## Tuesday, September 24, 2013

### *sighs*

ye gods, i hate asking for money.

it's clearer to me now that there is a "rat race" to academia in general and to the sciences in particular. more and more i envision a future where i'll never stop writing grants and there will always be another meeting to sit in, another memorandum that i should have read (but have skimmed over, at best).

for a while i've wondered if i was cut out to be a mathematician, but i've made my peace with it now. it's been long enough that i wasn't going to cut it, then i would probably be doing something else by now.

i'm starting to wonder, though, if i'm cut out to be a professional mathematician.

the research is fine and the teaching, though time-consuming, is also fine and often enough fulfilling (if not enjoyable). as for the grants .. and the applications .. and the meetings, and so on;

i can see why many faculty "give up" upon earning tenure.

these professional aspects of the job were never advertised to me, as a ph.d. student; maybe the advisor was deliberately putting it in the background, if only so that we could have a greater focus, when working together. as a postdoc there seemed more and more of it, when discussing the nature of work with my colleagues.

who knows? maybe i've just always been naive;

my colleagues, near and far, seem quite able to maintain research as their primary focus and if anything, shape their other duties to complement this one singular priority. more and more i find this admirable.

maybe i'm just too new to this position, that these are all just growing pains, and that these shall pass with time and enough patience and a little humor. i don't know and it's hard to say.

i'm not giving up. it's just that i can see why others do.

## Friday, September 20, 2013

### ANH: from end to start, for now.

so it feels like ages since i last thought about a blog post of any kind. it seems like there's so much to saybut at the same time, none of it is really worth mentioning. that's always the difficulty of beginning a story at the beginning ..

.. so, being lazy at the moment, i'll not. i'll begin at the ending instead, which is today.

so today i gave a lecture about metric spaces to my students. it's a first course in analysis and the textbook [1] happens to cover the topic, which to me sounds like a license to expound on it for 75 minutes.

so i showed them the discrete metric on any set, and how the unit circle would look if the set were the euclidean plane. i showed them the L-infinity norm, how the unit circle looks like the usual unit square, and how short the proof is for its triangle inequality. this is in contrast to how the proof of the triangle inequality goes for the usual L-2 distance, which uses Cauchy-Schwarz and in turn, a nod to Pythagoreas's theorem.

i thought it was cool. it would be the kind of lecture that would have inspired me as a student .. but i don't know. i'm getting to know the students in my class, but i'm still learning all the time.

[1] we're using baby Rudin.

## Thursday, September 19, 2013

### ARR! more machine now, than man .. twisted and evil.

"On the one hand, today’s computers feature programming and writing tools more powerful than anything available in the twentieth century. But, in a different way, each of these tasks would be much harder: on a modern machine, each man would face a more challenging battle with distraction ... Kafka, Kerouac, and Wozniak had one advantage over us: they worked on machines that did not readily do more than one thing at a time, easily yielding to our conflicting desires. And, while distraction was surely available—say, by reading the newspaper, or chatting with friends—there was a crucial difference. Today’s machines don’t just allow distraction; they promote it. The Web calls us constantly, like a carnival barker, and the machines, instead of keeping us on task, make it easy to get drawn in—and even add their own distractions to the mix. In short: we have built a generation of “distraction machines” that make great feats of concentrated effort harder instead of easier."

~ from "HOW TODAY'S COMPUTERS WEAKEN OUR BRAIN @newyorker "

## Sunday, September 15, 2013

### on how our choices can haunt us later.

if i sit and think about it, then it feels i have a lot to say about the last two weeks, of this new job, at this university.

i don't know where to begin, though;
if i start now, then it will all come out as chaos.

maybe i've been writing too many lectures lately, and habit urges me to put some order or narrative into it. after all, life is simply a sequence of events; any additional order or structure on it is an inherently human contribution.

my guess is that it will take months for me to make sense of it all: these experiences, mistakes, small joys, and frequent setbacks. (i don't know.)

as for something small to share ..
.. during the first lecture of multivariable calculus, on a whim i decided to pronounce the letter z as zed, just like how they seem to do in europe and the u.k.

as a result, now i feel compelled to be consistent and remember, from now on, to refer to the vertical axis (in 3 dimensions) as the 'zed-axis" .. or else risk being caught as a pretentious snob!

## Saturday, September 14, 2013

### ARR!.. apparently i still have more trigοnometry to learn.

well, i learned something new today:
It sounds cumbersome now, but doing multiplication by hand requires a lot more operations than addition does. When each operation takes a nontrivial amount of time (and is prone to a nontrivial amount of error), a procedure that lets you convert multiplication into addition is a real time-saver, and it can help increase accuracy.

The secret trig functions, like logarithms, made computations easier. Versine and haversine [1] were used the most often. Near the angle $\theta = 0$, $\cos(\theta)$ is very close to $1$. If you were doing a computation that had $1-\cos(\theta)$ in it, your computation might be ruined if your cosine table didn’t have enough significant figures. To illustrate, the cosine of $5$ degrees is $0.996194698$, and the cosine of $1$ degree is $0.999847695$. The difference $\cos(1^o)-\cos(5^o)$ is $0.003652997$. If you had three significant figures in your cosine table, you would only get 1 significant figure of precision in your answer, due to the leading zeroes in the difference. And a table with only three significant figures of precision would not be able to distinguish between 0 degree and 1 degree angles. In many cases, this wouldn’t matter, but it could be a problem if the errors built up over the course of a computation.

~ from "10 Secret Trig Functions Your Math Teachers Never Taught You" @sciam
in other news: it's been more than two weeks into this new job, and i still feel disoriented. often i feel exhausted, too.

on the bright side: i finally found an expensive apartment and signed a lease .. after a month of searching (and simultaneously teaching, for the last 2 1/2 weeks).

[1] these are defined, respectively, as $\textrm{versin}(\theta) = 1-\cos(\theta)$ and $\textrm{haversin}(\theta) = \frac{1}{2}\textrm{versin}(\theta)$. suggestively, "ha" mean half.