I have had a smartphone for about 7 years now, and for at least the last 4 or 5, I had it *permanently* silenced; I mean NO ringers, NO bloops or blurps, no dings, no rings, NO notifications, no vibrations... NOTHING, because someone ELSE'S "urgent" ain't MY "urgent".
I trained myself by deliberately using an old clamshell phone for about a decade. When I switched to a smartphone a few years ago, I had zero need for anything else but a basic phone and a browser (for local bus, train, and metro timetables and public transport travel planner, which happens to be excellent here, and very useful because I use public transport exclusively). I do not have anything personal installed on the thing, especially not email.
When I go for a walk in the nearby park, or go grocery shopping, that thing ain't coming with me.
On the other hand, I've never had any kind of interest or urge to be on social media like Twatter, Fakebook, Instagrand, or such.
When I was younger, before the turn of the century, having grown up in the frozen wastelands of the far north where one went to the local library for information, and recently gained access to the scientific knowledge and research from all around the world, I did use to be afraid of falling behind. The sphere of human activity is so large that the daily advancements in knowledge seemed to indicate an inhuman rate of expansion of that sphere.. but it isn't. If you have true understanding (as opposed to memorization), and stay out of your field for a few years, all you need is a few weeks to completely catch up. The boundary is large and therefore the volume expansion rate is utterly amazing, but in any single field, the boundary is nothing you cannot catch up to even at a leisurely pace.
What changes at a hard-to-understand rate, is human opinion and politics. But, once you accept being plain ol' yourself and drop the need to go with the apparent flow, even that is not at all important, just feels silly. My point is, there is no need to fear of falling behind, and no need to be continuously "connected". Much better to be yourself and stop to smell the flowers once in a while. I only wish somebody had told me this when I was younger.