A personal pet peeve is when I need to apply a beautiful piece of theory which I forget the “melody” to. In fact, the feeling is uncannily similar to the agitation of remembering the name of a song but not its tune. I contest that every scientist/engineer/mathematician can relate to this regardless of field seniority. It is well known that much of formal education is not about absorbing knowledge for immediate active recall, but rather exposure to a set of ideas, practice of a set of problem-solving tactics, and an archiving of the aforementioned for a quicker future recall.
We are where we are because we are “standing on the shoulders of giants” (Newton). It would be painfully arduous to blank-slate rederive calculus every time I needed to use it, simply because I “don’t remember how this was arrived at” right? Anyone who does is stupid in both their inefficiency and their arrogant implication of proximity to the brilliance of Newton.
On the other hand, I dislike spoonfed knowledge (unquestioned application of formulas as you will). It is the epistemological responsibility of the individual to logically convince themselves of non-obvious facts at least once (slog through the derivations as you will). Afterwards, many have found intuition as an effective long-term retainer. This is a popular mindset among investigators.
Thus raises the question: how do you manage a desire for internalized, self-sufficient knowledge and powerful, external, accumulated knowledge when constrained by an unfortunately limited working memory?. It is for this reason I have created these running notes. In these notes, you will find efficient refreshers of top-shelved theory personally curated to my own “AHA” moments. They are compilations of an ensemble of lectures, books, websites, et cetera that I have digested and organized. The quantitative or qualitative explanations of concepts are all uniquely my own path towards understanding - a comforting reassurance of epistemological ownership.
These notes exist in hopes that when enough time passes such that an old concept begins to feel foreign again (at which point I begin feeling uncomfortably irresponsible wielding the concept), I may quickly and confidently return to a state of satisfactory internalized understanding. If you find these notes particularly useful too, GENIAL - we think alike :).
Thank you for reading this unabridged edition of “why did I spend my time making these notes”.