what i did today: a list.
- i woke up at 9 am, to the sound of lumber and hammering and loud slamming noises. looking outside, i see that the apartment upstairs undergoes renovation, including a new balcony deck with more solid wooden planks. though i tried and tried, i couldn't return to sleep and eventually got up when my phone rang.
i suppose a little construction is better than chancing an old, decrepit balcony falling onto ours .. especially in the case if i am seated on the lawn chair on our balcony!
- i played basketball, wore out my right knee, but managed to hit the game winning shot of our final game. afterwards i iced my knee and it was stiff and weak for the rest of the day.
the thought recurred, from time to time: maybe i should invest in a good cane. at the very least, it would only exacerbate that "old man" feeling i've had of late.
- using intuitive techniques [1], i proved a little lemma. basic little notion that it is, it nevertheless clinches the proof of a theorem which my advisor and i have been seeking.
if today's work holds water, then this side project will round out in about a month's time. then i can finally return to the actual wording of the thesis problem.
- i went to leopold bro's brewery, or as i'm more apt to think of it, valhalla; i imagine that a mead hall would not appear dissimilar.
i had to convince a friend that valhalla is different from doomed heorot of beowulf fame.
[1] the intuition being that: convolving a function with an appropriate bump function is essentially a smooth, weighted version of taking the characteristic function of a neighborhood of a point.
it would make more sense if i drew a picture, but probably not by much. \: