A person waving in your direction briefly gives you a choice between hope and embarrassment.

A raised hand in your direction sets up a small, fast dilemma. Wave back and risk being wrong; do nothing and risk having ignored someone. The stakes are almost zero and the discomfort is real, which says something about how much we care about small social exposure.

The generous move is usually to risk the embarrassment. Being briefly foolish costs you nothing that lasts, and failing to acknowledge someone who meant it can sting them for longer than you would guess. When in doubt, wave, and let yourself be the person who was wrong in the friendly direction.