makes the head spin

Have been reading Galileo's Finger: ten great ideas in science, and have slowed right down towards the end - the last two chapters being on special and general relativity (great idea: spacetime is curved by matter) and arithmetic (great idea: if arithmetic is consistent then it is incomplete). My abstraction antennae in these fields have been blunted by time and lots of concrete.

The idea of the author (chemistry professor and science wizz Peter Atkins) is that the early chapters, properly understood, will prepare the ground for the increasingly abstract later ones. Maybe I haven't understood the early chapters as completely as I should have, but I've always had these problems, probably conceptual, when reading about spacetime, multi-dimensionality and almost anything with equations in it. Not that I don't take anything from these readings - I at least understand why the dodgy lynchpin of Euclidian geometry, the parallel postulate, is blown away by the idea that space is curved. However, Atkins' attempts to illustrate and pin down the properties of hypercubes and such are largely lost on me.

I usually get bogged down by simple consequences, and how intriguing they are - for example, gravitation and kids. One of the interesting things to observe about kids learning to throw a ball to you for the first time is that they aim it straight at you, believing - not particularly consciously of course, but very sensibly - that it will travel in a straight line in the direction of the force they've imparted until it reaches you. That the ball immediately starts to fall to earth because of the gravitational force acting on it is something that has to be learned, and it is quite counter-intuitive, something that adults don't notice because we so habitually compensate for gravitational effects, not only for the fact of the effect but, of course, for its degree. Learning to throw properly is really learning about how gravity works. Even learning to walk is essentially about gravity, and this can be extended to just about every physical activity on the micro-environment of our planet. It's just fascinating to think and dream on.