Paolo Totaro introduces the article ‘Biological Recursion and Digital Systems: Conceptual Tools for Analysing Man-Machine Interaction‘
The theory of numbers, the theory of computation and well-known biological and neurological studies on cognition and consciousness all indicate the concept of recursion as their common denominator. Mathematical recursion owes its meaning and properties to a dual relationship between its results, which always constitute a sequence, and the operator that generated them, which is instead invariant. This article proposes that this duality in recursion originates from the duality between the biological homeostatic equilibrium in living systems and the adaptive physico-chemical changes required to sustain such equilibria. Such duality gives order and meaning to the experiences of a living system. One of the many implications of this innovative perspective is that this duality can decouple computational results from our intuitive order relations, and that this can cause a rarefaction of the capacity of digital systems to convey communication and favour adaptation to the environment.
For more information on recursion, see:
Hofstadter DR (1979) Gödel, Escher, Bach: an Eternal Golden Braid. Basic Books, New York,1 pp. 127-152 (Chapter V).
Odifreddi P (2012) Recursive Functions. Stanford Encyclopedia of Philosophy Archive (as an introduction, only sections 1.1-1.3). Available: https://plato.stanford.edu/archives/spr2020/entries/recursive-functions/.
Dean W (2020) Recursive Functions. Stanford Encyclopedia of Philosophy (Section 1: Historical Background). Available: https://plato.stanford.edu/entries/recursive-functions/.