{"corpus":"steiner","locus":"GA 73a/1920-06-17/p082","lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"text":"Rudolf Steiner: Dearly beloved attendees, who can really prove the Pythagorean theorem? The Pythagorean theorem cannot be proved by drawing a right-angled triangle on the blackboard and then using one of the usual methods to prove it. That is only one illustration of the proof. The point is that anyone who wants to prove the Pythagorean theorem is forced to have what can be constructed mathematically in their inner vision - even if only in the inner vision of the geometric spatial vision. So imagine a consciousness that did not have this spatial vision. He would not have before him the substantial element of that Pythagorean proposition, and it would be quite senseless to prove the Pythagorean theorem. We can only prove the Pythagorean theorem by having before us the substantial element of the conception and shaping of space. The moment we ascend to another form of consciousness, something else is added to the ordinary view of space. [...] The point, then, when it comes to the Pythagorean theorem, if it is to be proved, is that this view of space must underlie it. But for this it is first necessary to find one's way, as it were, into this new configuration of consciousness. But as long as one has no conception of the configuration of space, one cannot arrive at the observation that leads to the proof of the Pythagorean theorem. And one believes that the results of spiritual scientific research cannot be proved in the same way only as long as one has not yet made the transition from ordinary consciousness to the experiencing consciousness that I have described.","text_trust":"verbatim","quote_safe":true,"title":"15. Spiritual Science, Natural Science and Technology","site_heading":null,"date":"1920-06-17","location":null,"word_count":271,"url":"https://anthroposophy.ai/v1/steiner/en/ga/73a/1920-06-17/p082","alignment_confidence":"high","alignment_reason":"beads:identity","two_voice_volume":false,"translation_credit":{"scope":"unit","status":"established","translator":"Steiner Online Library","identified_edition":"SOL2024","book_title":"Scientific Disciplines and Anthroposophy","publisher":"Steiner Online Library","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA073a/English/SOL2024/19200617p01.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/73a/1920-06-17/p082"},{"lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"url":"https://anthroposophy.ai/v1/steiner/en/ga/73a/1920-06-17/p082","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},"other_renderings":{"loci":[{"locus":"GA 75/1920-06-17","ga":"75","lecture":"1920-06-17","kind":"reprint","relation":"the same text served under another volume (a reprint or another edition)"}],"note":"The same lecture is also served at the loci listed, each with how it relates to this one. They are ONE witness, not independent attestations: quote the rendering you fetched, and do not cite another as corroborating it. Wording differs between translations, so a quotation found in one need not occur in the other."},"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."},"witness_completeness":{"ratio":1.02,"band":"comparable","note":null,"word_count":15311,"original_word_count":15001,"may_be_abridged":false},"witness_quality":{"translator":{"scope":"unit","status":"recorded","translator":"Steiner Online Library","identified_edition":"SOL2024","book_title":"Scientific Disciplines and Anthroposophy","publisher":"Steiner Online Library","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA073a/English/SOL2024/19200617p01.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 73a/1920-06-17/p082"],"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. See witness_completeness for how much of the original this witness holds."}}