Show Other Parents of the Active Thought's Children
Previously suggested in the abstract, but I wanted to offer a clear rationale and an implementation idea.
Imagine you're searching for Car Stereos with particular features. If you click on the Thought "MP3-CD" you'll see all the child thoughts, fifty different models. That's not what you want to happen. You really want to see the other parents of those fifty, so you can restrict the results further, to stereos with USB or Bluetooth or Satellite, and additional criteria beyond.
To implement this, PB should have a View Toggle that shows Filtered Counters, rather than Children, beneath the active thought. So, instead of the fifty stereo models, we'd show virtual Thoughts like these:
(Children:50) (Parents Filtered:11) (Parents Unfiltered: 12). You'd click on (Parents Filtered) to access additional selection criteria, and on until you have just a few Children, your final candidates.
And to make it really powerful, you could break out those Filtered Counters by Type. So instead of (Parents Filtered:11) you could actually say (Features: 6) and (Brands: 5) because those were Thought Types of the other parents. Strong typing would offer an end-user benefit.
I think this is a great application for Brain, whether for an individual narrowing down choices, or for a web site that offers comparison shopping.
Props: this is an implementation-level version of an idea earlier proposed by lerone:
http://thebrain.uservoice.com/pages/general/suggestions/81406
...so please remember to add their votes together.