Where Does the "I" Live: From the Metaphor of the Strange Loop to the Hopf Fiber
Zenodo (CERN European Organization for Nuclear Research) April 2, 2026 Roman Radchenko
Douglas Hofstadter's strange loop—a self-referential structure moving through hierarchical levels back to its start—has long been a metaphor for consciousness. This essay proposes that the Hopf fibration, a 1931 mathematical structure, offers the most elegant formal language for this idea, though not a proof. In the Hopf fibration, a loop, two hierarchical levels, an indestructible link, and continuous transitions all arise from a single construction. The argument draws on topological data analysis of brain dynamics, EEG null-spike computations, and geometry in brain activity, distinguishing formal, analogical, and speculative parts.