11:53 am, 23 Dec 08
that clicking sound
Some intellectual pursuits I've studied and enjoyed -- linear algebra comes to mind, or maybe how hidden markov models work -- took some effort to understand, made sense for a while, and then were gradually lost again. When I lived in Japan in 2006 I brought along my linear algebra textbook and worked through it again, and again I understood and enjoyed it and failed to retain it all.
Other "difficult" things to understand -- Haskell's monads, or the way Git represents the world -- also took some effort but once understood become so simple that it became difficult to recall what there was that was difficult to get. The understanding seems qualitatively different, permanently etched in my head; I'd describe it with a word like "intuitive".
Having written the above out, the latter category seems to be maybe just simpler at its core, which produces the proselytizing aspect: "look at this beautiful geometric proof of the Pythagorean theorem!" But this makes me suspect there's some sort of hierarchy-of-difficulty thing going on, where somewhere else there's someone who really gets linear algebra in this same way and would also itch to watch me struggle along.
(PS: A bit of Git zen. You have a base branch A and another B that has some extra work relative to A. Say B has a complicated history, with work-in-progress commits and reverts and merges and you really want to just commit its change as a single commit on A. How to do it? The novice would say
Other "difficult" things to understand -- Haskell's monads, or the way Git represents the world -- also took some effort but once understood become so simple that it became difficult to recall what there was that was difficult to get. The understanding seems qualitatively different, permanently etched in my head; I'd describe it with a word like "intuitive".
Having written the above out, the latter category seems to be maybe just simpler at its core, which produces the proselytizing aspect: "look at this beautiful geometric proof of the Pythagorean theorem!" But this makes me suspect there's some sort of hierarchy-of-difficulty thing going on, where somewhere else there's someone who really gets linear algebra in this same way and would also itch to watch me struggle along.
(PS: A bit of Git zen. You have a base branch A and another B that has some extra work relative to A. Say B has a complicated history, with work-in-progress commits and reverts and merges and you really want to just commit its change as a single commit on A. How to do it? The novice would say
git rebase -i and then squashing, or maybe merge --squash, but now I see that the commit graph is merely annotations as to the relationships between trees and the trees are already in the proper state; the right thing is git reset --soft A; git commit.)
Yup, there's lots of them out there! You don't *use* Linear Algebra, so how could you get it in the same way?
E.g. Taking ordinary differential equations is a good way to reinforce linear algebra knowledge because you're using it to solve systems.
I've thought about this retention business for a while; I think it may be more random than we'd like to think (excepting of course stuff we really do use in our work, or teach, or otherwise employ often). I forgot a great amount of things I learned and didn't want to forget; and I can't see a regular pattern in what I've managed to retain. The number of retries doesn't correlate strongly (I used to re-learn how to solve the Rubik's cube every 2-3 years). The abstract beauty doesn't correlate strongly (monads are beautiful).
I think one thing that helps me is being able to center the knowledge in my head around a satisfyingly deep (or deep-seeming to me, anyway) Insight; or a satisfying Story. This isn't the same thing as a compact and orderly logical structure, although that helps (contingent details tend to fade away; I can easily forget some of the basic syntax of a programming language after a year of not using it).
Another thing that I believe in, although less strongly now than before, is a Great Book. Two examples dear to me are Halmos's Finite-Dimensional Vector Spaces for linear algebra, and Rudin's Principles of Analysis for calculus. In a Great Book, the exposition, the level of details, the progression of material are so pitch-perfect that I sometimes end up recalling stuff later just by vaguely imagining its location w.r.t. the rest of the book.