Never be embarrassed. I do it all the time ;) I'd be walking home from work, focussing hard not to walk. Just staring blindly ahead, allowing auto-pilot to take me home, and focus on every sensation of every muscle in every part of my body.
Then again, this was in Hong Kong, where you see groups of oldies doing Taichi and what-not in every corner of the city. I still do it occasionally here in Vancouver, the city of Yoga, so it's still fine ;)