Topologies of the Word: Recursion and Emotional Calculation

This work emerges from a research pathway that connects Gödel’s formal recursion, the emotional recursion intrinsic to linguistic mechanisms, and the mathematical structure of quantum foam as the natural transition from human language to formal computation. Only recently have I recognized that recursion—identified by Gödel as the generative core of logical thought—is also an emotional and perceptual process: a returning movement, an echo that appears in poetry, music, phonology, and in the hidden patterns of consciousness. A scientific dialogue with Michel Planat’s models (SU(2)ₖ, Graph Coverings, Anyon Hypothesis) revealed that this recursion is not merely linguistic or cognitive, but topological. In the quantum foam, the minimal structure of matter is already a network of relations, a fabric of interference and resonance: the same fabric that shapes poetic form, emotional resonance, and phonological rhythm. From this insight emerges the central idea: recursion is the zero point of knowledge, the deep unity linking: - poetic language (Silvestri, Bittner) - emotional calculation (Bacchia, Ribas) - rigidity and memory of bodies (Ivanov) - topological structures (Planat) - formal logical systems (Gödel) - symbolic AI architectures.