To wave or shake something, usually a weapon like a sword or gun, in a bold or threatening way, or to display something proudly.
From Old French 'brandir,' based on Old Norse 'brandr' (sword or fire). The word originally meant to swing a sword in combat, then generalized to mean any showy or aggressive display.
A knight brandishing a sword and someone brandishing their new phone are doing the exact same ancient gesture of 'look at what I have and you should be impressed or afraid'—it's the human peacock display encoded in one word.
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