blog suggestion: opinionator.

i don't read the new york times regularly, at least not in print form.

for me, the density of its prose takes a few weeks of readjustment; i'm never patient enough to make the commitment. [1]

on the other hand, there are a host of NYT blogs that are tremendous fun. of these, one is particularly gears for us mathmos and techies:

"opinionator" by steνen strοgatz

personal anecdote. in my first year of grad school, i ran supplementary problem sessions for a linear algebra class, and even subbed for one or two of its lectures, during hallowe'en [2]. one economics student was particularly interested in the subject, though she had taken little/no mathematics since her calculus days. we became pleasant acquaintances.

one day there was a distinguished mathematical lecture by strοgatz, who was an unknown to me at the time. we had snuck into the reception tea earlier. when the crowd started towards the lecture room, i suggested that we attend. in retrospect i think she agreed out of guilt -- cookies can do that to you -- but we enjoyed the talk immensely. it mixed well physical intuitions from nature and a little maths from beyond the classroom.

"this is great!" she said, "are all the mathematics colloquia this interesting?"

ummm .. (-:

at any rate, strοgatz is a fine expositor. he has this way of taking something simple but, in a seamless process, pointing out its depths.

for instance, consider arithmetic .. which is also considered in "rock groups." trivial stuff, right?

each of us can imagine arithmetic in the form of making patterns with little stones. however, a neat little pattern, such as

[image borrowed from NYT]

serves as a wonderful intuition: why sums of odd numbers give perfect squares.

sure, it's trivial when you have the picture. it's not research-level maths ..but still, it makes me smile. it makes me feel like a boy again, realising a little depth, learning these facts for the first time.

then there is empathy. some representations don't make sense, initially, because we may encounter matters beyond our intuition. for example, in "division and its discontents," strοgatz writes:

The bafflement began when Ms. Stanton pointed out that if you triple both sides of the simple equation

$\frac{1}{3} \;=\; 0.33333\ldots$

you’re forced to conclude that $1$ must equal $.9999\ldots$

At the time I protested that they couldn’t be equal. No matter how many 9’s she wrote, I could write just as many 0’s in $1.0000\ldots$ and then if we subtracted her number from mine, there would be a teeny bit left over, something like $.0000\ldots01$.

i remember experiencing the same sense of mystery, as well as trying to explain it to my calculu∫ 2 students.

"the reason why it was confusing back then is that, as children, we were ignorant of geοmetric series," i offered.

"put another way, it's probably the first time you were exposed to the notion of a limit, which isn't quite fair. for most of us, we learned decimals in grade school, whereas we learned about limits in our first calculus class."

anyway, i like the exposition in "opinionator." i like (re)discovering the depths in seemingly simple ideas.

[1] for the same reason, i don't often read novels. lately the only ones i've read are (i) suggestions from friends and (ii) those, upon inspection of their spines, i estimated would take at most one sitting to read.

[2] it's not hard to remember that day. somehow i procured some orange chalk for the occasion. (-: