We commonly discuss compartmentalization as if it were an active process, something you do. Eliezer suspected his altruism, as well as some people's "clicking", was due to a "failure to compartmentalize". Morendil discussed compartmentalization as something to avoid. But I suspect compartmentalization might actually be the natural state, the one that requires effort to overcome.
I started thinking about this when I encountered an article claiming that the average American does not know the answer to the following question:
If a pen is dropped on a moon, will it:
A) Float away
B) Float where it is
C) Fall to the surface of the moon
Now, I have to admit that the correct answer wasn't obvious to me at first. I thought about it for a moment, and almost settled on B - after all, there isn't much gravity on the moon, and a pen is so light that it might just be unaffected. It was only then that I remembered that the astronauts had walked on the surface of the moon without trouble. Once I remembered that piece of knowledge, I was able to deduce that the pen quite probably would fall.
A link on that page brought me to another article. This one described two students randomly calling 30 people and asking them the question above. 47 percent of them got the question correct, but what was interesting was that those who got it wrong were asked a follow-up question: "You've seen films of the APOLLO astronauts walking around on the Moon, why didn't they fall off?" Of those who heard it, about 20 percent changed their answer, but about half confidently replied, "Because they were wearing heavy boots".
While these articles were totally unscientific surveys, it doesn't seem to me like this would be the result of an active process of compartmentalization. I don't think my mind first knew that pens would fall down because of gravity, but quickly hid that knowledge from my conscious awareness until I was able to overcome the block. What would be the point in that? Rather, it seems to indicate that my "compartmentalization" was simply a lack of a connection, and that such connections are much harder to draw than we might assume.
The world is a complicated place. One of the reasons we don't have AI yet is because we haven't found very many reliable cross-domain reasoning rules. Reasoning algorithms in general are quickly subject to a combinatorial explosion: the reasoning system might know which potential inferences are valid ones, but not which ones are meaningful in any useful sense. Most current-day AI systems need to be more or less fine-tuned or rebuilt entirely when they're made to reason in a domain they weren't originally built for.
For humans, it can be even worse than that. Many of the basic tenets in a variety of fields are counter-intuitive, or are intuitive but have counter-intuitive consequences. The universe isn't actually fully arbitrary, but for somebody who doesn't know how all the rules add up, it might as well be. Think of all the times when somebody has tried to reason using surface analogies, mistaking them for deep causes; or dismissed a deep cause, mistaking it for a surface analogy. Somebody might present us with a connection between two domains, but we have no sure way of testing the validity of that connection.
Much of our reasoning, I suspect, is actually pattern recognition. We initially have no idea of the connection between X and Y, but then we see X and Y occur frequently together, and we begin to think of the connection as an "obvious" one. For those well-versed in physics, it seems mind-numbingly bizarre to hear someone claim that the Moon's gravity isn't enough to affect a pen, but is enough to affect people wearing heavy boots. But as for some hypothetical person who hasn't studied much physics... or screw the hypotheticals - for me, this sounds wrong but not obviously and completely wrong. I mean, "the pen has less mass, so there's less stuff for gravity to affect" sounds intuitively sorta-plausible for me, because I haven't had enough exposure to formal physics to hammer in the right intuition.
I suspect that often when we say "(s)he's compartmentalizing!", we're operating in a domain that's more familiar to us, and thus it feels like an active attempt to keep things separate must be the cause. After all, how could they not see it, were they not actively keeping it compartmentalized?
So my theory is that much of compartmentalization is simply because the search space is so large that people don't end up seeing that there might be a connection between two domains. Even if they do see the potential, or if it's explicitly pointed out to them, they might still not know enough about the domain in question (such as in the example of heavy boots), or they might find the proposed connection implausible. If you don't know which cross-domain rules and reasoning patterns are valid, then building up a separate set of rules for each domain is the safe approach. Discarding as much of your previous knowledge as possible when learning about a new thing is slow, but it at least guarantees that you're not polluted by existing incorrect information. Build your theories primarily on evidence found from a single domain, and they will be true within that domain. While there can certainly also be situations calling for an active process of compartmentalization, that might only happen in a minority of the cases.