged” than the effector layer) that leads to two very hard problems: first, coupled oscillator models seem to work only with external fine-tuning of free parameters, and second, the system/subsystem distinction is taken to be ontological. In this Paper, I, following Rosen’s work on representation and measurement of natural systems, present a new framework of approaching multiscale coordination that is non-reductionistic and one that does not seem to need external free-parameter fine-tuning. The abstract framework utilizes the notion of topological conjugacy (Rosen’s dynamical similarity principle) between models of different levels of organization. This means that the order parameter at any level obeys a dynamical model that is similar to the model that an order parameter of any other level satisfies. Thereby, formal similarity is postulated to be the key principle in understanding multiscale phenomena. This leads to some very novel implications for understanding complex systems in general from the foundational standpoint. Firstly, the system/subsystem distinction becomes, logically, impredicative and self-reflexive. Secondly and consequently, the new framework is observer dependent. Similar ideas (from a computational mechanical viewpoint) have been proposed by Crutchfield. Baas and Emmeche’s theory of “logical loops” in complex systems are also shown to lead to similar conclusions. I systematically review the foundational problems with existing models of multiscale coordination and, then, present, the new framework. I conclude by suggesting experimental tests that could confirm or refute the same.