@ACuriousMind i'm auditing an astronomy class and the units are. something
the hubble constant, for instance, is apparently standardly written in units of km per s per Mpc - so, yes, it should just be 1/s, but nope. have to have the km/Mpc in there
Feynman commented in "Surely..." that a mathematician friend "got him up to homotopy groups" before he gave up... so mere bundles are well within scope :)
I think he enjoyed any mathematical subject the moment he saw there's any use to it. I get that for example, from him telling how when he was 13 or so, he read "Calculus for the practical man"... but then, he enjoyed reading advanced calculus textbooks where he learned stuff like "integrating under the sign"
I wonder why Dirac in his GR book chose to "immerse" the 4d spacetime in a flat N-dim space to define parallel transport. It's almost like he not only wanted to be brief, but wanted to see if he can briefly write a complex derivation like that
As far as visualization goes I tend to agree. Also, maybe it's actually what allowed him to use the physicists approach to differential geometry... he writes a lot of stuff like "$x$ and $x+\delta{x}$ are nearby points"...
I've just spent about 30 minutes convincing myself that what he did here was sensible... "vector like the right-hand side" is the stuff that makes mathematicians shudder I think lol
the $y$ thing is a transformation from the N-dim flat space to the 4d spacetime
eh the other way around, sorry
@ACuriousMind Yes that much I heard of, that it's all equivalent, it's nice to know that
When I think of it, indeed I think the "intrinsic" treatments of parallel transport I encountered were more like just definitions rather than derivations. So perhaps Dirac really knew why he was doing what he was doing... again... lol
