Hmm. Well I certainly hope that messing around in the pip-boy menu pauses. Can't stand all these modern games that have gone to "doesn't pause ever", generally due to them being built on an online/multiplayer core (ARPGs like Path Of Exile, for instance). Not having the ability to check out your inventory, read notes, etc, without feeling some kind of pressure to rushrushrush would be really annoying.
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What I wonder is how a phone app will communicate with the game. Will the game itself have some sort of Bluetooth communication code built in? Will there be a need to have your game and phone both logged in to some online service? Something else?
(will I be able to run it on my iPad? Don't have a smartphone....)
edit: actually, aside from messing with it once or twice for novelty's sake, I doubt I'd use it anyway. Waste of battery power.... if I'm playing a game on my computer, why divide my attention to my mobile device, including having to make sure it doesn't go to sleep/etc. Seems like just an opportunity for confusion & inefficiency. The in-game pip-boy is much more convenient.