Now time for my rebuttal...
First of all, let's assume that an iPad has a reliability of 95%, and an iPhone also of 95%. I believe both are higher than that. Let's also assume that the built in IFR rated GPS with WAAS capabilities has a reliability of 99%. What is the probability that all three will disappear in a puff of smoke, permanently (not talking about a temporary loss of signal or crash)? Yes, indeed, it is 0.0025%. A rather small number, a number I would say is significantly less than the probability that your engine will stop turning or even, for some of you old codgers buzzing around up there, better odds than your tickers continuing for the duration of the flight.
But let's assume all three die. It is a very unpleasant day. Luckily we have something called a radio. And if it is not a complete pile of junk that you're flying, you may even have two radios! Wonderful!
You: Um, ATC dude, 6PC here
(Try to sound old and use a hick accent if you can, Texan always works well. If you sound old and senile, they will cut you some slack).
ATC Dude: 6PC, go ahead.
You: Er, my iPhone died on me and I demand a vector to the nearest airport
(Remember he works for you, he is your own personal *****, even though the MFers in Washington aren't paying him right now)
ATC Dude: 6PC, squawk XXXX and ident.
You: Okey dokey
ATC Dude: 6PC, radar contact XX miles NW of YY VOR, nearest airport is KABC 20 miles at a heading of 240.
See how easy that is? No paper required.
Some of you probably needed blankey's as kids. I understand, this is your blankey. You probably also didn't get enough time at your Mama's teat. I heard you can get a large rubber teat that you can hang up on one side and comfort yourself occasionally.
Try to wean yourself off paper. You will survive, I promise.
It will be alright.