Notifications that interrupt a person the very instant a network event occurs are less and less the most effective ways to inform people.
I think that it's entirely possible for computers to encourage focus and clear thinking, rather than unprioritized interruption.
Linda Stone coined the term "continuous partial attention" several years ago, mostly to describe the world of IM/email. Automated notifications cause people to continually scan for interesting information and then adapt their mental state to choose among these activities. This happens at a cost; giving something your partial attention simply doesn't let you accomplish as much.
Lately I'm feeling utterly lost in these types of activities, and I remember reading a few years ago about Don Knuth's self-described Batch Mode for writing, lecturing, and responding to communications. He simply refuses to switch tasks more than every so often, and the outside world keeps reading his books and articles, and generally regarding him highly.
Similarly for CPUs: when an application inundates a CPU with interrupts (as do simple network cards and disk controllers), we typically see the CPU grind to a crawl. The fix is to put a buffering controller in front--not a complex device, but enough to buffer a few ethernet frames or DMA a bit of disk activity, so the CPU can do some regular work between packets of information.
Even our model for task switching on a computer involves relatively few task-switches a second. The external impression of a computer is of one that's "multitasking" but it's really just time-slicing, and at a coarse granularity (sometimes up to a second is spent on one task.)
So what we've done to ourselves is something that fails in many other circumstances, even for a computer's processor, which could switch tasks 1000 times a second if it had to.
It seems that we must limit the rate of notifications ("batch" them), and that we must treat notifications as suggestions, and not ones that a user can poll for (Lorna calls this the "rat on a lever" syndrome and it's also a time-killer). If your email or blog reader were to show data once every two hours, and there was nothing you could do to speed it up, not hit "refresh" fifty times a second or anything else, you'd probably get a lot more work done in the interim.
Of course, people should be able to describe which kinds of notifications they want gated in this way. Some kinds of messages are time-critical and need to be interruptions. But this is the incredible minority -- many would work much better if we redefined notification in some dramatic ways.
It's currently my intention to think up some tools for measuring and solving this, and I'll be posting them in an open format if I come up with anything unique enough to share.