{
    "schema": "prokopton42-public-passage-v1",
    "id": "einstein.geometry_experience_fr",
    "canonical_url": "https://prokopton42.com/en/works/einstein/geometry-experience-fr/reference-section-0016/",
    "language": "en",
    "title": "Geometry and Experience, French Translation",
    "author": "Albert Einstein",
    "date": "1921 lecture",
    "summary": "Einstein asks how axiomatic geometry, valid by deduction, can describe physical bodies and measurements. This French translation clarifies the difference between a formal system, practical geometry, and the choice of a framework for relativity.",
    "learning": "Distinguish axiomatic from practical geometry, understand the role of reference bodies, and connect physical measurement, curvature, and relativity theory.",
    "long_summary": "The lecture first separates mathematical propositions, whose certainty follows from conventions, from physical claims tested by experience. Rulers, rigid bodies, and light rays then connect geometrical concepts with the observed world.\n\nGeneral relativity makes this relation more difficult because matter distribution and gravitational field affect measured geometry. The text does not say every geometry is equivalent; it clarifies what experience can decide once physical definitions are fixed.",
    "historical_context": "The corpus manifests do not yet establish the precise place and circumstances of composition. The images below document the author’s world or the text’s transmission. They do not claim to show the exact scene of writing.",
    "material_world_label": "World of the world wars, 1914-1945",
    "material_world": {
        "technology": "Electricity, internal combustion, steel, aviation, radio, cinema, and mass production transform civilian life and warfare.",
        "science": "Relativity, quantum physics, chemistry, psychology, and genetics reshape knowledge within powerful institutions that are sometimes militarized.",
        "medicine": "X-rays, surgery, transfusion, antisepsis, and early antibiotics save more lives without universal access.",
        "transport": "Rail, cars, trams, ocean liners, and aircraft coexist. Armies mechanize mobility rapidly.",
        "agriculture": "Tractors, fertilizers, and breeding advance; rationing, blockade, and requisition expose fragile supplies.",
        "communication": "Telephone, telegraph, radio, newsreels, and newspapers reach mass audiences; propaganda and censorship use the same networks.",
        "clothing": "Suits, shorter dresses, coats, and hats coexist with uniforms and workwear. Shortages simplify cuts and materials."
    },
    "material_world_scenes": [
        {
            "asset": "/assets/timeline/landmarks/26-1939-ce/world-01.webp",
            "title": "Technology, science, and care",
            "description": "Electricity, internal combustion, steel, aviation, radio, cinema, and mass production transform civilian life and warfare. Relativity, quantum physics, chemistry, psychology, and genetics reshape knowledge within powerful institutions that are sometimes militarized. X-rays, surgery, transfusion, antisepsis, and early antibiotics save more lives without universal access."
        },
        {
            "asset": "/assets/timeline/landmarks/26-1939-ce/world-02.webp",
            "title": "Travel and communication",
            "description": "Rail, cars, trams, ocean liners, and aircraft coexist. Armies mechanize mobility rapidly. Telephone, telegraph, radio, newsreels, and newspapers reach mass audiences; propaganda and censorship use the same networks."
        },
        {
            "asset": "/assets/timeline/landmarks/26-1939-ce/world-03.webp",
            "title": "Farming and food",
            "description": "Tractors, fertilizers, and breeding advance; rationing, blockade, and requisition expose fragile supplies."
        },
        {
            "asset": "/assets/timeline/landmarks/26-1939-ce/world-04.webp",
            "title": "Clothing, women and men",
            "description": "Suits, shorter dresses, coats, and hats coexist with uniforms and workwear. Shortages simplify cuts and materials."
        }
    ],
    "intellectual_tradition": {
        "id": "science",
        "label": "Science and scientific thought"
    },
    "period": {
        "id": "contemporary",
        "label": "Contemporary era"
    },
    "languages": [
        "fr",
        "en"
    ],
    "manifestations": [
        {
            "coverage": "complete",
            "file": "data/corpus/normalized/einstein/geometry_experience_fr/representations/fr.ndjson",
            "language": "fr",
            "records": 18,
            "role": "complete_source_selection",
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            "source_id": "geometry_experience_fr"
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            "file": "data/corpus/normalized/einstein/geometry_experience_fr/representations/ai-generated/en-gpt-5-6-sol-corpus-passage-translation-v1.ndjson",
            "generated_on": "2026-09-11",
            "language": "en",
            "model": "gpt-5.6-sol",
            "official_status": "non_official",
            "prompt_version": "corpus-passage-translation-v1",
            "provider": "codex_subscription",
            "records": 18,
            "role": "ai_generated_translation_non_official",
            "sha256": "0d69628dfdb08d5ed09cfd47b5d9d035b1c0d24804a85de74913e02288940b26",
            "source_id": "prokopton42-codex-translation:gpt-5.6-sol:corpus-passage-translation-v1",
            "translation_type": "ai_generated_translation"
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    ],
    "concepts": [
        {
            "id": "anger",
            "label": "Anger"
        },
        {
            "id": "empirical_test",
            "label": "Empirical test"
        },
        {
            "id": "family",
            "label": "Family"
        },
        {
            "id": "geometry_physics",
            "label": "Geometry and physical experience"
        },
        {
            "id": "invariance",
            "label": "Physical invariance"
        },
        {
            "id": "law",
            "label": "Law"
        },
        {
            "id": "messiah",
            "label": "Messiah"
        },
        {
            "id": "reason",
            "label": "Reason"
        }
    ],
    "source_work_ids": [
        "einstein.geometry_experience_fr"
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    "passages": 18,
    "word_count": 4856,
    "word_counts_by_language": {
        "en": 4856,
        "fr": 5129
    },
    "editorial_status": "gpt_5_6_semantic_draft_v1",
    "structure": {
        "citation_scheme": "source-section-v1",
        "kind": "native",
        "levels": [
            {
                "key": "section",
                "label_fr": "Section",
                "label_en": "Section"
            }
        ],
        "leaf_fr": "Section",
        "leaf_en": "Section"
    },
    "canonical_passage_id": "passage:einstein.geometry_experience_fr:section-0016",
    "canonical_ref": "section-0016",
    "canonical_parent_ref": null,
    "canonical_parent_id": null,
    "representations": [
        {
            "language": "fr",
            "text": "Nous demandons maintenant : Quelles sont les lois de position des ombres des petits disques L′ sur le plan E ? Eh bien, exactement les mêmes que les lois de position des petits disques L sur la surface de la sphère. Car à chaque figure originale sur K correspond une figure d’ombre sur E. Si deux petits disques se touchent sur K, leurs ombres se touchent de même sur E. La géométrie des ombres sur le plan concorde avec la géométrie des petits disques sur la sphère. Si nous considérons les ombres des petits disques comme des figures rigides, la géométrie sphérique est valable par rapport à celles-ci sur le plan E. Il faut noter particulièrement que le plan est fini par rapport aux ombres des petits disques, étant donné que les ombres ne peuvent trouver place sur le plan qu’en nombre fini. Mais on pourrait nous dire : « Cela est absurde ; les ombres des petits disques ne sont précisément pas des figures rigides. Il nous suffirait de déplacer une règle sur le plan E pour nous convaincre que les ombres deviennent de plus en plus grandes, lorsqu’elles glissent sur le plan de S vers l’infini. » Mais qu’arriverait-il si les règles sur le plan E se comportaient de la même façon que les ombres des petits disques L′ ? Alors on ne pourrait plus constater que les ombres croissent en s’éloignant de S ; cette affirmation n’aurait plus aucun sens. La seule chose qu’on puisse énoncer objectivement sur les ombres des petits disques est précisément qu’elles se comportent, géométriquement, exactement de la même façon que de petits disques rigides sur la surface de la sphère dans le sens de la géométrie euclidienne. Il faut bien dire que notre affirmation sur l’accroissement des ombres des petits disques, quand elles glissent de S vers l’infini, n’a en elle-même aucune signification objective, tant que nous n’avons pas pris comme termes de comparaison des corps rigides euclidiens qui peuvent être déplacés sur E. Le point S sur le plan est, par rapport aux lois de position des ombres L′, aussi peu privilégié que sur la surface de la sphère.",
            "translator": "Maurice Solovine",
            "source_id": "geometry_experience_fr",
            "translation_type": "historical_translation"
        },
        {
            "language": "en",
            "text": "We now ask: what are the positional laws of the shadows L′ of the small disks on the plane E? They are exactly the same as the positional laws of the small disks L on the surface of the sphere. For every original figure on K corresponds to a shadow figure on E. If two small disks touch on K, their shadows likewise touch on E. The geometry of the shadows on the plane agrees with the geometry of the small disks on the sphere. If we regard the shadows of the small disks as rigid figures, spherical geometry is valid for them on the plane E. It should be noted in particular that the plane is finite with respect to the shadows of the small disks, since only a finite number of shadows can find room on the plane.\n\nBut we might be told: “This is absurd; the shadows of the small disks are precisely not rigid figures. We need only move a ruler over the plane E to convince ourselves that the shadows become larger and larger as they glide over the plane from S toward infinity.” But what would happen if the rulers on the plane E behaved in the same way as the shadows L′ of the small disks? It would then no longer be possible to determine that the shadows grow as they recede from S; the assertion would no longer have any meaning. The only objective statement that can be made about the shadows of the small disks is precisely that, geometrically, they behave in exactly the same way as small rigid disks on the surface of the sphere in the sense of Euclidean geometry. We must indeed say that our assertion concerning the growth of the shadows of the small disks as they glide from S toward infinity has in itself no objective meaning so long as we have not adopted as standards of comparison Euclidean rigid bodies that can be moved over E. With respect to the positional laws of the shadows L′, the point S on the plane is no more privileged than any point on the surface of the sphere.",
            "translator": "Codex gpt-5.6-sol",
            "edition": "Prokopton42 non-official AI translation, 2026-09-11",
            "source_id": "prokopton42-codex-translation:gpt-5.6-sol:corpus-passage-translation-v1",
            "translation_type": "ai_generated_translation",
            "official_status": "non_official",
            "generation_model": "gpt-5.6-sol"
        }
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}