{"corpus":"steiner","locus":"GA 82/1922-04-12/p054","lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"text":"Things become interesting when they are followed mathematically and cross over into the physical, and much could still be contributed to the solution of borderline problems if these theories, which begin to become very real here, were developed. But there is still a terrible lack of understanding for this. For example, I once gave a lecture at a mathematical university society where I tried to introduce these things. I explained that if you have the asymptotes of a hyperbola here and the branches of the hyperbola here, what you have to imagine on the right here, spreading out, you have to imagine on the left here, spreading together, so that a complete reversal takes place. These things gradually lead to a more concrete treatment of space. But today there is little understanding for this. Even pure analysts often show a certain dislike of synthetic geometry. And this newer synthetic geometry is the way to get out of the purely formal mathematical and to the problem where one has to grasp the empirical. As long as one calculates with mere analytical geometry, one does not approach the realms of reality. There one has only developed the end points of the coordinates, the geometric location of the coordinates and so on. If one remains with constructing with the linear and with circles, then one stands in lines within them, but is compelled to take a certain visualization to help. This is what makes synthetic geometry so beneficial for getting out of the formal and showing how to think the mathematical in nature.","text_trust":"verbatim","quote_safe":true,"title":"6. Anthroposophy and Agnosticism","site_heading":null,"date":"1922-04-12","location":null,"word_count":260,"url":"https://anthroposophy.ai/v1/steiner/en/ga/82/1922-04-12/p054","alignment_confidence":"high","alignment_reason":"beads:identity","two_voice_volume":false,"translation_credit":{"scope":"unit","status":"established","translator":"Steiner Online Library","identified_edition":"SOL2025","book_title":"So That Man may Become Fully Human","publisher":"Steiner Online Library","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA082/English/SOL2025/19220412p01.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/82/1922-04-12/p054"},{"lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"url":"https://anthroposophy.ai/v1/steiner/en/ga/82/1922-04-12/p054","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},"paired_german":{"status":"paired","german":[{"locus":"GA 82/1922-04-12/p054","passage_number":54,"text":"Die Dinge werden, wenn sie mathematisch verfolgt werden und ins Physikalische hinüberkommen, interessant, und manches würde gerade zur Lösung von Grenzproblemen auch noch beigetragen werden können, wenn man einmal diese Theorien, die hier anfangen sehr real zu werden, ausbilden würde. Allein, dafür ist noch furchtbar wenig Verständnis vorhanden, Ich habe zum Beispiel einmal in einer mathematischen Universitätsgesellschaft einen Vortrag gehalten, wo ich versuchte, an diese Dinge heranzuführen. Ich habe ausgeführt, daß, wenn man hier die Asymptoten einer Hyperbel hat und hier die Hyperbeläste, man sich dasjenige, was man sich hier rechts vorzustellen hat, und zwar auseinandersprühend, hier links vorzustellen hat zusammensprühend, so daß eine völlige Umkehr stattfindet. Diese Dinge führen allmählich hinaus in eine konkretere Behandlung des Raumes. Aber man findet dafür heute wenig Verständnis. Man findet vielfach sogar bei reinen Analytikern eine gewisse Abneigung gegen die synthetische Geometrie. Und diese neuere synthetische Geometrie ist einmal der Weg, aus dem rein formalen Mathematischen herauszukommen zu dem Problem, wo man das Empirische fassen muß. Solange man mit der bloßen analytischen Geometrie rechnet, kommt man nicht an die Gebiete der Wirklichkeit heran. Da hat man nur die Endpunkte der Koordinaten ausgebildet, den geometrischen Ort der Koordinaten und so weiter. Bleibt man beim Konstruieren beim Linearen und bei Kreisen, dann steht man in Linien darinnen, ist aber genötigt, eine gewisse Anschaulichkeit zu Hilfe zu nehmen. Das ist das, was synthetische Geometrie so wohltätig macht, um herauszukommen aus dem Formalen und zu zeigen, wie man das Mathematische in der Natur darinnen zu denken hat.","text_trust":"verbatim","quote_safe":true,"word_count":250,"url":"https://anthroposophy.ai/v1/steiner/de/ga/82/1922-04-12/p054"}],"english":["GA 82/1922-04-12/p054"],"method":"identity","confidence":"high","correspondence":"established","length_check":{"de_words":250,"en_words":260,"ratio":1.04,"partial":false},"pairing_state":"verified","verified":true,"evidence":["length","meaning","audit"]},"witness_completeness":{"ratio":1.04,"band":"comparable","note":null,"word_count":12477,"original_word_count":12023,"may_be_abridged":false},"witness_quality":{"translator":{"scope":"unit","status":"recorded","translator":"Steiner Online Library","identified_edition":"SOL2025","book_title":"So That Man may Become Fully Human","publisher":"Steiner Online Library","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA082/English/SOL2025/19220412p01.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 82/1922-04-12/p054"],"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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