January 22, 2008

It was 20 years ago today, Green's theorem began to play... (oh, how WRONG)

I don't do paid work or shop on legal holdidays. (Today, I did a bit of civic duty and a bit of personal stuff.) Or I try not to. This story is of how my effort not to work on MLK day has succeeded, but also failed.

Not today, quite, but around 20 years ago, I was in the middle of my first year in college, taking the second-year calculus sequence (linear algebra, multivariate calculus, and ordinary differential equations). Except for linear algebra, it was a fairly smooth (second-order differentiable) experience. (Lame calculus joke, there.) Last night, I happened onto an online multivariate calculus text and the description of Stokes's theorem. I looked at it, thought, "Well, that's vaguely familiar, but what the heck is a curl again?" So I backtracked, and today I tried to follow the bit about line integrals and Green's theorem. (Both Green's and Stokes's theorems are generalized multi-dimensional versions of the fundamental theorem of calculus. That part I remembered.) I had to reread the explanation of how one can derive the formula for the area of a circle using different choices for P and Q, and then I saw a connection to one of the issues I'm working on for a grant proposal resubmission due in March. Briefly, can one take a Lexis diagram in demography and use Green's theorem?

So I brave Work Land, take out a piece of paper, draw a rectangle, and confirm that the line integral of N(a,t) (population at age a, time t), taken over the boundary of a Lexis-diagram rectangle, is the net number of deaths in the period and age interval. Yep, Sherman, you just re-defined the demographic balancing equation, and couldn't get any further. In reality, I think there is something more to be done here, especially since I'm working with a puzzle that I haven't yet solved (why estimates of the proportion of school life spent in certain grades is more robust with migration/transfer misspecifications than estimates of graduation).

But may be there is a lesson here in just letting the mind wander away from Workland when it should. It's just past midnight on the East Coast, so the holiday's over. With luck I'll be able to sleep without having this keep me awake, since I'm not capable of relearning this on the fly after midnight. (I suspect I never was able to do that, even in college.)

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Posted in Research on January 22, 2008 12:02 AM |