"Make up the top one's head" is an idiomatic expression that means to come up with an answer or idea quickly, without giving it much thought. There are numerous synonyms for this phrase, including "spur of the moment," "off the cuff," "impromptu," "ad lib," "extemporaneous," "unrehearsed," and "unplanned." All these synonyms suggest that something is done spontaneously without any prior preparation. When people use such expressions, they try to emphasize that they are giving their honest opinion, and they haven't researched or calculated any data beforehand. These phrases are particularly useful when people are discussing opinions, views, and judgments.
