Pullbacks and frozen peas

I've spent this weekend studying for a differential geometry exam.

Differential geometry's the mathematical equivalent of the TV dinner. It was invented one afternoon by some disillusioned engineer or physicist, who got bored doing her 47th messy multivariable calculus computation of the week, and told herself that there had to be a better way of doing things. So she rewrote all the calculus into lots and lots of meaningless abstract symbols, and spent ten years doing every conceivable convoluted computation on the meaningless symbols for once and for all. Then she settled down happily on the couch, knowing that for the rest of her life she'd only have to defrost her pre-computed meaningless-symbol solutions and not actually cook new ones herself.

(There is a problem with this approach, though. The engineer realised it a few years later, prematurely aged and trying unsuccessfully one day to get her mental microwave to do its reheating stuff. All this high-falutin' time-saving mathematical technology is kind of complicated, and once you forget how the meaningless symbols work, you're back to the chopping board again.)

Anyway, my exam tomorrow is on the convoluted mechanics of differential geometry -- the 129 pages just before the engineer sits down to her first TV dinner -- and may well be both difficult and dull. But every computation I do tomorrow is another 388 that no one else will ever have to. And for this, you should all be very grateful.