Really, instead of doing nothing for 24 hours or even 2 minutes try to really concentrate on what you're doing for a change. People - all people, not just programmers - are wired to do stuff, not to do nothing. And it's surprisingly hard to give something your full attention.
We are far too easily distracted and 'doing nothing' is just as hard as concentrating on one task for the exact same reason: you are easily distracted.
The attempt to concentrate fully on a productive task is a far more useful way to spend that time, and it doesn't have to be some 'set' time either.