Having a chronological inbox is good. It's the right way to do things. But we should also have a "smart" inbox.
I think a smart inbox would show you activities similar to the ones that you've already interacted with. By interact with, I mean:
A bayesian filter could be used to learn which things you interact with; it could probably work the same way as the Activity Spam server (but with different criteria per user).
There's also the affinity network; it may make sense to show activities that people you follow have interacted with.
perhaps an option to deactivate (1) this would be also nice:
(1) or showing this "smart inbox" distinguished to all info ?