Ultimately, search is not just the web but literally all of your information - your email, the things you care about, with your permission - this is personal search, for you and only for you.While I agree with the idea of heavily localized and personalized searches, especially on mobile devices, I think this autonomous search feature sounds really annoying. You don't want to get in people's way. You don't want to interrupt them with something unimportant, especially if you are interrupting someone who is trying to get something done.
"The next step of search is doing this automatically. When I walk down the street, I want my smartphone to be doing searches constantly - 'did you know?', 'did you know?', 'did you know?', 'did you know?'.
This notion of autonomous search - to tell me things I didn't know but am probably interested in, is the next great stage - in my view - of search.
Perhaps what might be desirable would be better described as recommendations and personalized advertising, not as some Googly version of Clippy popping up and chirping, "Did you know? Did you know?"
Update: Interesting discussion in the comments about whether what Google is building is really personalized advertising, not search.