I've been thinking about the introverted perceiving lately, and I think I have figure out a decent way of looking at them. I would appreciate any feedback on this, and whether it fits with people's personal experiences.
Both Ni and Si function like huge databases of associations. Ni builds associations for contexts and perspectives, while Si builds associations for sensations and images.
So, when Si "notices" something, it will pull up whatever is associated with it. For example, an Si dominant might notice a scent (say, of strawberries) and have it bring to mind any number of related experiences (gathering strawberries with family in the summer, eating strawberry pancakes, etc).
On the other hand, when Ni "notices" something, it will bring up the state of mind / way of thinking associated with what it notices. For example, an Ni dominant might notice that there is a crack in a pavement, which will make them think about ways of looking at or thinking about things with cracks (how to fix them, what hazards they pose, etc.). On a more complex level, an Ni dominant studying a system would notice various features of the system, which will bring up multiple perspectives... and then find a way to reconcile these perspectives together. If that succeeds, they end up with a comprehensive way of looking at the entire system, which explains the "aha" moments that Ni is famous for (at the moment that Ni manages to merge the perspectives together, it comes up with a new perspective which makes everything clear).