Learning (alec green)
Observations on maximizing learning productivity, where 'l-unit' (learning unit) is used as a compact representation for any equation, method, theorem, fact, etc. The form is as follows:
TITLE . analogy . claim . justification . counter
[1] 'MAXIMIZING SHARPNESS'
If your goal is to climb to the top of a rock wall the fastest, you don't blindly adhere to a straight vertical path up (you might run out of footholds), nor do you just move horizontally sideways (you won't make any progress upwards). rather, you move vertically until your rate of advancement is slowed to a point that sidestepping the obstacle above and scaling a new vertical path would result in a faster net movement upward.
Likewise, switch subjects often (for me, 2-3hrs), attempting to reach some 'goal' over each interval (digest a book chapter or video lecture, implement something in code, complete a proof).
This keeps you alert, and avoids inherent decay in productivity due lack of 'pressure' or due to boredom with material. Additionally, this will force you to recall l-units in an 'unprimed state' (not 'recently' exposed to media explaining the given l-unit) a greater number of times. The ability to recall an l-unit in an unprimed state is what we often want as the outcome of learning, and is proportional to number of times you've attempted to recall that l-unit before.
However, if you jump around too much, you may suffer significant 'context switching', or undesirable overhead associated with refamiliarizing yourself with a given subject.
[2] 'NONLINEAR LEARNING'
When you chop down a tree, it often becomes useful to chop from different directions, otherwise, your axe/saw may get 'pinched' and not make much progress.
Likewise, don't constrain yourself to a linear learning path through a subject, in which you don't move ahead until you fully master the current material. Attack the subject from different directions.
How an l-unit works (operation), and what it's used for (utility) often don't become clear until you look further into the material, where the l-unit is compared and contrasted against similar l-units. Therefore, it can be useful to superficially memorize the formula/method for the time being, and move ahead with the intention of returning to earlier material--in other words, jumping forward and working back. I've inefficiently spent much time trying to understand pedantic details that turn out to be trivially easy to understand once I progress further into the material.
A balance must be made, however, so that you still have the discipline to spend the multiple hours often required to comprehend a concept. Otherwise, you may learn a lot of high level concepts with no ability to implement them. ('If you can't build it, you don't understand it.')
