To think about something deeply and at length, often turning it over repeatedly in one's mind.
From the verb 'mull' meaning to ponder or meditate, possibly related to 'mull' meaning to grind or pulverize. The phrase emerged in the 19th century, suggesting the slow, thorough mental grinding of ideas like grain in a mill.
The grinding metaphor is perfect - just as a mill slowly breaks grain into flour through repeated action, mulling breaks complex problems into digestible thoughts through patient, repetitive consideration. It's mental slow food.
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