{"corpus":"steiner","locus":"GA 324/1921-03-16/p032","lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"text":"One must really experience what goes on in one's soul when one makes mathematical formulas; one must experience this correctly. One must see that a mathematical formula actually is constructed within us. One must realize that this inner human construction has been achieved apart from the outer world, and yet in a sense it has brought one closer to the outer world. Even so, this inner mathematical construction cannot be regarded as inner reality as compared to what we find in the outer world. If this were not true, we would have the feeling that this mathematical construction contained true reality instead of a bland version of the outer world which it does actually present to us. Think what the situation would be if in our spiritual contemplation of a mathematical construction we had the whole content of the eyes' original experience in all its color intensity. If this were the case, we would experience in the formula itself the lighting up, the intensity of colors, when considering the wave theory, or “interference phenomena,” in mathematical form. This we certainly do not see. The fact that we do not see this proves that with our mathematical formulas we penetrate only to some degree into the outer world. We do come closer to it, but at the same time we no longer have the full reality of it.","text_trust":"verbatim","quote_safe":true,"title":"Lecture I","site_heading":"Mathematical Knowledge and the Path to Spiritual 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 Cite the unit by its title and locus, never by this heading, and do not quote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":"1921-03-16","location":null,"word_count":227,"url":"https://anthroposophy.ai/v1/steiner/en/ga/324/1921-03-16/p032","alignment_confidence":"low","alignment_reason":"count_diverges","two_voice_volume":false,"translation_credit":{"scope":"unit","status":"established","translator":"Walter Stuber and Mark Gardner","identified_edition":"MP1991","book_title":"Anthroposophy and Science","publisher":"Mercury Press","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA324/English/MP1991/19210316p01.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":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"url":"https://anthroposophy.ai/v1/steiner/en/ga/324/1921-03-16/p032","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":"1921-03-16","de_passages":[{"locus":"GA 324/1921-03-16/p023","url":"https://anthroposophy.ai/v1/steiner/de/ga/324/1921-03-16/p023"}],"bead_confidence":"high","pairing_state":"verified","verified":true,"evidence":["reader"],"reader_german":["GA 324/1921-03-16/p023"],"reader_part":true,"length_check":{"de_words":418,"en_words":358,"ratio":0.86,"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 324/1921-03-16/p023","passage_number":23,"text":"Wenn man richtig durchschaut, wie die Sehnsucht nach mathematischer Naturerklärung auf diesem innerlichen Aneignen der Außenwelt beruht, dann wird man nicht mehr übersehen können, wie man doch eine ganz andere Art von Erkenntnis hat in dem Mathematischen als in dem rein äußerlichen, sinnesgemäßen und die Sinneserfahrung verstandesmäßig zusammenfassenden empirischen Erkennen. Man geht tiefer in das menschliche Innere hinein mit dem mathematischen Erkennen und glaubt gerade dadurch der Außenwelt entsprechend näher zu kommen, man glaubt gerade dadurch eben innerlich zu erleben, was das Wesen der Außenwelt repräsentiert. Man macht nur dann die Erfahrung, daß man nun eigentlich mit dem, was man in mathematische Formulierung umgewandelt hat, im Grunde genommen die volle Fülle der Außenwelt verloren hat. Man muß sich bewußt sein: man verbindet dasjenige, was einem die Außenwelt gibt, mit etwas rein innerlich Konstruiertem. Und man muß dasjenige, was da eigentlich in der Seele vorgeht, wenn man mathematische Formulierungen macht, richtig erleben können. Man muß durchschauen, daß das Mathematische ein innerliches Menschheitserzeugnis ist, und daß man dennoch, trotzdem man es in diesem Mathematischen mit einem innerlichen Menschheitserzeugnis zu tun hat, dennoch ein Gefühl — wir werden später sehen, daß es eine Erkenntnis ist— davon hat, daß mit diesem innerlich mathematisch Konstruierten, das ganz abseits von der Außenwelt konstruiert wird, etwas gegeben ist, was uns näher an die Außenwelt heranbringt, als wir ihr sonst sind. Aber dennoch, wiederum kann dieses innerlich in solcher Weise mathematisch Konstruierte nicht innerliche Realität sein, wenigstens nicht unmittelbar innerliche Realität der realen Außenwelt gegenüber. Denn sonst müßte man, wenn man das mathematische Bild als Ergebnis der Forschungen vor sich hat, nicht das Gefühl haben, jetzt ist die volle Fülle der Außenwelt erblaßt und es steht nur die mathematische Formulierung da, sondern man müßte das Gefühl haben, man hat in dieser mathematischen Formulierung etwas, was innerlich erst recht Realität hat. Denken Sie einmal, wie anders die Sache läge, wenn wir das ganze Feld der Erlebnisse des Auges vor uns hätten mit aller intensiven Farbenempfindung, und wir würden dann noch, wenn wir mathematische Formulierung gepflogen haben, in dieser mathematischen Formulierung geistig dasjenige vor uns sehen, was wir erst aufgenommen haben. Wir würden in unseren mathematischen Formeln der Undulationstheorie die Farben aufblitzen, aufleuchten sehen, Interferenzerscheinungen erleben und so weiter. Das tun wir nicht. Daß wir es nicht tun, bezeugt uns, daß wir zwar die Außenwelt mit unseren mathematischen Formulierungen so durchdringen, daß wir ihr näherkommen, aber daß wir zu gleicher Zeit dies auf Kosten davon tun, daß wir die volle Wirklichkeit der Außenwelt eigentlich dann nicht mehr haben.","text_trust":"verbatim","quote_safe":true,"word_count":418,"url":"https://anthroposophy.ai/v1/steiner/de/ga/324/1921-03-16/p023"}],"english":["GA 324/1921-03-16/p031","GA 324/1921-03-16/p032"],"method":"reader","confidence":"high","correspondence":"established","length_check":{"de_words":418,"en_words":358,"ratio":0.86,"partial":false},"pairing_state":"verified","verified":true,"evidence":["reader"],"reader_german":["GA 324/1921-03-16/p023"],"reader_part":true},"witness_completeness":{"ratio":0.89,"band":"comparable","note":null,"word_count":5618,"original_word_count":6316,"may_be_abridged":false},"witness_quality":{"translator":{"scope":"unit","status":"recorded","translator":"Walter Stuber and Mark Gardner","identified_edition":"MP1991","book_title":"Anthroposophy and Science","publisher":"Mercury Press","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA324/English/MP1991/19210316p01.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 324/1921-03-16/p023"],"missing_from_translation":[],"present_only_in_translation":[],"bead_confidence":"high","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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