Learning
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.')
[3] 'CONSISTENT PEDAGOGICAL SOURCE'
In an electrical circuit, you need one and only one rock-solid ground voltage--a consistent point of reference. This ensures that everything within a circuit is 'on the same page'. Switching among additional 'reference voltages' that are not at the same potential as the ground source are useless, and in fact harmful: they only serve to obfuscate the meaning of the signals measured relative to the reference voltages.
Likewise, extract content from a pedagogical source (in-person teacher, textbook, video lectures) of consistent presentation/teaching style as long as possible, and avoid trying to learn a single subject from multiple sources simultaneously.
When switching among various pedagogical sources, one often must become familiar with a new set of notation for identical concepts. While consulting an auxiliary source may be useful in understanding a singular concept, understanding the whole of a subject is more efficient when the time to learn notation and conventions can be minimized, and the time spent on mentally visualizing concepts (the most important part of learning) can be maximized. I observed this effect first-hand when taking the consecutive courses ECE 270 and ECE 362: ECE 362 could dive right into the material where ECE 270 had left off because Prof. Meyer knew exactly what material ECE 270 had covered, and where it finished since Prof. Meyer also taught ECE 270. Additionally, allusions to digital logic concepts (like open drain or flip-flops) required very little review because they were being described in the same terminology defined in ECE 270. I also observed the complement of this effect when taking ECE 201H and ECE 311 from different professors: the first two weeks of ECE 311 was spent on vector algebra and vector calculus that the previous course had already rigorously defined conventions for.
In practice, humans are 'experts' (relative to other humans) in a limited number of domains, so one should analyze whether a new or current pedagogical source should be pursued when learning a new subject. Eg, learning computer architecture from an English teacher who has mentored you for five years is likely to be more inefficient than learning from an entirely new source. Additionally, despite the claim of this section, it may turn out that the maximum rate of learning occurs by only learning one subject from each source, so that in practice no source is ever used for more than one subject. An intuitive balance (defined by the individual) must be struck between using the same source or a new source in order to maximize rate of learning.
