The behavior, conduct, or practices characteristic of a clown; foolish or ridiculous behavior treated as a systematic activity.
From clown + -age (a suffix meaning 'a system, practice, or collection of,' as in baggage, vintage, or heritage). Medieval and early modern word formation creating abstract nouns from concrete ones.
The '-age' suffix is amazingly productive in English—add it to almost any noun and you've got a new abstract concept. 'Clownage' sounds Shakespearean because it kind of is—writers in that era loved inventing these words.
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