To think over carefully; to ponder or consider thoughtfully.
Originally meaning 'to grind or pulverize' from Middle English, related to 'mill'. The metaphorical sense of grinding over thoughts in one's mind developed in the 19th century, creating the modern meaning of careful consideration.
The connection between 'mulling' thoughts and 'mulling' wine isn't coincidental - both involve a slow, warming process that transforms the original material into something richer and more complex.
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