The ultimate tactics of self-referential systems

TL;DR

This paper proposes that mathematics transcends language by embodying the fundamental self-referential nature of the universe, revealing deep insights into autonomous systems and consciousness.

Contribution

It introduces the concepts of irreducibility and insaturation as features of self-referentiality, linking mathematics to the fundamental conditions of autonomous physical systems.

Findings

Mathematics embodies self-referentiality features of the universe.

Self-referential systems require a form of metabolism for autonomy.

Mathematics reveals the fundamental existence condition for self-referentiality.

Abstract

Mathematics is usually regarded as a kind of language. The essential behavior of physical phenomena can be expressed by mathematical laws, providing descriptions and predictions. In the present essay I argue that, although mathematics can be seen, in a first approach, as a language, it goes beyond this concept. I conjecture that mathematics presents two extreme features, denoted here by {\sl irreducibility} and {\sl insaturation}, representing delimiters for self-referentiality. These features are then related to physical laws by realizing that nature is a self-referential system obeying bounds similar to those respected by mathematics. Self-referential systems can only be autonomous entities by a kind of metabolism that provides and sustains such an autonomy. A rational mind, able of consciousness, is a manifestation of the self-referentiality of the Universe. Hence mathematics is here proposed to go beyond language by actually representing the most fundamental existence condition for self-referentiality. This idea is synthesized in the form of a principle, namely, that {\sl mathematics is the ultimate tactics of self-referential systems to mimic themselves}. That is, well beyond an effective language to express the physical world, mathematics uncovers a deep manifestation of the autonomous nature of the Universe, wherein the human brain is but an instance.