The first time Martha encountered the Doctor, when he accosted her in the street and took his tie off at her, she wondered if he was high on drugs. The odd behaviour, the manic grin… maybe he’d been smoking pot or something. Or maybe he was an escaped lunatic. Whatever; he definitely wasn’t playing with a full deck.
Later, after the hospital being transported to the moon, the space rhinos, and the bikers in black, she decided she’d been wrong. The Doctor lived more completely in the moment than anyone she’d ever met. She wanted to experience that for herself.