{"corpus":"steiner","locus":"GA 165/1916-01-16/p009","lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"text":"Tertullian developed a certain way of thinking. He had to break out of the old, clairvoyant way of thinking and come to a clear understanding of concepts and their relationship to realities, including higher, spiritual realities. I would like to insert an episode here that will help you to see not what Tertullian became aware of, but what dominated his thinking. I will insert a purely intellectual episode, but I ask you to take it very much to heart. I do the following. I write the number 1 and then its double 2, 2 - 4, 3 - 6, etc. And now imagine: I do not stop at all, I keep writing, that is, I write to infinity. How many such numbers would I have written then? Infinitely many, aren't they! But how many have I written here? Have I written a number on the right for every number on the left? Without a doubt, I have written exactly as many numbers on the right as I have written on the left, and if I continue into infinity, there would always be a number on the right for every number on the left. But now imagine: every number on the right is also on the left. But that means nothing other than: I have as many numbers on the right as I have on the left, but at the same time I have only half as many numbers on the right as on the left. Because it is quite obvious that there must always be one in between two numbers that are double, I must have only half as many numbers on the right as on the left. One is always left out, that is obvious, so I can only have half as many on the right as on the left. That is obvious. But consider that one is always missing, that 1, 3, 5, 7 and so on are missing, so half the numbers are missing on the right! So I only have half as many on the right as on the left. Nevertheless, I have exactly the same number of numbers as on the left. That is to say: as soon as I enter infinity, half is equal to the whole. That is quite clear: as soon as I enter infinity, half is equal to the whole – you cannot escape it. As soon as you enter infinity with your concepts from the finite, something like that comes out by itself, that half is equal to the whole. You can write all the numbers on the left and all the square numbers on the right: 1 - 1, 2 - 4, 3 - 9, 4 - 16, 5 - 25. Certainly there is a square number for every number, but as true as many numbers are missing here, it can only be a part. Think about it: after all, it is always only the square numbers.","text_trust":"verbatim","quote_safe":true,"title":"Second Lecture","site_heading":"Bridging Clairvoyance and Reason: The Trinity's Emergence","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":"1916-01-16","location":null,"word_count":488,"url":"https://anthroposophy.ai/v1/steiner/en/ga/165/1916-01-16/p009","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":"The Conceptual World and Its Relationship to Reality","publisher":"Steiner Online Library","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA165/English/SOL2025/19160116p01.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/165/1916-01-16/p009"},{"lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"url":"https://anthroposophy.ai/v1/steiner/en/ga/165/1916-01-16/p009","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 165/1916-01-16/p009","passage_number":9,"text":"Tertullian bildete sich namentlich eine gewisse Art und Weise zu denken aus. Er mußte heraus aus dem alten Hellseherischen, er mußte über die Begriffe und ihre Beziehungen zu Wirklichkeiten, auch zu höheren, geistigen Wirklichkeiten, ins klare kommen. Ich will hier eine Episode einschalten, aus der Sie ersehen sollen, nicht was Tertullian sich bewußt gemacht hat, aber was in seinem Denken waltete. Ich will eine rein denkerische Episode einschalten, die ich Sie aber bitte, sich recht sehr zu Gemüte zu führen. Ich mache folgendes. Ich schreibe die Zahl 1 und dann ihr Doppeltes 2, 2 — 4, 3 — 6 usw. Und nun denken Sie sich: ich höre gar nicht mehr auf, ich schreibe immer fort, das heißt, ich schriebe bis ins Unendliche hinein. Wieviel solche Zahlen hätte ich denn da geschrieben? Unendlich viele, nicht wahr! Wieviel habe ich denn aber hier geschrieben? Habe ich zu jeder Zahl links eine Zahl rechts geschrieben? Ganz zweifellos, ich habe genau ebensoviel Ziffern rechts geschrieben, wie ich links geschrieben habe, und wenn ich in alle Unendlichkeit hinein fortfahre, immer würde es zu der Zahl links eine Zahl rechts geben. Aber nun denken Sie sich: Jede Zahl, die hier rechts steht, die steht da links auch. Das heißt aber doch nichts anderes als: ich habe da rechts so viel Zahlen, als ich links Zahlen habe, aber zu gleicher Zeit habe ich nur halb so viel Zahlen rechts als links. Denn es ist doch ganz selbstverständlich, es muß immer zwischen zwei Zahlen, die das Doppelte sind, eine drinnen liegen, ich muß rechts nur halb so viel Zahlen haben als links. Es ist immer eine ausgelassen, das ist doch klar, also kann ich rechts nur halb so viele haben als links. Das ist doch einzusehen. — Aber denken Sie, daß doch immer eine fehlt, daß 1, 3, 5, 7 und so weiter fehlt, also die Hälfte der Zahlen fehlt rechts! Also habe ich doch rechts nur halb so viel als links. Dennoch habe ich gerade so viele Zahlen als links. Das heißt: Sobald ich ins Unendliche hineinkomme, ist die Hälfte gleich dem Ganzen. Das ist ganz klar: Sobald ich ins Unendliche hineinkomme, ist die Hälfte gleich dem Ganzen — man entkommt dem gar nicht. Sobald man mit seinen Begriffen von dem Endlichen ins Unendliche hineingeht, kommt so etwas von selbst heraus, daß die Hälfte gleich dem Ganzen ist. Sie können hier links alle Zahlen schreiben und rechts alle Quadratzahlen: 1 — 1, 2 — 4, 3 — 9, 4 — 16, 5 — 25. Gewiß gibt es zu jeder Zahl eine Quadratzahl, aber so wahr als hier viele Zahlen fehlen, kann bier nur ein Teil sein. Denken Sie sich: es sind ja doch immer nur die Quadratzahlen.","text_trust":"verbatim","quote_safe":true,"word_count":450,"url":"https://anthroposophy.ai/v1/steiner/de/ga/165/1916-01-16/p009"}],"english":["GA 165/1916-01-16/p009"],"method":"identity","confidence":"high","correspondence":"established","length_check":{"de_words":450,"en_words":488,"ratio":1.08,"partial":false},"pairing_state":"verified","verified":true,"evidence":["length","meaning","anchors","audit"]},"witness_completeness":{"ratio":1.02,"band":"comparable","note":null,"word_count":9551,"original_word_count":9343,"may_be_abridged":false},"witness_quality":{"translator":{"scope":"unit","status":"recorded","translator":"Steiner Online Library","identified_edition":"SOL2025","book_title":"The Conceptual World and Its Relationship to Reality","publisher":"Steiner Online Library","publisher_inferred":true,"match_score":1.0,"source_url":"https://www.rsarchive.org/Lectures/GA165/English/SOL2025/19160116p01.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 165/1916-01-16/p009"],"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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