{"corpus":"steiner","locus":"GA 326/1922-12-26/p010","lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"text":"Try to sense the tremendous difference between this mathematical feeling bound to human experience, and the bare, bleak mathematical space layout of analytical geometry, which establishes a point somewhere in abstract space, draws three coordinating axes at right angles to each other and thus isolates this thought-out space scheme from all living experience. But man has in fact torn this thought-out spatial diagram out of his own inner life. So, if we are to understand the origin of the later mathematical way of thinking that was taken over by science, if we are to correctly comprehend its self-sufficient presentation of structures, we must trace it back to the self-experienced mathematics of a bygone age. Mathematics in former times was something completely different. What was once present in a sort of dream-like experience of three-dimensionality and then became abstracted, exists today completely in the unconscious. As a matter of fact, man even now produced mathematics from his own three-dimensionality. But the way in which he derives this outline of space from his experiences of inward orientation is completely unconscious. None of this rises into consciousness except the finished spatial diagram. The same is true of all completed mathematical structures. They have all been severed from their roots. I chose the example of the space scheme, but I could just as well mention any other mathematical category taken from algebra or arithmetic. They are nothing but schemata drawn from immediate human experience and raised into abstraction.","text_trust":"verbatim","quote_safe":true,"title":"Lecture III","site_heading":"Mathematics, Blood Experience, and the Birth of Modern Science","site_heading_note":"A heading the site wrote for this unit from a summary of it; not in the edition, and not the words of Rudolf Steiner or of the translator. Cite the unit by its title and locus, never by this heading, and do not quote it.","date":"1922-12-26","location":null,"word_count":244,"url":"https://anthroposophy.ai/v1/steiner/en/ga/326/1922-12-26/p010","alignment_confidence":"medium","alignment_reason":"beads:length","two_voice_volume":false,"translation_credit":{"scope":"unit","status":"established","translator":"Maria St. Goar","identified_edition":"AP1985","book_title":"The Origins of Natural Science","publisher":"Anthroposophic Press","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA326/English/AP1985/19221226p01.html","evidence":"lecture_page_line","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/326/1922-12-26/p010"},{"lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"url":"https://anthroposophy.ai/v1/steiner/en/ga/326/1922-12-26/p010","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},"german_anchor":{"de_prefix":"1922-12-26","de_passages":[{"locus":"GA 326/1922-12-26/p008","url":"https://anthroposophy.ai/v1/steiner/de/ga/326/1922-12-26/p008"}],"bead_confidence":"medium","pairing_state":"proposed","verified":false,"length_check":{"de_words":252,"en_words":244,"ratio":0.97,"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 326/1922-12-26/p008","passage_number":8,"text":"Man muß nur einmal empfinden, was für ein gewaltiger Unterschied besteht zwischen dieser an das menschliche Erleben gebundene mathematischen Empfindung und dem kahlen, öden mathematischen Raumschema der analytischen Geometrie, die irgendwohin in einen abstrakten Raum einen Punkt stellt, drei aufeinander senkrechte Koordinatenachsen zieht und das erdachte Raumschema von allem Erleben abgesondert hat. Aber dieses erdachte Raumschema hat sich der Mensch erst aus seinem eigenen Innenleben herausgerissen. So daß man tatsächlich die Entstehung der späteren mathematischen Anschauungsweise, die dann die Naturwissenschaft ergriffen hat, wenn man sie richtig verstehen will in ihrem selbstgenugsamen Hinstellen ihrer Gebilde, daß man sie ableiten muß aus der erlebten Mathematik einer früheren Zeit. Die Mathematik einer früheren Zeit war eben etwas ganz anderes. Und dasjenige, was einmal vorhanden war in einem, ich möchte sagen, traumhaften Erleben der inneren Dreidimensionalität und was sich dann verabstrahiert hat, das ist heute völlig im Unbewußten vorhanden. In der Tat ist es auch heute beim Menschen noch so, daß er sich die Mathematik aus seiner eigenen inneren Dreidimensionalität herausholt. Aber dieses Herausholen des Raumschemas aus demjenigen, was der Mensch an innerer Orientierung erlebt, geschieht auf völlig unbewußte Weise. Davon kommt nichts ins Bewußtsein herauf. Ins Bewußtsein kommt herauf zum Beispiel das fertige Raumschema, wie überhaupt alle fertigen, von ihrer Wurzel abgelösten mathematischen Gebilde. Ich habe das Beispiel des Raumschemas gewählt. Ich könnte ebensogut irgendeine andere mathematische Kategorie anführen, auch noch mathematische Kategorien aus der Algebra, aus der Analysis, aus der Arithmetik. Sie sind nichts anderes, als aus unmittelbarem menschlichem Erleben ins Abstrakte heraufgeholte Schemata.","text_trust":"verbatim","quote_safe":true,"word_count":252,"url":"https://anthroposophy.ai/v1/steiner/de/ga/326/1922-12-26/p008"}],"english":["GA 326/1922-12-26/p010"],"method":"length","confidence":"medium","correspondence":"established","length_check":{"de_words":252,"en_words":244,"ratio":0.97,"partial":false},"pairing_state":"proposed","verified":false},"witness_completeness":{"ratio":1.0,"band":"comparable","note":null,"word_count":4571,"original_word_count":4559,"may_be_abridged":false},"witness_quality":{"translator":{"scope":"unit","status":"recorded","translator":"Maria St. Goar","identified_edition":"AP1985","book_title":"The Origins of Natural Science","publisher":"Anthroposophic Press","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA326/English/AP1985/19221226p01.html","evidence":"lecture_page_line","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 326/1922-12-26/p008"],"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. 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