Dithering

I've had some time to think about the Varignon idea, and it's every bit as interesting as I hoped. It behaves in half a dozen different ways, depending on certain easily determined factors; at least some of the time, it provides a link between two things that I knew had to be connected, but couldn't define the connection until now.

One fact that I've run into repeatedly in my study of polygons: if the number of sides is odd, one set of phenomena occurs; if it's a multiple of four, a sharply different set occurs; and if it's neither - if it's even, but not a multiple of four - what happens is sort of a hybrid of the other two cases. This trichotomy recurs as regards the Varignon transform, and in most cases the result is somewhere between "Hmm, that's interesting" and "Wow!".

I really really want to start writing this stuff up, but it *has* to wait until I write the paper on isolated classes. Unfortunately, I keep changing my mind about how to structure that paper; I'd hoped to finish before the end of last summer, but now my best shot is to get it out the door by the end of the next semester.

:is frustrated:

Music Again

I like Bruce Springsteen. I've liked him ever since I saw the video of "Dancing in the Dark" (and cried, "Is that who I think it is?" when Courteney Cox jumped up on stage). I have four of his albums on my hard drive. (I didn't put "The Rising" on; I can't listen to more than a couple of songs from that album without breaking down. 9/11 left a lot of scars.)

I think my favorite album of his (of those that I have) is "Wrecking Ball". The grim determination of "We Take Care of Our Own", the controlled fury of "Death to My Hometown", the sombre "Rocky Ground", "We Are Alive"... I don't think there's a song on the album I don't like.

There are singers who can do politically-flavored songs, and singers who can't. Most of Gordon Lightfoot's songs of that type do nothing for me (with the exceptions of "Pride of Man" and "Don Quixote"). The Turtles managed it once with "Earth Anthem", but their other forays into politics were pretty bad IMO. I used to like the songs on "Four Way Street" by Crosby, Stills, Nash and Young, but most of them feel dated or facile to me nowadays.

On this front, The Boss is The Best.

What's It Called?

Is there a name for the kind of "dive" you see in cartoons sometimes, where the diver jumps up and slightly forward from the edge of the pool, holds their nose and tucks their legs, and hits the water bottom first?