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.

翻译：科学革命始于一种排除。为使自然在数学上可处理，伽利略剥离了科学世界模型中的质性特征——颜色、声音、味觉、触感——仅保留容许数值化表征的部分。四个世纪后，这些质性特征仍未得到解释。它们构成了意识的"困难问题"：为何及如何物理加工会产生感受性体验这一谜题。意识量化视界理论（QHT）提出，这一谜题源于数学描述本身的结构必然性。量化模型仅能捕捉现实的量化特征。当某处空无一物时，模型赋值为零；当存在可量化对象时，模型赋予数值；但当存在不可量化对象——即感受质——时，模型将退化：产生奇点。QHT将神经动力学信息几何中的奇点识别为现象体验的数学指纹：这是量化描述无法触及的量化视界。基于此，QHT推导出意识的标志性属性——不可言说性、私密性、主观性、统一性与因果效力——并为判定哪些系统具有意识提供了基质独立的标准。该理论避免了泛心论，作出可检验的预测，并对人工智能与人工意识提出具体启示。其核心直觉——奇点对应于感受性体验——可能已由斯里尼瓦瑟·拉马努金所预见。