We tend to forget complicated things

I think you are describing overlearning and chunking (once concepts become chunked they "feel easy", and one reliable way to chunk ideas is to overlearn them).

Some related links:

• A comment by Qiaochu Yuan [LW(p) · GW(p)]
• Bryan Caplan's "Libertarianism as Moral Overlearning"
• Augmenting Long-term Memory (search "chunk")

This sounds like: "Learn until you actually get it (or don't learn at all)."

Because if it feels difficult, it's likely there is something missing. Either some connections between different parts (so instead of a connected network, it feels like a list of isolated facts), or you memorized some rules but you don't actually know why it works that way (you wouldn't be able to re-derive [LW · GW] those rules). Or perhaps you actually get it, but you didn't have enough practice; which is also bad, because repetition is good for memory.

Just wanted to say I appreciate the brevity. :) I'm guilty of overly long LessWrong posts.

I agree in general, but I think it can also have a general sense of what a particular topic is about, so if you come across a situation that calls for that topic, you'll know to read up on that topic and remind yourself.

Also consider that people are different and some people might have an easy time learning and reliably remembering a lots of (unconnected) facts while other people have much bigger problems with that but will have an easy time learning highly connected concepts.

I've taken the principle of never learning anything (or claiming to know it) unless I can deeply understand it to a very extreme place.

By "deeply understand" I mean, be able to apply it on a whole other set of inputs/problems than those that you saw it applied to. Or, if that is not doable, the more abstract version of "be able to explain it with your own words in such a way that it could reach vastly different people than those that would have understood it from the original author's words" (which, to some extent, is based of Feyman idea).

By "never learning" I mean not starting to learn something unless I plan to reach this point and see it as feasible to reach.

Which essentially removes the "complicated" problem since using this method nothing stays complicated once you learn it almost by definition. (not, nothing stays complicated but most things still stay complex, by "complicated" I understand "hard to navigate or use", by "complex" I understand "requiring a very large map or frequent checking of the manual").

I think it helps create some very efficient primitives in one's brain, at least for certain things, but I'm not sure it's an approach I'd recommend, it puts you at odds with many things. I think wrote-memorization has it's place and in a way it's good to "learn" things that way, or at least necessary.

It is commonly claimed that if you make it to 'level N' in your mathematics education you will only remember level n - 1 or level n-2 longterm. Obviously there is no canonical way to split knowlege into levels. But one could imagine a chain like:

1) Algebra

2) Calculus (think AP calc in the USA)

3) Linear Algebra and Multi-variable Calculus

4) Basic 'Analysis' (roughly proofs of things in Calculus)

5) Measure Theory

6) Advanced Analysis topic X (ex Evan's Partial Differential Equations)

This theory roughly fits my experience.

In my experience learning something complicated isn't hard and I don't forget it easily if I am interested in the topic and have a use for it. I venture to guess most students don't particularly enjoy or have a use for all the complicated mathematics they learn. Thus, they forget it quickly because it never stimulated the mind.

Interest allows us to commit more memory and having a use helps us understand the topic as a tool that can be built upon and potentially used in other areas.

A long (long, long) time ago a friend of mine said: Being smart is not about how much information you know but knowing where to get the information you need.

I tend to agree with that general statement.

I also agree that we will remember the things we actually understand much better than those cases were we just memorized a set of rules or other "facts" that have little meaning to us -- except when they become those meaningless things we have to use regularly ;-)

I think this has some important aspects related to how we think about our personal optimization or efficiencies regarding knowledge and information management -- what we "know" (stored in our head) and what we have ready access to and can retrieve without much search effort that is in that "off-line" memory (books, notes, computers, more generalized things like operational procedures...)

I do understand this changes the focus of the OP and I am not rejecting that view -- we do remember the things that we really understand and those things just seem "easy" and tent to "just make sense" without the need to (consciously) rederive the rule(s).

But I do wonder if it is really inefficient to study something only until you have a beginning understanding even if you know you don't have an interest or need to fully understand as long as you learned enough to know where to apply that and created a good "index" to where to quickly locate that information should you need to actually use that "knowledge" in the future.