The Cognitive Origin of the Continuum and the Discrete

> Context • According to Humberto Maturana and Francisco Varela, faced with perturbations from the environment, a living system reacts by reproducing its components under the condition of preserving the organization, that is, the set of relationships between all its components. This activity is recursive, as it operates to preserve its own ability to operate. It not only defines the living but also the way in which the living system understands its environment. This makes the concept of recursion a key interpretative framework for phenomena of life and cognition. > Problem • Since experience emerges from biological recursion, we address the question of how experiences of the continuum and the discrete can result from it. > Method • Even if we draw on set and number theories in our arguments, the topic is not primarily addressed as a mathematical problem, but rather as a cognitive one. The arguments are developed using tools of analytic philosophy. > Results • We argue that, as with all recursive processes, the operator of a biological process remains unchanged, while its results vary in an inductive (and therefore historical) manner. We conclude that the phenomenon of the continuum originates from the invariance of this operator, while that of the discrete originates from the operator’s results. > Implications • This work is part of the authors’ research aimed at proposing a metamathematics based on the concept of number as a biological process rather than as a “thing.” This is done using the concepts of “objectivity in parentheses” and “without parentheses” introduced by Maturana. Furthermore, the article may contribute to studies on the relationship between digital systems and human intelligence. In contrast to the latter, the former are discrete not only concerning inputs and outputs but also in terms of operators, which are constituted by discrete sets of algorithms, themselves composed of discrete sets of instructions. > Constructivist content • This work employs the ideas of Humberto Maturana and Francisco Varela. © 2024 Vrije Universiteit Brussel.