Metaphorising and bayesian inference according to biology of cognition and enaction

Abstract The most accepted paradigm of brain function sustaining mathematical thinking is the “Brain as Computer” metaphor. Since the early 1970s, however, a new viewpoint based on the Biology of Cognition, created by Humberto Maturana and Francisco Varela, has slowly positioned itself as a challenger to the computer metaphor. Here, we interpret the notion of metaphorising in mathematics in the context of Biology of Cognition. Specifically, we introduce the fundamental concept of Structural Coupling, which is the mechanism by which living systems create the “objects” populating their niche by exploiting correlations in the never-ending Perception ⟲ Action loop. Furthermore, we show that how a living system decides which action to perform is the outcome of a Bayesian Inference mechanism; therefore, randomness is fundamental to living systems and not just a consequence of the mere lack of sufficient information to compute the next action. Additionally, in Bayesian inference, the underlying conditional probability distribution P ( action|perception ) changes by the very execution of every Perception ⟲ Action loop, performing a biased random walk according to a Hebbian-like rule. With this rich set of concepts derived from cutting-edge biology, we show that Biology of Cognition is a good fit to understand mathematical metaphorisation.