Abstract

The scientific revolution began with an exclusion. To make nature mathematically tractable, Galileo stripped the scientific model of the world of its qualities—colors, sounds, tastes, feels—leaving only what admits of numerical characterization. Four centuries later, the qualities remain unexplained. They are the “hard problem” of consciousness: the enigma of why and how physical processing gives rise to felt experience. The Quantification Horizon Theory of Consciousness (QHT) proposes that this enigma arises from a structural necessity of mathematical description itself. Quantitative models can only capture quantifiable features of reality. Where there is nothing, a model assigns zero; where there is something quantifiable, it assigns a value; but where there is something unquantifiable—a quale—the model degenerates: it produces a singularity. QHT identifies singularities in the information geometry of neural dynamics as the mathematical fingerprint of phenomenal experience: a quantification horizon beyond which quantitative description cannot reach. From this basis, QHT derives the hallmark properties of consciousness—ineffability, privacy, subjectivity, unity, and causal efficacy—and provides substrate-independent criteria for determining which systems are conscious. The theory avoids panpsychism, makes testable predictions, and offers concrete implications for artificial intelligence and artificial consciousness. Its core intuition—that singularities correspond to felt experience—may have been foreshadowed by Srinivasa Ramanujan.