Predictive capacity of a dynamical system*

Organisms need to extract information about their environment and interact with it. To do this, their internal degrees of freedom(d.o.f), say N of them, must carry information about the environment. A large body of work has argued how the number (N) and structure of the internal d.o.f are “efficient” in representing the external information. Typically, this information is provided by K d.o.f coupled to the environment with K << N, and as a consequence, the information about the current state of the environment scales as O(K). From this perspective, having K << N seems rather inefficient. Prior work has appealed to notions of robustness or accessibility of the encoded information to reconcile this. Here we propose an alternative explanation based on Prediction -- i.e. larger N allows us to better predict the entire future state of the environment from the current internal state. Our starting point is to define the Predictive Capacity of a dynamical system. We then calculate the predictive capacity of a linear model its scaling with N; ongoing work aims to delineate aspects of dynamics which will maximise the predictive capacity.