Edit: I am now much more relaxed about people looking at their phones during conversations. This TEDx talk speaks about how our devices are augmenting our minds, in the way that a hammer or sword augments our body. I prefer to interact with upgraded humans, thanks.
Every time you look at your smartphone screen at a social occasion, you are signalling to everybody around you that you would rather be someplace else. You would rather have a shallow communication with someone who is not present than you would a deep connection with anybody in the room. You focus on something else enormously insult everyone present.
In a modern society where more are connected than ever before, people feel more alone than ever before.This random post also talks about digital isolation.