FIFA unveiled the mascot for the 2006 World Cup, and it turns out to be ... Bear from the Big Blue House? I didn't even know he played association football. Oh, they call him Goleo VI, but I know when their backs are turned he's off figuring out what unnecessarily complicated situation otters Pip and Pop have gotten into. I'm also curious about sidekick mascot, Pille, ``a talking football with an encyclopedic knowledge of the game,'' according to Reuters. I can't imagine the conversations with it.
About eight pages today, most transcribing papers again. I realize now I have to include an overview of functional analysis. This is the study of operators, like integration and differentiation, which act on functions the way that functions act on real numbers. The subject spirals outward into wonderful things like Hilbert spaces, although in one of those strange ironies it's an easier topic than real analysis, the study of why freshman calculus works.
In another strange irony complex analysis -- the study of integrals and derivatives on numbers with a real and an imaginary component -- is easiest of all. There's some deep reason for this, though I've only got a rough sketch of it. It all comes down to symmetries, I'm sure, but everything comes down to symmetries.
Trivia: The vertices of a dodecahedron, resting on one face, sweep out four horizontal planes; if the dodecahedron is divided along these planes, each of the three segments has an equal volume. Source: Platonic and Archimedean Solids, Daud Sutton. Something new to ponder while staring at your d20's.
Currently Reading: The Struggle For Mastery In Europe, 1848-1918, A.J.P. Taylor.