Apparently there is a new name out for a phenomenon which you see every day - and this is people playing on your mobile phone while talking to someone. I don't think there is a word yet for playing on your iPad while talking- maybe it will be pudding.
I am afraid I am frequently guilty of both and it does seem to annoy some people - especially those of my own generation. It is not that I am disinterested in what the person is telling me. It is simply that I can't concentrate on anything unless there are several streams of input going to to my head at once. If I didn't have distractions I would end up day dreaming and drifting off and then I really would miss what the other person is saying.
Cognitive psychology uses the term the ascending reticular activation system for nuclei within the brain stem which regulate arousal. People whose ARAS is set a high level of activity need peace and quiet to reduce their arousal levels and are most likely to be introverts. People whose ARAS is set at a low level quest for stimulation and need a high level of social interaction and novel experiences.
Despite the traditional association with nerdyness computers and social networks actually provide a great potential for additional interaction and stimulation for people who need it.
When I check out messages or emails when I am talking to someone I am usually looking for information which will be useful to them within the context of our current conversation. Sometime something you have just been sent can answer a query or problem someone has come to you with. Sometimes when you are in a conversation with several other people dropping out for part of the conversation which isn't relevant to you to answer an email is actually a good use of time in a very fast paced world.
So- What is the answer to the phubbing problem. I guess for me the short term answer is to tell people why I am looking at something and make it clear that I am not just ignoring them or getting bored.
Ultimately, however, I think a better answer is something like Google Glass- where you have a screen display which nobody else can see. Then they wont know what media sources you are receiving. Or better still - a direct computer link into your brain. From there its on to full scale cyberization which is hopefully not so far on the future that I won't get to enjoy it.