Oliver Steele

“Aargh!” But how do you spell it?

(Click here to skip straight to the visualization.)

In the late nineties, I tried using internet search as a spelling corrector. (I think I was using AltaVista at the time. It was the latest and greatest search engine, supplanting — was it Lycos?)

At the time, for the words I tried, there were about two orders of magnitude between a misspelling and the correct word. A spelling variant, such as “color” and “colour”, were typically less than one order of magnitude.

Here’s a picture I drew to explain addition and subtraction of fractions to the sixth-grader:

We also ended up using a variant on Euclid’s algorithm for finding the GCD. It uses subtraction instead of division and remainder; it’s in general less efficient, but it’s easier to explain and can be easier to do in your head, when the numbers are small.

Construct a series whose first two terms are the inputs, and then continue as follows: each successive term is the absolute value of the difference between the preceding two terms — that is, simply subtract the smaller from the larger. If you reach one, the GCD is one; if you reach zero, the GCD is the previous term. (Or, you could also let the series peter out to zero, but the way I’ve stated it is simpler in practice.)

PackageMapper shows you a map of your FedEx, UPS, USPS package routes. Enter a carrier and a tracking number to see your package’s progress plotted on the map. Sign in to enter a list of packages and see their current locations on a table or map.

This is an itch I’ve wanted to scratch for about a year now: being able to see where all my packages are on a map. On Thanksgiving morning I discovered SimpleTracking.com, which gives you an RSS feed for a UPS or USPS package. Over Thanksgiving weekend I added FedEx and mashed it up with Google Maps, and this is the result.

One warm Monday morning last August my father died. The previous Wednesday he had been planning to see March of the Penguins, a movie he probably would have discussed with his grandchildren over the phone and video chat. Instead, that night he was taken to the hospital, after falling down his apartment stairs. Early Monday I leaned way over him in the ICU and held him as tightly as I could, and felt on my cheek his last, familiar, breath.

I know it’s callous, but when I hear about a man in his eighties dying, I picture someone whose life is done. It doesn’t evoke in me the automatic sorrow, the rage against mortality, that comes from an encounter with the death of a twenty year old, or a teen, or a child. I’m less than half of eighty now, and yet I’m older than most people have lived to for most of time: older than the life expectancies of many countries; older than my friends when we were young and promising; older than Mozart, older than Keats. Despite the extended American adolescence, by the time a man is thirty he’s had time to make his mark. Anything after that is bonus time.

I posed a second-grader the question of what nine squared was. She reasoned that ten squared is 100, and nine times ten is ten less then that, and nine times nine is nine less than that, so the answer is 81. Then I asked her what eight squared was, and she was flummoxed. She saw that it was a similar problem to the one she’d just solved, but wasn’t sure how to apply the analogy.

Here are the pictures that showed her how to figure out the answer. We drew the location of the squares on a multiplication grid:

and I introduced the idea of a “solution structure”. A solution structure is a graphical representation of the steps of a solution. This is the section that represents the relation between 9² and 10².