{"corpus":"steiner","locus":"GA 206/1921-07-22/p027","lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"text":"Now let us consider mathematical truths, the truths of geometry. A superficial observer would say: Oh yes, of course man gets his mathematics out of his head, or from somewhere or other (ideas on the subject are not very precise). But it is not so. Mathematics derives from an altogether different sphere. And if you study the human being, you will get to know the sphere from which mathematics comes. It is from the sense of movement and the sense of balance. It is from such depths that mathematical thought comes, depths to which we no longer penetrate with our ordinary soul-life. What enables us to develop mathematics lives at a deeper level than our ordinary soul-life. And thus we see that mathematics is really rooted in that part of us which is at the same time cosmic. In fact, we are only really subjective in what lies here (see diagram) from the sense of sight upwards. In respect of what lies down there we are like logs, as much so as the rest of the outer world. Hence we can never say that geometry, for instance, has anything of a subjective nature in it, for it originates from that in us wherein we ourselves are objective. It is concerned with the very same space which we measure when we walk, and which our movements communicate to us—the very same space which, when we have elicited it from ourselves in pictorial form, we then proceed to apply to what we see. Nor can there be any question of describing space as in any way subjective, for it does not come from the sphere whence the subjective arises.","text_trust":"verbatim","quote_safe":true,"title":"Lecture I","site_heading":"The Twelve Senses: Mapping Human Perception and Consciousness","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 Cite the unit by its title and locus, never by this heading, and do not quote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":"1921-07-22","location":null,"word_count":277,"url":"https://anthroposophy.ai/v1/steiner/en/ga/206/1921-07-22/p027","alignment_confidence":"medium","alignment_reason":"beads:length","two_voice_volume":false,"translation_credit":{"scope":"unit","status":"established","translator":"Dorothy Lenn","identified_edition":"APC1958","book_title":"Man as a Being of Sense and Perception","publisher":"Anthroposophical Publishing Co.","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA206/English/APC1958/19210722p01.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/206/1921-07-22/p027"},{"lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"url":"https://anthroposophy.ai/v1/steiner/en/ga/206/1921-07-22/p027","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":"1921-07-22","de_passages":[{"locus":"GA 206/1921-07-22/p026","url":"https://anthroposophy.ai/v1/steiner/de/ga/206/1921-07-22/p026"}],"bead_confidence":"medium","pairing_state":"proposed","verified":false,"length_check":{"de_words":269,"en_words":277,"ratio":1.03,"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 206/1921-07-22/p026","passage_number":26,"text":"Wir haben mathematische Wahrheiten, geometrische Wahrheiten. Ein oberflächliches Menschenbetrachten denkt: Nun ja, der Mensch nimmt aus seinem Kopfe oder irgendwo heraus — nicht wahr, so bestimmt sind ja die Vorstellungen nicht, die man sich da macht — die Mathematik. — Aber das ist ja nicht so. Diese Mathematik kommt aus ganz andern Gebieten. Und wenn Sie den Menschen betrachten, so haben Sie ja die Gebiete gegeben, aus denen das Mathematische kommt: Es ist der Gleichgewichtssinn, es ist der Bewegungssinn. Aus solchen Tiefen herauf kommt das mathematische Denken, bis zu denen wir nicht mehr hinreichen, hinuntergehen mit unserem gewöhnlichen Seelenleben. Unter unserem gewöhnlichen Seelenleben lebt dasjenige, was uns heraufbefördert, was wir in mathematischen Gebilden entfalten. Und so sehen wir, daß das Mathematische eigentlich wurzelt in dem, was in uns zugleich kosmisch ist. Wir sind ja wirklich subjektiv nur mit dem, was vom Sehsinn hier nach aufwärts liegt; mit dem, was da hinunter liegt, wurzeln wir in der Welt. Wir sind darinnen in der Welt; mit dem, was aber darunter liegt, sind wir wie ein Holzklotz, ebenso wie die ganze übrige Außenwelt. Wir können daher niemals sagen, daß zum Beispiel die Raumlehre irgend etwas Subjektives haben könnte, denn sie entspringt aus dem in uns, worinnen wir selber objektiv sind. Es ist genau derselbe Raum, den wir durchmessen, wenn wir gehen und den uns unsere Bewegungen vermitteln, genau derselbe Raum, den wir dann, wenn wir ihn im Bilde aus uns herausgebracht haben, auf das Angeschaute verwenden. Vom Raume kann auch nicht die Rede sein, daß er irgendwie etwas Subjektives sein könnte, denn er entspringt nicht jenem Gebiete, aus dem das Subjektive entspringt.","text_trust":"verbatim","quote_safe":true,"word_count":269,"url":"https://anthroposophy.ai/v1/steiner/de/ga/206/1921-07-22/p026"}],"english":["GA 206/1921-07-22/p027"],"method":"length","confidence":"medium","correspondence":"established","length_check":{"de_words":269,"en_words":277,"ratio":1.03,"partial":false},"pairing_state":"proposed","verified":false},"witness_completeness":{"ratio":1.02,"band":"comparable","note":null,"word_count":5289,"original_word_count":5188,"may_be_abridged":false},"witness_quality":{"translator":{"scope":"unit","status":"recorded","translator":"Dorothy Lenn","identified_edition":"APC1958","book_title":"Man as a Being of Sense and Perception","publisher":"Anthroposophical Publishing Co.","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA206/English/APC1958/19210722p01.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 206/1921-07-22/p026"],"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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