To confuse or muddle someone's thinking; to become rotten or spoiled (said of eggs).
From Old English 'adela' (filth, mud). The word evolved to mean 'muddled thinking' because mud clouds clear water, then extended to describe eggs that spoil and become rotten inside.
Eggs can literally 'addle'—if a bird sits on an unfertilized egg for too long, the contents turn into a murky, rotten mess, which is why we call confused thinking 'addled'—your brain becomes as mushy as a rotten egg!
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