Making loud, persistent, or annoying noise; repeatedly saying something forcefully until it is internalized.
From din (loud noise) + -ing gerund/present participle suffix. The continuous action of creating the kind of repetitive noise or insistent speech described by din.
Psychologically, 'dinning' something into someone's head is disturbingly effective—repetition through noise and force is exactly how propaganda and advertising work, which is why the word appears so often in dystopian literature describing social control mechanisms.
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