{"corpus":"steiner","locus":"GA 300a/1921-01-16/p071","lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"text":"Dr. Steiner: Well, that is a more general question. It is not a good idea to use things in projective geometry that do not exist. There are no light rays and still less shadow rays. It is not necessary to work with such concepts in teaching projections. You should work with spatial forms. There are no light rays and no shadow rays. There are cylinders and cones. There are shadows that arise when I place a cone at an angle and illuminate it from a point and allow a shadow to fall upon an appropriately angled plane. Then I have a shadow form. The form of the shadow as such is the boundary of the shadow, and even a child should understand that. It is the same later in projective geometry when the child learns what occurs when a cylinder cuts through another with a smaller diameter. It is very useful to teach children that, but it does not detract from the artistic. It guides children into the artistic. It makes their imagination flexible. You can imagine flexibly if you know what section occurs when two cylinders intersect one another. It is very important to teach these things, but not as abstractions. A teacher asks about plane geometry.","text_trust":"verbatim","quote_safe":true,"title":"Twenty-Second Meeting","site_heading":null,"date":"1921-01-16","location":null,"word_count":208,"url":"https://anthroposophy.ai/v1/steiner/en/ga/300a/1921-01-16/p071","alignment_confidence":"medium","alignment_reason":"beads:length+anchor_constrained","two_voice_volume":false,"translation_credit":{"scope":"unit","status":"established","translator":"Ruth Pusch and Gertrude Teutsch","identified_edition":"AP1998","book_title":"Faculty Meetings with Rudolf Steiner I","publisher":"Anthroposophic Press","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA300a/English/AP1998/19210116d01.html","evidence":"lecture_list_row","publisher_note":"The publisher is inferred from the edition code in this lecture's source URL, not stated by the source page. The translator IS verified for this lecture: its own source names the translator (evidence: the lecture's page, rsarchive's lecture list, or the cover of the book it was published in), and that page's text was matched against this unit (see match_score and source_url). Cite the translator with confidence; attribute the publisher only as probable."},"edition_coverage":{"de":["original"],"en":["English"]},"available_versions":[{"lang":"de","edition":"original","edition_basis":null,"is_original":true,"is_default_edition":true,"url":"https://anthroposophy.ai/v1/steiner/de/ga/300a/1921-01-16/p071"},{"lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"url":"https://anthroposophy.ai/v1/steiner/en/ga/300a/1921-01-16/p071","paragraph_aligned":true}],"record":{"record_type":"unknown","scope":"volume","note":"How this text was taken down (shorthand transcript, listeners' notes or manuscript) is not on record here. Unknown is not an assurance of a stenogram: check the edition's own notes before resting an argument on one word.","evidence":null,"evidence_translation":null,"evidence_source":null},"authorship":{"kind":"dialogue","is_steiner":true,"speaker":"Rudolf Steiner","note":"A labelled turn in a transcript: this passage is Rudolf Steiner's own speech, not a questioner's."},"german_anchor":{"de_prefix":"1921-01-16","de_passages":[{"locus":"GA 300a/1921-01-16/p110","url":"https://anthroposophy.ai/v1/steiner/de/ga/300a/1921-01-16/p110"},{"locus":"GA 300a/1921-01-16/p111","url":"https://anthroposophy.ai/v1/steiner/de/ga/300a/1921-01-16/p111"},{"locus":"GA 300a/1921-01-16/p112","url":"https://anthroposophy.ai/v1/steiner/de/ga/300a/1921-01-16/p112"}],"bead_confidence":"medium","pairing_state":"proposed","verified":false,"length_check":{"de_words":218,"en_words":208,"ratio":0.95,"partial":false},"correspondence":"established","note":"English passage numbering is edition-relative, so the same number need not name the same paragraph in the German. The German original passage(s) above are the edition-invariant anchor — fetch them (lang='de') to verify wording before quoting across editions."},"paired_german":{"status":"paired","german":[{"locus":"GA 300a/1921-01-16/p110","passage_number":110,"text":"RUDOLF STEINER: Das ist nun ja eine allgemeinere Frage. Es ist nicht gut, Dinge gerade jetzt in der projektiven Geometrie anzuwenden, die es nicht gibt. Es gibt keine Lichtstrahlen, noch weniger Schattenstrahlen. Das ist nicht nötig, dass man mit diesen Begriffen in der Projektionslehre arbeitet. Man sollte arbeiten mit gestalteten Rauminhalten. Es gibt nicht Lichtstrahlen und Schattenstrahlen. Es gibt Zylinder und Kegel. Es gibt [einen] Schattenkörper, der entsteht, wenn ich einen Kegel habe, der schief ist und von einem Punkt beleuchtet wird, und den Schatten auffallen lässt auf eine geneigte Ebene. Dann habe ich einen Schattenkörper, der da ist. Diesen Schattenkörper als solchen, die Kurvenbegrenzung des Schattenkörpers, das sollte auch schon das Kind verstehen. Geradeso, wie es später in der projektiven Geometrie verstehen muss, wenn ein Zylinder [einen anderen mit] kleinerem Durchmesser durchschneidet. Das ist ungemein nützlich, die Kinder dies zu lehren. Es bringt nicht ab vom Künstlerischen. Es lässt die Kinder im Künstlerischen. Es macht das Vorstellen geschmeidig. Man kann geschmeidig vorstellen, wenn man von vornherein weiß, was für eine Schnittkurve entsteht, wenn sich Zylinder durchschneiden. Das ist ganz wichtig, dass man diese Dinge bringt, aber nicht Abstraktionen.","text_trust":"verbatim","quote_safe":true,"word_count":189,"url":"https://anthroposophy.ai/v1/steiner/de/ga/300a/1921-01-16/p110"},{"locus":"GA 300a/1921-01-16/p111","passage_number":111,"text":"*KARL STOCKMEYER spricht über darstellende Geometrie.*","text_trust":"verbatim","quote_safe":true,"word_count":6,"url":"https://anthroposophy.ai/v1/steiner/de/ga/300a/1921-01-16/p111"},{"locus":"GA 300a/1921-01-16/p112","passage_number":112,"text":"RUDOLF STEINER: Da bin ich vielleicht mitten [in die Stunde] hineingekommen. Da würde ich in diesem Teil finden, dass man anschaulicher vorgehen soll.","text_trust":"verbatim","quote_safe":true,"word_count":23,"url":"https://anthroposophy.ai/v1/steiner/de/ga/300a/1921-01-16/p112"}],"english":["GA 300a/1921-01-16/p071"],"method":"length+anchor_constrained","confidence":"medium","correspondence":"established","length_check":{"de_words":218,"en_words":208,"ratio":0.95,"partial":false},"pairing_state":"proposed","verified":false},"witness_completeness":{"ratio":0.82,"band":"watch","note":"This witness is somewhat shorter than the original. Minor omissions or condensation are possible.","word_count":6495,"original_word_count":7946,"may_be_abridged":false},"witness_quality":{"translator":{"scope":"unit","status":"recorded","translator":"Ruth Pusch and Gertrude Teutsch","identified_edition":"AP1998","book_title":"Faculty Meetings with Rudolf Steiner I","publisher":"Anthroposophic Press","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA300a/English/AP1998/19210116d01.html","evidence":"lecture_list_row","publisher_note":"The publisher is inferred from the edition code in this lecture's source URL, not stated by the source page. The translator IS verified for this lecture: its own source names the translator (evidence: the lecture's page, rsarchive's lecture list, or the cover of the book it was published in), and that page's text was matched against this unit (see match_score and source_url). Cite the translator with confidence; attribute the publisher only as probable."},"entity_parity":{"status":"ok","checked_against":["GA 300a/1921-01-16/p110","GA 300a/1921-01-16/p111","GA 300a/1921-01-16/p112"],"missing_from_translation":[],"present_only_in_translation":[],"bead_confidence":"medium","note":"Every load-bearing name in the German counterpart appears in this English passage. That is a check on NAMES only: a translation can keep every name and still reverse who acts on whom, change a number, or soften a claim. Read the German for anything you intend to rest an argument on."},"note":"quote_safe certifies the bytes of this text. This block is about the translation as a WITNESS: who made it, and whether it carries the same names as the original. See witness_completeness for how much of the original this witness holds."}}