Blushing is caused by the dilation of blood vessels in the facial skin at times
Darwin considered it “the most peculiar and most human of all expressions”, and it appears to be unique to ourselves. That’s at least partly because we are rare in having our facial skin exposed to the scrutiny of others (though bald uakari monkeys deploy their bright red faces as signals of physiological health).
Moreover, embarrassment is a highly complex emotion that requires knowing what others are thinking about you, which may well be beyond the ken of any other species.
It remains a mystery why evolution should favour a signal that is effectively an admission of guilt, though there’s evidence that, after making a social faux pas, people are regarded more sympathetically if they blush.
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