My SIM card is damaged, and since it's registered under my ex and I need her to get replacement (and she's busy), I've been without GSM connectivity for 2 weeks now.
At first I felt really clueless, like an addict craving to check email and nothing to bury my head in while waiting for train.
But then I start using my "new" free time to let my mind wander and brainstorm for ideas, or simply close my eyes and nap. I feel more in control. I'm not entirely disconnected though, I still use the Wifi at work/home.
Obviously I still need a SIM card. I can't do internet banking since they always send SMS verification, and I can't use Uber since the app doesn't allow me to attach notes to the driver (they always call me right after I book to pinpoint my location).
Having this experience makes me realize how a smartphone can make you dumb (or, at least, make you always occupied).