To exhaust yourself through overwork or excessive activity, becoming worn out and frayed around the edges.
The phrase dates to the early 20th century, combining 'run' in the sense of operating continuously with 'ragged,' meaning torn or frayed. The imagery evokes clothing or fabric becoming tattered from overuse, applied metaphorically to a person's physical and mental state.
This phrase beautifully captures the visual of literal raggedness - imagine a piece of cloth being pulled and stretched until its edges fray and tear. The metaphor suggests that humans, like fabric, have limits to how much stress and activity they can endure before showing wear.
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