The Geometry of Sensibilities — Geometria Sensibilitatum: De Historiae Olfactoriae Reconstructione Riemanniana

The subtlety of nature is greater many times over than the subtlety of the senses and understanding. — Francis Bacon, Novum Organum, I, Aphorism X (1620) --- This article proposes a methodological framework for applying Riemannian geometry — specifically, the pipeline of Geometric Intelligence (GI) theory (Étale Cohomology, 2026) — to the history of sensibilities (histoire des sensibilités) as founded by the third generation of the French Annales school. The works of Alain Corbin (Le Miasme et la Jonquille, 1982; Les Cloches de la terre, 1994), Roselyne Rey (Histoire de la douleur, 1993), and Georges Vigarello (Le propre et le sale, 1985) stand among the most accomplished achievements of qualitative historical scholarship of the past century. They extended the reach of historical enquiry from politics and economics to sensation, the body, and affect. Yet their methodology possesses no instrument capable of measuring the structural transformation of a sensory space — its depth, its velocity, its spatial heterogeneity, its tipping points. The present article addresses this gap through three contributions. First, it proposes three methodological pathways for the mise en variété of qualitative sources — the conversion of historical texts (sanitary reports, correspondence, medical treatises, police ordinances) into numerical representations from which Riemannian manifolds may be constructed via variational autoencoder: Pathway A (embedding by natural language processing), Pathway B (manual coding by the historian, following the conceptual categories established by Corbin's own qualitative analysis), and Pathway C (their combination, governed by a principle of triangulation). Second, it presents a proof of concept on synthetic data. Twelve Parisian quartiers across fifteen decadal periods (1750–1900), encoded in eight variables drawn from the conceptual framework of Le Miasme et la Jonquille, are submitted to the full GI pipeline. All four conditions of Proposition 2. 1 (compactness, C∞ smoothness, full-rank Jacobian, injectivity) are verified. The Lie derivative analysis yields the principal quantitative finding: Haussmann's grands travaux (1853–1870) produced a degree of olfactory structural transformation — measured by the Frobenius norm of the Lie derivative of the pullback metric — 2. 74 times that of sewer improvements alone. The Pasteurian revolution, a cognitive rather than physical transformation, produced a factor of 1. 75. Both results are consonant with Corbin's central thesis that olfactory experience is a socially constituted phenomenon whose transformation proceeds as much from a shift in medical paradigm as from a modification of the material substrate. Third, it sets out with equal clarity the limits of the undertaking. The loss of information attendant upon the conversion of text to number is irreducible. The applicability of language models to eighteenth-century French is subject to verification. The manifold hypothesis is not guaranteed a priori for textual data. Mathematical abstraction inevitably eliminates the singularity of individual sources. The article maintains throughout that mathematical analysis supplements historical interpretation; it does not supplant it. The article bridges two historiographic traditions — cliometrics (Fogel, North) and the history of sensibilities (Corbin, Rey) — that have until now remained strangers to each other. It responds, eighty years later, to Lucien Febvre's 1941 call for 'new tools' (outils nouveaux) for the history of sensibility — and, in a longer perspective, to the aspiration stated by Francis Bacon in the Novum Organum: that the subtlety of nature, which exceeds the subtlety of unaided sense, may yet be rendered legible by a new instrument. IMPORTANT: The synthetic dataset does not substitute for analysis of actual historical sources. The proof of concept demonstrates computational feasibility, not historical findings. The accompanying Python code (proofₒfconcept. py), provided separately, permits full reproducibility of all numerical results. --- Français Le présent article jette les fondements méthodologiques d'une application de la géométrie riemannienne — le pipeline de la théorie de l'Intelligence Géométrique — à l'histoire des sensibilités de l'École des Annales. Une preuve de concept sur données synthétiques démontre la faisabilité computationnelle: les grands travaux haussmanniens produisent un degré de transformation structurelle olfactive 2, 74 fois supérieur au seul curage des égouts. L'article jette un pont entre la cliométrie et l'histoire des sensibilités, et répond à l'appel de Lucien Febvre (1941) pour des « outils nouveaux ». --- 日本語 本論文は、フランス・アナール学派の「感性の歴史」にGI理論のリーマン幾何学的枠組みを適用する方法論的基盤を構築する。オスマンのパリ改造の嗅覚構造変革度が下水道整備単独の2. 74倍であることを定量的に示した。計量歴史学と感性の歴史を架橋し、フェーヴル (1941) の「新しい道具」の要請に応答する。 --- Related publications: • Étale Cohomology, Geometric Intelligence, Volume 1 (DOI: 10. 5281/zenodo. 19140918) • Étale Cohomology, Geometric Intelligence, Volume 2 (DOI: 10. 5281/zenodo. 19157891) • Étale Cohomology, La géométrie des sensibilités (French edition, published separately on Zenodo) • Étale Cohomology, 感性の幾何学 (Japanese edition, published separately on Zenodo)