The h Bar

skull patrol

22:00

Hi @alarge

0celo7

@obe I can't do algebraic geometry or even analysis

why are we revisiting this

obe

I missed it.

0celo7

it's over, let it be

obe

Though it doesn't make sense to me, analysis is easier than all the things you've learned.

0celo7

hardly

obe

22:01

At uoft they use rudin in the first year, in fact I'm doing that next year.

it's considered easy

0celo7

and when you really think about it, I haven't learned much

obe

compared to say, qft or gr.

0celo7

Rudin makes no sense to me

obe

then read lecture notes instead.

analysis has a lot of good ones i've seen.

0celo7

I'm taking it next year anyway

it's irrelevant now

obe

22:03

@0celo7 you know more than a graduate student from a regular university.

0celo7

@obe bullshit

that's such bullshit

obe

hey I worked with phd students in theoretical optics.

0celo7

I don't know ODEs, linear algebra, electrodynamics, optics

stat mech, thermo

obe

because you rushed.

you skipped them.

who cares?

lol

ok let's not continue.

FenderLesPaul

This is like watching a guy tell his wife that she's really pretty but she replies with "That's bullshit I don't even have a weave"

:p

0celo7

22:05

no it's like if the woman is fucking paraplegic

why are you bringing this back up

@FenderLesPaul what are the prereqs for HE, ignoring the preface

obe

aww you said ignoring the preface.

FenderLesPaul

@0celo7 in all honesty I would say Wald

alarge

@skullpatrol Hello?

0celo7

it uses Poincare-Hopf randomly, so algebraic topology?

obe

HE would be considered a 3rd read in GR. right?

FenderLesPaul

22:06

yeah something like a 3rd read

@0celo7 idk if that would make alg top a pre-req though

because you can look it up

you don't need to have a working knowledge of alg top to get through the book

by any means

0celo7

also they use that one Hodge theorem, so harmonic analysis too

FenderLesPaul

hehe

0celo7

yeah I think if you get Wald you're set

obe

If only you could learn by osmosis.

I would use wald as a pillow.

skull patrol

.techinsights @alarge

0celo7

22:10

@FenderLesPaul list all GR/related books you have experience with

alarge

@skullpatrol Cool, I guess. I don't remember talking about phones here, though.

skull patrol

Just some random food for thought :-)

0celo7

is someone messing with this list

I can't type A. Zee

skull patrol

Welcome @MarkMitchison

DanielSank

22:25

@TanMath you here?

Mark Mitchison

@skullpatrol Hi

DanielSank

@MarkMitchison Hi.

We're all hi.

Mark Mitchison

ha

hey

skull patrol

:-)

0celo7

@MarkMitchison hello stranger

Mark Mitchison

22:28

Hi @0celo7

0celo7

tfw cable falls behind desk

skull patrol

What does "celo" between 0 and 7 stand for? @0celo7

0celo7

skull patrol

Got it.

bolbteppa

@ACuriousMind what is the joy/fetish of closing serious questions, what power thrill is associated with that, if I may ask?

0celo7

22:42

Wow, that's a harsh question.

bolbteppa

@0celo7 were you reading string theory books without ode's, linear algebra, EM, stat mech, real analysis?

0celo7

@bolbteppa Yes.

skull patrol

Do you play that instrument? @0celo7

0celo7

Well saying I don't know linear algebra is wrong.

I can't solve a linear system offhand because I haven't practiced.

As for ODEs...I've never needed to solve one that wasn't trivial.

EM and stat mech, I know the basics.

bolbteppa

I think it's telling that Woit replied to me with a lovely understanding response, and offered to try a longer response and even blog post on this whole topic, while here I get complaints about amateurish formality, the values are backwards...

0celo7

22:44

Real analysis I don't know shit about, that is correct.

bolbteppa

I know people, good people, have quit or abandoned these kinds of sites over exactly this kind of silly behaviour

skull patrol

Welcome to the internet

It ain't no paradise

People will always behave silly IRL

bolbteppa

@0celo7 a sneaky way to look at Rudin is interpreting it as though it is talking about representation theory:
"R is a field, and hence an additive group, real analysis is the representation theory of R acting by translation on infinite-dimensional spaces such C(R), Ck(R) and L2(R). Fourier series and the Fourier transforms are instances of this perspective. Differentiation itself arises as the infinitesimal generator of the action of translation." P. 2
http://www.math.harvard.edu/~ctm/home/text/class/harvard/55b/10/html/home/course/course.pdf

0celo7

22:59

. It is easy to show that there is no x ∈ Q such that x
2 = 2.

Trial and error?

Else I have no clue :/

bolbteppa

That part of Rudin is like the most insane thing ever, other than that one thing in the first chapter the book is okay, but that proof drives me crazy

0celo7

which one

the expoenential?

or the one I just named

because trial and error works for me man

bolbteppa

In the first chapter about the square root of 2

I mean he have the (a/b)^2 = 2 proof, the other one is ridiculous, and it's actually just some sneaky Newton's method trick with all the intuition hidden so it looks complicated

0celo7

do these notes expect me to know how to prove that already?

because I can't

skull patrol

It drove the Pythagoreans crazy too :P

0celo7

23:03

math.utah.edu/~pa/math/q1.html

oh I remember that

obe

from spivak?

0celo7

numberphile

holy crap are freshmen supposed to be taking this? I guarantee none of my classmates in BC calc could understand any of this

skull patrol

It is the ultimate math course

Math 55

bolbteppa

Yeah, Rudin gives that proof first in ch. 1 then he gives a complicated re-proof of the exact same thing, which drove me to tears personally, but it is actually easy when you know where it comes from math.stackexchange.com/a/141941/82615

The passage is quoted in that thread

skull patrol

Actual tears?

bolbteppa

23:08

:'(

skull patrol

:,(

bolbteppa

"a little more closely"
https://i.sstatic.net/eZpsn.jpg
wtf why go closer?

obe

Why are you reading Rudin? Folland is the new standard for analysis ca.wiley.com/WileyCDA/WileyTitle/productCd-0471317160.html.

bolbteppa

So equation (3) made me cry, where did it come from, who in the world would even think to make something up like that, let alone use it in a proof, let alone re-prove something you've already proven, I don't see why it's closer or different, gah...

0celo7

wtf

I can't do that

why do you people insist on making me feel inferior

skull patrol

23:12

Motivation?

obe

Dude why do you have that impression?

Besides I'm far more inferior.

QFT and GR are harder than analysis.

0celo7

you said you read rudin

no analysis is hardest thing ever

bolbteppa

This is why I hate math books in a sense, because we all already know how to do it haha math.stackexchange.com/a/141941/82615 (read the wiki derivation of the method! it's just using $y = y_0 + f'(x_0)(x - x_0)$!) but the book tricks us into thinking we don't know how to do it

0celo7

the proofs are so nonobvious

obe

@0celo7 Barely.

bolbteppa

23:13

and they don't tell you they found equation (3) by using baby calculus methods

obe

Apr 21 at 23:17, by 0celo7

@ᴇʏᴇs Math's only purpose is to further physics. Remember that.

0celo7

I said that

so?

obe

I agree.

skull patrol

26 mins ago, by skull patrol

It ain't no paradise

bolbteppa

Real analysis is an absolute nightmare, way harder than general relativity, until you realize it's easier than it haha, that it is literally just calculus but using set-theoretical words to describe easy easy ideas

(That took me like 3 years to see!)

0celo7

23:15

GR is easy, just some indices

bolbteppa

I don't know how you guys coped with the definition of a manifold in GR without real analysis, topology, metric spaces?

0celo7

you don't need metric spaces

why do you need real analysis?

bolbteppa

I mean a 'second countable Hausdorff space locally homeomorphic to a subset of R^n' blah blah ...

0celo7

yeah

what about it

why do you need metric spaces for that

bolbteppa

Second countable, which depends on the notion of a topological basis, and Hausdorff, are words coming from general topology implemented in the context of metric spaces

0celo7

23:18

I know the topology

metric spaces?

how?

GR manifolds are not metric spaces

unless you Wick rotate or some BS

bolbteppa

Okay cool, I'm assuming you studied calculus then came across topology through metric spaces first

0celo7

I came across topology though Wald

then I had to do some exloring

metric spaces never played a significant part

bolbteppa

Well a metric space is just a topological space where the topology is generated by a distance function, so if you have the topology down you basically have chapters 1, 2, 3 and 4 of Rudin down tbh if you can get past this root 2 proof haha, but formulating it in terms of metric spaces might seem too specific compared to general topology, but you could definitely hack it

0celo7

I know what a metric space is

bolbteppa

Then I don't understand your fear or concerns with real analysis

Sounds like you know a lot of it already

0celo7

23:23

I can't do the proofs

they're not obvious

I can't remember the definitions

NeuroFuzzy

@bolbteppa That's neat.

I never thought of it like that

I wonder how many of the theorems are easily reinterpretable...

bolbteppa

Well my advice would be to spend like 2/3 years on general topology from books like Kelley and then re-formulate every statement in real analysis as either something about general topology or representation theory (or measure theory) haha, then it will be obvious :p

0celo7

Idk measure theory either

bolbteppa

If there's one thing mathematical physics will do, it will beat it into your brain that you not only need to learn all these things, you'll even have to face the horrendous beasts known as number theory and combinatorics haha :(

7 = 2*3 + 1 :(

NeuroFuzzy

@bolbteppa So ramanujan and hardy are sitting in the back of a taxicab, and hardy looks at the cab number and sees that it's 4. And he says, "what a boring number to hold a number theorist" or something like that, and ramanujan says "no it's not"

"it's the smallest number that can be written as the sum of two primes in two different ways"

bolbteppa

23:39

modern physicist: it's the smallest number which gives you the double cover of SO(4) by two SU(2)'s

TanMath

@DanielSank i was

0celo7

@NeuroFuzzy 2+2 and 7-3 or am I really dumb :/

TanMath

@MarkMitchison hello! nice to see you again!

NeuroFuzzy

@0celo7 oh, right, 1 isn't prime, i'm dumb. Okay... um...

TanMath

@DanielSank I was, and I am back...why do you ask?

0celo7

23:50

@NeuroFuzzy so...

NeuroFuzzy

@0celo7 okay, 10 is the smallest positive integer that is the sum of two primes in two different ways.

TanMath

@MarkMitchison to be honest, i am really sorry for all I have done.. I admit i was rude..but thanks for the help!

Mark Mitchison

@TanMath Hi, not a problem. Glad you are keeping the physics up.

0celo7

@NeuroFuzzy how about two distinct primes?

@bolbteppa a number gives you a double cover?

TanMath

@MarkMitchison did you see my latest question?

NeuroFuzzy

23:55

@0celo7 I checked to 14 :/

TanMath

@MarkMitchison BTW, have you finished your thesis?

Mark Mitchison

@TanMath No, feel free to send me a link

@TanMath No, still a fair way away from finishing :(

Or potentially I should put :)

Depends on how you look at it ;)

TanMath

@MarkMitchison physics.stackexchange.com/questions/201599/…

Transcript for