Plural of fatuity; instances or examples of extreme foolishness or the quality of being absurdly stupid and senseless.
From Latin 'fatuus' (foolish, insipid) through Old French, adding the plural suffix '-ies', which changes '-ty' to '-ties' in English.
The concept of 'fatuity' was especially popular in 18th and 19th century literature to describe the breathtaking stupidity of characters—it's almost a genteel way to call someone an idiot.
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