Man without a head

L’Homme Sans Tête, a short by Juan Diego Solanas (2003).
Spoiler alert: watch, then read. To see the film in a better resolution, in one part and with English subtitles, try here.
A futuristic world, set between us and a 1984.
A man with no head. At least some people must share his problem; heads are advertised and sold. Yet, the man seems to be the only one not wearing any.
A woman. She has one on.
The man has tickets for le bal. Before his rendez-vous, he is shopping for a head.
What does he need it for?
To see?
To kiss?
To smell?
By the end, the man looks most like himself, most real, when headless.