Which is presumably what Facebook, etc do. Presumably through some sort of Comet connection to the server. (http://en.wikipedia.org/wiki/Comet_(programming) )
I wonder if a time will come when most Moodle pages have a Comet connection to the server, for instant push notifications, etc.
(As probably the most experienced Moodle developer out there, I would be particularly interested to know your thoughts on that, Petr, if you have any.)