Ramble, Part 28: Symbols of Change

Having devoted something like two and a half posts to Newton, I should probably give Gottfried Leibniz his turn. Of Leibniz' contributions to calculus, I'm not going to say much; philosophically, his work suffered from the same general defects as Newton's, and there's not much point in rehashing that. I do, however, want to say a few words about the one respect in which Leibniz' formulation is clearly superior to Newton's, under the cut.

( dot-age and d-ism )

Ramble Contents

Casting

I was leafing through one of my Girl Genius volumes when it hit me.

Kevin Kline is the perfect choice to play Othar. (On the one hand, A Fish Called Wanda; on the other, the scene with Agatha, Krosp, and Othar aboard the airship as they flee from Castle Wulfenbach.)

Oddity

Rubric: Problems intended to test students' skills should be nice, in the sense that proper application of the skills should lead to fairly simple results and, though the intermediate calculations may be complex, they should not be unnecessarily so. Students should complete such problems with a feeling of accomplishment, not exhaustion. (The combination is sometimes acceptable.)

Caveat: Nice problems are sparsely distributed. Thus, changing the parameters of a nice problem slightly is almost certain to transform it into a not-nice problem. Furthermore, beyond the most elementary levels, small computational errors are liable to have the same effect.

Note: This last is not necessarily a bad thing, as an astute student, seeing his/her computations going awry, may well realize that an error has been made.

Corollary: Problems intended to test students' skills absolutely must be carefully designed. Furthermore, when going over such a problem on the board, one must take special care to avoid computational errors.

All of which makes the following incident striking. On Wednesday, at the beginning of class, I went over some of the homework problems. In the course of one of them - finding the eigenvalues and eigenvectors of a 3x3 matrix - I made a computational error while calculating the characteristic equation. The resulting erroneous equation had small-integer solutions. It was not until I tried to find the corresponding eigenvectors that I realized I'd made a mistake. (The correct equation also had small-integer solutions.)

Very very unusual, in my experience.

Varia

So, this morning I took Ben over for his dental work. It's an all-day deal, so I dropped him off around 8AM, with the promise that they'd call me when he was ready for pickup.

On the way back I stopped off at Target. I was out of blank DVDs; they're the nearest source, and pretty near on the direct line between my place and the vet. They didn't have the 10-packs I've been buying, so I had to get a set of 50. (They're on a spindle, and I don't know what the deal with labeling will be.) I also picked up a couple of CDs. One is The Cream of Clapton; it's got a selection of his work from all phases of his career - Cream, Blind Faith, Derek & the Dominos, and solo - and it looks pretty good. The fast version of "Layla", "I Shot the Sheriff", "Sunshine of Your Love", "Wonderful Tonight" - about the only major pieces that are missing are the slow version of "Layla" and "Tears in Heaven". I also took a flyer on Experience Hendrix. The only piece by Hendrix that I've ever knowingly heard is his Woodstock rendition of "The Star Spangled Banner", but he has such a reputation that I figure I ought to give him a try.

I got the call from the vet an hour or so ago. In addition to the dental work, they drained the fatty tumor on his chest (and it was, indeed, nothing but fat), but that means he'll be wearing a shunt for the next few days. In particular, he can't go outside, which means I can't walk him back home. I've made arrangements with a friend to pick him up tomorrow morning. (The overnight stay is free.) Of course, this means I'll have to block the doggie door; I'll have two dogs making messes in the house instead of just one. Sigh. It'll just be for a few days...