Thanks for this explanation it was really helpful!
Glad to help. But I noticed the analogy is a bit flawed; testing for membership does not add anything to the set, but the analogy might imply asking yaSeenThisFaceBefore(x) will make the savant remember x. I should change the story and the 2 functions to "remember this terrorist" and "is this a terrorist?" or something like that.
In computing terms the interface has 2 methods:
- takeALookAtThisFace(x)
- yaSeenThisFaceBefore?(x) which returns either "no way" or "hmm, I guess so".
"no way" means P(x is a member) = 0. Its negation is not "hell yes" (P(x is a member) = 1), it's "maybe" (P(x is a member) > 0).