段 is a compound ideograph: 殳 (a hand-held weapon / tool) on the right + 厂 (a cliff / hillside) on the left. The original meaning was concrete and craft-related: striking a stone hillside with a tool to carve out steps — quarrying or stair-cutting. From this physical labor of cutting steps into stone grew the abstract meanings: physical step → grade / rank / level → stage of progress → paragraph (a step in a text). The semantic chain runs cleanly from carving stone steps to organizing prose.

Korean reading "dan." 段階 (dangye, stage / phase — used for project phases, life stages, education levels), 階段 (gyedan, stairs — physical staircase), 手段 (sudan, "hand-step" = means / method — Machiavellian sense: "the end justifies the means"), 一段 (ildan, "one step / first step" — adverbial: 일단 ildan = "first / for now / initially"), 段落 (danrak, paragraph — used in writing instruction), 三段論法 (samdan-nonbeop, "three-step method" = syllogism — formal logic term).

Mandarin duàn, 4th tone. 段 (duàn, section / paragraph / stretch), 段落 (duànluò, paragraph), 阶段 (jiēduàn, stage / phase), 手段 (shǒuduàn, means / method). Crucially, 段 functions as a measure word in Mandarin for stretches of time, narrative, road, or speech: 一段时间 (yī duàn shíjiān, "a stretch of time"), 一段路 (yī duàn lù, "a section of road"), 一段话 (yī duàn huà, "a passage of speech"). The 段 measure word counts continuous extents.

Japanese on-reading ダン (dan) — 段階 (dankai, stage), 階段 (kaidan, stairs), 手段 (shudan, means / method), 段落 (danraku, paragraph). And distinctively in Japanese culture: 段 names the formal grading system in martial arts, board games, and traditional crafts. 黒帯三段 (kuro-obi sandan, "black-belt third dan") in karate, judo, kendo. 囲碁五段 (igo godan, "fifth dan in Go") for board games. Even traditional arts like ikebana and shogi assign dan rankings up to perhaps tenth dan. The 段 system gives Japanese practitioners a graded path of competency public to all. The 段 below black-belt level is 級 (kyū, "grade") — 級 counts down (e.g. 三級 third grade is below first grade), then 段 counts up after one reaches expert level.

Memory aid: a hand-tool (殳) carving steps into a hillside (厂) — physical steps became metaphorical stages, paragraphs, ranks.