during the few free evenings i had, though, i did run into a few interesting articles. though the subject matter varies considerably among them, i couldn't help but identify a general theme:
not everything is as apparent as it seems;
if things go wrong, often they do so unexpectedly.
i've told my colleagues before:
sometimes i like washing dishes, because i know that afterwards, they will be clean;
i like cooking dinner because i know that i will definitely have dinner ready in a 1/2 hour.
in contrast, there are plenty of days when i think about maths and nothing comes out.
come to think of it, most days are "unproductive"  in that sense .. which is why the following advice resonates with me.
"Burnout is caused when you repeatedly make large amounts of sacrifice and or effort into high-risk problems that fail…You effectively condition your brain to associate work with failure… The best way to prevent burnout is to follow up a serious failure with doing small things that you know are going to work."
~ from "The Antidote to Burnout is Progress" @tomtunguz (via d.ribeiro)
beauty (but not truth) in simplicity.
as i've said before: those people who consistently claim that "mathematics should be beautiful" probably don't give enough details in their proofs.
"For all of the appearances of the golden ratio, there many be even more erroneous sightings of it. The spiral of the nautilus’ shell is often said to fit precisely within a golden rectangle regardless of its size. But that is untrue. Each nautilus shell does maintain the same proportions throughout the animal’s life (that is, it’s a logarithmic spiral), but that proportion is generally not the golden ratio. Many have also claimed that the golden ratio is found in the proportions of various parts of the human body, the shape of the Gutenberg Bible, the Mona Lisa, and the Parthenon. None of these assertions have stood up to skeptical scrutiny, yet these myths stick with us. The mathematician Keith Devlin once gave a talk about the golden ratio, discussing numerous misunderstandings and debunking them, but when a radio station re-broadcast a portion of his lecture, it crucially omitted the fact that the examples were all false."
~ from "Math as Myth" @nautilus
when it goes wrong: being accepted.
the following is an excerpt from an academic in the humanities, and it gives a long, hard look into socially institutionalised disenfranchisement. in doing so, the author gives plenty of good insights into academia in general:
"My frenetic periods are praised—I take on more than I should, produce fast; my thinking feels sharp, precise. I overproduce, keep multiple drafts waiting, multiple projects at the edge of completion, hoping that their incompleteness will be enough to nudge me out of the near-catatonia of the depressive periods.thinking about it, maybe i've always been unconsciously comfortable in mathematics because of how open it is for everyone. if it weren't for the support groups of friends and peers, i don't think i could have come as far as i have now. i have been mentored by men and women, worked with white americans and immigrants and international visitors, and kept close contacts with older and younger generations ..
We are trained to hang in, hang on, hang together. This, after all, is the lesson of graduate training. “It will get better,” we assure students who struggle to learn. We are so definite. Were we more honest, we would say, “it might get better,” “perhaps,” “maybe,” or, simply, “we don’t know.” Instead, we say, “there are no guarantees, but.” And that “but,” that barely uttered, barely hearable “but” carries so much weight. Everyone wants to hear the “but.” Everyone invested in the academy is always hearing the “but.” We are a community organized around “but.” Lauren Berlant calls this “cruel optimism.”"
~ from "On Quitting" @thenewinquiry
.. which suggests, yes, that i am getting older .. but not old, yet!
vicious circles in student learning.
as an educator, sometimes i wonder how much we can do for our students, in contrast to what they will have to do for themselves in order to learn. the following excerpt and article came up from my social media circles last week; if you've not read it yet, then i suggest it.
"My failure began as most do: gradually, quietly. I took dutiful notes from my classmates’ lectures, but felt only a hazy half-comprehension. While I could parrot back key phrases, I felt a sense of vagueness, a slight disconnect – I knew I was missing things, but didn’t know quite what, and I clung to the idle hope that one good jolt might shake all the pieces into place.in fact, the experience of the author reminds me of when i took my second course in analysis as an undergraduate. by rights, i should have failed after the midterm exam. then again, so would have half the class; in the end i did all right, but i remember being absolutely confused at the notion of unifοrm cοnvergence for a very long time, as well as missing the point of a caυchy sequeηce.
But I didn’t seek out that jolt. In fact, I never asked for help. (Too scared of looking stupid.) Instead, I just let it all slide by, watching without grasping, feeling those flickers of understanding begin to ebb, until I no longer wondered whether I was lost. Now I knew I was lost."
~ from "What It Feels Like to Be Bad at Math" @slate (as reposted from mathwithbaddrawings.com
when there are too many dots, it's hard to connect them.
in the wake of the boston bombings, i'd like to avoid any political stances .. and at the risk of being an apologist, this opinion piece does shed some light into the quantitative nature of prediction.
" We have no idea how many potential "dots" the FBI, CIA, NSA and other agencies collect, but it's easily in the millions. It's easy to work backwards through the data and see all the obvious warning signs. But before a terrorist attack, when there are millions of dots -- some important but the vast majority unimportant -- uncovering plots is a lot harder.
Rather than thinking of intelligence as a simple connect-the-dots picture, think of it as a million unnumbered pictures superimposed on top of each other. Or a random-dot stereogram. Is it a sailboat, a puppy, two guys with pressure-cooker bombs or just an unintelligible mess of dots? You try to figure it out.
It's not a matter of not enough data, either.
Piling more data onto the mix makes it harder, not easier. The best way to think of it is a needle-in-a-haystack problem; the last thing you want to do is increase the amount of hay you have to search through."
~ from "Why FBI and CIA didn't connect the dots" @cnn
 i used to think that i was a highly unproductive person and that i wasn't cut out for mathematics, in light of how many days of this kind would happen. these days i take a happier perspective and decide that such days have their value: sometimes it's equally important to know what doesn't work as what actually does.