GÖDEL'S LEGACY: FORMAL THINKING, LLM AND THE EVOLUTION OF ARTIFICIAL INTELLIGENCE (AI)

Gödel, Escher, Bach: An Eternal Golden Braid (GEB) constitutes a seminal work by Douglas R. Hofstadter, first published in 1979. This treatise delves into concepts such as recursion, self-reference, formal systems, and intelligence, interrelating the contributions of three pivotal figures: •Kurt Gödel: The mathematician renowned for formulating the Incompleteness Theorem, which posits that no formal system can be entirely self-sufficient. •M.C. Escher: The artist celebrated for his paradoxical and self-reflective imagery, engendering perceptual illusions and symmetrical constructs. •Johann Sebastian Bach: The composer is famed for his recursive fugues and canons, mirroring repetitive and stratified musical structures. Principal Themes of GEB: 1.Gödel's Theorem: Demonstrates the inherent limitations of formal systems and mathematics. 2.Escher's Oeuvre: Illustrates concepts of self-reference and visual paradox. 3.Bach's Music: Presents recursive patterns and repetitive structures, paralleling the Back model, which underscores recursion in musical architectures. 4.Recursion and Self-Reference: Central themes in artificial intelligence, linguistics, and cognitive systems. 5.Artificial Intelligence and Consciousness: Hofstadter hypothesizes that intelligence can emerge from formal systems, akin to how consciousness arises from neuronal activity. Hofstadter employs dialogues, enigmas, and logical games to guide the reader through intricate concepts in mathematics, music, and philosophy of mind. This study, then, aims to analyze the connections between Gödel, Escher, and Bach, and the concept of musical and linguistic recursion, with a particular focus on the link between Bach and musical recursivity, and the comparison to linguistic recursivity in the poetic text of Divine Comedy. This parallelism inevitably leads to an investigation of Sentiment Analysis, transferring Fibonacci's tool from tonal to phonal analysis, with the detection of phonal gradations that, in recursivity, generate emotions, vibrations, and sound structures capable of transmitting profound sensations.