the lifespan of work notes, on a plane.

currently i'm latexing work notes that i took during my arrival flight into the west coast, last friday.

six pages of handwritten text have become 1.5 pages of latex. at first i was dismayed by the difference in count. looking back at the handwrit notes, however,

page 1 contained a lemma that i proved before,
but at the time i couldn't remember why it was true;

page 2 contained an idea for a very general proof,
page 3 asserted my suspicions that something was wrong,
page 4 formulated my suspicions well, and i tried to construct a counterexample;

i had given up this endeavor up by page 5,
and proved a special case instead.

page 6 showed that the special case caught the critical elements of the idea: it sidesteps the potential counterexample and shows that the results i want(ed) actually fit in that special case.

on a slightly related note or two,

1. the first flight was actually quite enjoyable. the other people in my row were antisocial and i had the full 4-hour stretch to sort out ideas. the time was very apt; all that past week i was distracted by exam prep for my 0DE class -- which turned out to be fruitless -- and had no time for these side thoughts.

2. as for the work notes during yesterday's return flight, the thoughts aren't as good and they are not ready to be turned into latex. more on them later, perhaps.