More Than Two Piles To Sort Memories Into

I've been thinking about characters with memory loss. It came up as I watched the anime Noir over the last few days, and it came up again this morning when I started playing Arx Fatalis. You have a character with no knowledge of who they are (maybe they remember their name), but they possess impressive skills when it comes to fighting or killing. Jason Bourne, Wolverine, those kinds of folks. But even though they're proficient in the use and maintenance of firearms, first aid, martial arts, infiltration, whatever, they haven't retained any personal memories. What's their favorite color, their first kiss, what their best birthday was, where they went to school, so on.

I started wondering if those characters retain memories unrelated to their work, but also aren't memories with a strong personal component*. If you asked them about the American Revolution, could they tell you about it? Do they know who Mick Jagger is (or whichever entertainer is suitably notable in their world that most people are aware of them)? Do they remember high school algebra**?

It seems the character is usually vexed by how they can recognize which people in a room know how to fight, or that they know how to dress bullet wounds, yet they don't know how they ended up where they are, with the skills in question. But not everything a person knows would fall into either of those categories. I don't think knowing "I coulda been a contender" is from On the Waterfront would be useful for an assassin, but it's also not knowledge I have any strong connection to, which are the kinds of knowledge and remembrances that are forgotten/wiped out/blocked/whatever.

That seems like it could be fun, the character gradually realizing they remember certain random things, but not others, and perhaps trying to use what they can recall as a thread to find other memories.

* It came up when the character in Noir with the memory issue, Kirika, didn't recognize the name Prince Myshkin, from Dostoevsky's "The Idiot", indicating she didn't have any knowledge of Russian literature. Unfortunately, I can't blame the fact the name was only vaguely familiar to me on memory loss.

** For some reason, the question of whether they'd remember algebra has been foremost in my mind. I guess I don't think of alegbra as something vital to the work of finely honed killing machines, so it wouldn't be part of the operational knowledge they retained. Which means I didn't believe my teachers when they told me algebra would be useful in everyday life.