{"corpus":"steiner","locus":"GA 82/1922-04-08/p028","lang":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"text":"On looking back to the way in which we came to know in early childhood the structure of space—by walking and standing upright, by orientating ourselves to right and left, by learning to gauge the depth-dimension, by connecting all this with the abstractly perceived space of geometry (which the child learns to know from inner experience)—we realise the serious and important consequences that follow if we cannot look back to the living origin, within our own being, of space—of our conception and perception of space—but simply accept it in its already transformed shape, independent of ourselves. For example, in recent times we have come to regard this space (with its three dimensions) in such a way that we have gone on to postulate a fourth and higher dimensions. These spaces and their geometries are widely known to-day. Anyone who has once learnt to know the living structure of space finds it most interesting to follow such an extension of mathematical operations (applicable to three dimensions) and to arrive at a fourth dimension that cannot be visualised, and so on. These operations are logical (in the mathematical sense) and quite correct. But anyone who knows the genesis of our idea of space, as I have described it, will detect something quite special here. We could take a pendulum, for example, and watch it oscillate. Watching it purely externally, we might expect it to swing further and further out. But it does not. When it has reached a definite point, it swings back again to the opposite side. If we know the relation between the forces involved, we know that the pendulum oscillates and cannot go further because of the relation between the forces.","text_trust":"verbatim","quote_safe":true,"title":"2. The Position of Anthroposophy among the Sciences","site_heading":null,"date":"1922-04-08","location":null,"word_count":282,"url":"https://anthroposophy.ai/v1/steiner/en/ga/82/1922-04-08/p028","alignment_confidence":"low","alignment_reason":"count_diverges","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/SOL2025/19220408p01.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":"en","edition":"English","edition_basis":null,"is_original":false,"is_default_edition":true,"url":"https://anthroposophy.ai/v1/steiner/en/ga/82/1922-04-08/p028","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":"1922-04-08","de_passages":[{"locus":"GA 82/1922-04-08/p014","url":"https://anthroposophy.ai/v1/steiner/de/ga/82/1922-04-08/p014"}],"bead_confidence":"high","pairing_state":"verified","verified":true,"evidence":["reader"],"reader_german":["GA 82/1922-04-08/p014"],"reader_part":true,"length_check":{"de_words":468,"en_words":405,"ratio":0.87,"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 82/1922-04-08/p014","passage_number":14,"text":"Was Hellsehen auf höherem Gebiete ist, studieren kann es jeder Mensch am Mathematisieren. Und am meisten wundern könnte man sich darüber, daß gerade Mathematiker, die den Prozeß kennen sollten, der im Menschen vorgeht, wenn man mathematisiert, daß die nicht eigentlich ein tieferes Verständnis demjenigen entgegenbringen, was als ein höheres, qualitatives Mathematisieren in der hellsichtigen Forschung, wenn ich mich dieses Ausdrucks bedienen darf, aufzutreten hat. Denn dasjenige, was die erste Stufe dieser Forschung ist, die imaginative Erkenntnis, es ist nichts anderes als ein durch Übungen erlangtes Hineinschauen in noch andere Gebiete des Daseins, als das Mathematisieren es gestattet. Aber allerdings, es ändert sich so manches mit Bezug auf das menschliche Anschauen, wenn man diese ganze innere Natur des Mathematisierens einmal in wahrhaftiger menschlicher Selbsterkenntnis überschaut. Da kommt man nämlich zum Beispiel zu folgendem: Indem man darauf zurückblickt, wie man in der ersten Kindheit durch das Aufrechtgehen und Aufrechtstehen, durch das Orientieren von Links und Rechts, durch das Bestimmen der Tiefendimension zur Raumesstruktur gekommen ist, indem man daran anknüpft und den sonst nur abstrakt angeschauten Raum der Geometrie aus dem inneren menschlichen Erleben kennenlernt, da lernt man auch erkennen, welche verhängnisvollen Folgen eintreten, wenn man nicht zurückblicken kann auf dieses lebendige Hervorgehen des Raumes, der Vorstellung und der Anschauung des Raumes aus der Menschenwesenheit, sondern einfach den Raum schon in metamorphosierter Gestalt, unabhängig vom Menschen hinnimmt. Da ist man ja in der neueren Zeit dazu gekommen, diesen Raum in seinen drei Dimensionen so zu betrachten, daß man rein mathematisch zu einer vierten und zu weiteren Dimensionen übergegangen ist. Die mehrdimensionalen Räume und die Geometrien, die sich auf sie beziehen, sind ja heute etwas, was auch schon in weiteren Kreisen bekannt geworden ist. Aber für denjenigen, der nun die lebendige Gestaltung des Raumes einmal kennengelernt hat, ist es zwar außerordentlich interessant, so etwas zu verfolgen wie das Fortsetzen der Rechnungs- und Funktionsoperationen, die man für den dreidimensionalen Raum vornimmt, indem man gewisse Dinge erweitert, so daß man dann die nicht mehr anschaubare vierte Dimension bekommt und so weiter - diese Dinge sind mathematisch-logisch nicht nur interessant, sondern auch vollständig richtig -, aber für denjenigen, der eben so die Entstehung der Raumanschauung kennt, wie ich es beschrieben habe, für den liegt hier etwas ganz Besonderes vor. Wir können nämlich zum Beispiel, wenn ich diesen Vergleich gebrauchen darf, ein Pendel haben und das Pendel ausschlagen sehen. Wir können rein äußerlich dieses Ausschlagen des Pendels ansehen, und uns nun denken, das Pendel ginge im Ausschlagen immer weiter und weiter. Es tut es aber nicht. Wenn es an einem bestimmten Punkt angekommen ist, geht es wieder zurück nach der entgegengesetzten Seite. Wenn wir die Kraftverhältnisse kennen, die in dem Pendel leben, dann wissen wir, daß das Pendel eben oszilliert, daß es nicht einfach weitergehen kann wegen der in ihm liegenden Kr af t verhältniss e.","text_trust":"verbatim","quote_safe":true,"word_count":468,"url":"https://anthroposophy.ai/v1/steiner/de/ga/82/1922-04-08/p014"}],"english":["GA 82/1922-04-08/p027","GA 82/1922-04-08/p028"],"method":"reader","confidence":"high","correspondence":"established","length_check":{"de_words":468,"en_words":405,"ratio":0.87,"partial":false},"pairing_state":"verified","verified":true,"evidence":["reader"],"reader_german":["GA 82/1922-04-08/p014"],"reader_part":true},"witness_completeness":{"ratio":0.92,"band":"comparable","note":null,"word_count":6598,"original_word_count":7163,"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/SOL2025/19220408p01.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 82/1922-04-08/p014"],"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."}}