@ACuriousMind Imagine what trauma I had when, after months of Heaviside-Lorentz and afterwards natural units, the superconductivity class used SI

@Mr.Feynman Are you hooked on GR yet though? :D

@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

@Amit I'm still on the QFT side

@Mr.Feynman Wow.. that QFT thing must be something else then.... not just a hype bubble?? :) lol jk

Rather than GR I'm hookes on differential geometry, how can something possibly be so perfect?

@Amit It's just I enjoy particles :P

@Mr.Feynman Oh... well I would say GR taught in a certain way can only emphasize how majestic differential geometry is...

Ah, I guess your name proves to be suitable once more then

@Amit Not quite because I haven't done much Physics last week :P

Lemme guess, you were in Brazil?? :D

I've been more focused on differential ge- yeah I was playing bongos in Brazil

loll

differential strip clubs

I'll learn something about principal bundles and then I'll go back to Physics I guess

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've never understood what to what extent Feynman enjoyed Math

Like doing Math for Math's sake

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"

@Mr.Feynman Since you asked:

Also he probably intentionally downplayed how much he liked math... maybe to emphasize that physics was much more important to him

I think that says it all as to what he thought about math

That only establishes he preferred Physics :P

Can this be corroborated though, that he said it

@Amit I would suspect that, yes

Oh I wouldn't be surprised at all, but I wonder what's the source

I was quoting another message

Oh sorry

Ah, okay :)

I would ask in hsm.SE about this quote if I wasn't so lazy ^_^

Is there a name for measures of the form $\mu = f \ell$

with f some smooth function and ell the Lebesgue measure

@Slereah see en.wikipedia.org/wiki/Radon%E2%80%93Nikodym_theorem

Probable since I need it for manifolds and stuff

Trying to figure out if you can derive the scale bundle purely from geometric measure theory

I am FORBIDDING the use of the exterior bundle

Vectors do not exist

but unfortunately "geometric measure theory" seems to encompass a lot more stuff than I am comfortable with

Also need to figure out how to relate it to the measure theory of curves

wrt the Finsler structure

@Amit homotopy groups are easier for me to understand than bundles tbh

the concept of a bundle isn't so bad, but i have no idea how to actually prove anything in it

Oh, all I know is that homotopy groups are covered in books / courses apparently only after a lot of bundles are introduced

if so you're not reading books on homotopy :P

homotopy groups are usually part of introductions to algebraic topology

usually no bundles at all there

ahh right I see. and the differential geometry books apparently push them towards the end :)

Is algebraic topology good for anything in physics? :)

It must be I guess, mentioning Penrose again, he did his PhD in it and he figured out that incomprehensible (to me) black hole theorem

@Amit pops up now and again in condensed matter (defects etc)

Ohh.. cool... is that also in relation to "Topological qubits"? :)

sure, see e.g. the toric code

@bolbteppa you'll do a lot of maths in undergrad even though you signed up for physics?

@fqq obligatory SMBC

You know your mind is math-warped when your skim read of the comic legitimately thought it was talking about fields

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

some people find embedded/immersed geometry more approachable than abstract geometry

and since there's a bunch of embedding theorems there is no loss of generality when you assume something is embedded

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