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琴里がいるのは、士道たちのいる天宮アリーナから縦方向に距離を隔てること一万五〇〇〇メートル、夜闇の中に浮遊する空中艦<フラクシナス>の艦橋だった。

Hi. What is the function of the こと here? I have never seen the construction “verb+こと+数量”. Is it a fixed pattern? Thank you.

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It is a fixed and rather bookish expression. It originated from 漢文訓読 tradition, a translation method to read Chinese text word-by-word in Japanese. Japanese needs all elements before the main verb, but Chinese put some adjuncts after the verb and the object, like English. In this case, it is customary to parse it as if the verb is an outer subject to the adjunct.

不絶如縷 "as protracted as a thread" → 絶えざること縷のごとし
処門下三年 "be a follower for three years" → 門下に処ること三年
君美甚 "you are handsome, very much" → 君の美しきこと甚だし

This becomes a fixed pattern to focus on the adverbial element, emphasizing how much the degree or amount is, not limited to numbers.

感動することしきりだった "deeply I was grateful"
心強いことこの上ない "more than ever it is reassuring"
世話になったこと数知れず "countless times one owes to somebody"
悪戦苦闘すること半日 "a half day of hard struggle"

Note that the style itself is a part of idiom, so no particle follows こと.

  • Thank you. By the way, could you translate the three expressions? And which part is the adverbial element? 感動することしきりだった 心強いこと限りない 世話になったこと数知れず – chino alpha Aug 6 '20 at 14:02
  • @chinoalpha Edited, improved a bit. – broken laptop Aug 7 '20 at 6:05

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