{ "schema": "prokopton42-public-passage-v1", "id": "einstein.geometry_experience_fr", "canonical_url": "https://prokopton42.com/en/works/einstein/geometry-experience-fr/reference-section-0013/", "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", "sha256": "3a748e133d47ea6432dfccc3d07e5565929a1883971b6b070aa8e9c0f6bc962b", "source_id": "geometry_experience_fr" }, { "coverage": "complete", "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" } ], "concepts": [ { "id": "empirical_test", "label": "Empirical test" }, { "id": "geometry_physics", "label": "Geometry and physical experience" }, { "id": "invariance", "label": "Physical invariance" }, { "id": "law", "label": "Law" } ], "source_work_ids": [ "einstein.geometry_experience_fr" ], "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-0013", "canonical_ref": "section-0013", "canonical_parent_ref": null, "canonical_parent_id": null, "representations": [ { "language": "fr", "text": "Un autre exemple d’un continu infini est le plan. Nous pouvons disposer sur un plan de petites pièces de carton de telle façon qu’à chaque côté d’un carré de carton soit appliqué un autre carré de carton. La construction ne sera jamais finie ; on peut toujours ajouter de nouveaux carrés de carton — à condition que leurs lois de disposition soient conformes à celles des figures planes de la géométrie euclidienne. Le plan est ainsi infini par rapport aux carrés de carton. On dit en conséquence que le plan est un continu infini à deux dimensions et que l’espace en est un à trois dimensions ; je suppose qu’on sait parfaitement ce qu’il faut entendre ici par nombre de dimensions.", "translator": "Maurice Solovine", "source_id": "geometry_experience_fr", "translation_type": "historical_translation" }, { "language": "en", "text": "Another example of an infinite continuum is the plane. We can arrange small pieces of cardboard on a plane in such a way that another cardboard square is placed against every side of each cardboard square. The construction will never be finished; new cardboard squares can always be added, provided that the laws governing their arrangement conform to those of the plane figures of Euclidean geometry. The plane is thus infinite with respect to the cardboard squares. Accordingly, the plane is said to be an infinite two-dimensional continuum, and space an infinite three-dimensional continuum; I assume that it is perfectly well understood what is meant here by the number of dimensions.", "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" } ], "content_checksum": "8cb9f432d2bd6d1e863bb813fdea9321346147aa2ffe44dcebec7295a59fc392" }